SECOND EUROPEAN CONFERENCE ON EARTHQUAKE
ENGINEERING AND SEISMOLOGY(2ECEES)
NONLINEAR SEISMOLOGY AND THE
IMPLICATIONS ON ENGINEERING
SEISMOLOGY AND EARTHQUAKE
ENGINEERING by
ISTANBUL August 25-29 2014 TURKEY
Gheorghe MAMUREANU Carmen Ortanza CIOFLAN
Alexandru MARMUREANU Constantin IONESCU
Elena - Florinela MANEA
National Institute for Earth Physics Bucharest Romania
SECOND EUROPEAN CONFERENCE ON EARTHQUAKE
ENGINEERING AND SEISMOLOGY(2ECEES)
ISTANBUL August 25-29 2014 TURKEY
Motto
The nonlinear seismology is the rule
The linear seismology is the exception
Paraphrasing Tullio Levi-Civita Padova
N B All generalizations are false including this onehellip
(Mark Twain)
Robert HOOKE 1635-1703
1660 UT TENSIO SIC VIS bdquoAs is the extension so is the forcerdquo σ = E ε
The leading question is how many cities villages
metropolitan areas etc in seismic regions are
constructed on rock Most of them are located on soil
deposit A soil is of basic type sand or gravel (termed
coarse soils) silt or clay (termed fine soils) etc
ProfPeter M Shearer [710]
(i)- Strong ground accelerations from large earthquakes
can produce a non-linear response in shallow soils
(ii)-When a non-linear site response is present then the
shaking from large earthquakes cannot be predicted by
simple scaling of records from small earthquakes
(iii)-This is an active area of research in strong motion
and engineering seismology
AKI in 1993
bdquoNonlinear amplification at sediments sites appears to
be more pervasive than seismologists used to
thinkhellipAny attempt at seismic zonation must take into
account the local site condition and this nonlinear
amplificationrdquo [1]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Soils exhibit a strong non-linear behavior under cyclic
loading conditions In the elastic zone soil particles do not
slide relative to each other under a small stress
increment and the stiffness is at its maxim value The
stiffness begins to decrease from the linear elastic value as
the applied strains or stresses increase and the
deformation moves into the nonlinear elastic zone [349]
Stress and strain states are not enough to determine
the mechanical behavior of soils It is necessary in
addition to model the relation between stresses and strains
by using specific constitutive laws to soils Currently there are not constitutive laws to describe all real
mechanical behaviors of deformable materials like soils
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Figure 1Stiffness degradation curve in terms of shear modulus G and Youngrsquos
modulus E plotted against logarithm of typical strain levels observed during
construction of typical geotechnical structures [69]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
The variation of dynamic torsion modulus function (G daNcm2) and torsion
damping function (G) of specific strain (γ) for sand and gravel samples with normal
humidity obtained in Hardin amp Drnevich resonant columns (USA patent) from NIEP
Laboratory of Earthquake Engineering Normalized values [4-8]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Keiiti Aki [1]bdquoNonlinear amplification at sediments sites
appears to be more pervasive than seismologists used to
think Any attempt at seismic zonation must take into
account the local site conditions and this nonlinear
amplificationrdquo(Aki1993)
2RDBorcherdt [2] Compared the intensities for the 1906
San Francisco earthquake with the amplification factors
determined from the weak motion generated by
underground explosions in the Nevada test (NTS) and found
without exception that an increase in intensity corresponds
to an increase in the amplification factor (Aki1993 p102
idem)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From mechanical behavior point of view there are two
main groups of main importance sands and clays
These soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependentrdquoone[11]names used in mechanical
deformable bodies
However the complexity of these ldquosimplerdquo models
exceeds the possibility of solving and requires to introduce
of simplifying assumptions or conditions which are
restricting the loading conditions which makes additional
permissible assumptions
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Sands typically have low rheological properties and
can be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized using
Boltzmannrsquos formulation of the constitutive law[2]Theory of
viscoelasticity is approaching completionhellipBoltzmannrsquos formu-
lation of the constitutive relation between stress and strain as
expressed by the convolution integrals (1)amp(2) is general in the sense
that all linear behavior may be characterized by such a relation
Conversely if the response is characterized by one of the convolution
integrals then the Boltzmannrsquos superposition principle is valid
p(t) =
)()( detr (1) amp e(t)=
)()( dptc (2)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
If the material response is characterized by one of the
convolution integrals then Boltzmanrsquos superposition principle is
valid[2] Nonlinear viscoelastic model Displacement vector u the tensors T amp E for tension and
strain in case of nonlinear viscoelastic materials are function of
position x and time t functions that define the viscoelastic body state
For a given time and set t = ct these functions will define a state
elastic body The reduction of viscoelastic states to elastic states is
observed experimentally in samples of clay behaviour subjected to
a triaxial creep tests the isochronous σ(ε) = σ(εt)|t=ct şi or τ(γ) =
τ(γt) |t=ct being tension-strain curves which can be modelled with a
linear elastic model The model presented here is based on reducing
viscoleastice states to elastic states and the nonlinear relaxation
functions K=K (ε t) and G=G (γt) are reduced to nonlinear elastic
modulus functions K = K (ε) and G = G ( γ) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Relaxation functions of the nonlinear viscoelastic soil along the
time variable bdquot should contain as arguments the strain tensor
invariants K = K (ε t) and G = G (γ t) Under these conditions the
nonlinear viscoelastic constitutive equations for soils take the
form[34]
t
dsstGt0
)()()(
In these constitutive
equations K(εt) and G(γt) are the nonlinear
relaxation functionshellip
t
dsstKt0
)()()(
and we can accept a strain-
history of form (harmonic amp
stationary)
ε(t)=εoexp(-iωt)
γ(t)=γoexp(-iωt)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of dynamic torsional modulus function (G
daNcm2) with shear strains(γ) and frequency (ω)[34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
SECOND EUROPEAN CONFERENCE ON EARTHQUAKE
ENGINEERING AND SEISMOLOGY(2ECEES)
ISTANBUL August 25-29 2014 TURKEY
Motto
The nonlinear seismology is the rule
The linear seismology is the exception
Paraphrasing Tullio Levi-Civita Padova
N B All generalizations are false including this onehellip
(Mark Twain)
Robert HOOKE 1635-1703
1660 UT TENSIO SIC VIS bdquoAs is the extension so is the forcerdquo σ = E ε
The leading question is how many cities villages
metropolitan areas etc in seismic regions are
constructed on rock Most of them are located on soil
deposit A soil is of basic type sand or gravel (termed
coarse soils) silt or clay (termed fine soils) etc
ProfPeter M Shearer [710]
(i)- Strong ground accelerations from large earthquakes
can produce a non-linear response in shallow soils
(ii)-When a non-linear site response is present then the
shaking from large earthquakes cannot be predicted by
simple scaling of records from small earthquakes
(iii)-This is an active area of research in strong motion
and engineering seismology
AKI in 1993
bdquoNonlinear amplification at sediments sites appears to
be more pervasive than seismologists used to
thinkhellipAny attempt at seismic zonation must take into
account the local site condition and this nonlinear
amplificationrdquo [1]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Soils exhibit a strong non-linear behavior under cyclic
loading conditions In the elastic zone soil particles do not
slide relative to each other under a small stress
increment and the stiffness is at its maxim value The
stiffness begins to decrease from the linear elastic value as
the applied strains or stresses increase and the
deformation moves into the nonlinear elastic zone [349]
Stress and strain states are not enough to determine
the mechanical behavior of soils It is necessary in
addition to model the relation between stresses and strains
by using specific constitutive laws to soils Currently there are not constitutive laws to describe all real
mechanical behaviors of deformable materials like soils
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Figure 1Stiffness degradation curve in terms of shear modulus G and Youngrsquos
modulus E plotted against logarithm of typical strain levels observed during
construction of typical geotechnical structures [69]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
The variation of dynamic torsion modulus function (G daNcm2) and torsion
damping function (G) of specific strain (γ) for sand and gravel samples with normal
humidity obtained in Hardin amp Drnevich resonant columns (USA patent) from NIEP
Laboratory of Earthquake Engineering Normalized values [4-8]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Keiiti Aki [1]bdquoNonlinear amplification at sediments sites
appears to be more pervasive than seismologists used to
think Any attempt at seismic zonation must take into
account the local site conditions and this nonlinear
amplificationrdquo(Aki1993)
2RDBorcherdt [2] Compared the intensities for the 1906
San Francisco earthquake with the amplification factors
determined from the weak motion generated by
underground explosions in the Nevada test (NTS) and found
without exception that an increase in intensity corresponds
to an increase in the amplification factor (Aki1993 p102
idem)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From mechanical behavior point of view there are two
main groups of main importance sands and clays
These soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependentrdquoone[11]names used in mechanical
deformable bodies
However the complexity of these ldquosimplerdquo models
exceeds the possibility of solving and requires to introduce
of simplifying assumptions or conditions which are
restricting the loading conditions which makes additional
permissible assumptions
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Sands typically have low rheological properties and
can be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized using
Boltzmannrsquos formulation of the constitutive law[2]Theory of
viscoelasticity is approaching completionhellipBoltzmannrsquos formu-
lation of the constitutive relation between stress and strain as
expressed by the convolution integrals (1)amp(2) is general in the sense
that all linear behavior may be characterized by such a relation
Conversely if the response is characterized by one of the convolution
integrals then the Boltzmannrsquos superposition principle is valid
p(t) =
)()( detr (1) amp e(t)=
)()( dptc (2)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
If the material response is characterized by one of the
convolution integrals then Boltzmanrsquos superposition principle is
valid[2] Nonlinear viscoelastic model Displacement vector u the tensors T amp E for tension and
strain in case of nonlinear viscoelastic materials are function of
position x and time t functions that define the viscoelastic body state
For a given time and set t = ct these functions will define a state
elastic body The reduction of viscoelastic states to elastic states is
observed experimentally in samples of clay behaviour subjected to
a triaxial creep tests the isochronous σ(ε) = σ(εt)|t=ct şi or τ(γ) =
τ(γt) |t=ct being tension-strain curves which can be modelled with a
linear elastic model The model presented here is based on reducing
viscoleastice states to elastic states and the nonlinear relaxation
functions K=K (ε t) and G=G (γt) are reduced to nonlinear elastic
modulus functions K = K (ε) and G = G ( γ) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Relaxation functions of the nonlinear viscoelastic soil along the
time variable bdquot should contain as arguments the strain tensor
invariants K = K (ε t) and G = G (γ t) Under these conditions the
nonlinear viscoelastic constitutive equations for soils take the
form[34]
t
dsstGt0
)()()(
In these constitutive
equations K(εt) and G(γt) are the nonlinear
relaxation functionshellip
t
dsstKt0
)()()(
and we can accept a strain-
history of form (harmonic amp
stationary)
ε(t)=εoexp(-iωt)
γ(t)=γoexp(-iωt)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of dynamic torsional modulus function (G
daNcm2) with shear strains(γ) and frequency (ω)[34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
The leading question is how many cities villages
metropolitan areas etc in seismic regions are
constructed on rock Most of them are located on soil
deposit A soil is of basic type sand or gravel (termed
coarse soils) silt or clay (termed fine soils) etc
ProfPeter M Shearer [710]
(i)- Strong ground accelerations from large earthquakes
can produce a non-linear response in shallow soils
(ii)-When a non-linear site response is present then the
shaking from large earthquakes cannot be predicted by
simple scaling of records from small earthquakes
(iii)-This is an active area of research in strong motion
and engineering seismology
AKI in 1993
bdquoNonlinear amplification at sediments sites appears to
be more pervasive than seismologists used to
thinkhellipAny attempt at seismic zonation must take into
account the local site condition and this nonlinear
amplificationrdquo [1]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Soils exhibit a strong non-linear behavior under cyclic
loading conditions In the elastic zone soil particles do not
slide relative to each other under a small stress
increment and the stiffness is at its maxim value The
stiffness begins to decrease from the linear elastic value as
the applied strains or stresses increase and the
deformation moves into the nonlinear elastic zone [349]
Stress and strain states are not enough to determine
the mechanical behavior of soils It is necessary in
addition to model the relation between stresses and strains
by using specific constitutive laws to soils Currently there are not constitutive laws to describe all real
mechanical behaviors of deformable materials like soils
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Figure 1Stiffness degradation curve in terms of shear modulus G and Youngrsquos
modulus E plotted against logarithm of typical strain levels observed during
construction of typical geotechnical structures [69]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
The variation of dynamic torsion modulus function (G daNcm2) and torsion
damping function (G) of specific strain (γ) for sand and gravel samples with normal
humidity obtained in Hardin amp Drnevich resonant columns (USA patent) from NIEP
Laboratory of Earthquake Engineering Normalized values [4-8]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Keiiti Aki [1]bdquoNonlinear amplification at sediments sites
appears to be more pervasive than seismologists used to
think Any attempt at seismic zonation must take into
account the local site conditions and this nonlinear
amplificationrdquo(Aki1993)
2RDBorcherdt [2] Compared the intensities for the 1906
San Francisco earthquake with the amplification factors
determined from the weak motion generated by
underground explosions in the Nevada test (NTS) and found
without exception that an increase in intensity corresponds
to an increase in the amplification factor (Aki1993 p102
idem)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From mechanical behavior point of view there are two
main groups of main importance sands and clays
These soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependentrdquoone[11]names used in mechanical
deformable bodies
However the complexity of these ldquosimplerdquo models
exceeds the possibility of solving and requires to introduce
of simplifying assumptions or conditions which are
restricting the loading conditions which makes additional
permissible assumptions
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Sands typically have low rheological properties and
can be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized using
Boltzmannrsquos formulation of the constitutive law[2]Theory of
viscoelasticity is approaching completionhellipBoltzmannrsquos formu-
lation of the constitutive relation between stress and strain as
expressed by the convolution integrals (1)amp(2) is general in the sense
that all linear behavior may be characterized by such a relation
Conversely if the response is characterized by one of the convolution
integrals then the Boltzmannrsquos superposition principle is valid
p(t) =
)()( detr (1) amp e(t)=
)()( dptc (2)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
If the material response is characterized by one of the
convolution integrals then Boltzmanrsquos superposition principle is
valid[2] Nonlinear viscoelastic model Displacement vector u the tensors T amp E for tension and
strain in case of nonlinear viscoelastic materials are function of
position x and time t functions that define the viscoelastic body state
For a given time and set t = ct these functions will define a state
elastic body The reduction of viscoelastic states to elastic states is
observed experimentally in samples of clay behaviour subjected to
a triaxial creep tests the isochronous σ(ε) = σ(εt)|t=ct şi or τ(γ) =
τ(γt) |t=ct being tension-strain curves which can be modelled with a
linear elastic model The model presented here is based on reducing
viscoleastice states to elastic states and the nonlinear relaxation
functions K=K (ε t) and G=G (γt) are reduced to nonlinear elastic
modulus functions K = K (ε) and G = G ( γ) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Relaxation functions of the nonlinear viscoelastic soil along the
time variable bdquot should contain as arguments the strain tensor
invariants K = K (ε t) and G = G (γ t) Under these conditions the
nonlinear viscoelastic constitutive equations for soils take the
form[34]
t
dsstGt0
)()()(
In these constitutive
equations K(εt) and G(γt) are the nonlinear
relaxation functionshellip
t
dsstKt0
)()()(
and we can accept a strain-
history of form (harmonic amp
stationary)
ε(t)=εoexp(-iωt)
γ(t)=γoexp(-iωt)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of dynamic torsional modulus function (G
daNcm2) with shear strains(γ) and frequency (ω)[34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
AKI in 1993
bdquoNonlinear amplification at sediments sites appears to
be more pervasive than seismologists used to
thinkhellipAny attempt at seismic zonation must take into
account the local site condition and this nonlinear
amplificationrdquo [1]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Soils exhibit a strong non-linear behavior under cyclic
loading conditions In the elastic zone soil particles do not
slide relative to each other under a small stress
increment and the stiffness is at its maxim value The
stiffness begins to decrease from the linear elastic value as
the applied strains or stresses increase and the
deformation moves into the nonlinear elastic zone [349]
Stress and strain states are not enough to determine
the mechanical behavior of soils It is necessary in
addition to model the relation between stresses and strains
by using specific constitutive laws to soils Currently there are not constitutive laws to describe all real
mechanical behaviors of deformable materials like soils
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Figure 1Stiffness degradation curve in terms of shear modulus G and Youngrsquos
modulus E plotted against logarithm of typical strain levels observed during
construction of typical geotechnical structures [69]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
The variation of dynamic torsion modulus function (G daNcm2) and torsion
damping function (G) of specific strain (γ) for sand and gravel samples with normal
humidity obtained in Hardin amp Drnevich resonant columns (USA patent) from NIEP
Laboratory of Earthquake Engineering Normalized values [4-8]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Keiiti Aki [1]bdquoNonlinear amplification at sediments sites
appears to be more pervasive than seismologists used to
think Any attempt at seismic zonation must take into
account the local site conditions and this nonlinear
amplificationrdquo(Aki1993)
2RDBorcherdt [2] Compared the intensities for the 1906
San Francisco earthquake with the amplification factors
determined from the weak motion generated by
underground explosions in the Nevada test (NTS) and found
without exception that an increase in intensity corresponds
to an increase in the amplification factor (Aki1993 p102
idem)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From mechanical behavior point of view there are two
main groups of main importance sands and clays
These soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependentrdquoone[11]names used in mechanical
deformable bodies
However the complexity of these ldquosimplerdquo models
exceeds the possibility of solving and requires to introduce
of simplifying assumptions or conditions which are
restricting the loading conditions which makes additional
permissible assumptions
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Sands typically have low rheological properties and
can be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized using
Boltzmannrsquos formulation of the constitutive law[2]Theory of
viscoelasticity is approaching completionhellipBoltzmannrsquos formu-
lation of the constitutive relation between stress and strain as
expressed by the convolution integrals (1)amp(2) is general in the sense
that all linear behavior may be characterized by such a relation
Conversely if the response is characterized by one of the convolution
integrals then the Boltzmannrsquos superposition principle is valid
p(t) =
)()( detr (1) amp e(t)=
)()( dptc (2)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
If the material response is characterized by one of the
convolution integrals then Boltzmanrsquos superposition principle is
valid[2] Nonlinear viscoelastic model Displacement vector u the tensors T amp E for tension and
strain in case of nonlinear viscoelastic materials are function of
position x and time t functions that define the viscoelastic body state
For a given time and set t = ct these functions will define a state
elastic body The reduction of viscoelastic states to elastic states is
observed experimentally in samples of clay behaviour subjected to
a triaxial creep tests the isochronous σ(ε) = σ(εt)|t=ct şi or τ(γ) =
τ(γt) |t=ct being tension-strain curves which can be modelled with a
linear elastic model The model presented here is based on reducing
viscoleastice states to elastic states and the nonlinear relaxation
functions K=K (ε t) and G=G (γt) are reduced to nonlinear elastic
modulus functions K = K (ε) and G = G ( γ) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Relaxation functions of the nonlinear viscoelastic soil along the
time variable bdquot should contain as arguments the strain tensor
invariants K = K (ε t) and G = G (γ t) Under these conditions the
nonlinear viscoelastic constitutive equations for soils take the
form[34]
t
dsstGt0
)()()(
In these constitutive
equations K(εt) and G(γt) are the nonlinear
relaxation functionshellip
t
dsstKt0
)()()(
and we can accept a strain-
history of form (harmonic amp
stationary)
ε(t)=εoexp(-iωt)
γ(t)=γoexp(-iωt)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of dynamic torsional modulus function (G
daNcm2) with shear strains(γ) and frequency (ω)[34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Soils exhibit a strong non-linear behavior under cyclic
loading conditions In the elastic zone soil particles do not
slide relative to each other under a small stress
increment and the stiffness is at its maxim value The
stiffness begins to decrease from the linear elastic value as
the applied strains or stresses increase and the
deformation moves into the nonlinear elastic zone [349]
Stress and strain states are not enough to determine
the mechanical behavior of soils It is necessary in
addition to model the relation between stresses and strains
by using specific constitutive laws to soils Currently there are not constitutive laws to describe all real
mechanical behaviors of deformable materials like soils
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Figure 1Stiffness degradation curve in terms of shear modulus G and Youngrsquos
modulus E plotted against logarithm of typical strain levels observed during
construction of typical geotechnical structures [69]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
The variation of dynamic torsion modulus function (G daNcm2) and torsion
damping function (G) of specific strain (γ) for sand and gravel samples with normal
humidity obtained in Hardin amp Drnevich resonant columns (USA patent) from NIEP
Laboratory of Earthquake Engineering Normalized values [4-8]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Keiiti Aki [1]bdquoNonlinear amplification at sediments sites
appears to be more pervasive than seismologists used to
think Any attempt at seismic zonation must take into
account the local site conditions and this nonlinear
amplificationrdquo(Aki1993)
2RDBorcherdt [2] Compared the intensities for the 1906
San Francisco earthquake with the amplification factors
determined from the weak motion generated by
underground explosions in the Nevada test (NTS) and found
without exception that an increase in intensity corresponds
to an increase in the amplification factor (Aki1993 p102
idem)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From mechanical behavior point of view there are two
main groups of main importance sands and clays
These soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependentrdquoone[11]names used in mechanical
deformable bodies
However the complexity of these ldquosimplerdquo models
exceeds the possibility of solving and requires to introduce
of simplifying assumptions or conditions which are
restricting the loading conditions which makes additional
permissible assumptions
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Sands typically have low rheological properties and
can be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized using
Boltzmannrsquos formulation of the constitutive law[2]Theory of
viscoelasticity is approaching completionhellipBoltzmannrsquos formu-
lation of the constitutive relation between stress and strain as
expressed by the convolution integrals (1)amp(2) is general in the sense
that all linear behavior may be characterized by such a relation
Conversely if the response is characterized by one of the convolution
integrals then the Boltzmannrsquos superposition principle is valid
p(t) =
)()( detr (1) amp e(t)=
)()( dptc (2)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
If the material response is characterized by one of the
convolution integrals then Boltzmanrsquos superposition principle is
valid[2] Nonlinear viscoelastic model Displacement vector u the tensors T amp E for tension and
strain in case of nonlinear viscoelastic materials are function of
position x and time t functions that define the viscoelastic body state
For a given time and set t = ct these functions will define a state
elastic body The reduction of viscoelastic states to elastic states is
observed experimentally in samples of clay behaviour subjected to
a triaxial creep tests the isochronous σ(ε) = σ(εt)|t=ct şi or τ(γ) =
τ(γt) |t=ct being tension-strain curves which can be modelled with a
linear elastic model The model presented here is based on reducing
viscoleastice states to elastic states and the nonlinear relaxation
functions K=K (ε t) and G=G (γt) are reduced to nonlinear elastic
modulus functions K = K (ε) and G = G ( γ) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Relaxation functions of the nonlinear viscoelastic soil along the
time variable bdquot should contain as arguments the strain tensor
invariants K = K (ε t) and G = G (γ t) Under these conditions the
nonlinear viscoelastic constitutive equations for soils take the
form[34]
t
dsstGt0
)()()(
In these constitutive
equations K(εt) and G(γt) are the nonlinear
relaxation functionshellip
t
dsstKt0
)()()(
and we can accept a strain-
history of form (harmonic amp
stationary)
ε(t)=εoexp(-iωt)
γ(t)=γoexp(-iωt)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of dynamic torsional modulus function (G
daNcm2) with shear strains(γ) and frequency (ω)[34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Figure 1Stiffness degradation curve in terms of shear modulus G and Youngrsquos
modulus E plotted against logarithm of typical strain levels observed during
construction of typical geotechnical structures [69]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
The variation of dynamic torsion modulus function (G daNcm2) and torsion
damping function (G) of specific strain (γ) for sand and gravel samples with normal
humidity obtained in Hardin amp Drnevich resonant columns (USA patent) from NIEP
Laboratory of Earthquake Engineering Normalized values [4-8]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Keiiti Aki [1]bdquoNonlinear amplification at sediments sites
appears to be more pervasive than seismologists used to
think Any attempt at seismic zonation must take into
account the local site conditions and this nonlinear
amplificationrdquo(Aki1993)
2RDBorcherdt [2] Compared the intensities for the 1906
San Francisco earthquake with the amplification factors
determined from the weak motion generated by
underground explosions in the Nevada test (NTS) and found
without exception that an increase in intensity corresponds
to an increase in the amplification factor (Aki1993 p102
idem)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From mechanical behavior point of view there are two
main groups of main importance sands and clays
These soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependentrdquoone[11]names used in mechanical
deformable bodies
However the complexity of these ldquosimplerdquo models
exceeds the possibility of solving and requires to introduce
of simplifying assumptions or conditions which are
restricting the loading conditions which makes additional
permissible assumptions
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Sands typically have low rheological properties and
can be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized using
Boltzmannrsquos formulation of the constitutive law[2]Theory of
viscoelasticity is approaching completionhellipBoltzmannrsquos formu-
lation of the constitutive relation between stress and strain as
expressed by the convolution integrals (1)amp(2) is general in the sense
that all linear behavior may be characterized by such a relation
Conversely if the response is characterized by one of the convolution
integrals then the Boltzmannrsquos superposition principle is valid
p(t) =
)()( detr (1) amp e(t)=
)()( dptc (2)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
If the material response is characterized by one of the
convolution integrals then Boltzmanrsquos superposition principle is
valid[2] Nonlinear viscoelastic model Displacement vector u the tensors T amp E for tension and
strain in case of nonlinear viscoelastic materials are function of
position x and time t functions that define the viscoelastic body state
For a given time and set t = ct these functions will define a state
elastic body The reduction of viscoelastic states to elastic states is
observed experimentally in samples of clay behaviour subjected to
a triaxial creep tests the isochronous σ(ε) = σ(εt)|t=ct şi or τ(γ) =
τ(γt) |t=ct being tension-strain curves which can be modelled with a
linear elastic model The model presented here is based on reducing
viscoleastice states to elastic states and the nonlinear relaxation
functions K=K (ε t) and G=G (γt) are reduced to nonlinear elastic
modulus functions K = K (ε) and G = G ( γ) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Relaxation functions of the nonlinear viscoelastic soil along the
time variable bdquot should contain as arguments the strain tensor
invariants K = K (ε t) and G = G (γ t) Under these conditions the
nonlinear viscoelastic constitutive equations for soils take the
form[34]
t
dsstGt0
)()()(
In these constitutive
equations K(εt) and G(γt) are the nonlinear
relaxation functionshellip
t
dsstKt0
)()()(
and we can accept a strain-
history of form (harmonic amp
stationary)
ε(t)=εoexp(-iωt)
γ(t)=γoexp(-iωt)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of dynamic torsional modulus function (G
daNcm2) with shear strains(γ) and frequency (ω)[34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
The variation of dynamic torsion modulus function (G daNcm2) and torsion
damping function (G) of specific strain (γ) for sand and gravel samples with normal
humidity obtained in Hardin amp Drnevich resonant columns (USA patent) from NIEP
Laboratory of Earthquake Engineering Normalized values [4-8]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Keiiti Aki [1]bdquoNonlinear amplification at sediments sites
appears to be more pervasive than seismologists used to
think Any attempt at seismic zonation must take into
account the local site conditions and this nonlinear
amplificationrdquo(Aki1993)
2RDBorcherdt [2] Compared the intensities for the 1906
San Francisco earthquake with the amplification factors
determined from the weak motion generated by
underground explosions in the Nevada test (NTS) and found
without exception that an increase in intensity corresponds
to an increase in the amplification factor (Aki1993 p102
idem)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From mechanical behavior point of view there are two
main groups of main importance sands and clays
These soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependentrdquoone[11]names used in mechanical
deformable bodies
However the complexity of these ldquosimplerdquo models
exceeds the possibility of solving and requires to introduce
of simplifying assumptions or conditions which are
restricting the loading conditions which makes additional
permissible assumptions
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Sands typically have low rheological properties and
can be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized using
Boltzmannrsquos formulation of the constitutive law[2]Theory of
viscoelasticity is approaching completionhellipBoltzmannrsquos formu-
lation of the constitutive relation between stress and strain as
expressed by the convolution integrals (1)amp(2) is general in the sense
that all linear behavior may be characterized by such a relation
Conversely if the response is characterized by one of the convolution
integrals then the Boltzmannrsquos superposition principle is valid
p(t) =
)()( detr (1) amp e(t)=
)()( dptc (2)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
If the material response is characterized by one of the
convolution integrals then Boltzmanrsquos superposition principle is
valid[2] Nonlinear viscoelastic model Displacement vector u the tensors T amp E for tension and
strain in case of nonlinear viscoelastic materials are function of
position x and time t functions that define the viscoelastic body state
For a given time and set t = ct these functions will define a state
elastic body The reduction of viscoelastic states to elastic states is
observed experimentally in samples of clay behaviour subjected to
a triaxial creep tests the isochronous σ(ε) = σ(εt)|t=ct şi or τ(γ) =
τ(γt) |t=ct being tension-strain curves which can be modelled with a
linear elastic model The model presented here is based on reducing
viscoleastice states to elastic states and the nonlinear relaxation
functions K=K (ε t) and G=G (γt) are reduced to nonlinear elastic
modulus functions K = K (ε) and G = G ( γ) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Relaxation functions of the nonlinear viscoelastic soil along the
time variable bdquot should contain as arguments the strain tensor
invariants K = K (ε t) and G = G (γ t) Under these conditions the
nonlinear viscoelastic constitutive equations for soils take the
form[34]
t
dsstGt0
)()()(
In these constitutive
equations K(εt) and G(γt) are the nonlinear
relaxation functionshellip
t
dsstKt0
)()()(
and we can accept a strain-
history of form (harmonic amp
stationary)
ε(t)=εoexp(-iωt)
γ(t)=γoexp(-iωt)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of dynamic torsional modulus function (G
daNcm2) with shear strains(γ) and frequency (ω)[34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Keiiti Aki [1]bdquoNonlinear amplification at sediments sites
appears to be more pervasive than seismologists used to
think Any attempt at seismic zonation must take into
account the local site conditions and this nonlinear
amplificationrdquo(Aki1993)
2RDBorcherdt [2] Compared the intensities for the 1906
San Francisco earthquake with the amplification factors
determined from the weak motion generated by
underground explosions in the Nevada test (NTS) and found
without exception that an increase in intensity corresponds
to an increase in the amplification factor (Aki1993 p102
idem)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From mechanical behavior point of view there are two
main groups of main importance sands and clays
These soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependentrdquoone[11]names used in mechanical
deformable bodies
However the complexity of these ldquosimplerdquo models
exceeds the possibility of solving and requires to introduce
of simplifying assumptions or conditions which are
restricting the loading conditions which makes additional
permissible assumptions
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Sands typically have low rheological properties and
can be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized using
Boltzmannrsquos formulation of the constitutive law[2]Theory of
viscoelasticity is approaching completionhellipBoltzmannrsquos formu-
lation of the constitutive relation between stress and strain as
expressed by the convolution integrals (1)amp(2) is general in the sense
that all linear behavior may be characterized by such a relation
Conversely if the response is characterized by one of the convolution
integrals then the Boltzmannrsquos superposition principle is valid
p(t) =
)()( detr (1) amp e(t)=
)()( dptc (2)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
If the material response is characterized by one of the
convolution integrals then Boltzmanrsquos superposition principle is
valid[2] Nonlinear viscoelastic model Displacement vector u the tensors T amp E for tension and
strain in case of nonlinear viscoelastic materials are function of
position x and time t functions that define the viscoelastic body state
For a given time and set t = ct these functions will define a state
elastic body The reduction of viscoelastic states to elastic states is
observed experimentally in samples of clay behaviour subjected to
a triaxial creep tests the isochronous σ(ε) = σ(εt)|t=ct şi or τ(γ) =
τ(γt) |t=ct being tension-strain curves which can be modelled with a
linear elastic model The model presented here is based on reducing
viscoleastice states to elastic states and the nonlinear relaxation
functions K=K (ε t) and G=G (γt) are reduced to nonlinear elastic
modulus functions K = K (ε) and G = G ( γ) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Relaxation functions of the nonlinear viscoelastic soil along the
time variable bdquot should contain as arguments the strain tensor
invariants K = K (ε t) and G = G (γ t) Under these conditions the
nonlinear viscoelastic constitutive equations for soils take the
form[34]
t
dsstGt0
)()()(
In these constitutive
equations K(εt) and G(γt) are the nonlinear
relaxation functionshellip
t
dsstKt0
)()()(
and we can accept a strain-
history of form (harmonic amp
stationary)
ε(t)=εoexp(-iωt)
γ(t)=γoexp(-iωt)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of dynamic torsional modulus function (G
daNcm2) with shear strains(γ) and frequency (ω)[34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From mechanical behavior point of view there are two
main groups of main importance sands and clays
These soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependentrdquoone[11]names used in mechanical
deformable bodies
However the complexity of these ldquosimplerdquo models
exceeds the possibility of solving and requires to introduce
of simplifying assumptions or conditions which are
restricting the loading conditions which makes additional
permissible assumptions
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Sands typically have low rheological properties and
can be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized using
Boltzmannrsquos formulation of the constitutive law[2]Theory of
viscoelasticity is approaching completionhellipBoltzmannrsquos formu-
lation of the constitutive relation between stress and strain as
expressed by the convolution integrals (1)amp(2) is general in the sense
that all linear behavior may be characterized by such a relation
Conversely if the response is characterized by one of the convolution
integrals then the Boltzmannrsquos superposition principle is valid
p(t) =
)()( detr (1) amp e(t)=
)()( dptc (2)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
If the material response is characterized by one of the
convolution integrals then Boltzmanrsquos superposition principle is
valid[2] Nonlinear viscoelastic model Displacement vector u the tensors T amp E for tension and
strain in case of nonlinear viscoelastic materials are function of
position x and time t functions that define the viscoelastic body state
For a given time and set t = ct these functions will define a state
elastic body The reduction of viscoelastic states to elastic states is
observed experimentally in samples of clay behaviour subjected to
a triaxial creep tests the isochronous σ(ε) = σ(εt)|t=ct şi or τ(γ) =
τ(γt) |t=ct being tension-strain curves which can be modelled with a
linear elastic model The model presented here is based on reducing
viscoleastice states to elastic states and the nonlinear relaxation
functions K=K (ε t) and G=G (γt) are reduced to nonlinear elastic
modulus functions K = K (ε) and G = G ( γ) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Relaxation functions of the nonlinear viscoelastic soil along the
time variable bdquot should contain as arguments the strain tensor
invariants K = K (ε t) and G = G (γ t) Under these conditions the
nonlinear viscoelastic constitutive equations for soils take the
form[34]
t
dsstGt0
)()()(
In these constitutive
equations K(εt) and G(γt) are the nonlinear
relaxation functionshellip
t
dsstKt0
)()()(
and we can accept a strain-
history of form (harmonic amp
stationary)
ε(t)=εoexp(-iωt)
γ(t)=γoexp(-iωt)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of dynamic torsional modulus function (G
daNcm2) with shear strains(γ) and frequency (ω)[34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Sands typically have low rheological properties and
can be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized using
Boltzmannrsquos formulation of the constitutive law[2]Theory of
viscoelasticity is approaching completionhellipBoltzmannrsquos formu-
lation of the constitutive relation between stress and strain as
expressed by the convolution integrals (1)amp(2) is general in the sense
that all linear behavior may be characterized by such a relation
Conversely if the response is characterized by one of the convolution
integrals then the Boltzmannrsquos superposition principle is valid
p(t) =
)()( detr (1) amp e(t)=
)()( dptc (2)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
If the material response is characterized by one of the
convolution integrals then Boltzmanrsquos superposition principle is
valid[2] Nonlinear viscoelastic model Displacement vector u the tensors T amp E for tension and
strain in case of nonlinear viscoelastic materials are function of
position x and time t functions that define the viscoelastic body state
For a given time and set t = ct these functions will define a state
elastic body The reduction of viscoelastic states to elastic states is
observed experimentally in samples of clay behaviour subjected to
a triaxial creep tests the isochronous σ(ε) = σ(εt)|t=ct şi or τ(γ) =
τ(γt) |t=ct being tension-strain curves which can be modelled with a
linear elastic model The model presented here is based on reducing
viscoleastice states to elastic states and the nonlinear relaxation
functions K=K (ε t) and G=G (γt) are reduced to nonlinear elastic
modulus functions K = K (ε) and G = G ( γ) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Relaxation functions of the nonlinear viscoelastic soil along the
time variable bdquot should contain as arguments the strain tensor
invariants K = K (ε t) and G = G (γ t) Under these conditions the
nonlinear viscoelastic constitutive equations for soils take the
form[34]
t
dsstGt0
)()()(
In these constitutive
equations K(εt) and G(γt) are the nonlinear
relaxation functionshellip
t
dsstKt0
)()()(
and we can accept a strain-
history of form (harmonic amp
stationary)
ε(t)=εoexp(-iωt)
γ(t)=γoexp(-iωt)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of dynamic torsional modulus function (G
daNcm2) with shear strains(γ) and frequency (ω)[34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
If the material response is characterized by one of the
convolution integrals then Boltzmanrsquos superposition principle is
valid[2] Nonlinear viscoelastic model Displacement vector u the tensors T amp E for tension and
strain in case of nonlinear viscoelastic materials are function of
position x and time t functions that define the viscoelastic body state
For a given time and set t = ct these functions will define a state
elastic body The reduction of viscoelastic states to elastic states is
observed experimentally in samples of clay behaviour subjected to
a triaxial creep tests the isochronous σ(ε) = σ(εt)|t=ct şi or τ(γ) =
τ(γt) |t=ct being tension-strain curves which can be modelled with a
linear elastic model The model presented here is based on reducing
viscoleastice states to elastic states and the nonlinear relaxation
functions K=K (ε t) and G=G (γt) are reduced to nonlinear elastic
modulus functions K = K (ε) and G = G ( γ) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Relaxation functions of the nonlinear viscoelastic soil along the
time variable bdquot should contain as arguments the strain tensor
invariants K = K (ε t) and G = G (γ t) Under these conditions the
nonlinear viscoelastic constitutive equations for soils take the
form[34]
t
dsstGt0
)()()(
In these constitutive
equations K(εt) and G(γt) are the nonlinear
relaxation functionshellip
t
dsstKt0
)()()(
and we can accept a strain-
history of form (harmonic amp
stationary)
ε(t)=εoexp(-iωt)
γ(t)=γoexp(-iωt)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of dynamic torsional modulus function (G
daNcm2) with shear strains(γ) and frequency (ω)[34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly Relaxation functions of the nonlinear viscoelastic soil along the
time variable bdquot should contain as arguments the strain tensor
invariants K = K (ε t) and G = G (γ t) Under these conditions the
nonlinear viscoelastic constitutive equations for soils take the
form[34]
t
dsstGt0
)()()(
In these constitutive
equations K(εt) and G(γt) are the nonlinear
relaxation functionshellip
t
dsstKt0
)()()(
and we can accept a strain-
history of form (harmonic amp
stationary)
ε(t)=εoexp(-iωt)
γ(t)=γoexp(-iωt)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of dynamic torsional modulus function (G
daNcm2) with shear strains(γ) and frequency (ω)[34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of dynamic torsional modulus function (G
daNcm2) with shear strains(γ) and frequency (ω)[34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Dependence of torsional damping function (D) with
shear strains (γ) and frequency (ω) [34]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
1Sand with gravel Gn = 0344 +0656 ( 1+14651 γ0716)
Dn = 1428 -1212 ( 1+243 γ0682)
2Loess Gn = 0107+0903 (1+1312 γ 0682
Dn = 1556 -1367 ( 1+1780 γ 0655)
3Diluvian clay Gn = 0176+0824( 1+27357 γ0986)
Dn = 1085 -0888(1+10674 γ0950)
4Grey marl Gn = 0542 +0468 ( 1+18724 γ073)
Dn = 1711-1476(1+141 γ0593)
5Limestone Gn = 0737+0263(1+3974 γ0456)
Dn = 1902-1627(1+0732 γ0691)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
In engineering applications we are interested in the soil behavior to earthquakes dangerous frequenciesthat are between 01 and 10 Hz In this domain we can consider Gk and Dk to be constant in relation to frequensy abd will depend of shear strain γThen the dynamic functions are
G(γ) =
20
)(k
k
kG
D(γ) =1 k
k
kD )(20
and all of them are function of shear strains (γ)
developed during of earthquake
GOTHENBURG July 22-26 2013 SWEDEN
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
To avoid these uncertainties we are coming with a new way In fact from response spectra we can find all nonlinearities from source to free field for each strong Vrancea earthquake
The
seismic
model
from
source
to
free field
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
The concept was used also for last Stress Test asked by IAEA
Vienna for Romanian Cernavoda Nuclear Power Plant where we
recorded last three deep strong Vrancea earthquakes August
301986 (MW = 71)May 30(MW = 69) and May 311990 (MW = 64)
The authors in order to make quantitative evidence of large
nonlinear effects used introduced and developed the concept of the
nonlinear spectral amplification factor (SAF) as ratio between
maximum spectral absolute acceleration (Sa) relative velocity
(Sv )relative displacement (Sd) from response spectra for a fraction of
critical damping (ζ ) at fundamental period or any period and peak
values of acceleration (amax) velocity (vmax) and displacement (dmax)
respectively from processed strong motion records that are(SAF)a=
Saamax (SAF)v= Sv vmax (SAF)d= Sddmax where amax = yuml(t)max vmax
=x(t)max and dmax = x(t)max[5]
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
Strain transfer from the active Adriatic Aegean and Vrancea deformation
fronts throughout the ALCADI ndash Pannonian system
VranceaVrancea
AdrianAdrian
AegeanAegean
Strain transfer from the active Adriatic Aegean and Vrancea
deformation fronts through the ALCADI- Pannonia System[6]
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
Simplified tectonic map of late Neogene Pannonian Basin and
its surroundings[6-8]
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
Topography and Moho layer and the isosurface of the 22 p-wave
velocity anomaly of the Vrancea area from the seismic tomography
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF
c Sa(g)
( β=5)
a
04031977 1884 440 cms2 233 1214 10252 2287 214
08301986 1091 249 cms2 228 1241 3090 1354 241
05301990 989 280 cms2 283 1000 2800 989 -
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
(β=5) a
04031977 20690 650 cms2 314 1322 8593 2735 322
08301986 9696 255 cms2 262 1583 4036 1534 583
05301990 6621 275 cms2 415 1000 2750 662 -
Table 2Bucharest-INCERC Seismic Station(N-S Comp) Φ0 =44442 λ0=26105
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908 345 cms2 387 1217 41986 10441 217
05301990 6313 270 cms2 427 1103 29781 6963 103
05311990 1590 75 cms2 471 1000 7500 1590 -
Table 3Bucharest-Balta Albă Seismic Station(E-W Comp) Φ0 =44413 λ0=26169
Table 1Bucharest-INCERC Seismic Station(E-W Comp) Φ0 =44442 λ0=26105
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax
(recorded)
Samax
(β=5)
Samaxamax
(SAF) c Sa
(g)
( β=5) a(g)
08301986 837 cms2 295 cms2 352 1235 3643 1033 235
05301990 2150 cms2 800 cms2 372 1169 9352 2513 169
05311990 356 cms2 155 cms2 435 1000 1550 356 -
Table 4Bucharest-Bolintinu Vale Seismic Station(N155E Comp)Φ0 =44444λ0=25757
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8908cmss 345 cms2 387 1217 41986 1044 21
05301990 6313cmss 270 cms2 427 1103 29781 696 10
05311990 1590cmss 75 cms2 471 1000 7500 159 -
Table 5Bucharest- Brăneşti Seismic Station(N107W Comp) Φ0 =44460 λ0=26329
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7107cms2 220 cms2 306 1483 32626 10539 483
05301990 554 cms2 220 cms2 397 1143 25146 6332 143
05311990 121cms2 55 cms2 454 1000 5500 1210 -
Table 6Bucharest-Metalurgiei Seismic Station(N127W Comp) Φ0 =44376 λ0=26119
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 894cms2 295 cms2 329 1513 44633 13526 513
05301990 1313cms2 590 cms2 449 1109 65431 14561 109
05311990 330 cms2 160 cms2 498 1000 16000 3300 -
Table 7Bucharest-Panduri Seismic Station(N131E Component) Φ0 =44426 λ0=26065
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 8754 395 cms2 451 1142 45109 9997 142
05301990 5680 210 cms2 369 1395 29295 7891 395
05311990 1067 55 cms2 515 1000 5500 1067 -
Table 8Bucharest-Titulescu Seismic Station(N145W Component) Φ0 =44452 λ0=26080
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7960 240 cms2 3015 1276 30624 10164 276
05301990 1147 305 cms2 2659 1447 21078 16597 447
05311990 1948 75 cms2 3850 1000 7500 1948 -
Table 9Bucharest-Carlton Seismic Station(N75E Comp) Φ0 =44436 λ0=26102
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6910 220 cms2 3183 1334 29348 9217 334
05301990 7423 250 cms2 3368 1260 31500 9353 260
05311990 4711 200 cms2 4245 1000 20000 4711 -
Table 10Galaţi-IPJ(GLT2)Seismic Station(N97WE Comp)Φ0 =45430 λ0=28058
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6410 190cms2 2964 1363 56316 8736 363
05301990 1095 390cms2 3561 1135 44265 12428 135
05311990 4576 185cms2 4042 1000 18500 4576 -
Tabel 11Iaşi-Centru(IAS2)Seismic Station(N-S Comp)Φ0 =47160 λ0=27570
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6818 225 cms2 3300 1293 29092 8815 293
05301990 9722 395 cms2 4063 1050 41475 10208 135
05311990 4944 211 cms2 4267 1000 21100 4944 -
Table 12Iaşi-Copou(IAS2)Seismic Station(N-S Comp)Φ0 =47193 λ0=27562
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 11380 307 cms2 26982 1329 4086 15146 329
05301990 9025 324 cms2 35869 1000 3240 9025 -
Table 13Bucharest-Măgurele Seismic Station(E-W Comp)Φ0 =47347 λ0=26030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 2072 730 cms2 3523 1124 8205 23289 124
05301990 726 235 cms2 3236 1224 2876 8886 224
05311990 164 65 cms2 3963 1000 6500 1640 -
Table 14Ploieşti-(PLS)Seismic Station(N100E Comp)Φ0 =44930 λ0=26020
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 7220 292 cms2 40443 1457 42544 10519 457
05301990 13243 684 cms2 51649 1141 78044 15110 241
05311990 6307 372 cms2 58942 1000 37200 6307 -
Table 15Bacău-(BAC2)Seismic Station( E-W Comp)Φ0 =46567 λ0=26900
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 6278 256 cms2 40777 1420 36352 8914 420
05301990 10006 475 cms2 47471 1219 57902 12197 219
05311990 4973 288 cms2 57912 1000 28800 4973 -
Table 16Cernavoda -(CVD2)Seismic Station(E-W Comp)Φ0 =44340 λ0=28030
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
( β=5)
a
08301986 14070 690 cms2 49040 11435 78901 16089 144
05301990 6241 350 cms2 56080 1000 35000 6241 -
Table 17Craiova-(CRV) Seismic Station (N05E Comp)Φ0 =47321 λ0=23798
Earthquake amax(cms2)
(recorded)
Samax
(β=5)
Samaxamax
(SAF)
c Sa(g)
(β=5)
a
08301986 1403 400 cms2 28510 1215 4860 17046 215
05311990 664 230 cms2 34638 1000 2300 6640 -
Table 18Racircmnicu Sărat -(RMS2)Seismic Station(N55E Comp)Φ0 =45380 λ0=27040
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
Figure 3The geological structure under Bucharest Isobars
are generally oriented East-West with slope of 8permil down from South
to North In the same direction the thickness of layers becomes
larger[6]
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
At the same seismic station for example at Bucharest-
Panduri Seismic Station (Table 7) and Figure 3 close to borehole
172 for horizontal components and β=5 damping the values
of the SAF for accelerations are 329 for August 301986
Vrancea earthquake (MW=71) 449 for May 30 1990 (MW=69)
and 498 for May 31 1990 (MW =64) Vrancea earthquake on
May 311990 (MW=64) could be assumed that the response is
still in elastic domain and then we have the possibility to
compare to it In RG 160 SAF= 313 and is constant at allhellip
Damping August 30 1986
(MS=70 Mw=71)
May 301990
(MS=67 Mw =69)
May 311990
(MS=62 Mw =64)
ξ Samaxamax Sv
maxvmax Samaxamax Sv
maxvmax Samaxamax Sv
maxvmav
2 474 361 558 372 622 484
5 326[313] 269 363[313] 295 416[313] 348
10 243 199 256 214 292 269
20 178 150 182 158 213 186
Table 19 Median values of (SAF) for last three strong Vrancea earthquakes
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
On the other hand from
Tables 1-19 and Figure 4
we can see that there is a
strong nonlinear depen-
dence of the spectral
amplification factors(SAF)
on earthquake magnitude
for other seismic stations on
Romanian territory on
extra-Carpathian area (Iasi
Bacau Focsani Bucharest-
NIEP NPP Cernavoda
Bucharest-INCERC etc)
SAF=313 (Regulatory Guide 160
of the US Atomic
Commission) amp IAEA
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
CONCLUSIONS
The central question of the discussion was in last time
whether soil amplification is function of earthquake
amplitude dependent The dependence of soil response on
strain amplitude become a standard assumption in the
geotechnical field in earthquake engineering and
engineering seismology
Laboratory data shows a typical stiffness degradation
curve in term of G modulus and increasing of damping
along with strain levels developed during strong
earthquakes In other words a variation of dynamic
torsion modulus function (G daNcm2) and torsion
damping function (G) of specific shear strain (γ)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Stress and strain states are not enough to determine the
mechanical behavior of soils It is necessary in addition to
model the relation between stresses and deformations by
using specific constitutive laws to soils Currently there are
not constitutive laws to describe all real mechanical
behaviors of deformable materials like soils
Soils although have many common mechanical
properties require the use of different models to describe
behavior difference Soils are simple materials with
memory sands are bdquorate-independentrdquo type and clays are
bdquorate-dependent rdquo
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Sands typically have low rheological properties and can
be modeled with an acceptable linear elastic model and
clays which frequently presents significant changes over
time can be modeled by a nonlinear viscoelastic model
Viscoelastic material behavior could be characterized
using Boltzmannrsquos formulation of the constitutive law
Displacement vector u the tensors T amp E for tension
and strain in case of nonlinear viscoelastic materials are
function of position x and time t functions that define the
viscoelastic body statehellip
From resonant columns between 01 and 10 Hz
dynamic functions G(γ) and D(γ) are constant and functions
of shear strains (γ)hellip
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
To avoid these uncertainties we are coming with a new
way In fact from response spectra we can find all
nonlinearities from source to free field for each strong
Vrancea earthquake
The quantitative evidence of large nonlinear effects used
introduced and developed the nonlinear spectral amplification
factor (SAF) concept as ratio between (SAF)a= Saamax
(SAF)v= Sv vmax (SAF)d= Sddmax at fundamental periods
or at any one where amax = yuml(t)max vmax =x(t)max and dmax =
x(t)max
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
From Tables 1-18 and 19 for median values we can see
that there is a strong nonlinear dependence of the spectral
amplification factors (SAF) for absolute accelerations on
earthquake magnitude for all records made on extra-
Carpathian area from Iasi to Craiova for last strong
Vrancea earthquakes inclusively for NPP Cernavoda site
The amplification factors are decreasing with increasing
the magnitudes of deep strong Vrancea earthquakes and
this values are far of that given by Regulatory Guide 160
of the U S Atomic Energy Commission[12] The spectral
amplification factors(SAF) and in fact the nonlinearity
are functions of Vrancea earthquake magnitude The
amplification factors decrease as the magnitude increases
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
References [1]AkiA(1993)Local Site Effects on Weak and Strong Ground MotionTectonophysics 218 p93-111 [2] BorcherdtRD(2009)Visoelastiv Waves in Layered MediaCambridge Univ PressISBN 970-521-
89853-9 [3]BratosinD(2002)Elements of Soil Dynamics Romanian Academy Publishing House (in Romanian)
[4]Marmureanu GhBratosin DCioflan CO(2000)The dependence of Q with seismic induced strains and
frequencies for surface layers from resonant columnsPure and Applied Geophysics(PAGEOPH)
Birkhaumluser VerlagBasel2000pp269-279 [5]Mărmureanu G Mişicu M Cioflan C Bălan FS (2005)Nonlinear Seismology-The Seismology of
the XXICentury in Lecture Notes of Earth Sciences Perspective in Modern Seismology vol105 Springer Verlag Heidelberg 47-67
[6]MarmureanuGhCioflan COMarmureanuA2010Researches on local seismic hazard(microzonation) of Bucharest metropolitan area Microzoning maps with accelerations fundamental periods and intensities for maximum Vrancea earthquake magnitude of 75 on Richter scale Tehnopress EdIasi ISBN 978-974 702-809-9 472 pages (in Romanian)
[7]MarmureanuGhCioflanCOMarmureanuA(2012)Nonlinear seismology a realityThe quantitative data EGU General Assembly April 22-272012Section NH4 Vienna Austria
[8]MarmureanuGh MarmureanuACioflanCOIoescuC(2013) Esential Tools to Mitigate Vrancea Strong earthquak Effects on Moldavian Urban Environment Environmental Engrg ampManagement JournalJannuaryVol12No165-79
[9]Mitchell JK SogaK(2005)Fundamentals of Soil Behavior Wiley John Willey amp Sons I N [10]ShererPM(2009)Introduction to Seismology Cambridge University Press [11] TruesdellCNolW(1965)The Nonlinear Field Theories of MechanicsHandbuch der Physik
III3Springer Verlag [12] Design Response Spectra for Seismic Design of Nuclear Power Plants U S Atomic Commission
Regulatory Guide 160(1973)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)
KNOWLEDGE FOR THE FUTURE
IAHS-IAPSO-IASPEI Joint Assembly
GOTHENBURG July 22-26 2013 SWEDEN
Thank you
for your
attention
ACKNOWLEDGEMENT
This work is performed in the frame of the REAKT
Collaborative Project ldquoStrategies and tools for Real Time
EArthquake RisK ReducTion ldquo- FP7 (2012-2014)