Upload
liz
View
47
Download
0
Embed Size (px)
DESCRIPTION
A RSM Method for Nonlinear Probabilistic Analysis of NPP Reinforced Concrete Structures. Králik Juraj. Outline. Brief look at the principal problems of PSA 3 level analysis. Scenario of possible accidents. Monitoring of NPP and definition of the investigation tasks. - PowerPoint PPT Presentation
Citation preview
Scenario Scenario of possible accidentsof possible accidents Scenario Scenario of possible accidentsof possible accidents
22
Brief look atBrief look at the principal problems of the principal problems of PSA 3 level analysisPSA 3 level analysis Brief look atBrief look at the principal problems of the principal problems of PSA 3 level analysisPSA 3 level analysis
Nonlinear analysis Nonlinear analysis of the concrete containmentof the concrete containment Nonlinear analysis Nonlinear analysis of the concrete containmentof the concrete containment
Probability analysis Probability analysis of the concrete containment failure using of the concrete containment failure using RSM methodRSM method Probability analysis Probability analysis of the concrete containment failure using of the concrete containment failure using RSM methodRSM method
ConclusionsConclusions ConclusionsConclusions
FE - modelFE - model of the NPP structures of the NPP structures FE - modelFE - model of the NPP structures of the NPP structures
MonitoringMonitoring of NPP and definition of the of NPP and definition of the investigation tasksinvestigation tasks MonitoringMonitoring of NPP and definition of the of NPP and definition of the investigation tasksinvestigation tasks
26 April 1986
Chernobyl power plant in 2003 with the sarcophagus containment
structureAerial view of the damaged core on
May 3, 1986. Roof of the turbine hall
is damaged (image center). Roof of
the adjacent reactor 3 (image lower
left) shows minor fire damage.
The battle to contain the contamination and avert a greater catastrophe ultimately involved over 500,000 workers and cost an estimated 18 billion rubles. A 2006 report predicted 30,000 to 60,000 cancer deaths as a result of Chernobyl fallout. 33
Unit 1 und 3
Hydrogen burn inside the
reactor service floor
Destruction of the steel-frame
roof
Reinforced concrete reactor
building seems undamaged
Spectacular but minor safety
relevant
2. Accident progression
44
PCCV Model after the Structural Failure Mode Test
The design pressure is 0.39 MPa. *** Failure pressure is 1.42 MPa
55
Definition fo the Definition fo the scenario for LOCAscenario for LOCA loads loads Definition fo the Definition fo the scenario for LOCAscenario for LOCA loads loads
Program Program ANSYS ANSYS and own programs and own programs CREEP, SHRINK and CRACKCREEP, SHRINK and CRACK Program Program ANSYS ANSYS and own programs and own programs CREEP, SHRINK and CRACKCREEP, SHRINK and CRACK
Consideration of the longConsideration of the long-term-term influence of the influence of the temperature, creep temperature, creep
and shrinkageand shrinkage of concrete after 20 yearsof concrete after 20 years
Consideration of the longConsideration of the long-term-term influence of the influence of the temperature, creep temperature, creep
and shrinkageand shrinkage of concrete after 20 yearsof concrete after 20 years
Consideration of the Consideration of the soil-structure interactionsoil-structure interaction, the influence of the soil, the influence of the soil
consolidation after 20 yearsconsolidation after 20 years
Consideration of the Consideration of the soil-structure interactionsoil-structure interaction, the influence of the soil, the influence of the soil
consolidation after 20 yearsconsolidation after 20 years
Investigation of the Investigation of the concrete cracking and crushing concrete cracking and crushing Investigation of the Investigation of the concrete cracking and crushing concrete cracking and crushing
CheckingChecking of calculation model and its of calculation model and its accuracyaccuracy CheckingChecking of calculation model and its of calculation model and its accuracyaccuracy
66
77
88
Definition PSA 3 levelDefinition PSA 3 level
Systematic study of the possibilities of the Systematic study of the possibilities of the penetration hermetic zone penetration hermetic zone due to due to
accident of the various technology segments considering the accident of the various technology segments considering the uncertainties of uncertainties of
the structures and accident posibilities. the structures and accident posibilities.
Aim of the PSA 3 levelAim of the PSA 3 level
Definition of Definition of failure pression failure pression ppuu and its and its probability distribution probability distribution in in
dependency of all posibility uncertainties dependency of all posibility uncertainties ((action effects and structure action effects and structure
resistanceresistance))
Three sourses of uncertainties for PSA 3 levelThree sourses of uncertainties for PSA 3 level
1. Definition of 1. Definition of plant damage states plant damage states (PDS)(PDS)
2. 2. SimulationSimulation of the problem, including of the problem, including eventevent treetree construction and models construction and models
3. Input 3. Input datadata used to feed models used to feed models
Each PDS consists of a collection of Each PDS consists of a collection of core damage sequencescore damage sequences, which are , which are
expected to behave similarly following the onset of core damage. expected to behave similarly following the onset of core damage.
The PDS set includes The PDS set includes 69 possible combinations 69 possible combinations of PDS parameter values. It of PDS parameter values. It
should be noted that not all of the possible combinations of PDS parameter should be noted that not all of the possible combinations of PDS parameter
values need to be considered. The grouping diagram for core damage sequences values need to be considered. The grouping diagram for core damage sequences
in the full power state is shown in follow schemein the full power state is shown in follow scheme
99
1010
1111
Four main source of Accident progression Four main source of Accident progression
1.1. Large LOCA (2x Large LOCA (2x 500mm) 500mm)
2.2. Transients or small LOCA (Transients or small LOCA (13mm, 13mm, 32mm, 32mm, 71mm )71mm )
3.3. Interfacing LOCAInterfacing LOCA
4.4. Open reactor (or fuel pool)Open reactor (or fuel pool)
CTMT and EWST pressure in time
020406080
100120140160180200220240
0 319 618 948 1264 1636 2030 2948
Time [min]
Pre
ss
ure
[k
Pa
]
CTMT
EWST
CTMT and EWST pressure in time
020406080
100120140160180200220240
0 319 618 948 1264 1636 2030 2948
Time [min]
Pre
ss
ure
[k
Pa
]
CTMT
EWST
ppmax max = 135,5kPa= 135,5kPappmax max = 135,5kPa= 135,5kPa
ppmax max = 222,7kPa= 222,7kPappmax max = 222,7kPa= 222,7kPa
CTMT and EWST pressure
0
40
80
120
160
200
240
0,00 0,10 0,34 0,55 0,81 1,03
Time [min]
Pre
ssu
re [
kP
a]
CTMT
EWST
CTMT and EWST pressure
0
40
80
120
160
200
240
0,00 0,10 0,34 0,55 0,81 1,03
Time [min]
Pre
ssu
re [
kP
a]
CTMT
EWST
1212
pp = 87kPa= 87kPapp = 87kPa= 87kPa
CTMT and EWST temperature in time
0
20
40
60
80
100
120
140
160
180
0 319 618 948 1264 1636 2030 2948
Time [min]
Te
mp
era
ture
[o
C]
Box PG
HN
CTMT and EWST temperature in time
0
20
40
60
80
100
120
140
160
180
0 319 618 948 1264 1636 2030 2948
Time [min]
Te
mp
era
ture
[o
C]
Box PG
HN
TTmax max = 156= 156ooCCTTmax max = 156= 156ooCC
TTmax max = 149= 149ooCCTTmax max = 149= 149ooCC
CTMT and EWST temperature
0
30
60
90
120
150
180
0,00 1,03 8,81 40,38 83,02 129,03
Time [min]
Tem
per
atu
re [
oC
]
CTMT
EWST
CTMT and EWST temperature
0
30
60
90
120
150
180
0,00 1,03 8,81 40,38 83,02 129,03
Time [min]
Tem
per
atu
re [
oC
]
CTMT
EWST
1313
TT = 60= 60ooCCTT = 60= 60ooCC
1414
1515
EWSTEWST
1616
1717
1818
1919
Steel corrosion
11,211,311,411,511,611,711,811,912,012,1
0 5 10 15 20 25 30 35Time [years]
Dia
me
ter
[mm
] Sommer
Faraday
Steel corrosion
11,211,311,411,511,611,711,811,912,012,1
0 5 10 15 20 25 30 35Time [years]
Dia
me
ter
[mm
] Sommer
Faraday
t
tcorrot
o
dttiDD 0232.0 t
tcorrot
o
dttiDD 0232.0 D(t) = Do A tcorrBD(t) = Do A tcorrB
Faraday’s law Sommer’s law
2020
NPP V1 Jaslovské Bohunice
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
0 10 20 30 40 50 60 70 80 90
Steam pressure [kPa]
Dis
plac
emen
t [m
m]
S7_exp
S7_num
S9_exp
S9_num
S8_exp
S8_num
NPP V1 Jaslovské Bohunice
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
0 10 20 30 40 50 60 70 80 90
Steam pressure [kPa]
Dis
plac
emen
t [m
m]
S7_exp
S7_num
S9_exp
S9_num
S8_exp
S8_num
2121
2222
IInn tthhiiss mmooddeell tthhee bbiilliinneeaarr ssttrreessss--ssttrraaiinn ddiiaaggrraamm ffoorr ccoonnccrreettee aanndd KKuuppffeerr''ss bbiiddiimmeennssiioonnaall
ffaaiilluurree ccrriitteerriioonn ooff ccoonnccrreettee iiss ccoonnssiiddeerreedd.. TThhee ssttrreessss--ssttrraaiinn ddiiaaggrraamm iiss iinnttrroodduucceedd iinn tthhee
mmooddiiffiieedd ffoorrmm iinnttoo tthhee EENNVV 11999922--11--11 ((11999911))
-- iinn ccoommpprreessssiioonn 0 cu
.2.1
..
2
k
kfc ,,
c
)0035.0,0022.0( cuc ((55))
--iinn tteennssiioonn mt
)/).(2exp(. tmttf SShheeaarr mmoodduulluuss iiss rreedduucceedd aafftteerr ccrraacckkiinngg aaccccoorrddiinngg ttoo tthhee llaaww ddeerriivveedd bbyy KKoollmmaarr..
IInn tthhiiss mmooddeell tthhee bbiilliinneeaarr ssttrreessss--ssttrraaiinn ddiiaaggrraamm ffoorr ccoonnccrreettee aanndd KKuuppffeerr''ss bbiiddiimmeennssiioonnaall
ffaaiilluurree ccrriitteerriioonn ooff ccoonnccrreettee iiss ccoonnssiiddeerreedd.. TThhee ssttrreessss--ssttrraaiinn ddiiaaggrraamm iiss iinnttrroodduucceedd iinn tthhee
mmooddiiffiieedd ffoorrmm iinnttoo tthhee EENNVV 11999922--11--11 ((11999911))
-- iinn ccoommpprreessssiioonn 0 cu
.2.1
..
2
k
kfc ,,
c
)0035.0,0022.0( cuc ((55))
--iinn tteennssiioonn mt
)/).(2exp(. tmttf SShheeaarr mmoodduulluuss iiss rreedduucceedd aafftteerr ccrraacckkiinngg aaccccoorrddiinngg ttoo tthhee llaaww ddeerriivveedd bbyy KKoollmmaarr..
efcf
loading
eq
t
ef etf
efcf
c cu cm
tm
loading
unloading
efcf
loading
eq
t
ef etf
efcf
c cu cm
tm
loading
unloading
2323
In this model is considered the bilinear stress-strain diagram for concrete and Kupfer's
bidimensional failure criterion of concrete (see fig.6). The failure function is
- In compression-compression state
cefc f
a
af .
.1
.65.3.12
,
2
1
c
ca
- In tension-compression state
eccefc rff . ,
c
cec fr 13278.5.1
,
9,0ecr - In tension-tension state
ettef rfft
. , BA
BAAret .
.1 ,
AxKB . , cc fx 2 ,
0.1 xret , .12,0 xret
c2efc f
a1
a65.31f
Compressive Failure
Fig.6 Bidimensional conrete model
TensilFailure2
1
c
ca
fc
effc
1c2c
fc
2424
The matrix of material stiffness is diagonal l in the case of concrete cracking in one
direction. If c is the orientation angle of the principal direction of the relative deformation
in the concrete layer and s is the reinforcement orientation, we can get a global matrix of a
constitution relation for lth layer in the form
n
j
ls
ls
Tls
lc
lc
Tlc
lcr
1
TDTTDTD ,
where Tc , Ts are the transformation matrices for the concrete and steel elements.
s
lzx
s
lyz
lxy
ly
llx
lxy
l
lx
lxy
llx
l
l
k
Gk
G
G
EBEB
EBEB
00000
00000
00000
000000
0000
0000
D,
lx
lxy
ly
lyl
EE
EB
2
,
2525Shell91
Concrete - Ec = 16,4Gpa, = 0,2, fc= -43Mpa, ft= 2Mpa Steel - Es = 201Gpa, = 0,3, fs= 670Mpa Concrete - Ec = 16,4Gpa, = 0,2, fc= -43Mpa, ft= 2Mpa Steel - Es = 201Gpa, = 0,3, fs= 670Mpa
65
9
9
2x23,5
Plate D3
0
10
20
30
40
50
60
0 5 10 15 20Displacement w [mm]
Fo
rce
F [
kN]
Experiment
Numerical
Plate D3
0
10
20
30
40
50
60
0 5 10 15 20Displacement w [mm]
Fo
rce
F [
kN]
Experiment
Numerical
2626
2727
2828
2929
3030
Non-linear containment analysis
0
20
40
60
80
100
120
0 50 100 150 200 250 300
Overpressure in HZ [kPa]
Uti
liza
tio
n o
f s
ec
tio
n [
%]
with steel liner
without steel liner
Non-linear containment analysis
0
20
40
60
80
100
120
0 50 100 150 200 250 300
Overpressure in HZ [kPa]
Uti
liza
tio
n o
f s
ec
tio
n [
%]
with steel liner
without steel liner
210kPa210kPa260kPa260kPa
3131
3232
The reliability condition is defined in the form
SF = R - E ≥ 0, various in the form relative SF = R / Ed -1 ≥ 0
where R is the capacity of structure, E - the load action.
The reliability of the shell structure is defined depending on concrete
failure condition for layered shell as follow
R = Fui (pvar(t,) ; up ; ) + up ,
where pvar(t,) is the variable strain vector
The total strain vector for l th load level
gvar , Tvar , pvar and evar are the variable defined by histograms
3333
var var var var var, , . , . , . .l l l lg th pt t g t T t p e
Input quantities
V a r i a b l e c o n s t a n t s
Elasticity modul
evar
Tempe-rature
Tvar
Live load
gvar
Failure criterium
fvar
Mean value 1 1 1 1
Standard deviation σ
0,111 0,10 0,10 0,15
var var var var var, , . , . , . .l l l lg th pt t g t T t p e
3434
1 1 1
ˆ .NRV NRV NRV
o i i ij i ji i j
Y c c X c X X
1 1 1
ˆ .NRV NRV NRV
o i i ij i ji i j
Y c c X c X X
3535
( ) ( ) ( ) ( )f f E R E Rp dp f x x dx x f x dx
where where ffEE(x), f(x), fRR(x) (x) are the density functions and are the density functions and EE(x)(x),, RR(x) (x) are the distribution are the distribution
functions of action functions of action EE and resistance and resistance RR
Probability of failureProbability of failure
Aproximation and simulationAproximation and simulation
Number of variability input : 4Number of variability input : 4 Number of simulations CCD : 25Number of simulations CCD : 25
Intelligent System Design Lab.Intelligent System Design Lab.
Original System
x1
x
2-1 0
1
1
0
-1
DOE and Experiments
Black BoxedSystem
Black BoxedSystem
Input
1x
2x
Response
y
RS Model
20 i i ii i ii i jy c c x c x c x x 20 i i ii i ii i jy c c x c x c x x
RSM : Response Surface MethodRSM : Response Surface Method : Response Surface Model: Response Surface Model
3636
1 1 1
ˆ .NRV NRV NRV
o i i ij i ji i j
Y c c X c X X
Central Composite DesignCentral Composite Design Box-Behnken MatrixBox-Behnken Matrix
3737
Number of variability input : 4Number of variability input : 4Number of simulations CCD : 25Number of simulations CCD : 25
Number of variability input : 4Number of variability input : 4Number of simulations BBM : 25Number of simulations BBM : 25
AproximaAproximationtion met methodshods - RS - RSMM : :
AdvantagesAdvantages
• • reduction of simulation quantitiesreduction of simulation quantities
• • posibilities to use the posibilities to use the „design experiments“ „design experiments“ or or „„regresion analysis”regresion analysis”
• • independence of simulationsindependence of simulations
DisadvantagesDisadvantages
• • Number of simulation increase with the number of input simplesNumber of simulation increase with the number of input simples
• • Non acceptable for non continuous problemsNon acceptable for non continuous problems
3838
3939
PPmm=320kPa=320kPaModel without deqradation SF=83,4%Model without deqradation SF=83,4%
Model with deqradation SF=94,8%Model with deqradation SF=94,8%
4040
Pressure pPressure pmm=260 kPa=260 kPa
Pressure pPressure pmm=320 kPa=320 kPa
4141
Probability of the containment failure is less as 10-6 for overpressure 320kPa
and the original model without degradation effects.
Probability of the containment failure is equal to 1,375.10-4 for overpressure 320
kPa considering degradation effects.
The The degradationdegradation - the bottom EWST plate and wall vertical microcracks – - the bottom EWST plate and wall vertical microcracks –
decrease the safety of CTMT structure, but not significant decrease the safety of CTMT structure, but not significant (about 15%)
The RSM method is very effective method for nonlinear problems on robust
FE- models.