NEAR FAULT GROUND MOTIONS:NEAR-FAULT GROUND MOTIONS:Outstanding Problems

APOSTOLOS S. PAPAGEORGIOUUniversity of Patras

OutlineOutline• Characteristics of near-fault ground motions

N f lt t d ti d t b• Near-fault strong ground motion database• A mathematical expression for near-fault ground

motions:motions:– Calibration– Scaling laws of the parametersg p– Spectral properties– Interpretation of empirical observations

El ti d i l ti t• Elastic and inelastic response spectra• Synthesis of near-fault ground motion time histories

C l i• Conclusions• Additional considerations – Directions of future research

Characteristics of Near-Fault Ground Motions

• Significant seismic events where theevents where the special character of the near-fault ground

timotions was originally observed.

• Note the intense• Note the intensevelocity and displacement pulsesi fi ld iin near-field regions.

Characteristics of Near-Fault Ground MotionsF d Di ti it Eff t• Forward Directivity Effect:

– Fault rupture propagates toward a site with Vr ≈ β (and slip vector points toward the site).– Appears in the form of two-sided velocity pulse.– Observed in the strike-normal direction for strike-slip and dip-slip faults. [References: e.g., Aki, 1968; Somerville & Graves, 1993; Somerville, 2000; Abrahamson, 2000].

l i ff• Permanent Translation Effect:– Related to the permanent tectonic deformation at a site.– Appears in the form of step displacement and one-sided velocity pulse.pp p p y p– Observed in the strike-parallel and strike-normal directions for strike-slip and dip-slip

faults, respectively. [Reference: Abrahamson, 2000].

• Other factors that influence the near-fault ground motions:- Type of rupture: Shear dislocation vs. crack [Aki & Richards, 1980; Campillo et al., 1989].

“H i ll” “F t ll” ff t [Ab h & S ill 1996 O l b t l 1998]- “Hanging wall” vs. “Foot wall” effect [Abrahamson & Somerville, 1996; Oglesby et al., 1998].

- Surface vs. buried faulting [Aki, 1980; Somerville, 2000].- Surface or interface P-wave [Bouchon, 1978; Kawase & Aki, 1990].

Special geometrical conditions [Oglesby & Archuleta 1997]- Special geometrical conditions [Oglesby & Archuleta, 1997].- Supershear rupture velocity [Bouchon et al., 2001; O’Connell and Ake, 2003].

Characteristics of Near-Fault Ground Motions:Examples of Directivity and Permanent Translation EffectExamples of Directivity and Permanent Translation Effect

Near-Fault Strong Ground Motion Database

• Thorough documentation of the existing near-source di f d t d l trecordings of moderate and large events

(31 events worldwide; 165 stations; fault-to-station distance less than 20 km)than 20 km).

• Collection and uniform processing of these data and f p gpresentation in visually informative form relative to the causative faults.

• Approximately 40 near-source ground motion records (f 20 t ld id ) h t i d b di i(from 20 events worldwide) are characterized by distinctvelocity pulses.

N F lt St G d M ti D t bNear-Fault Strong Ground Motion Database

Near-Fault Strong Ground Motion Database

• Near-fault ground motion records withmotion records with distinct velocity pulses (incorporating forward directivity anddirectivity and permanent translation effects).

P l h t i ti• Pulse characteristics: amplitude, duration, as well as number and phase of half cyclesphase of half cycles.

• These records are being used for the calibrationof the proposed analytical model.

Near-fault velocity pulses: Iceland 2000

•Significant coherent part in the near-fault ground motions during the 17 June and 21 June, 2000, Mw6.5 earthquakes, , q

(Halldorsson et al., 2007)

Velocity – north-southIceland 2008: Velocity – strike-normal

H lld & Si bj (2009 SDEE)Halldorsson & Sigbjornsson (2009, SDEE)

Halldorsson et al. (2009, in progress)

Iceland 2008: Velocity – strike-normal

Halldorsson et al. (2009, in progress)

An Analytical Model for Near-Fault Ground MotionsAn Analytical Model for Near Fault Ground Motions

• Objective:Representation of near-source ground motions in terms of simple analytical waveforms, the parameters of which have an unambiguous unambiguous physical meaningphysical meaning and scalescale (to the extent possible) with earthquakewith earthquakephysical meaningphysical meaning and scalescale (to the extent possible) with earthquake with earthquake sizesize.

• Advantages:- “Objective” assessment of duration and amplitude of pulse.- These models can be easily used to effectively generate near-fault ground motion time histories appropriate for engineering design.- These models facilitate the parametric study of the elasticelastic andThese models facilitate the parametric study of the elasticelastic and inelastic responseinelastic response of long-period structures subjected to near-fault ground motions.

An Analytical Model for Near-Fault Ground Motions: Mathematical ExpressionMathematical Expression

( ) ( )[ ]⎪⎨

⎧>+≤≤−+−⎥

⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎜⎝

⎛−+

=with

ftt

ftttftt

fA

tv PP 1

22,2cos

2cos1

21

)( 0000 γγγνπγπ

where:

⎪⎩

⎨ ⎦⎣ ⎠⎜⎝=

otherwise

fftv PP

,0

222)( γ

where:• A is the amplitude of the signal,• f is the frequency of the amplitude modulated harmonic• fP is the frequency of the amplitude-modulated harmonic

(or the prevailing frequency of the signal),• ν is the phase of the amplitude modulated harmonic• ν is the phase of the amplitude-modulated harmonic,• γ is a parameter that defines the oscillatory character (i.e.,

zero crossings) of the signal andzero-crossings) of the signal, and• t0 specifies the epoch of the envelope’s peak.

An Analytical Model for Near-Fault Ground Motions: Calibration

• The proposed analytical model has been fitted to

f

Calibration

the entire set of near-fault ground motions with distinct velocity pulse. p

• It successfully simulates the displacement, velocity and the coherentcomponent ofcomponent of acceleration time histories, as well as the elastic response spectra.A ti i t d th• As anticipated, the proposed model does not replicate the incoherent(high-frequency)

t f dcomponent of ground motion (clearly evident in the accelerograms and in the low-period range of h )the response spectra).

An Analytical Model for Near-Fault Ground Motions: CalibrationCalibration

• Utilization of multiple synthetic pulses to fit more complicated waveforms.• Two (2) and three (3) synthetic pulses have been combined to model the YPT• Two (2) and three (3) synthetic pulses have been combined to model the YPT

(1999 Izmit, Turkey) and KOB (1995 Kobe, Japan) time histories, respectively.

An Analytical Model for Near-Fault Ground Motions: Regression Analysis & Scaling LawsRegression Analysis & Scaling Laws

• Both forward directivity and fling l ill d

wP MT 5.09.2log +−=• The pulse duration is defined as the

kmRforscmPGV 7,/13070 ≤−≈

pulses are illustrated.

• With the exemption of TCU052 and TCU068 stations, all other records are

inverse of the prevailing frequency.

• Only forward directivity pulses have been considered for the derivation of effectively described by a PGV of

100 cm/s. (Note: A ≈ PGV).

been considered for the derivation of the expression above.

The Specific Barrier Model:Barrier Interval 2ρ0 vs. Moment Magnitude Mwρ0 g w

( ) WM5.06.22log 0 +−=ρAccording to the Specific Barrier Model the Rise Time τ is estimated as follows:follows:

( ) ( )VV /2/ 00 ρτρ ≤≤

We previously obtained:

( ) WP MT 5.09.2log +−=( ) WP 5.09.ogCombining the above we obtain:

PP TT 70.035.0 ≤≤τTherefore, we propose:

PT5.0≈τ

An Analytical Model for Near-Fault Ground Motions: Spectral Properties Fourier SpectraSpectral Properties – Fourier Spectra

• Normalized Fourier lit d t famplitude spectrum of

velocity pulse vs. normalized frequency for a suite of γ and ν values.γ

• Narrow-band velocity pulse with its bandwidth and Fourier amplitudeand Fourier amplitude being a function of γ for constant ωP and A values.

• The phase parameter νaffects the Fourier amplitude spectrum only when γ approaches unity γ pp yand then only for periods longer than TP.

An Analytical Model for Near-Fault Ground Motions: Spectral Properties Response SpectraSpectral Properties –Response Spectra

An Analytical Model for Near-Fault Ground Motions: Spectral Properties Elastic Response SpectraSpectral Properties – Elastic Response Spectra

An Analytical Model for Near-Fault Ground Motions: Interpretation of Empirical Observations

It has been observed (originally by Somerville, 2000) that:• the near-source acceleration response spectra of moderate earthquakes are stronger than

those of large earthquakes in the high-frequency range. This trend is reversed at longer

p p

g q g q y g gperiods, and

• the peak spectral acceleration values of moderate earthquakes are regularly higher than the corresponding values of large earthquakes.

We may interpret the above observations through the mathematical formulation of our model:

• Consider 2 seismic events with M 1 > M 2 that produce near-source groundConsider 2 seismic events with Mw1 > Mw2 that produce near source ground velocity pulses effectively replicated by the proposed analytical model.

Equal-Ductility Pseudo-Velocity Response Spectraof Elastic Perfectly Plastic SDOF Systemsy y

Equal-Ductility Pseudo-Velocity Response Spectraof Elastic Perfectly Plastic SDOF Systemsy y

Schematic Illustration of Idealized Response SpectraI F W L ith i Pl tIn Four-Way Logarithmic Plots

Elastic Response Spectra(Damping Ratio ξ = 5%)(Damping Ratio ξ = 5%)

Elastic Response Spectra(Damping Ratio ξ = 5%)(Damping Ratio ξ 5%)

Earthquake Characterization Moment Magnitude (Mw) (Tn/TP)a (Tn/TP)b (Tn/TP)c (Tn/TP)d (Tn/TP)f

Moderate 5.6 – 6.3 0.035 0.350 0.75 0.90 11.0

Moderate-to-Large 6.4 – 6.7 0.010 0.200 0.75 0.90 8.0g

Large 6.8 – 7.6 0.002 0.055 0.75 1.00 5.0

All sizes 5.6 – 7.6 0.004 0.300 0.75 0.90 11.0

Earthquake Characterization Moment Magnitude (Mw) αV,cd αV,b

Moderate 5.6 – 6.3 2.10 0.95

Moderate-to-Large 6.4 – 6.7 2.00 0.75

Large 6.8 – 7.6 1.55 0.43

All sizes 5.6 – 7.6 1.85 0.90

Strength Reduction Factor Ry:Comparison With Veletsos-Newmark-Hall Design EquationsComparison With Veletsos-Newmark-Hall Design Equations

Synthesis of Near-Fault Ground Motion Time Histories:A Simplified Methodology for Engineering Applicationsp gy g g pp

Demonstration Case A• Generation of ground motion for a

Mw 6.8 earthquake event and for the fault-station geometry di l d i h fidisplayed in the figure.

• The site characterization at the station is assumed to be NEHRP Site Class CSite Class C.

• The selected values for the parameters of the Specific Barrier Model are consistent with those ofModel are consistent with those of Chin and Aki (1991) inferred for a comparable size Californian event.

• As expected, the incoherent pcomponent of motion controls the accelerations while the coherent component of motion controls the velocity and displacementvelocity and displacement.

Synthesis of Near-Fault Ground Motion Time Histories:A Simplified Methodology for Engineering ApplicationsA Simplified Methodology for Engineering Applications

Demonstration Case B

Demonstration Case B (Cont’d)

Fast and efficient simulation of broad-band near-fault ground motions

Halldorsson, Mavroeidis & Papageorgiou (2009) – Journal of Structural Engineering (in press)

Conclusions• The proposed mathematical model describesdescribes adequatelyadequately thethe naturenature ofof

thethe impulsiveimpulsive nearnear--faultfault groundground motionsmotions both qualitatively andpp gg q yquantitatively.

• The model inputinput parametersparameters have an unambiguousunambiguous physicalphysical meaningmeaning.

• The analytical model has been calibratedcalibrated usingusing aa largelarge numbernumber ofofactualactual nearnear--fieldfield groundground motionmotion recordsrecords; it successfully simulates theentire set of available near-fault displacement, velocity and, in manyentire set of available near fault displacement, velocity and, in manycases, acceleration time histories, as well as the corresponding responsespectra.

h d l ii ii i ii i ii• The model cancan bebe usedused toto explainexplain analyticallyanalytically empiricalempirical observationsobservationsthat are based on available near-source records.

• We have proposedproposed elasticelastic andand inelasticinelastic responseresponse spectraspectra forfor designdesign.

• We have proposedproposed aa veryvery simplifiedsimplified methodologymethodology forfor generatinggeneratingrealisticrealistic syntheticsynthetic groundground motionsmotions that are adequate for engineeringanalysis and designanalysis and design.

Additional ConsiderationsAdditional Considerations:Scaling of Pulse Period TP vs. Moment Magnitude Mw

for Intra-Plate Earthquake Events

Additional Considerations Additional Considerations – Super-shear Rupture

•A supershear rupture leads to large amplitudes on both the FP and FN components of motion.

• Rupture growth into a region of increased stress drop triggers a set ofincreased stress drop triggers a set of transient diffractions that accelerate the rupture from sub-Rayleigh to

h l itisupershear velocities.

•This process is accompanied by the release of a Rayleigh wave on the faultrelease of a Rayleigh wave on the fault surface.

•This appears as a secondary slip pulse pp y p pthat manifests itself primarily in FN ground motion, explaining late arriving FN pulses recorded at PS10 that are notFN pulses recorded at PS10 that are not explained in supershear kinematic models.

[Taken from Durham and Archuleta (2005), GRL]

Additional Considerations – Directions of Future Research(cont’d)( )

• Seismic energy radiated from the high-isochrone-velocity region of the fault arrives atregion of the fault arrives at the receiver within a time interval that coincides with the time window of the ground

ti l d d t thmotion pulse recorded at the site.

• Near-fault strong motion l t l l t dpulses are strongly correlated

with large slip on the fault plane locally driven by high stress drop.p

• For smaller earthquakes, the area of the fault that contributes to the formation of the near-fault pulse encompasses more than one “patches” of significant moment release (subevents).

Additional Considerations – Directions of Future Research (cont’d)(cont d)

Additional Considerations – Directions of Future Research (cont’d)

• For larger earthquakes the area of the fault that contributes to the formation of• For larger earthquakes, the area of the fault that contributes to the formation of the near fault pulse encompasses an individual “patch” of significant moment release (subevent).

• The foreshock and aftershock seismic activity in combination with the shear• The foreshock and aftershock seismic activity in combination with the shear-stress images may offer insight into the type of mechanism (i.e., barrier or asperity) that controlled the mainshock rupture.

Dynamic Ground Deformations in the Near-Fault Region:Th 1979 I i l V ll E h kThe 1979 Imperial Valley Earthquake

• Remarkable waveform similarity between velocity time histories and derivatives of the displacement components with respect to the x coordinate (Bouchon and Aki, 1982).

• This indicates that most of the energy (which controls the peak amplitudes of motion) propagates at each observation point within a relatively small range of phase velocities.

X-axis in the Fault-Parallel direction Y-axis in the Fault-Normal direction Z-axis in the Vertical Direction

Dynamic Ground Deformations in the Near-Fault Region:Th 1979 I i l V ll E h kThe 1979 Imperial Valley Earthquake

• The relationship is approximately valid, with c being the average phasetu

cxu ii

∂∂

−≈∂∂ 1

velocity.

• The phase velocities are controlled either by the basement rock shear velocity or the

tcx ∂∂

rupture velocity and may be estimated from synthetic time histories. In our case, the estimated phase velocities are close to the shear wave velocity of the basement rock (4 to 5 km/s).

• The axial strain along the strike direction (εxx = ∂ux/∂x), the rocking about an axis along the transverse direction (ωy = -∂uz/∂x), and the torsional motion (ωz ≈0 5*∂u /∂x) may be estimated with reasonable accuracy via the above equation by0.5 ∂uy/∂x) may be estimated with reasonable accuracy via the above equation by using synthetic or recorded ground velocities and properly selected phase velocities.

• The analytical model for the representation of the long-period component of the near-fault ground motions proposed by Mavroeidis and Papageorgiou (2003) may be used to approximate the torsional component of the near fault ground motion; that is:

yy uu 111 ∂∂g

yyz V

ctcx 21

21

21

−=∂

−≈∂

≈ω