2015_Chandra_In Situ Assessment of the G-γ Curve for Characterizing the Nonlinear Response of Soil_Application to the Garner Valley Downhole Array and the Wildlife Liquefaction Array

In Situ Assessment of the G–γ Curve for Characterizing the Nonlinear

Response of Soil: Application to the Garner Valley Downhole

Array and the Wildlife Liquefaction Array

by Johanes Chandra, Philippe Guéguen, Jamison H. Steidl, and Luis Fabian Bonilla

Abstract We analyze the nonlinear and near-surface geological effects of twoNetwork for Earthquake Engineering Simulation at University of California, SantaBarbara (NEES@UCSB) instrumented sites: the Garner Valley Downhole Array(GVDA) and the Wildlife Liquefaction Array (WLA). The seismic interferometry bydeconvolution method is applied to earthquake data recorded by the multisensor ver-tical array between January 2005 and September 2013. Along the cross section, localshear-wave velocity is extracted by estimating travel time between sensors. TheS-wave velocity profiles are constructed and compared with classical in situ geophysi-cal surveys. We show that velocity values change according to the amplitude ofthe ground motion, and we find anisotropy between east–west and north–south direc-tions at the GVDA site. The ratio between average peak particle velocity v� and localS-wave velocity V�

S between two boreholes is tested as a deformation proxy. Usingaverage peak particle acceleration a�, the a� versus v�=V�

S curve is used to representthe stress–strain curve for observing the site’s nonlinear responses under different lev-els of excitation. Nonlinearity is observed from quite low shear-strain levels(∼1 × 10−5) and a classic hyperbolic model is derived. v�=V�

S proves to be a good de-formation proxy. Finally, the shear modulus degradation curves are constructed foreach depth and test site, and they are similar to previous laboratory measurementsor in situ geophysical surveys. A simple comparison regarding nonlinear behaviorbetween GVDA and WLA is performed.

Introduction

The effects of near-surface geology have been docu-mented for many previous earthquakes, such as the 1985Michoacán earthquake (e.g., Campillo et al., 1989; Chávez-Garcia and Bard, 1994), the 1989 Loma Prieta, California,earthquake (Chin and Aki, 1991; Rubinstein and Beroza,2004), and the 1994 Northridge, California, earthquake (Fieldet al., 1997; Beresnev et al., 1998; Hartzell, 1998). One con-sequence is the amplification of seismic ground motion insedimentary sites compared to rock sites, which often hasthe maximum amplification at the fundamental frequencyf0 of the soil column and may have a broadband amplificationin the cases of 2D or 3D effects. Under a 1D assumption, f0 ofa sedimentary layer overlaying stiff bedrock depends on theshear-wave velocity VS and the thickness H of the layer,and is approximated by f0 � VS=4H. For strong ground mo-tion, nonlinear soil response may occur. In this case, the soilresponse depends on the strength of the material and the straininduced by the incoming wavefield. Many authors have re-ported observations of nonlinear response by examiningchanges in f0 (e.g., Beresnev and Wen, 1996; Bonilla et al.,

2003; Tsuda and Steidl, 2006; Wu et al., 2009), the variationof mode shape (Guéguen et al., 2011), or reduction of am-plification of the sediment response (Assimaki et al., 2006).This nonlinear response is mainly driven by the strain-dependent dynamic parameters of the soil, that is, shearmodulus G and damping D. Variations in these parametersare the consequence of the increase in shear strain related tothe increase in shear stress that occurs during strong shaking.G is related to shear stress τ and shear strain γ according tothe classical formula τ � G�γ� × γ. For the largest deforma-tion expected during strong ground motion, degradation ofthe shear modulus is observed as damping increases. Assum-ing constant density ρ, this implies that shear-wave velocityVS decreases with the reduction in shear modulus, throughthe relation

VS ��G=ρ

p: �1�

For earthquake engineering applications involving soilnonlinearity, the site is generally characterized by establish-ing the G versus γ (modulus reduction) curve, using data

993

Bulletin of the Seismological Society of America, Vol. 105, No. 2A, pp. 993–1010, April 2015, doi: 10.1785/0120140209

from cyclic laboratory tests that are performed on samplescollected in situ. Based on laboratory tests, Vucetic (1994)distinguished two different shear-strain thresholds relatedto soil nonlinearity: linear cyclic γtl and volumetric γtv shearstrains. For γ < γtl, the soil behaves in a linear manner; forγtl < γ < γtv, the soil exhibits nonlinear elastic behavior withnegligible permanent deformation; and for γ > γtv, the soilshows hysteretic nonlinear behavior with permanent deforma-tion. The order of magnitude of γtv is around 10−4 (Hardin andBlack, 1968; Drnevich and Richart, 1970; Dobry and Ladd,1980) or 2 × 10−4 (Youd, 1972; Vucetic, 1994). Using com-pressional waves, Johnson and Jia (2005) reported the linearnormal strain threshold εtl around 1 × 10−7 to 5 × 10−6, as-sociated with a Young’s modulus degradation of 5% at a strainlevel of 1 × 10−6. Furthermore, Vucetic (1994) observed aplasticity index dependence on γtl, starting around 5 × 10−6.Because of the lack of in situ data covering a wide range ofstrain levels for assessing the G–γ curve, the significance oflaboratory tests compared with in situ conditions is seldomdiscussed. In addition, due to the high cost of collecting insitu vertical array data combined with the time between sig-nificant earthquakes, there is a paucity of in situ data to com-pare with laboratory tests. Finally, the competing effects ofground-motion amplification (due to the presence of differentimpedance contrasts at different depths) and ground-motiondeamplification (due to near-surface nonlinearity) induce fur-ther complexity (Archuleta et al., 1992; Bonilla et al., 2011).

An effective solution for observing in situ nonlinear re-sponse consists of measuring the shear-wave velocity varia-tion under different levels of excitation (Haskell, 1953;Ohmachi et al., 2011; Dobry, 2013). Using a vertical arrayhaving a series of accelerometers located at different depths,the measurement of the wave’s arrival time provides an esti-mation of VS, assuming the soil column undergoes shear de-formation. The classical methods to compute these velocitiesuse cross-correlation analysis (Rubinstein and Beroza, 2004;Rubinstein and Beroza, 2005) and cross-spectral analysis(Coutant, 1996). Recently, the seismic interferometry by de-convolution method has been successfully applied (Mehtaet al., 2007; Sawazaki et al., 2009; Nakata and Snieder, 2012;Pech et al., 2012) to detect very small changes in velocity. Inaddition, the representation of soil nonlinearity by the G–γcurve also relies on the measurement of deformation directlyestimated by relative displacement between the borehole sen-sors (e.g., Zeghal and Elgamal, 1994).

This study was designed to test the efficiency of non-invasive assessment of the nonlinear response of a site, ap-plied to the Garner Valley Downhole Array (GVDA) and theWildlife Liquefaction Array (WLA) test sites at moderateor strong strain levels. For that, a proxy of the stress–strainrelationships is proposed by computing the ratio between theaverage peak particle velocity and the equivalent-linearshear-wave velocity, as used for example by Hill et al. (1993)and Idriss (2011) and validated on synthetic results and cen-trifuge tests by Chandra et al. (2014). The description of theGVDA and WLA test sites and the data selection criteria used

in this study are presented in the first part. The seismic inter-ferometry by deconvolution method is then applied to thevertical arrays, and the shear-wave velocity (VS) profiles areobtained, along with the variation of VS with respect to thelevel of shaking. Finally, the stress–strain relationship is ac-quired through the wave-based nonlinear proxy PGV=VS

(PGV is peak ground velocity) for strain, and the in situ non-linear response is discussed in the last section.

The Network for Earthquake Engineering Simulationat University of California, Santa Barbara for the

GVDA and WLA Test Sites

The GVDA and the WLA are part of the George E. Brown,Jr., Network for Earthquake Engineering Simulation at theUniversity of California, Santa Barbara (NEES@UCSB).The GVDA test site (33°40.127′N, 116°40.427′W) is situatedin a valley within the Peninsular Ranges batholith, 23 km eastof Hemet and 20 km southwest of Palm Springs, California. Itis located 7 km and 35 km from the San Jacinto fault (SJF) andthe San Andreas fault (SAF), respectively. The SJF is histor-ically the most active strike-slip fault in the SAF system, with aslip rate of ∼10 mm=yr, and the southern SAF is an activefault with a slip rate of ∼25 mm=yr.

The WLA test site (33°05.843′N, 115°31.827′W) is situ-ated in California’s Imperial Valley on the west bank of theAlamo River, 13 km north of Brawley and 160 km east of SanDiego. It is located southeast of the southernmost terminus ofthe SAF. For more extensive details on these sites, readers arereferred to Youd, Bartholomew, Proctor (2004), Steidl andSeale (2010), Steidl et al. (2012, 2014), and the NEES@UCSBwebsite (see Data and Resources). The locations of GVDA andWLA test sites are shown in Figure 1.

The GVDA near-surface geological conditions consist ofsoft alluvial lake deposits to a depth of 18–25 m overlayingweathered granite (Fig. 2a). The cross section of GVDAshows multiple impedance contrasts at several depths, result-ing in a complex amplification of ground motion. The fun-damental frequency is around 1.7 Hz (Archuleta et al., 1992;Steidl et al., 1996; Theodulidis et al., 1996; Bonilla et al.,2002), and several higher resonance frequencies exist at 3,6, 8, and 12 Hz. According to Pecker (1995) and Bonilla et al.(2002), we assumed a 1D model of the site. Furthermore,Coutant (1996) and Bonilla et al. (2002) detected velocityanisotropy in the shallow layers, confirming the complexityof the site in terms of seismic response. In situ surveys havebeen performed, providing an extensive description of thesite in terms of geotechnical and geophysical characteristics(Pecker and Mohammadioun, 1991; Archuleta et al., 1992;Gariel et al., 1993; Pecker, 1995; Steidl et al., 1998; Youd,Bartholomew, Proctor, 2004; NEES@UCSB website, seeData and Resources). The shear-wave velocity ranges from90 m=s in the uppermost layer to 3500 m=s at the bottom(500 m depth). Stokoe and Darendeli (1998) performed lab-oratory tests to extract the G–γ curve of the surficial sedi-ments; these results will be used as a reference for our

994 J. Chandra, P. Guéguen, J. H. Steidl, and L. F. Bonilla

analysis. Moreover, Lawrence et al. (2008) studied the non-linear response of GVDA using induced vibration with accel-eration of more than 1g. By inverting the dispersion curves,they observed the greatest change in S-wave velocity nearestthe surface (up to a depth of 4 m) related to the nonlinearresponse of the uppermost layers. Since its installation in1989, GVDA’s instrumentation has been upgraded and en-hanced several times (Steidl et al., 2012). In this study, weconsider data recorded using the most recent configuration,which was updated in 2004. The seismic vertical array con-sists of seven accelerometers located at ground level (GL)-0 mand at GL-6, GL-15, GL-22, GL-50, GL-150, and GL-501 m.Data from these accelerometers are collected using continuousdata acquisition at 200 samples per second, transmitted backto UCSB in real time, and archived.

The WLA test site was first instrumented in 1982. Thenear-surface geology of this site consists of a layer of satu-rated silty sand of around 2–7 m in between silty clay layers(Fig. 2b). The presence of the sandy layer in addition to ashallow water table at around 1.2 m render the site liquefi-able, as observed from field evidence during regional earth-quakes (e.g., 1979 Mw 6.5 Imperial Valley earthquake; 1981Mw 5.9 Westmorland earthquake), and from instrumentalevidence of liquefaction or strain hardening (Bonilla et al.,2005) during the 1987Mw 6.6 Superstition Hills earthquake.No data on the bedrock are available at this site. In 2002,20 yrs after the site was first instrumented, the original sensors

Figure 1. Test site location (source: Google maps, see Data and Resources).

Figure 2. Geotechnical cross section of (a) the Garner ValleyDownhole Array (GVDA) and (b) the Wildlife Liquefaction Array(WLA) test sites, including the position of the accelerometers usedin this study (black squares).

In situ Assessment of the G–γ Curve for Characterizing the Nonlinear Response of Soil 995

failed and the datalogger became obsolete. New instrumenta-tion was deployed 65 m north of the original site under theNEES program in 2004 and is now operated by UCSB. Thecurrent vertical array, used in this study, is composed of sixaccelerometers at GL-0, GL-2.5, GL-5.5, GL-7.7, GL-30, andGL-100 m (Fig. 2b). Information from geophysical surveyshas been reported by Cox (2006), providing shear-wave veloc-ity ranging from 100 m=s at the surface to 300 m=s at the bot-tom (100 m depth).

In total, data from 5080 events with magnitudes rangingfrom 1:0 ≤ ML ≤ 5:5 were recorded during January 2005 toSeptember 2013 from the GVDA test site, and data from 8515events with magnitudes ranging from 1:0 ≤ ML ≤ 5:5 werecollected from WLA test site during the same period. Hypo-central distances vary from 1 to 100 km for both sites. Therecorded data are mostly from weak to moderate events, withpeak ground acceleration (PGA) of 0:12g and 0:30g for GVDAand WLA, respectively. For all of the events used in this study,the observed pore pressure data showed that liquefaction hasnot occurred.

Deconvolution Method

The seismic interferometry by deconvolution method isapplied to the selected data for the assessment of shear-wavevelocity. Seismic interferometry obtains the Green’s functionby cross correlating the seismic motion between differentreceivers, thus removing the propagation from the sourceto the first receiver (Wapenaar et al., 2010). Instead of usingsingle cross correlation, Snieder and Şafak (2006) proposedthe seismic interferometry by deconvolution method for ap-plication to buildings assuming a 1D shear model. By decon-volving these waves, the causal and acausal propagation ofwaves within the system is obtained, as well as a better es-timation of the arrival times and amplitudes (Clayton andWiggins, 1976). Depending on the frequency content of thesignal, in some cases a mixture of upward and downwarddeconvolved waves is unavoidable in the uppermost layers.Assuming the soil to be a shear deformation system, severalauthors (Mehta et al., 2007; Nakata and Snieder, 2012, Pechet al., 2012) have applied this method to vertical soil profilesto extract the shear-wave velocity. They monitored small var-iations of VS related to environmental changes or seismicshaking levels.

We deconvolved the earthquake record at each down-hole instrument within the soil profile with the GL-0 m rec-ord. The response of the deconvolved waves Di−0m�ω� iscomputed as

Di−0m�ω� �Ai�ω�A�

0m�ω�jA0m�ω�j2 � ε

; �2�

in which Ai�ω� is the ith wavefield in the frequency domainrecorded at receiver i, A0m�ω� is the reference signal at GL-0 m, ω is the angular frequency, � is the complex conjugatesymbol, and ε (set at 10% of the average spectral power) is

the stabilization parameter to avoid instability caused bydeconvolution (Clayton and Wiggins, 1976). Having com-puted Di−0m�ω�, travel time between each receiver Δt is ob-tained by the inverse Fourier transformation of Di−0m�ω�,and the equivalent linear shear-wave velocity V�

S is obtainedas V�

S � Δh=Δt, in which Δh is the distance betweenreceivers.

Data Processing

An initial data selection is made from the GVDA andWLA databases, taking only events recorded at all accelerom-eters in the two horizontal directions (east–west and north–south) with a signal-to-noise ratio (SNR) greater than 3 forfrequency bands between 0.1 and the Shannon frequency(i.e., 100 Hz). These criteria give 401 and 1066 recordingsat GVDA and 7146 and 6864 recordings at WLA for the east–west and north–south directions, respectively. The data hasbeen rotated to true north by the standard NEES@UCSBprocessing procedures for the borehole sensors that are notalready aligned north (GVDA sensors GL-6, GL-15, GL-22,GL-50). We use the complete records collected from theNEES@UCSB database, including P and S waves withoutapplying magnitude criteria and allowing the time windowto vary 72–252 s, depending on the original data availableat the NEES@UCSB website. Before deconvolution, themean and trend of the data were removed, a 5% Tukey taper-ing function was applied, and zero-padding was applied upto 216 samples. Finally, we applied a third-order Butterworthfilter between 0.5–10 Hz and 0.5–20 Hz for GVDA and WLA,respectively, which is large enough to ensure accurate travel-time estimation (Todorovska and Rahmani, 2013) and coversthe fundamental frequency of the sites. Having computed thedeconvolution, the inverse Fourier transform of the Di−0m(equation 2) is resampled 80 times using a polyphase imple-mentation to increase the accuracy of the automatic travel-time picking.

Three typical examples of deconvolved waves are shownin Figure 3, corresponding to three earthquakes recorded atGVDA in the east–west direction: (a) a weak earthquake (9June 2006, ML 1.24, and R � 23:88 km); (b) a moderateearthquake (9 February 2007, ML 4.73, and R � 74:8 km);and (c) the strongest earthquake (7 July 2010, ML 5.43, andR � 32:53 km). For the first event (Fig. 3a), the deconvolveddata at GL-150 m resulted in an erroneous estimation of V�

S atthis level due to sensor malfunction. In addition, one horizon-tal component is no longer functioning at GL-501 m, whichaffects both components because the rotation to true north andeast is no longer valid. For the second and third events(Fig. 3b,c), we obtain clear traveling waves. Interferometryby deconvolution produces a virtual source that excites thesystem at t � 0 (Snieder and Şafak, 2006), with causal andacausal waves referring to the waves in the positive and neg-ative times, respectively. The waveforms in Figure 3b,c arealmost symmetric in time; and, as shown by Nakata andSnieder (2012), the estimated velocity in the positive or


negative parts provides similar values. In this study, we es-timate the equivalent linear velocity by automatic picking ofarrival times at each sensor applied to the GVDA and WLAevent databases. The arrival time is selected using the maxi-mum amplitude of the pulse in the negative (acausal) inter-ferometry at each sensor depth. For the second event(Fig. 3b), because the upward and downward waves overlapin the uppermost layer, we cannot pick their arrival accu-rately. For the third event (Fig. 3c), the wave arrival time can-not be picked accurately at the bottom (GL-501 m), whereonly one horizontal component is functioning. This sensor isremoved from our analysis. These three typical examples arealso found for WLA recordings.

To overcome the problem shown in Figure 3a related tosensor malfunction, we run a manual check and removed allthe data producing this error. To limit the artificial time-delayor the picking inaccuracy due to the lack of separation be-tween the upward and downward waves at close sensor spac-ing near the surface, the GL-6 m sensor at GVDA and theGL-2.5 and GL-5.5 m sensors at WLA are not used in ouranalysis. The GL-501 m sensor at GVDA is also not used, aspreviously mentioned, and the analysis focuses on the upper-most layers between the GL-0 and GL-150 m sensors atGVDA and the GL-0 and GL-100 m sensors at WLA. Theresulting usable event databases considered in this study cor-respond to 368 east–west and 956 north–south events forGVDA and 6461 east–west and 6012 north–south eventsfor WLA (Fig. 4). In Figure 4, the data truncated at lowermagnitude are the result of the preselection carried out byNEES@UCSB to consider the most relevant ground motionfor earthquake and geotechnical engineering applications.This truncation is due to the fact that the NEES@UCSB teamdoes not segment out events from the continuous data whenthe magnitude is small and the distance is large, as the SNRratio is assumed to be insufficient.

Velocity Profile and Site Anisotropy

The seismic interferometry by deconvolution process isapplied to the overall dataset selected for north–south andeast–west recordings, and the velocity profiles for GVDA andWLA are shown (Fig. 5), considering east–west and north–south directions separately. The results are compared with re-ference velocity profiles proposed by Stellar (1996) at GVDAand Cox (2006) at WLA. In our case, V�

S is computed betweentwo sensors in the vertical array, smoothing the velocity con-trasts found by Stellar (1996) and Cox (2006). This is whywe also show the average VS profile (“avg” in Fig. 5) derivedfrom the references, assuming constant VS between each ofthe vertical array sensors used at each site.

At GVDA (Fig. 5a), the results are compared with thevelocity profile provided by Stellar (1996) from suspensionlog results. In the uppermost layers (GL-0–to GL-50 m), ourresults provide a good match with the reference velocityprofile, with V�

S equal to 175–260 m=s from the surfaceto GL-15 m, between 175 and 500 m=s from GL-15 toGL-22 m, and 400–700 m=s between GL-22 and GL-50 m.Differences are observed below GL-100 m (V�

S between 900and 1300 m=s) due to the interface between the weatheredgranite (VS ∼ 400–700 m=s) and crystalline bedrock(VS ∼ 3000 m=s) between 90 and 110 m, and the lack of sus-pension log data beyond 94 m in Stellar (1996) since the drill-ing encountered the crystalline bedrock. At WLA (Fig. 5b),our results match the reference velocity profile provided byCox (2006) quite well, with V�

S equal to 100–170 m=s fromthe surface down to GL-7.7 m, between 170 and 230 m=sfrom GL-7.7 to GL-30 m, and 265–300 m=s betweenGL-30 and GL-100 m.

Depending on the earthquake, V�S profiles show variabil-

ity at the two sites and in each layer. At WLA, the variabilityis largest in the uppermost layers. On the contrary, the GVDAtest site manifests an inverse trend, where the variability

Figure 3. Three typical examples of interferograms of deconvolved waves for GVDA east–west data recorded at GL-0, GL-6, GL-15, GL-22, GL-50, GL-150, and GL-501 m. (a) 9 June 2006 ML 1.24, R � 23:88 earthquake. (b) 9 February 2007 ML 4.73, R � 74:8 km earth-quake. (c) 7 July 2010 ML 5.43, R � 32:53 km earthquake.


seems to be largest in the lowermost layers. Therefore, wefound that our a priori knowledge of the nonlinear responseof sites, assuming the strongest nonlinear effects near the sur-face of the soil column, might not manifest in all the cases.

We also observe velocity anisotropy between east–west andnorth–south directions at GVDA regardless of the layer, aspreviously reported by Coutant (1996) and Bonilla et al.(2002). In these studies, anisotropy at GVDA is observed

Figure 4. Distribution of the data selected for this study, displayed as function of magnitude and distance (left) and magnitude and peakground acceleration (PGA) (right) in the (a) east–west and (b) north–south components.

Figure 5. Velocity profiles computed by seismic interferometry (in gray) for (a) the GVDA site and (b) the WLA site, using east–west (left)and north–south (right) horizontal recordings. The dotted black lines correspond to the original velocity profiles from Stellar (1996) and Cox(2006) for the GVDA and WLA sites, respectively. Solid black lines represent their equivalent averaged velocity profiles derived from theoriginal profile and considering the position of the ground level (GL) sensors.


between GL-22 and GL-220 m and seems to persist in theupper layers (GL0-22 m) despite data dispersion, thus avoid-ing a definitive conclusion. One possible explanation is thatthe fast and slow axis in the deeper layers (weathered graniteand granite) had to do with the preferred fracture orientationrelated to the tectonic stress field. This would likely be lessprevalent in the soil than in the rock, as supported by ourresults and those of Coutant (1996). The origin of the aniso-tropy may also be related to the inhomogenous properties ofthe soil between two sensors, but for classical geophysicaland geotechnical surveys, the differences between east–westand north–south direction reflects different soil properties inboth directions. In Figure 5a, the interferometry profile in thenorth–south direction below GL-50 m shows results centeredon values above the reference profile at 1000 m=s, whereas inthe east–west direction, velocity profiles are centered below1000 m=s. The same observations are possible in the upper-

most layers. According to Coutant (1996), the percentage ofanisotropy can be computed along the GVDA and WLA pro-files as the difference of travel time between both horizontaldirections, expressed in velocity in our case as

a�%� � V�SNS − V�

SEW

V�SNS

: �3�

In Figure 6, anisotropy is plotted as a function of theaverage peak particle velocity v� recorded by the two sensorsbordering each layer and the local shear-wave velocity V�

Scomputed by interferometry in each layer. As proposed byChandra et al. (2014), and discussed later in this study, thisratio provides a proxy for strain and will be used as a nonlinearcriterion. At GVDA, we observe anisotropy variations at depth(Fig. 6a), consistent with the values provided by Coutant(1996), especially for depths below 22 m. Anisotropy occurs

Figure 6. Variation of anisotropy a�%� at different depths, displayed as a function of the v�=V�S ratio at (a) the GVDA site and (b) the

WLA site.


at all depth levels, equal to 4.5% between GL-0 and GL-15 mand to −5:6% between GL-15 and GL-22 m. The strongestvalues are found between GL-22 and GL-50 m, where theyare equal to 10.19%, and they are 6.67% below GL-50 m. AtWLA (Fig. 6b), no strong anisotropy is observed, the maxi-mum value being equal to 1.78% between GL-7.7 andGL-30 m and less than 1% otherwise. Furthermore, regard-less of depth and site, no variation of anisotropy is observedwith respect to v�=V�

S, which suggests that, at least for the setof data used in this study, there is no relationship between theanisotropy and the level of deformation.

The stability of the VS and the good correlation whencompared with VS profiles from other studies (Stellar, 1996;Cox, 2006) support the conclusion that the method allows agood estimation of VS in situ. Therefore, this method can beapplied to detect changes in elastic properties during earth-quake shaking in relation to the level of strain and nonlinearity.

Assessment of Nonlinear Site Behavior

Assuming shear stress τ as the spatial derivative of PGAfollowing τ � PGA × ρ × z, and the displacement-based shearstrain γDB as the derivative of the displacement following:

γDB � dudz

� du=dtdz=dt

� PGVVS

; �4�

PGA versus PGV=VS is considered herein as the representationof the stress–strain relationships that can be used to test the non-linear susceptibility of a site under seismic loading. PGAversusPGV=VS was previously introduced as a stress–strain proxybased on wave propagation by Hill et al. (1993), Rathje et al.(2004), and Cox et al. (2009). Idriss (2011) proposed a stress–strain proxy using the PGV=VS30 ratio, in which VS30 is theaverage shear-wave velocity in the upper 30 m, commonlyused in seismic-code site classification schemes. The effi-ciency of this proxy has been successfully demonstratedby Idriss (2011) on Next Generation Attenuation datasets,De Martin et al. (2012) on KiK-net data, and Chandra et al.(2014) on K-NET and KiK-net data. Because we use an es-timation of V�

S, in this study the peak ground accelerationsand velocities along the borehole are replaced by the averagepeak particle velocity v� and average peak acceleration a�

recorded between each pair of sensors. For all the strain com-putations, we assumed homogeneity of the soil layer betweentwo successive sensors in the vertical array.

To test the validity of the plane shear-wave propagationproxy for strain, v�=V�

S is first compared with the displace-ment-based shear strain γDB calculated by:

γDB � γZZ−ij �duzdz

� �uzj�t� − uzi�t��zj − zi�

; �5�

in which γzz−ij is the vertical deformation between two suc-cessive sensors i and j, uzi and uzj represent horizontal dis-placement at points i and j, respectively, and zi and zj are the

respective depths of sensors i and j. Velocities and displace-ments were calculated by integrating and double integratingacceleration following the procedure proposed by Boore(2005). This method implicitly transforms the signals to havethe same length by applying zero-padding before filteringand integration. To compute the stress and strain in eachlayer, several options can be considered, depending onwhether the maximum strain is assumed to arrive (or not) atthe same time as maximum displacement uzj�t� and uzi�t�and maximum velocity. Hence, in our study, we test two sol-utions for computing shear strain using displacement-basedmethods and three definitions of maximum particle velocity.

The first strain value γDB−1 is computed as the absolutevalue of the average maximum displacement between twosensors zi and zj divided by the distance (zj–zi):

γDB−1 ��max�uzj�t�� max�uzi�t��

�zj − zi�

��: �6�

The second strain value γDB−2 is computed as the maximumrelative displacement as follows:

γDB−2 � max��uzj�t� − uzi�t��

�zj − zi�

��: �7�

Simultaneously, the maximum particle velocities v1, v�, andv3 are computed as the average value of the maximum veloc-ities V in a layer between sensors i and j (equation 8), themaximum absolute value of velocity (equation 9), and the ab-solute average velocity (equation 10) at the time correspond-ing to the maximum strain γDB−2, respectively:

v1 ��max�vi�t�� max�vj�t��

2

�; �8�

v� � max��vi�t� � vj�t�

2

��; �9�

v3 ��vi�t � t�γDB−2�� vj�t � t�γDB−2��

2

��: �10�

Figure 7 displays the comparison between displace-ment-based strain (γDB−1 and γDB−2) and wave-based strainrepresented by the proxy v�=V�

S (Fig. 7a), as well as the dis-tribution of the residual values (Fig. 7b). We observe a slightdispersion of the data around the 1:1 line shown on Figure 7a.The lowest residual values are obtained considering v�=V�

S.Rathje et al. (2004) reported that shear strain computed usingplane shear-wave propagation overpredicts displacement-based shear strain. In our case, as shown in the residual dis-tribution (Fig. 7b), the v�=V�

S strain proxy underpredicts thedisplacement-based strain: the mean and standard deviationvalues of the residues are −4:78 × 10−7 6:34 × 10−6

and −1:66 × 10−7 4:71 × 10−6 at GVDA and WLA,


respectively. These values are very small and v�=V�S may be

therefore considered as the strain proxy in this study. To beconsistent with this definition, we also defined acceleration-based shear stress, a� used for the stress–strain curve as

a� � max��a�t� � aj�t�

2

��: �11�

V�S may change during loading due to the nonlinear response of

the soil layers and the equivalent-linear strain, v�=V�S, along

the borehole might change with the amplitude of the loadingrepresented herein by a�. The nonlinear response can be studiedat various depths along the vertical array, thanks to shallow andintermediate-depth strain (i.e., between two successive sensors).

Finally, the a� versus v�=V�S results are inverted to fit the

classic two-parameters nonlinear hyperbolic model proposedby Seed et al. (1984) and Ishihara (1996):

τ � G0γ

1� γγr

; �12�

in which G0 (or Gmax) is the initial/maximum shear modulusand γr is the reference strain that is the ratio between maxi-mum shear stress τmax and maximum shear modulus Gmax.An equivalent shear modulus degradation can be obtainedusing V�2

S =V�2S0 to represent G=G0. The nonlinear model is

derived from equation (12) by

GG0

� 1

1� γ τ0γ0

: �13�

Finally, a function of the nonlinear representation is fitted toour results, derived from equation (13) as

y � ax1� a

b x; �14�

in which y and x correspond to shear stress τ (i.e., a�) andshear strain (i.e., v�=V�

S), respectively, and a and b are theinitial shear modulus G0 and shear strength a�0 , respectively.In the rest of this article, only the hyperbolic model was usedto fit data, based on physical justification of the geotechnicalmodels and considered valid from low to large strain levels.

Results and Discussion

To evaluate the validity of the v�=V�S strain proxy, we

plot the variation of the proxy with respect to acceleration(i.e., the a�–v�=V�

S curve) for the GVDA (Fig. 8a) and WLA(Fig. 8b) test sites. Figure 9 shows an enlargement of Figure 8to display the results in a small strain area. V�

S; v�, and a�

values are computed in each layer and for all events. In ad-dition, the degradation of local V�

S along the borehole withstrain (v�=V�

S) is studied. In these figures, assuming that a�

represents shear stress, the curve can be considered as equiv-alent to the in situ stress–strain curve. Because of the deg-radation of shear-wave velocity during the earthquake, data

Figure 7. (a) Comparison and (b) residual values of displacement-based strain and wave-based strain proxies at the GVDA and WLA testsites. (left) γDB−1 versus v1=V�

S, (middle) γDB−2 versus v�=V�S, and (right) γDB−2 versus v3=V�

S (see equations 6–10 for definition).


are grouped according to the value of VS30 found in Eurocode8 (2003). The average velocity in each layer V�

S is obtainedby deconvolution and thus accounts for the degradation ofthe S-wave velocity with respect to strain. We also groupthe data in terms of magnitude to introduce the possible con-sideration of source effects, associated, for example, with thefrequency content of the waveforms recorded along the bore-hole, rather than only considering the peak values. Finally,we consider the engineering representation of the stress–strain curve, PGAversus PGV=V�

S30 for all events (where PGAand PGV represent acceleration and velocity at GL-0 m fornorth–south and east–west directions), and V�

S30 is the aver-age velocity over the 30 m depth layer computed from theequivalent linear shear-wave velocity V�

S. Figures 8 and 9show the nonlinear behavior of the GVDA and WLA sites byfitting the hyperbolic model (equation 13) to the data: as forall theoretical nonlinear stress–strain curves, for a certainlevel of strain corresponding to the yield point, the slope ofthe curve decreases up to a horizontal line.

It is not clear at which strain level the nonlinearity starts.Nevertheless, we observed nonlinearity appears at GVDA at2:5 × 10−5 in the east–west direction and at 1 × 10−5 in thenorth–south direction for the 180 < VS < 360 soil class.Few data at large strain are available; however, as shownby Chandra et al. (2014) using K-Net and KiK-net Japanesedata, nonlinearity seems to be directly related to the velocityclass. In fact the equivalent stiffest (VS > 800 m=s) and soft-est (180 < VS < 360 m=s) soils border the nonlinear modelsat GVDA (180 < VS < 360) and WLA (VS < 180 m=s). Dur-ing shaking, the degradation of V�

S can be directly related toacceleration and strain. As a result of the V�

S computed ineach layer and taking into account the shear degradation dur-ing shaking (not only from the elastic VS profile provided byin situ survey), the strain proxy (v�=V�

S) points out the in situnonlinear behavior of the soil: the hyperbolic models for thestiffest soil are more linear compared with the softest soilmodels. If we consider V�

S30 as the proxy and PGV as Idriss(2011) did, we observe the hyperbolic model smooths thestrain between the classes of soils at GVDA and WLA, aver-aging the stiffest and the softest soil hyperbolic models.

At GVDA theV�S30 hyperbolic model fits the data according

to the magnitude level, as expected from the strongest accel-eration. The same observation is made at WLA, for ML <5:5events. No clear dependence on magnitude is seen whenML <5:5 andML <5:5 classes of events are compared, as thestrongest nonlinear effect is not always apparent for the strongestevents. With WLA ML <5:5 data, for instance, several largermagnitude events give smaller values of v�=V�

S for equivalentacceleration with smaller magnitude inside the same class of soil(e.g., the last two circles on the right side of Fig. 8b that cor-respond to the largest strain). Gélis and Bonilla (2012) discussedthe frequency dependence of the nonlinearity. At WLA (Fig. 8b),for the largest magnitude events (ML <5:5, square), a�–v�=V�

S(without soil classification; dashed line) shows greater nonli-nearity compared with lower magnitude event. TheseML <5:5events correspond to distant large events, such as the 4 April

2010 El Mayor earthquake (ML 7:2, distance of 99.93 km)and 15 June 2010 event (ML 5:7, distance of 77.43 km). ThePGA on the site reached only 0:12g and 0:07g for the April2010 and June 2010 events, respectively. Nevertheless, theseevents produced a moderate strain.

The coefficient of correlationR is provided in Figure 8. TheR value ranges from 0 to 1, in which 1 represents a perfect cor-relation between the fit and the data. TheR value is computed as

R ��1 −

Pni�1�yi − yfiti�2Pni�1�yi − �y�2

s; �15�

in which n is the number of data, yi is the data of the dependentvariable, yfiti is the vector values of the fit, and �y is the meanvalue of the dependent variable. For example, R values for PGAversus PGV=VS30 fit are 0.9917 and 0.9804 for GVDA and0.9615 and 0.9614 for WLA in the north–south and east–westdirections, respectively. Despite the lack of large strain values,the high values of R show a good estimation of the nonlinearhyperbolic model using the strain proxy (PGV=VS30 or v�=V�

S)derived from in situ data.

Finally, as shown in Figure 6, we observe (Fig. 10a) differ-ences in the hyperbolic models used in the two horizontal di-rections at GVDA for equivalent deformation, contrary to WLA(Fig. 10b). These differences might suggest anisotropy of soilnonlinearity, as also supported by the V�

S values (Fig. 6a), butthe lack of data at large strain does not allow definitive conclu-sions on this effect. The anisotropy issue may raise some ques-tions about the velocity profile derived from in situ geotechnicalor geophysical surveys, usually performed in one direction andconsidered for nonlinear analysis of the site response. More-over, starting from the elastic velocity given by classical geo-physical and/or geotechnical surveys, the in situ nonlinearresponse of the site may be underestimated because the degra-dation of V�

S with the level of shaking is not taken into account.Finally, in Figure 10c, a simple comparison of the GVDA andWLA sites shows that even for the east–west direction (showingless nonlinearity at the GVDA site), the nonlinear responseseems to start at a lower strain value compared to the WLA site,which must be confirmed in the future with higher strain data.

Because v�=V�S represents strain, one interesting solu-

tion to define the in situ nonlinear response of the site is toderive the shear modulus degradation with respect to thestrain (i.e., the so-called G–γ curve) from the site data. Usingthis method, it is possible to obtain the nonlinear curves atdifferent depths. However, we have no direct value for G andhave only the VS value. Nevertheless, by discerning the re-lation between V�

S andG (equation 1), theG=G0 value can besubstituted by V2

S=V2S0 (equation 13). VS0 is defined as the

average shear-wave velocity corresponding to the smallestdeformation for which a linear response is expected, thatis, between 5 × 10−8 and 5 × 10−7 of strain. The VS degra-dation analysis is carried out at different depths, and the datais inverted to fit the model according to equation (14).

Figures 11 and 12 display the V2S=V

2S0 variation accord-

ing to the v�=V�S proxy computed in the (a) east–west and


(b) north–south directions for the GVDA and WLA test sites,respectively. The smallest deformation shows the largest dis-crepancy of data, but overall the figures show rather limitedscattering. As expected, the uppermost layers exhibit strongernonlinear behavior than the deeper layers. In the uppermost

layers, we found that nonlinear behavior starts at a verylow level of deformation (∼1 × 10−5) and corresponds to thecyclic γtl threshold, becoming more significant above the γtvthreshold (∼1 × 10−4). For example, G degradation starts at alevel of strain equal to 1 × 10−6 and 2 × 10−6 at GVDA for the

Figure 8. Equivalent stress (a�) strain (v�=V�S) results at (a) GVDA and (b) WLA test sites in the (left) east–west and (right) north–south

directions, color-ranked according to the Eurocode 8 (2003) VS30-based site classification. The type of symbol represents the v�=V�S proxy

computed usingML <5:5 (circle) orML <5:5 (square) events. The size of the symbol is proportional to the rank of magnitude. The trianglescorrespond to the v�=V�

S30 strain proxy. Solid lines represent the hyperbolic models (equation 13) fitted to data by VS rank. The dashed line atWLA is the hyperbolic model for ML <5:5 data regardless of VS due to the small number of events. The x- and y-axis scales for GVDA aredifferent in the north and east directions.


north–south and east–west directions between GL-0 andGL-15 m and at 1 × 10−5 at WLA in both directions. Compar-ing the different depths at each site, we observe an increase inthe strain threshold for the nonlinear response (i.e., shift of thefitted model to the largest deformation), in accordance with thefact that the lowermost layers are less nonlinear. As discussedpreviously, the degradation of G is much more sensitive to thestrongest PGA (circles) than to the strongest magnitudes (size

of the symbols), as systematically observed at the WLA site,confirming that magnitude is not sufficient as a parameter toreflect the possibility of an event to generate nonlinearity.This is understandable because a large magnitude eventcould generate a low intensity level due to the distance. Con-versely, a small magnitude event could produce a large in-tensity value due to the proximity between the source andthe site. Even though nonlinearity is less present at greater

Figure 9. Enlarged view of Figure 8 for strain level up to 2 × 10−5 and 2:7 × 10−4, for (a) GVDA and (b) WLA, respectively (differentscale). For legends, see Figure 8.


depths, nonlinear response is also observed: for example, at3 × 10−6 of strain between GL-15 and GL-22 m at GVDA orat 1 × 10−5 of strain between GL-7.7 and GL-30 m at WLA.Although the data are not sufficient, we observe a slight non-linear trend in the fitted curve below 30 m, suggesting thatnonlinearity may occur at depth, even for moderate deforma-tions generated by moderate earthquakes.

Stokoe and Darandeli (1998) performed laboratory res-onant column and torsional shear tests on samples extractedat GL-3.5, GL-6.5, GL-27, and GL-41.3 m at the GVDA testsite and provided the G–γ curve. The laboratory tests arecompared in Table 1 with the degradation values found usingvertical arrays in this study. Furthermore, the curves at differ-ent depths are given for comparison in Figures 11 and 12,with the average strain computed for different ranks of strain(average value standard deviation in red).

For larger deformations (1 × 10−4 to 1 × 10−5), our resultsmatch very well with laboratory measurements, whatever thedepth. Scattering of results may be due to the smaller numberof events having a statistical representation of strain and degra-dation or to the natural variability of the nonlinear response fordifferent types of seismic loading. Because the laboratory testswere performed considering only cyclic loading, we can alsoassume that the site’s nonlinear response may depend onground-motion characteristics, producing real in situ uncertain-ties concerning the dynamic response and not included in labo-ratory-induced curves. This also applies to the consideration ofanisotropy, which is not provided by in situ classical surveys.

Cox (2006) performed in situ dynamic loading tests atthree different locations of the WLA test site. In this study, wecompare our results with his results at test location C (Cox,2006), for which more information is available. Two dynamicloading experiments with multiple loading stages were carriedout for his study using T-Rex apparatus to apply dynamic shearload to the surface array. The comparison of the results isshown in Figure 12 only at the first 7.7 m depth measurementbecause noninvasive methods are available for the uppermostlayers. Our results for the WLA test site match the Cox (2006)results very well for the shallowest layer. At the WLA test site,

the degradation modulus may be the result of both the non-linear behavior of the site and the pore water pressure gen-erated (Cox, 2006), as indeed the largest event at WLA hasexcess pore pressure generation (Ru), with the largest havinga 60% Ru value (Steidl et al., 2014). In this study, however,pore water pressure generation is not discussed. It is alsoimportant to note that nonlinearity does not occur only atshallow depth, but also in the lowermost layers, at strain of1 × 10−4. Therefore, generation of nonlinearity is not restrictedto levels only near the surface. However, this is rarely investi-gated due to the difficulty of extracting samples at greater depthsand of reproducing the in situ stress level in the laboratory.

Finally, Figure 13 shows a comparison of the resultsfrom the two test sites. Because the site characteristics aredifferent, we use the strain parameter PGV=V�

S30 to comparethe behavior between the two sites. Shear modulus degrada-tion is represented by V�

S30=V�S30max, in which V�

S30 corre-sponds to the average particle velocity computed using v�

between GL-0 and GL-30 m and V�S30max corresponds to the

average V�S30 for the smallest deformation at which a linear

response is expected (i.e., between 5 × 10−8 and 5 × 10−7 ofstrain). Despite the fact that liquefaction is expected at WLA,with the data collected at GVDA so far, nonlinear behaviornonetheless appears to start at a lower strain level than atWLA. Because GVDA has not suffered significant deforma-tion, and has had many fewer events above 1 × 10−5, this ispreventing us from being able to compare the results for thehighest levels of deformation. Once again, we observe thatboth v�=V�

S and PGV=VS30 are reliable proxies for predictingnonlinearity, the degradation of the equivalent shear modulusbeing related to the increased values of the proxy.

In Figure 13, we also plot the volumetric strain γtv �1 × 10−4 (Hardin andBlack, 1968;Drnevich andRichart, 1970;Dobry and Ladd, 1980) and linear strain γtl � 1 × 10−6 (Vu-cetic, 1994; Johnson and Jia, 2005). The nonlinear responseclose to 1 × 10−6 and corresponding to the cyclic strain is lessvisible compared to those in Figures 11 and 12, because cor-responding PGV (rather than v�) and V�

S30 (rather than inter-mediate depth V�

S) smooth the results and do not represent the

Figure 10. PGA–PGV=V�S30 data for (a) GVDA, (b) WLA, and (c) comparison between both sites. The solid and dashed lines are the

hyperbolic model fitted to the data for the east (circle) and north (triangle) direction data, respectively.


actual stress–strain relationship. Nevertheless, above 1 × 10−4,the nonlinear response is clearly observed and estimated bythe PGV=VS30 proxy, allowing us to assume an efficientprediction of the nonlinear response from the ratio betweenPGV and VS30.

Conclusion

The near-surface geology effects of the GVDA and theWLA, both situated in the active SAF system, are analyzed for

nonlinearity assessment using in situ data. We monitor the

Figure 11. Equivalent shear modulus degradation curve for different depths at the GVDA test site (a) east–west and (b) north–southdirections. The solid black line represents the fitted-curve of our data, and the gray lines represent (when available) the results from laboratorytests performed by Stokoe and Darandeli (1998) on samples taken at different depths. The red circles indicate the mean values of the mea-sured data, as well as the sigma for different bands of strain, that is, <1 × 10−8, 1 × 10−8–5 × 10−8, 5 × 10−8–1 × 10−7, 1 × 10−7–5 × 10−7,5 × 10−7–1 × 10−7, 1 × 10−7–5 × 10−6, 5 × 10−6–1 × 10−5, and 1 × 10−5–5 × 10−5.


changes in the in-situ shear-wave velocity, measured usingthe seismic interferometry by deconvolution technique.

We are able to estimate the velocity profile and to mon-itor the nonlinear response of the sites with respect to thelevel of shaking. In our case, we consider the loading usingthe strain proxy v�=V�

S, reproducing in each layer the shearstrain accounting for the degradation of shear-wave velocity.

At the GVDA test site, slight anisotropy is clearly demon-strated between east and north components, in agreementwith previous studies. The anisotropy at the WLA test siteis negligible, and anisotropy is not influenced by the defor-mation (shear strain) level at either site.

We show that the v�=V�S ratio (as well as PGV=VS30) is a

deformation proxy. In the first case, deformation is accurate

Figure 12. Equivalent shear modulus degradation curve for different depths at the WLA test site: (a) east–west and (b) north–south directions. The solid black line represents the fitted curve of our data, and the gray-filled circles represent the results from Cox(2006). The red circles indicate the mean value of the measured data, as well as the sigma for different bands of strain, that is,<1 × 10−8, 1 × 10−8–5 × 10−8, 5 × 10−8–1 × 10−7, 1 × 10−7–5 × 10−7, 5 × 10−7–1 × 10−7, 1 × 10−7–5 × 10−6, 5 × 10−6–1 × 10−5,1 × 10−5–5 × 10−5, 5 × 10−5–1 × 10−4, 1 × 10−4–5 × 10−4, 5 × 10−4–1 × 10−3.


enough to observe in the uppermost layers the cyclic deforma-tion due to the nonlinear elastic behavior of the soil at valuesclose to 1 × 10−6, as reported by Vucetic (1994) and Johnsonand Jia (2005). The a� versus v�=V�

S curve represents theproxy evolution of the stress–strain relationship of the soil col-umn under different levels of excitation. For the lowest S-wavevelocities (softer soil), typical nonlinearity trends are observedcompared with the higher velocity group (stiffer soil). The mag-nitude and the PGA are shown to be complementary for pre-dicting nonlinearity, and source effects of the ground motion(such as the frequency of the seismic energy) may also influ-ence the nonlinear behavior of the site. By comparing a� versusv�=V�

S with PGA–PGV=VS30, we show that although the useof VS30 is convenient in practice, the results are more dispersivecompared with the use of V�

S. Nevertheless, in both cases theinverted classic hyperbolic model offers a good fit with the dataand, with further study, could be used for nonlinear prediction.

This study has shown a possible solution for in situ estima-tion of the shear modulus degradation curve of each layer locatedat different depths. The results are comparablewith the laboratorymeasurements obtained previously when available. Nonlinearbehavior starts at a low level of deformation (∼1 × 10−6) insidethe soil column and becomesmore significant at a deformation ofaround ∼1 × 10−4. The data is also inverted with the classic hy-perbolic model that fits the data with moderate scattering usingVS30 and/or V�

S. We demonstrated that despite the lack of largestrain values, the high values of the correlation coefficients Rconfirm the good prediction of the nonlinear hyperbolic modelusing the strain proxy (PGV=VS30 or v�=V�

S) derived from in situdata. This type of analysis might finally be integrated into theprediction of the groundmotion, including nonlinearity. Analysisof the efficiency of our methodwith other classical methods (e.g.,based on f0, mode shape variation, and amplification reduction)might be performed in further studies for comparison.

Table 1Comparison of Shear Modulus G Reduction Values at GVDA

Stokoe and Darandeli (1998) In Situ (This Study)

Depth (m) 1 − G=G0�%�* Shear Strain (γ) Direction Depth (m) 1 − V�2S =V�2

S0�%�†

3.5 28 1 × 10−4 East 0–15 286.5 15 3:3 × 10−5 North 17

27 9 2 × 10−5 East 22–50 1141.3 727 1 9 × 10−6 North 22–50 841.3 1

The table compares the G reduction values between in situ assessment (our study) and laboratory tests from Stokoe andDarendeli (1998) at the GVDA test site for equivalent shear-strain values provided by laboratory tests or by the strain proxy.(GVDA, Garner Valley Downhole Array)*Shear modulus degradation, 1 −G=G0 (G0, shear modulus elastic).†1 − V�2

S =V�2S0 , equivalent shear modulus degradation; V�

S , equivalent linear shear-wave velocity; and V�S0, equivalent

linear shear-wave velocity elastic.

Figure 13. Comparison of equivalent shear modulus degradation curves between the GVDA (blank) and WLA (filled) test sites. Thecircles represent the east direction data, and the triangles represent the north direction data. The solid (east direction) and dashed (northdirection) lines represent the fitted hyperbolic model from equation (4) for GVDA (black) and WLA (gray) test sites. The dotted-dashed linesrepresent the γtl of 1 × 10−6 and γtv of 1 × 10−4.


Data and Resources

The Garner Valley and Wildlife data used in this studywere collected as part of the Network for Earthquake Engi-neering Simulation at University of California, Santa Barbara(NEES@UCSB). Data can be obtained from the NEES@UCSB website at http://nees.ucsb.edu/ (last accessed March2014). Figure 1 is taken from https://www.google.com/maps/(last accessed February 2014).

Acknowledgments

The authors wish to acknowledge the California Department of Fish andWildlife, which provides access to the monitoring site at the Wildlife Liquefac-tion Array, and the Lake Hemet municipal water district, which provides accessto the monitoring site at Garner Valley. The Network for Earthquake Engineer-ing Simulation at University of California, Santa Barbara (NEES@UCSB) fieldsite facility received support from the George E. Brown, Jr., Network for Earth-quake Engineering Simulation program through CMS-0217421 and CMMI-0927178. The authors are grateful to Stefano Parolai, Marco Mucciarelli, andan anonymous reviewer for their comments that helped to improve this work.The authors would also like to gratefully thank the NEES@UCSB and EarthResearch Institute (UCSB) team, in particular Paul Hegarty and FrancescoCivilini, for all the help and discussions during the data collection and process-ing. We thank the Ecole Doctorale Terre, Univers, Environnement (ED TUE)Université de Grenoble for the travel grant to collect the necessary data. Wealso thank IFSTTAR, France, for funding this research.

References

Archuleta, R. J., S. H. Seale, P. V. Sangas, L. M. Baker, and S. T. Swain(1992). Garner Valley Downhole Array of accelerometers: Instrumen-tation and preliminary data analysis, Bull. Seismol. Soc. Am. 82, no. 4,1592–1621.

Assimaki, D., J. H. Steidl, and C. L. Peng (2006). Attenuation and velocitystructure for site response analyses via downhole seismograminversion, Pure Appl. Geophys. 163, 81–118.

Beresnev, I. A., and K.-L. Wen (1996). Nonlinear soil response—A reality?Bull. Seismol. Soc. Am. 86, no. 6, 1964–1978.

Beresnev, I. A., G. M. Atkinson, P. A. Johnson, and E. H. Field (1998).Stochastic finite-fault modeling of ground motions from the 1994Northridge, California, earthquake. II. Widespread nonlinear responseat soil sites, Bull. Seismol. Soc. Am. 88, no. 6, 1402–1410.

Bonilla, L. F., R. J. Archuleta, and D. Lavallée (2005). Hysteretic anddilatant behavior of cohesionless soils and their effects on nonlinearsite response: Field data observations and modeling, Bull. Seismol.Soc. Am. 95, no. 6, 2373–2395.

Bonilla, L. F., F. Cotton, and R. J. Archuleta (2003). Quelques renseignementssur les effets de site non-linéaires en utilisant des données de forage:La base de mouvements forts Kiknet au Japon, in Proc. of the 6èmeColloque National AFPS, Palaiseau, France, 1–3 July 2003.

Bonilla, L. F., C. Gélis, and J. Regnier (2011). The challenge of nonlinear siteresponse: Field data observations and numerical simulations, Proc. ofthe ESG4 Conference @ UCSB—4th IASPEI/IAEE InternationalSymposium, Santa Barbara, California, 23–26 August 2011.

Bonilla, L. F., J. H. Steidl, J. C. Gariel, and R. J. Archuleta (2002). Boreholeresponse study at the Garney Valley Downhole Array (GVDA),southern California, Bull. Seismol. Soc. Am. 92, no. 8, 3165–3179.

Boore, D. (2005). On pads and filters: Processing strong-motion data, Bull.Seismol. Soc. Am. 95, no. 82, 745–750.

Campillo, M, J. C. Gariel, K. Aki, and F. J. Sánchez-Sesma (1989).Destructive strong ground motion in Mexico City: Source, path,and site effects during great 1985 Michoacán earthquake, Bull.Seismol. Soc. Am. 79, 1718–1735.

Chandra, J., P. Guéguen, and L.-F. Bonilla (2014). Application of PGV/VS

proxy to assess nonlinear soil response–from dynamic centrifuge test-ing to Japanese K-NET and KiK-net data, Proceedings of the 2ndEuropean Conference on Earthquake Engineering and Seismology,Istanbul, Turkey, 24–29 August 2014.

Chávez-Garcia, F. J., and P.-Y. Bard (1994). Site effects in Mexico City eightyears after the September 1985 Michoacan earthquakes, Soil Dynam.Earthq. Eng. 13, 229–247.

Chin, B., and K. Aki (1991). Simultaneous study of the source, path, and siteeffects on strong ground motion during the 1989 Loma Prieta earth-quake: A preliminary result on pervasive nonlinear site effects, Bull.Seismol. Soc. Am. 81, 1859–1884.

Clayton, R. W., and R. A. Wiggins (1976). Source shape estimation anddeconvolution of teleseismic bodywaves, Geophys. J. Roy. Astron.Soc. 47, 151–177.

Coutant, O. (1996). Observation of shallow anisotropy on local earthquakerecords at the Garner Valley, southern California, Downhole Array,Bull. Seismol. Soc. Am. 86, no. 2, 477–488.

Cox, B. R. (2006). Development of a direct test method for dynamicallyassessing the liquefaction resistance of soils in situ, Ph.D. Disserta-tion, The University of Texas at Austin.

Cox, B. R., K. H. Stokoe, and E. M. Rathje (2009). An in-situ test method forevaluating the coupled pore pressure generation and nonlinear shearmodulus behavior of liquefiable soils, ASTM Geotech. Test. J. 32,no. 1, 11–21.

De Martin, F., H. Kawase, and F. Bonilla (2012). Inversion of equivalentlinear soil parameters during the 2011 Tohoku earthquake, Japan,JST/ANR Joint Research ONAMAZU Project–International Sympo-sium on Engineering Lessons Learned from the Giant Earthquake,Kenchiku-kaikan, Tokyo, Japan, 1–4 March 2012.

Dobry, R. (2013). Radiation damping in the context of one-dimensional wavepropagation: A teaching perspective, Soil Dynam. Earthq. Eng. 47, 51–61.

Dobry, R., and R. Ladd (1980). Discussion of “Soil liquefaction andcyclic mobility evaluation for level ground during earthquakes,” byH. B. Seed and “Liquefaction potential: Science versus practice,”by R. B. Peck, J. Geotech. Eng. Div. 106, no. 6, 720–724.

Drnevich, V. P., and F. E. Richart Jr. (1970). Dynamic prestraining of drysand, J. Soil Mech. Found. Div. 96, no. 2, 453–469.

Eurocode 8 (2003). Design of structures for earthquake resistance—Part 1:General rules, seismic actions and rules for buildings, European Commit-tee for Standardization (CEN), available at https://www.cen.eu (lastaccessed January 2015).

Field, E. H., P. A. Johnson, I. Beresnev, and Y. Zeng (1997). Nonlinearground-motion amplification by sediments during the 1994 Northridgeearthquake, Nature 390, 599–602.

Gariel, J. C., B. Mohammadioun, and G. Mohammadioun (1993). L’experimen-tation sismique de Garner Valley: Resultats Preliminaires, Proc. of the 3rdColloque National AFPS, Saint-Remy-les-Chevreuse, France, ES18–ES27.

Gélis, C., and F. Bonilla (2012). 2D P-SV numerical study of soil-source in-teraction in a nonlinear basin, Geophys. J. Int. 191, no. 3, 1374–1390.

Guéguen, P., M. Langlais, P. Foray, C. Rousseau, and J. Maury (2011). Anatural seismic isolating system: The buried mangrove effects, Bull.Seismol. Soc. Am. 101, no. 3, 1073–1080, doi: 10.1785/0120100129.

Hardin, B. O., and W. L. Black (1968). Vibration modulus of normallyconsolidated clay, J. Soil Mech. Found. Div. 94, no. 2, 353–369.

Hartzell, S. (1998). Variability in nonlinear sediment response during the1994 Northridge, California, earthquake, Bull. Seismol. Soc. Am.88, no. 6, 1426–1437.

Haskell, N. A. (1953). The dispersion of surface waves on multilayeredmedia, Bull. Seismol. Soc. Am. 43, no. 1, 17–34.

Hill, D. P., P. A. Reasenberg, A. Michael, W. J. Arabaz, G. Beroza, D.Brumbaugh, J. N. Brune, R. Castro, S. Davis, D. dePolo, et al.(1993). Seismicity remotely triggered by the magnitude 7.3 Landers,California, earthquake, Science 260, 1617–1623.

Idriss, I. M. (2011). Use of VS30 to represent local site condition, 4th IASPEI/IAEE International Symposium: Effects of Source Geology on SeismicMotion, University of Santa Barbara California, 23–26 August 2011.


http://nees.ucsb.edu/



https://www.google.com/maps/

https://www.cen.eu

https://www.cen.eu

https://www.cen.eu

http://dx.doi.org/10.1785/0120100129

Ishihara, K. (1996). Soil Behaviour in Earthquake Geotechnics, OxfordEngineering Science Series, Oxford University Press, Oxford, UnitedKingdom.

Johnson, P. A., and X. P. Jia (2005). Nonlinear dynamics, granular mediaand dynamic earthquake triggering, Nature 437, 871–874.

Lawrence, Z., P. Bodin, C. A. Langston, F. Pearce, J. Gomberg,P. A. Johnson, F.-Y. Menq, and T. Brackman (2008). Induced dynamicnonlinear ground response at Garner Valley, California, Bull. Seismol.Soc. Am. 98, no. 3, 1412–1428.

Mehta, K., R. Snieder, and V. Graizer (2007). Downhole receiver Function:A case study, Bull. Seismol. Soc. Am. 97, no. 5, 1396–1403.

Nakata, N., and R. Snieder (2012). Estimating near-surface wave velocitiesin Japan by applying seismic interferometry to KiK-net data,J. Geophys. Res. 117, no. B01308, 1–13.

Ohmachi, T., S. Inoue, K.-I. Mizuno, and M. Yamada (2011). Estimatedcause of extreme acceleration records at the KiK-net IWTH25 stationduring the 2008 Iwate-Miyage Nairiku earthquake, Japan, J. Jpn.Assoc. Earthq. Eng. 11, no. 1, 1_32–1_47.

Pech, A., F. J. Sánchez-Sesma, R. Snieder, F. Ignicio-Caballero,A. Rodríguez-Castellanos, and J. C. Ortíz-Alemán (2012). Estimateof shear wave velocity, and its time-lapse change, from seismic datarecorded at the SMNH01 station of KiK-net using seismic interferom-etry, Soil Dynam. Earthq. Eng. 39, 128–137.

Pecker, A. (1995). Validation of small strain properties from recorded weakseismic motions, Soil Dynam. Earthq. Eng. 14, 399–408.

Pecker, A., and B. Mohammadioun (1991). Downhole instrumentation forthe evaluation of non-linear soil response on ground surface motion,11th SmiRT (Structural Mechanics in Reactor Technology)Conference, Tokyo, Japan, 18–23 August 1991, 33–38.

Rathje, E. M., W.-J. Chang, K. H. Stokoe, and B. R. Cox (2004). Evaluationof ground strain from in situ dynamic response, Proceeding of the 13thWorld Conference on Earthquake Engineering, Vancouver, British Co-lumbia, Canada, 1–6 August 2004.

Rubinstein, J. L, and G. C. Beroza (2004). Evidence for widespread non-linear strong ground motion in the Mw 6.9 Loma Prieta earthquake,Bull. Seismol. Soc. Am. 94, no. 5, 1595–1608.

Rubinstein, J. L, and G. C. Beroza (2005). Depth constraints on nonlinearstrong ground motion from the 2004 Parkfield earthquake, Geophys.Res. Lett. 32, L14313, doi: 10.1029/2005GL023189.

Sawazaki, K, H. Sato, H. Nakahara, and T. Nishimura (2009). Time-lapsechanges of seismic velocity in the shallow ground caused by strongground motion shock of the 2000 Western-Tottori earthquake, Japan,as revealed from coda deconvolution analysis, Bull. Seismol. Soc. Am.99, no. 1, 352–366.

Seed, H. B., R. T. Wong, I. M. Idriss, and T. Tokimatsu (1984). Moduli anddamping factors for dynamic analyses of cohesionless soils, Earth-quake Engineering Research Center, Report No. UCB/EERC-84/14,37 pp.

Snieder, R., and E. Şafak (2006). Extracting the building response usingseismic interferometry: Theory and application to the Milikan Libraryin Pasadena, California, Bull. Seismol. Soc. Am. 96, no. 2, 586–598.

Steidl, J. H., and S. Seale (2010). Observations and analysis of ground motionand pore pressure at the NEES instrumented geotechnical field sites,Proc. of the 5th International Conference on Recent Advances in Geo-technical Earthquake Engineering and Soil Dynamics, San Diego, Cal-ifornia, 24–29 May 2010, Paper Number 133b, ISBN: 887009-15-9.

Steidl, J. H., R. J. Archuleta, A. G. Tumarkin, and L.-F. Bonilla (1998). Ob-servations and modeling of ground motion and pore pressure at theGarner Valley, California, test site, in The Effects of Surface Geologyon Seismic Motion, K. Irikura, K. Kudo, H. Okada, and T. Sasatani(Editors), A. A. Balkema, Rotterdam, The Netherlands, 225–232.

Steidl, J. H., F. Civilini, and S. Seale (2014). What have we learned after adecade of experiments and monitoring at the NEES@UCSB permanentlyinstrumented field sites? Proc. of the 10th U.S. National Conference onEarthquake Engineering, Anchorage, Alaska, 21–25 July 2014.

Steidl, J. H., R. Gee, S. Seale, and P. Hegarty (2012). Recent enhancementsto the NEES@UCSB permanently instrumented field sites, Proc. of the

15th World Conference on Earthquake Engineering, Lisboa, Portugal,24–28 September 2012.

Steidl, J. H., A. G. Tumarkin, and R. J. Archuleta (1996). What is a referencesite? Bull. Seismol. Soc. Am. 86, no. 6, 1733–1748.

Stellar, R. (1996). New borehole geophysical results at GVDA, NEES@UCSBInternal Report, 20 pp., available at http://nees.ucsb.edu/sites/eot‑dev.nees.ucsb.edu/files/facilities/docs/GVDA‑Geotech‑Stellar1996.pdf(last accessed January 2015).

Stokoe, K. H., and M. B. Darendeli (1998). Laboratory evaluation of thedynamic properties of intact soil specimens: Garner Valley, California,Geotechnical Engineering Report GR98-3, The University of Texas atAustin.

Theodulidis, N., P.-Y. Bard, R. Archuleta, andM. Bouchon (1996). Horizontal-to-vertical spectral ratio and geological conditions: The case of GarnerValley Downhole Array in southern California, Bull. Seismol. Soc. Am.86, no. 2, 306–319.

Todorovska, M. I., and M. T. Rahmani (2013). System identification of build-ings by wave travel time analysis and layered shear beammodels—Spatialresolution and accuracy, Struct. Contr. Health Monit. 20, no. 5, 686–702.

Tsuda, K., and J. H. Steidl (2006). Nonlinear site response from the 2003 and2005 Miyagi-Oki earthquakes, Earth Planets Space 58, 1593–1597.

Vucetic, M. (1994). Cyclic threshold shear strains in soils, J. Geotech. Eng.120, 2208–2228.

Wapenaar, K., D. Draganov, R. Snieder, X. Campman, and A. Verdel (2010).Tutorial on seismic interferometry: Part 1–Basic principles and appli-cations, Geophysics 75, no. 5, 75A195–75A209.

Wu, C., Z. Peng, and D. Assimaki (2009). Temporal changes in site responseassociated with the strong ground motion of the 2004 Mw 6.6 Mid-Niigata earthquake sequences in Japan, Bull. Seismol. Soc. Am. 99,no. 6, 3487–3495.

Youd, T. L. (1972). Compaction of sands by repeated shear straining, J. SoilMech. Found. Eng. Div. 98, no. 7, 709–725.

Youd, T. L., H. A. J. Bartholomew, and J. S. Proctor (2004). Geotechnical logsand data from permanently instrumented fields sites: Garner ValleyDownhole Array (GVDA) and Wildlife Liquefaction Array (WLA),NEES@UCSB internal report, 53 pp., available at http://nees.ucsb.edu/sites/eot‑dev.nees.ucsb.edu/files/facilities/docs/geotech‑data‑report.pdf (lastaccessed January 2015).

Zeghal, M., and A. W. Elgamal (1994). Analysis of site liquefaction usingearthquake records, J. Geotech. Eng. 120, no. 6, 996–1017.

Institut des Sciences de la TerreUniversité Grenoble Alpes/CNRS/IFSTTAR38041 Grenoble CEDEX 9, Francejohanes.chandra@ujf‑grenoble.frphilippe.gueguen@ujf‑grenoble.fr

(J.C., P.G.)

Earth Research Institute (ERI)University of CaliforniaSanta Barbara, California [email protected]

(J.H.S.)

Université Paris EstInstitut Français des Sciences et Technologies des Transportsde l’Aménagement et des RéseauxParis 77447, [email protected]

(L.F.B.)

Manuscript received 10 July 2014;Published Online 24 February 2015


http://dx.doi.org/10.1029/2005GL023189

http://nees.ucsb.edu/sites/eot-dev.nees.ucsb.edu/files/facilities/docs/GVDA-Geotech-Stellar1996.pdf







http://nees.ucsb.edu/sites/eot-dev.nees.ucsb.edu/files/facilities/docs/geotech-data-report.pdf








Documents

2015_Chandra_In Situ Assessment of the G-γ Curve for Characterizing the Nonlinear Response of Soil_Application to the Garner Valley Downhole Array and the Wildlife Liquefaction Array