Probabilistic Evaluation of Field Liquefaction Potential Using Relative State Parameter Index (ξ R )

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1 Missoui Univesity of Science nd Technology Schols' Mine Intentionl Confeences on ecent Advnces in Geotechnicl Ethquke Engineeing nd Soil Dynmics Fifth Intentionl Confeence on ecent Advnces in Geotechnicl Ethquke Engineeing nd Soil Dynmics My 24th - My 29th obbilistic Evlution of Field iquefction otentil Using eltive Stte mete Index (ξ ) Yse Jfin Semnn Univesity, In Mohmmd H. Bzi In Univesity of Science nd Technology, In Aliez Sdeghi In Univesity of Science nd Technology, In ouzbeh Vkili In Univesity of Science nd Technology, In Follow this nd dditionl woks t: t of the Geotechnicl Engineeing Commons ecommended Cittion Jfin, Yse; Bzi, Mohmmd H.; Sdeghi, Aliez; nd Vkili, ouzbeh, "obbilistic Evlution of Field iquefction otentil Using eltive Stte mete Index (ξ )" (200). Intentionl Confeences on ecent Advnces in Geotechnicl Ethquke Engineeing nd Soil Dynmics This Aticle - Confeence poceedings is bought to you fo fee nd open ccess by Schols' Mine. It hs been ccepted fo inclusion in Intentionl Confeences on ecent Advnces in Geotechnicl Ethquke Engineeing nd Soil Dynmics by n uthoized dministto of Schols' Mine. This wok is potected by U. S. Copyight w. Unuthoized use including epoduction fo edistibution uies the pemission of the copyight holde. Fo moe infomtion, plese contct scholsmine@mst.edu.

2 OBABIISTIC EVAUATION OF FIED IQUEFACTION OTENTIA USING EATIVE STATE AAMETE INDEX ( ) Yse Jfin Semnn Univesity Semnn, In Mohmmd H. Bzi In Univesity of Science nd Technology, Tehn, In Aliez Sdeghi In Univesity of Science nd Technology, Tehn, In ouzbeh Vkili In Univesity of Science nd Technology, Tehn, In ABSTACT Fom the eliest studies of soil behvio unde cyclic loding, it is found tht the cyclic stess uied fo liquefction onset is stongly ffected by the eltive density ( D ) nd initil effective ovebuden pessue of the soil. In this ppe, eltive stte pmete index ( ), which ccounts fo both eltive density nd effective stess, is used to evlute the likelihood of liquefction initition in field condition. Two compehensive dtbses of field cse histoies bsed on ST nd CT e incopoted in the nlyses. ogistic egession method is employed to deive pobbilistic expession tht yields the pobbility of liquefction initition in tems of. The most dvntge of this expession is its consistency with both field ST nd CT dt. In ddition, eltive stte pmete index hs been evolved fom diltncy concept which hs esonble consistency with liquefction phenomenon. The boundy cuve tht obtins 20% likelihood of liquefction initition is found to be the most consevtive boundy nd is ecommended s deteministic -bsed liquefction citeion. Finlly, eltionship is poposed to coelte liquefction pobbility to the fcto of sfety ginst liquefction tiggeing. INTODUCTION Ethquke is one of the most ctstophic phenomen tht could hve diect nd indiect effects on stuctues. iquefction cn esulted in get impct on stuctue s foundtion nd led to consideble settlements. Thus, evluting liquefction potentil nd consideing the liquefction effects in design pocedue is cucil. Use of field nd lbotoy tests fo the ssessment of liquefction is pevlent but cyclic lbotoy testing on gnul mteils include some limittion such s smple distubnce. Accodingly, employing simplified method tht ws oiginlly poposed by Seed nd Idiss (97) bsed on empiicl evlution of field obsevtions hs been stte of the pctice in liquefction evlution. This pocedue tht ws fuently updted by eseches (e.g. Youd et l. 200; Cetin et l. 2004; nd Moss et l. 2006) is the most ccepted ppoch mong geotechnicl enginees. Common field tests fo liquefction evlution could be divided into fou mjo ctegoies including Stndd enettion Test (ST), Cone enettion Test (CT), She Wve Velocity (Vs) nd Becke enettion Test. Among these site chcteizing techniques, ST nd CT-bsed coeltions e the most popul due to thei simplicity nd lso the lge numbe of cse histoies. These methods tht hve been poposed nd modified by vious eseches e bsed on the eltion between liquefction esistnce of the soil (i.e. penettion esistnce) nd seismic demnd (i.e. epesenttive of ethquke loding ction). Although eliest ST nd CT bsed coeltions of liquefction ssessment pe No. 4.37

3 wee deteministic, moe ecent studies hve include pobbility in thei nlyses. As n ccepted deteministic ppoch, Youd et l. (200) s deteministic citeion hs been ecommended in diffeent codes nd guidelines. Although, the pobbilistic ppoches e still out of the minstem of stndd pctice, developing of this pocedue in the ecent yes is ppeling. Use of pobbilistic concept fo the ssessment of liquefction fistly ecommended by io et l. (988) fo ST bsed dt though logistic egession model. Using lge dtbse, Youd nd Nobel (977) nd Topk et l. (999) employed the sme method nd lso consideed the effect of fines content to popose othe eltions. The sme logistic egession methodology ws cied out by i et l. (990), Topk et l. (999), Jung et l. (2002), nd i et l. (2006) fo developing CT bsed pobbilistic models. Futhemoe, some othe eseches such s Cetin et l. (2004) nd Moss et l. (2006) implemented highe-ode pobbilistic tool (Byesin Updting) nd developed new coeltions espectively fo ST nd CT. Although they indicted tht the new ppoch getly educe ovell uncetinty, it possesses its own disdvntges nd limittions, like ny nlyticl nd sttisticl method. A pobbilistic model cn be ffected by pobbilistic egession method, numbe nd qulity of dt, nd lso method of intepettion (i.e. choice of epesenttive vible fo egession). In the pesent ppe, eltive stte pmete index ( ) is employed in plce of ST nd CT dt in ode to chieve lge dtbse. eltive stte pmete index ( ) tht ws gdully intoduced by Been nd Jeffies (985), Bolton (986), nd Boulnge (2003) hs been found to be useful fo this pupose becuse this pmete cn be obtined using the existing coeltions between soil eltive density nd stndd o cone penettion esistnces. Theefoe, use of this pmete impoves the sufficiency condition of the dtbse nd cn obtin moe genelized pobbilistic model. On the othe hnd, consides the effect of eltive density nd initil ovebuden stess t the sme time becuse it ws deived fom diltncy concept tht hs close consistency with liquefction phenomenon. This cn be n impotnt dvntge of bsed pobbilistic model ove the peviously poposed pobbilistic ST nd CT bsed models tht conside initil ovebuden pessue sttisticlly. Two compehensive nd high qulity field dtbses of ST nd CT bsed liquefction cse histoies epoted by Cetin et l. (2004) nd Moss et l. (2006) hve been used to deive the -bsed pobbilistic model. ogistic egession method hs been employed becuse of its fuent usge in field liquefction ssessment nd wide populity mong eseches. OGISTIC EGESSION ogistic egession is sttisticl pocedue which llows ssigning degees of belief (i.e. pobbility levels) in multidimensionl spce of independent vibles (explntoy), by mens of deived empiicl model. The scope of logistic egession is to estblish n expession fo conditionl pobbility of liquefction ( ) s function of explntoy vibles ( X ), which e fctos tht ffect the occuence of liquefction, by identifying the best-fitting fo egession model to descibe the unknown eltionship between n outcome vible nd set of vibles. Explntoy vible vecto ( X ) should epesent seismic loding, soil popeties nd in-situ stesses. The function is deived fom biny o dichotomous egession nlyses becuse ech cse in liquefction ctlog is epesented by biny vible which indictes whethe o not liquefction is occued (0 fo non-liquefction, fo liquefction). ogistic egession my be pefeed ove othe distibution functions vilble fo nlyzing dichotomous outcome vibles due to its simplicity, flexibility nd intepetbility (e.g. Cox nd Snell 989; Hosme nd emeshow 2000). io et l. (988) initilly pplied logistic egession fmewok to conside the uncetinties involved in deteministic citei nd to estimte the likelihood of liquefction tiggeing in tems of ST esistnce nd the othe fctos implemented in the simplified she stess-bsed method. The pobbility function tht should be fitted by employing field obsevtion dt cn be defined s follows (Cox 970 nd io et l. 988): exp[ x... x ] exp[... ] 0 n n 0 x nxn Whee exp0 n i ixi () = likelihood of liquefction occuence nd X x x2 x n 0 n 0, n = totl numbe of explntoy vibles, [,,...., ] [,,...., ] = vecto of explntoy vibles, = egession coefficients tht e detemined fom logit nlysis. cn be mpped into Q so tht Q vies fom to while vies fom 0 to (io et l. 988, i et l. 2006): pe No

4 Q log it[ ] ln x.... x 0 Eqs. () nd (2) e the bsis of logistic egession nlysis. ESTIMATION OF EGESSION COEFFICIENTS est sques egession o mximum likelihood of estimtion cn be utilized to detemine the vecto of egession coefficients, [ 0,,...., n ], by fitting the pobbility function to field obsevtion dt. Method of mximum likelihood is one of the best methods to estimte point estimto of pmete nd hs eceived moe ttention mong sttisticins due to its desible dvntges. As the nme implies, the estimtos e the vlues tht mximizes the likelihood function nd e known s mximum likelihood estimtos (i.e. vecto). The likelihood function fo m independent obsevtions tht coeltes explntoy vible vecto X with vecto is: n y j j X ( ; ) [ ] n (2) m y (3) j Whee X ( ; ) =likelihood function with explntoy vible vecto X tht is mximized with espect to vecto, y j =biny indicto fo cse j, which is in liquefied nd 0 in non-liquefied cses, nd m =totl numbe of cses. The vecto of mximum likelihood estimtos ( ) coesponding to the mximum of the likelihood function is the best fit of. Mximum likelihood estimtos would be found by uting the fist ptil deivtives of likelihood function to zeo nd solving the esulting system of utions. To void the computtions of lge vlues nd lge mount of multiplictions, the fist deivtives of the ntul logithm of the likelihood function, ln[ X ( ; )], e computed insted of X ( ; ). As indicted by io et l. (988) nd i et l. (2006), one of the pocedues tht cn be used to evlute the ducy of biny egession model nd detemine its goodness-of-fit is the modified likelihood tio index (MI) poposed by 2 Hoowitz (982). The MI ws denoted by s follows: ˆ 2 ( ) ( m)/2 (4) (0) ( ˆ ) = the log-likelihood function evluted using Whee the vlues of mximum likelihood estimtos, ; (0) = vlue of the mximum likelihood function ssuming i 0 ; nd m =totl numbe of explntoy vibles. In theoy, 2 vlues of vy between 0 nd nd egession model is 2 sid to be sufficiently well fitted when is lge thn 0.4 (Henshe nd Johnson 98). Moe detils bout the logistic egession cn be found in io (986) nd io et l. (988). MODE DEVEOING Development of pobbilistic model fo liquefction ssessment needs the following steps: ) Collecting suitble dtbse 2) Selecting explntoy vible 3) Anlyzing the biny dt with selected explntoy vibles The mentioned pocedue is pesented s follows. Dt bse As mentioned bove, qulity nd sufficiency of input dt hs get impct on the geneliztion of pobbilistic model. In fct, model with poo geneliztion cnnot obtin esonble estimtion fo the futue unseen dt. Cetin et l. (2004) nd Moss et l. (2006) pesented two dependble liquefction cse histoy ctlogs, espectively, bsed on ST nd CT dt ecoded in the field condition. They pefomed esonble pocedue to clssify numeous dt bsed on thei qulity nd compiled the finl dtbses (20 ST nd 88 CT dt) with the dt possessing the gete nks. In this study, thnks to use of eltive stte pmete index, both of these dtbses hve been employed nd theefoe the numbe of dt hs been duplicted. In the dtbse, liquefied cses e significntly moe thn non-liquefction cses nd my ffect the esult by poducing n undesible bis in logistic egession. Simil to the countemesue used in Myfield (2007), Moss et l. (2006), nd Cetin et l. (2004), this bis is educed by pio pobbility ssigned to ech liquefied o non-liquefied clss such s the popotion of clss's popultion in the dtbse. pe No

5 Explntoy vible An explntoy vible in logistic egession would be consideed s qulified vible if stisfy cetin pesumptions. Sttisticins, howeve, hve no complete geement on the detils of these pesumptions. Fo exmple, Andeson (2003) nd Johnson nd Wichen (2002) descibed tht ll explntoy vibles in sttisticl nlysis of clssifiction must be independent of ech othe, nomlly distibuted, linely dependent with the expected vlue, nd the expected vlue [i.e., (X) in Eq. ()] must be nomlly distibuted. In ddition, Johnson nd Wichen (2002) suggested tht even though (X) is not nomlly distibuted, the logistic tnsfomtion of (X) (i.e., Q (X) in Eq. (2)) still must be nomlly distibuted nd thee must be line eltionship between Q (X) nd the explntoy vibles. On the othe hnd, Gson (2003) decled tht the expected vlue in logistic egession nlysis should neithe be stictly nomlly distibuted no be linely dependent with the expected vlue, howeve its distibution must still be within the domin of the fmily of exponentil distibutions, such s noml, oisson, binomil, o gmm distibutions (i et l. 2006). In summy, the cuent feeling mong mny sttisticins is tht logistic egession is moe vestile nd bette suited fo most situtions thn the othe nlyses method becuse it does not ssume tht the independent vibles e nomlly distibuted. Howeve, this fct should be consideed tht selecting explntoy vible with noml distibution could led to moe logicl esults. To be intoduced in logistic egession, some explntoy vibles tht stisfy the mentioned sttisticl popeties nd suitbly epesent soil chcteistics should be selected. Since, this study is pesented bsed on the simplified method, the seismic distubnce induced by ethqukes is epesented s uivlent cyclic stess tion (CS ). On the opposite side, soil chcteistics is cptued by eltive stte pmete index ( ), which ccounts fo both eltive density nd effective stess. The eduction of liquefction esistnce with incesing initil effective ovebuden t constnt CS is diectly consideed by. Thus, the common lbotoy bsed coection fo ovebuden pessue ( K ) is not necessy to be consideed in this study. eltive density of ech cse histoy in both ST nd CT dtbses should be detemined to clculte thei coesponding. Fo this pupose, existing eltions between D nd penettion esistnce (i.e. N,60 nd q cn ) hve been used. Becuse of incesing uncetinties in detemining the eltive densities of snds contining high fctions of fines content, this study is only limited on clen snds nd silty snds hving up to 5% silts. Boulnge nd Idiss (2006) indicted tht mixed soils with plsticity index less thn 7 (i.e. I 7 ) exhibit snd-like behvio. Theefoe, it is esonble to expect tht snd smple contining up to 5% fines exhibit snd-like behvio even though they contin smll fction of cly. egession model consists of 3 vibles including, CS nd M w (moment mgnitude) tht epesent mesues of soil popeties nd seismic loding. All of these pmetes e descibed s follows. eltive stte pmete index ( ) Fom the eliest studies of soil behvio unde cyclic loding condition, it hs been deduced tht the cyclic stess uied to develop liquefction e pofoundly influenced by the eltive density ( D ) of the soil (Seed 979). Convenient detemintion of D fo snds nd silty snds in lbotoy nd lso its esonble consistency with the field ST nd CT tests e the most impotnt dvntges of this pmete tht hs been widely used to coelte lbotoy nd field studies (e.g. Yoshimio et l. 994 nd Suzuki et l. 995). On the othe hnd, sevel eseches showed the influence of initil effective confining pessue on liquefction esistnce (e.g. ee nd Seed 967). At given smll effective confining pessue, dense snds show diltive esponse unde sheing while loose snds behve contctively. Incesing initil effective confining pessue cn evese the diltive behvio of the dense snd to contctive behvio. Been nd Jeffies (985) indicted tht popeties of snds cnnot be expessed in tems of eltive density lone nd desciption of effective stess level must lso be included. As they showed, snds nd silty snds behve similly if test conditions ssue n ul initil poximity to the stedy stte line. This poximity ws identified by Been nd Jeffies (985) s the stte pmete, which ws defined s the diffeence between the initil nd stedy stte void tios t the sme men effective stess (Eq. 5). This pmete ppopitely eflects the combined effects of density nd confining pessue in gnul mteils. ee ( e e )( D D ) (5) cs mx min, cs Whee e = void tio of the soil, e cs = void tio of the soil on citicl stte line t the sme effective stess, e mx nd e min = D = eltive density mximum nd minimum void tios, cs, on citicl stte line t the sme effective stess, nd eltive density. D = Bolton (986) studied n extensive dtbse including the stength nd diltncy of 7 snds t diffeent densities nd confining pessues nd intoduced eltive density index s mesue to eflect diltncy potentil of gnul soils with esonble ccucy: pe No

6 I (6) 00 p ' D( Qln ) Whee, D =eltive density, p ' =men effective confining pessue, (+2k 0 ) v0 /3, = tmospheic pessue, nd Q =n empiicl constnt dependent to the minelogy nd bekge of soil (fo exmple Q 0 fo qutz snds). Since I 0 descibes citicl stte condition, eltive density t this condition cn be obtined s follows: D cs, 00 p ' Q ln( ) Eq. (7) cn be substituted into Eq.(5) to obtin vlue fo ny given gnul soil. Kond (988) nd Boulnge (2003) nomlized the stte pmete ( ), Eq. (5), with espect to e mx emin nd poposed eltive stte pmete index ( (7) ) s pmete tht is moe useful nd pplicble thn in the field condition. Kond (988) indicted tht the nomliztion of stte pmete is uied becuse given negtive my coespond closely to the densest stte in unifom well-ounded soil, whees it would only explin the behvio of well-gded ngul snd in medium-dense stte. The need fo such nomliztion of ws lso ecognized by Been nd Jeffeies (986). Kond (988), lso, eevluted the dt of sevel snds pesented by Been nd Jeffeies (985) nd found tht pek diltion te ( d v /d ) shows moe popotionlity to thn. Accodingly, eltive stte pmete index ( ) is obtined s: -D (8) 00 p ' Q -ln It is suggested tht cn be useful pmete eflecting liquefction esistnce of soils, since it inheently consides the influence of both void tio nd initil effective stess. 2 (9) N,60 Cd D Skempton (986) suggested C d vlues ul to 44 fo eltive densities vying between 30% nd 90%. Cubinouski nd Ishih (999) poposed moe compehensive ecommendtion fo C d nd indicted its dependence on bsic popeties of soil. Idiss nd Boulnge (2004) poposed tht consideing Cd 46 fo clen snds cn be moe elistic becuse it obtins eltive density of 8% fo coected ST blow counts of 30 ( N,60 30 ). In the pesent study, Skempton (986) s ecommendtion is used tht yields esonble D of 80% t N, Using Skempton (986) s ecommendtion, Eq. (8) is enged in tems of N :,60 N 00 p ' Q ln( ) 44 (0),60 Boulnge (2002) nd Idiss nd Boulnge (2004) summized Slgdo et l. (997,b) woks on CT nd poposed the following ution to obtin D fom coected vlues of CT tip esistnce ( q CN ) fo clen snds: D q () CN This eltionship cn be used to esult in eltive density of bout 80% t the limiting vlue of q CN of 75 ( q ) 75). ( CN lim Eq. () ws poposed fo clen snds tht cn quickly dissipte the excess poe wte pessue developed duing sounding. Co et l. (2003) studies on clibtion chmbes, howeve, shows tht the sounding pocedue of cone emins in dined condition even by incesing silts content up to 5%. Accodingly, ppliction of Eq. () is genelized to silty snds contining up to 5% silts. The following ution is esulted by substituting Eq. () into Eq. (8). Fo detemining of field ST nd CT dt, coeltions between penettion esistnce nd D hve been used. Ove the pst decdes, sevel eseches hve tied to coelte field penettion esistnce (i.e. ST nd CT esistnces) to eltive density of gnul soils. The common fom of the eltionship between N,60 nd D is: q p Q ln( ) CN.063 (2) pe No

7 In ode to be in consevtive side, the vlue of Q in Eqs. (0) nd (2) is ssumed to be ul to 0 ccoding to Boulnge (2003) s ssumption. Cyclic esistnce tio (CS) Fo consideing the ethquke ction, cyclic stess tio ( CS ) hs been used s ecommended in the simplified she stess ppoch. mx v CS.. g v Whee d (3) mx = pek hoizontl gound cceletion, v nd ' = totl nd effective veticl ovebuden stess nd d v depth eduction fcto. = To ccount the ndom ntue of ethquke excittion, Dution Weighting Fcto hs been intoduced though lbotoy studies nd bsed on this fcto, uivlent CS hs been ecommended s follows: CS * CS / DWF m (4) Whees, in some pobbilistic ecommendtions such s Cetin et l. (2004) nd Moss et l. (2006), ethquke mgnitude is consideed s n explntoy vible beside CS. ln( ).835M 3 w C exp (6) C Whee; stnds fo cyclic esistnce tio t vious levels of liquefction isk. Figue shows pobbilistic five fmily cuves tht e poduced by Eq. (6) nd denote on the contous of uivlent liquefction pobbility t 7.5 w M. In contst to the limit stte cuves obtined fom deteministic ppoch, ny pobbilistic cuve individully eflects unifom level of isk. Eqs. (5) nd (6) cn be used to evlute pobbilistic liquefction potentil of snds nd silty snds (up to 5% silt) in tems of pmete. This -bsed pobbilistic citeion hs been oiginted fom citicl stte concept nd consides the influence of ST nd CT esistnces togethe with effective ovebuden pessue. Accoding to Fig. 0, the boundy cuve epesenting 20% pobbility of liquefction is sufficiently consevtive nd is suggested to be consideed s deteministic boundy cuve tht guntees uied sfeties. The poposed model The expeiences gtheed duing pevious studies (e.g. io et l. 988; Cetin et l. 2004; nd Moss et l. 2006) evels tht ln( CS ) is moe ntully distibuted thncs. Thus, in this study,, moment mgnitude, M w, nd ntul logithm of CS, i.e. ln( CS ), e selected s explntoy vibles. The following expession is obtined by fitting the 202 ST nd CT dt: function to (5) CS * exp [ M w ln( ) ] 3 Fig.. obbilistic -bsed liquefction citeion developed by logistic egession method pplied on ST nd CT dt, only fo clen nd silty snds contining up to 5% silts Moeove, the -bsed cyclic esistnce tio fo given liquefction pobbility is obtined s: pe No

8 EATIONSHI BETWEEN SAFETY FACTO AND OBABIITY OF IQUEFACTION The conventionl fcto of sfety ( F s ) is consideed s elibility index (Jung et l. 2006, i et l. 2006) to obtin pobbility-sfety fcto eltionship fo estimting liquefction pobbility fo given fcto of sfety. This eltionship povides pope estimtion of the level of uncetinty behind the fcto of sfety tht is obtined fom deteministic nlysis. The fcto of sfety ginst liquefction is obtined by dividing cyclic esistnce tio t 20% * liquefction pobbility C,20% by CS. Figue 3 illusttes pobbility of liquefction (obtined fom Eq. 5) vesus conventionl fcto of sfety fo ll the ST nd CT cses. This eltion indictes tht incese in fcto of sfety does not decese the pobbility of liquefction linely. The following eltionship is deived by nonline egession nd Fig. 2 shows how it fits the field dt: (7) 5.3F s Figue lso compes Eq. (7) with the eltions poposed by Jung et l. (2000) fo ST dt nd i et l. (2006) fo CT dt. Note tht these eseches consideed 50% s liquefction filue (i.e. Fs ), s seen in Fig.. The tend of the poposed S-type cuve is logicl nd hs consistency with the pevious suggestion but the poposed cuve is moe consevtive. CONCUSION obbilistic model fo evluting field liquefction potentil bsed on eltive stte pmete index is developed. The dvntge of this pmete is consideing eltive density nd effective stess t the sme time. ogistic egession is used fo poposing the pobbilistic model. It hs been found tht 3 using of leds to bette logistic model the thn. The esulted pobbilistic cpcity cuves hve logicl tend nd enough consistency with the pevious studies. It hs been shown tht the pobbilistic cuve coesponding to 20% pobbility ( =20%) povides uied consevtism nd shows successful behvio in the clssifiction of liquefied nd non-liquefied dt to be poposed s deteministic cuve. Finlly, eltion between sfety fcto ginst liquefction nd liquefction pobbility is poposed. EFEENCES Andeson, T. W. [2003]. An intoduction to multivite sttisticl nlysis, 3d Ed., Wiley, New Yok. Been, K., nd Jeffeies, M. G. [985]. A stte pmete fo snds. Geotechnique, 35(2), Bolton, M. D. [986]. The stength nd diltncy of snds. Geotechnique, 36(), Boulnge,. W. [2002]. Evluting liquefction esistnce t high ovebuden stesses., oceedings, 3d US-Jpn Wokshop on Advnced esech on Ethquke Engineeing fo Dms, Sn Diego, CA, June Boulnge,. W. [2003]. High ovebuden stess effects in liquefction nlyses. J. Geotech. Geoenvion. Eng., ASCE, 29(2), Boulnge,. W., nd Idiss, I. M. [2006]. iquefction susceptibility citei fo silts nd clys. J. Geotech. Geoenvion. Eng., ASCE, 32(), Co, J. A. H., Bndini,., nd Slgdo,. [2003]. iquefction esistnce of clen nd nonplstic silty snds bsed on cone penettion esistnce. J. Geotech. Geoenvion. Eng., ASCE, 29(), Csto, G. [975]. iquefction nd cyclic mobility of stuted snds. J. Geotech. Eng. Div., ASCE, Vol. 0, No. GT6, oc. pe 388, Fig. 2. Fcto of sfety vesus liquefction pobbility nd the fitted cuve Cetin, K. O., Seed,. B., De Kiueghin, A., Tokimtsu, K., Hde,. F., J., Kyen,. E., nd Moss,. E. S. [2004]. Stndd penettion test-bsed pobbilistic nd deteministic ssessment of seismic soil liquefction potentil. J. Geotech. Geoenvion. Eng., 30(2), pe No

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10 Yoshimi, Y., Tokimtsu, K., nd Oh, J. [994]. In situ liquefction esistnce of clen snds ove wide density nge. Geotechnique, 44(3), Youd, T.., nd Noble, S. K. [997]. iquefction citei bsed sttisticl nd pobbilistic nlysis. oc., NCEE Wokshop on Evlution of iquefction esistnce of Soil, NCEE , Stte Univ. of New Yok t Bufflo, Bufflo, N.Y. Youd, T.., et l. [200]. iquefction esistnce of soils: Summy epot fom the 996 NCEE nd998 NCEE/NSF wokshops on evlution of liquefction esistnce of soils. J. Geotech. Geoenvion. Eng., 27(0), pe No