Empirical models for estimating liquefaction-induced lateral spread displacement

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1 Empirical models for estimating liquefaction-induced lateral spread displacement J.J. Zang and J.X. Zao Institute of Geological & Nuclear Sciences Ltd, Lower Hutt, New Zealand NZSEE Conference ABSTRACT: Existing empirical models for estimating liquefaction-induced lateral spread displacement (D LL ) were derived from a dataset poorly-distributed wit respect to eartquake magnitude and source distance, and also, te dataset are from eartquakes wit different tectonic source types and faulting mecanisms. Tese drawbacks may lead to unacceptably large uncertainties. To overcome tese problems, we used modification factors, accounting for effects of topograpic features, material properties and te nonlinear nature of te soil response, to scale te pseudo-displacement obtained from a spectral acceleration attenuation model for soft soil class. We selected an attenuation model derived from a very large and reasonably well-balanced Japanese dataset, supplemented by world-wide near-source records and tis model accounts for effects of eartquake tectonic source types and faulting mecanisms. We determined te model coefficients of te modification factors by selecting te pseudo-displacements calculated from a number of spectral periods to acieve unbiased residuals distribution wit respect to eartquake magnitude and source distance. Comparison wit a limited number of data from te 1997 Kocaeli, Turkey eartquake suggests adequate estimates of te present model wic can be considered as more robust tan te existing models. 1 INTRODUCTION Liquefaction-induced lateral spread displacement (D LL ) is one of te major seismic azards for pipelines, suc as in te 1994 Nortridge eartquake, te 1995 Kobe eartquake and te 1999 CiCi eartquake. Normally D LL was estimated by analytical approaces, suc as te Newmark rigid block model. During te last few decades, a useful number of recorded D LL ave been collected from moderately large and very large eartquakes, and a number of researcers ave attempted to develop reliable empirical models for estimating D LL. At present, most proposed empirical models are comprised of seismologic parameters, usually moment magnitude and pat parameters (geometric and anelastic attenuation rate), topograpic parameters, and site material parameters. Te Youd et al model (2002) is likely to be representative of tese empirical models. To sorten lengt of te introduction, only te Youd et al model (2002) is given a brief description. Youd et al (2002) corrected te erroneously measured ground displacements of teir1992 dataset, added some new data, and ten proposed two revised empirical models. Log * ( D ) = M w LogR R LogS gs (1a) LogT Log (100 F ) Log ( D ) Log ( D ) = M LogT w LogR Log (100 * R LogW F ) Log ( D 50 ff + 0.1) (1b) Paper Number 20

2 were D =D LL +0.01, D LL is estimated lateral ground displacement, in meters and R * =R+10 (0.89Mw-5.64). Tere are tree groups of parameters: (1) eartquake source and pat terms, moment magnitude M w and te nearest orizontal distance from a site to te seismic energy source R, in kilometres; (2) topograpic terms, T, te cumulative tickness of saturated granular layers wit corrected blow counts, (N 1 ) 60, less tan, in meters, S gs, te ground slope, in percentage, and W ff, te free-face ratio defined as te eigt (H) of te free face divided by te distance (L) from te base of te free face to te position of measured displacement, in percentage; and (3) material property parameters, F, te average fines content (fraction of sediment sample passing a No. 200 sieve) for granular materials witin te saturated granular layers aving a tickness T, in percentage, and D50, te average mean grain size for granular materials witin te saturated granular layers, in millimetres. Te standard deviation is 0.197, sligtly improved compared wit te 1992 model wit 0.2. Te new models are similar to tose proposed in 1992, but wit an added magnitude-dependent distance term and a Log(D50 ) term instead of D50 : Te added distance term is presumably from te consideration of distance saturation effect at near source region. 2 EARTHQUAKE-INDUCED LATERAL SPREAD DATASET In te present study, we used te dataset compiled by Youd et al (2002) and four new data available from te 1999 Kocaeli Turkey eartquake wic we use to ceck adequacy of different empirical models, rater tan including te four new data in our regression analysis. Unfortunately, among te recorded D LL compiled by Youd, et al, (2002), over 60% of te data are from te 1964 Niigata eartquake at a source distance of 21 km and % are from te 1983 Nionkai- Cubu eartquake at a source distance of 27 km (Figure 1). Among te rest of te dataset, 88 records (approximately 18% of te total data) are from recent eartquakes tat ave reliable eartquake parameters suc as moment magnitude and fault rupture models, and te oter records are from eartquakes before 1950s. Obviously, te data are poorly-distributed wit respect to magnitude and source distance. For eartquakes wit a reasonably large number of records in te dataset, te tectonic source types and faulting mecanisms are different. For example, te 1964 Alaska and te 1983 Kionkai-Cubu eartquakes (comprising approximately 16% of te total records) are subduction interface events; among te crustal eartquakes, te 1964 Niigata eartquake and te 1971 San Fernando eartquake, wit 322 records (approximately 66% of te total records), ave reverse faulting mecanisms, and te 1979 Imperial Valley eartquake and te 1995 Kobe eartquake (50 records) ave strike-slip faulting mecanisms. Te poorly-distributed data wit respect to magnitude and source distance are te mixture of tectonic source types and faulting mecanisms wic reduce te statistical power of te dataset. Zao & Zang (2002) found tat for a given M w and source distance, spectral accelerations at 2.0s period from sallow subduction interface and intra-slab events are, respectively, 65% and 80% of tat from a crustal event and tat eartquake dept as a profound effect on spectral accelerations from subduction eartquakes at sort period, but still significant at 1.0s period. Tese findings are similar to tose of te oters (Youngs et al 1997). Our analysis suggested tat it would be difficult to derive a robust empirical model from te dataset compiled by Youd et al (2002). In contrast to te distribution wit respect to eartquake magnitude and source distance, te dataset compiled by Youd et al (2002) covers a good range of topograpic and material properties and is reasonably well-distributed wit respect to tose properties. 3 EMPIRICAL EQUATIONS FOR PREDICTING D LL To overcome te drawbacks of te data distribution, we attempt to derive an empirical model by modifying ground motions predicted from suitable spectral acceleration attenuation models, to account for te effects of nonlinear ground deformation (or failure of soils in liquefied sites) and te material properties of te liquefied soils. In te selection of attenuation models, we used a recent model developed for Japan (Zao & Zang, 2002) from following considerations; (1) te number of strong motion records from events of different source types and wit different faulting mecanisms is large; (2) te records are all consistently processed; (3) consistent site classes ave been assigned; (4) source 2

3 distances (te closest distance from a site to te rupture plane) ave been evaluated for most large eartquakes tat special studies ave been performed for estimating fault rupture planes; (5) tectonic source types, event locations and event dept ave been all evaluated. Tis dataset is possibly one of te best, if not te best, datasets from Japan. Anoter reason to coose tis model is tat te attenuation model developed by Zao & Zang (2002) uses simple scaling factors for ground motions from events wit different source types and faulting mecanisms. Using tis attenuation model, we were able to use only one additional modification parameter to produce a simple model, but capable of capturing all important aspects. Because te closest distance from a site to te rupture plane of an event was used in te Zao & Zang attenuation models (2002), we modified te source distances reported by Youd et al (2002) for tose eartquakes in wic rupture does not come up to te ground surface. Tese modifications ave only small to moderate effects on te model parameters. We excluded tose data from events witout reliable tectonic source types or faulting mecanisms. A number of modification metods can be used and te first attempt was to modify te ground motions by D LL = SD ( T ) F S f ( T ) g ( F ) ( D 50 ) q ( S, W gs ff were SD(T) is te pseudo-displacement calculated from te spectral acceleration attenuation model for soft soil sites at a spectral period T, F s is a scale factor, and f, g, and q are functions of relevant topograpic parameters or material properties. Te soft soil sites defined in te Zao & Zang (2002) model are tose sites wit a dominant site period larger tan 0.6s and tis site class would be most suitable for our purpose of estimating D LL. However, for te modification suggested in Equation 2, te site class selection as no effect on te combination of topograpic parameter, scale factor F s and any constant terms in te material property function, wic will be combined as a single constant term in te regression analysis. Equation 2 implies tat if a soil layer responds elastically and as a viscous damping ratio of 5%, ground displacement can be obtained from a spectral acceleration attenuation model at a cosen period. As SD is a function of period and site class, we attempted to calculate te residuals of D LL from a number of periods and to select an appropriate period by acieving a minimum standard deviation and unbiased residuals distribution wit respect to magnitude and source distance. Tis modification is equivalent to using te coefficients of magnitude term, geometric and anelastic attenuation terms, tectonic source term and faulting mecanism term from te Zao & Zang model (2002) in Equation 2, wic can be rewritten in te form of Equation 1. We used te same functional forms as tose of te Youd et al model (2002) for topograpic parameters and material properties. Using coefficients of te Zao & Zang (2002) model for different spectral periods results little cange in te standard deviation for D LL. However, te trends of residuals distribution wit respect to magnitude and source distance are very sensitive to te selection of periods for te parameters of te attenuation model. Te modification sown in Equation 2 was not successful because simultaneous unbiased residuals distribution wit respect to magnitude and source distance cannot be acieved. Te unsuccessful modification sown in Equation 2 is not surprising because elastic deformation is implied (constant scale factor F s in Equation 2) and terefore nonlinear deformation of soil at a liquefied site is not accounted for. To overcome tis problem, we proposed te modification as follows, D LL γ = [ SD ( T )] f ( T ) g ( F ) ( D 50 ) q( S, W gs ff were parameter γ is to account for te effect of nonlinear soil deformation due to liquefaction and sould be larger tan 1.0. Again we used te same functional forms for f, g, and q as tose of te Youd et al model (2002). A linear regression was used to determine te coefficients γ and te terms associated wit topograpic parameters and material properties, and by sweeping troug a number of spectral periods nearly simultaneous unbiased residuals distributions wit respect to magnitude and source distance were acieved in a period range of 0.7 to 1.0s (Figure 2). Te variation of standard deviation (in log 10 scale) wit respect to spectral periods is small, toug te smallest standard ) ) (3) (2) 3

4 deviation is at 0.8s period. However, suc a small cange in te model prediction uncertainty is practically negligible and te modification presented in Equation 2 can also lead to similar values. Figures 2a and 2b sow te slope of te straigt lines fitted to te residuals wit respect to magnitude and source distance. An unbiased residuals distribution wit respect to magnitude is acieved at 1.0s and between 0.7 and 0.8s for te residuals distribution wit respect to source distance. Te amplitude of te slopes for te residuals distribution is small, especially for source distance but even a small value would result an unacceptably biased residuals distribution because te dataset includes large magnitude and distance ranges. Note tat, in te modification sown in Equation 3, source and pat parameters in te attenuation model are not coupled and little trade off between te estimates of te attenuation model and te estimates of coefficients for te material property terms would occur in te regression analysis. We selected te coefficients at a spectra period of 0.8s from te Zao & Zang model (2002) and te following models are proposed; Equation 4a for ground slope and Equation 4b for free face: Log ( D ) = * Log ( SD ) * LogS gs (4a) * LogT * Log (100 F ) * Log ( D ) Log ( D ) = * Log ( SD ) * LogW ff (4b) * LogT * Log (100 F ) * Log ( D ) M w SD = * exp( M w R Ln ( R * e ) + (4c) e * ( c ) * δ + S R + S I + S S ) were M w is te moment magnitude, R is te closest distance to rupture surface for large events and ypocentral distance for small eartquakes for wic rupture plane is not available, is te focal dept, c =km is a constant, S R= applies only to crustal events wit a reverse-faulting mecanism, S I= applies to subduction interface events and S S= applies to subduction slab events. Te standard deviation of tis model is 0.19 on te log 10 scale. Furter investigation of residuals reveals a moderately biased residuals distribution wit respect to te tickness of liquefiable layers T, as sown in Figure 3a. Te extent of bias is significant for te free face case and ground slope case, respectively. Figure 3a sows tat for te free face case D LL is underestimated at large T values, but overestimated for T <10m, and for ground slope case D LL is underestimated for T <10m. We found tat te bias could be corrected by replacing te log(t ) term wit T and used different coefficients for te free face case and ground slope case, as suggested by te residuals distribution sown in Figure 3a. We followed te same procedure as tat for deriving te model sown in Equation 4 and te following models were obtained; Equation 5a for ground slope and Equation 5b for free face: Log ( D ) = * Log ( SD ) * LogS gs (5a) * T * Log (100 F ) * Log ( D ) Log ( D ) = * Log ( SD ) * LogW ff (5b) * T * Log (100 F ) * Log ( D ) were SD is determined by Equation 4c. Note tat te parameter for te pseudo-displacement term is almost uncanged between te models in Equations 4 and 5. Te standard deviation for Equation 5 is 0.18, sligtly improved compared wit tat for te model in Equation 4. Figure 4 sows te residuals distribution wit respect to magnitude and distance, te distribution is not significantly biased as indicated by te straigt lines fitted to te residuals. Te residuals distribution wit respect to T is sown in Figure 3b and an unbiased distribution was acieved as indicated by te quadratic curves fitted to te residuals wit respect to T. Te factors used to scale D LL from a crustal strike-slip event to obtain te D LL for a crustal reverse fault event and subduction interface and intra-slab events can be derived from Equation 5 and tese factors are 1.21 for reverse faulting mecanism, 0.88 for subduction interface events and 1.06 for subduction intra-slab events. 4

5 4 COMPARISONS OF MODEL PREDICTION WITH EARTHQUAKE DATA AND WITH THOSE OF THE YOUD ET AL MODEL (2002) In te 1999 Kocaeli Turkey eartquake, large D LL was considered as one of major causes of damage for pipelines as reported by Cetin et al (2002). After a detailed geotecnical investigation at te Hotel Sapanca site, tey obtained valuable data of topograpy and soil properties at liquefied sites SPT-SH4. Based on Figures 5 and 6 of Cetin et al (2002), we determined ticknesses of te liquefiable layers and ground slope at SPT-SH7, SPT-SH9, and SPT-SH11, and we also assume tat F and D50 in SPT- SH9 and SPT-SH11 are te same as SPT-SH4 toug te largest distance between SPT-SH4 and SPT- SH11 is about 80m. Table 1 lists observed and estimated values from tree models, wit te present model aving te smallest mean residuals (Equation 5). Te largest average residual is from te Hamada et al model (1986) presumably because teir model does not directly account for eartquake magnitude and source distance. Te mean residual of te Youd et al model (2002) is about 1.8 times tat of te present model. Altoug te present model predicts muc better displacement tan tat of te Youd et al model (2002), it would be difficult to ascertain te robustness of te present model based on tis comparison alone, because of te small number of data from tis eartquake. However, because our model is establised by modification of pseudo-displacement from an attenuation model tat was derived from a very large dataset, we believe tat our model can provide reasonably robust estimates for eartquakes aving different faulting mecanisms and tectonic source types. Table 1. Comparison between estimated and observed D LL. Model Boreoel No SPT-SH4 SPT-SH7 SPT-SH9 SPT-SH11 Observed Mean residual Hamada et al (1986) Youd et al (2002) Te present model Next, we present te estimated D LL from te present model and te Youd et al model (2002). As te distance measurement used in te Youd et al model (2002) is te orizontal distance from site to te nearest bound of te seismic energy source, we modified te distance used in te calculation from te Youd et al model (2002) by assuming te buried dept, d, of fault rupture for strike-slip event. We selected d=2km in Figure 5 for all events, toug tis is an unlikely value for interface events. Figure 5a compared te D LL predicted by te Youd et al model (2002) and te present model for a Mw=6.5 event from crustal strike-slip and reverse faults and subduction interface event at a dept of 20km. Te predicted D LL by te Youd et al model (2002) is close to tose predicted by our interface model at a source distance beyond 5km, is about 25% less tan tat predicted by te present model for a crustal strike-slip event, and is about 55% less tan te present model for crustal event wit a reverse faulting mecanism. Figure 5b sows te comparison of model predictions for a magnitude 7 event. Te present model for strike-slip event predicts very similar D LL values to tose from te Youd et al model (2002) in a distance range of 5-30km. Tis is not surprising as te average magnitude of all eartquakes is around 7.0 and te two largest groups of data ave source distances of 21km and 27km respectively. Figure 5c sows a magnitude 7.5 event, in wic te Youd et al model (2002) predicts D LL values between tose by te present model wit strike-slip and reverse faulting mecanisms Figure 5d sows te model predictions for a magnitude 8 event. Te Youd et al model (2002) predicts D LL values close to tose of te present model wit crustal reverse faulting mecanism in a distance range of 3-30km. Te dept of large subduction eartquake as large effect on te ground motions and te scale factor used to scale D LL values calculated at a dept of km can be derived from Equation 5 by using te coefficient of te dept term from te Zao & Zang model (2002). For an event at depts of 20, 30 and 40km te corresponding scale factors are 1.04, 1.13 and 1.23 respectively at te same source distance. 5

6 5 CONCLUSIONS In te present study, te following conclusions can be reaced, 1) Wit a dataset aving poor distributions wit respect to magnitude and source distance and te mixture of eartquake tectonic source types and faulting mecanisms, we attempted to develop an empirical model for estimating D LL by modifying te pseudo-displacement from a spectral acceleration attenuation model wic was derived from a well balanced dataset and accounts for effects of tectonic source types and faulting mecanisms. We introduced a simple modification parameter to account for nonlinear soil response and te effects of topograpic parameters and material properties. 2) Wit tese modification factors, we selected coefficient values of te spectral acceleration attenuation model from a number of spectral periods and performed regression analyses to determine te modification factor and coefficients for te topograpic parameters and material properties. We found tat te cange of standard deviation of te model is small at different spectral periods selected. However, te residuals distribution wit respect to magnitude and source distance varies considerably wit te spectral period. Te model parameters were determined by nearly simultaneously acieving unbiased residuals distributions wit respect to bot magnitude and source distance. 3) We found tat te residuals distribution wit respect to T, te tickness of te liquefiable layers, are biased for te free face case and ground slope case wen log(t ) was used. Te biased distribution was eliminated by replacing log(t ) wit T in te model and allowing different coefficients of te T term for te free face case and ground slope case. 4) Te mean residuals from te present model, calculated from te data at four sites in te 1999 Kacaeli Turkey eartquake, are muc smaller tan tose of two existing models. Toug te number of data is far too small to confirm te adequacy of any empirical model, our model can be considered to be reasonably robust as all source and pat factors in te present model are derived from an attenuation model wic was developed from a very large dataset. 5) Te proposed model predicts similar D LL values to tose of te Youd et al model (2002) for a magnitudes 7 crustal event wit strike-slip faulting mecanism in a distance range of 3-30km. In a range of 5-30km, for magnitude 6.5 and 8.0 events, te Youd et al model (2002) predicts D LL values about 55% and close to tose predicted by te present model wit reverse faulting mecanism. ACKNOWLEDGEMENT Te autors wis to tank Dick Beetam and Peter Davenport for teir review of manuscript. Tis study is supported in part by te Foundation for Researc and Science and Tecnology of New Zealand, Contract Number C05X0208 and C05X0301 REFERENCES: Cetin, K.O. Youd, T.L. Seed, R.B. Bray, J.D. Sancio, R. Lettis, W. Yilmaz, M.T. & Durgunoglu, T Liquefaction-induced ground deformations at Hotel Sapanca during Kocaeli (Izmit), Turkey eartquake, Soil Dynamics and Eartquake Engineering, 22: Hamada, M. Yasuda, S. Isoyama, R. & Emoto, K 1986 Study on liquefaction-induced permanent ground displacement, report for te Association for te Develpment of Eartquake Prediction. Youd, T.L Hansen, C.M. & Bartlett, S.F Revised multilinear regression equations for prediction of lateral spread displacement, Journal.of Geotecnical and Geoenvironmental Engineering, 128(12): Youngs, R.R. Ciou, S.-J. Silva, W.J. & Humprey J.R Strong ground motion attenuation relationsips for subduction zone eartquakes. Seismological Researc Letters, 68(1): Zao, J.X. & Zang, J.J Development of attenuation models from Japanese strong-motion data accounting for source-type effects, Institute of Geological & Nuclear Sciences Limited, Client Report 2002/142 6

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