Identification and modeling of earthquake ground response - II. Site liquefaction

Downhole records of seismically-induced soil liquefaction are a valuable source of information on the associated mechanisms of stiffness degradation and lateral spreading. In this paper, free-field downhole array seismic records are employed to identify and model the recorded response at Wildlife Refuge (California, USA) and Port Island (Kobe, Japan) sites. The Wildlife Refuge site was instrumented in 1982 with a two-accelerometer array and six piezometers that recorded a case of seismically induced site liquefaction. At Port Island, a four-accelerometer down-hole array recorded strong motion during the recent 1995 Hyogoken-Nanbu earthquake. This earthquake resulted in widespread liquefaction and major ground deformations at Port Island. Using the recorded downhole accelerations at these two sites, the actual seismic shear stress-strain histories are directly evaluated. These histories provide valuable insight into the mechanisms of site liquefaction and associated loss of stiffness and strength. Based on the identified dynamic soil behaviors, computational simulations of the observed seismic response are performed. Optimization techniques are employed to estimate the necessary computational modeling parameters. This document constitutes the second part of a set of two companion papers about site amplification and liquefaction.     

土层平均剪切波速确定及其可靠性验证——基于钻井台阵强震动记录

震害资料显示,场地条件对地震动特性以及工程结构破坏程度影响显著。为减少因场地效应而造成的经济损失和社会影响,在进行场地地震反应分析时,需最大限度地减小因场地土层模型参数的不确定性引起的地震动评估偏差,为工程结构地震反应分析选取并生成适当的地震动输入。随着强震动观测技术的逐渐发展,大量可靠的钻井台阵记录为地震过程中场地观测点的动力反应提供了直接数据。以美国加州地区La Cienega钻井台阵强震动观测数据为基础,利用互相关函数,对不同强度地震作用下场地土层的平均剪切波速进行分析,并在此基础上,以Cyclic 1D为模拟平台,建立一维自由场地地震反应有限元分析模型。分析结果表明：通过钻井台阵地震动观测数据识别,得到场地平均剪切波速,能够反映该场地的动力特性,数值模拟计算结果和台阵地震动记录基本吻合,可为数值模型参数选取提供依据。     

Identification of soil degradation during earthquake excitations by Bayesian inference

A Bayesian inference approach is introduced to identify soil degradation behaviours at four downhole array sites. The approach of inference is based on a parametric time‐varying infinite impulse response filter model. The approach is shown to be adaptive to the changes of filter parameters and noise amplitudes. Four sites, including the Lotung (Taiwan), Chiba (Japan), Garner Valley (California), and Treasure Island (California) sites with downhole seismic arrays are analysed. Our results show two major types of soil degradation behaviour: the well‐known strain‐dependent softening, and reduction in stiffness that is not instantaneously recoverable. It is also found that both types of soil degradation are more pronounced in sandy soils than in clayey soils. The mechanism for the second type of soil degradation is not yet clear to the authors and suggested to be further studied. Copyright © 2003 John Wiley & Sons, Ltd.     

Non-linear soil response in ground motions

From both theoretical and empirical studies, we know that a soft soil layer will amplify seismic waves of certain frequencies and cause damage to structures, depending on the physical properties and the thickness of the layer. Most developed cities are situated on a plane or a basin with soft geological strata. Thus, understanding the characteristics of soft soil response to seismic loading is important. Seismologists and engineers are interested in questions of linear versus non-linear soil response and isotropy versus anisotropy as a soil property. The records of the downhole accelerographs of an array in Lotung provide an opportunity to study these problems. The results show that the soil response in Lotung does not have an anisotropy effect, and significant non-linear soil response occurred during the strong ground motions in which peak ground acceleration values at ground surface are larger than 150 gal.     

金银岛岩土台阵原位剪切波速剖面评估

土层的剪切波速是描述土动力学特性的重要参数之一。利用金银岛岩土台阵记录的8次浅源地方震的弱震动数据,使用解卷积的地震干涉测量法识别的剪切波走时,评估了该台阵两个水平方向的原位剪切波速剖面。结果表明:在44.2m深度以上,估计与实测的平均剪切波速剖面基本一致,而在44.2m到103.6m深度范围前者大于后者;本研究估计的平均剪切波速剖面比MEHTA等（2007）估计的平均剪切波速剖面更接近实测结果,在44.2m到103.6m深度范围,本研究估计的平均剪切波速与MEHTA等（2007）估计的平均剪切波速相近,二者均大于实测的平均剪切波速。     

Analysis of ground motions at Treasure Island site during the 1989 Loma Prieta earthquake

Site response analyses and coherence studies were conducted at the Treasure Island site where surface motions were recorded during the Loma Prieta earthquake. The analyses were conducted using a nonlinear dynamic effective stress method which took into account the effects of the liquefaction that occured at the site. The rock motions recorded at nearby Yerba Buena Island were used as input motions. Computed and recorded ground motions transverse to the direction of wave propagation and associated response spectra were in good agreement. Agreement was also good in the radial direction, except in certain frequency bands higher than 1·25 Hz. Coherence studies showed that some of these discrepancies may be due to low coherence between the Treasure Island and Yerba Buena motions in these same frequency bands.     

Seismological evidence for nonlinear elastic ground behavior during large earthquakes

Amplification of earthquake-induced seismic waves by soft superficial deposits often causes significant damages in the urban areas. In predicting this effect for large future earthquakes, the linear elastic response of soils is customarily assumed. To check this assumption, we have analyzed surface and downhole acceleration data from the SMART1 and SMART2 strong motion arrays in Taiwan, covering peak accelerations of up to 0·3 g. First, frequency-dependent amplification induced by the alluvial deposits at the SMART1 array was estimated using spectral ratio technique, where the records at rock site were taken as a reference motion. Statistically validated reduction in soil amplification in the strong motion relative to the weak motion in the frequency range between approximately 1 and 9 Hz was detected. Secondly, relative site responses between the Pleistocene and recent sedimentary deposits at the SMART2 array were studied. Relative amplification was shown to be clearly dependent on the excitation level. Thirdly, we compared experimentally recorded uphole/downhole spectral ratios on weak and strong ground motion with the theoretical response yielded by the geotechnical code DESRA2 which assumes hysteretic constitutive relationship of soil. Major symptoms of nonlinear ground behavior predicted by the model were found in the observed data. Back-calculation of the shear wave velocities to the depth of 47 m shows nearly 50% decrease in the strongest quakes, also accounted for by the nonlinear soil behavior.     

Analysis of nonlinear site response using the LSST downhole accelerometer array data

Both linear and nonlinear behaviors of soil deposits were evaluated by strong and weak motion data observed on the surface and at depths of 6, 11, 17, 47 m at the Large Scale Seismic Test (LSST) array in Lotung, Taiwan. The soil properties measured by well logging and by the shear wave velocity profile measured by uphole and cross-hole methods are available. Both one-dimensional equivalent-linear method and nonlinear method are used for the evaluation have been used. The synthetic records at various depths are obtained by using the records at the bottom as input motion. These synthetic records are then compared with actual records at corresponding depths. Records of 13 earthquakes are used. We find that the synthetic records obtained from a linear model match well with actual records for small input motions, but the results obtained from a nonlinear model match poorly. On the other hand, the synthetic records using both the nonlinear model and equivalent-linear model are in good agreement with the observed records for large input motions. In these cases, the predicted response spectra using the linear model consistently overestimate the observed records. The threshold distinguishing the large and small input motions is 0.04 g at depth of 47 m for the LSST data. Thus, the nonlinearity started at 0.04 g and occurred unequivocally at 0.075 g. Furthermore, the dominant frequencies shift toward lower values when input motions become large. Clearly, the observed records at the LSST site manifest nonlinearity of soil response. The hysteresis loops evaluated by the nonlinear method show a permanent strain of about 0.01% in soil layers at higher ground motion input levels in this case.     

A hypoplastic model for site response analysis

Site response analyses must take into account the nonlinear behavior of soils. This is typically achieved using an equivalent linear approach or using numerical analyses with an appropriate constitutive model. In this work a family of hypoplastic models is proposed for use in site response analyses. These nonlinear models use a rate-type tensorial equation and are capable of reproducing plastic deformation of soils for cyclic loading under both drained and undrained conditions. A methodology for the calibration of hypoplastic parameter for dynamic loading is proposed. The hypoplastic constitutive models are implemented in a finite element code and the site response of the Lotung downhole array site is used to validate the use of hypoplastic models for site response analysis. The hypoplastic models reproduce accurately site response at the Lotung site. The advantages and disadvantages of the hypoplastic models compared to other models are discussed.     

Stochastic model of seismic torsional ground motion: Application to Lotung soft site

The purpose of this paper is to present a stochastical approach, which analyse the torsional ground motion, induced by the spatial variability of seismic motions. For this purpose, a torsional ground motion analytical model is proposed and a normalised differential motion parameter is introduced. The approach regards the seismic motion as the combination of a travelling wave on the site (coherent component) and a zero mean randomizing factor that introduces a loss of correlation effect. The soil parameters as fundamental frequency and damping coefficient are integrating by modeling the coherent component with the commonly used Kanai-Tajimi power spectral density. The parametric analysis of the model shows an increase of the induced torsion with both the soil frequency and the motion scattering parameter, and a decrease with the separation distance, the apparent wave velocity and the correlation length. Finally, in order to test the proposed torsional ground motion model prediction, it is compared to the experimental results recorded by the EPRI LSST array in Lotung, Taiwan (Laouami and Labbé, 2002). The comparison leads to the identification of the model parameters for the Lotung soft site.     

Seismic ground response at Lotung: Hysteretic elasto-plastic-based 3D analyses

This paper presents a non-linear finite element study to back-interpret the free field seismic response recorded at the Lotung Large-Scale Seismic Test site. The study is carried out in the time domain by the Finite Element (FE) code PLAXIS 3D, considering the vertical wave propagation of both the horizontal components of motion. The non-linear soil behaviour is simulated through a constitutive model, the Hardening Soil model with Small-Strain Stiffness (HSsmall), capable of describing the cyclic response of the material at different strain levels. In the paper, the constitutive response of the HSsmall model is firstly investigated through numerical simulations of strain-controlled cyclic shear tests under single and multi-directional conditions at low strain levels. Then, it is adopted to back-analyse the recorded free field seismic response, comparing the FE numerical results to the in-situ down-hole and surface signals recorded during two earthquakes occurred on May 20th and July 17th 1986, characterized by different peak ground accelerations.     

回填土不确定性对场地地震反应的影响

选取某核电场地控制性钻孔的厚度、剪切波速、密度等实际勘探数据,通过改变回填土剪切波速,分析了回填土不确定性对场地地震动参数的影响。研究结果表明:在回填土层厚度不变和模型总厚度不变的情况下,地表的水平向峰值加速度随着回填土剪切波速的增大而减小,但水平向峰值加速度增幅逐渐减小;回填土剪切波速到达一定的波速就不再影响地表水平峰值加速度;随着回填土剪切波速的增加,整个反应谱的谱值都普遍减小。     

土层场地的放大作用随深度的变化规律研究——以金银岛岩土台阵为例

为了探究土层场地放大作用的机制,利用金银岛岩土台阵在四次地震中记录的26组弱震动的三分量加速度时程,采用考虑上行波场与下行波场相消干涉作用的传统谱比法,研究了土层场地的放大作用随深度的变化规律.结果表明：（1）地震波从基岩传播到土层中时,土层的多个振型被激励,放大作用随深度的变化是按照不同振型的特征而有规律地变化.自下而上直至地表,一阶振型的场地放大作用是逐渐增大的;二阶振型的场地放大作用经历了逐渐减小和逐渐增大两个过程;三阶振型的场地放大作用经历了逐渐增大、逐渐减小和逐渐增大三个过程;四阶振型的场地放大作用经历了逐渐减小、逐渐增大、逐渐减小和逐渐增大四个过程;更高阶振型的场地放大作用可以据此类推.（2）四次地震中同一振型的NS和EW两个水平分量的自振频率相差很小;二阶到六阶5个振型与一阶振型的自振频率之比小于相应的理论模型之比.（3）四次地震中均存在一些高阶振型的放大系数大于其一阶振型相应分量的放大系数的现象.目前的场地反应分析中,往往将最大放大系数对应的频率作为场地的卓越频率,这么做的结果,很有可能将不同振型的自振频率作为场地的卓越频率,导致同一地震中不同水平分量的卓越频率相差较大,或者在不同地震中同一水平分量的卓越频率差别较大,难以描述场地的固有特性;而按照不同振型分析场地放大作用的特征,可以从本质上揭示场地的固有特性.     

Surface and downhole shear wave seismic methods for thick soil site investigations

Shear wave velocity–depth information is required for predicting the ground motion response to earthquakes in areas where significant soil cover exists over firm bedrock. Rather than estimating this critical parameter, it can be reliably measured using a suite of surface (non-invasive) and downhole (invasive) seismic methods. Shear wave velocities from surface measurements can be obtained using SH refraction techniques. Array lengths as large as 1000 m and depth of penetration to 250 m have been achieved in some areas. High resolution shear wave reflection techniques utilizing the common midpoint method can delineate the overburden-bedrock surface as well as reflecting boundaries within the overburden. Reflection data can also be used to obtain direct estimates of fundamental site periods from shear wave reflections without the requirement of measuring average shear wave velocity and total thickness of unconsolidated overburden above the bedrock surface. Accurate measurements of vertical shear wave velocities can be obtained using a seismic cone penetrometer in soft sediments, or with a well-locked geophone array in a borehole. Examples from thick soil sites in Canada demonstrate the type of shear wave velocity information that can be obtained with these geophysical techniques, and show how these data can be used to provide a first look at predicted ground motion response for thick soil sites.     

Modelling non‐linear ground response of non‐liquefiable soils

A non‐linear finite element (FE) model is presented to account for soil column effects on strong ground motion. A three‐dimensional bounding surface plasticity model with a vanishing elastic region, appropriate for non‐liquefiable soils, is formulated to accommodate the effects of plastic deformation right at the onset of loading. The elasto‐plastic constitutive model is cast within the framework of a FE soil column model, and is used to re‐analyse the downhole motion recorded by an array at a Large‐Scale Seismic Test (LSST) site in Lotung, Taiwan, during the earthquake of 20 May 1986; as well as the ground motion recorded at Gilroy 2 reference site during the Loma Prieta earthquake of 17 October 1989. Results of the analysis show maximum permanent shearing strains experienced by the soil column in the order of 0.15 per cent for the Lotung event and 0.8 per cent for the Loma Prieta earthquake, which correspond to modulus reduction factors of about 30 and 10 per cent respectively, implying strong non‐linear response of the soil deposit at the two sites. Copyright © 2000 John Wiley & Sons, Ltd.     

Estimation of soil shear modulus softening during strong ground shaking using ground surface and downhole acceleration recordings

An algorithm for estimating the average shear modulus for a soil site containing a downhole accelerometer array is described. For distant or weak earthquakes, the usual procedure for estimating shear modulus is to perform time‐series correlation of two downhole records. The vertical distance between instruments divided by the peak correlation lag time gives the average shear wave velocity. The shear modulus follows easily. This method is not applicable for stronger earthquakes where non‐linear softening effects lead to progressively slower shear wave velocities. The method presented here overcomes the softening effect by compressing the time scale of the upper acceleration record. Time compression is accomplished in such a way that the peak correlation of the two records is maximized. The algorithm steps through the records, maximizing the correlation peak by adjusting the time scale within an active time interval. The resulting compressed upper record can be interpreted as the ground motion that would have occurred had softening not taken place. The summation of the various time scale adjustments shows both the amount of softening and the time at which it occurred. Copyright © 2000 John Wiley & Sons, Ltd.     

Site response study in Abruzzo (Central Italy): underground array versus surface stations

In this site response study we examined local earthquakes recorded at surface stations of a local seismic network and at a temporary underground seismic array installed in a tunnel underneath the Gran Sasso Massif in Abruzzo (central Italy). This allowed us to compare the seismic site response beneath the mountain and on the surface in similar geological environment (soft rock sites). We applied spectral ratios method on different segments of the seismograms and used different reference spectra in the 1–20 Hz frequency band. We found little or no amplification effects at most of the surface stations whereas site transfer functions evaluated with respect to underground sites show an amplification factor up to 6 in the 1–8 Hz frequency range. Coda spectral ratios estimated at soft rock sites are confirmed as good estimates of shear wave transfer function.     

Simulation of synthetic ground motions for specified earthquake and site characteristics

A method for generating a suite of synthetic ground motion time‐histories for specified earthquake and site characteristics defining a design scenario is presented. The method employs a parameterized stochastic model that is based on a modulated, filtered white‐noise process. The model parameters characterize the evolving intensity, predominant frequency, and bandwidth of the acceleration time‐history, and can be identified by matching the statistics of the model to the statistics of a target‐recorded accelerogram. Sample ‘observations’ of the parameters are obtained by fitting the model to a subset of the NGA database for far‐field strong ground motion records on firm ground. Using this sample, predictive equations are developed for the model parameters in terms of the faulting mechanism, earthquake magnitude, source‐to‐site distance, and the site shear‐wave velocity. For any specified set of these earthquake and site characteristics, sets of the model parameters are generated, which are in turn used in the stochastic model to generate the ensemble of synthetic ground motions. The resulting synthetic acceleration as well as corresponding velocity and displacement time‐histories capture the main features of real earthquake ground motions, including the intensity, duration, spectral content, and peak values. Furthermore, the statistics of their resulting elastic response spectra closely agree with both the median and the variability of response spectra of recorded ground motions, as reflected in the existing prediction equations based on the NGA database. The proposed method can be used in seismic design and analysis in conjunction with or instead of recorded ground motions. Copyright © 2010 John Wiley & Sons, Ltd.     

Extracting rotational components of earthquake ground motion using data recorded at multiple stations

Rotational components of earthquake ground motion have not been considered for seismic analysis, design and performance assessment because recordings of these components are unavailable. A number of procedures have been proposed to extract rotational components of ground motion from translational time series recorded at multiple, closely spaced recording stations. In this paper, a new procedure that is capable of capturing higher frequency content in rotational time‐series is presented. The frequencies at which numerical errors are introduced in the solution, which are a function of apparent wave velocity and array dimension, are identified. Results are presented for the proposed procedure, the widely accepted geodetic method, and a single‐station procedure developed by the authors, all using data recorded at the Lotung array in Taiwan. Copyright © 2012 John Wiley & Sons, Ltd.