A comparative study on linear and nonlinear site response analysis

Site response analysis is usually the first step of any seismic soil-structure study. Geotechnical earthquake engineers and engineering geologist have been trying to find both practical and most appropriate solution techniques for ground response analysis under earthquake loadings. The paper attempts to give a critical overview of the field of site response analysis. In this paper, the influences of nonlinearity on the site response analysis summarized and were evaluated with a numerical example. Site response of a two layered soil deposit with the assumption of linear and rigid base bedrock (or viscoelastic half-space) was analyzed by using linear and nonlinear approaches. The amplification spectrum of the soil column is computed between the top and the bottom of this soil deposit. Nonlinear analysis was compared with the linear method of analysis. Steps involved in ground response analyses to develop site-specific response spectra at a soil site are briefly summarized. Some of the well-known site response analysis methods are summarized and similarities and differences between linear and nonlinear methods are compared by a numerical example.     

液化自由场地震响应大型振动台模型试验分析

开展了含上部黏土层、饱和砂土层、密实砂土层的可液化自由场地在水平地震动激励下的大型振动台模型试验研究,分析了地震动激励时饱和砂土液化后场地加速度、位移、孔压比时空响应等动力响应。试验结果表明：在小震激励时,场地动力反应较小,加速度反应自下而上不断放大,各深度处孔压比均较小,模型地基整体处于弹性反应阶段;0.3g汶川地震卧龙台地震记录输入时,孔压积累迅速,可液化土体最上部土层孔压比达到1,饱和土体液化,模型地基表现出明显的非线性反应特征,加速度反应在饱和砂土层中未有明显放大,土体卓越周期对应的反应加速度自下而上有不断增大趋势。该研究是土-群桩-上部结构体系大型振动台系列试验中可液化自由场动力反应部分,可供今后做对比分析和验证数值模拟参考。     

Physical and Numerical Modeling of Seismic Soil-Structure Interaction in Layered Soils

The structural response of buildings subjected to seismic loads is affected by local site conditions and the interaction between the structure and the supporting soil media. Seismic centrifuge model tests were conducted on two layered clay soil profiles at 80 g field to investigate soil-structure interaction and dynamic response of foundation. Several earthquake-like shaking events were applied to the models using an electro-hydraulic shaking table to simulate linear and nonlinear soil behavior. Results showed that the foundation input motion was significantly amplified in both models, especially for weak earthquake motions. Seismic soil-structure interaction was found to have an important effect on structure response by increasing the amplification of foundation input motion. A 3D finite difference numerical model was also developed to simulate the response of centrifuge model tests and study the parameters that affect the characteristics of earthquake at the base of the structure. The results indicated that the stiffness and stratification of the soil profiles had a significant effect on modifying the foundation input motion.     

Nonlinear Analysis of Local Site Effects on Seismic Ground Response in the Bam Earthquake

The influence of local geologic and soil conditions on the intensity of ground shaking is addressed in this study. The amplification of the ground motion due to local site effects resulted in severe damage to dwellings in the Bam area during the 2003 Bam Earthquake. A unique set of strong motion acceleration recordings was obtained at the Bam accelerograph station. Although the highest peak ground acceleration recorded was the vertical component (nearly 1 g), the longitudinal component (fault-parallel motion) clearly had the largest maximum velocity as well as maximum ground displacement. Subsurface geotechnical and geophysical (down-hole) data in two different sites have been obtained and used to estimate the local site condition on earthquake ground motion in the area. The ground response analyses have been conducted considering the nonlinear behavior of the soil deposits using both equivalent linear and nonlinear approaches. The fully nonlinear method embodied in FLAC was used to evaluate the nonlinear soil properties on earthquake wave propagation through the soil layer, and compare with the response from the equivalent linear approach. It is shown that thick alluvium deposits amplified the ground motion and resulted in significant damage in residential buildings in the earthquake stricken region. The comparison of results indicated similar response spectra of the motions for both equivalent and nonlinear analyses, showing peaks in the period range of 0.3–1.5 s. However, the amplification levels of nonlinear analysis were less than the equivalent linear method especially in long periods. The observed response spectra are shown to be above the NEHRP building code design requirements, especially at high frequencies.     

Evaluation of a nonlinear seismic geotechnical site response analysis method subjected to earthquake vibrations (case study: Kerman Province, Iran)

Equivalent static load and dynamic analyses methods are usually used for designing structures under and subjected to earthquake excitations. Estimation of site response from an earthquake is fundamental step to anticipate the possible damages and then to try to mitigate them. In this paper, the effect of nonlinearity on site response analyses summarized and evaluating ground surface response taking into account the local soil and subsurface soils properties for the proposed bridge over the river at Sirdjan Boulevard road subjected to earthquake vibration and provokes with assumption of rigid (viscoelastic) and elastic half space bedrock and quantify the site effect on the surface over a number of geotechnical areas has been notified. First, by field investigation, the required data were collected and by primary processing the acceptable data were selected. Then, in nonlinear analysis, for elastic and rigid half space bedrock, standard hyperbolic model was selected and executed, and then the results were compared to each other. The critical point of this work was to develop and use a computer code by the authors, named the “Abbas Converter”, with several advantages, such as work and quick installation, operating as a connecter function between the used softwares and generating the input data corresponding to defined format for them. Its output results can easily be exported to the other used softwares in this study. This code can make and render this study more easily than the previous softwares have done, and take over the encountered problem. This study clearly showed the applicability of the “Abbas Converter” for evaluation of site response with bedrock-type assumption on soil behavior under the earthquake excitations. The proposed scheme is used to analyze the ground motion data from the Bam earthquake in Kerman Province, Iran (2003, M_w 6.5).     

Factors affecting site response to multi-directional earthquake loading

This paper presents an investigation into various factors that may affect the ground response to multi-directional earthquake loading, focusing mainly on the behavior of vertical ground motion and its relation with the horizontal counterpart. The factors investigated herein include the intensity of input motion and the associated soil nonlinearity, the location of input motion (rock outcrop versus bedrock), the variation of water table, and the damping property of soil. Influence of these factors is studied on the characteristics of site amplification in both vertical and horizontal directions, the response spectra of vertical and horizontal ground surface motions, the spectral ratio between the two components (V/H) at the ground surface, and the distributions of stresses and strains in the ground. One of the main results is that varying water table can bring about a significant impact on vertical motion and the relationship between vertical and horizontal motions. The surface response spectral ratio (V/H) can largely exceed the rule-of-thumb value of 2/3 at low periods with lowering the water table, but does not appear to be substantially affected at long periods.     

Evaluation of ground motion characteristics,effects of local geology and liquefaction susceptibility: the case of Itea,Corinth Gulf (Greece)

In the present paper we analyze the effect of local geology on ground motion by means of numerical calculations (numerical models) using total (TS) and effective stress (ES) methods. These numerical calculations have been applied to the site of Itea, Corinth Gulf, which was chosen based on liquefaction susceptibility criteria and field inspection. Data from seismic refraction experiments and cone penetration test N-values as well as selected records of ground motion in nearby areas were used to construct the input file for the numerical model. By means of␣dynamic analysis such characteristics of ground motion as acceleration time histories, response spectra, and amplification function were evaluated. A one-dimensional soil amplification effect was clearly shown. Liquefaction probability at the Itea site was predicted based on the safety factor and the calculation of the induced settlement at the test site. Results of the TS and ES modeling lead us to conclude: (1) the presence of soft soil at Itea caused significant amplification (almost 2.5-fold higher magnitude) of the underlying bedrock motion and, therefore, can contribute to damage; (2) the area of Itea is highly susceptible to liquefaction due to presence of silty sand deposits at depths between 2.48 m (the position of the water table) and 12 m that demonstrate the rapid growth of the excess pore water pressure (EPWP) ratio with an increase in peak ground acceleration values.     

场地土对基岩峰值加速度放大效应分析

通过实际土层地震反应结果的统计分析和强震加速度观测结果的对比, 讨论了不同场地条件对基岩峰值加速度的放大效应及其特点。该分析可为地震动参数区划图编制和地震安全性评价中场地效应的估计、由基岩地震动估算场地地面地震动提供参考。     

远场大地震作用下大尺度深软场地的非线性地震效应分析

基于ABAQUS软件自行研制的并行计算显式算法集群平台,针对苏州城区典型地层剖面,建立了大尺度深软场地的二维精细化非线性有限元分析模型,对人工地震波和大地震远场地震动作用下深软场地的非线性地震效应进行了比较研究。研究结果表明：（1）与人工地震波作用时深软场地的地表峰值加速度放大效应相比,大地震远场地震波作用时的放大效应尤为显著,由于土介质的横向不均匀性及其非线性,使不同地表的峰值加速度放大效应存在明显的变异性。（2）深软场地对周期小于0.3 s的高频地震波均具有显著的滤波效应;大地震远场地震波作用时,深软场地对周期0.85～1.65 s的长周期地震波的放大效应非常显著,但对2.5～7.0 s的长周期地震波呈现出明显的滤波效应。（3）地震动峰值加速度PGA值沿土层深度和横向的分布形态呈现出明显的高低起伏现象,在不同成因的土层更迭面附近及土介质横向不均匀性显著的区域,地震波的局部聚焦放大和过滤减小现象尤为明显,且大地震远场地震动作用时,20 m以浅土层的PGA值呈现出非常显著的放大效应。（4）地震波的频谱特性、土层的横向不均匀性对深软场地地表加速度反应谱? 谱的谱形有显著影响;给出了描述加速度反应谱沿土层深度变化特征的三维谱形曲线,可以直观地展示出深软场地中细长地下结构地震反应可能存在类共振现象的土层深度。     

Equivalent-Linear Seismic Ground Response Analysis of Some Typical Sites in Mumbai

Any earthquake event is associated with a rupture mechanism at the source, propagation of seismic waves through underlying rock and finally these waves travel through the soil layers to the particular site of interest. The bedrock motion is significantly modified at the ground surface due to the presence of local soil layers above the bedrock beneath the site of interest. The estimation of the amplifications in ground response due to the local soil sites is a complex problem to the designers and the problem is more important for mega cities like Mumbai in India, where huge population may get affected due to devastations of earthquake. In the present study, the effect of local soil sites in modifying ground response is studied by performing one dimensional equivalent-linear ground response analysis for some of the typical Mumbai soil sites. Field borelog data of some typical sites in Mumbai city viz. Mangalwadi site, Walkeswar site, BJ Marg near Pandhari Chawl site are considered in this study. The ground responses are observed for range of input motions and the results are presented in terms of surface acceleration time history, ratio of shear stress to vertical effective stress versus time, acceleration response spectrum, Fourier amplitude ratio versus frequency etc. The typical amplifications of ground accelerations considering four strong ground motions with wide variation of low to high MHA, frequency contents and durations are obtained. Results show that MHA, bracketed duration, frequency content have significant effects on the amplification of seismic accelerations for typical 2001 Bhuj motion. The peak ground acceleration amplification factors are found to be about 2.50 for Mangalwadi site, 2.60 for Walkeswar site and 3.45 for BJ Marg site using 2001 Bhuj input motion. The response spectrum along various soil layers are obtained which will be useful for designers for earthquake resistant design of geotechnical structures in Mumbai for similar sites in the absence of site specific data.     

Ground motion amplification due to shallow cavities in nonlinear soils

Subsurface cavities or stiff inclusions represent mechanical discontinuities for seismic waves propagating in soils. They modify the propagation pattern of seismic waves and alter soil response in correspondence to the ground level or building foundations. In the literature, different analytical and numerical solutions have been proposed to account for the effect of underground cavities or inclusions on the motion generated by P, S or R waves. In these former studies, the subsoil was assimilated to a homogeneous, isotropic and linear elastic halfspace containing one or more cavities. In the present study, the effect of subsurface cavities on ground motion amplification has been analysed accounting for soil stiffness degradation and associated damping increase with increasing levels of shear strains, a fundamental aspect of soil behaviour under earthquakes. The analysed model was inspired to a real case represented by the village of Castelnuovo (Italy), which during the 2009 Abruzzo earthquake suffered huge damage. The main shock (6 April 2009) caused the collapse of 50 % of the whole built environment. The historical centre of Castelnuovo rises on a hill. In its subsoil, there are many cavities with roofs 2–3 m below the ground level. The longitudinal NW–SE section of the hill has been investigated by 2D nonlinear site response analyses. A preliminary site response analysis was performed without modelling cavities, to identify ground motion amplification due to mere stratigraphic and topographic factors. The numerical model was later refined inserting: (1) a single cavity below the hilltop, (2) multiple cavities placed below the ground surface of the hill and (3) multiple cavities filled with concrete (inclusions). The performed study highlights the important role exerted by underground cavities on the ground motion computed at the hill surface. This effect should be properly considered for both microzonation studies and the correct determination of the seismic actions on specific buildings.     

Three‐dimensional inverse analyses of a deep excavation in Chicago clays

Numerical models are commonly used to estimate excavation‐induced ground movements. Two‐dimensional (2D) plain strain assumption is typically used for the simulation of deep excavations which might not be suitable for excavations where three‐dimensional (3D) effects dominate the ground response. This paper adapts an inverse analysis algorithm to learn soil behavior from field measurements using a 3D model representation of an excavation. The paper describes numerical issues related to this development including the generation of the 3D model mesh from laser scan images of the excavation. The inverse analysis to extract the soil behavior in 3D is presented. The model captures the measured wall deflections. Although settlements were not sufficiently measured, the predicted settlements around the excavation site reflected strong 3D effects and were consistent with empirical correlations. Copyright © 2010 John Wiley & Sons, Ltd.     

Impact of Higher Frequency Content of Input Motion Upon Equivalent Linear Site Response Analysis for the Study Area of Delhi

While travelling through the subsoil layers, earthquake generated bedrock motions get modified significantly due to local soil and should be quantified using ground response analysis. Present study concentrates on equivalent linear method of site response analysis in SHAKE2000 software. It is a frequency based analysis tool having default frequency set to 15 Hz. While due consideration is given to amplitude, no to very limited information about the frequency content of the input motion to be considered in ground response analysis is available. In the present work, the effect of the maximum frequency of ground motion in site response analysis using SHAKE2000 is examined. Two sets of analyses are carried out in this work based on 30 globally recorded input motions. In the first analyses, input motion up to 15 Hz maximum frequency, which is a default value in SHAKE2000 is considered while second analyses are based on considering each of the 30 input motions up to the Nyquist frequency. Comparing the results from the two sets of analyses highlight that selection of maximum frequency in SHAKE2000 has considerable effect in ground motion amplification at different depths. As a result, even the peak ground acceleration which controls the building behavior and damage scenario, is going to change considerably even in case same input motion is used in the analysis.     

桩柱结构在地震作用下非线性响应研究

基于试验基础上建立的经典弹塑性模型--剑桥模型能够准确描述正常固结土的应力-应变关系。当土体的应力历史上经历过卸载或受到循环交变荷载作用即进入超固结状态,它作为土的应力历史的反映,相比正常固结土受力特性有着显著的差异。为研究超固结因素对土体加载特性的影响,在引入能考虑超固结状态影响的下负荷面剑桥模型后,通过三轴压缩和剪切试验对处于超固结状态下土体的受力特性进行了对比分析,并对循环剪切加载下的应力-应变关系以及超固结比的演化规律进行了研究。结果表明,下负荷面剑桥模型能准确反映超固结因素对土体力学特性的影响,相比原状土有着更高的屈服强度。而通过数值模拟自由场地基在地震作用下的动力响应可以看出,超固结因素对地基的动力响应起到了不可忽略的影响,尤其在强震下更需要考虑其影响。在自由场地基地震动力响应基础上,通过对桩柱结构桩-土耦合系统在地震作用下非线性动力响应的模拟对土体非线性以及超固结因素的影响进行了对比研究,研究表明：土体的非线性因素能显著降低结构振动响应中的高频成分,由于土体在交变加载下很快进入超固结状态,相对于剑桥模型,下负荷面剑桥模型在考虑超固结因素后土体的承载性能显著提高,尤其在强震作用下超固结因素带来的影响更加明显,因此,建议对桩基结构物地震响应研究考虑超固结因素影响,以提高桩基结构物地震响应模拟的精确度和可靠性。     

汶川地震远场黄土场地地震动场地放大效应机制研究

通过汶川地震震后科学考察发现,汶川地震局部场地的震害和地震动放大效应明显,地震对甘肃省境内远离震中的黄土地区造成了较为严重的破坏。在此基础上,结合钻孔波速测试,运用二维等价线性时程响应动分析法对甘肃省平凉市典型黄土塬进行了地震动力响应计算,分析了该地区局部场地条件对地震动放大效应的影响。研究发现,黄土塬具有地震动放大效应,随着塬高的增加,加速度、速度、位移均出现放大效应;随着地震动在黄土覆盖层中的传递,卓越频率向低频移动,高频成分被吸收,加速度反应谱中长周期分量逐渐增大。数值计算结果与实际震害基本吻合,其结果对黄土地区进行合理的抗震设防具有一定的科学意义。     

Site-specific earthquake response study for hazard assessment in Kolkata city,India

The assessment of local site effects on seismic ground motions is of great importance in earthquake engineering practice. Several destructive earthquakes in the past have demonstrated that the amplification of ground motion and associated damage to structures due to local site conditions is a significant consideration in earthquake hazard analysis. A recent paper published in this journal highlights the hazard posed by earthquakes in the megacity of Kolkata in India due to its seismic and geological settings. The seismic hazard assessment study speculates that the deep alluvial deposit in the city may increase the seismic hazard probably due to the amplification of the seismic energies. This paper focuses on the seismic response studies of the various soil strata (i.e. for local subsurface conditions) obtained from various construction sites in the city for predicted earthquake. It is very well recognized that site response studies (a part of seismic microhazard zonation for urban areas) are the first step towards performance-based foundation design or seismic risk analysis and mitigation strategy. One of the problems for carrying out site-specific study in Kolkata is the lack of recorded strong motion data in the city. Hence, this paper outlines a methodology to carry out site-specific study, where no strong motion data or seismic data are available. The methodology uses wavelet-based spectrum compatibility approach to generate synthetic earthquake motions and equivalent linear method for seismic site response analysis. The Mega City of Kolkata has been considered to explain the methodology. Seismic hazard zonation map by the Bureau of Indian Standards classifies the City of Kolkata as moderate seismic zone (Zone III) with a zone factor 0.16. On the other hand, GSHAP(Global Seismic Hazard Assessment Program) map which is based on 10% probability of exceedance in 50 years specifies a maximum peak ground acceleration (PGA) of 1.6 m/s² (0.163 g) for this region. In the present study, the seismic response has been carried out based on GSHAP. The results of the analysis indicate the amplification of ground motion in the range of 4.46–4.82 with the fundamental period ranging from 0.81 to 1.17 s. Furthermore, the maximum spectral accelerations vary in the range of 0.78–0.95 g.     

刚度和阻尼频率相关的等效线性化方法

在实际工程中发现,在强地震动作用下等效线性化方法低估了地表地震动的峰值加速度反应。通过与场地效应竖向台阵观测记录的对比分析证实了这一现象,其主要原因是等效剪应变水平的取值高于高频段实际剪应变水平,从而抑制了土层地震反应中的高频成份。若干分析表明,动力反应过程中土体的剪应变是随频率而变化的,且试验表明土体的刚度和阻尼是与剪应变相关的,据此假设土体刚度和阻尼是与频率相关的。基于这一假设,对传统等效剪应变的选取如何使得土层对基底地震动输入中的高频成分产生滤波效应的原理进行探讨,且通过频率相关的等效线性化方法对该原理进行证明。将该方法应用于Port Island场地效应竖向台阵的分析,并与实际地震动记录进行了对比,结果表明,较之传统等效线性化方法,能更加合理地考虑地震动输入中的高频成分。     

天津软土场地对地震动参数的影响

天津市区的场地条件为很厚而松软的第四纪沉积物,覆盖层较厚,地貌属海积—冲积平原,对地震动参数的影响很大。本文以海河东岸的天津嘉里中心工程场地为例,通过场地地震动效应分析,研究场地特征对地震动的影响。结果表明,土层地震反应分析得到的地震动峰值和反应谱与GB50011-2001《建筑抗震设计规范》的规定有明显的差别,抗震设计中的根据场地类别调整地震动的方法不足以完全描述场地地震反应特性,也难以反映天津厚软土场地的实际情况。可以认为,对于天津软土场地,采用经场地土层地震动效应分析所得地震动参数更为合理安全。     

覆盖层上土石坝非线性动力响应分析的地震波动输入方法

较多已建和待建的土石坝直接修筑于覆盖层上,合理描述土石坝与覆盖层之间的动力相互作用对大坝抗震安全评价至关重要。基于等效荷载和人工边界的地震波动输入方法能较好地反映出结构-地基之间的相互作用并得到了广泛应用。等效荷载和人工边界参数在均质线弹性地基条件下易于获得,而对于覆盖层地基,土体动力非线性特性给求解带来很大困难。鉴于此,首先根据覆盖层侧向边界的位移模式,发展了能高效、精确地获取多向地震动垂直入射时均质或成层覆盖层自由场非线性动力响应的简化模型;结合能动态实时获取地基材料参数的非线性人工边界,发展了一套覆盖层上土石坝非线性动力响应分析的地震波动输入方法。算例表明,发展的地震波动输入方法可大大减小计算网格量,并能较好地反映覆盖层对地震动频谱特性的影响且具有较高的精度。     

Evaluation of local site effects on earthquake damages of Fatih Mosque

Fatih Mosque and its Kulliye (complex) are one of the most important historical monuments in Istanbul. Since it has been built between 1463 and 1470, Fatih Mosque had been subjected to nine strong earthquakes and suffered various degrees of structural damage at every case, including the latest August 17, 1999 Kocaeli Earthquake (M_w = 7.4, epicentral distance approximately 100 km). Recently, a project has been initiated first to study the possible causes of earthquake damage and then develop retrofitting and strengthening techniques to protect this invaluable monument from further damages in the future earthquakes. As part of this investigation, local site soil conditions had been determined and site behavior during earthquakes had been studied in detail. In this paper, the results of 1-D site response analysis, which included convolution and deconvolution analyses utilizing the strong ground motions recorded during the August 17, 1999 Kocaeli Earthquake are presented. The results of the analyses had demonstrated the considerable degree of site amplification, compatible with the recorded motions and the damage suffered. The expected site behavior during a probable future earthquake is also studied using a site specific simulated bedrock motion, and earthquake parameters to be used in dynamic structural analysis are estimated.