Numerical evaluation of slope topography effects on seismic ground motion

This paper presents results of numerical analyses for the seismic response of step-like ground slopes in uniform visco-elastic soil, under vertically propagating SV seismic waves. The aim of the analyses is to explore the effects of slope geometry, predominant excitation frequency and duration, as well as of the dynamic soil properties on seismic ground motion in a parametric manner, and provide qualitative as well as quantitative insight to the phenomenon. Among the main conclusions of this study is that this kind of topography may lead to intense amplification or de-amplification variability at neighboring (within a few tens of meters) points behind the crest of the slope, especially for high frequency excitations. Nevertheless, a general trend of amplification near the crest and de-amplification near the toe of the slope seems to hold for the horizontal motion. As a result of these two findings, it becomes evident that reliable field evidence of slope topography aggravation is extremely difficult to establish. Furthermore, this study highlights the generation of a parasitic vertical component of motion in the vicinity of the slope, due to wave reflections at the slope surface, that under certain preconditions may become as large as the horizontal. Criteria are established for deciding on the importance of topography effects, while approximate relations are provided for the preliminary evaluation of the topographic aggravation of seismic ground motion and the width of the affected zone behind the crest.     

Site response analyses using downhole arrays at various seismic hazard levels of Singapore

Local site conditions can significantly influence the characteristics of seismic ground motions. In this study, site response analyses using one-dimensional linear elastic (LE), equivalent-linear (EQL) and nonlinear (NL) approaches are performed at different seismic hazard levels of Singapore. Two seismic stations, namely, the KAP and BES stations located at soft soil sites, are selected from the national network of Singapore. Firstly, site response estimates using the LE, EQL (SHAKE04) and NL (DEEPSOIL) approaches are compared with the borehole recordings. Results show favorable matches between the predictions and the observations at the KAP site, while under-predictions are observed for all the three site effect approaches at the BES site. Secondly, the applicability of the LE, EQL and NL models is examined at different hazard levels of Singapore. It is found that for the hazard level at a return period of 475 years, the computed maximum strain (γ_max) is 0.06% and then the EQL model can provide accurate site response predictions. However, for the hazard level at a return period of 2475 years, the calculated γ_max is larger than 2%, resulting in notable differences in the predictions of different site response models. This study highlights the importance of site effects in seismic hazard analysis of Singapore.     

Analysis of the role of diffraction in topographic site effects using boundary element techniques

The role played by the diffraction field on the problem of seismic site effects is studied. For that purpose we solve and analyze simple scattering problems under P and SV in-plane wave assumptions, using two well known direct boundary-element-based numerical methods. After establishing the difference between scattered and diffracted motions, and introducing the concept of artificious and physically based incoming fields, we obtain the amplitude of the Fourier spectra for the diffracted part of the response: this is achieved after establishing the connection between the spatial distribution of the transfer function over the studied simple topographies and the diffracted field. From the numerical simulations it is observed that this diffracted part of the response is responsible for the amplification of the surface ground motions due to the geometric effect. Furthermore, it is also found that the diffraction field sets in a fingerprint of the topographic effect in the total ground motions. These conclusions are further supported by observations in the time-domain in terms of snapshots of the propagation patterns over the complete computational model. In this sense the geometric singularities are clearly identified as sources of diffraction and for the considered range of dimensionless frequencies it is evident that larger amplifications are obtained for the geometries containing a larger number of diffraction sources thus resulting in a stronger topographic effect. The need for closed-form solutions of canonical problems to construct a robust analysis method based on the diffraction field is identified.     

2D equivalent linear site effect simulation: example applications to two deep valleys

In the framework of the Sismovalp European project, an equivalent linear 2D code was developed to compute the response of a valley to SH waves, using the discrete wave-number method proposed by Aki and Larner (Aki K, Larner KL (1970) J Geophys Res 75:5). To overcome the frequency upper bound limitation, the Aki and Larner’s method is combined with a one-dimensional computation using a classical multi-layer method (Aki K, Richards PG (1980) Quantitative Seismology: Theory and Methods, vols. 1 & 2. W.H. Freeman & Co, San Francisco). The so-called “Aki–Larner extended method” is associated to an iterative algorithm, as proposed by Seed and Idriss (Seed HB, Idriss IM (1969) Report No. EERC 70–10, Earthquake Research Center, University of California, Berkeley, California) which accounts for the modulus and damping degradation using a linear visco-elastic model. A comparison of the results in the linear and the equivalent linear cases, for a magnitude 6.0 earthquake, shows that the account for the equivalent linear behaviour of the soil significantly reduces the amplification level, especially at frequencies higher than the fundamental resonance frequency of the site. In the case of site effects or microzonation studies devoted to produce design spectra for engineering structures, this can have a major impact on the associated results and costs, depending on the frequency of interest for the considered structure. As a first application of the developed technique, 2D equivalent linear Aki–Larner computations are used to perform the seismic microzonation study of the upper Rhone valley, in the Visp area (Switzerland), a typical 2D alpine valley. These investigations made it possible to determine site specific spectra, associated with different zones, to be used instead of the code spectra that do not take into account the local 2D amplification.     

深厚场地上特大桥墩-群桩-土相互作用体系地震反应特性的二维和三维分析

本文以某特大型跨江大桥主墩为研究对象,对相应于抗震设防水准为1000a和2500a地震重现期的6条人工地震波,首先采用一维波动模型分析了主桥墩场地的地震动效应,进而,采用二维整体有限元法和三维子结构有限元法对特大桥墩-群桩-土相互作用体系的地震反应进行了数值计算,分析了桩体不同深度处的地震加速度反应峰值、反应谱特征,探讨了深厚软弱场地上特大桥墩-群桩-土动力相互作用效应对群桩地震反应的影响。结果表明：桥墩场地的深厚软弱覆盖层对输入地震波具有明显的滤波和放大效应;由于特大桥墩-群桩-土体动力相互作用的影响,二维和三维计算得到的桩体加速度反应峰值较同高程处的自由场加速度反应大,且两者的频谱特性有显著的差别,群桩加速度反应峰值的空间分布与输入地震波特性有很大关系,不同桩在同一高程处的加速度反应峰值可能相差20％以上;二维和三维地震反应分析结果之间存在一定的差距,群桩中桩体的加速度反应峰值平均相差10％-25％左右,但两种方法得到的加速度反应峰值沿高程的分布具有相似的规律性。     

An equivalent linear algorithm with frequency- and pressure-dependent moduli and damping for the seismic analysis of deep sites

The seismic analysis of soil deposits is most often carried out with an iterative computational scheme, proposed by Seed and Idriss, in which inelastic effects are only approximately modeled through soil degradation curves. Laboratory experimental data indicate that for highly confined materials, the standardized reduction curves commonly used overestimate the capacity of soils to dissipate energy. This paper first presents the results obtained with a simple four-parameter constitutive soil model, which when used to simulate cyclic loading, produces results that agree well with available laboratory experiments for soils under arbitrarily large confining pressures. Thereafter, a frequency- and pressure-dependent iterative algorithm for seismic amplification is proposed, which provides time histories that match well the results obtained with a true non-linear model. Finally, the modified linear iterative analysis is successfully used for the seismic analysis of a 1 km deep model for the Mississippi embayment near Memphis, Tennessee, and a class-A prediction of the seismic amplification in Treasure Island during the Loma Prieta earthquake.     

用双向反应谱比法估计地形对结构反应的影响

基于汶川地震发生时自贡市西山公园地形影响台阵的加速度记录,利用双向反应谱比法分析了山脊地形对单自由度体系结构反应的放大效应,结果表明:(1)水平向结构反应在结构自振频率小于1Hz的低频段放大效应不明显;在1～ 10Hz频段山顶放大效应最大,最大值达3.25,对应频率为6.25Hz;在10 ～ 20Hz频段,各台站放大效应趋于平稳,靠近山顶的7号台站放大效应最明显,最大值为2.3,对应频率为16.7Hz.(2)结构反应的最大放大系数有随高度的增加而增大的趋势,且在1 ～ 10Hz频段这种趋势比较明显.(3)与其它场地效应估计方法相比较,该方法能够体现地形效应对结构反应的影响,从而更有利于研究建筑结构震害的分布.     

用震级和距离参数修正土层反应的等效线性化方法

传统等效线性化波动法主要的缺陷之一,是当基岩输入地震动较强时,高频段算得的频响放大倍率比实际场地的实测结果明显偏低.该缺陷可能导致低估重大工程的设计地震动参数的严重后果,因而是亟待解决的重要问题.本文认为,现行基于土的剪切模量和阻尼比的频率相关性修正等效剪应变的做法有其合理性,但不便应用并可能具有较大的不确定性;由于震级可以影响地震动的频谱特征,通过震级调整等效剪应变的做法也可视为按照频率调整等效剪应变.由于距离与震级一样也可以影响地震动的频谱特征,本文提出通过震级M和距离R参数修正等效线性化的方法EQLM(M,R),并用算例说明,等效线性化方法的上述缺陷可以通过本文提出的EQLM(M,R)方法得到一定程度的改善.     

Regional subsidence of Mexico City and its effects on seismic response

Changes expected in Mexico City's seismic response due to land subsidence caused by groundwater extraction are examined. Settlements of the land surface observed in the recent past are compiled and processed to predict regional subsidence in the near future. This information is used in combination with the iso-depth and iso-period maps stipulated by the building code to estimate the compaction of surface sediments and the shortening of soil periods. The time-progressive evolution of the official seismic zoning maps and the associated site-specific response spectra is predicted. The same is done with spectral response contours expressed in terms of the site and structure periods. The subsidence effects are considered through an impact factor, which represents the increase or decrease in the spectral ordinates with respect to the current values specified for design purposes. The detrimental or beneficial effects depend on the relative values of the structure and site periods.     

土层地震反应等效线性化方法综述

当前土层地震反应分析所用的主要方法是一维等效线性化波动方法。简单阐述了等效线性化方法的基本原理,总结了其发展历程和现状。根据其原理和多年的应用实践,指出了其优点和缺点。其优点主要是概念简单明确,计算量较小,便于工程应用。其缺点主要是该方法本身不能反应地震波在土体传播的真实过程,在工程实践中处理软弱土层和强震动输入时所表现出的一些不合理的地方。并对这些优缺点的机理进行了简要地分析。     

Parametric analysis of the seismic response of a 2D sedimentary valley: implications for code implementations of complex site effects

A detailed 2D model has been constructed and validated for Euroseistest valley, in northern Greece. We take advantage of this model to investigate what parameters, in addition to surface soil conditions (obviously the most important parameter), can be used to correctly characterize site response in a 2D structure. Through a parametric analysis using 2D numerical simulations for SH waves, we explore the differences between the computed ground motion for different simplifications of the valley's structure. We consider variations in the velocity structure within the sediments, and variations of the shape between sediments and bedrock. We also compare the results from different 1D models reflecting current approaches to the determination of site response. Our results show clearly that, in the case of Euroseistest, site response owes fundamentally to its closed basin shape because it is largely controlled by locally generated surface waves. Thus, in terms of predicting site response, a rough idea of its shape ratio and of the average mechanical properties of the sediments are better than a very detailed 1D profile at the central site. Although the details of ground motion may vary significantly between the models, the relative amount of surface waves generated in the 2D models seems to be relatively constant. Moreover, if we quantify the additional amplification caused by the lateral heterogeneity in terms of the ‘aggravation factor’ introduced by Chávez-García & Faccioli [7], a roughly constant factor between 2 and 3 seems to appropriately take into account the effects of lateral heterogeneity. Of course, a correct estimate of the overall impedance contrast is necessary to correctly predict the maximum amplification, a caveat that also applies to 1D models. In this sense, Euroseistest rings an alarm bell. In this valley the more significant impedance contrast lies at about 200 m depth, and it is missed both by consideration of the average shear wave velocity of the first 30 m (the V_s30 criterion) or using the detailed velocity profile down to a depth where a shear wave velocity larger than 750 m/s is found. Our conclusions indicate that, in order to improve current schemes to take into account site effects in building codes, the more to be gained comes from consideration of lateral heterogeneity, at least in the case of shallow alluvial valleys, where locally generated surface waves are likely to be important.     

地形效应对于核电场地地震反应分析影响研究

目前,在进行核电场地安全性评价时,主要采用一维等效线性化程序LSSRLI-1,而一维等效线性化方法在考虑地形效应时有很大的局限性,特别是在研究场地地形效应的影响时偏差较大。对于抗震设计要求远高于一般建筑的核电站来说,选用合适的方法进行二维建模分析是非常必要的。选取了某核电场地典型剖面15个钻孔资料,在MIDAS二维等效线性分析环境下进行了建模,并选取了以年超越概率10^-4合成的地震动中10条最大样本时程作为基底输入进行分析。通过与LSSRLI-1的计算结果进行对比,研究了地形效应对地表和核岛基础处（8.5m）加速度反应谱的影响,并提出了设计建议。分析得出:二维分析中地形效应对地表加速度最大值反应谱的双峰形态影响较大,并且计算结果对AP1000谱的超越情况有所变化;对核岛基础处（8.5m）峰值加速度的影响程度比地表要小,没有表现双峰形态变化较大的形态。     

Non-uniqueness in surface-wave inversion and consequences on seismic site response analyses

Surface-wave tests are based on the solution of an inverse problem for shear-wave velocity profile identification from the experimentally measured dispersion curve. The main criticisms for these testing methodologies are related to the inverse problem solution and arise from the possible equivalence of different shear-wave velocity profiles. In this paper, some implications of solution non-uniqueness for seismic response studies are investigated using both numerical simulations and experimental data. A Monte Carlo approach for the inversion problem has been used to obtain a set of equivalent shear-wave velocity models. This selection is based on a statistical test which takes into account both data uncertainty and model parameterization. This set of solutions (i.e., soil profiles) is then used to evaluate the seismic response with a conventional one-dimensional analysis. It is shown that equivalent profiles with respect to surface-wave testing are equivalent also with respect to site amplification, thus countering the criticism related to inversion uncertainty for the engineering use of surface-wave tests.     

Effects of three-dimensionality on seismic response of Gaussian-shaped hills for simple incident pulses

In this paper the boundary element algorithm which uses the time-convoluted traction kernels is applied to a numerical parametric study on the seismic behavior of three-dimensional Gaussian-shaped hills subjected to vertically propagating incident waves. All calculations were executed in the time-domain and the medium was assumed to have a linear elastic constitutive behavior. Results are discussed in both time and frequency domain with respect to the dimensionless parameters. It was shown that wave length and site geometry, including shape and dimension ratios and, to some extent, wave type are the key independent parameters governing hill amplification behavior. Comparing two- and three-dimensional hills with similar shape ratios, two-dimensional hill had greater characteristic periods, where the three-dimensional hill had greater maximum amplification potential. Three-dimensionality has a strong effect on the seismic responses of the hill; however the rate of seismic response variation with the three-dimensionality factor depends on the shape ratio. It was shown that two-dimensional behavior was dominant in low height three-dimensional hills, however, as the shape ratio increased, three-dimensionality effects appeared and the seismic response of the hill tends toward the axisymmetric three-dimensional hill.     

Site effects in 3D basins using 1D and 2D models: an evaluation of the differences based on simulations of the seismic response of Euroseistest

Site effects are one of the most predictable factors of destructive earthquake ground motion but results depend on the type of model chosen. We compare simulations of ground motion for a 3D model of the Mygdonian basin in northern Greece (Euroseistest) using different approximation for this basin. Site effects predicted using simple 1D models at many points inside the basin are compared to site effects predicted using four different 2D cross sections across the basin and with results for a full 3D simulation. Surface topography was neglected but anelastic attenuation was included in the simulations. We show that lateral heterogeneity may increase ground motion amplification by 100 %. Larger amplification is distributed in a wide frequency range, and amplification may occur at frequencies different from the expected resonant frequencies for the soil column. In contrast, on a different cross section, smaller conversion of incident energy into surface waves and larger dispersion leads to similar amplitudes of ground motion for 2D and 1D models. In general, results from 2D simulations are similar to those from a complete 3D model. 2D models may overestimate local surface wave amplitudes, especially when the boundaries of the basin are oblique to the selected cross section. However, the differences between 2D and 3D site effects are small, especially in regard of the difficulties and uncertainties associated to building a reliable 3D model for a large basin.     

Assessment of expected damage on buildings subjected to Lorca earthquake through an energy-based seismic index method and nonlinear dynamic response analyses

The city of Lorca (Spain) was hit on May 11th, 2011, by two consecutive earthquakes of magnitudes 4.6 and 5.2 M \(_\mathrm{w}\) , causing casualties and important damage in buildings. Many of the damaged structures were reinforced concrete frames with wide beams. This study quantifies the expected level of damage on this structural type in the case of the Lorca earthquake by means of a seismic index \(I_{v}\) that compares the energy input by the earthquake with the energy absorption/dissipation capacity of the structure. The prototype frames investigated represent structures designed in two time periods (1994–2002 and 2003–2008), in which the applicable codes were different. The influence of the masonry infill walls and the proneness of the frames to concentrate damage in a given story were further investigated through nonlinear dynamic response analyses. It is found that (1) the seismic index method predicts levels of damage that range from moderate/severe to complete collapse; this prediction is consistent with the observed damage; (2) the presence of masonry infill walls makes the structure very prone to damage concentration and reduces the overall seismic capacity of the building; and (3) a proper hierarchy of strength between beams and columns that guarantees the formation of a strong column-weak beam mechanism (as prescribed by seismic codes), as well as the adoption of counter-measures to avoid the negative interaction between non-structural infill walls and the main frame, would have reduced the level of damage from \(I_{v}\) \(\,=\,\) 1 (collapse) to about \(I_{v}\) \(\,=\,\) 0.5 (moderate/severe damage).     

中外烈度表“人的感觉”和“器物的反应”对比研究

随着震害经验的积累以及人们对地震认识的深化,不断修改烈度标准,使烈度评定更加客观与科学是地震工程界一直所追求的.人的感觉和器物的反应都是评定一次地震时相应烈度的宏观标志,是烈度表的重要组成部分.鉴于此,本文简要介绍了中国历代地震烈度表(《新的中国地震烈度表》、《中国地震烈度表(1980)》、《中国地震烈度表( 1999...     

Evaluation of site effects on ground motions based on equivalent linear site response analysis and liquefaction potential in Chennai,south India

We study local site effects with detailed geotechnical and geophysical site characterization to evaluate the site-specific seismic hazard for the seismic microzonation of the Chennai city in South India. A Maximum Credible Earthquake (MCE) of magnitude 6.0 is considered based on the available seismotectonic and geological information of the study area. We synthesized strong ground motion records for this target event using stochastic finite-fault technique, based on a dynamic corner frequency approach, at different sites in the city, with the model parameters for the source, site, and path (attenuation) most appropriately selected for this region. We tested the influence of several model parameters on the characteristics of ground motion through simulations and found that stress drop largely influences both the amplitude and frequency of ground motion. To minimize its influence, we estimated stress drop after finite bandwidth correction, as expected from an M6 earthquake in Indian peninsula shield for accurately predicting the level of ground motion. Estimates of shear wave velocity averaged over the top 30 m of soil (V_S30) are obtained from multichannel analysis of surface wave (MASW) at 210 sites at depths of 30 to 60 m below the ground surface. Using these V_S30 values, along with the available geotechnical information and synthetic ground motion database obtained, equivalent linear one-dimensional site response analysis that approximates the nonlinear soil behavior within the linear analysis framework was performed using the computer program SHAKE2000. Fundamental natural frequency, Peak Ground Acceleration (PGA) at surface and rock levels, response spectrum at surface level for different damping coefficients, and amplification factors are presented at different sites of the city. Liquefaction study was done based on the V_S30 and PGA values obtained. The major findings suggest show that the northeast part of the city is characterized by (i) low V_S30 values (<?200 m/s) associated with alluvial deposits, (ii) relatively high PGA value, at the surface, of about 0.24 g, and (iii) factor of safety and liquefaction below unity at three sites (no. 12, no. 37, and no. 70). Thus, this part of the city is expected to experience damage for the expected M6 target event.     

非线性多自由度结构地震反应的共振特性与突变分析

由渐近解法，在主坐标中给出了非线性多自由度结构地震反应的渐近解，利用渐近解计算了共振区振幅-频率响应的一系列数值结果，进而分析了系统参数对共振区反应特性的影响及突变性质。地震反应中表现出来的突变性、共振畸变、“路径”效应等复杂的非线性特性，对结构系统的动力特性有重要影响。     

Topographic effects on seismic response of long-span rigid-frame bridge under SV seismic wave

Seismic ground motions of two neighboring mountains and the free surface between them are calculated under the SV seismic waves with three different incident angles. The results are then taken as the inputs of multi-point seismic excitations for the foundation of a long-span bridge built over the valley in the analysis considering the integrated influence of traveling wave and topography. On the basis of a dynamic analytical method, a finite element model is created for the seismic responses of a four-span rigid-frame bridge of 440 m. The pier-top displacement and the pier-bottom internal force of the bridge are calculated. Then the results are compared with those considering traveling-wave effect only. The conclusions can serve as a seismic design reference for the structures located on the complex mountain topography.