The plurality effect of topographical irregularities on site seismic response

Topography can have significant effects on seismic ground response during an earthquake because topographic irregularities cause considerable differences between the seismic waves emitted by the source and the waves reaching the ground surface. When a seismic motion happens in a topographically irregular area, seismic waves are trapped and reflected between the topographic features. Therefore, the interaction between topographies can amplify seismic ground response. In order to reveal how interaction between topographies influences seismic response, several numerical finite element studies have been performed by using the ABAQUS program. The results show that topographic features a greater distance between the seismic source and the site would cause greater seismic motion amplification and is perceptible for the hills far away from the source and the ridges. Also, site acceleration response is impacted by surrounding topography further than site velocity and displacement response.     

Slope topography effects on ground motion in the presence of deep soil layers

An extensive investigation has been made into the interaction between topographic amplification and soil layer amplification of seismic ground motion. This interaction is suggested in the literature as a possible cause for the differences between topographic amplification magnitudes observed in field studies and those obtained from numerical analysis. To investigate this issue a numerical finite element (FE) parametric study was performed for a slope in a homogeneous linear elastic soil layer over rigid bedrock subjected to vertically propagating in-plane shear waves (Sv waves). Analyses were carried out using two types of artificial time history as input excitation, one mimicking the build-up and decay of shaking in the time histories of real earthquake events, and the other to investigate the steady-state response. The study identified topographic effects as seen in previous numerical studies such as modification of the free-field horizontal motion, generation of parasitic vertical motion, zones of alternating amplification and de-amplification on the ground surface, and dependence of topographic amplification on the frequency of the input motion. For the considered cases, topographic amplification and soil layer amplification effects were found to interact, suggesting that in order to accurately predict topographic effects, the two effects should not be always handled separately.     

Regional seismic responses of shallow basins incorporating site‐city interaction analyses on high‐rise building clusters

This study assesses the 3D amplification effects in shallow basins and quantifies the effects of site‐city interaction (SCI) on high‐rise buildings. A regional‐scale 3D spectral element simulation is conducted on the Tuen Mun‐Yuen Long basin, which contains multiple subbasins with heterogeneous and nonlinear soil profiles, while 3D city models with various building layouts are fully integrated into the basin model for our SCI study. We found a good correlation between spectral amplification factors and soil depths. Site response is significantly amplified at basin edges and centers due to surface waves generated at basin edges and the focusing effects stemming from 3D basin geometry. Transfer functions of 3D basins can be up to fourfold at fundamental frequencies as compared to 1D response, and further amplifications occur at high frequencies due to surface waves. In the SCI simulations, we observe wave trapping in the open space amid buildings resulting in energy concentration and up to twofold PGA amplifications. The wave trapping effect diminishes as the space between buildings increase beyond their range of influence (～100 m). The SCI analyses show that destructive kinetic energy in superstructures increases 28% in one horizontal direction but decreases 22% in the other. Our study concluded that, 1D site response analysis can significantly underestimate the seismic demand in shallow basins. Site‐city interaction of high‐rise buildings increases the short‐period spectra of ground motions, leading to an increase in their story accelerations by up to 50% and to a substantial decrease in the seismic safety of short structures in their vicinity.     

三维复杂山地多级次群推进迎风混合法多波型走时计算

三维复杂山地条件下的各种地震波型的走时计算技术,可以直接用于复杂山地区域地震波运动学特性的分析、地震数据采集观测系统的设计以及直接基于三维复杂地表的地震数据处理技术的研发.为了在三维复杂地表条件下准确、灵活且稳定地计算各种地震波型的走时,提出一种多级次群推进迎风混合法.该算法利用不等距迎风差分法简洁稳定地处理三维复杂地表及附近的局部走时计算问题,利用计算精度不错的迎风双线性插值法处理绝大部分均匀正方体网格中的局部走时计算问题,利用群推进法模拟三维复杂地表条件下地震波前的扩展问题,利用多级次算法处理各种类型的地震波的走时计算问题.算法分析和计算实例表明:新方法具有很好的计算精度与效率,且能灵活稳定地处理三维复杂地表复杂介质条件下的多波型走时计算问题.     

Coupling of topographic and stratigraphic effects on seismic response of slopes through 2D linear and equivalent linear analyses

In this paper the seismic response of simple slope geometries under vertically propagating in-plane shear waves (SV waves) is assessed through two-dimensional finite element analyses to investigate the amplification of the ground motion induced by soil topography. Topographic horizontal and vertical amplification factors were evaluated through different sets of analyses focused on slopes in homogeneous half space and on slopes overlying either a rigid or a compliant bedrock. Soil was assumed to behave as a linear visco-elastic or as an equivalent-linear visco-elastic material. In the analyses the effects of slope inclination and of the characteristics of the input motion were also investigated.In order to calibrate the numerical model, the results obtained in linear visco-elastic analyses were compared with the results of parametric numerical analyses available in the literature, showing a good agreement. The results confirmed that a complex interaction exists between stratigraphic and topographic effects on the amplification of the ground motion and that the two effects cannot be evaluated independently and easily uncoupled. In the case of compliant bedrock the effect of the impedance ratio was also investigated.The results of the equivalent-linear analyses pointed out the remarkable dependence on soil non-linear behavior and, when compared to the results of linear visco-elastic analyses, showed that without accounting for soil non-linear behavior, topographic amplification factors may result underestimated.     

Three-dimensional dynamic soil–structure interaction analysis in the time domain

A new numerical procedure is proposed for the analysis of three-dimensional dynamic soil–structure interaction in the time domain. In this study, the soil is modelled as a linear elastic solid, however, the methods developed can be adapted to include the effects of soil non-linearities and hysteretic damping in the soil. A substructure method, in which the unbounded soil is modelled by the scaled boundary finite-element method, is used and the structure is modelled by 8–21 variable-number-node three-dimensional isoparametric or subparametric hexahedral curvilinear elements. Approximations in both time and space, which lead to efficient schemes for calculation of the acceleration unit-impulse response matrix, are proposed for the scaled boundary finite-element method resulting in significant reduction in computational effort with little loss of accuracy. The approximations also lead to a very efficient scheme for evaluation of convolution integrals in the calculation of soil–structure interaction forces. The approximations proposed in this paper are also applicable to the boundary element method. These approximations result in an improvement over current methods. A three-dimensional Dynamic Soil–Structure Interaction Analysis program (DSSIA-3D) is developed, and seismic excitations (S-waves, P-waves, and surface waves) and externally applied transient loadings can be considered in analysis. The computer program developed can be used in the analysis of three-dimensional dynamic soil–structure interaction as well as in the analysis of wave scattering and diffraction by three-dimensional surface irregularities. The scattering and diffraction of seismic waves (P-, S-, and Rayleigh waves) by various three-dimensional surface irregularities are studied in detail, and the numerical results obtained are in good agreement with those given by other authors. Numerical studies show that the new procedure is suitable and very efficient for problems which involve low frequencies of interest for earthquake engineering. Copyright © 1999 John Wiley & Sons Ltd     

单体边坡地形的地震动力响应及其放大效应的数值分析

本文采用隐式动力有限单元法研究了不同的边坡角度和边坡高度对地形放大效应的影响,并以位移峰值放大系数为衡量地震动放大效应的标准,计算了不同边坡角度和边坡高度条件下的地震响应,在此基础上对模型关键监测点的输出波形以及位移峰值放大系数的变化趋势进行了分析,获得了不同监测点处的地震动时程曲线,揭示了坡角和坡高对单体边坡地震动放大效应的定量作用规律。数值结果表明,相同高度处坡面监测点的水平向位移峰值放大系数大于坡内监测点的,地形放大效应在水平方向具有趋表效应。由于坡面存在入射波和反射波的叠加,因此竖直向位移峰值放大系数的最大值出现在坡体内部。      

Comparison of 3D, 2D and 1D numerical approaches to predict long period earthquake ground motion in the Gubbio plain, Central Italy

In this work we studied the performance of different numerical approaches to simulate the large amplifications of long period earthquake ground motion within the Gubbio plain, a closed-shape intra-mountain alluvial basin of extensional tectonic origin in Central Italy, observed during the Umbria-Marche 1997 seismic sequence. Particularly, referring to the Sep 26 1997 M_w6.0 mainshock, we considered the following numerical approximations: (a) 3D model, including a kinematic model of the extended seismic source, a layered crustal structure, and the basin itself with a simplified homogeneous velocity profile; (b) 2D model of a longitudinal and transversal cross-section of the basin, subject to vertical and oblique incidence of plane waves with time dependence at bedrock obtained by the 3D simulations; (c) 1D model. 3D and 2D numerical simulations were carried out using the spectral element code GeoELSE, exploiting in 3D its implementation in parallel computer architectures. 3D numerical simulations were successful to predict the observed large amplification of ground motion at periods beyond about 1 s, due to the prominent onset of surface waves originated at the southern edge of the basin and propagating northwards. More specifically, the difference of 3D vs 2D results is remarkable, since the latter ones fail to approach such large amplification levels, even when an oblique incidence of plane waves is considered.     

局部山体地形对强地面运动的影响研究

基于曲线网格有限差分方法研究了地震波在不同坡度的山体地形及水平地表模型中的传播,得到了各模型速度波形及地表峰值速度特征,从地形自身特征及震源特征两方面出发讨论了地形效应:一是相同的震源模型下地形坡度、形状对地震动的影响;二是同一山体模型下地震动对不同震源机制的点源以及相对复杂的有限断层的响应.主要结论如下:(1)一般情况下,地形放大效应在坡度较大的地方比较明显,并随着坡度的增加而增大,但在某些特定情况下,放大效应与坡度并不满足正相关,且这种情况的发生与震源性质无关,可能仅受地形形态自身的影响;(2)对于不同的震源机制,地面运动各分量受地形影响程度不同,总体上水平分量受地形影响程度更大;(3)震源机制和震源激发的波的频率会影响放大效应最大值出现的位置,放大效应最大值不一定出现在山顶处,有可能会出现在起伏地形的震源对侧,出现位置可能与波的相互作用有关;(4)有限断层模型下,地面运动特征相对更为复杂,地形效应不仅受断层模型几何特征的影响,同时断层破裂过程对其也有着重要的影响.     

2013年6月2日台湾南投地震强地面运动模拟

2013年6月2日台湾省南投县发生一次里氏6.5级地震,这次地震是最近几年内发生的最大的一次地震,台湾大部分地区以及中国大陆东南沿海城市均有明显震感.为了更深入的理解此次地震的地震波能量传播过程以及强地面运动过程,本文采用三维有限差分方法对此次地震的强地面运动过程进行了模拟.结果显示,台湾中央山脉起伏的地形对此次地震的强地面运动分布特征具有较大的影响,出现了比较明显的地形放大效应;此外,台湾的平原和盆地中的沉积层也对地震波有较强的放大效应.     

Effect of irregular structural configuration on floor acceleration demand in hill‐side buildings

A suite of reinforced‐concrete frame buildings located on hill sides, with 2 different structural configurations, viz step‐back and split‐foundation, are analyzed to study their floor response. Both step‐back and split‐foundation structural configurations lead to torsional effects in the direction across the slope due to the presence of shorter columns on the uphill side. Peak floor acceleration and floor response spectra are obtained at each storey's center of rigidity and at both its stiff and flexible edges. As reported in previous studies as well, it is observed that the floor response spectra are better correlated with the ground response spectrum. Therefore, the floor spectral amplification functions are obtained as the ratio of spectral ordinates at different floor levels to the one at the ground level. Peaks are observed in the spectral amplification functions corresponding to the first 2 modes in the upper portion of the hill‐side buildings, whereas a single peak corresponding to a specific kth mode of vibration is observed on the floors below the uppermost foundation level. Based on the numerical study for the step‐back and split‐foundation hill‐side buildings, simple floor spectral amplification functions are proposed and validated. The proposed spectral amplification functions take into account both the buildings' plan and elevation irregularities and can be used for seismic design of acceleration‐sensitive nonstructural components, given that the supporting structure's dynamic characteristics, torsional rotation, ground‐motion response spectrum, and location of the nonstructural components within the supporting structure are known, because current code models are actually not applicable to hill‐side buildings.     

Numerical modeling of zero-offset laboratory data in a strong topographic environment: results for a spectral-element method and a discretized Kirchhoff integral method

Accurate simulation of seismic wave propagation in complex geological structures is of particular interest nowadays. However conventional methods may fail to simulate realistic wavefields in environments with great and rapid structural changes, due for instance to the presence of shadow zones, diffractions and/or edge effects. Different methods, developed to improve seismic modeling, are typically tested on synthetic configurations against analytical solutions for simple canonical problems or reference methods, or via direct comparison with real data acquired in situ. Such approaches have limitations, especially if the propagation occurs in a complex environment with strong-contrast reflectors and surface irregularities, as it can be difficult to determine the method which gives the best approximation of the “real” solution, or to interpret the results obtained without an a priori knowledge of the geologic environment. An alternative approach for seismics consists in comparing the synthetic data with high-quality data collected in laboratory experiments under controlled conditions for a known configuration. In contrast with numerical experiments, laboratory data possess many of the characteristics of field data, as real waves propagate through models with no numerical approximations. We thus present a comparison of laboratory-scaled measurements of 3D zero-offset wave reflection of broadband pulses from a strong topographic environment immersed in a water tank with numerical data simulated by means of a spectral-element method and a discretized Kirchhoff integral method. The results indicate a good quantitative fit in terms of time arrivals and acceptable fit in amplitudes for all datasets.     

北部湾软土吹填场地不同地下水位动力响应研究

为了探究不同地下水位的场地条件下对吹砂填海场地动力响应的影响,以广西北部湾吹砂填海场地为研究对象,基于FLAC3D软件结合前期室内试验结果建立了场地模型,进行了数值模拟分析。在此研究中着重分析地下水位的变化对场地加速度放大系数、加速度反应谱和地震液化效应的影响,为减轻吹砂填海建设场地的震害程度提供参考依据。结果表明:随着地下水位埋深的增加,地表加速度放大系数呈现出逐渐减小的趋势,地震放大作用主要集中在短周期,卓越周期也在短周期处取得;随着地下水位埋深的减小,地震波高频成分被过滤,低频成分被放大,场地特征周期与卓越周期均有增大趋势;地下水位变化对吹填沙土层液化的产生和发展具有显著的影响,随着地下水位的上升,砂土表现出更强的液化效应,并且液化现象随着地震峰值加速度的增大逐渐沿土层深部发展。     

地震动参数对斜坡加速度动力响应规律的影响

2008年‘5.12’汶川大地震诱发斜坡地质灾害在空间分布上表现出了明显的高程效应和岩性效应。本文采用上硬下软和上软下硬两种典型岩性组合斜坡模型,完成了1:100比尺的振动台试验。文中重点分析了地震波类型(频谱)、激振方向和地震动三参数对斜坡模型水平向加速度动力响应规律的影响。分析结果表明:(1)水平单向激振时,15Hz正弦波和汶川地震波作用下的高程放大效应主要体现在斜坡模型中上段,两者在上软下硬组合斜坡模型中产生了近乎相同的水平向加速度动力响应规律,原因主要在于两者的卓越频率接近。(2)模型对合成向汶川地震波的放大作用依次超过单向水平向和竖直向汶川波的作用,且合成向与水平单向汶川地震波的作用规律基本相同。(3)随着振动强度增加,模型对低频波的放大作用增强。(4)在合成向汶川地震动作用下,随着振动强度增加,模型各高程处的水平向加速度峰值(PGA)逐渐增加,其相应的放大系数在模型中上段逐渐降低至2.0以下,最终趋于平缓,表明模型沿高程向的放大效应逐渐减弱。此外,各参数对模型的水平向加速度响应因模型自身的岩性组合结构而异,随着振动强度增加,上硬下软斜坡模型中上部的水平向速度响应值基本保持在1.0～2.7倍于上软下硬斜坡模型中上部的水平向加速度响应值这一水平。     

SH波垂直入射下的斜坡地形放大因子分析

现有大量观测记录表明:斜坡地形对地震波的传播有着非常强烈的影响。为服务于工程抗震设计,基于显式有限元方法,定量分析SH波垂直入射下二维斜坡地形的地震动响应与斜坡角度、土层厚度以及介质阻抗比的关系,总结了位于一维土层基本频率附近斜坡上台面各区域放大因子的变化规律。研究表明:（1）斜坡面对SH波的反射使二维斜坡地形的放大倍数较一维土层存在显著放大,且该现象在缓坡中更加明显。（2）当土层厚度为斜坡高度的1/4,介质阻抗比为0.368,坡度为30°时,放大因子在距坡顶1.67倍斜坡高度处取到最大值1.930。（3）斜坡覆盖土层薄时,放大因子受斜坡角度的影响大,斜坡覆盖土层厚时,阻抗比成为影响放大因子的主要因素。（4）分别考虑土层厚度、斜坡角度、介质阻抗比以及观测点位置对二维斜坡地形地表地震动响应的影响,取1倍斜坡高度作为区域间隔,统计每个区域内各参数对应的放大因子最大值,对比现有规范给出工程抗震设计参考值及放大因子大于1的基频比范围。     

Directional dependence of site effects observed near a basin edge at Aegion,Greece

We study site effects using 520 weak motion earthquake records from a vertical array in Aegion, Greece. The array is inside a basin, has four stations in soil, and one in bedrock (178 m depth). The site is marked by high seismicity and complex surface geology. We first use the records to establish the downhole accelerometer orientations and their evolution with time. Then we estimate site effects using empirical spectral ratios with and without a reference site (standard and horizontal-to-vertical spectral ratio). We find significant site amplification which cannot be accounted for by 1D model predictions, along with a significant difference in the amplification level between the two horizontal components. These are indications of 2D effects, namely surface waves generated at the basin edge. The difference in amplification between the horizontal components is maximised when these are rotated with respect to the orientation of the basin edge. The strongest amplification takes place in the direction parallel to the basin edge (SH, or out-of-plane motion), and is up to 2 times higher than in the perpendicular direction (SV, or in-plane motion). This directional effect on the amplification is corroborated by numerical 2D modelling using incident SH and SV waves, with the former possibly generating strong Love waves. In the records, the directionality is clear for windows containing the largest amplitudes of the records (S waves and strong surface waves), while it tends to vanish for coda-wave windows. This directionality is also observed when using response spectral ratios rather than Fourier ratios. We compute soil-to-rock amplification factors for peak ground acceleration (PGA) and find it is significantly higher than what is predicted by current design codes. We attribute this difference to the basin edge amplification, linear soil behaviour, and to the inability of simple scalar values like PGA to describe complex amplification effects. Finally, we analyse the earthquake records at a surface station near the slope crest and do not observe significant topographic amplification.     

Seismic ground amplification by unlined tunnels subjected to vertically propagating SV and P waves using BEM

Recent researches have revealed that the seismic ground response above tunnels can be different from the free-field motion during earthquakes. Nevertheless, to the best of the authors׳ knowledge, neither building codes nor seismic microzonation guidelines have yet considered this matter. In the present study, the seismic response of a linear elastic medium including a buried unlined tunnel subjected to vertically propagating incident SV and P waves are addressed. For analysis purposes, a numerical time-domain analysis is performed by utilizing a robust numerical algorithm working based on the boundary element method. It is observed that the amplification of the ground surface underlain by a tunnel is increased in long periods. The variation of the amplification factor and characteristic period of the medium versus the buried depth of the tunnel are depicted as the major results of this study. Some simple and useful relations are proposed for estimating the seismic microzonation of the areas underlain by tunnels. These relations can also be used for the preliminary seismic design of structures located on underground structures.     

Ground motion amplification by cylindrical valleys embedded in a layered medium

The phenomenon of localized amplification of seismic waves due to subsurface irregularities has attracted the attention of seismologists and engineers for many years. In this paper we present a hybrid numerical method to investigate the ground motion amplification due to sedimentary basins. This method combines the integral representation and the finite element to solve the scattering problem due to an arbitrary cylindrical scatterer. A study is done on two shapes of valleys to show the effect of the angle of incidence, the incident wave type and the layering on the amplification of the surface displacement components by different valleys.     

Nonlinear numerical assessment of the seismic response of hillside RC buildings

Major damage has been reported in hilly areas after major earthquakes,primarily because of two special conditions:the variation in the seismic ground motion due to the inclined ground surface and the irregularities caused by a stepped base level in the structure.The aim of this study is to evaluate possible differences in the responses of Chilean hillside buildings through numerical linear-elastic and nonlinear analyses.In the first step,a set of response-spectrum analyses were performed on four simplified 2D structures with mean base inclination angles of 0°,15°,30°,and 45°.The structures were designed to comply with Chilean seismic codes and standards,and the primary response parameters were compared.To assess the seismic performance of the buildings,nonlinear static(pushover)and dynamic(time-history)analyses were performed with SeismoStruct software.Pushover analyses were used to compare the nonlinear response at the maximum roof displacement and the damage patterns.Time-history analyses were performed to assess the nonlinear dynamic response of the structures subjected to seismic ground motions modified by topographic effects.To consider the topographic modification,acceleration records were obtained from numerical models of soil,which were calculated using the rock acceleration record of the Mw 8.01985 Chilean earthquake.Minor differences in the structure responses(roof displacements and maximum element forces and moments)were caused by the topographic effects in the seismic input motion,with the highly predominant ones being the differences caused by the step-back configuration at the base of the structures.High concentrations of shear forces in short walls were observed,corresponding to the walls located in the upper zone of the foundation system.The response of the structures with higher angles was observed to be more prone to fragile failures due to the accumulation of shear forces.Even though hillside buildings gain stiffness in the lower stories,resulting in lower design roof displacement,maximum roof displacements for nonlinear time-history analyses remained very close for all the models that were primarily affected by the drifts of the lower stories.Additionally,vertical parasitic accelerations were considered for half the time-history analyses performed here.The vertical component seems to considerably modify the axial load levels in the shear walls on all stories.     

3D Response analysis of an instrumented hill at Matsuzaki, Japan, by a spectral method

Strong ground motion observed at an instrumented hill site is first analysed through the standard (SSR) and the horizontal-to-vertical (HVSR) spectral ratio techniques. A reasonable agreement is found between these approaches. The observations are then compared with 3D numerical simulations, performed with a highly efficient numerical code based on a spectral method, that allowed for reasonable computer times also on a PC. The observed amplification is significantly higher than that computed with a 3D homogeneous model of the mountain, suggesting that local response is governed by large-scale and small-scale soil heterogeneities rather than by topographic site effects. The introduction of a local near-surface inclusion of nonhomogeneous soil material under one of the recording stations has not significantly improved the numerical results. The observed data are also compared with the results of simplified simulations, either using 2D homogeneous models or coupling the 3D response with a 1D local soil profile. The results of such simplified approaches are discussed and their usefulness is emphasised.