TWO-DIMENSIONAL SCATTERING OF P,SV AND RAYLEIGH WAVES: PRELIMINARY RESULTS FOR THE VALLEY OF MEXICO

A direct boundary element method for calculating the two-dimensional scattering of seismic waves from irregular topographies and buried valleys due to incident P-, SV- and Rayleigh waves is employed to model a section of the Mexico City Valley. The method has been formulated with isoparametric quadratic boundary elements and contains, with respect to previous works in the field, some improvements that are briefly presented. Because the Mexico City Valley is relatively flat and shallow and the contrast of S-waves between the clays and the basement rock is very high, it is believed that the one-dimensional theory is enough to explain the amplification patterns. Although this is true for most sites, results from recent accelerometric data suggest that two- and three-dimensional models are needed to explain the amplification behaviour at some places. In this work, two accelerometric sites have been chosen: Site 84 to probe that the one-dimensional model works well for most sites, and Site TB, as an example of irregular response. The two-dimensional method presented here was used to model a section of the valley where site TB is located, showing that this method yields results closer to the observations than the one-dimensional approach. © 1997 John Wiley & Sons, Ltd.     

Azimuth dependent wave amplification in alluvial valleys

An extension of the indirect boundary element method (IBEM) to three-dimensional scattering by two-dimensional alluvial valleys is presented. While the valley is two-dimensional, the incident plane waves can arrive outside the 2D plane so the scattering is three-dimensional with coupling of P---SV---SH waves. Such a method makes it possible to take earthquake location into account in the estimation of site effects in alluvial valleys. The method is validated by transparency tests, by comparison with 2D simulations, and by comparison with results of other authors. The advantage of the method is that is combines high accuracy with cost-efficiency in terms of computer-time. It is applied to theoretically estimate site effects across a simplified model of an alluvial valley in the French Alps where azimuth dependence of local amplification has been observed. A parametric study with simulations for a range of azimuths and incidence angles shows that (1) the local amplification depends strongly on both azimuth and incidence of the incoming waves, (2) the global pattern of amplification across the valley is very complex for all azimuths, and (3) it is not possible to predict the 3D response of the valley from 2D modeling. Theoretical spectral ratios are in approximate agreement with observed ones for a station in the center of the valley where the local structure justifies use of a simplified model for the comparison.     

A Study on the Influencing Factors on Ground Motion in a Valley Site

A trapezoid valley site is chosen as a research site, and according to numerical models based on orthogonal design, the factors influencing ground motion in the valley site are studied with two-dimensional finite difference method. The influencing factors are ranked, and then the calculation results are verified by ground motion analysis. The conclusions are as follows: there are four factors that have important effects on ground motion of trapezoid valley sites, but the effects are different as the location of sites changes, the influencing factors rank differently with different site locations;The ranking of the influencing factors is the same for all the sites located within a distance of 40m from the valley''s side, among them, the most effective one is the valley slope angle ranks,followed by depth-to-width ratio, overburden thickness, at last the input ground motion intensity. The impact of the factors on surface ground motion is roughly the same in the valley sites within a certain distance to the valley side,and the geometric parameters of the valley terrain play a greater part in influencing ground motion. With the increase of distance away from the valley''s side, the ranking of the influencing factors also changes, the rating of slope angle moves backward, the ranking of the input ground motion and overburden thickness move ahead. The effect of valley geometric parameters on ground motions is gradually weakened, but the effect of other two influence factors are gradually increased, similar to cases of a horizontal layered site. Strong motion records in Anning River valley site were analyzed,and the results show that the valley topography has a significant amplification effect on ground motion, and that the numerical results of this paper are credible.     

平面SH波作用下部分充填圆弧形沉积谷的二维土层和地形放大效应

场地效应通常包含土层放大效应和地形放大效应,为了揭示二者的相对贡献,本文构造了平面SH波作用下部分充填沉积谷的解析模型,借助于区域分解策略,在波函数展开法的框架下,提出了超定方程组解法,得到了部分充填圆弧形沉积谷对平面SH波散射的波函数级数解,而且级数解的收敛测试表明了超定方程组解法的必要性.通过与文献结果进行对比,验证了本文方法的正确性.通过调整解析模型中两个子区域内的材料参数,计算了沉积谷引起的场地放大效应和相应的空河谷引起的地形放大效应.对二维土层与地形效应进行对比分析,结果显示,在沉积谷内二维土层放大效应通常强于地形放大效应,而地形放大效应决定了沉积谷外的地面运动放大形态.针对最大地面运动,进行了沉积谷和相应空河谷的参数分析,进一步描述了二维土层放大效应,研究结果表明二维土层放大效应引起的最大地面运动通常远远大于地形放大效应引起的最大地面运动,并且二维土层效应通常随着土层与基岩的阻抗比的增大而增大,但不是一维土层放大效应与二维地形放大效应的简单线性叠加.      

Two-dimensional nonlinear site response analysis of Adapazarı plain and predictions inferred from aftershocks of the Kocaeli earthquake of 17 August 1999

The objective of this study is to investigate the effects of local site conditions in the Adapazarı plain crossing the severely damaged central part of Sakarya during the 17th August earthquake. A two-dimensional model has been used to obtain the free-field motions in the valley and on surface formations. A preliminary geotechnical profile model developed from available but limited soil data was checked using recordings of some specific locations where a strong ground motion accelerometer array was in operation after the main earthquake. The range of validity of the model was assessed and modifications were made to compare with the actual recorded motions. The purpose of building such a model, which was used to study the aftershocks in Adapazarı, is to provide an improved database to be used for the design of structures in the city. This study also attempts to provide greater insight into the local site response phenomena through the use of a two-dimensional nonlinear analysis. Simulated site responses are in global agreement with the recorded data. In general agreement between the amplification functions of the computed and recorded data is satisfactory for the frequencies of engineering interest. Alluvial sites show amplification factors in the range of 4–6 in the frequencies between 0.6 and 2 Hz. A relatively shallow alluvial station, HASTAHANE, experienced considerable amplification for small aftershocks and deamplification for the strongest aftershock in frequencies between 0.5 and 2 Hz. Another station, TOYOTA, with significant deamplification characteristics and a clearly observed peak response frequency shift at the soil resonant frequency may have experienced soil shear failure during the strongest aftershock. Other alluvial stations, SEKER and GENC, show deamplification characteristics at 0.55 and at around 1 Hz. with the peak frequency shifts during the magnitude 5.8 aftershock. In general, site responses are larger in the alluvial basin for all aftershocks except the magnitude 5.8 event.     

Time-domain two-dimensional site response analysis of non-homogeneous topographic structures by a hybrid BE/FE method

In this paper, an advanced formulation of the time-domain, two-dimensional hybrid finite element–boundary element method (FEM/BEM) is presented, and applied to carry out site response analysis of homogeneous and non-homogeneous topographic structures subjected to incident in-plane motions. Seismic responses of half-plane, horizontally layered site, alluvial valley and ridge sections subjected to incident P and SV waves are analyzed in order to demonstrate the applicability and efficiency of the presented method. The numerical results show that hybrid BE/FE methods require smaller time steps than those needed by BEM schemes. They also show that in case of surface irregularities with height to half-width ratio of up to one, the topography effect could be noticeable, if incident waves have wavelengths of less than approximately eight times the width.     

ENGINEERING PERSPECTIVE FOR THE SEISMIC SITE RESPONSE OF ALLUVIAL VALLEYS

The seismic site response of alluvial valleys with limited width is evaluated using three engineering models. The models are based on the one-dimensional, two-dimensional and the frame model approaches. The objective is to analyse the effects of the main parameters governing surface motions and provide engineering guidance for predicting them. The limitations on the use of the one-dimensional model in site response evaluation in valleys are pointed out. The frame model, which accounts for the limited width of valley, gives response results that are in good agreement with the two-dimensional model results. It is found that the effect of the two-dimensional amplification is significant over a distance from the valley edges beyond which the response may be adequately represented by one-dimensional analysis. The soil amplification varies depending on the soil type, site location relative to the valley and the dominant period and amplitude of input rock record. © 1997 by John Wiley & Sons, Ltd.     

Evaluation of the change in dominant periods in the lake-bed zone of Mexico City produced by ground subsidence through the use of site amplification factors

We compute site amplification functions for several sites in Mexico City using actual accelerograms recorded from 1985 to 2010 and we present field evidence of the change in the dominant period of a given site (T_s) as a consequence of ground subsidence produced by groundwater withdrawal. The changes in T_s are larger in the lake-bed zone where thicker clay deposits exist, although there are sites in the southwest part of the lake-bed zone where T_s has remained constant. With the information obtained from the site amplification functions and available geotechnical soundings we develop an empirical model to estimate the future value of T_s for several sites in Mexico City. Because the practical application of the model requires extrapolation we also present a method to compute the uncertainty of the model when it is used to forecast a future value of T_s at a given site. Our results suggest that significant changes in the dominant period at several sites in Mexico City can be expected in the future.     

Dynamic response of an alluvial valley consists of three types of soil

Dynamic response of an alluvial valley consisting of three different types of soil was studied. In the two-dimensional model, the alluvial valley was assumed to have half-cylindrical shape. The alluvial valley contained three different types of soil with different shapes. The valley was surrounded by a half-space. All of the soil types and the half-space were assumed to be isotropic, homogeneous and linear elastic. The half-space was excited by simple harmonic SH-waves radiated from a strike-slip fault. The fault was assumed to have circular-arc shape in the mathematical model. The governing equations were solved by using wave function expansion method where boundary conditions were relatively simple. In the regions where boundary conditions were more complex, finite difference method was employed. Consequently, the wave propagation problem was solved semi-analytically. The obtained numerical results showed that surface displacement amplitudes are significantly affected by the material properties of the different soil types of the alluvial valley. It was also observed that the shapes of the soil types in the alluvial valley played a considerable role in surface displacements.     

地震动河谷场地效应研究

本文以梯形河谷场地为研究对象,采用二维显式有限差分和透射人工边界理论,根据设计的正交表建立计算模型,计算分析了梯形河谷场地对地震动的影响因素,对其影响程度进行了排名,并采用强震记录分析法对计算结果进行了初步验证。结果表明,4个因素对梯形河谷场地的地表地震动有重要的影响,但是其影响程度随着位置的变化表现也不同,不同位置的影响因素排名不同;距河谷谷坡40m以内的场地,各影响因素排位相同,首位是河谷坡角,其次是深宽比、覆盖层厚度,最后是输入地震动强度,因此,河谷场地距谷坡一定距离时各因素对地表地震动影响程度基本相同,该段场地河谷地形的几何参数对地震动影响起较大作用;随着场地距河谷谷坡越远,影响因素的排位也发生了变化,总体上是坡角排位后移,输入地震动和覆盖层厚度排位前移,河谷几何参数对地震动影响逐渐减弱,覆盖层厚度和输入地震强度2个因素的影响逐渐加大,该段场地对地震动影响与水平成层场地类似。对安宁河河谷场地强震记录分析验证的结果表明,河谷地形对地震动有显著的放大作用,同时也验证了本文的数值模拟结果是可信的。     

Simulation of the seismic response of sedimentary basins with constant-gradient velocity along arbitrary direction using boundary element method:SH case

We presented a boundary element method using the approximate analytical Green's function given by Sánchez-Sesma et al.Coordinate transform is introduced to extend the method to deal with the model with constant-gradient velocity along oblique direction.The method is validated by comparing the numerical results with other independent methods.This method provides a useful tool for analyzing local site effects.We computed seismic response for two series of models.The results in both frequency and time domains are analyzed and show complex amplification patterns.The fundamental mode of resonance is dependent not only on the velocity at the free surface but also on the velocity distribution of the whole basin.For the higher modes of vibration the heterogeneous basin also has its own characteristic.     

Site effects in the Aterno River Valley (L’Aquila,Italy): comparison between empirical and 2D numerical modelling starting from April 6th 2009 Mw 6.3 earthquake

In this paper, we focused our attention on a cross-section of the Aterno River Valley where a good quality geological and geophysical dataset allowed to reconstruct accurately the geometry and the Vs profiles along all the plane of the section. Its trace is deliberately aligned close to the strong motion stations that recorded the Mw 6.3 (April 6th 2009) L’Aquila earthquake. We analysed strong and weak motion data available at these latter stations as well as at one of the temporary stations installed during the Microzonation activities and located on outcropping bedrock, in proximity of the cross-section. We used the H/V technique to select a reliable reference site and once we found it, we applied the SSR technique to compute amplification functions in correspondence of two strong motion stations. In turn, for both sites we performed a site response numerical modelling with two different 2D codes and we compared simulated versus experimental transfer functions. We found that the cross-section is well constrained based on the very reasonable agreement between results of numerical modelling and earthquake data analysis. We pointed out also a strong amplification of the deposit at the centre of the valley due to the constructive interference of S and surface waves, not predictable by means of 1D numerical modelling. We also compared the H/V as well as the SSR obtained from strong motion data with the ones computed from weak motion finding evidences of non-linearity in soil behaviour.     

Seismic site effects by an optimized 2D BE/FE method II. Quantification of site effects in two-dimensional sedimentary valleys

This paper deals with the evaluation of seismic site effects due to the local topographical and geotechnical characteristics. The amplification of surface motions is calculated by a numerical method combining finite elements in the near field and boundary elements in the far field (FEM/BEM). The numerical technique is improved by time truncation. In the first part of this article, the accuracy and the relevance of this optimized method are presented. Moreover, parametric studies are done on slopes, ridges and canyons to characterize topographical site effects. The second part deals with sedimentary valleys. The complexity of the combination of geometrical and sedimentary effects is underlined. Extensive parametrical studies are done to discriminate the topographical and geotechnical effects on seismic ground movement amplifications in two-dimensional irregular configurations. Characteristic coefficients are defined to predict the amplifications of horizontal displacements. The accuracy of this quantitative evaluation technique is tested and discussed.     

A Compatible Single-Phase/Two-Phase Numerical Model: 1. Modeling the Transient Salt-Water/Fresh-Water Interface Motion

Abstract A numerical model (NEWVAR) to simulate the transient movement of a discrete interface between salt water and fresh water has been developed. NEWVAR is designed to allow the analysis of a regional two-dimensional ground-water flow in coastal aquifers. The numerical solution permits the prediction of both regional fresh-water levels and two-dimensional fresh-water/salt-water interface by using nested square meshes.
The numerical solution is based on the finite-difference method; the Gauss-Jordan direct method is used for solving steady- and unsteady-state linear equations. Different procedures are used to avoid numerical difficulties in the transient position of the interface toe for two-dimensional areal flow.
The numerical solution was tested against the analytical ones for the cases of an advancing interface and of a floating fresh-water lens over sea water. These tests showed good agreement, thus verifying the finite-difference approximation. The results of an application of this model to a real aquifer are discussed in a companion paper entitled: "A Compatible Single-Phase/Two-Phase Numerical Model 2. Application to a Coastal Aquifer in Mexico."     

Seismic site effects by an optimized 2D BE/FE method I. Theory, numerical optimization and application to topographical irregularities

This paper deals with the evaluation of seismic site effects due to the local topographical and geotechnical characteristics. The amplification of surface motions is calculated by a numerical method combining finite elements in the near field and boundary elements in the far field (FEM/BEM). The numerical technique is improved by time truncation. In the first part of this article, the accuracy and the relevance of this optimized method are presented. Moreover, parametric studies are done on slopes, ridges and canyons to characterize topographical site effects. The second part deals with sedimentary valleys. The complexity of the combination of geometrical and sedimentary effects is underlined. Extensive parametrical studies are done to discriminate the topographical and geotechnical effects on seismic ground movement amplifications in two-dimensional irregular configurations. Characteristic coefficients are defined to predict the amplifications of horizontal displacements. The accuracy of this quantitative evaluation technique is tested and discussed.     

A numerical study on the 2D behavior of clayey basins

In this numerical study the effects of basin edge on the dynamic behavior of the clayey basins are investigated. For this purpose a range of bedrock inclinations at the valley sides from slighter 10° and 20° to steeper 30° and 40°, and three types of stiff, medium plasticity and soft clay materials are selected. The results of the 2D analyses show that not only the amplification pattern of different clay types is different, but also it differs for each material type under different motion intensities. Also, the frequency domain results show that different parts of the valleys are sensitive to different periods. It was seen that under two-dimensional conditions the amplification of clay types other than soft clay could be higher. Finally, the results of this research show the important effect of motion intensity on the 2D behavior of valleys.     

弹性层状半空间中沉积谷地对入射平面SH波的放大作用

对Wolf理论进行拓展,使之可解决沉积谷地对波的散射问题,进而利用间接边界元法,求解了弹性层状半空间中沉积谷地对入射平面SH波的放大作用问题。通过自由场反应分析,求得假想边界上各点的位移和各单元的应力反应。施加虚拟均布荷载,求得位移和应力的格林函数。根据应力和位移连续边界条件确定虚拟分布荷载,将自由场反应和虚拟分布荷载产生的反应叠加起来,即得到问题的解答。最后,以基岩上单一土层中沉积谷地对入射平面SH波的放大作用为例进行了数值计算分析,结果表明,层状半空间中沉积谷地和均匀半空间中沉积谷地对波的放大作用存在显著差别。文中分析了造成差别的原因,并讨论了覆盖层厚度和刚度对放大作用的影响。     

Three-dimensional response of a layered cylindrical valley embedded in a layered half-space

An indirect boundary integral method to obtain the three-dimensional response of an infinitely long, layered, viscoelastic valley of arbitrary cross-section embedded in a layered viscoelastic half-space is presented. The valley is excited by homogeneous plane waves impinging at an oblique angle with respect to the axis of the valley. The method and associated computer programs are tested by comparison with available results in the limiting two-dimensional case of incidence normal to the axis of the valley. Additional comparisons with previous three-dimensional results obtained by a hybrid finite element-boundary integral method for cylindrical valleys subjected to obliquely incident waves show large differences. However, the results obtained here for an infinitely long valley appear to be in some agreement with earlier results for an elongated prolate semi-ellipsoidal valley and with results obtained by a discrete wavenumber boundary element approach. An extensive bibliography on the dynamic response of valleys is also presented.     

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.     

Local amplification of deep mining induced vibrations part.2: Simulation of ground motion in a coal basin

This work investigates the impact of deep coal mining induced vibrations on surface constructions using numerical tools. An experimental study of the geological site amplification and of its influence on mining induced vibrations has already been published in the previous paper (Part 1: Experimental evidence for site effects in a coal basin). Measurements have shown the existence of an amplification area in the southern part of the basin where drilling data have shown the presence of particularly fractured and soft stratigraphic units. The present study, using the boundary element method (BEM) in the frequency domain, first investigates canonical geological structures in order to get general results for various sites. The amplification level at the surface is given as a function of the shape of the basin and of the velocity contrast with the bedrock. Next, the particular coal basin previously studied experimentally (Driad-Lebeau et al. [1]) is modeled numerically by BEM. The amplification phenomena characterized numerically for the induced vibrations are found to be compatible with the experimental findings such as: amplification level, frequency range and location. Finally, the whole work was necessary to fully assess the propagation and amplification of mine induced vibrations. The numerical results quantifying amplification can also be used to study other coal basins or various types of alluvial sites.