Seismic analysis of semi-sine shaped alluvial hills above subsurface circular cavity

In this study, a seismic analysis of semi-sine shaped alluvial hills above a circular underground cavity subjected to propagating oblique SH-waves using the half-plane time domain boundary element method (BEM) was carried out. By dividing the problem into a pitted half-plane and an upper closed domain as an alluvial hill and applying continuity/boundary conditions at the interface, coupled equations were constructed and ultimately, the problem was solved step-by-step in the time domain to obtain the boundary values. After solving some verification examples, a semi-sine shaped alluvial hill located on an underground circular cavity was successfully analyzed to determine the amplification ratio of the hill surface. For sensitivity analysis, the effects of the impedance factor and shape ratio of the hill were also considered. The ground surface responses are illustrated as three-dimensional graphs in the time and frequency domains. The results show that the material properties of the hill and their heterogeneity with the underlying half-space had a significant effect on the surface response.

     

相邻地形对地震动特性的影响分析

基于采用透射人工边界的显式动力有限元方法,研究了相邻凸起地形对地震动反应谱特性的影响,分析了相邻凸起之间距离的变化对地形效应的影响。研究结果表明：1）与单一凸起地形对地震动的放大效应相比,相邻地形的存在对地震动反应谱谱比曲线的形状影响不大,但是却对谱比的值具有较大影响,而且其影响程度的大小与地表观测点的位置有关;2）相邻凸起地形的存在对凸起平台段中点地震动高频成分的放大效应具有较大影响,随着相邻凸起之间距离的增大,该影响效应逐渐减弱,多个相邻凸起构成的组合地形对地震动的放大效应逐渐接近单一凸起地形。     

三维分层流动过双山脉地形激发的大气船舶重力波动力学理论和数值试验

利用我们建立的三维分层线性理论计算模式和中尺度数值模式ARPS, 分别研究了三维分层流动过双山脉地形产生的三维线性和非线性山脉重力波和大气船舶的结构特征及其形成机制.线性理论计算结果表明三维三层流动过双山脉地形时,两个山脉各自强迫出一个发散模态的山脉背风波,在第二个山脉背风面,三维三层流动过双山脉地形可以强迫出两个发散模态的拦截背风波,大大加强了对大气环流的拖曳作用.非线性数值模拟结果表明,流动过山所产生的非线性山脉重力波和大气船舶完全不同于三维分层线性理论计算模式所产生的山脉重力波和大气船舶的结构和特征,由于分层流体之间的非线性相互作用,三维三层流动过双山脉地形时,可在第二个山脉背风面激发4个发散模态的拦截背风波. 三维三层流动过双山脉地形所强迫的山脉重力波和大气船舶,具有同三维三层流动过孤立山脉所产生的山脉重力波和大气船舶完全不同的结构和特征,三维流动过双山脉地形对两个山脉之间的距离表现出极大的敏感性.对于相距较远的两个山脉,流动过双山脉所强迫的山脉重力波表现为4个发散模态的拦截背风波,波动的能量相对于相距较近的两个山脉能传播到更高的高度.     

山谷地形对入射SV波地震反应分析

基于黏弹性人工边界的显式动力有限元方法,研究了突出平台状山谷地形场地的地形效应,分析了山谷地形对地表地震动的影响.结果表明:(1)沿着地震动输入方向地表反应较其他方向上的反应强烈;(2)与单一凸起山体地形对地表地震动的放大效应相比,相邻地形的存在对地表地震动位移傅里叶谱谱比曲线的形状影响不大,但是对PGD有着较大的影响...     

Experimental study of seismic behavior of two hilly sites in Tehran and comparison with 2D and 3D numerical modeling

Two hilly sites were selected to study seismic site response due to topography effects. The sites were selected in a manner to be as much as possible homogenous and free of the soft soil layers effects. The hills were instrumented by nine velocimetric stations to record microtremors and the obtained data were analyzed using horizontal to vertical spectral ratios. Some standard spectral ratio tests were performed on noise as well. Then the instrumented hills were modeled (both 2D and 3D) assuming a linear elastic constitutive behavior subjected to vertically propagating SV and P Ricker wavelets. All calculations were performed in time domain using direct boundary element method. Different transfer function components, amplification patterns and spectral ratios were calculated in frequency domain. The frequency of vibration, obtained by experimental studies, is between 4 and 5 Hz for both of the hills. The spectral ratios derived by numerical simulations were compared with the observed spectral ratios. They show relatively good similarities between the results of these two methods. The frequencies of vibration derived from different methods seem to be nearly identical. The agreement in term of resonance frequency between microtremors and numerical modeling suggests that noise measurements could represent a simple, even if preliminary, tool in order to identify possible topographic amplification.     

Surface motion of a semi-cylindrical hill for incident plane SV waves： Analytical solution

Introduction Scattering of incident waves by local topographies is one of the most attractive topics in the field of engineering seismology. They can be resolved by either a numerical method or an analyti-cal method. The numerical methods include finite difference method, finite element method, boundary element method, etc. The analytical method is the wave function expansion method. Al-though numerical methods can be used for arbitrary-shaped topographies, the analytical solutions are still …     

Interactions between topographic irregularities and seismic ground motion investigated using a hybrid FD-FE method

A hybrid method combining finite element and 4th-order finite difference techniques is developed to model SH and P-SV seismic wave propagation in a 2D elastic medium with irregular surface topography. Both the classic staggered grid finite difference scheme and the partially staggered grid scheme are tested. The accuracy of the hybrid method is studied by comparison with a semi-analytical and another numerical method. Subsequently, to study the amplification, numerical simulations of seismic wave propagation in a series of hills are carried out and compared with the single-hill case. Depending on the position of the source in relation to the topography, the ratio between the heights and lengths of the hills or the ratio between the lengths of the hills and the wavelength, the presence of several hills as opposed to a single one can increase the amplification effect due to topography. This study highlights the fact that, when evaluating topographic site effects, surrounding topography must be taken into account in addition to local topography.     

On terrain corrections in terrestrial heat flow

The theory of heat-flow variation over a Lees-type hill is well known for evaluating terrain effects on terrestrial heat flow. However, a hill cannot be converted into a valley by simply changing the sign of one of the terrain-defining parameters, nor can several Lees' hills be superposed to simulate a series of hills and valleys for correcting a terrain-induced disturbance of heat flow. The proper derivations for a Lees-type valley are presented and the superposition is compared with analytic solutions for two parallel semi-cylindrical valleys and two semi-spherical basins embedded in an otherwise planar ground. Generally, heat flux climaxes over central valleys or basins, and dips toward their margins where rapid change in topography occurs. Variation of heat flux induced by a three-dimensional terrain is relatively large, as compared to two-dimensional features, but its areal extent is relatively limited. The two-dimensional effects also extend relatively deeper. In applying two-dimensional algorithms to a three-dimensional terrain, the correction may be over- or underestimated depending on the distance from a borehole to prominent terrain features in the surrounding area.     

平面SV波入射下半圆凸起地形地表运动解析解

采用波函数展开法,并借助辅助函数思想,给出了平面SV波入射下半圆凸起地形地表运动的一个解析解,并对解答的收敛性和截断计算精度进行了检验;最后通过若干算例分析了入射频率和入射角度以及凸起地形宽度对地表运动的影响. 数值结果表明,凸起地形对入射SV波具有显著的放大作用, 该放大作用可达自由场的4倍以上. 当入射频率较低时, 位移峰值多位于半空间地表; 而当入射频率较高时,位移峰值多位于凸起地形表面.      

黄土边坡动力响应分析

运用有限差分软件FLAC3D,建立了某一黄土边坡三维模型,首先对其在地震作用下的动力响应规律进行了总结,然后探讨了地震动参数对黄土边坡动力响应的影响。结果表明：黄土边坡对地震波存在垂直放大和临空面放大作用;当输入地震波振幅或频率增加时,坡面监测点加速度放大系数随坡高增加呈＂增加→衰减→增加＂的三段形态;速度放大系数随坡高的增大而增大,并在坡顶达到最大值;位移放大系数随振幅和频率的增加而增加;地震持时对加速度、速度峰值的影响不大,但坡体位移随持时的增加而显著增加。强震作用下的最大剪应变增量区域的位置和形状表明,黄土边坡的破坏模式仍是沿着某一弧形潜在滑动面失稳破坏。研究结果有助于进一步揭示黄土边坡在地震作用下的失稳机制,为黄土地区边坡抗震设计与防灾减灾提供参考。     

The effectiveness of trenches in reducing seismic motion

The effect of placing barriers in the travel path of P, SV and SH seismic waves has been studied using time-domain solutions of plane-strain finite element programs for two-dimensional crustal models. The wavefields considered propagate parallel to the free surface of an elastic medium consisting of a single layer over a halfspace. Barriers take the form of open-air trenches. Effects of damping are assessed by considering representative viscoelastic conditions. Computations are presented as the ratio of spectral energy observed at a point with the barrier system in place in the model to the spectral energy observed at the same point without the barrier system in the model. These spectral ratios are dependent upon the direction of wave propagation. The calculations brought to light the marked role of surficial layering and attenuation properties of the surface rocks or soils on the effectiveness of seismic trench barriers. Barrier models without these features cannot in general reliably predict seismic wavefields at the surface. In the range of cases studied, trench depth d rather than width is the most sensitive parameter. When the ratio d/λ, the ratio of trench depth to the wavelength of shear waves, is greater than about 0·6, power spectral ratios of 0·06 and less are found for SH waves and the vertical component of SV motion for frequencies of 4–6 Hz. By contrast, for frequencies less than 3–4 Hz, power spectral ratios from unity to about two and greater are observed, indicating amplification for the horizontal component of wave motion. Spectral ratios calculated at some locations in front of the barrier system show over two-fold amplification. Spectral ratios also change significantly with the relative location of the free surface observation point.     

三维沉积盆地对地震动的放大效应间接边界元法模拟

基于一种高精度间接边界元法(IBEM), 实现了沉积盆地三维地震响应的频域、 时域精细求解, 并以半空间中椭球形沉积盆地对平面P波和SV波的散射为例, 着重探讨了入射角度、 入射波型、 入射频率、 盆地长宽比和深宽比对沉积盆地地震动放大效应的影响规律． 结果表明: 盆地形状对地震波的放大效应和空间分布状态具有显著影响, 且具体规律受控于入射波频段． ① 随着盆地深度增大, 盆地边缘面波发育更为充分, 在较宽频段内均会出现显著的地震动放大效应, 且深盆地的放大区域集中于盆地中部． ② 圆形盆地对地震波的汇聚效应最为显著, 而狭长盆地对地震波的汇聚作用相对较弱, 高频情况下可在盆地内部形成多个聚焦区域． ③ 不同波型入射下, 盆地对地震动放大效应的机制有所差异: P波入射下, 竖向位移放大主要是由于盆地边缘面波由四周向中部汇聚所致; SV波入射下, 边缘面波汇聚效应相对较弱, 而当盆地较深时, 底部透射体波和边缘面波易形成同相干涉从而显著放大地震动． 按盆地内外介质波速比为1/2, P波和SV波垂直入射下频域最大放大倍数分别为25和15, 时域放大倍数约为4.0和3.7(雷克子波)． ④ 低频波入射下, 位移从盆地中部向边缘逐渐减小, 且浅层沉积盆地对地表位移幅值的放大作用不明显． ⑤ P波和SV波的入射角度对盆地地震动放大幅值及空间分布特征也具有显著影响．      

钢筋混凝土空心桥墩的振动台试验研究

为研究空心桥墩的抗震性能及影响参数,对9个不同配筋率、配箍率和轴压比的试件进行振动台试验。研究了不同性能量化参数对破坏现象、加速度响应、动力放大系数、延性和耗能等的影响。结果表明:轴压比和配筋率较小时,裂缝开展较多且位置距墩底相对偏高。增大配筋率,加速度响应、动力放大系数和位移延性系数增大,耗能减小;轴压比的影响与配筋率相反。增大配箍率,加速度响应和动力放大系数减小,位移延性系数和试件耗能增大。可为矩形空心桥墩的抗震设计提供参考。     

A new boundary element solution to evaluate the geometric effects of the canyon site on the displacement response spectrum

This paper presents a step-by-step procedure using the three-dimensional boundary element approach to study the behavior of semi-circular canyons under seismic shear waves. The boundary element code TDASC allows utilization for various canyon geometries, evaluation of concurrent seismic waves and calculation of the ground motions on canyons due to an excitation at any arbitrary point of the incident field. Considering the widening ratio of the canyon(including prismatic, semi-prismatic and non-prismatic canyons), wave characteristics(wavelength, dimensionless period, direction) and maximum amplification pattern, the solution was applied to carry out a series of parametric studies. It was shown that canyon form can significantly affect the displacement amplification, especially at the points located on its edges. By increasing the wave dimensionless frequency(η 1), the amplification pattern becomes more complex. On the basis of the results from a variety of considered cases, a new expression has been presented for the limiting wavelength beyond which the widening of the canyon will not have a major effect on the displacement amplification. To verify the reliability of the proposed approach, the obtained results, expressed in terms of displacement amplitude, were compared with those from the available published literature and a reasonably good agreement was observed.     

Scattering of plane sh waves by a semi-cylindrical hill

A new analytical method is presented to study the problem of scattering of plane SH waves by a semi-cylindrical hill in an otherwise homogeneous, isotropic and elastic two-dimensional half-space, using the series of wave functions and a new expansion technique. The results obtained show that (1) the hill has quite considerable effects on ground motions for both the points on the hill and its environs, (2) these effects depend mainly on the frequency, the angle of wave incidence and the ratio of radius of hill to one-half the wave length of incident waves, and (3) prominent and depression topographies having equal form and radius for the same incident waves would cause quite different mechanisms of wave propagation in both response performance and magnitude. The results, doubtless, would be useful for further deepening knowledge of the effects of prominent topography on seismic ground motion and for testing the accuracy of various approximate methods so far available.     

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.     

Seismic ground motion amplification pattern induced by a subway tunnel: Shaking table testing and numerical simulation

A series of 1 g shaking table tests, followed by the numerical simulations, is performed to investigate the effect of a circular subway tunnel on the ground motion amplification pattern. Effects of various parameters, including shear wave velocity of soil, frequency content of input motion, flexibility ratio and tunnel depth on the amplification pattern is investigated. Experimental study revealed that the tunnel did not affect free field response at dimensionless period greater than 10. Subsequent parametric study demonstrated that the amount of amplifications were mainly controlled by dimensionless period, dimensionless depth and flexibility ratio. Tunnel effect on the amplification pattern is more prominent for dimensionless period between 3 to 10, flexibility ratio greater than 1 and dimensionless depth less than 3. The study revealed that subway tunnel influences the seismic response of low period buildings, constructed above the tunnel.     

Analytic wave series solution of out-of-plane(SH) waves diffraction by an almost semi-circular shallow cylindrical hill

A closed-form wave equation analytic solution of two-dimensional scattering and diffraction of outof-plane(SH) waves by an almost semi-circular shallow cylindrical hill on a flat, elastic and homogeneous half space is proposed by applying the discrete Fourier series expansions of sine and cosine functions. The semi-circular hill problem is discussed as a special case for the new formulated equation.Compared with the previous semi-circular cases solutions, the present method can give surface displacement amplitudes which agrees well with previous results. Although the proposed equation can only solve the problem of SH-waves diffracted by almost semi-circular shallow hills, the stress and displacement residual amplitudes are numerical insignificantly everywhere. Moreover, the influences of the depth-towidth ratio(a parameter defined in this paper to evaluate the shallowness of the topography of hills) on ground motions are presented and summarized. The limitations and errors of truncation from Graf's addition theorem and Fourier series equations in the present paper are also discussed.     

The effect of glaciation on the intensity of seismic ground motion

Seismicity is known to contribute to landscape denudation through its role in earthquake‐triggered slope failure; but little is known about how the intensity of seismic ground motions, and therefore triggering of slope failures, may change through time. Topography influences the intensity of seismic shaking – generally steep slopes amplify shaking more than flatter slopes – and because glacial erosion typically steepens and enlarges slopes, glaciation may increase the intensity of seismic shaking of some landforms. However, the effect of this may be limited until after glaciers retreat because valley ice or ice‐caps may damp seismic ground motions. Two‐dimensional numerical models (FLAC 6.0) were used to explore how edifice shape, rock stiffness and various levels of ice inundation affect edifice shaking intensity. The modelling confirmed that earthquake shaking is enhanced with steeper topography and at ridge crests but it showed for the first time that total inundation by ice may reduce shaking intensity at hill crests to about 20–50% of that experienced when no ice is present. The effect is diminished to about 80–95% if glacier ice level reduces to half of the mountain slope height. In general, ice cover reduced shaking most for the steepest‐sided edifices, for wave frequencies higher than 3 Hz, and when ice was thickest and the rock had shear stiffness well in excess of the stiffness of ice. If rock stiffness is low and shear‐wave velocity is similar to that of ice, the presence of ice may amplify the shaking of rock protruding above the ice surface. The modelling supports the idea that topographic amplification of earthquake shaking increases as a result of glacial erosion and deglaciation. It is possible that the effect of this is sufficient to have influenced the distribution of post‐glacial slope failures in glaciated seismically active areas. Copyright © 2012 John Wiley & Sons, Ltd.     

基于台阵记录的土层山体场地效应分析

选取2008年5月25日至8月7日期间由甘肃省文县上城山地形效应台阵获取的12次汶川地震余震事件(M_S≥4.0),在分析其地震动基本参数的基础上,采用参考场地谱比(RSSR)法和水平-竖向谱比(HVSR)法,研究了不同地震作用下上城山地形台阵的场地效应.分析结果显示:随着高程和覆盖层的增加,记录台站地震动的PGA呈增大趋势,地震频谱形状由宽变窄;上城山台阵记录到的地震波在地形基阶频段(2—4 Hz)和浅部土层频段(7—9 Hz)的幅值明显放大,RSSR曲线显示山顶NS向的土层频段谱比大于山体地形频段谱比;由于土层山体竖向地震动在中高频段放大,使得HVSR方法谱比结果在中高频段较RSSR方法所得结果明显偏低,而在山体基阶频段附近两种方法的谱比值接近.松散土层山体的台阵记录特征体现了地形和土层对地震动的联合作用,揭示了强震区起伏地形场地震害加重及地震滑坡集中发生的原因所在.