Axisymmetric soil–structure interaction by global–local finite elements

A version of the global–local finite element method is presented for studying dynamic steady-state soil–structure interaction wherein the soil medium extends to infinity. Herein, only axisymmetric behaviour is considered. In this approach, conventional finite elements are used to model the structure and some portion of the surrounding soil medium considered to be homogeneous and isotropic. A complete set of outgoing waves in the form of spherical harmonics for the entire space is used to represent the behaviour in the half-space beyond the finite element mesh and these are termed the global functions. Full traction and displacement continuity is enforced at the finite element mesh interface with the outer region. On the free surface of the half-space in the outer field, traction-free surface conditions are enforced by demanding that a sequence of integrals of the weighted-average tractions must vanish. Numerical examples are presented for the response of different shaped foundations, resting on the free surface or at various submerged levels, due to a normal seismic plane compressional wave. Plots of differential scattering cross-sections show the angular distribution of the energy (its directional nature) of the scattered field.     

Diffraction of obliquely incident waves by a cylindrical cavity embedded in a layered viscoelastic half-space

The three-dimensional harmonic response in the vicinity of an infinitely long, cylindrical cavity of circular cross-section buried in a layered, viscoelastic half-space is obtained when the half-space is subjected to homogeneous plane waves and surface waves impinging at an oblique angle with respect to the axis of the cavity. The solution is obtained by an indirect boundary integral method based on the use of moving Green's functions for the viscoelastic half-space. Numerical results describing the motion on the ground surface and the motion and stresses on the wall of the cavity are presented for obliquely incident P-, SV-, SH- and Rayleigh waves with different horizontal angles of incidence.     

弹性层状半空间中无限长洞室对斜入射 平面SH波的三维散射(Ⅱ) 数值结果与分析

以基岩上单一土层场地为例, 计算分析了在斜入射平面SH波作用下弹性层状半空间中无限长洞室附近的地表位移. 研究表明, 层状半空间中地下洞室对波的散射与均匀半空间情况存在显著差别. 层状场地由于考虑了场地自身的动力特性, 使得洞室附近地表位移幅值的空间变化更为复杂, 基岩与土层刚度比、 土层厚度对散射效应均有着重要影响. 随着基岩与土层刚度比的增大, 地表位移幅值整体上逐渐增大; 随着土层厚度的增大, 土层对地表位移幅值的影响逐渐减小. 在频域解答的基础上, 给出了层状半空间中洞室对斜入射SH波散射的时域解答, 并以Ricker波为例进行了数值计算.      

弹性层状半空间中无限长洞室对斜入射平面SH波的三维散射（Ⅰ）——方法及验证

利用间接边界元法, 求解了弹性层状半空间中无限长洞室对斜入射平面SH波的三维散射问题. 通过与文献结果进行对比, 验证了本方法的正确性. 与工程中常用的二维模型比较表明, 工程中将三维散射问题简单地分解为平面内问题和平面外问题的做法存在较大误差. 文中并研究了斜入射角度对散射的影响, 表明斜入射角度对地表位移幅值有着重要影响.      

Scattering of plane harmonic SH,SV, P and rayleigh waves by non-axisymmetric three-dimensional canyons: A wave function expansion approach

Scattering of elastic waves by three-dimensional canyons embedded within an elastic half-space is investigated by using a wave function expansion technique. The geometry of the canyon is assumed to be non-axisymmetric. The canyon is subjected to incident plane Rayleigh waves and oblique incident SH, SV and P waves. The unknown scattered wavefield is expressed in terms of spherical wave functions which satisfy the equations of motion and radiation conditions at infinity, but they do not satisfy stress-free boundary conditions at the half-space surface. The boundary conditions are imposed locally in the least-squares sense at several points on the surface of the canyon and the half-space. Through a comparative study the validity and limitations of two-dimensional approximations (antiplane strain and plane strain models) have been examined. It is shown that scattering of waves by three-dimensional canyons may cause substantial change in the surface displacement patterns in comparison to the two-dimensional models. These results emphasize the need for three-dimensional modelling of realistic problems of interest in strong ground motion seismology and earthquake engineering.     

Influences of type of wave and angle of incidence on seismic bending moments in pile foundations

When analysing the seismic response of pile groups, a vertically‐incident wavefield is usually employed even though it does not necessarily correspond to the worst case scenario. This work aims to study the influences of both the type of seismic body wave and its angle of incidence on the dynamic response of pile foundations. To this end, the formulation of SV, SH and P obliquely‐incident waves is presented and implemented in a frequency‐domain boundary element‐finite element code for the dynamic analysis of pile foundations and piled structures. Results are presented in terms of bending moments at cap level of single piles and 3 × 3 pile groups, both in frequency and in time domains. It is found that, in general, the vertical incidence is not the most unfavourable situation. In particular, obliquely‐incident SV waves with angles of incidence smaller than the critical one, a situation in which the mechanism of propagation of the waves in the soil changes and surface waves appear, yield bending moments much larger than those obtained for vertically‐incident wavefields. It is also shown that the influence of pile‐to‐pile interaction on the kinematic bending moments becomes significant for non‐vertical incidence, especially for P and SV waves. Copyright © 2013 John Wiley & Sons, Ltd.     

三维椭球形盆地对球面波的散射

针对三维沉积盆地对球面波的散射问题,发展一种快速宽频间接边界元方法(IBEM).利用ANSYS建立求解模型,基于Intel-Fortran编译器编译相应的计算程序,对基岩半空间三维半椭球形盆地对球面波的散射进行了数值分析,着重探讨入射波频率、波源埋深、波源与不规则地形(沉积盆地)距离等参数对地震动特性的影响规律,计算方...     

地震体波斜入射下的断层台阶地震反应分析

应用显式有限元法对倾斜断层台阶在地震体波斜入射下的地震反应进行了数值模拟。模拟结果表明，P波入射时的竖向运动分量和SV波入射时的水平向运动分量在台阶上角点处存在极大值、在台阶下角点处存在极小值，同时在上下台面还出现由角点激发、向台阶外传播的转换体波与面波。这一结果说明，在断层台阶场地建设重大工程时应离开上角点一定距离，并考虑上下水平表面地面运动的差异性。     

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.     

Seismic response of a cylindrical shell embedded in a layered viscoelastic half-space. II: Validation and numerical results

A procedure to calculate the three-dimensional harmonic response of a infinitely long cylindrical shell of circular cross-section embedded in a layered viscoelastic half-space and subjected to harmonic plane waves impinging at an oblique angle with respect to the axis of the shell is validated by extensive comparisons with previous two- and three-dimensional results for the particular case of a shell embedded in a uniform half-space. New numerical results describing the motion and stresses within a shell embedded in a multilayered half-space and subjected to obliquely incident P-, SV- and SH-waves with different horizontal angles of incidence are presented and discussed.     

Time domain method for calculating free field motion of a layered half-space subjected to obliquely incident body waves

In numerical simulation of wave scattering under oblique incident body waves using the finite element method, the free field motion at the incident lateral boundary induced by the background layered half-space complicates the computational area. In order to replace the complex frequency domain method, a time-domain method to calculate the free field motion of a layered half-space subjected to oblique incident body waves is developed in this paper. The new method decouples the equations of motion used in the finite element method and offers an interpolation formula of the free field motion. This formula is based on the fact that the apparent horizontal velocity of the free field motion is constant and can be calculated exactly. Both the theoretical analysis and numerical results demonstrate that the proposed method offers a high degree of accuracy.     

Scattering of obliquely incident seismic waves by a cylindrical valley in a layered half-space

Three-dimensional scattering of seismic waves by a cylindrical alluvial valley embedded in a layered half-space is investigated by using the combination of the boundary integral representation and the finite element method. The surface displacements due to incident plane harmonic body waves (P, SV and SH) propagating at an arbitrary angle to the axis of the cylindrical valley are evaluated numerically for two semi-elliptical alluvial valleys. The presence of the layer is found to have a strong effect on the amplification of the surface displacements in some cases. The three-dimensional motion seems to be quite critical and may cause large amplification. The surface ground motion becomes significant when compared with corresponding free-field motion as the wavelengths become comparable to the characteristic length of the valley. The maximum amplification always occurs atop the valley. Numerical results show that the amplitude and the amplification pattern of the surface displacement strongly depend upon the frequency, the angle and the type of the incident waves.     

RESPONSE OF EARTH DAMS TO P AND SV WAVES USING COUPLED FE-BE FORMULATION

A study of the effects of dam–foundation interaction on the response of earth dams to obliquely incident P and SV waves is presented. Emphasis is placed on the effects of the foundation flexibility and the spatial variability of the ground motion. The study is based on a rigorous hybrid numerical formulation that combines the efficiency and versatility of the Finite Element Method (FEM) and the ability of Boundary Element Method (BEM) to account for the radiation conditions at the far field. The developed hybrid method is very powerful and can be used efficiently to obtain accurate solutions of problems of complex geometry, material heterogeneity and, for time-domain analyses, material nonlinearity. The 2-D frequency-domain formulation is used here to investigate the response of infinitely long earth dams to obliquely incident P and SV waves. By accounting rigorously for the energy radiated back into the half-space, the study demonstrates the dramatic effect of the flexibility of the foundation rock in reducing the overall response of the dam. The effects of the spatial variability of the ground motion for P and SV waves travelling across the width of the dam are also important, but somewhat less pronounced than those of the foundation flexibility.     

A note on three-dimensional scattering and diffraction by a hemispherical canyon–I: Vertically incident plane P-wave

The three-dimensional scattering by a hemi-spherical canyon in an elastic half-space subjected to seismic plane and spherical waves has long been a challenging boundary-value problem. It has been studied by earthquake engineers and strong-motion seismologists to understand the amplification effects caused by surface topography. The scattered and diffracted waves will, in all cases, consist of both longitudinal (P-) and shear (S-) shear waves. Together, at the half-space surface, these waves are not orthogonal over the infinite plane boundary of the half-space. Thus, to simultaneously satisfy both zero normal and shear stresses on the plane boundary numerical approximation of the geometry and/or wave functions were required, or in some cases, relaxed (disregarded). This paper re-examines this boundary-value problem from the applied mathematics point of view, and aims to redefine the proper form of the orthogonal spherical-wave functions for both the longitudinal and shear waves, so that they can together simultaneously satisfy the zero-stress boundary conditions at the half-space surface. With the zero-stress boundary conditions satisfied at the half-space surface, the most difficult part of the problem will be solved, and the remaining boundary conditions at the finite canyon surface will be easy to satisfy.     

地震波斜入射下层状场地中地下综合管廊地震响应分析

利用黏弹性人工边界和等效地震荷载时域波动输入方法,结合土层和半空间的精确动力刚度矩阵,实现了地震波斜入射下层状场地地下综合管廊地震反应分析,建立了不同场地条件下地下综合管廊分析模型。计算结果表明:地震波倾斜入射情况下,综合管廊结构地震响应与垂直入射时具有显著差异,一般SV波以30°临界角附近入射时结构地震反应最为剧烈;地下综合管廊动应力集中主要分布在管廊角部、中柱上下端;成层土波速结构变化对地下综合管廊地震反应亦具有显著影响。总体上看:当穿越软夹层时管廊结构地震反应更为剧烈,且覆盖层越厚,管廊结构内力幅值越大。因此地下综合管廊结构抗震设计宜考虑地震波倾斜入射及场地土层性质的影响。     

弹性层状半空间中凸起地形对入射平面SH波的放大作用

对Wolf理论进行拓展,使之可解决凸起地形对波的散射问题,进而利用间接边界元法,求解了弹性层状半空间中凸起地形对入射平面SH波的放大作用问题。本文模型的显著特点之一是考虑了层状半空间的动力特性以及层状半空间和凸起地形的阻尼;特点之二是计算精度高。文中以基岩上单一土层中半圆凸起地形对入射平面SH波的放大作用为例进行了数值计算分析。研究表明,基岩上单一土层中凸起地形对入射平面SH波放大作用和均匀半空间中凸起地形有着本质的差别;土层动力特性不仅影响凸起地形地表位移的幅值,还会影响地表位移的频谱;阻尼会显著降低凸起地形对高频波的放大作用。     

SV波全反射作用下地震动的合成及振动特性

越来越多的研究表明来自基岩的地震波并不是垂直地面向上传播的。地震波在斜入射与垂直入射时所产生的场地效应有很大不同,由于存在全反射现象,SV波在斜入射时产生的场地效应更为复杂。文章基于均匀弹性半空间地震波传播理论,分别推导得到SV波入射角在小于、大于等于临界角时地震动的计算表达式,通过模型算例研究SV波全反射作用下的地震动特性。研究发现：由SV波产生的地震动主要由入射波和反射波构成,滑行波作用可以忽略;地面运动轨迹具有面波旋转振动特点;随着入射角的增大,地面震动从以水平方向振动为主逐渐过渡到以垂直方向振动为主,两个方向的振动均小于入射波峰值的2倍。     

Torsional response of structures to obliquely incident seismic sh waves

A study is made of the torsional response of an elastic structure placed on a rigid circular foundation supported on an elastic half-space and subjected to the action of obliquely incident plane SH waves. The problem is solved by considering first the steady-state response of a massless rigid foundation excited externally by a harmonic torque and through the soil by an obliquely incident plane SH wave. In a second stage the coupling between the structure and the soil is considered to obtain the torsional response at the base and top of the superstructure. The results obtained indicate a range of conditions under which the torsional effects will be most pronounced.     

Dynamic response of a group of flexible foundations to incident seismic waves

The dynamic response of a finite number of flexible surface foundations subjected to harmonic incident Rayleigh or SH waves is presented. The foundations are assumed to be resting on an elastic half-space. The results show that the foundation stiffness has a marked effect on the vertical response, while there is only a minor effect on the horizontal displacements. In general, the dynamic response decreases with increasing foundation stiffness. In cases of Rayleigh wave incidence, the existence of an adjacent foundation generates a certain amount of horizontal response in the direction perpendicular to the incident wave and subsequently causes the system to undergo a torsional motion; while in cases of horizontally incident SH waves, a vertical response has been observed and its magnitude is comparable to the response in the direction of the incident wave.     

3D Diffraction of obliquely incident SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space

This paper studies three-dimensional diffraction of obliquely incident plane SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space using indirect boundary element method. The approach is validated by comparison with the literature, and the effects of cavity interval, incident frequency, and boundary drainage condition on the diffraction are studied through numerical examples. It is shown that, the interaction between two cavities is significant and surface displacement peaks become large when two cavities are close, and the surface displacement may be significantly amplified by twin cavities, and the influence range with large amplification can be as wide as 40 times of the cavity radius. Surface displacements in dry poroelastic case and saturated poroelastic cases with drained and undrained boundaries are evidently different under certain circumstances, and the differences may be much larger than those in the free-field response.