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.     

瑞雷波斜入射下层状半空间中沉积谷地周围的三维散射研究

针对层状半空间中沉积谷地对斜入射瑞雷波的三维散射问题, 采用直接刚度法计算自由场波场, 以层状半空间中移动斜线均布荷载动力格林影响函数求解三维散射波场, 建立了求解该问题的间接边界元方法. 通过与已有结果的比较, 验证了该方法的正确性, 并以均匀半空间以及弹性基岩上单一土层场地中沉积谷地为例进行了计算分析. 研究结果表明： 层状半空间与均匀半空间中沉积谷地对瑞雷波的散射存在显著差别; 层状半空间中瑞雷波的振动模态对沉积附近位移幅值有着重要影响; 土层刚度和厚度等参数也对沉积附近位移幅值大小及空间分布有着显著的影响.     

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.     

3D scattering of obliquely incident plane SV waves by an alluvial valley embedded in a fluid-saturated,poroelastic layered half-space

The indirect boundary element method is used to study the 3D dynamic response of an infinitely long alluvial valley embedded in a saturated layered half-space for obliquely incident SV waves. A wave-number transform is first applied along the valley’s axis to reduce a 3D problem to a 2D plane strain problem. The problem is then solved in the section perpendicular to the axis of the valley. Finally, the 3D dynamic responses of the valley are obtained by an inverse wave-number transform. The validity of the method is confirmed by comparison with relevant results. The differences between the responses around the valley embedded in dry and in saturated poroelastic medium are studied, and the effects of drainage conditions, porosity, soil layer stiffness, and soil layer thickness on the dynamic response are discussed in detail resulting in some conclusions.     

3D scattering of obliquely incident plane SV waves by an alluvial valley embedded in a fluid-saturated,poroelastic layered half-space

The indirect boundary element method is used to study the 3D dynamic response of an infinitely long alluvial valley embedded in a saturated layered half-space for obli- quely incident SV waves. A wave-number transform is first applied along the valley＇s axis to reduce a 3D problem to a 2D plane strain problem. The problem is then solved in the section perpendicular to the axis of the valley. Finally, the 3D dynamic responses of the valley are obtained by an inverse wave-number transform. The validity of the method is con- firmed by comparison with relevant results. The differences between the responses around the valley embedded in dry and in saturated poroelastic medium are studied, and the effects of drainage conditions, porosity, soil layer stiffness, and soil layer thickness on the dynamic response are dis- cussed in detail resulting in some conclusions.     

斜入射平面SH波在层状半空间中沉积谷地周围的三维散射

采用直接刚度法计算自由场动力响应,以层状半空间中移动斜线均布荷载动力格林函数模拟散射波场,采用间接边界元方法求解了层状半空间中沉积谷地对斜入射平面SH波的三维散射问题.由于文中采用的层状场地三维动力刚度矩阵是精确的,且用于模拟散射波场的均布移动斜线荷载可以直接施加在沉积交界面处而不存在奇异性,所以本文方法具有很高精度.文中以均匀半空间和基岩上单一土层中沉积谷地对入射SH波的散射为例进行了数值计算,研究表明,沉积谷地对地震波的三维散射与二维散射之间存在本质差别;层状半空间中沉积谷地与均匀半空间中沉积谷地附近地表位移存在显著差异.     

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.     

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。     

柱面波在半空间中洞室周围的散射

采用一种间接边界积分方程法求解了柱面波在半空间中洞室周围的散射问题。通过边界条件的验算以及退化解答与精确解的比较,验证了本文方法的计算精度。文中主要分析了入射波频率、波源与洞室距离等参数对洞室附近地表位移响应和洞室动应力集中的影响,得出了一些有益的结论。     

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.     

2.5D scattering of incident plane SV waves by a canyon in layered half-space

This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method (IBEM). A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green’s functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fic...     

2.5D scattering of incident plane SH waves by a canyon in layered half-space

This paper presents 2.5D scattering of incident plane SH waves by a canyon in layered half-space by the indirect boundary element method (IBEM). The free field response is carried out to give the displacements and stresses on the line which forms boundary of the canyon. The fictitious uniform moving loads are applied to the same line to calculate the Green’s functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The displacements due to the free ...     

倾斜入射快纵波在饱和土中单个圆柱体周围的散射

在Biot饱和土波动理论的基础上,采用波函数展开法,研究了饱和土体中单个圆柱体对倾斜入射PI波的散射特性,计算了背向散射谱和总散射截面积。结果表明,饱和土体中PI波倾斜入射时,随着倾斜入射角的增大,总散射截面积在减小,产生的散射波主要以PI波和SV波为主;随着饱和土体渗透系数的减小,PI波、PⅡ波和SV波背向散射谱平均幅值均呈增大趋势,但PI波背向散射谱幅值变化程度较小。     

Dynamic response of rectangular foundations to obliquely incident seismic waves

A study is made of the harmonic response of a rigid massless rectangular foundation bonded to an elastic half-space and subjected to the action of both external forces and obliquely incident plane seismic waves. The associated mixed boundary value problem is discretized and solved numerically. The results obtained indicate that the angle of incidence of the seismic wave has a marked effect on the nature and magnitude of the foundation response.     

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.     

Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section

A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section in a half-space is presented using the wave functions expansion. The solution is reduced to solving a set of infinite linear algebraic equations using the exterior region form of Graf's addition theorem. Numerical solutions are obtained by truncation of the infinite equations and their accuracies are demonstrated by convergence of the numerical results to the exact boundary condition with the increasing of the truncation order. The present solution is compared with the existing one presented by Todorovska and Lee for the same problem and their differences are analysed. Complicated effects of the depth-to-width ratio of the alluvial valley on surface ground motion are finally illustrated.     

Dynamic soil-tunnel interaction in layered half-space for incident plane SH waves

The dynamic soil-tunnel interaction is studied by indirect boundary element method (IBEM), using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.     

平面SV波在层状半空间中沉积谷地周围的散射

采用间接边界元方法求解了入射平面SV波在层状半空间中沉积谷地周围的散射问题.问题的解答包含自由场和散射场两部分.自由场可由直接刚度法求得,散射场由层状半空间中斜线荷载动力格林函数来模拟.文中以入射平面SV波在基岩上单一土层中沉积谷地周围散射为例研究了土层和沉积谷地周围的影响.结果表明,由于考虑了土层的动力特性,平面SV...     

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。     

Longshore current generation by obliquely incident internal waves

Abstract

It is shown that a significant longshore current of maximum amplitude v = (3 × 10^4/v ) cm sec^?1 (for typical oceanic values) can be forced between the breaker zone and shore by internal gravity waves obliquely incident on a plane beach. In the mean longshore momentum balance Reynolds stress terms appear which can be calculated to O (α), α being a bottom slope parameter, using a WKB approach. With appropriate assumptions being made about the amplitude behaviour of the motion after breaking, the divergence of these stresses does not vanish and forces a current whose magnitude is determined by a balance with viscous stresses derived from vertical eddy motions.