Diffraction of plane SV waves by a cavity in poroelastic half-space

This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space.The Green’s functions of compressive and shear wave sources are derived based on Biot’s theory. The scattered waves are constructed using fi ctitious wave sources close to the boundary of the cavity, and their magnitudes are determined by the boundary conditions. Verifi cation of the accuracy is performed by: (1) checking the satisfaction extent of the boundary c...     

平面SV波在饱和半空间中沉积谷地周围的散射

采用一种特殊的间接边界积分方程法,求解了平面SV波在饱和半空间中任意形状沉积谷地周围的二维散射问题。结合饱和半空间中膨胀波源和剪切波源格林函数,由分布在沉积和半空间交界面附近两虚拟波源面上的波源分别构造沉积内外的散射波场,由交界面连续条件建立方程并求解确定虚拟波源密度,总波场反应即可由自由波场和散射波场叠加而得。然后通过边界条件验算、退化解答与现有结果的比较以及稳定性检验,验证了方法的计算精度。通过一组典型算例,研究了平面SV波在饱和半空间中沉积谷地周围散射的基本规律,详细给出了不同参数情况沉积谷地附近地表位移幅值和孔隙水压,着重分析了入射SV波频率和角度、边界渗透条件、沉积孔隙率等因素对场地反应的影响,得出了一些有益的结论。     

Effects of a covering layer in a circular-arc canyon on incident plane SV waves

Introduction The effect of local topographies on seismic wave propagation is one of the most attractive topics in seismology. It may be resolved by either an analytical method or a numerical method. Here, the analytical method is the wave function expansion method; numerical methods include the finite difference, finite element, boundary integration equation, and discrete wave number method, etc. The advantage of these numerical methods is that they can be applied to local inhomogeneity and ir…     

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...     

The reflection of plane waves in a poroelastic half-space saturated with inviscid fluid

This paper discusses surface displacements, surface strain, rocking, and energy partitioning during reflection-of-plane waves in a fluid-saturated poroelastic half-space. The medium is modeled by Biot's theory, and is assumed to be saturated with inviscid fluid. A linear porosity-modulus relation based on experimental data on sandstones is used to determine the material parameters for Biot's model. Numerical results in terms of angle of incident waves and Poisson's ratio are illustrated for various porosities and degrees of solid frame stiffness. The results show that the amount of solid frame stiffness controls the response of a fluid-saturated porous system. A poroelastic medium with essentially dry-frame stiffness behaves like an elastic medium, and the influence of pore fluid increases as dry-frame stiffness is reduced. The effects of a second P-wave become noticeable in poroelastic media with low dry-frame stiffness.     

Diffraction of plane P waves around an alluvial valley in poroelastic half-space

Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green’s functions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of fictitious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary...     

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

A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section in a half-space is studied using the wave functions expansion method. The solution is reduced to solving infinite linear algebraic equations using the Graf's addition theorem in an appropriate form. Numerical results of the solution are obtained by truncation of the infinite equations and accuracies of the truncation are checked by the extent to which the numerical results fit the boundary condition and by convergence of the numerical results with the truncation order. Complicated effects of the depth-to-width ratio of the canyon on surface ground motion are shown by the numerical results for typical cases.     

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...     

饱和层状场地中任意凹陷地形对入射SV波的散射

利用饱和土层的精确动力刚度矩阵和动力格林(Green)函数,采用间接边界元法,在频域内求解了层状饱和场地中任意凹陷地形对入射SV波的散射问题.通过自由场反应分析,求得凹陷地形表面各点的位移和各单元的应力响应;同样计算了虚拟分布荷载的格林影响函数,求得相应的位移和应力响应;根据边界条件确定虚拟分布荷载,将自由场位移响应和...     

Diffraction of plane sh waves in a half-space

Scattering of antiplane shear waves (SH) in two dimensions by surface and near-surface defects in a homogeneous, isotropic elastic semi-infinite medium has been studied. Attention has been focused here in the range of medium to long wavelengths. A combined finite element and analytical technique has been used to study the problems of scattering by semi-circular and triangular canyons. The results for the former case are compared with the known exact solution and those for the latter case are compared with some available approximate solutions. Finally a problem of multiple scattering by a triangular canyon and a nearby circular tunnel is studied. Numerical results are presented showing the effects of multiple scattering and different angles of incidence. These results are of interest in earthquake engineering.     

Scattering of SV waves by a canyon in a fluid-saturated, poroelastic layered half-space, modeled using the indirect boundary element method

The scattering of SV waves by a canyon in a fluid-saturated, poroelastic layered half-space is modeled using the indirect boundary element method in the frequency domain. The free-field responses are calculated to determine the displacements and stresses at the surface of the canyon, and fictitious distributed loads are then applied at the surface of the canyon in the free field to calculate the Green's functions for displacements and stresses. The amplitudes of the fictitious distributed loads are determined from the boundary conditions, and the displacements arising from the waves in the free field and from the fictitious distributed loads are summed to obtain the solution. The effects of fluid saturation, boundary conditions, porosity, and soil layers on the surface displacement amplitudes and phase shifts are discussed, and some useful conclusions are obtained. It is shown that the surface displacement amplitudes due to saturation and boundary conditions, different porosities, or the presence of a soil layer can be very dissimilar, and large phase shifts can be observed. The resulting wavelengths for an undrained saturated poroelastic medium are slightly longer than those for a drained saturated poroelastic medium; and are longer for a drained saturated poroelastic medium than those for a dry poroelastic medium. As porosity increases, the wavelengths become longer; and a layered half-space produces longer wavelengths than a homogeneous half-space.     

Diffraction of plane SH waves by a semi-circular cavity in half-space

This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.     

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.     

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 ...     

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.     

Scattering of plane P waves by circular-arc alluvial valleys with saturated soil deposits

This paper presents an analytical solution for two-dimensional scattering and diffraction of plane P waves by circular-arc alluvial valleys with shallow saturated soil deposits. The solution is based on Biot's dynamic theory for saturated porous media, and derived by employing Fourier–Bessel series expansion technique. In this analysis, soil deposits in the circular-arc valley are modeled as saturated porous media based on Biot's dynamic theory, and the circular-arc valley is assumed to be imbedded in an infinite half-space, filled with elastic single-phase media. Numerical results from this solution show that the amplitudes of displacement at the surface of an alluvial valley are mainly relative to the angle of incidence, the dimensionless frequency of incident P wave, the degree of saturation and porosity of soil deposits, and the stiffness and Poisson's ratio of the solid skeleton of the soil deposits. Furthermore, the proposed solution is compared with the previous solution, in which the soil deposit was modeled as an elastic single-phase solid.     

圆弧状多层沉积谷地在平面SV波入射下的动力响应

利用波函数的Fourier-Bessel级数展开法,推导出了含任意多个圆弧状沉积层的谷地在平面SV波入射下稳态动力响应的解析解,并分析了该级数形式的解析解随着截断项数的收敛问题.其结果表明,该级数解能够在一个非常宽的频带范围内收敛;通过在简化条件下与现有其他解析解的比较,验证了该解析解的正确性;并利用该解析解,以稳态地面运动的位移幅值和相位差为基本参数,在一个较宽的频带范围内讨论了谷地中沉积介质的成层性对地面运动的影响,其结果表明对于多层谷地而言,当入射波频率较高时,散射波之间的干涉显著并且出现了能量聚焦现象.     

Scattering of plane SV waves by cylindrical canyons in saturated porous medium

On the basis of Biot dynamic theory, an analytic solution of two-dimensional scattering and diffraction of plane SV waves by circular cylindrical canyons in a half space of saturated porous media is presented in this paper for the first time. The solution is obtained by employing the Fourier–Bessel series expansion technique. Parametric studies had been carried out, which includes: the angle of incidence, the frequency of the incident SV wave, the porosity of saturated porous medium and the stiffness and Poisson's ratio of the solid-skeleton. All the outcomes are useful for the seismic analysis of the surface topography conditions.     

Scattering of plane sh waves by a semi-elliptical canyon

In this paper we analyse the two-dimensional scattering and diffraction of plane SH waves by a semi-elliptical canyon. The exact series solution of the problem, for general angle of incidence of the plane SH waves, has been used to examine the dependence of surface amplifications inside and near the canyon. The nature of ground motion has been found to depend on two key parameters: (a) The angle of incidence. (b) The ratio of the canyon width to the wave length of incident SH waves. For short incident waves surface displacement amplitudes change rapidly from one point to another, while for the long waves and shallow canyons displacement amplitudes display only minor departure from the uniform half-space amplification of 2. For shallow canyons and long incident waves, the angle of incidence introduces only minor changes into the overall behaviour of surface amplitudes. For deep canyons and nearly grazing incidences, a prominent shadow zone is realized behind the canyon.     

Scattering of plane sh waves by a semi-cylindrical canyon

The two-dimensional scattering and diffraction of plane SH waves by a semi-cylindrical canyon is analysed for a general angle of wave incidence. The closed-form solution of the problem shows that the surface topography can have prominent effects on incident waves only when the wavelengths of incident motion are short compared to the radius of a canyon. The surface amplification of displacement amplitudes around and in the canyon changes rapidly from one point to another, but the amplification is always less than 2. The over-all trends of amplification pattern are determined by two principal parameters: (1) γ, the angle of incidence of plane SH waves, and (2) η, the ratio of radius of the canyon to one-half wave length of incident waves. The higher η leads to greater complexity of the pattern of surface displacement amplitudes characterized by more abrupt changes of amplification from one point to another, while γ mainly determines the over-all trends of displacement amplitudes. For grazing and nearly grazing incidences, for example, a strong shadow zone is developed behind the canyon. The qualitative analysis of the topographic effects on the Pacoima Dam accelerogram,¹ based on the semi-cylindrical canyon, suggests that this strong-motion record was not seriously affected by surface topography of the recording site.