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1.
The time-history responses of the surface were obtained for a linear elastic half-plane including regularly distributed enormous embedded circular cavities subjected to propagating obliquely incident plane SH-waves. An advanced numerical approach named half-plane time-domain boundary element method(BEM), which only located the meshes around the cavities, was used to create the model. By establishing the modified boundary integral equation(BIE)independently for each cavity and forming the matrices, the final coupled equation was solved step-by-step in the timedomain to obtain the boundary values. The responses were developed for a half-plane with 512 cavities. The amplification patterns were also obtained to illustrate the frequencydomain responses for some cases. According to the results,the presence of enormous cavities affects the scattering and diffraction of the waves arrived to the surface. The introduced method can be recommended for geotechnical/mechanical engineers to model structures in the fields of earthquake engineering and composite materials.  相似文献   

2.
A theoretical approach is presented to study the antiplane seismic response of underground structures, subjected to the incidence of both plane and cylindrical waves. The structure is assumed to be a circular inclusion embedded in a homogenous, isotropic and linear visco‐elastic halfspace. The inclusion may consist either of a cavity, with or without a ring‐shaped boundary, or it may be filled in with a linear‐elastic material, without loss of generality. The analytical solution is obtained using expansions of wave functions in terms of Bessel and Hankel functions, relying on the technique of images and the use of Graf's addition theorem to enforce the boundary conditions. The effects of underground cavities on surface earthquake ground motion are studied as a function of the size of the cavity, its embedment depth, the frequency content of the excitation, the incidence angle and the distance from the axis of symmetry of the cavity itself. A simple application of Rayleigh's method allows us to verify that the ground surface response is dominated by the fundamental vibration mode of the portion of soil between the cavity and ground surface itself, in the frequency range of interest for engineering purposes. A simple relationship to estimate the fundamental natural frequency as a function of the embedment depth of the cavity is given. Finally, amplification factors on response spectra are obtained, to provide a practical insight into the effect of an underground cavity on surface ground motion during real earthquakes. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

3.
In this paper the applicability of an approximate Boundary Element Method to uniform half-plane elastodynamic problems is investigated. This method employs the concept of images to construct approximate fundamental solutions for the half-plane and does not require any half-plane surface discretization. The method is formulated in the frequency domain for the case of harmonic disturbances or the Laplace transform domain for the case of transient disturbances. In the latter case a numerical inversion of the transformed solution is necessary to obtain the time domain response. The proposed method can be used as an alternative to boundary element methods that either utilize the infinite plane fundamental solution and thus require a half-plane surface discretization, or employ the exact half-plane fundamental solution, which even though leads to no surface discretization, is of a very lengthy and complicated form. Two characteristics numerical examples are used to illustrate the proposed method and study its advantages and disadvantages.  相似文献   

4.
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.  相似文献   

5.
本文采用辅助函数的思想,利用复变函数和多级坐标的方法给出了SH波入射条件下多个半圆形沉积谷地附近浅埋圆形孔洞动力分析问题的解答。将整个求解区域分割成两部分来处理,区域I为多个半圆形沉积谷地,区域II为浅埋圆形孔洞附近带半圆形凹陷的半无限弹性空间。在区域I和II中分别构造位移解,并在二个区域的“公共边界”上实施位移应力的连续条件,建立求解该问题的无穷代数方程组。最后,本文给出了算例和数值结果,并对其进行了讨论。  相似文献   

6.
In this paper, the degenerate kernels and Fourier series expansions are adopted in the null-field integral equation to solve the exterior Helmholtz problems with alluvial valleys. The main gain of using degenerate kernels in integral equations is free of calculating the principal values for singular integrals by locating the null-field point exactly on the real boundary. An adaptive observer system is addressed to fully employ the property of degenerate kernels for circular boundaries in the polar coordinate. Image concept and technique of decomposition are utilized for half-plane problems. After moving the null-field point to the real boundary and matching the boundary conditions, a linear algebraic system is obtained without boundary discretization. The unknown coefficients in the algebraic system can be easily determined. The present method is treated as a “semi-analytical” solution since error only attributes to the truncation of Fourier series. Earthquake analysis for the site response of alluvial valley or canyon subject to the incident SH-wave is the main concern. Numerical examples including single and successive alluvial valleys are given to test our program. Limiting cases of a single canyon and two successive canyons are also addressed. Amplification of soft basin is also observed in this study. The validity of the semi-analytical method is verified. Our advantages, well-posed model, principal value free, elimination of boundary-layer effect and exponential convergence and mesh-free, by using the present method are achieved.  相似文献   

7.
The method of wave-function expansion in elliptical coordinates,elliptical cosine half-range expansion and Mathieu function were applied to obtain an exact analytical solution of the dynamic stress concentration factor(DSCF)around an elliptical cavity in a shallow,semi-elliptical hill.An infinite system of simultaneous linear equations for solving this problem was established by substituting the wave expression obtained by the Mathieu function including the standing wave expression of elliptical lining given herein into the boundary condition obtained by the region-matching method.The finite equations system with unknown coefficients obtained by truncation were solved numerically,and the results in the case of an ellipse degenerating into a circle were compared with previous results to verify the accuracy of the method.The effects of different aspect ratios,incident wave angles and aperture ratios on the dynamic stress concentration around the elliptical cavity were described.Some numerical results,when the elliptical hill was changed into a circular one,were analyzed and compared in detail.In engineering,this model can be regarded as a semi-cylindrical hill with an elliptical cylindrical unlined tunnel under the action of SH waves,and the results are significant in aseismic design.  相似文献   

8.
Following the success of seismic analysis of a canyon [1], the problem of SH-wave diffraction by a semi-circular hill is revisited using the null-field boundary integral equation method (BIEM). To fully utilize the analytical property in the null-field boundary integral equation approach in conjunction with degenerate kernels for solving the semi-circular hill scattering problem, the problem is decomposed into two regions to produce circular boundaries using the technique of taking free body. One is the half-plane problem containing a semi-circular boundary. This semi-infinite problem is imbedded in an infinite plane with an artificial full circular boundary such that degenerate kernel can be fully applied. The other is an interior problem bounded by a circular boundary. The degenerate kernel in the polar coordinates for two subdomains is utilized for the closed-form fundamental solution. The semi-analytical formulation along with matching boundary conditions yields six constraint equations. Instead of finding admissible wave expansion bases, our null-field BIEM approach in conjunction with degenerate kernels have five features over the conventional BIEM/BEM: (1) free from calculating principal values, (2) exponential convergence, (3) elimination of boundary-layer effect, (4) meshless and (5) well-posed system. All the numerical results are comparing well with the available results in the literature. It is interesting to find that a focusing phenomenon is also observed in this study.  相似文献   

9.
The scattering and diffraction of plane SV waves underground, circular, cylindrical cavities at various depths in an elastic half space is studied in this paper. The cavities, studied here, are at depths of two to five cavity radii, measured from the surface to the center of the cavity. Fourier-Bessel series are used to satisfy the wave equation and the boundary conditions. When the angle of incidence of the plane SV wave exceeds the critical angle, surface waves are generated, which are expanded in terms of Fourier series, which also involve Bessel functions. The surface displacement amplitudes and phases that are presented show that the results depend on the following parameters: (1) The angle of incidence, θβ; (2) the ratio cavity depth to the cavity radius, h/a; (3) the dimensionless frequency of the incident SV wave, η; and (4) Poisson's ratio, v. The presence of the cavity in the half space results in significant deviation of both the displacement amplitudes and phases on the nearby half space surface from that of a uniform half space.  相似文献   

10.
SH波入射时半圆形凸起与凹陷地形的地震动   总被引：2，自引：0，他引：2  
研究了弹性半空间中半圆形凸起与凹陷相连地形对SH波的散射问题。将整个求解区域分割为2部分,在其中分别构造满足边界条件的位移解,通过移动坐标使之满足“公共边界”以及半圆形凹陷表面上的边界条件,从而建立起求解该问题的无穷代数方程组。最后,给出了地表位移幅值的数值结果以及凸起地形顶点和凹陷地形最低点处位移幅值的反应谱并进行了讨论。  相似文献   

11.
The problem of water flow around a tunnel cavity located in the saturated capillary fringe on top of a very permeable, freely draining substratum is considered for the critical non-leakage condition when there is uniform vertical downward flow through the upper surface of the saturated region. In this critical condition the soil–water pressure is equal to zero everywhere on the cavity wall that is also a streamline. The conditions at the upper fringe boundary are that the soil–water pressure is equal to the air-entry value of the soil and the flux through this surface is the uniform infiltration rate. The cavity surface and the fringe boundary which is elevated above the cavity position, are found through conformal mapping and the use of integral representations of non-standard mixed boundary-value problems. They are calculated for a range of infiltration rates and compared with those obtained by assuming the upper fringe boundary to be horizontal. The exact analysis given here gives larger tunnel cavities than those given by the approximate treatment of the problem. The results have application in the design of underground repositories against entry of seepage water, the construction of protective capillary barriers and in the design of interceptor drainage systems.  相似文献   

12.
本文给出了地下圆形衬砌结构与地面上的半圆形凸起地形对垂直于地面入射的SH波散射问题的解答。方法是将求解区域分割成两部分。其一为包含半圆形凸起地形在内的圆形区域Ⅰ，其二为带有一个半圆形凹陷和一个圆形衬砌结构的弹性半空间Ⅱ，半圆形凹陷部分为其公共边界，在区域Ⅰ和Ⅱ中分别构造其位移解，然后再通过移动坐标，使其满足“公共边界”上的条件和地下衬砌的边界条件，建立起求解该问题的无穷代数方程组。最后，本文给出了算例，并讨论了数值结果，给出了圆形衬砌结构周边上的动应力集中系数变化规律。  相似文献   

13.

In this study, a theoretical approach is used to investigate the scattering problem of circular holes under a scalene triangle on the surface. The wave displacement function is obtained by solving the Helmholtz equation that meets the zero-stress boundary conditions by adopting the method of separation of variables. Based on the complex function, multi-polar coordinate method, and region-matching technique, algebraic equations are established at auxiliary boundaries and free boundaries conditions in a complex domain. The auxiliary circle is used to solve the singularity of the reflex angle at the triangle corner. Then, according to sample statistics, the least squares method is used instead of the Fourier expansion method to solve the undetermined coefficient of the algebraic equations by discrete boundary. Numerical results show that the continuity of the auxiliary boundaries and the accuracy of the zero-stress boundaries are adequate, and the displacement of the free surface and the stress of the circular hole are related to the shape of the triangle, the position of the circular hole, the direction of the incident wave, and the frequency content of the excitation. Finally, time-domain responses are calculated by FFT based on the frequency domain theory, and the results reveal the wave propagation mechanism in a complicated structure.

  相似文献   

14.
A closed-form analytical solution of surface motion of a semi-elliptical cylindrical hill for incident plane SH waves is presented. Although some previous analytical work had already dealt with hill topography of semi-circular and shallow circular, our work aims at calculating surface motion of very prolate hill for high incident frequency, and explaining the special vibrating properties of very prolate hill. Accuracy of the solution is checked by boundary conditions, numerical results for surface motion of oblate and prolate hills are calculated, and some conclusions are obtained.  相似文献   

15.
刘中宪  尚策  王小燕  王冬 《地震学报》2017,39(1):111-131
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．   相似文献   

16.
In this paper the boundary element algorithm which uses the time-convoluted traction kernels is applied to a numerical parametric study on the seismic behavior of three-dimensional Gaussian-shaped hills subjected to vertically propagating incident waves. All calculations were executed in the time-domain and the medium was assumed to have a linear elastic constitutive behavior. Results are discussed in both time and frequency domain with respect to the dimensionless parameters. It was shown that wave length and site geometry, including shape and dimension ratios and, to some extent, wave type are the key independent parameters governing hill amplification behavior. Comparing two- and three-dimensional hills with similar shape ratios, two-dimensional hill had greater characteristic periods, where the three-dimensional hill had greater maximum amplification potential. Three-dimensionality has a strong effect on the seismic responses of the hill; however the rate of seismic response variation with the three-dimensionality factor depends on the shape ratio. It was shown that two-dimensional behavior was dominant in low height three-dimensional hills, however, as the shape ratio increased, three-dimensionality effects appeared and the seismic response of the hill tends toward the axisymmetric three-dimensional hill.  相似文献   

17.
The total system studied in this paper is a layered soil stratum with a rigid bedrock and a cylindrical cavity on the surface. Analytic solutions for the layered medium with prescribed harmonic displacement time history on the surface of the cylindrical cavity are presented. The whole soil domain is divided into interior and exterior domains. The interior domain is the projection of the cylindrical cavity down to the rigid bedrock, whereas the exterior domain is then the soil medium complement to the interior domain. The displacement and stress fields in both domains are expanded as an infinite series of Fourier components with respect to the azimuth. For each Fourier component in the infinite series, the solutions for both domains are found independently by solving the general differential equations of wave propagation satisfying the boundary conditions of the top surface and the lower rigid boundary. Displacement and stress continuity conditions are then imposed on the vertical interface between the two domains using the formulation of a weighted residual. For the soil-structure interaction problem, the impedance matrix at the interface between the structure and the soil medium can be easily generated using the analytic solutions, which can then be combined with the finite element model of the structure. A simple example is presented to demonstrate the effectiveness of the procedure presented.  相似文献   

18.
采用有限元模拟方法建立了建筑群-沉积谷地二维模型,并在土体截断边界上施加粘弹性人工边界,在频域与时域中对比分析此体系和单独沉积谷地的地震反应,观察地震时沉积谷地与建筑群之间的动力相互作用规律。分析表明,沉积谷地中建筑群对谷地本身的地震反应具有显著影响。入射波频率较低时,由于共振效应的存在,在部分区域处建筑群-沉积谷地体系的地表位移响应幅值会大于单独沉积谷地,但随着入射波频率的增加,建筑群的存在又会对地震反应产生明显的减弱效果;建筑群对谷地的影响还与建筑高度和建筑间距有关,且不同位置处的响应也存在很大差异。计算结果可为沉积谷地中设防烈度的设置以及工程抗震设计提供部分理论依据。  相似文献   

19.
In this study, the null-field boundary integral equation method (BIEM) and the image method are used to solve the SH wave scattering problem containing semi-circular canyons and circular tunnels. To fully utilize the analytical property of circular geometry, the polar coordinates are used to expand the closed-form fundamental solution to the degenerate kernel, and the Fourier series is also introduced to represent the boundary density. By collocating boundary points to match boundary condition on the boundary, a linear algebraic system is constructed. The unknown coefficients in the algebraic system can be easily determined. In this way, a semi-analytical approach is developed. Following the experience of near-trapped modes in water wave problems of the full plane, the focusing phenomenon and near-trapped modes for the SH wave problem of the half-plane are solved, since the two problems obey the same mathematical model. In this study, it is found that the SH wave problem containing two semi-circular canyons and a circular tunnel has the near-trapped mode and the focusing phenomenon for a special incident angle and wavenumber. In this situation, the amplification factor for the amplitude of displacement is over 300.  相似文献   

20.
圆弧状沉积盆地与软土单覆盖层出平面地表运动对比   总被引：2，自引：0，他引：2  
采用解析方法，通过圆弧状沉积盆地与同样参数的软土均匀单覆盖层的对比，研究沉积盆地对平面SH波二维散射效应和其出平面地表运动。数值对比结果表明：（1）波垂直入射时盆地中央地表位移幅值反应，其随频率变化形式与软土单覆盖层的地表运动有较强的对应性，且此时单覆盖层地表位移幅值为其下降；（2）盆地的二维散射效应特点显著波的汇聚作用使盆地中的地表运动显著放大，总体上较软土单覆盖层的地表位移幅值要大，其频域内的最大反应则明显大于单覆盖层情况，但最大反应在盆地表面出现的位置依赖于入射波角度、盆地深宽比和盆地的软硬程度；（3）沉积盆地中地表位移运动有强烈扭转效应，且随盆地变软和入射波频率增高而增强。  相似文献   

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