Effect of shallow buried cavity on anti-plane motion of ground surface in anisotropic half-space
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摘要: 本文采用复变函数方法研究了稳态水平剪切波(SH波)在各向异性弹性半空间中任意形状孔洞上的散射及其对地面运动的影响.在变换空间中构造出自动满足各向异性半空间水平表面上应力为零的散射波函数,并根据孔洞表面应力为零的边界条件,采用最小二乘法求解散射波函数的系数.用介质的各向异性性质来模拟地质条件,给出了SH波作用下含圆孔、椭圆孔和方孔的各向异性半空间表面位移幅值的数值结果,并分析了介质特性、孔洞的形状、埋深、入射波波数及入射角度等因素对地面运动的影响规律.数值结果表明:介质的各向异性对含有孔洞的半空间表面的地表位移具有显著的影响;沿一定角度的入射波在某一频段内所引起的地表位移幅值比各向同性介质的可能要大,且随着孔洞埋深的增加,地表位移的幅值逐渐减小.Abstract: The scattering of steady-state horizontal shear wave (SH-wave) by arbitrary cavity in anisotropic half-space is investigated together with its effect on ground motion by using the complex variable function method.The scattered wave function stratifying the condition of the stress free on the horizontal surface of anisotropic-half space automatically is constructed in the transformed space.Based on the zero-stress boundary condition of the cavity surface,the coefficient of scattered wave function is solved by means of the least squares method.By simulating the geological condition of the media anisotropy,the ground surface displacement amplitudes of anisotropic half-space with circular cavity,elliptical cavity and quadrate cavity are illustrated numerically.The effect of ground motion on the media property,the cavity shape,buried depth,the wave number and incident angle of incident wave are analyzed.Numerical result shows the media anisotropy has great effects on the ground surface displacement of half-space with a cavity.The ground surface displacement amplitude caused by incident wave with a certain angle may be much greater than that of the isotropic media in a certain frequency range,and decreases with the increase of the cavity depth.
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Keywords:
- anisotropic half-space /
- scattering of SH wave /
- cavity /
- ground motion /
- complex variable function
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图 1 SH波入射各向异性半空间中孔洞示意图
Figure 1. Schematic diagram of incident SH wave on a cavity in an anisotropic elastic half-space
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图 2 介质参数变化对浅埋圆孔附近地表位移幅值的影响
(a) η=0.1; (b) η=0.5; (c) η=1.0; (d) η=2.0
Figure 2. Effect of media parameters on surface displacement amplitude near shallow-buried circular cavity
(a) η=0.1; (b) η=0.5; (c) η=1.0; (d) η=2.0
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图 3 含圆孔正交各向异性半空间表面位移随频率的变化
(a) SH波垂直入射; (b) SH波水平入射
Figure 3. Surface displacements in orthotropic half-space with a circular cavity versus the dimensionless frequencies
(a) Vertical incident SH wave; (b) Horizontal incident SH wave
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图 4 正交各向异性半空间圆孔埋深对地表位移幅值的影响
(a) SH波水平入射； (b) SH波垂直入射
Figure 4. Effect of the buried depth of circular cavity on surface displacement amplitude in orthotropic half-space
(a) Horizontal incident SH wave； (b) Vertical incident SH wave
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图 5 介质参数变化对浅埋椭圆孔附近地表位移幅值的影响
(a) η=0.1; (b) η=0.5; (c) η=1.0; (d) η=2.0
Figure 5. Effect of media parameters on surface displacement amplitude near shallow-buried elliptical cavity
(a) η=0.1; (b) η=0.5; (c) η=1.0; (d) η=2.0
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Manolis G D,Beskos D E.1988.Boundary Element Methods in Elastodynamics[M].London:Unwin-Hyman:83-115.
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