浅埋夹塞的任意圆弧凸起地形对SH波散射的影响

发布时间：2018-03-13 12:47

本文选题：波函数展开法　切入点：圆形夹塞　出处：《中国地震局工程力学研究所》2017年硕士论文　论文类型：学位论文

【摘要】：大量计算数据显示,浅埋夹塞圆弧凸起地形对地面运动有着明显放大作用。目前针对这类问题的解析解很少,仅给出了浅埋空腔任意圆弧凸起地形和浅埋夹塞半圆弧凸起地形的解析解。因此本文做了以下工作:(1)本文基于波函数展开法和Graf加法公式,首次给出了地下圆形夹塞及任意圆弧凸起地形对二维出平面SH波散射的封闭级数解答,结合边界条件引入两个恒为零的辅助函数,通过对边界处条件方程组进行傅里叶展开最终使问题简化为对一组无穷级数代数方程组的求解。本文给出的解析解可退化为单独考虑地形或夹塞(空腔)的解。(2)通过对无穷方程组进行有限项的截断计算我们得到了浅埋夹塞的圆弧凸起地形的地表位移幅值的数值结果,同时为了与其退化模型(仅存在地形和仅存在浅埋夹塞的情况)作对比,本文同时计算了退化模型的地表位移幅值,结果表明,SH波垂直入射下,浅埋夹塞的圆弧凸起地形退化到无夹塞和无地形的两个模型后,当两者地面运动放大区域重合时,原模型对应区域的地表位移一般明显放大。另外,当夹塞退化为空腔时,圆弧凸起部分某些频率的位移幅值很大,且这些频率具有明显周期性,频率值可通过半空间介质波速及空腔到水平地表的距离确定。(3)由于浅埋夹塞圆弧凸起地形与其退化模型之间的关系,本文对纯夹塞(空腔)水平地形和纯凸起地形分别进行了研究。研究发现,当地下不均匀构造埋深加大和圆弧凸起地形高宽比减小时,地表位移幅值逐渐接近自由半空间,通过加大埋深和减小凸起地形高宽比,本文得到了可忽略对地表运动影响的夹塞埋深和凸起高宽比。(4)最后本文忽略波的二次反射后利用波的叠加原理简单计算了半空间浅埋空腔时地表产生较大位移幅值的位置和频率,与利用波函数展开法解析解得到的数值结果进行对比发现,该方法能较准确的预测地表出现较大位移幅值的位置和频率。另外,对于分析得到的垂直入射下地表在空腔圆心正上方点处的运动规律与已有结论一致。
[Abstract]:A large number of calculated data show that the shallow buried plug arc uplift has a significant effect on the ground motion. At present, there are few analytical solutions to this kind of problems. Only the analytical solutions of arbitrary arc raised terrain and shallow buried plug semi-circular arc raised terrain are given. Therefore, the following work is done in this paper: this paper is based on the wave function expansion method and the Graf addition formula. For the first time, the closed series solution for scattering of 2-D plane SH waves by underground circular plug and arbitrary arc raised terrain is given. Two auxiliary functions with constant zero are introduced in combination with boundary conditions. The problem is simplified to a set of infinite series algebraic equations by Fourier expansion of the equations of conditions at the boundary. The analytical solution given in this paper can be reduced to a solution which considers only the terrain or the stopper (cavity). By truncating the finite term of the infinite equations, we obtain the numerical results of the surface displacement amplitude of the circular arc uplift terrain with shallow plug. In order to compare with the degradation model (only the terrain and the shallow plug), the amplitude of the surface displacement of the degradation model is also calculated. The results show that the SH-wave is incident vertically. After the arc uplift of shallow buried plug degenerates to two models without clamping and no topography, when the ground motion amplification region of the two models coincides with each other, the surface displacement of the corresponding area of the original model is obviously enlarged. In addition, when the clamping plug degenerates into an empty cavity, The displacement amplitudes of some frequencies in the arc protrusions are very large, and these frequencies have obvious periodicity. The frequency value can be determined by the wave velocity of the half-space medium and the distance between the cavity and the horizontal surface. In this paper, the horizontal topography of pure plug (cavity) and the terrain of pure uplift are studied. It is found that when the buried depth of non-uniform underground structure increases and the ratio of height to width decreases, the amplitude of surface displacement gradually approaches the free half-space. By increasing the depth of burying and reducing the aspect ratio of the raised terrain, In this paper, the plugged depth and the ratio of height to width are obtained. Finally, after ignoring the secondary reflection of the wave, the superposition principle of the wave is used to calculate the large displacement amplitude of the surface when the cavity is shallow buried in half space. The position and frequency of the. Compared with the numerical results obtained by using the analytical solution of the wave function expansion method, it is found that this method can accurately predict the position and frequency of large displacement amplitude on the surface of the earth's surface. The law of the surface motion at the point directly above the center of the cavity under vertical incidence is consistent with the existing conclusions.
【学位授予单位】：中国地震局工程力学研究所
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P315.9

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