【作者】 吕晓棠；

【导师】 刘殿魁；

【作者基本信息】 哈尔滨工程大学 ， 固体力学， 2007， 博士

【摘要】 研究地震时局部地形对地面运动的影响是地震工程学的重要课题之一。本文采用“分区”的思想，利用复变函数和移动坐标法研究了稳态SH波入射时，夹杂、裂纹附近的半圆形凸起地形，以及半圆形凸起与半圆形凹陷或半圆形沉积层相连地形的情况下，凸起地形部分的地震动问题。求解时，根据具体求解模型，将求解区域分为几个部分，其中之一为包括半圆形凸起在内的圆域，该圆域的下半部边界为“公共边界”。首先采用复变函数的形式，利用波函数展开法在各个区域内分别构造满足边界条件的位移解，然后通过移动坐标使之满足“公共边界”上位移、应力连续条件以及其他边界条件，从而建立起求解问题的无穷代数方程组．。本文具体工作如下：1．研究了SH波作用下，浅埋弹性夹杂和可移动刚性夹杂附近的半圆形凸起地形的地震动问题。采用“分区”方法，将求解区域分为两个部分，在区域Ⅰ中构造一个上半部边界应力为零，其余部分位移、应力任意的驻波解，在区域Ⅱ中构造“公共”边界和夹杂产生的散射波，且要求其满足水平边界应力自由的边界条件。然后移动坐标，满足“公共边界”和夹杂的边界条件，从而建立起求解该问题的无穷代数方程组。通过具体算例，给出半圆形凸起地形及其附近两侧水平地表位移幅值的数值结果，并对其进行了讨论。2．对SH波作用下，半圆形凸起与半圆形凹陷或半圆形沉积层相连地形的散射问题进行了研究。同样采用“分区”的方法进行求解。首先给出在半圆形凹陷的影响下，半圆形凸起地形对SH波散射的位移场；在此基础上，又求解了半圆形凸起地形在半圆形沉积层影响下对SH波的散射。分别给出具体算例，对凸起部分地表位移幅值随入射波波数，入射角，凹陷半径等各种参数的变化规律进行了讨论。3．采用“分区”的方法，求解出适合本文问题的Green函数，即含有半圆形凸起的弹性半空间内任意一点承受时间谐和的出平面线源荷载作用时位移场的解答。4．利用本文构造的Green函数，对SH波作用下浅埋裂纹附近的半圆形凸起地形的地震动问题进行了讨论。从半圆形凸起地形对SH波的散射问题出发，利用Green函数在基体内构造出裂纹，建立起浅埋裂纹附近的半圆形凸起地形的求解模型。给出SH波入射时，在裂纹影响下半圆形凸起地形的位移场。最后，通过具体算例给出了半圆形凸起地形地震动的数值结果。讨论了入射波波数、入射角等各种参数对半圆形凸起地形及其附近两侧水平地表位移幅值的影响。更多还原

【Abstract】 Researching the influence of local irregular topography on ground motion is one of the most important problems in earthquake engineering. Based on the idea of domain division, the complex function and moving coordinate are used to study the scattering of steady-state SH wave by a semi-cylindrical hill above a subsurface inclusion or a crack, and a semi-cylindrical hill adjoins a semi-cylindrical canyon or a semi-cylindrical alluvial valley, as well as the ground motion of the hill. According to idiographic model, the whole solution domain is divided into several parts during the press of solving. One of them is a circle domain, which includes the boundary of the hill and the junction interface. First, the displacement solutions satisfying the boundary conditions are constructed in every domain by complex function and wave function expansion. Second, the method of moving coordinate is used to make the displacement solutions conjoin at the common boundary and satisfiy other boundary conditions. Then the solutions of the problem are reduced to solve several series of infinite linear algebraic equations. The work of this paper can be detailed as follows:1. Scattering of SH wave by a semi-cylindrical hill above a subsurface elastic inclusion or a removable rigid inclusion is determined. According to the domain division idea, the solution domain is divided into two parts. A standing wave function is constructed in part I , which satisfies the condition that traction free at the hill edge and arbitrary at the other part. In domain II, including the junction interface and the subsurface inclusion in half-pace, the scattered wave function satisfying the condition of traction free at the horizontal surface is constructed. Then emploied to the method of moving coordinate, the two solutions are matched up on the junction interface, and satisfying the boundary conditions at the inclusion edge. Then the problem can be reduced to solve a series of infinite linear algebraic equations. The computational results of surface displacement are presented together with the discussion. 2. This paper presents the models and solutions for the scattering of SH wave by a semi-cylindrical hill adjoins a semi-cylindrical canyon or a semi-cylindrical alluvial valley. The idea of domain division is also the key step during the press of solving. At first, the displacement field of the semi-cylindrical hill including a semi-cylindrical canyon under SH wave is provided. Then the scattering of SH wave by a semi-cylindrical hill adjoins a semi-cylindrical alluvial valley is solved based on the idea of domain division. The calculating results are provided respectively, and the variation of surface displacement amplitudes with wave numbers, angle of incidence and the ratio of canyon are discussed.3. A suitable Green function is constructed employed to the idea of domain division. That is the fundermental solution of displacement field for an elastic half space with a semi-cylindrical hill under an out-plane harmonic line source loading at an arbitrary point in matrix.4. The Green function is employed to discuss the influence of subsurface crack on the motion of semi-cylindrical hill under SH wave. Based on the problem of scattering of SH wave by a semi-cylindrical hill, the Green function is used to make a subsurface crack, and then the model of a semi-cylindrical hill above a subsurface crack can be built. The displacement field of semi-cylindrical hill including a subsurface crack under SH wave is given. Finally, the calculating results of the hill motion are plotted to show the effect of wave numbers, angle of incidence and the other parameters on the surface displacement amplitudes.更多还原