直角域中凸起和夹杂对SH波的散射和地震动

发布时间：2019-06-05 03:10

【摘要】：地震是对人类威胁最大的自然灾害之一。中国位处太平洋地震带和欧亚地震带之间,这样就决定了我国强震多发、震灾严重的基本国情。地震通过地球内部的板块运动积聚累积足够的能量,这些能量通过地震波从震源被释放到地球表面,造成剧烈的地震灾害。地球表面可视作应力自由面,由于自由面的约束条件,地震波将在地表发生反射,在临近地表处产生应力异常。地表复杂的地形地貌和地下空间工程结构的存在增加了额外的约束条件,它们在地震波的作用下发生散射,诱发动应力集中,造成显著的场地地震反应。地球的表层部分可以简化为弹性固体,地震波可以简化为弹性波。根据振动矢量和传播矢量之间的关系,可以把地震波分为P波和S波,按照偏振方向和观察平面之间的关系,S波又可分为SH波和SV波。注意到地球表层的主要组成部分是岩土,岩土的抗拉强度和抗压强度有着显著的差异,其抗剪性能尤差,地震波的剪切分量在地震灾害中起着重要的作用。综上所述,本文将地震体波的一种剪切分量简化为SH波,将地球表面的某个局部简化为直角域,将地表的某个复杂地形地貌简化为半圆形凸起,将地下空间工程结构简化为圆柱夹杂。这样,地震波场地反应的工程问题就被抽象为弹性直角域中凸起和夹杂对稳态SH平面波散射的科学问题。本文就研究内容而言,可以分为三部分。第一部分研究了稳态SH平面波对弹性直角域中半圆形凸起的散射及其地震动。按分区契合方法,分割含半圆形凸起的直角域,得到一个直角域和一个半圆域,分别构造其中的Green函数;按契合条件,得到定解积分方程,数值求解,得到对应数学物理定解问题的级数形式的解析解答。根据量纲分析方法,讨论相似律和相似准数,得到对应的无量纲数,无量纲位移和动应力集中因子。通过数值结果对求解的正确性和精度进行了分析,评估了收敛性和误差,对波数、入射角和垂直边界的影响进行了讨论。第二部分研究了稳态SH平面波对弹性直角域中的半圆形凸起和圆形孔洞的散射及其地震动。按分区契合方法,分割含半圆形凸起和圆形孔洞的直角域,得到一个含圆形孔洞的直角域和一个半圆域,分别构造其中的Green函数;求解弹性直角域中圆形孔洞对平面SH波的稳态散射;按契合条件,得到定解积分方程,数值求解,得到问题的级数解答。根据量纲分析方法,讨论相似律和相似准数。通过数值结果对求解的正确性和精度进行了分析,评估了收敛性和误差,对孔洞的位置和大小的影响以及孔洞边沿的动应力集中进行了讨论。第三部分研究了稳态SH平面波对弹性直角域中的半圆形凸起和圆形夹杂的散射及其地震动。按分区契合方法,分割含半圆形凸起和圆形夹杂的直角域,得到一个含圆形夹杂的直角域和一个半圆域,分别构造其中的Green函数;求解弹性直角域中圆形夹杂对平面SH波的稳态散射;按契合条件,得到定解积分方程,数值求解,得到问题的级数解答。根据量纲分析方法,讨论相似律和相似准数。通过数值结果对求解的正确性和精度进行了分析,评估了收敛性和误差,对夹杂的剪切模量比和质量密度比的影响以及夹杂边沿的动应力集中进行了讨论。
[Abstract]:The earthquake is one of the greatest natural disasters to the human threat. The China is located between the Pacific seismic belt and the Eurasian seismic belt, thus determining the basic national conditions in which the strong earthquakes in China and the earthquake disaster are serious. The earthquake has accumulated enough energy through the movement of the plate in the earth, which is released from the source to the earth's surface through the seismic waves, resulting in a strong earthquake disaster. The earth's surface can be regarded as a stress free surface, and due to the constraints of the free surface, the seismic wave will be reflected on the surface, and the stress anomaly will be generated near the surface. The complex terrain and the existence of the structure of the underground space increase the additional constraint conditions, which are scattered under the action of the seismic wave, and the dynamic stress concentration is induced, resulting in a significant site seismic response. The surface part of the earth can be simplified as an elastic solid, and the seismic wave can be simplified as an elastic wave. According to the relation between the vibration vector and the propagation vector, the seismic wave can be divided into P wave and S wave, and the S wave can be divided into SH wave and SV wave according to the relation between the polarization direction and the observation plane. It is noted that the main part of the earth's surface layer is the rock and soil, the tensile strength and the compressive strength of the rock and soil are obviously different, the shear performance is especially bad, and the shear component of the seismic wave plays an important role in the earthquake disaster. To sum up, a shear component of the seismic body wave is simplified into the SH wave, a local simplification of the earth's surface is simplified into a right-angle domain, and a complex terrain of the surface is simplified into a semi-circular projection, and the structure of the underground space engineering is simplified into a cylindrical inclusion. In this way, the engineering problem of the seismic wave field reaction is abstracted as the scientific problem of the projection and inclusion on the steady-state SH plane wave scattering in the elastic right-angle domain. In this paper, three parts can be divided into three parts. The first part studies the scattering and ground motion of the semi-circular projection in the elastic right-angle domain by the steady SH plane wave. The method comprises the following steps of: dividing a right-angle domain containing a semi-circular protrusion according to a partition matching method to obtain a right-angle domain and a semi-circle domain, and respectively constructing a Green function; and obtaining a fixed-solution integral equation and a numerical solution according to the fitting condition, and obtaining an analytical solution corresponding to a series form of a mathematical physical fixed solution problem. According to the dimensional analysis method, the similarity law and the quasi-number are discussed, and the corresponding dimensionless number, the dimensionless displacement and the dynamic stress concentration factor are obtained. The correctness and precision of the solution are analyzed by numerical results. The convergence and error are evaluated, and the influence of wave number, incident angle and vertical boundary is discussed. The second part studies the scattering and the ground motion of the semi-circular and circular holes in the elastic right-angle domain of the steady SH plane wave. The method comprises the following steps of: dividing a right-angle domain containing a semi-circular protrusion and a circular hole according to a partition matching method to obtain a right-angle domain containing a circular hole and a semi-circle domain, respectively constructing a Green function; solving the steady-state scattering of the circular hole on the plane SH wave in the elastic right-angle domain; and according to the fitting condition, And obtaining a fixed solution integral equation and a numerical solution to obtain a series solution of the problem. The similarity law and the quasi-number are discussed according to the dimensional analysis method. The correctness and precision of the solution are analyzed by numerical results, and the convergence and error are evaluated. The influence of the position and size of the hole and the dynamic stress concentration of the hole edge are discussed. The third part studies the scattering and ground motion of the semi-circular and circular inclusions in the elastic right-angle domain of the steady SH plane wave. The method comprises the following steps of: dividing a right-angle domain containing a semi-circular convex and a round inclusion to obtain a right-angle domain containing a circular inclusion and a semi-circle domain, respectively constructing a Green function; solving the steady-state scattering of the circular inclusion on the plane SH wave in the elastic right-angle domain; and according to the fitting condition, And obtaining a fixed solution integral equation and a numerical solution to obtain a series solution of the problem. The similarity law and the quasi-number are discussed according to the dimensional analysis method. The correctness and precision of the solution are analyzed by numerical results. The convergence and error are evaluated, and the influence of the ratio of the shear modulus of the inclusion and the mass density ratio and the dynamic stress concentration of the inclusion edge are discussed.
【学位授予单位】：哈尔滨工程大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O347.4

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