【摘要】：地震是對人類威脅最大的自然災(zāi)害之一。中國位處太平洋地震帶和歐亞地震帶之間,這樣就決定了我國強震多發(fā)、震災(zāi)嚴重的基本國情。地震通過地球內(nèi)部的板塊運動積聚累積足夠的能量,這些能量通過地震波從震源被釋放到地球表面,造成劇烈的地震災(zāi)害。地球表面可視作應(yīng)力自由面,由于自由面的約束條件,地震波將在地表發(fā)生反射,在臨近地表處產(chǎn)生應(yīng)力異常。地表復雜的地形地貌和地下空間工程結(jié)構(gòu)的存在增加了額外的約束條件,它們在地震波的作用下發(fā)生散射,誘發(fā)動應(yīng)力集中,造成顯著的場地地震反應(yīng)。地球的表層部分可以簡化為彈性固體,地震波可以簡化為彈性波。根據(jù)振動矢量和傳播矢量之間的關(guān)系,可以把地震波分為P波和S波,按照偏振方向和觀察平面之間的關(guān)系,S波又可分為SH波和SV波。注意到地球表層的主要組成部分是巖土,巖土的抗拉強度和抗壓強度有著顯著的差異,其抗剪性能尤差,地震波的剪切分量在地震災(zāi)害中起著重要的作用。綜上所述,本文將地震體波的一種剪切分量簡化為SH波,將地球表面的某個局部簡化為直角域,將地表的某個復雜地形地貌簡化為半圓形凸起,將地下空間工程結(jié)構(gòu)簡化為圓柱夾雜。這樣,地震波場地反應(yīng)的工程問題就被抽象為彈性直角域中凸起和夾雜對穩(wěn)態(tài)SH平面波散射的科學問題。本文就研究內(nèi)容而言,可以分為三部分。第一部分研究了穩(wěn)態(tài)SH平面波對彈性直角域中半圓形凸起的散射及其地震動。按分區(qū)契合方法,分割含半圓形凸起的直角域,得到一個直角域和一個半圓域,分別構(gòu)造其中的Green函數(shù);按契合條件,得到定解積分方程,數(shù)值求解,得到對應(yīng)數(shù)學物理定解問題的級數(shù)形式的解析解答。根據(jù)量綱分析方法,討論相似律和相似準數(shù),得到對應(yīng)的無量綱數(shù),無量綱位移和動應(yīng)力集中因子。通過數(shù)值結(jié)果對求解的正確性和精度進行了分析,評估了收斂性和誤差,對波數(shù)、入射角和垂直邊界的影響進行了討論。第二部分研究了穩(wěn)態(tài)SH平面波對彈性直角域中的半圓形凸起和圓形孔洞的散射及其地震動。按分區(qū)契合方法,分割含半圓形凸起和圓形孔洞的直角域,得到一個含圓形孔洞的直角域和一個半圓域,分別構(gòu)造其中的Green函數(shù);求解彈性直角域中圓形孔洞對平面SH波的穩(wěn)態(tài)散射;按契合條件,得到定解積分方程,數(shù)值求解,得到問題的級數(shù)解答。根據(jù)量綱分析方法,討論相似律和相似準數(shù)。通過數(shù)值結(jié)果對求解的正確性和精度進行了分析,評估了收斂性和誤差,對孔洞的位置和大小的影響以及孔洞邊沿的動應(yīng)力集中進行了討論。第三部分研究了穩(wěn)態(tài)SH平面波對彈性直角域中的半圓形凸起和圓形夾雜的散射及其地震動。按分區(qū)契合方法,分割含半圓形凸起和圓形夾雜的直角域,得到一個含圓形夾雜的直角域和一個半圓域,分別構(gòu)造其中的Green函數(shù);求解彈性直角域中圓形夾雜對平面SH波的穩(wěn)態(tài)散射;按契合條件,得到定解積分方程,數(shù)值求解,得到問題的級數(shù)解答。根據(jù)量綱分析方法,討論相似律和相似準數(shù)。通過數(shù)值結(jié)果對求解的正確性和精度進行了分析,評估了收斂性和誤差,對夾雜的剪切模量比和質(zhì)量密度比的影響以及夾雜邊沿的動應(yīng)力集中進行了討論。
[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.
【學位授予單位】：哈爾濱工程大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O347.4

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