【摘要】：梯度飽和土的固結(jié)理論及其中彈性波的散射理論,是當今水利水電工程和巖土工程領(lǐng)域十分關(guān)注的研究課題之一。固結(jié)理論在地基沉降、地基承載極限計算等方面有重要的應(yīng)用,彈性波的散射在無損探傷、地震工程等方面有很好的應(yīng)用背景。本文針對現(xiàn)有梯度飽和土固結(jié)和彈性波散射問題研究的不足,利用邊界元方法系統(tǒng)的研究了梯度飽和土固結(jié)和彈性波散射。主要內(nèi)容包括： 第一章主要對研究現(xiàn)狀做了較為詳細的回顧。通過新型材料力學性能的現(xiàn)狀分析,給出了梯度飽和土的概念和性能；根據(jù)經(jīng)典飽和土固結(jié)理論的研究現(xiàn)狀的概述,說明了梯度飽和土固結(jié)研究的必要性；對彈性波散射文獻的回顧,確定了梯度飽和土中彈性波散射的研究方法；對數(shù)值分析方法的概述,說明了邊界元方法是解答梯度飽和土固結(jié)和彈性波散射最有效的方法；最后給出了論文的主要研究內(nèi)容。 第二章基于傳統(tǒng)的飽和多孔介質(zhì)理論,以Biot理論為基礎(chǔ),根據(jù)滲流理論、彈性力學知識等,在基本假設(shè)條件下,詳細推導了梯度飽和土介質(zhì)中的控制固結(jié)和彈性波散射的基本方程.這些基本方程和經(jīng)典飽和多孔介質(zhì)的區(qū)別是一些材料參數(shù)是隨位置坐標變化的。 第三章研究了梯度飽和土的固結(jié)問題,首先采用積分變化和微分方程數(shù)值方法,研究了梯度飽和球在表面受有恒定向心荷載作用下的固結(jié)問題,其次采用分離變量和正交函數(shù)方法,研究了常荷載作用下梯度飽和土層在兩面透水和上表面透水下表面不透水兩種情況下的固結(jié)問題,最后利用常數(shù)邊界元方法,研究了動態(tài)荷載作用下梯度飽和土在兩種邊界條件下的固結(jié)問題。 第四章研究了SH波在正交各向異性梯度飽和土中缺陷處的散射,首先利用常數(shù)邊界元方法,研究了梯度飽和土條中任意裂紋對SH波的散射,給出了裂紋面上入射波和散射波的位移計算公式；其次利用線邊界元方法研究了梯度飽和土條中橢圓空腔對SH波的散射,給出了橢圓邊界上入射波場和散射波場的位移計算方法。 第五章首先給出了預測和計算地基沉降的經(jīng)驗公式及其計算思路,然后根據(jù)居民住宅建筑物的觀測沉降時間關(guān)系,利用三種經(jīng)驗公式對其進行數(shù)據(jù)擬合,給出預測和估算公式,比較各種經(jīng)驗公式的優(yōu)點和缺點。 第六章對本文的主要內(nèi)容進行了總結(jié)和分析后,針對不足之處展望了今后的工作重點。 本文的創(chuàng)新工作包括： 1、通過飽和多孔材料和功能梯度材料的組合,引入了非均勻梯度飽和土的概念,研究了其中的固結(jié)和彈性波散射。 2、用數(shù)學方法嚴格推導了梯度飽和土中的Green函數(shù),并用常數(shù)邊界元和線邊界元進行了數(shù)值算例和分析。 3、用最簡潔的方法給出了二重積分和曲線積分的聯(lián)系,通過Green公式,給出了邊界積分方程的推導過程。
[Abstract]:The consolidation theory of gradient saturated soil and the scattering theory of elastic wave in gradient saturated soil are one of the most important research topics in the field of water conservancy and hydropower engineering and geotechnical engineering. Consolidation theory has important applications in foundation settlement and calculation of foundation bearing limit, and elastic wave scattering has a good application background in non-destructive testing, seismic engineering and so on. In this paper, the consolidation and elastic wave scattering of gradient saturated soil are systematically studied by using the boundary element method, aiming at the shortcomings of the existing researches on the consolidation and elastic wave scattering of gradient saturated soil. The main contents are as follows: the first chapter reviews the research status in detail. Based on the analysis of the present situation of the mechanical properties of the new materials, the concept and performance of the gradient saturated soil are given, and the necessity of the study on the consolidation of the gradient saturated soil is explained according to the summary of the present research situation of the classical saturated soil consolidation theory. Based on the review of the literature on elastic wave scattering, the research method of elastic wave scattering in gradient saturated soil is determined, and the numerical analysis method is summarized, which shows that the boundary element method is the most effective method for solving the consolidation and elastic wave scattering of gradient saturated soil. Finally, the main contents of the thesis are given. The second chapter is based on the traditional saturated porous media theory, based on the Biot theory, according to the seepage theory, elastic mechanics knowledge, under the basic assumptions, The basic equations for controlling consolidation and elastic wave scattering in gradient saturated soil are derived in detail. The difference between these basic equations and classical saturated porous media is that some material parameters vary with the position coordinates. In chapter 3, the consolidation problem of gradient saturated soil is studied. Firstly, the consolidation problem of gradient saturated sphere under constant concentric load on the surface is studied by means of integral variation and differential equation numerical method. Secondly, using the method of separating variables and orthogonal function, the consolidation problem of gradient saturated soil layer under constant load is studied under the condition of water permeation on both sides and impermeability on the surface of the upper surface. Finally, the constant boundary element method is used. The consolidation of gradient saturated soil under two boundary conditions under dynamic loading is studied. In chapter 4, the scattering of SH waves at defects in orthotropic gradient saturated soil is studied. Firstly, the scattering of SH waves by arbitrary cracks in gradient saturated soil strips is studied by using the constant boundary element method. The formulas for calculating the displacement of incident and scattered waves on the crack surface are given. Secondly, the scattering of SH wave by elliptical cavity in gradient saturated soil strip is studied by using the linear boundary element method. The displacement calculation method of incident wave field and scattering wave field on elliptic boundary is given. In the fifth chapter, the empirical formulas for predicting and calculating foundation settlement and their calculation ideas are given. Then, according to the time relationship of observed settlement of residential buildings, three empirical formulas are used to fit the data, and the prediction and estimation formulas are given. Compare the advantages and disadvantages of various empirical formulas. Chapter 6 summarizes and analyzes the main contents of this paper, and looks forward to the future work. The innovations of this paper are as follows: 1. Through the combination of saturated porous materials and functionally gradient materials, the concept of non-uniform gradient saturated soil is introduced, and the consolidation and elastic wave scattering are studied. 2. The Green function in the gradient saturated soil is derived strictly by mathematical method, and the numerical examples and analysis are given by using the constant boundary element and the line boundary element. 3. The relation between double integral and curve integral is given by the simplest method, and the derivation process of boundary integral equation is given by Green formula.
【學位授予單位】：寧夏大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TU43

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