梯度饱和土的固结及波散射问题

发布时间：2018-12-18 18:36

【摘要】：梯度饱和土的固结理论及其中弹性波的散射理论,是当今水利水电工程和岩土工程领域十分关注的研究课题之一。固结理论在地基沉降、地基承载极限计算等方面有重要的应用,弹性波的散射在无损探伤、地震工程等方面有很好的应用背景。本文针对现有梯度饱和土固结和弹性波散射问题研究的不足,利用边界元方法系统的研究了梯度饱和土固结和弹性波散射。主要内容包括：第一章主要对研究现状做了较为详细的回顾。通过新型材料力学性能的现状分析,给出了梯度饱和土的概念和性能；根据经典饱和土固结理论的研究现状的概述,说明了梯度饱和土固结研究的必要性；对弹性波散射文献的回顾,确定了梯度饱和土中弹性波散射的研究方法；对数值分析方法的概述,说明了边界元方法是解答梯度饱和土固结和弹性波散射最有效的方法；最后给出了论文的主要研究内容。第二章基于传统的饱和多孔介质理论,以Biot理论为基础,根据渗流理论、弹性力学知识等,在基本假设条件下,详细推导了梯度饱和土介质中的控制固结和弹性波散射的基本方程.这些基本方程和经典饱和多孔介质的区别是一些材料参数是随位置坐标变化的。第三章研究了梯度饱和土的固结问题,首先采用积分变化和微分方程数值方法,研究了梯度饱和球在表面受有恒定向心荷载作用下的固结问题,其次采用分离变量和正交函数方法,研究了常荷载作用下梯度饱和土层在两面透水和上表面透水下表面不透水两种情况下的固结问题,最后利用常数边界元方法,研究了动态荷载作用下梯度饱和土在两种边界条件下的固结问题。第四章研究了SH波在正交各向异性梯度饱和土中缺陷处的散射,首先利用常数边界元方法,研究了梯度饱和土条中任意裂纹对SH波的散射,给出了裂纹面上入射波和散射波的位移计算公式；其次利用线边界元方法研究了梯度饱和土条中椭圆空腔对SH波的散射,给出了椭圆边界上入射波场和散射波场的位移计算方法。第五章首先给出了预测和计算地基沉降的经验公式及其计算思路,然后根据居民住宅建筑物的观测沉降时间关系,利用三种经验公式对其进行数据拟合,给出预测和估算公式,比较各种经验公式的优点和缺点。第六章对本文的主要内容进行了总结和分析后,针对不足之处展望了今后的工作重点。本文的创新工作包括： 1、通过饱和多孔材料和功能梯度材料的组合,引入了非均匀梯度饱和土的概念,研究了其中的固结和弹性波散射。 2、用数学方法严格推导了梯度饱和土中的Green函数,并用常数边界元和线边界元进行了数值算例和分析。 3、用最简洁的方法给出了二重积分和曲线积分的联系,通过Green公式,给出了边界积分方程的推导过程。
[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.
【学位授予单位】：宁夏大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU43

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