层状地基三维问题的解析层元解

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摘要从弹性力学三维问题的基本控制方程出发，通过双重 Fourier 变换及解耦变换技术，推导出相应问题在积分变换域的解析解；根据该解析解，进而推导出三维弹性地基问题的精确刚度矩阵，即解析层元；然后根据有限层法原理，组装得到总体刚度矩阵；通过求解总体刚度矩阵形成的代数方程，得到三维层状地基问题在变换域内的解答；最后应用 Fourier 逆变换技术，得到其物理域内的解。与经典 Bounsinesq 解及有限元软件 ABAQUS 的结果进行比较，验证了本文理论及数值计算方法的正确性；计算分析结果还表明：土体的分层特性对地基沉降具有较显著的影响。

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	艾智勇
	曾凯
	曾文泽

关键词 ：解析层元, 三维层状地基, 解耦变换, Fourier 变换

Abstract：Starting from the basic equations of elasticity for three-dimensional problem, the analytical solution in the integral transform domain is obtained by use of the decoupled transform technique and the Fourier transform method. Based on the analytical solution, the exact stiffness matrix which is called analytical layer-element for the three-dimensional problem of multilayered elastic foundation is derived. The global stiffness matrix is assembled by means of the principle of finite layer method, and the solutions for the three-dimensional problem of multilayered foundation in the transform domain are obtained by solving the algebraic equations of the global stiffness matrix. Finaly, the solutions in the physical domain are acquired by inverting the Fourier transform. The validity of the proposed theory and numerical method is examined by comparing the results in this study with those of Boussinesq solution and the finite element soft ABAQUS, and numerical calculation shows that the influence of stratification on the displacement of foundation is remarkable.

Key words： analytical layer-element three-dimensional layered foundation decoupled transform Fourier transform

收稿日期: 2012-06-25

TU433

基金资助:国家自然科学基金项目(50578121)

作者简介: 艾智勇 (1966 – ),男，江西余江人，博士，教授，主要从事岩土及地下工程方面的教学和研究工作。

引用本文:

艾智勇, 曾凯, 曾文泽. 层状地基三维问题的解析层元解[J]. 岩土工程学报, 2012, 34(6): 1154-1158. AI Zhi-yong, ZENG Kai, ZENG Wen-ze. Analytical layer-element solution for three-dimensional problem of multilayered foundation. Chinese J. Geot. Eng., 2012, 34(6): 1154-1158.

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http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/ 或 http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/Y2012/V34/I6/1154

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