朱桂春, 张雯超, 陈胜.基于瑞利-里兹法的层状地基应变问题的近似解析解[J].河南理工大学学报（自然科学版）,2021,40(3):142-148.

ZHU G C, ZHANG W C, CHEN S.Approximate analytical solution to strain problem of the layered foundationbased on the Rayleigh-Ritz method[J].Journal of Henan Polytechnic University(Natural Science) ,2021,40(3):142-148.

基于瑞利-里兹法的层状地基应变问题的近似解析解

朱桂春1,2, 张雯超1, 陈胜3

1.苏州大学 轨道交通学院，江苏 苏州 215000;2.扬州工业职业技术学院 建筑工程学院，江苏 扬州 225000;3.中国地质大学（武汉新校 区建设指挥部），湖北 武汉 430074

摘要:为求解层状地基应变问题的解析解，探究土体分层特性对土层性质的影响，从各向同性平面问题的基本弹性方程出发，利用扩展的瑞利-里兹法构造泛函，并对泛函进行变分，求其驻值，编制Mathematica计算程序求解总体刚度矩阵的线性方程组，得到非对称荷载作用下层状地基平面应变问题的近似解析解。计算结果与有限元软件的模拟结果吻合，验证了程序的精确性，并分析了层状性质对地基变形的敏感程度。所求解不仅具有解析解精确求解的优点，还克服了传统有限元方法对无穷远处结构盲目截断的缺点，计算程序可编辑性强，同时计算结果表明土的分层特性对地基的位移具有显著影响，证明工程实践中采用模量与深度的加权平均近似模拟分层土的特性进行设计计算的方法是不妥当的。

关键词:各向同性;层状地基;瑞利-里兹法;平面应变

doi:10.16186/j.cnki.1673-9787.2020010029

基金项目:国家自然科学基金资助项目（51778386 ）；苏州市科技发展计划（民生科技）项目（SS201831 ）；扬州工业职业技术学院青蓝工程项目

收稿日期:2020/01/09

修回日期:2020/03/31

出版日期:2021/05/15

Approximate analytical solution to strain problem of the layered foundationbased on the Rayleigh-Ritz method

ZHU Guichun1,2, ZHANG Wenchao1, CHEN Sheng3

1.School of Rail Transportation， Soochaw University， Suzhou  215000 ,Jiangsu， China;2.School of Civil Engineering， Yangzhou Polytechnic Institute ，Yangzhou  225000 ， Jiangsu， China;3.Development & Construction Office of Cug （ Wuhan） New Campus， China University of Geosciences， Wuhan  430074 ， Hubei， China

Abstract:In order to solve the analytical solution of the strain problem of layered soil and to explore the influence of the layered soil on the soil properties， based on the basic elastic equation of the isotropic plane problem ，the extended Rayleigh Ritz method was used to construct the functional， and the variation of the functional was carried out to find its standing value. By compiling the Mathematica calculation program， the linear equations of the overall stiffness matrix were solved， and the approximate analytical solution of the plane strain problem of layered foundation under the action of the symmetrical load was obtained. The accuracy of the program was verified， and the sensitivity of layered properties to foundation deformation was analyzed. The solution not only had the advantages of accurate analytical solution， but also overcame the shortcomings of traditional finite element method for blind truncation of infinite structure. The calculation program was highly editable. At the same time， the calculation results showed that the layered soil characteristics had a significant impact on the displacement of the foundation. In engineering practice， the weighted average of modulus and depth used to approximate the characteristics of layered soil for design and calculation was not appropriate.

Key words:isotropy;layered foundation;Rayleigh-Ritz method;plane strain

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