doi:10.16186/j.cnki.1673-9787.2020010029

Received:2020/01/09

Revised:2020/03/31

Published: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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