Analytic Solutions for Stress and Displacement of a Compressible Soil Layer above Bedrock
Publication: International Journal of Geomechanics
Volume 21, Issue 12
Abstract
In practical engineering projects, bedrock is often encountered under a compressible soil layer. Compared with the soil layer, the hard bedrock has negligible deformation, so the displacement at the bottom of the soil layer is considered to be zero. In this case, it is difficult to use the Boussinesq solution to accurately calculate the stress and displacement of the soil layer under the action of shallow foundations. In the past, the solution has mostly been approximated by the layer-wise summation method or the finite-element method. So far, there is no analytic method to accurately calculate the stress and displacement of the elastic compressible soil layer. In this paper, an analytic method is proposed to solve the plane strain problem under the action of strip foundations. By using a mapping function to convert a soil layer with a finite thickness into the unit circle in the image plane, the stress boundary conditions at the ground surface and the displacement boundary conditions at the bottom of the soil layer are represented by a combined expression for the boundary values of the two analytic functions. A system of linear equations to find the coefficients of the analytic functions is established using a new power series method, and it is solved using the least-squares method. The stress and displacement at any point in the soil layer can be calculated quickly and efficiently using the derived analytic function. The effects of soil layer thickness on soil layer stress and ground surface settlement are discussed, and the results are compared with those obtained by the finite-element method.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The study was supported by the Natural Science Foundation of China (Grant Nos. 51974124 and 51704117).
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Published In
International Journal of Geomechanics
Volume 21 • Issue 12 • December 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Nov 11, 2020
Accepted: Jul 15, 2021
Published online: Sep 29, 2021
Published in print: Dec 1, 2021
Discussion open until: Mar 1, 2022
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