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ISSN (Print): 1872-2121
ISSN (Online): 2212-4047

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Analytical Solution and Consolidation Analysis of One-dimensional Large Strain Consolidation Differential Equation

Author(s): Shijia Liu, Huifeng Su*, Tao Yu, Shuo Zhao and Zhicheng Cui

Volume 16, Issue 1, 2022

Published on: 23 November, 2020

Article ID: e211221188280 Pages: 8

DOI: 10.2174/1874476105999201123204611

Price: $65

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Abstract

According to the universal one-dimensional consolidation equation introduced by Gibson, the governing equation with the excess pore water pressure as the control variable is derived, and the Fourier series solution under the boundary condition of single-sided drainage is deduced in detail by the standard mathematical and physical method. It verifies the correspondence between the analytical solution and the numerical solution from a theoretical point of view. Using this analytical solution, the nonlinear distribution of the excess pore pressure along the depth direction is obtained, and the traditional small strain consolidation is compared in terms of the average consolidation degree and the final settlement.

In the project, the one-dimensional consolidation theory established by Terzaghi is obviously no longer applicable to the foundation built on saturated soft clay with a compressive amount of 80%, so the research on the large strain theory began.

The purpose of this article is to give a detailed derivation process of the differential equation with excess pore pressure as the control variable in the analytical theory of one-dimensional nonlinear large-strain consolidation, and verify it based on calculation examples, hoping to provide suitable theoretical basis for large-deformation foundations.

This article mainly uses detailed formula derivation and standard mathematical and physical methods to derive the Fourier series solution of the consolidation differential equation according to the boundary conditions of single-sided permeable water and compare and verify the analysis according to an example of calculation.

Based on Gibson's general equation of consolidation and its theory, the detailed derivation process of differential equations with excess pore water pressure as the control variable is given.

According to the example, the image shows the distribution of excess pore pressure with depth, and comparative analysis of large and small strains. If all other conditions are the same, when mv1=1 MPa-1, it can be calculated according to the large and small strains, but when mv1≥3MPa-1, for the soil that should be calculated according to large strain, it is unreasonable to calculate according to small strain. Therefore, the calculation error of the two methods is very large, so it is necessary to distinguish the large and small strains.

Keywords: Large strain, one-dimensional, consolidation, series solution, single-sided drainage, small strain consolidation.

Graphical Abstract

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