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Mathematical Problems in Engineering
Volume 2016, Article ID 3047213, 13 pages
Research Article

Finite Element Analysis of Biot’s Consolidation with a Coupled Nonlinear Flow Model

1Institute of Geotechnical Engineering, Ningbo University, Ningbo 315211, China
2Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China

Received 24 September 2015; Revised 20 December 2015; Accepted 22 December 2015

Academic Editor: Thibault Lemaire

Copyright © 2016 Yue-bao Deng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A nonlinear flow relationship, which assumes that the fluid flow in the soil skeleton obeys the Hansbo non-Darcian flow and that the coefficient of permeability changes with void ratio, was incorporated into Biot’s general consolidation theory for a consolidation simulation of normally consolidated soft ground with or without vertical drains. The governing equations with the coupled nonlinear flow model were presented first for the force equilibrium condition and then for the continuity condition. Based on the weighted residual method, the finite element (FE) formulations were then derived, and an existing FE program was modified accordingly to take the nonlinear flow model into consideration. Comparative analyses using established theoretical solutions and numerical solutions were completed, and the results were satisfactory. On this basis, we investigated the effect of the coupled nonlinear flow on consolidation development.