An analytical solution of finite two-dimensional Biot’s consolidation due to surface loading within a fluid-saturated porous medium

LI Pei-chao; XU Zhen-hua

doi:10.16285/j.rsm.2016.09.022

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An analytical solution of finite two-dimensional Biot’s consolidation due to surface loading within a fluid-saturated porous medium

更新时间：2026-06-25

- An analytical solution of finite two-dimensional Biot’s consolidation due to surface loading within a fluid-saturated porous medium
- Vol. 37, Issue 9, Pages: 2599-2602(2016)
- 作者机构：
  
  上海工程技术大学机械工程学院,上海,201620
- 作者简介：
- 基金信息：
- DOI：10.16285/j.rsm.2016.09.022
  CLC： O357.3
- Online First：09 June 2018，
  
  Published：2016
- 稿件说明：
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LI Pei-chao, XU Zhen-hua. An analytical solution of finite two-dimensional Biot’s consolidation due to surface loading within a fluid-saturated porous medium[J]. 2016, 37(9): 2599-2602.
DOI：

LI Pei-chao, XU Zhen-hua. An analytical solution of finite two-dimensional Biot’s consolidation due to surface loading within a fluid-saturated porous medium[J]. 2016, 37(9): 2599-2602. DOI： 10.16285/j.rsm.2016.09.022.

摘要

推导了有限矩形区域饱和多孔介质因表面载荷诱发的Biot固结的一个解析解。假设多孔介质为均匀各向同性和线弹性，并被单相流体所饱和；控制方程组采用不可压缩多孔介质模型；孔隙压力场采用狄利克雷边界条件，上下表面位移场符合物理边界，而左右侧面位移场边界条件则由人为特别给定。利用有限正余弦变换和拉普拉斯变换及数值反演获得了物理空间孔隙压力场和位移场的半解析解，其体现为双重级数和的封闭形式。最后以某软黏土层平面应变固结为例，利用有限元分析软件ABAQUS对所给出的解析解进行了验证，同时基于该解析解考察了孔隙压力场和位移场的时空演化规律。所给出的解析解可用于深入分析有限二维饱和多孔介质的流-固耦合力学行为。

Abstract

An analytical solution is presented for Biot’s consolidation induced by surface loading within a finite two-dimensional (2D)

isotropic

homogeneous and fluid-saturated poroelastic media. Here

the consolidation is assumed to be governed by the incompressible porous media model. The Dirichlet boundary conditions are adopted for the pore pressure field

and the displacements field on the upper and lower surfaces conforms to physical boundaries. However

the boundary conditions of the displacements field on the lateral sides are specifically given. Finite sine and cosine transforms

Laplace transforms and Laplace numerical inversions are implemented; and the analytical solutions in the closed-form of double summations of series are obtained. Finally

an example of plane strain consolidation is studied. The proposed exact solution is validated against the numerical solution by the finite element analysis software ABAQUS. And based on the presented analytical solution

the spatiotemporal evolution of the pore pressure field and the displacements field is briefly examined. The presented analytical solution can be of great potential to further understand the behavior of flow and deformation coupling in a finite 2D fluid-saturated porous medium.

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