An analytical solution of two-dimensional Biot’s consolidation due to a point sink within a saturated porous media

LI Pei-chao

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An analytical solution of two-dimensional Biot’s consolidation due to a point sink within a saturated porous media

更新时间：2026-06-25

- An analytical solution of two-dimensional Biot’s consolidation due to a point sink within a saturated porous media
- Vol. 32, Issue 9, (2011)
- 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：
  CLC： O357.3
- Online First：13 September 2011，
  
  Published：2011
- 稿件说明：
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LI Pei-chao. An analytical solution of two-dimensional Biot’s consolidation due to a point sink within a saturated porous media[J]. 2011, 32(9).
DOI：

LI Pei-chao. An analytical solution of two-dimensional Biot’s consolidation due to a point sink within a saturated porous media[J]. 2011, 32(9). DOI：

摘要

给出了有限二维饱和多孔介质因点汇诱发的Biot固结的一个解析解。其中假设多孔介质为均匀各向同性和线弹性，假设孔隙压力场符合第1类边界条件，数学模型采用可压缩多孔介质模型。利用傅里叶和拉普拉斯变换及相应反演获得了双重无穷项级数和形式的精确解。然后特别探讨了定流量点汇诱发的稳态解析解，并用文献现有解析解进行了验证。所提出的解析解适合于验证数值解，并可用于深入分析有限二维多孔介质的流-固耦合行为。

Abstract

An analytical solution is proposed for the Biot’s consolidation theory within a finite two-dimensional (2D)

isotropic

homogeneous

and fluid-saturated poroelastic media due to a point sink when the pore pressure is prescribed on the boundary. The analysis is based on compressible porous media models. Fourier and Laplace transforms and related inversions are implemented; and the exact solutions in the form of double summations of infinite series are obtained. In particular

the steady-state analytical solution due to a point sink of constant pumping rate is presented and validated by the exact solution available in the literature. The proposed analytical solution is applicable for testing the accuracy of numerical schemes; and it also can be used to further understand the behaviour of flow and deformation coupling in a finite 2D domain.

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