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Research Papers

An Analytical Solution of Two-Dimensional Flow and Deformation Coupling Due to a Point Source Within a Finite Poroelastic Media

[+] Author and Article Information
Peichao Li

College of Mechanical Engineering,   Shanghai University of Engineering Science, Shanghai, 201620, Chinawiselee18@163.comDepartment of Modern Mechanics,  University of Science and Technology of China, Hefei, 230027, Chinawiselee18@163.com

Detang Lu

College of Mechanical Engineering,   Shanghai University of Engineering Science, Shanghai, 201620, ChinaDepartment of Modern Mechanics,  University of Science and Technology of China, Hefei, 230027, China

J. Appl. Mech 78(6), 061020 (Sep 09, 2011) (6 pages) doi:10.1115/1.4004524 History: Received October 09, 2009; Accepted May 02, 2011; Posted July 06, 2011; Published September 09, 2011; Online September 09, 2011

An analytical solution is derived for the time-dependent flow and deformation coupling of a saturated isotropic homogeneous incompressible poroelastic media within a two-dimensional (2D) finite domain due to a point source at some arbitrary position. In this study, the pore pressure field is assumed to conform to the second type of boundary conditions. Boundary conditions of the displacement field are chosen with care to match the appropriate finite sine and cosine transforms and simplify the resulting solution. It is found that the analytical solution is always independent of the Poisson’s ratio. The detailed solutions are given for the case of a periodic point source with zero pressure derivatives on the boundaries and for an imposed pressure derivative on the lower edge in the absence of a source. The presented analytical solutions are highly applicable for calibrating numerical codes, and meanwhile they can be used to further investigate the transient behavior of flow and deformation coupling induced by fluid withdrawal within a 2D finite poroelastic media.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 5

Contour of P at time t=π/2 due to a point source at (0.25, 0.25). Parameter values are a=1,b=1,ω=1,α=2..

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Figure 4

Contours of u and w at time t=π/2 due to a point source at (0.25, 0.25). Parameter values are a=1,b=1,ω=1,α=2.

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Figure 3

Vector of the displacement at time t=π/2 due to a point source at (0.25, 0.25). Parameter values are a=1,b=1,ω=1,α=2..

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Figure 2

Specific boundary conditions in this study

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Figure 1

Schematic diagram of a finite poroelastic media of dimensionless lengths x = a and y = b. Illustrated are an inner point source Q at (x0 , z0 ) and the boundary conditions in Ref. [22].

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