Poroelasticity by Alexander H.-D. Cheng

Author:Alexander H.-D. Cheng
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(7.805)

(7.806)

where

(7.807)

The layered geometry investigated here allows the application of integral transform in the x-direction to the above set of equations to remove the dependence on the x-coordinate. When Laplace transform is further applied to the time variable, the governing equations (7.805) and (7.806) reduce to ordinary differential equations whose solutions are readily found.

7.17.1 General Solution for Layered Problem

For a domain made of multiple layers, with each layer containing a homogeneous poroelastic material, we define a set of dependent variables, displacement, stress, pore pressure, etc., for each layer. Using the displacement function representation, these reduce to the set of functions and , with i = 1, 2, …, n, for an n-layer system.

The Fourier transform and its inverse are defined as follows [151]

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