DISPLACEMENT FUNCTIONS AND LINEAR TRANSFORMS APPLIED TO DIFFUSION THROUGH POROUS ELASTIC MEDIA

Abstract

It is sshown that the stresses and the pore pressure in porous elastic media through which a liquid is diffusing can be expressed in terms of two displacement functions. These functions are particularly useful in problems relating to a semi-infinite body or infinite layer when the stresses or displacements are prescribed on the surface. Problems of plane or axially symmetric strain are closely related when expressed in terms of these functions and the introduction of suitable repeated transforms (Fourier or Hankel followed by a Laplace transform) permits a parallel development of solutions for these two types of strain. The process is time-dependent since it involves diffusion. After an infinite time the pore pressure reduces to zero and the governing equations for the stresses and displacements in the medium reduce to the ordinary equations of infinitesimal elasticity. The limiting forms of the functions used in the paper can then be related to known stress functions. The Fourier and Hankel transforms can be regarded as specializations of the double Fourier transform, and it is shown in conclusion how the plane strain analysis can be generalized into a three-dimensional treatment.