Analytical Solution of Green's Functions for a Poroelastic Medium

Subsurface rocks (by their nature) are filled with cracks and pores which are saturated with one or more fluid phases (water، air، oil، etc.). These fluids have a significant influence on the mechanical behavior of a rock mass. Closing the state of the stress to failure surface and pore pressure effect on the rock deformation are among these influences of pore fluids. To account for these effects، one should investigate the rock mass response in an elastic medium with porosity. Therefore، poroelastic theory should be used. In poroelastic medium the governing equations، stress-strain and strain-displacement relations are affected by pore pressure and reciprocal effects of displacements and pore pressure. In this paper، firstly the constitutive equations and other required relations for describing a poroelastic medium are presented. Then the coupled effect of pore pressure and displacements is removed by using a potential method. Differential equations of time-dependent and time-independent are solved for a point force and point source which gives Green’s functions. Resulted Green’s functions can be used in any suitable numerical method such as boundary element method to investigate the response of rock mass to poroelastic effects.