Nonlinear poroelasticity equations for a fluid-filled granular medium

Robert Burridge and Sergio Kostek
Schlumberger-Doll Research
Ridgefield, Connecticut

Abstract: An elastic granular material contains a compressible Newtonian liquid in its intergranular space. Because of the local Hertzian deformations in the neighborhoods of the grain contacts the elastic response of the granular matriz is nonlinear. We derive a form of the Biot equations appropriate to this situation starting from the elastodynamic equations in the solid, the Stokes equations in the fluid, and a non-slip condition with continuity of traction components of stress at the interface. Using two-scale homogenization we modify the general scheme of Burridge and Keller (1981), which was used for a linearly elastic matrix, for this nonlinear situation.