ABSTRACT
Deformation of saturated, porous, fractured solids involves interaction between fluid flow and solid deformation, that is, “coupling”, much as heat transfer and solid deformation interact through thermal stresses. Coupling is often one way in that temperature change induces thermal stresses, but the stresses do not influence heat transfer. While fluid flow influences stress, stress does not influence fluid flow, so permeability and hydraulic conductivity remain constant. Two-way coupling is possible. But the analysis assumes that coupling is just one way, embodied in the concept of “effective” stress in stress–strain relations such as Hooke’s law in elasticity and hydraulic conductivity in Darcy’s law, which implies a slow, laminar flow. Application of the divergence theorem to total stress and to fluid stress leads to a continuum result suitable for finite element approximation. The fluid moves relative to the solid, so additional work is done and power is needed.
