Biot constitutive relation and porosity perturbation equation

ABSTRACTIn a porous medium, the porosity perturbation, i.e., the change in porosity, is an integral part of a deformation process. Yet, there is no explicit statement about that in the Biot theory. By linking its constitutive relation to the continuity equations, the tacit assumption about the porosity perturbation in this theory is inferred. The linear dependence of the porosity perturbation on the pressure difference of the two phases is embedded in its constitutive relation. The solid and fluid pressures affect the change in porosity in equal magnitude but in opposite sense. By assuming that the fluid pressure may affect the porosity perturbation to an extent different than that of the solid pressure, the Biot constitutive relation is generalized. This introduces a nondimensional parameter. It could be named the porosity effective pressure coefficient, because the measure of the extent the fluid pressure affects the change in porosity relative to the solid pressure. In the regime in which the fluid pre...