Toward phenomenological universality of the mechanical behavior of arbitrarily anisotropic porous rocks

The great diversity of the microstructures of rocks impedes the use of a universal rock physics model with idealized geometry to correctly describe the mechanical behavior of rocks. In this quest for universality, by ignoring the detailed description of the causes of the observed phenomenon and only focusing on the empirical relation between the cause (applied stress) and the effect (resulting strain), phenomenological models such as the linear elastic Hooke’s law roughly describe the mechanical behavior of rocks of contrasted microstructures. However, in detail, numerous laboratory experiments covering broad frequency and strain ranges (both typically more than eight orders of magnitude) on various types of rocks have also shown deviations from Hooke’s law due to anisotropy, frequency dependence, nonlinearity, possibly with the presence of hysteresis, and poroelasticity. A phenomenological model has been recently proposed that synthesizes all these behaviors in a single model, but unfortunately does not integrate the porous nature of rocks. The new model is based on a reformulation in modified spectral decomposition of the previous work using the 7D poroelastic tensor linking the dynamic parameters (i.e., the six stress components and fluid pressure) and the kinematic parameters (i.e., the six strain components and the local increase of fluid content ζ). In addition to the elastic hysteresis of the stress-strain curves, the model also predicts the existence of a second hysteresis, or hydraulic hysteresis, of the curve fluid pressure p versus fluid content ζ, qualitatively similar to the first one. Indeed, the elastic hysteresis is due to the opening and the closure of some compliant pores at different stress levels. These pores represent possible access radii for the saturating fluid; the hysteresis in the geometry of the porous network also induces the hydraulic hysteresis in the p-ζ curves.