Stress-induced anisotropic poroelasticity in granular materials and porous rock

Homogeneous, isotropic poroelastic theory predicts that pore pressure in an undrained medium should vary with changes in applied mean stress only. However, for undrained granular materials a small increase in differential stress at constant mean stress results in a reversible decrease in pore pressure [Lockner and Stanchits, 2002] reflecting a dilatant elastic volumetric strain. The magnitude of the pore pressure change increases as the differential stress increases. Situations where this dependence of pore pressure on differential stress may modulate the standard expected response of pore pressure to stress change are studies of Coulomb stress change, the stability of undrained fault zones during earthquake nucleation, and pore pressure during dynamic stress drop. Assumption of isotropic poroelasticity is probably invalid for granular aggregates if differential stress is high, as it is near failure. We present an idealized, qualitative elastic model of granular aggregates which simply explains the observed sensitivity of pore pressure to differential stress. We assume the response is determined by the elastic behavior in the region of contact between grains. The stiffness of grain contacts is a non-linear function of macroscopic applied contact-normal stress (e.g., Hertzian contact), and highly stressed contacts are stiffer than ones at lower contact normal stress. Thus application of differential stress induces an anisotropic elastic stiffness that reflects the magnitude of the differential stress. We propose a model incorporating Hertzian contact between grains and find that an increase in differential stress at constant mean stress results in a pore volume increase and corresponding decrease in pore pressure. The model predicts a stress sensitivity of pore volume which increases with the differential stress as observed in experiments. From this model and general considerations, we conclude that the poroelastic response of undrained granular materials, e.g., soils and faults gouges, in the shallow crust should generally be non-linear. For significant differential stress, the poroelastic response of rocks in the shallow crust should be non-linear and anisotropic. This stress-induced anisotropy should increase with differential stress.