Micromechanics of brittle creep in rocks

Abstract

In the upper crust, the chemical influence of pore water promotes time dependent brittle deformation through sub‐critical crack growth. Sub‐critical crack growth allows rocks to deform and fail at stresses well below their short‐term failure strength, and even at constant applied stress (“brittle creep”). Here we provide a micromechanical model describing time dependent brittle creep of water‐saturated rocks under triaxial stress conditions. Macroscopic brittle creep is modeled on the basis of microcrack extension under compressive stresses due to sub‐critical crack growth. The incremental strains due to the growth of cracks in compression are derived from the sliding wing crack model of Ashby and Sammis(1990), and the crack length evolution is computed from Charles' law. The macroscopic strains and strain rates computed from the model are non linear, and compare well with experimental results obtained on granite, low porosity sandstone and basalt rock samples. Primary creep (decelerating strain) corresponds to decelerating crack growth, due to an initial decrease in stress intensity factor with increasing crack length in compression. Tertiary creep (accelerating strain as failure is approached) corresponds to an increase in crack growth rate due to crack interactions. Secondary creep with apparently constant strain rate arises as an inflexion between those two end‐member phases. The minimum strain rate at the inflexion point can be estimated analytically as a function of model parameters, effective confining pressure and temperature, which provides an approximate creep law for the process. The creep law is used to infer the long term strain rate as a function of depth in the upper crust due to the action of the applied stresses: in this way, sub‐critical cracking reduces the failure stress in a manner equivalent to a decrease in cohesion. We also investigate the competition with pressure solution in porous rocks, and show that the transition from sub‐critical cracking to pressure solution dominated creep occurs with increasing depth and decreasing strain rates.