Rate- and strain-dependent brittle deformation of rocks

We develop a unifying framework to quantify rate-dependent deformation in the brittle field and establish links between the microscale time-dependent crack growth processes and the macroscopically observed rate dependency. Triaxial deformation experiments have been performed under both constant strain rate and constant stress (creep) conditions on three types of sandstone. The measured relative evolution of P wave speeds as a function of inelastic axial strain is similar for both types of test, despite differences in strain rate of up to 3 orders of magnitude. This similarity indicates that there exists a direct, time-independent link between the microstructural state (as reflected by the variations in P wave speed) and the inelastic axial strain. Comparison of applied stresses between constant strain rate and creep experiments as a function of inelastic strain indicates that creep deformation requires less mechanical work to bring the sample to failure. This energy deficit corresponds to a stress deficit, which can be related to a deficit in energy release rate of the microcracks. We establish empirically that the creep strain rate is given by (epsilon) over dot proportional to exp(Delta Q/sigma*), where Delta Q is the stress deficit (negative) and sigma* is an activation stress. This empirical exponential relation between creep strain rate and stress deficit is analogous to rate-and-state friction law. We develop a micromechanical approach based on fracture mechanics to determine the evolution of an effective stress intensity factor at crack tips during creep deformation and estimate the activation volume of the stress corrosion reaction responsible for brittle creep.