The Modeling of Time-Dependent Deformation and Fracturing of Brittle Rocks Under Varying Confining and Pore Pressures

A numerical hydro-mechanical model for brittle creep is proposed to describe the time-dependent deformation of heterogeneous brittle rock under constant confining and pore pressures. Material heterogeneity and a local material degradation law are incorporated into the model at the mesoscale which affects the mechanical behavior of rocks to capture the co-operative interaction between microcracks in the transition from distributed to localized damage. The model also describes the spatiotemporal acoustic emissions in the rock during the progressive damage process. The approach presented in this contribution differs from macroscopic approaches based on constitutive laws and microscopic approaches focused on fracture propagation. The model is first validated using experimental data for porous sandstone and is then used to simulate brittle creep tests under varying constant confining and pore pressures and applied differential stresses. We further explore the influence of sample homogeneity on brittle creep. The model accurately replicates the classic creep behavior observed in laboratory brittle creep experiments. In agreement with experimental observations, our model shows that decreasing effective pressure, increasing the applied differential stress, and decreasing sample homogeneity increase the creep strain rate and decrease the time-to-failure, respectively. The model shows that complex macroscopic time-dependent behavior can be explained by the microscale interaction of elements. The fact that the simulations are able to capture a similar hydro-mechanical time-dependent response to that of laboratory experiments implies that the model is an appropriate tool to investigate the complex time-dependent behavior of heterogeneous brittle rocks under coupled hydro-mechanical loading.