A meso-mechanical approach to time-dependent deformation and fracturing of partially saturated sandstone

Abstract In the present paper, we investigate how water acts to weaken rock in two complementary ways: mechanically through the generalized effective stress principle, and chemically through time-dependent rock-fluid reactions that allow subcritical crack growth. These processes, together with capillary suction and stress corrosion , were incorporated into a three-dimensional discrete element grain-based model to investigate both the time-independent and the time-dependent mechanical behavior of partially saturated sandstone at the mesoscale . The capillary parameters related to capillary suction and subcritical parameters related to stress corrosion in the model were calibrated to match the deformation behavior of partially saturated sandstone observed in laboratory. Following this calibration, numerical simulations of partially saturated sandstone with different levels of saturation were performed in uniaxial compression. The simulations show that both the peak strength and elastic modulus of the sandstone decrease as a function of increasing saturation and that the relationships between these properties can be expressed by negative exponential functions. The simulations are in good agreement with the experimental results. Second, the long-term brittle deformation of partially saturated sandstone with different levels of saturation under a constant stress level was modeled. The results show that time-to-failure during brittle creep decreases, and the initial strain and the minimum creep strain rate increases, as a function of increasing saturation, as also observed in laboratory. The simulations also highlight the formation of tensile cracks as the main deformation mechanism during brittle creep. Finally, brittle creep in partially saturated sandstone samples with different levels of saturation was studied under different stress levels. These simulations show that the minimum creep strain rate and the time-to-failure as a function of stress can be well described by exponential relations. We conclude that the proposed model permits a deeper understanding of time-independent and time-dependent deformation and failure of partially saturated sandstone at the mesoscale.