Creep of unconsolidated sand due to delayed grain breakage

Hydrocarbon production or other activities involving extraction of underground fluids often cause surface subsidence with a time-lag. Such delay is often attributed to the rate-dependent rheological behavior of reservoir rocks. This paper proposes a thermomechanical model able to capture the rate-dependent behavior of unconsolidated sand while tracking grain breakage processes at the microscale. The energetics of subcritical crack propagation at grain scale is firstly investigated and the characteristics of its dissipation function are observed. A similar strategy is then used to generalize the dissipation function of a continuum breakage model. The extended model is characterized by a mathematical structure resembling Perzyna-type viscoplastic formulations and only involves two additional parameters, one controlling the magnitude of rate effects, and another coincident with the intrinsic corrosion index of the grain-forming mineral which controls both the intensity of the rate effects and the shape of the creep curves. The model is benchmarked against oedometric compression data for quartz sand. The predicted creep responses at various stress levels agree well with recorded measurements. In addition, the stress corrosion index indirectly calibrated from macroscopic data falls within the range observed from fracture tests on typical rock-forming minerals, thus corroborating the validity of the selected approach.