A dual-scale approach to model time-dependent deformation, creep and fracturing of brittle rocks

A physically-motivated dual-scale modeling approach is proposed to model the time-dependent damage, deformation and fracturing behavior of heterogeneous brittle rocks during creep. The proposed model uses a microcrack-based damage constitutive law established at the elemental scale, in which the time-dependent degradation of elastic stiffness and damage-induced anisotropy are directly linked to microcrack growth. The evolution of mechanical heterogeneity is based on a Weibull distribution that captures the transition from distributed damage to localized failure. The key feature of the proposed model is to establish an adequate prediction of macroscopic creep behavior based on the microscopic kinetics of microcrack growth rather than the phenomenological material degradation laws adopted in previously-developed statistical models. The general capabilities of the proposed model are illustrated with numerical simulations of biaxial creep tests. The influences of differential stresses, heterogeneities and microscopic element sizes on creep behavior in brittle rocks are also examined. Results from such analyses indicate that the proposed model not only accurately replicates the trimodal phases of creep deformation and the associated temporal evolution of acoustic emission but also follows the progressive evolution of fracture modes and morphology commonly observed. Thus, subject to suitable calibration, this model provides an attractive virtual experimental tool to probe process-based understanding of complex long-term problems related to structures on an in geologic media.