Predicting brittle creep in porous rock with rate-sensitive material stability analyses

Abstract

Brittle creep allows porous rock to fail under stresses significantly lower than its conventional strength, making its onset critical for both natural and engineered geomechanical processes, as well as the long-term stability of underground structures. This study presents a novel theoretical framework to evaluate the conditions for the initiation of brittle creep at the constitutive level. To achieve this, we simulate the brittle creep through a viscoplastic framework equipped with bounding surface techniques proposed by the authors, which at variance with previous studies reflects explicitly the possibility of initiating delayed cracking prior to traditional rock strength (e.g., sub-critical cracking) and frames it in the concept of time-dependent stability. The stability criteria for the onset of brittle creep are derived by examining the spectral properties of the system matrix associated with the ordinary differential equation governing creep dynamics. The performance of the proposed constitutive model and stability criteria is then evaluated against experimental data on porous sandstone. The theoretical framework is subsequently used to investigate the influence of stress conditions on creep response, identifying four distinct stress regions based on creep stability behavior. Finally, we apply the stability criterion to explore the deterioration of long-term strength of porous rock due to brittle creep and examine the relationship between this strength degradation and confining pressures. The findings of this study provide theoretical support for understanding the similarities between the failure mechanisms underlying brittle failure caused by varying and sustained loads (i.e., creep). They also offer insights into the connection between the bifurcation of accelerated creep, which can lead to either uncontrolled failure or regained stability, as influenced by volume changes in the rock.