An analytical micro-macro model of stress drops during brittle creep in rocks

Stress drops during long-term creep in brittle rocks have a great significance for evaluating earthquake mechanisms. Microcracks initiation, growth, nucleation, and coalescence play an essential role in stress drop of rocks. However, the micro-macro relationship between stress drops and time-dependent microcracks development in intact brittle rocks is rarely proposed during long-term creep. In this study, a Damage Rate- and State- Fracture Model (DRSFM) is proposed to explain the mechanism of creep stress drops in intact brittle rocks. This DRSFM is formulated by combining the wing crack growth model, the subcritical cracking law, the relationship between axial and shear mechanical behaviors, the suggested crack-strain relationship and the step function of time-dependent initial damage. This suggested crack-strain relationship is established by linking the micro-macro damage definitions in brittle solids. The step function of time-dependent initial damage qualitatively describes the damage variables caused by the presence of shear bands from microcracks accumulation and coalescence under different time in brittle rocks during creep. A step initial damage variable is corresponding to the presence of an individual shear band, which causes a drop of shear stress in rocks. In the scale of earth crusts, this DRSFM provides an implication for the evolution of earthquake mechanisms. The smaller step initial damage variable may be corresponding to a smaller tremor or earthquake, and the larger step initial damage variable may be corresponding to a larger tremor or earthquake. The time variation explains the time difference between the two earthquakes. The rationality of this DRSFM is approximately verified by comparing the published theoretical and experimental results. Furthermore, the relationship between the friction in faults and the shear stress in intact rocks is explained in detail, which provides a certain help for the understanding of the conclusion that the onset of stress drop caused by shear fracture is similar to the onset of stress drop caused by frictional stick-slip.