Modeling of rheological fracture behavior of rock cracks subjected to hydraulic pressure and far field stresses

Mathematical modelling of rheological fracture of rock cracks under the combined effect of hydraulic pressure and far field stresses has not been fully studied so far. The objectives of this study are to investigate the rheological fracture behavior and to establish a simple and practical model for rheological fracture of rock cracks under the combined effect of hydraulic pressure and far field stresses. Research results show that rheological fracture behavior of rock cracks is similar to the rock rheological process and can be decomposed into two stages: the decay and steady creep stages. By conducting a series of calculation analyses of the crack rheological fracture under different hydraulic pressures, it is found that wing crack propagation can be divided into two parts: the transient crack propagation at very high velocity and subcritical crack propagation at extreme low velocity. Moreover, both the transient crack propagation and subcritical crack propagation increase with an increase in the hydraulic pressure. Based on the introduction of an equivalent stress, an equivalent Burgers model for rock crack rheological fracture is proposed. The proposed equivalent Burgers model curves agree well with the theoretical curves under various hydraulic pressures, and generate a crack rheological propagation rate that is comparable to the theoretical analysis results. The proposed equivalent Burgers model lays the foundations for revealing the rheological behavior of fractured rock mass subjected to the combined action of hydraulic pressure and stresses.