Nonlinear creep model of rock considering stress hardening-damage coupling

In this study, a nonlinear creep constitutive model for rock considering stress hardening-damage coupling is established. A power-law hardening function is introduced to reflect the stiffness enhancement caused by pore compaction in the primary creep stage, and a nonlinear damage evolution equation is adopted to characterize the accelerated creep induced by internal crack propagation. The explicit analytical solutions of each creep stage are derived through strict variable separation and integration, and the one-dimensional model is extended to a three-dimensional stress state. Based on triaxial creep test data under confining pressures of 5, 10, 15 and 20 MPa, model parameters are identified by the nonlinear least squares method. The results show that the proposed model is in good agreement with experimental curves, and can accurately describe the full-stage creep behavior including transient creep, steady-state creep and accelerated creep. Compared with the traditional Nishihara model, the new model has higher fitting accuracy, especially in the accelerated creep stage dominated by damage evolution. The long-term strengths determined from isochronous stress–strain curves are 60 MPa, 84 MPa, 150 MPa and 160 MPa under the four confining pressures, respectively, showing an approximately linear increasing trend. The research can provide a theoretical basis for long-term deformation prediction and stability analysis of deep rock engineering.