Rheological constitutive model and numerical method for rock mass anchored by NPR cable

To gain a deeper understanding of the anchoring mechanism in deep roadway engineering under long-term stable loading, this study establishes a three-dimensional rheological constitutive model for NPR cable anchored rock mass (NCAR). Based on the traditional Nishihara model, a nonlinear viscous element with a strain threshold triggering mechanism is introduced to characterize the entire process of rock mass degradation, steady-state, and accelerated creep. Meanwhile, an elastic–plastic series element is used to construct the mechanical constitutive relationship of the NPR cable. According to the mechanical response characteristics of the NPR cable and rock, the NCAR model is divided into six conditions: Case 1 (rock viscoelasticity, NPR cable elastic state); Case 2 (rock viscoelasticity, NPR cable constant resistance state); Case 3 (rock viscoplasticity, NPR cable elastic state); Case 4 (rock viscoplasticity, NPR cable constant resistance state); Case 5 (rock accelerated creep, NPR cable elastic state); Case 6 (rock accelerated creep, NPR cable constant resistance state). After obtaining the three-dimensional rheological constitutive equations for each working condition through theoretical derivation, a UMAT subroutine is developed on the ABAQUS platform for numerical solution, and the reliability of the model is validated by comparing theoretical and numerical solutions. Furthermore, a parameter sensitivity analysis is conducted to study the effects of engineering geological parameters (P₀, k, c), rock creep parameters (G₀, G₁, ${\eta }_1^{\prime }$, ${\eta }_2^{\prime }$, ${\eta }_3^{\prime }$,) and NPR cable anchoring parameters (G_b, n_b) on the creep evolution of roadway walls. Finally, the model is applied to the deep roadway engineering at the Shandong Wanfu Coal Mine, and the engineering applicability of the model is validated by comparing field monitoring data with numerical simulation results.