Catastrophic failure mechanism of deep roadways and stress gradient control models

Numerous factors influence the deformation and control of roadway surrounding rock, with stress gradient and pre-tension being two key factors. To investigate the intrinsic relationship between stress gradient and pre-tension and determine the optimal pre-tension, a stress gradient solution model was developed based on the unified strength theory, incorporating the effects of intermediate principal stress. This model addresses the elastic-plastic behavior of a circular roadway under bidirectional unequal pressure conditions, analyzes the impact of various parameters on roadway surrounding rock support, and, by combining stress gradient theory with the stress gradient compensation criterion, derives the surrounding rock stress gradient compensation coefficient, thereby providing a theoretical foundation for the precise determination of pre-tension. In the model derivation, the redistribution of surrounding-rock stress, plastic zone expansion, and continuity conditions at the elastoplastic interface are considered. Key parameters, including the intermediate principal stress coefficient, lateral pressure coefficient, and support pretension, are introduced to derive analytical expressions for the surrounding-rock stress, plastic zone extent, and stress gradient, and to establish a quantitative relationship between pretension and the stress gradient compensation coefficient. The applicability of the stress gradient solution method was assessed through comparisons with existing case studies. The model shows that improper selection of the intermediate principal stress coefficient may increase the risk of roadway failure or lead to higher support costs. However, the application of anchor rod pre-tension mitigates the adverse effects caused by an inappropriate b value. Furthermore, as pre-tension increases, the stress gradient within the surrounding rock’s plastic zone increases, while the gradient in the elastic zone decreases, thereby reducing the degradation of the surrounding rock. Quantifying the distribution of the stress gradient and support effectiveness under varying pre-tension conditions reveals that pre-tension is positively correlated with roadway support effectiveness. The range of the plastic zone continuously decreases as pre-tension increases, and the stability of the surrounding rock improves as the stress gradient rises. Based on these findings, a compensation relationship between pre-tension and stress gradient has been established, and the optimal compensation ratio has been proposed. Engineering application results show that, when the pretension is determined using the stress-gradient compensation method, the field-measured cumulative roadway deformation is reduced from approximately 450 mm under conventional support conditions to approximately 250 mm. The deformation is reduced by approximately 40%, and the surrounding-rock deformation tends to stabilize, indicating that the method is applicable to the determination of rock-bolt support parameters.