Study on the Load-Bearing Mechanism of Tensile Prestressed Bolt–Cable Coupled Support in Deep Roadways

In response to the challenges of surrounding-rock control in deep high-stress roadways, this study focuses on a synergistic support system of actively tensioned prestressed bolts and cables. Utilizing a combination of theoretical analysis, numerical simulation, and field testing, a coupled load-bearing mechanism and the methodology for determining appropriate pre-tension were systematically investigated. A mechanical model of the anchored composite system was established, revealing the synergistic support mechanism between actively tensioned prestressed bolts and cables. Theoretical calculation formulas for the load-bearing strength of the anchored composite system under both individual and combined support conditions were derived. By analyzing the in situ stress environment of the surrounding rock, a calculation method was derived for the threshold of constraint strength required for the anchored composite system to maintain roadway stability; this threshold is directly related to the magnitude of the primary rock stress. Based on this, a support design criterion was established, centered on the equilibrium relationship between the constraint strength threshold and the bearing strength of the anchored composite system. This criterion can be used to evaluate the feasibility of support schemes, assess the rationality of applied pre-tension, and determine the reasonable matching range for the pre-tension of bolts and cables through a bivariate function defining their respective thresholds. Finally, using the transportation roadway Working Face 4209 as an engineering case, the feasibility and reliability of the proposed theoretical model and design method were verified through numerical simulations and field tests, providing a theoretical basis and practical reference for the supportive design of high-stress roadways.