Three-Dimensional Direct Solution Method for the Elastoplastic Analysis of Deep-Buried Soft Rock Tunnels Considering the Volumetric Force of Anchor Rods

The theoretical analysis of deep-buried soft rock tunnels with anchor rod support in the past generally employed simplified methods such as strength superposition or dividing anchorage zones into n microelements, which resulted in a certain discrepancy between the theoretical solutions and the field measurements. In this study, based on the positioning of anchor rods in tunnel dynamic construction, the differential equation for the equilibrium of the anchorage elastic zone was regarded as a nonhomogeneous Euler equation. Combining this with the Taylor series to simplify the complex second-order differential equation, a direct solution method for three-dimensional excavation of surrounding rock in deep-buried soft rock tunnels with elastoplastic behavior was proposed. Subsequently, the feasibility of the theoretical analytical method was verified through numerical simulations. It was found that using grouting anchorage and increasing the length of anchor rods can significantly reduce the displacement of the surrounding rock and the deformation of the surrounding rock wall, and the support pressure is also reduced accordingly. The pretightening force of anchor rods can alleviate the deformation and support pressure of the surrounding rock and prevent anchor rod failure. The method of composing anchor rods and surrounding rock into a composite load-bearing structure by equivalently treating the strength of anchor rods as the strength of surrounding rock is excessively conservative and should not be utilized. The results of this study can provide theoretical guidance for the elastoplastic analysis of deep-buried soft rock tunnels with anchor rod support.