Tunnel surrounding rock plastic zone in the layered rock mass with the elastoplastic theory

Existing theoretical studies on the plastic zone of tunnel surrounding rock mainly focus on the circular tunnel in the isotropic rock mass, with limited attention paid to layered rock mass. This study developed a theoretical framework to evaluate the plastic zone in circular tunnels embedded within layered rock formations. First, based on Kastner's method for calculating the surrounding rock plastic zone in the circular tunnel, the unified strength theory and the interaction mechanism of the surrounding rock and supporting structure were introduced to establish a calculation model for the surrounding rock plastic zone in the circular tunnel. This model accounts for σ₂ and the interaction of the surrounding rock and supporting structure. Based on the deformation and failure mode of the layered rock mass under compression, the calculation method of the equivalent shear strength and deformation parameters of the layered rock mass under compression was obtained, and then the modified plastic zone model in the circular tunnel of the layered rock mass was set up by substituting the above calculation methods into that of the circular tunnel in the isotropic rock mass. The results show that the plastic zone in layered rock exhibits pronounced anisotropy and directional dependence, reaching maximum or minimum extents along directions parallel or perpendicular to bedding planes. Parametric analysis shows that increases in rock layer cohesion, internal friction angle, and the intermediate principal stress coefficient (b) lead to reductions in the plastic zone area, though with diminishing marginal effects. Conversely, increasing the elastic modulus of the layers expands the plastic zone, albeit with a gradually decreasing rate of growth that approaches asymptotic behavior. For example, As the friction angle increases from 10° to 15°, 20°, 25°, and 30°, the surrounding rock plastic zone area decreases from 97.04 m² to 67.95, 50.90, 39.74, 31.85 m², respectively, with the reduction degree of 29.98%, 25.09%, 21.93%, and 19.85% respectively. The reduction degree decreases, indicates that with increasing the rock layer friction angle, its influence on the surrounding rock plastic zone gradually decreases. The research results can provide valuable information for tunnel construction in layered rock mass.