Analysis of softening characteristics of surrounding rock in plastic zones of deep roadways

The nonlinearity and heterogeneity of rock masses manifest across all scales, rendering the geometric and constitutive equations derived from the continuum assumption inadequate for characterizing post-peak deformation and failure processes in engineering rock masses. Given the inherent limitations of continuum mechanics in addressing stress and deformation analyses of surrounding rock, this study employs boundary conditions and equilibrium equations to approximate the stress distribution within surrounding rock softening zones through mean-value mathematical principles. Specifically, it estimates the initial radius of plastic softening zones in circular chambers and back-calculates the softening law governing the post-peak internal friction angle, which is effectively described by a Boltzmann function. By applying mass conservation principles to analyze surrounding rock deformation, this investigation provides theoretical support for the design of long-term stability support systems in deep engineering projects.