An elastoplastic analytical method for characterizing the plastic zone around a shallow circular tunnel

This research proposes an elastoplastic analytical method for characterizing the plastic zone around a shallow circular tunnel, based on Mohr-Coulomb yield criterion. Using conformal mapping, we transformed a semi-infinite planar region with a vertically axisymmetric hole with arbitrary shapes into an annulus with a simple boundary shape. The combined effect of the unit weight of surrounding rock and the uniform surface surcharge pressure is considered to derive the theoretical solutions for elastic stress functions of surrounding rock in a shallow circular tunnel and plastic stress components of surrounding rock based on Mohr-Coulomb yield criterion. Nonlinear equations involving the mapping function coefficients are established according to boundary stress and strain conditions at the ground surface, and stress continuity conditions at the elastic-plastic interface. These coefficients are set as design variables, and solutions are developed for elastic stress functions and plastic zone range of a shallow circular tunnel, with a newly proposed mapping function and a newly defined fitness function through differential- evolution algorithm. The rationality of the proposed method is verified by comparing to the numerical simulation results, showing improved accuracy compared to existing methods. Its engineering applicability is also verified by comparing to the field monitoring results. Finally, the main factors influencing the plastic zone around a shallow circular tunnel are characterized. The proposed method can provide theoretical support for optimizing engineering design and construction parameters, including surrounding rock stress, plastic radius, excavation depth, and radius of shallow buried tunnels.