An elastoplastic analytical method for characterizing the plastic zones around twin circular tunnels excavated at shallow depth

Accurate determination for the distribution pattern of plastic zones around twin shallow circular tunnels is essential for identifying surrounding rock instability mechanisms and optimizing tunnel design. This study presents an elastoplastic analytical method for characterizing plastic zones around twin circular tunnels excavated at shallow depth based on the Mohr-Coulomb yield criterion. A novel mapping function is developed through conformal transformation to convert a semi-infinite plane containing two mutually symmetric, arbitrarily shaped holes into a concentric tri-circular domain. Stress and displacement equilibrium equations for the ground surface boundary are established, and theoretical solutions for elastic stress combinations and plastic stress components in the surrounding rock are derived considering unit weight effects. By following stress continuity conditions along the elastic–plastic interfaces and equilibrium conditions at the ground surface, a nonlinear system of equations is formulated with the unknown mapping function coefficients as design variables. A closed-form solution for characterizing the plastic zones is obtained by solving these coefficients using a differential evolution algorithm. The method’s validity is verified through stress continuity examination, displacement boundary condition verification, and comparison with numerical simulations. Parametric analysis reveals that plastic zone distribution is positively correlated with tunnel center depth, tunnel radius, unit weight, and lateral pressure coefficients, while negatively correlated with cohesion and internal friction angle. The proposed method provides reliable theoretical guidance for design optimization and construction parameter selection in twin shallow-buried tunnel projects.