Optimal design on deep-buried non-circular tunnels under the influence of high geothermal temperature based on analytical calculation

This study explores the stress and deformation behavior of surrounding rock when excavating deeply buried, non-circular tunnels in high-geothermal environments. First, we derived the excavation mapping function for the tunnel cross-section using complex variable theory and conformal transformation, solved via a composite optimization algorithm. Next, we determined separate mapping functions for the geothermal-affected zone and the lining reinforcement region using a mixed penalty function approach. Stress and displacement fields in each domain were then obtained by solving the harmonic equation under prescribed boundary conditions and applying thermal-elastic theory alongside the Airy thermal-stress function. By invoking stress superposition and the separation of variables, we derived closed-form analytical solutions for stress and displacement throughout the model. Parameter studies reveal that both radial and tangential stresses in the lining increase markedly with rising temperature. Moreover, the introduction of a thermal insulation layer substantially reduces these stresses; when the insulation thickness reaches approximately 10–15 % of the lining thickness, additional stress reduction becomes marginal and stabilizes. These findings provide critical analytical guidance for controlling deformation and ensuring the structural safety of deep-buried, non-circular tunnels subject to high geothermal temperatures.