Roof stability analysis for a cylindrical tunnel under varied burial conditions in soil strata following the power-law strength criterion

This study investigates the stability of circular tunnel roofs in soil strata under varied burial conditions using the Power-Law strength criterion. Within the limit analysis framework, a three-dimensional (3D) roof-collapse model is adopted, building on established tunnel-roof failure mechanisms and extending them to nonlinear soil strength. Based on the energy-balance equation, analytical expressions are derived for three stability indicators: the stability number (N), factor of safety (FoS), and normalized support pressure (p/γR). Optimization algorithms are employed to obtain upper-bound solutions for these indicators. Parametric analyses examine the effects of soil strength parameters, 3D geometry, and burial depth on roof stability. For practical engineering applications, the required support pressure can be rapidly estimated using design charts for specified factors of safety, providing a theoretical basis for the preliminary design of circular shallow-buried tunnels.