Semianalytical Solutions for Elastic–Brittle–Plastic Surrounding Rock under Biaxial In Situ Stress Field Based on Unified Strength Criterion

Abstract

Semianalytical solutions for circular tunnels under biaxial in situ stress fields are developed in this study. The surrounding rock is assumed to behave as an elastic–brittle–plastic model and is characterized by the unified strength criterion. For the stress analysis, the perturbation solutions for arbitrary-orders plastic radius for deep-buried tunnels are presented with a newly developed numerical iterative method. Furthermore, a stress renewal algorithm is provided for determining the stress function in elastic zones more accurately. In accordance with the small deformation assumption and nonassociated flow rule, the analytical expressions for radial and circumference displacement in a plastic zone are presented for the first time. Subsequently, the undetermined coefficients in plastic displacement can be solved numerically with the least square method. Based on the proposed semianalytical solutions for circular tunnels, an improved equivalent circular method is developed for estimating the plastic radius and convergence of tunnels with arbitrary shaped cross sections approximately. The reliabilities of the proposed semianalytical solutions and the improved equivalent circular method are verified by comparing with numerical simulation and field data. Meanwhile, the whole calculating process is illustrated in a flow chart for the convenience of programming. From the perspective of practicality, the provided solutions can be employed for predicting plastic radius and ground response curves in tunnel excavation, which can supply important references for the tunnel stability assessment and support design.