Novel perturbation solutions for deep-buried non-circular tunnels under biaxial in situ stress field based on Mohr-Coulomb criterion

Abstract

Based on Mohr-Coulomb criterion, the generalized perturbation solutions for elastic-brittle-plastic rock surrounding deep-buried non-circular tunnels are presented in this study. The asymptotic expansions and a novel equivalent elliptical method adaptable for arbitrary shaped tunnel are provided for the perturbation analysis. Concerning the plastic analysis, the recurrence formulas and a simplified semi-analytical approach are developed for solving arbitrary-order approximations of stress functions conveniently. Subsequently, a novel undetermined coefficient method incorporating the stress continuity on elastoplastic interface is presented for determining the plastic radius and stress functions in elastic zone. On the basis of the preceding solutions, the extended solutions with equivalent elliptical method are developed for further expanding the applicable range of solutions. Besides, the perturbation analysis based on generalized Hoek-Brown criterion can be implemented in terms of the equivalent angles of friction and cohesive strengths. The whole computing process is provided in flow chart for the convenience of programming. The reliability of the solutions has been verified by comparing with the calculating results of numerical simulation. Significant improvements can be noticed for the predicted plastic radius compared with the results by the existing equivalent circular method. From a theoretical point of view, the developed perturbation solutions with equivalent section method complete the framework of the elastoplastic analysis for non-circular tunnels. From the perspective of practicality, the proposed solutions can provide preliminary insight for the rapid stability evaluation, plastic radius prediction, and tunnel outline design in practical engineering.