Elastic-plastic analysis of circular tunnel based on unified strength theory and considering multiple plastic zones

Abstract

Considering that the internal friction angle of the surrounding rock is not a constant but a function of the mean normal stress, and the unified strength theory (UST) is used as the plastic condition of the tunnel surrounding rock, the plastic zone of the circular tunnel surrounding rock is divided into multiple annular regions. For different plastic zones, there are different yield conditions represented by different stress functions, the elastic-plastic analysis of circular tunnels is performed by using the piecewise linearization of nonlinear yield function, stress and displacement in the elastic-plastic zone and the radius of the plastic zone are obtained by combining the equilibrium equations. It is shown that the radius of the plastic zone increases, the radial stresses in the elastic-plastic zone and the circumferential stresses in the plastic zone become smaller and the circumferential stresses in the elastic zone becomes larger compared with that of only one plastic zone. By using single factor analysis method, the calculated values of the tunnel displacements and plastic radii by UST were compared with those obtained by the Mohr-Coulomb (M-C) criterion, Drucker-Prager (D-P) criterion, and Zienkiewicz-Pande (Z-P) criterion. The analysis shows that under the same conditions, the solution of UST is smaller than M-C criterion and D-P criterion, therefore, the selection of rock strength criterion has great influence on the calculation of rock mechanics and engineering, the proper application of UST will guarantee the safety of engineering practice and have more practical value.