Elastoplastic analytical solutions for displacements of deep-buried circular tunnels considering intermediate principal stress

doi:10.3969/j.issn.1673-9787.2012.04.024

Abstract：The influence of intermediate principal stress was usually ignored for the problem of a deep-buried circular tunnel under a plane strain condition. But the deformations of surrounding rocks in a plastic area had a greater error. To consider the influence of intermediate principal stress to deep-buried circular tunnels, a plane strain hypothesis and a associated flow rule were given and Mohr-Coulomb strength criterion was precisely matched to Drucker-Prager strength criterion. The analytical expression of intermediate principal＇ stress in a plastic state for the perfect elastoplastic material was derived from Drucker-Prager strength criterion. Combi- ning the analytical expression and associated flow rule, any other hypothesis do not need introduced and the expression on volume dilatancy in a plastic area could be obtained. What is more, the analytical expressions of the displacement and stress in a plastic area for a deep-buried circular tunnel consider intermediate principal stress. In the expressions, the radial stress, the circumferential stress and the radius of a plastic area had the same form as the solutions of Kastner. But the form of intermediate principal stress could not be given in the solutions of Kastner and the new analytical expression of the displacement was entirely different from other literatures. Compared with the theoretic solutions of the displacement in other literatures, it was shown that the new solutions of the displacement were more reasonable. Thusly, the solutions considering intermediate principal stress could provide a reasonable theoretic basis for the calculation and design of a deep-buried circular tunnel.