ELASTOPLASTIC STRESS AND DISPLACEMENT ANALYTICAL SOLUTIONS TO DEEP-BURIED CIRCULAR TUNNELS CONSIDERING INTERMEDIATE PRINCIPAL STRESS AND DILATANCY

The influence of intermediate principal stress was usually ignored for the problem of a deep-buried circular tunnel under plane strain condition, which would lead to significant difference from the actual conditions of surrounding rocks in plastic areas. To consider the influence of intermediate principal stress on deep-buried circular tunnels, plane strain hypothesis and non-associated flow rule were adopted while Mohr-Coulomb strength criterion was precisely matched to Drucker-Prager strength criterion. The analytical expression of intermediate principal stress in plastic state for the perfect elastoplastic material with dilatancy was derived from Drucker-Prager strength criterion. The intermediate principal stress was closely relative to the dilation angle. By combining the analytical expression and non-associated flow rule, any other hypothesis need not to be introduced and the expression on volume dilatancy due to the dilation angle in plastic area could be obtained. Furthermore, the analytical expressions of the displacement and stress in plastic area for a deep-buried circular tunnel considering intermediate principal stress and dilatancy can also be obtained. In the expressions, the radial stress, the circumferential stress and the radius of plastic area have the same form as the solutions of Kastner. But the form of intermediate principal could not be given in 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 shows the new solutions of the displacement are more reasonable. The solutions considering intermediate principal stress and dilatancy could therefore provide reasonable theoretic basis for the calculation and design of a deep-buried circular tunnel.