A New Unified Solution for Circular Opening considering Different Strength Criteria and the Postpeak Elastic Strain Form

Abstract

The strength criterion is an extremely important basis for evaluating the stability of surrounding rock and optimizing the support pressure design. In this paper, nine different strength criteria are summarized and simplified based on the reasonable assumption. Then, a new unified criterion equation is established, which includes all strength theories proposed by this paper. Meanwhile, a new unified closed-form solution for circular opening based on the newly proposed unified criterion equation is deduced with the infinite and finite external boundary combining with the nonassociative flow rule under plane strain conditions. In the plastic zone, four different elastic strain assumptions are applied to solving the plastic zone deformation considering the effect of rock mass damage. The solution’s validity is also verified by comparison with the traditional solution. Finally, the influences of strength criteria, dilation coefficient, elastic strain form of plastic zone, and rock mass damage on the mechanical response of surrounding rock are discussed in detail. The research result shows that TR and VM criteria give the largest plastic zone radius, followed by IDP, MC, and MDP criteria, and seem to underestimate the self-strength of rock mass; The CDP criterion gives the smallest plastic zone radius and may overestimate the self-strength of rock mass; UST0.5, GSMP, GMC, and GLD criteria that reasonably consider the effect of internal principal stresses give an intermediate range and can be strongly recommended for evaluating the mechanics and deformation behavior of surrounding rock; as the dilation coefficient gradually increases, the dimensionless surface displacement presents the nonlinear increase characteristics; the deformation of plastic zone and the ground response curve, which are closely related to the strength criteria, are also greatly influenced by the elastic strain assumption in the plastic zone and rock mass damage degree. The assumption that the elastic strain satisfies Hook’s law (Case 3) may be more reasonable compared with the continuous elastic strain (Case 1) and thick-walled cylinders (Case 2) assumptions; in addition, the Young’s modulus power function damage model seems to give more reasonable solution for the deformation of plastic zone and is suggested to be a preferred method for solving plastic displacement. The research results can provide very important theoretical bases for evaluating the tunnel stability and support design reliability of different lithology rock masses in underground engineering.