Strength Criterion Effect on the Mechanical Response of Elasto-Brittle Plastic Rock Mass Considering Different Post-Peak Elastic Strain Forms

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 criterions are summarized and simplified based on the reasonable assumption. And then, a new unified criterion equation is established which includes all of the 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 non-associative flow rule under plane strain conditions. In the plastic zone, four different elastic strain assumptions are applied to solve the plastic zone deformation. The validity of the solution is also verified by comparing with the traditional solution. Finally, the influences of strength criterions, 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 Tresca(TR) and Von Mises (VM) criterions give a largest plastic zone radius, followed by Inscribe Drucker-Prager (IDP), Mohr-Coulomb (MC) and Middle Circumscribe Drucker-Prager (MDP) criterions and seem to underestimate the self-strength of rock mass. Circumscribe Drucker-Prager (CDP) criterion gives a smallest plastic zone radius and may be overestimated the self-strength of rock mass; Unified Strength Theory (UST0.5), Generalized SMP criterion (GSMP), Mogi- Coulomb (GMC) and Generalized Lade-Duncan (GLD) criterions which reasonably consider the effect of internal principal stresses give an intermediate range and can be strongly recommended for evaluating the mechanics and deformation behaviour of surrounding rock. As the dilation coefficient gradually increases, the dimensionless surface displacement presents the nonlinear increase characteristics; The deformation of plastic zone which are closely related to the strength criterions, 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 to 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 basis for evaluating the tunnel stability and support design reliability for different lithology rock mass in underground engineering.