A novel criterion for yield shear displacement of rock discontinuities based on renormalization group theory

Abstract

Research on the plastic shear deformation of rock discontinuities is essential to the structural design of rock engineering, and the yield point is an important indicator for plastic shear deformation. In this paper, a conceptual model based on renormalization group theory is proposed to qualitatively explain the evolution mode of shear deformation. Then, considering the stress transfer mechanism, the mathematical description of the critical failure point is derived. Subsequently, the criterion for yield shear displacement is obtained by combining the renormalization group model with the shear constitutive model. Finally, experimental results based on the ratio of yield stress to shear strength for different rock types are provided to verify the proposed criterion. The theoretical and mathematical analysis indicates that the yield point is the phase transition point during the shear deformation of rock discontinuities, which is equivalent to the critical failure point in the renormalization group theory. The relationship between the failure probability of n-order blocks and the basic failure probability can be obtained according to the stress transfer mechanism and the conditional probability, so that a mathematical description of the critical failure point can be established. The verification by both laboratory and in-situ tests shows that the results of the proposed criterion are consistent with those of classical methods. In addition, the determination of the parameters has little influence on the criterion's performance, which means the proposed criterion could eliminate the subjectiveness in determining the yield shear displacement.