The Elastoplastic Solutions of Deep Buried Roadway Based on the Generalized 3D Hoek-Brown Strength Criterion considering Strain-Softening Properties

The deep underground roadways are widely used in the mining industries at present, but the relevant theoretical bases are not fully understood. In this paper, the numerical solutions for strain-softening surrounding rock under the generalized three-dimensional (3D) Hoek-Brown (GZZ) strength criterion are developed incorporating the confinement-dependent characteristics of ψ and η ∗ and their influences on the stress and displacement of equivalent circular roadway. On the basic of a finite difference, method for the strain-softening model is proposed to consider the variation of ψ and η ∗ in analyzing the strain-softening behavior of rock masses. Combining the equilibrium equation and strength criterion, the stress conditions for each annulus are calculated analytically. The displacement for each step is obtained analytically by solving the differential equation through invoking flow rule and Hooke’s law. The accuracy of the proposed method is verified through the comparison between the results and the previous studies. The effect of intermediate principal stress of GZZ strength criterion is considered; the rationality of the proposed method is verified by two aspects. First, by comparing with the two-dimensional narrow and generalized H-B strength criterion, the advantage of GZZ strength criterion that considers the effect intermediate main stress is highlighted. On the other hand, compared with the three-dimensional linear D-P criterion, the advantage of GZZ strength criterion in the theoretical research of deep underground roadway in coal mine is highlighted. The results show that the strain-softening of the surrounding rock in the plastic zone of the roadway can reduce the pressure of the surrounding rock, but it will greatly increase its deformation. In the high field stress areas, the strain-softening of surrounding rock is the key reason for the destruction of the roadway. It is suggested that in the design and calculation of the support system of the roadway, the strain-softening characteristics of the surrounding rock should be considered, which is very important to avoid large deformation and damage of roadway.