Solution of Strain-Softening Surrounding Rock in Deep Tunnel Incorporating 3D Hoek-Brown Failure Criterion and Flow Rule

Abstract

In order to investigate the influence of the intermediate principal stress on the stress and displacement of surrounding rock, a novel approach based on 3D Hoek-Brown (H-B) failure criterion was proposed. Taking the strain-softening characteristic of rock mass into account, the potential plastic zone is subdivided into a finite number of concentric annulus and a numerical procedure for calculating the stress and displacement of each annulus was presented. Strains were obtained based on the nonassociated and associated flow rule and 3D plastic potential function. Stresses were achieved by the stress equilibrium equation and generalized Hoek-Brown failure criterion. Using the proposed approach, we can get the solutions of the stress and displacement of the surrounding rock considering the intermediate principal stress. Moreover, the proposed approach was validated with the published results. Compared with the results based on generalized Hoek-Brown failure criterion, it is shown that the plastic radius calculated by 3D Hoek-Brown failure criterion is smaller than those solved by generalized H-B failure criterion, and the influences of dilatancy effect on the results based on the generalized H-B failure criterion are greater than those based on 3D H-B failure criterion. The displacements considering the nonassociated flow rule are smaller than those considering associated flow rules.

Modeling of Post-Failure Behavior of the Rock Mass and its Effect on the Stress-Deformation State in the Vicinity of a Mining Excavation

“…The analysis assumes that in the plastic phase the compressive strength of the rock mass decreases to the value of R c =0.5R c 0 . This is reflected in the condition of the limit state for this phase: (35) In the phase of a cracked three-phase medium, the strength properties are described by the equation:…”

“…The weakening of strength in the strain-softening zone, resulting from the develop-ment of the rock mass's deformation, continues until the rock mass reaches the residual strength. The reports on this model can be found, among others in the works [1,3,13,14,31,32,35]. On the basis of the studies [13,31], the relationships showing the state of stresses, deformations and displacements of the rock mass with features of the elastic-plastic medium with strain-softening and relationship defining the rock mass pressure exerted on the support, were given.…”