Strain-softening Rock Mass Research Articles

A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass

A simple numerical procedure for calculating the distribution of stresses and radial displacements around a circular tunnel excavated in a strain-softening Mohr–Coulomb or generalized Hoek–Brown rock mass is proposed. The problem is considered as axisymmetric, i.e. the initial stress state is assumed to be hydrostatic and the rock mass is said to be isotropic. By invoking the finite difference approximation of the equilibrium and compatibility equations, the increments of stresses and strains for each ring, starting from the outmost one for which boundary conditions are known a priori, are calculated in a successive manner. In the proposed approach, the potential plastic zone is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium equation. For the strain-softening behavior, it is assumed that all the strength parameters are a linear function of deviatoric plastic strain. Several illustrative examples are given to demonstrate the performance of the proposed method. For the brittle–plastic case, the results show a very good agreement with the closed-form solution. For strain-softening cases, the predictions by the proposed method are also in good agreement with the known rigorous numerical solutions. It is shown that the approximate solution converges to the exact solution when the increment of stress for each ring becomes smaller. The influence of the strength parameter ‘a’, appearing in the generalized Hoek–Brown criterion, on the elasto-plastic solutions is examined through the establishment of ground reaction curves and the discussion for the locations of the plastic radii.

Study of bifurcation in the problem of unloading a circular excavation in a strain-softening material

Abstract This paper presents a study of bifurcation in the problem of unloading a circular excavation in a strain-softening rock mass. The analysis focuses on how bifurcation affects the calculation of ground reaction curves for tunnels. To begin with, the most important issues in strain-softening behaviour are discussed, with the concepts of bifurcation and localisation presented by reviewing physical observations of these phenomena in rocks and rock masses. Next, theoretical formulations and numerical approaches are briefly reviewed, and on this basis, a sufficiently good description of phenomena involved in bifurcation can be obtained using standard FDM or FEM codes with sufficiently fine meshes. A series of models of tunnels excavated in strain-softening materials were created and analysed using an FDM-based code, in which bifurcation and localisation could be clearly observed. These simulation results were compared with self-similar results, revealing that the effects of these phenomena are irrelevant when an appropriately large spatial scale, as in tunnels, is considered.

An empirical dilatancy index for the dilatant deformation of rock

The dilation angle is the most commonly used parameter to study nonlinear post-peak dilatancy (PPD) behavior and simulate surrounding rock deformation; however, simplified or constant dilatancy models are often used in numerical calculations owing to their simple mathematical forms. This study developed a PPD model for rocks (rock masses) based on the Alejano–Alonso (A–A) dilatancy model. The developed model comprehensively reflects the influences of confining pressure (σ3) and plastic shear strain (γp), with the advantages of a simple mathematical form, while requiring fewer parameters and demonstrating a clear physical significance. The overall fitting accuracy of the PPD model for 11 different rocks was found to be higher than that of the A–A model, particularly for Witwatersrand quartzite and jointed granite. The applicability and reliability of the PPD model to jointed granites and different scaled Moura coals were also investigated, and the model was found to be more suitable for the soft and large-scale rocks, e.g. deep rock mass. The PPD model was also successfully applied in studying the mechanical response of a circular tunnel excavated in strain-softening rock mass, and the developed semi-analytical solution was compared and verified with existing analytical solutions. The sensitivities of the rock dilatancy to γp and σ3 showed significant spatial variabilities along the radial direction of the surrounding rock, and the dilation angle did not exhibit a monotonical increasing or decreasing law from the elastic–plastic boundary to the tunnel wall, thereby presenting the σ3-or γp-dominated differential effects of rock dilatancy. Tunnel deformation parabolically or exponentially increased with increasing in situ stress (buried depth). The developed PPD model is promising to conduct refined numerical and analytical analyses for deep tunneling, which produces extensive plastic deformation and exhibits significant nonlinear post-peak behavior.