This paper discusses some numerical analyses performed with a generalized three-dimensional Hoek & Brown (HB) model which strength criterion has been considered to simulate the mechanical behavior of rocks in brittle conditions. For this purpose, this constitutive framework has been enhanced with hyperbolic softening and non-linear dilation, thus enabling to investigate failure modes in the form of dilating shear bands. To restore the objectivity of the numerical solution during the development of localized strain, a viscous regularization technique has been employed to simulate localization phenomena in two different initial boundary value problems, both computed by using the finite element software PLAXIS 2D: (i) a biaxial test, and (ii) a tunnel excavation problem simulated through a deconfinement process. While the former has been considered to test the effect of the viscous parameter in governing the structural behavior of the rock sample, the latter has been selected to model the shear bands propagation during the process of a tunnel excavation in which the rocks mass has been characterized by different mechanical properties. The computed solutions have been compared with existing formulations based on the framework of HB strength criteria, thus enabling to further validate the implementation of the proposed constitutive equations.

Hoek & Brown (HB) failure criteria have been employed over the past decades in common engineering applications due to their extended capability to capture the non-linear yielding of different types of rocks. Often implemented within a perfect plastic framework, this constitutive approach is here enhanced by introducing a softening rule to simulate the post-peak behaviour of rocks in the brittle regime. For this purpose, the degradation of the material properties has been expressed as a function of an internal variable (i.e., the cumulated value of deviatoric plastic strains) which allows one to simulate the rock failure resulting from dilating shearing. Furthermore, to accurately describe the non-linear dilatancy after the peak, the same hyperbolic trend has been applied also to the material properties governing the expression of the plastic potential. The performance of these constitutive equations has been inspected through parametric analyses to emphasize the role of the softening parameters at material point level, as well as to study the strain localization potential of the Hoek & Brown model with Softening (HBS). As a further validation, the shear band angles predicted with the theory have been compared by performing the same tests with finite element code PLAXIS 2D, thus confirming the model capability to simulate failure mechanisms within a strain localization regime.

Numerical methods and computing techniques are now integrated components in rock mechanics and rock engineering design, providing an opportunity to increase our fundamental understanding of the factors governing rock mass behavior. It is increasingly evident that models of rock mass behavior should incorporate realistic representation of fracture networks as well as should constitute an effective aid for the evaluation of scale-effects for those engineering problem where performing field tests at different scales is not technically or economically viable. This paper provides a discussion on proposed theoretical approach broadly adopted to study the stability of slopes that include intermittent joints. Limitations of the approach are demonstrated by showing the results of numerical analyses carried out with discontinuum (ELFEN) and continuum (PLAXIS) codes applied to the study of conceptual slope and foundation problems in fractured rock masses. The paper highlights the importance in rock engineering design of applying numerical modeling for rock bridge related problems, and emphasis is given to methods to account for rock bridge strength at the desired engineering scale.