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.@en

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.@en

Evidence shows that in the presence of extended stages of undrained creep, loose sands may approach liquefaction instabilities with a non-negligible time lag with respect to the application of loading. In this paper, a mechanical interpretation of such delayed failure events is provided by using stability criteria for rate-dependent materials. For this purpose, a viscoplastic constitutive law for sands has been calibrated to replicate delayed failure processes documented in the literature. To explain the origin of the transition from stable to unstable creep, the model predictions have been inspected from a mathematical standpoint and a strategy to evaluate the time required for the initiation of failure has been provided. The analyses show that the acceleration of the creep strains anticipates the sharp increase in the rate of pore water pressure, thus constituting a precursor to runaway failure. Furthermore, the computed stresses at which the two variables accelerate are located in proximity of the instability line for static liquefaction, with a shift from it that depends on the rate of loading prior to creep and the soil viscosity. These findings provide support to understand the interplay between rate-dependent soil properties and delayed liquefaction by offering a new conceptual platform to interpret the temporal evolution of flow failures observed under field or laboratory conditions.@en

This paper discusses the numerical results for a consolidation test studied by using a hydromechanical model formulated within a numerical homogenization approach, the so-called finite element squared method, FE2. This model is characterized by two observation scales: at the microscopic scale, the microstructure of the material is described as an assembly of hyperelastic grains connected by cohesive interfaces that define a network of channels in which fluid can percolate. This microstructure, periodically distributed in the small-scale, identifies the Representative Elementary Volume of the material. At the macroscopic scale, the material is treated as a continuum and the corresponding constitutive equations are obtained by means of a numerical homogenization process on the microscopic problem. In this manner, the total stress of the mixture, the density of the mixture, the fluid mass flow and the fluid mass content can be computed. The objective of this work is to compare the numerical results with the analytical solution of a classical oedometric test using the poroelastic theory of Biot (1941) [1]. For this purpose, it is shown that the hydromechanical behavior obtained with the selected FE2 method is characterized by a classical Biot-like porous medium and the resulting macroscopic properties can be illustrated in light of the hydromechanical mechanisms at the microscopic scale.@en