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

Energy foundation technology is expected to make a significant contribution to the use of renewable energy. In this context, this paper presents the use of Finite Element simulation using PLAXIS software for modelling different benchmark applications in Geothermal Foundations. An implicit fully-coupled numerical scheme with global adaptive time stepping are implemented to ensure computational efficiency and stability. Firstly, a transient simulation of thermal response tests [1], often used to estimate the thermal conductivity of ground and thermal resistance of pile, is presented. In the second part, a Thermo-Hydro-Mechanical analysis is performed to simulate the behavior of a single heat pile subject to a thermal load cycle [2]. Several ingredients (constitutive behavior, interface finite elements etc.) are employed to simulate soil-structure interactions. The obtained solutions are validated against available simulation and experimental data to demonstrate the applicability of the simulator to energy foundation analysis and design.@en

To simulate the behaviour of saturated sands under cyclic loading, the PM4Sand constitutive model (version 3.1) formulated by Boulanger & Ziotopoulou [1], is used. The model can realistically reproduce the pore pressure build-up, accumulation of strain as well as triggering of liquefaction. The effect of dif-ferent relative densities on liquefaction resistance is evaluated by comparing the results of a site response analysis performed on a soil column character-ized by a saturated sand layer and subjected to given earthquake signals. The analyses are performed using the finite element code PLAXIS.@en

When saturated soils are subjected to an earthquake, the excess pore pressuresincrease, and, in the case of sands, this may cause liquefaction. To simulate the behaviour of saturated sands under cyclic loading, the PM4Sand constitutive model (version 3.1) formulated by Boulanger & Ziotopoulou (2017), is used. The PM4Sand model represents an improvement of the elasto-plastic, stress ratio controlled, bounding surface plasticity model formulated by Dafalias & Manzari (2004). The model can realistically reproduce the pore pressure build-up, accumulation of strain as well as triggering of liquefaction. In this paper, the effect of different relative densities on liquefaction resistance is evaluated by comparing the results of a site response analysis performed on a soil column characterized by a saturated sand layer and subjected to given earthquake signals. The analyses are performed using the finite element code PLAXIS.@en

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

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