1. Introduction#

This note presents a mechanical behavior model for rocks. To represent the mechanical behavior of rocks the Code_Aster user can use the Drucker-Prager DRUCK_PRAGER law, the LAIGLE law or the HOEK_BROWN law presented here. The Drucker-Prager law is the simplest and the farthest from the real behavior of rocks. Eagle’s law is the most faithful to the physics of phenomena. Thus the law presented in this note is intermediate between these two laws, in terms of complexity as well as in terms of representation of reality. It uses fairly conventional formulations in the field of geomechanics.

This law can be used in mechanical models alone or in models of the THM type.

In thermo-hydro-mechanical modeling, it can be used in effective stresses or in total stresses:

  • In the first case, it is the actual constraints that are subject to meeting the Hoek and Brown criterion. Plastic deformations are calculated using the Drucker surface and the angle of friction in the space of the effective stresses

  • In the second case, it is the total constraints that are subject to meeting the Hoek and Brown criterion. Plastic deformations are calculated using the Drucker surface and the angle of friction in the total stress space.

Reference [1] provides useful information for understanding this law

The formulation is of the non-associated plasticity type:

  • The elasticity domain is defined by a Hoek-Brown criterion, whose parameters change with the work hardening parameter

  • The work hardening parameter is a combination of plastic shear deformation and plastic volume deformation

  • Plastic deformations derive from a Drucker-Prager criterion whose friction angle changes with plasticization.

1.1. Characteristics of the model#

The model simulates the short-term mechanical behavior of rocks in 4 phases, described in the reference [1]:

  1. Elastic phase characterized by a constant Young’s modulus and Poisson’s ratio

  2. Elastoplastic phase with positive work hardening that simulates the initiation of a form of damage and its progression towards the rupture of the rock. This phase is modelled by a Hoek-Brown plasticity criterion. This criterion changes according to the major irreversible deformation. The evolution of the irreversible deformation is determined by a plastic flow potential expressed by a Drucker-Prager type function.

  3. Elastoplastic phase with negative work hardening that represents the post-fracture behavior of rocks. The failure criterion is of the Hoek-Brown type. The deformation is determined by an unassociated plastic flow potential of the Drucker-Prager type.

  4. Residual resistance phase characterized by a modified Hoek-Brown type function.