.. _R7.01.15:

**r7.01.15** Behaviour law of LAIGLE
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**Summary:**


.. _OLE_LINK2:

The Lagle rheological model makes it possible to analyze the mechanical behavior of rocks. The development of this behavior model was initiated following the difficulty of correctly understanding the response of the massif during the excavation of an underground cavity, in order to:


* to define the need and the nature of the possible supports to be implemented;


* to determine the extent of the land around a structure influenced by digging.

The implementation of this elastoplastic model was mainly focused on simulating the post-peak behavior of the rock. In this perspective, it is assumed that there is no work hardening of the rock prior to its rupture. This results in linear elastic behavior up to the peak of resistance (there may however be damage to the rock while the material has not yet broken). The plasticity criterion defined is of the generalized Hoek and Brown type and takes into account the influence of the stress level on shear strength. The softening of the material is associated with a gradual decrease in the properties of cohesion and angle of friction accompanied by a change in volume. It is driven by the cumulative plastic deviatory deformation considered as the only work-hardening variable.

To facilitate the integration of this model in*Code_Aster*, the law initially developed in the main constraints formalism was rewritten with constraint invariants based on the Cambou‑Jafari-Sidoroff model (CJS). The numerical formulation is implicit in relation to the criterion and explicit in relation to the flow direction.

The sign convention used for the formulation of the equations, in the context of this note, is that of the mechanics of continuous media.




.. toctree::
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    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Notations
    Introduction
    Le_mod_le_continu
    Calcul_des_d_riv_es
    Op_rateur_tangent_en_vitesse
    Traitement_num_rique_adapt__aux_mod_les_non_r_guliers
    Les_variables_internes
    Pr_sentation_d_taill_e_de_l_algorithme
    Variante_sur_l_expression_du_crit_re_de_plasticit_
    Fonctionnalit_s_et_v_rification
    Bibliographie
    Description_des_versions_du_document