A bidimensional rock joint constitutive model accounting for couplings between normal and shear behaviours due to dilatancy, and basic degradation mechanisms of the asperities, has been proposed by Amadei and Saeb. The paper describes its extension to three dimensional situations as well as cyclic loadings and illustrates its possibilities on two simple examples.


Un modèle de fracture rocheux bidimensionnelle, permettant de rendre compte des couplages entre les comportements normal et tangentiel dus à la dilatance, et des mecanismes elementaires de degradation des asperites, a ete propose par Amadei et Saeb. L'article decrit son extension à des configurations tridimensionnelles et à des chargements cycliques. Ses performances sont illustrees par deux exemples simples.


Ein modell fuer zweimessigen felsigen bruchen wird von Amadei und Saeb Vorgestellt. Es legt von kuepplungen zwischen normalen und tangentialen verhalten und auch basichen verfahren von rauheiten verwitterung ab. In diesem artikel wird die verallgemeinerung zu dreimessigen raumlehren und auch zu zyklischen belastungen vorgesttelt und auf zwei einfachen beispielen geillustriert.


Rock joints are encountered in many situations, like mining engineering, oil engineering, underground waste management, etc. Very often, their presence leads to complex behaviour and severe stability problems. This is the reason why realistic mechanical models must be developed. A large amount of work has been published on the subject, based on two principal numerical methods, the joint finite element method, pioneered by Goodman [1], and the distinct element method, pioneered by Cundall [2]. In both cases, it is necessary to dispose of models describing the normal and tangential behaviours of the rock joint. These behaviours, which are described at a macroscopic scale, involve phenomena which occur at a lower scale, like contact with friction between asperities or rupture of an asperity. It is therefore not surprising to find a large variety of models in the literature, which try to describe some experiments performed in the laboratory. Unfortunately, many of them are limited to the tests conditions (for example constant normal stress test or constant normal stiffness test) and do not account for the couplings between normal and shear behaviour due to dilatancy. Some years ago, Amadei and Saeb [3] [4] have proposed an incremental model which fully takes these couplings into account and is based on the above mentioned physical degradation mechanisms. This model presents however two major shortcomings:

  • it has been derived only for the bidimensional cases, and

  • it is only valid for monotonic loading conditions. For practical situations like safety assessment of deep underground nuclear waste repositories, it is necessary to dispose of a three-dimensional tool, accounting for cyclic loading conditions

. Indeed, the possible migration of radionucleides will be strongly dependent upon the residual apertures of the rock joints, when the rock mass will cool down after the heating period due to the heat production by the wastes. In this paper, we propose an extension of the Amadei-Saeb's model to tridimensional rock joints, as well as a simple procedure to treat cyclic loadings. The performance of the model is illustrated on two simple test cases and the final results are discussed. The Amadei-Saeb's model In this paragraph, the original formulation of the Amadei-Saeb's model will be reminded for the sake of completeness. The following notations will be used hereafter: µ and v will denote respectively the stress and displacement along the normal to the joint, t and u will denote respectively the shear stress and the tangential displacement of the joint. The displacements which are considered here must be understood as the relative displacement of one side of the joint element with respect to the other.

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