This paper presents a computer simulation of a direct shear test carried out on an artificial material simulating a fractured medium. Fractures are divided into two persistent families having the same direction, orthogonal dips and constant spacings., forming prismatic blocks. The test results show that for certain family orientations, failure mechanisms involve block rotations in the interior of a planar shear zone. Such mechanism cannot be adequately modeled through classical equivalent continuum due to the fact it does not incorporate additional (rotational) degrees of freedom in its kinematics..On the other hand, equivalent generalized Cosserat media which incorporates such degrees of freedom make it possible to model the above mentioned mechanisms. The present work uses an elastoplastic Cosserat continuum model. Which was implemented numerically into a finite element code. The code uses a dynamic relaxation algorithm to the solution of the non linear equlibrium equations resulting from the discretization involved. The paper comments on relevant numerical details of the implementation.


Fractured media are very often modelled as classical elasto-plastic equivalent continua, fractures being considered as ubiquitous. Besdo (1985) noticed that there is a considerable lack of precision in this type of modelling when failure mechanisms involving rotations (collapse loads being relatively low) are present. The same author proposes the use of a different sort of equivalent continua, the ones based on the generalized mechanics of Cosserat (Cosserat & Cosserat, 1907). Other authors followed by using the same model as did Muhlha Us (1989), Dawson (1995), Adhikary & Dyskin (1998), etc.. These authors compared numerical solutions, obtained with generalized equivalent continua with both analytical solutions and numerical solutions obtained with discrete element methods. The behavior of fractured media is complex however and comparisons of numerical predictions with results obtained with physical models are desirable and should be done whenever possible. On the other hand, data collection and even the realization of tests in such models pose considerable difficulties besides being time consuming and expensive. Small scale physical models are more convenient for this type of modelling. The present work presents comparisons of numerical simulations using an numerically implemented Cosserat Continuum with results obtained on a physical, small scale model. The physical model in question was done by Walker (1971) and comprises the behavior in direct shear of a medium containing two families of persistent joints having the same direction orthogonal dips and constant spacing. The Cosserat equivalent generalized continuum used in the numerical part of the work is similar to the ones used by Besdo (1985) and Dawson (1995). A few modifications were introduced in the formulation in a way to adjust its predictions to the above mentioned test. The numerical implementation was carried out on a finite element code which uses dynamic relaxation technique as an algorithm to solve the non linear equilibrium equations. The paper presents aspects of the numerical implementation carried out and of the Cosserat equivalent generalized constinuum besides the comparisons with the test results.

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