FORMULATION OF A 3-D NUMERICAL-MODEL OF BRITTLE BEHAVIOR

A 3-D numerical model of brittle behaviour is proposed where matter is discretized in individual elements. These particles are linked by ten sile interaction forces generating cohesive media. These spring-like f orces are linear and elastic when a small stretching effect is applied and decrease linearly to zero if the stretching exceeds a rupture thr eshold. Hence, for infinitesimal strains, the medium has an elastic re sponse and elastic waves can propagate. For finite deformations, links can break, thus simulating microcracks, and eventually evolve into a macroscopic fracturing process. if the particles are stacked according to a face-centred cubic lattice structure and interact with the first and second nearest neighbours, then the medium is isotropic and elast ic. To determine the strength properties of this model, uniaxial compr essional tests are run. On the basis of Mohr circle analysis, the frac ture criterion of a reference model agrees with the Mohr-Coulomb crite rion. However, the evolution of the macroscopic fractures do not follo w the direction predicted by this criterion. The evolution of the volu metric strains is comparable to laboratory observations on rock sample s under uniaxial compression. Dilatancy begins at about half the failu re stress and microcracking propagates pervasively throughout the samp le prior to the failure. For small angles of dilatancy, the fractures are vertical. With an increase in the dilatancy angle the vertical fra ctures disappear and shear fractures appear at 45 degrees from the mai n axis of strain. Ultimately, with increasing angles these shear fract ure zones migrate to the centre of the sample. Fractures in the medium are aligned preferentially along the axes of symmetry of the FCC latt ice structure. This is emphasized by the use of central interaction fo rces and a low residual friction.