IMPLEMENTATION OF A COHESIVE CRACK MODEL IN GRAIN-BASED DEM TECHNIQUE FOR SIMULATING FRACTURE IN QUASI-BRITTLE GEOMATERIAL

Kiarash Farahmand, Mark Stephan Diederichs

In the proceedings of: GeoQuébec 2015: 68th Canadian Geotechnical Conference & 7th Canadian Permafrost Conference

Session: Rock Mechanics and Engineering Geology III / Mécanique des roches et génie géologique III

ABSTRACT: This paper presents a grain-based discrete element model for simulating the quasi-brittle failure of rocks under mechanical loading. In this approach, the development of crack along grain boundaries controls the degree of damage in rock. A cohesive crack model based on the theory of fiNon-linear Elastic Fracture Mechanics (NLEFM)fl is implemented into the UDEC distinct element numerical code to define the constitutive behavior of the grain interfaces under different modes of fracturing. Implementation of the crack model in the grain-based simulator aims at enhancing the capability of the UDEC-Voronoi scheme to simulate the micro-cracking mechanisms more realistically similar the micro-cracking mechanisms. Rock heterogeneity, due to the presence of different mineral grains, is introduced to the model by considering the mineral composition of real rock and contrast in mechanical properties of the constituent minerals. The elastic properties of the grains and the strength properties at grain boundaries are extracted based on the experimental data. Then, the capability of the model to replicate the mechanical behavior of Lac du Bonnet (LDB) granite under compression and tension is evaluated. To do so, a series of uniaxial and triaxial compression and Brazilian tests is simulated. The mechanical response of the numerical models is found to be in good agreement with the response of the real rock observed in laboratory.

RÉSUMÉ: Cet article présente un modèle par éléments discrets basé sur l™échelle du grain pour modéliser la rupture quasi fragile de roches sous chargement mécanique. Dans cette approche, le développement de la fissure le long des joints de grains contrôle le degré d™endommagement de la roche. Un modèle de cohésion de fissure basé sur les théories de la «mécanique non-linéaire de la rupture (NLEFM)" est mis en œuvre dans le code numérique par élément distinct UDEC pour établir le comportement des interfaces des grains sous différents modes de fracturation. La mise en œuvre du modèle de fissuration dans le simulateur basé sur les grains vise à renforcer la capacité de l™approche UDEC-Voronoi à modéliser de façon plus réaliste les mécanismes de microfissuration. L'hétérogénéité de la roche, causée par la présence de grains de différente minéralogie, est introduite dans le modèle en prenant en compte la composition minérale de roche et le contraste des propriétés mécaniques des minéraux constituants. Les propriétés élastiques des grains et les propriétés de résistance aux joints des grains sont extraites de la base des données expérimentales. Ensuite, la capacité du modèle, à reproduire le comportement mécanique du granite du Lac du Bonnet en compression et en tension, est évaluée. Pour ce faire, une série d™essais de compression uniaxiaux, d™essais triaxiaux et d™essais Brésiliens est simulée. La réponse mécanique des modèles numériques se trouve à être en bon accord avec la réponse de la roche réelle observée en laboratoire. 1. INTRODUCTION The process of brittle rock fracture during compression and tension is a result of the initiation, growth, and coalescence of multiple individual micro-cracks which eventually leads to formation of some clustered regions of macro-fractures in rock. As the compressive, or tensile stress applies across the boundaries of a rock sample, a complex heterogeneous stress system will be distributed through the rock in which the tensile and shear stresses will be concentrated at pre-existing flaws (i.e. micro-cracks, grain boundaries, cavities, cleavages) (Kranz, 1983). If the localized tensile stress exceeds the local strength of the microstructure some micro-cracks start to form at the point on the boundary of pre-existing flaw where tensile stress concentration is greatest. These axially aligned extensional micro-cracks occur during the early loading stages of compression tests. As the applied deviatoric stresses increase in the specimen, the density of compression-induced tensile cracks increases, and eventual interaction and coalescence of these cracks result in formation of some localized and macroscopic damaged zones in the material. It is the presence and creation of such micro-fractures that cause the compressional stress-strain curve of rock to deviate from true elastic (linearity) in the pre-failure region (Hazzard et al., 2000). In this paper, a grain-based Discrete Element Method (DEM) is used for modelling the progression of damage during brittle fracturing of the crystalline rock. The key concept of explicit DEM is that the domain of interest is represented as an assemblage of dense packing rigid or deformable blocks/particles interacting together at their contact boundaries. In the other words, the model is composed of a series of particles that are glued together by their cohesive bonds forming between their boundaries. As a result, crack nucleation is simulated through breaking of internal bonds while fracture propagation is obtained by coalescence of multiple bond breakages. In the DEM-Voronoi model the rock materials are represented by a pack of polygonal-shaped blocks. Owing

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Cite this article:
Kiarash Farahmand; Mark Stephan Diederichs (2015) IMPLEMENTATION OF A COHESIVE CRACK MODEL IN GRAIN-BASED DEM TECHNIQUE FOR SIMULATING FRACTURE IN QUASI-BRITTLE GEOMATERIAL in GEO2015. Ottawa, Ontario: Canadian Geotechnical Society.

@article{388,author = Kiarash Farahmand; Mark Stephan Diederichs,title = IMPLEMENTATION OF A COHESIVE CRACK MODEL IN GRAIN-BASED DEM TECHNIQUE FOR SIMULATING FRACTURE IN QUASI-BRITTLE GEOMATERIAL,year = 2015}