Publication informationEmpirical rock properties and continuum mechanics provide a basis for defining 11 relationships between a variety of mechanical properties, such as strength, friction 12 angle, Young's modulus, Poisson's ratio, on the one hand and both porosity and crack 13 density, on the other. This study uses the Discrete Element Method (DEM), in which 14 rock is represented by bonded, spherical particles, to investigate the dependence of 15 elasticity, strength and friction angle on porosity and crack density. A series of 16 confined triaxial extension and compression tests was performed on samples that were 17 generated with different particle packing methods, characterised by differing particle

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[1] We present a new method to implement realistic grain fracture in 3D numerical simulations of granular shear. We use a particle based model that includes breakable bonds between individual particles allowing the simulation of fracture of large aggregate grains during shear. Grain fracture simulations produce a comminuted granular material that is texturally comparable to natural and laboratory produced fault gouge. Our model is initially characterized by monodisperse large aggregate grains and gradually evolves toward a fractal distribution of grain sizes with accumulated strain. Comminution rate and survival of large grains is sensitive to applied normal stress. The fractal dimension of the resultant grain size distributions (2.3 ± 0.3 and 2.9 ± 0.5) agree well with observations of natural gouges and theoretical results that predict a fractal dimension of 2.58. Citation: Abe, S., and K. Mair (2005), Grain fracture in 3D numerical simulations of granular shear, Geophys. Res. Lett., 32, L05305,

[1] We investigate how existing veins interact with extension fractures in rocks using 3-D Discrete Element Method models with a geometry inspired by tension tests with notched samples. In a sensitivity study, we varied (a) the angle between the vein and the bulk extension direction and (b) the strength ratio between host rock and vein material. Results show a range of vein-fracture interactions, which fall into different, robust, "structural styles." Veins, which are weaker than the host rock, tend to localize fracturing into the vein, even at high-misorientation angles. Veins, which are stronger than the host rock, cause deflection of the fracture tip along the vein-host rock interface. Fractures are arrested at the interface from weak to stronger material. When propagating from a stronger to a weaker material, macroscopic bifurcation of the fracture is common. Complex interactions are favored by a low angle between the vein and the fracture and by high-strength contrast. The structural styles in the models show good agreement with microstructures and mesostructures of crack-seal veins found in natural systems. We propose that these structural styles form the basis for criteria to recognize strength contrasts and stress of crack-seal systems in nature.Citation: Virgo, S., S. Abe, and J. L. Urai (2013), Extension fracture propagation in rocks with veins: Insight into the crack-seal process using Discrete Element Method modeling,

[1] The friction of granular fault gouge plays an important role in governing the mechanical behavior and hence earthquake potential of faults. Using numerical modelling, significant progress has recently been made towards understanding the micro-mechanics that drive fault gouge evolution. Despite these insights, many previous numerical models have predicted unrealistically low macroscopic frictional strength. Here we describe modified 3D discrete element simulations of fault gouge evolution. Our particlebased simulations, modelled on laboratory experiments, include breakable bonds between individual particles (or particle clusters) allowing fracture of aggregate grains. With accumulated strain, grains break up, evolving in size and shape to produce a textural signature reminiscent of natural faults. Cluster-simulations, producing pseudo-angular daughter fragments yield realistic frictional strength (0.6). Non-cluster simulations, producing angular and spherical daughter fragments, have much lower friction levels. We therefore demonstrate that gouge fragment shape and resulting interactions dominate the frictional strength of faults. Citation: Abe, S., and K. Mair (2009), Effects of gouge fragment shape on fault friction: New 3D modelling results, Geophys. Res. Lett., 36, L23302,

Veins are ubiquitous in upper and middle crustal rocks. Due to strength and stiffness contrast to the host rock, veins can influence crack propagation. Here we present Discrete Element Models to investigate crack-vein interactions by simulating cycles of fracturing of a rock mass, sealing the cracks to form veins, and refracturing the rock mass after rotating the stress field. We observe different styles of interaction between new fractures and existing veins, depending on the strength ratio between vein and host rock and on the changes in the stress field between the different deformation stages. If the orientation of stress field does not change between deformation stages, ataxial crack seal veins are produced if the veins are weak and a bundle of subparallel microveins if the veins are strong. If the stress field is rotated between deformation stages, the interactions include reactivation, fracture deflection, and crosscutting. Reactivation of weak veins occurs even if the vein orientation is highly unfavorable relative to the stress field. Relays of fractures between reactivated veins form at a higher angle to the veins than expected. This demonstrates that the orientation of secondary veins does not reflect the regional stress field in a simple manner and that veins can strongly influence fracture connectivity, with implications for paleostress analysis and basin modeling. Simulation results compare well with field examples of multiphase vein networks in carbonates from Jebel Akhdar, Oman.

In this study, 3-D Lattice Solid Model (LSMearth or LSM) was extended by introducing particle-scale rotation. In the new model, for each 3-D particle, we introduce six degrees of freedom: Three for translational motion, and three for orientation. Six kinds of relative motions are permitted between two neighboring particles, and six interactions are transferred, i.e., radial, two shearing forces, twisting and two bending torques. By using quaternion algebra, relative rotation between two particles is decomposed into two sequence-independent rotations such that all interactions due to the relative motions between interactive rigid bodies can be uniquely decided. After incorporating this mechanism and introducing bond breaking under torsion and bending into the LSM, several tests on 2-D and 3-D rock failure under uniaxial compression are carried out. Compared with the simulations without the single particle rotational mechanism, the new simulation results match more closely experimental results of rock fracture and hence, are encouraging. Since more parameters are introduced, an approach for choosing the new parameters is presented.

[1] We use discrete element model simulations to model the full boudinage process from initial fracturing of intact material to post-fracture flow of material into gaps between fragments and to investigate the role which the material properties of the weak and strong layers play in this process. The models are deformed in 2D plane strain under a range of confining stresses, in coaxial bulk flow. Results show that the material properties, i.e. Mohr-Coulomb or quasi-viscous for the matrix and elastic-brittle for the competent layer, lead to the development of natural looking boudin morphologies and deformation patterns in the matrix. The details of the matrix rheology only have a minor influence on the morphology of the boudins. By varying the material properties of the competent layer between fully brittle and semi-ductile we obtain a wide range of deformation patterns ranging from pinch-and-swell structures to a variety of boudin types including drawn, shear band and straight sided torn boudins. In a number of models we observe rotation of the boudin blocks despite the applied deformation being purely coaxial. These rotations are generally related to asymmetrical (rhombic) boudin shapes. Some features observed in natural boudins such as concave block faces or the formation of veins between fragments are not modeled because pore fluids are not yet included in our model. Citation: Abe, S., and J. L. Urai (2012), Discrete element modeling of boudinage: Insights on rock rheology, matrix flow, and evolution of geometry,