The presented model offers the possibility to study fracture dynamics of rocks with varying initial microstructures. The model reproduces realistic behaviour of brittle materials. It is able to reproduce transitions between different types of fractures, shows realistic differences between materials under extension versus compression and produces realistic fracture patterns with a distinct spacing and geometry. Similar transitions from Mode I small-scale fractures toward large scale shear faults were found in experiments [Lockner et al. 1992], theoretical models [Toussaint and Pride 2002] and similar numerical approaches [Hazzard et al. 2000]. Hazzard et al. (2000) present a failure study mimicking compression tests with a commercial discrete element code (PFC). They compare their results with real rock experiments and conclude that this type of micro-mechanical model can reproduce real rock experiments including the full dynamics of crack propagation. The models also reproduce realistic stress-strain relationships. The different macroscopic behaviour of material in our simulations with varying distributions for fracture strength is similar to the results of Mogi (1962) who realized that the fracture process strongly depends on the degree of heterogeneity of materials. The material with narrow distributions of breaking strength in our simulations is more homogeneous and fails more suddenly whereas the material with a wide distribution behaves more ductile and shows small scale crack growth preceding failure. These differences are fundamental for earthquake prediction [Mogi 1962] and can be modelled with the presented approach. In addition this discrete type of model was found to reproduce the visual and statistical properties of fracture patterns from clay extension experiments [Malthe-Sørenssen et al. 1998]. The fracture patterns seen in animation 6 are similar to discharge patterns found during dielectric breakdown [Niemeyer et al. 1984] and colloidal aggregation, which have statistical similarities to natural fracture patterns [Meakin 1988].
The presented model can be used to simulate brittle failure in polycrystalline aggregates as shown. It is however also possible to combine the model with dissolution kinetics [Koehn et al. this volume], fluid pressure to model hydro fractures [Flekkøy et al. 2002], to use random lattices in order to avoid anisotropies of facture networks, to include visco-elastic behaviour and to evolve to a three-dimensional geometry. The model can have a very high resolution (Animation 5) in order to avoid effects of the discreteness of particles. Models up to two million particles are possible without using parallel coding since computer power has increased significantly over the last years. The model is not limited to any scale so that orogenic processes or metre scale faulting may be modelled as well as structures on a small scale as shown here.
A problem of the presented model is the triangular geometry of the network. It has the advantage that it reproduces linear elasticity on a large scale. However, it has the disadvantage that fracture propagation is not necessarily isotropic. Especially shear fractures along which slip takes place may develop along lattice directions. One possibility to suppress lattice directions is to define on the one hand a network of grains where grain boundaries break easier and on the other hand a distribution of spring strengths that is isotropic. This combination can help to avoid anisotropies of fracture networks due to the geometry of the underlying lattice. The distributions of breaking strengths work rather well with mode I fractures that show no preferred lattice orientation but is problematic for shear fractures. However, even shear fractures curve in the models (Animation 2) and change their propagation direction suggesting that the anisotropy of the underlying lattice is not that important. The same applies for the branching structures in animation 6 where a number of different orientations exist that are not triangular. However, small-scale anisotropies may still exist even with large distributions of spring breaking strengths.