A Statistical Bonded Discrete Element Model for heterogeneous brittle materials

Numerical modelling of the fracture of heterogeneous brittle materials is of interest for several industries,such as rock excavation and comminution applications. A numerical model of brittle materials needs tobe able to capture the unpredictable results, e.g. with regards to measured strength and fracture pattern,as observed experimentally. In this study a new approach, based on the Parallel Bond Model (PBM) [1] and theWeibull distribution, for modelling brittle heterogeneous materials in 3D is proposed and appliedto the Brazilian Disc Test (BDT) [2]. The PBM is used to generate irregular grains with varying bondstrengths and stiffnesses. For the grain generation, a parent particle is chosen at random in the rockbody and a randomized ellipsoid is generated around the particle. The mean grain bond stiffnesses andstrengths are associated with the grain and all particles within the ellipsoid surface are bonded togetherwithin +/- 10 % of these mean values. Further, the bond parameters of the cement between a grain andits neighbours is scaled based on the mean grain properties. An example of a generated sample is shownin Figure 1 a). In order to evaluate the model, a series of simulations of the BDT were conducted.The effects of the Weibull heterogeneity index and cement strengths on the predicted tensile strengthand crack pattern were evaluated. Specifically, the initiation, propagation, coalescence and branching ofcracks were examined in detail. Apart from demonstrating challenges with the BDT, the results also showthat the proposed model is able to capture key phenomena related to brittle heterogeneous materials, suchas unpredictable fracture pattern and a large variation in tensile strength, see Figure 1 b-c).GEOFI