As a pre-processing step, an inflation procedure to generate dense sphere packings is described. Sphere packings, that feature a significantly higher average coordination number than obtained from standard procedures, are generated with this inflation scheme, which uses a particle's coordination number to control its growth rate.

Particle bonds that restrict the relative motion in normal direction and may fail in tension and compression are applied between adjacent particles. A progressive failure model is introduced in order to reproduce the effects of singular stress concentrations near crack tips, which are not present in the DEM, by successive damage accumulation and weakening of bonds. The material model is calibrated to granite in uniaxial compression. Strength and failure of the granular solid are investigated in uniaxial and triaxial compression. For this purpose, an efficient approach for the simulation of a confining pressure system, which permits localization of lateral strain, is presented. Fracture initiation and propagation are investigated and discussed in detail. Wide agreement with strength and failure modes as observed in experiments is obtained.

A method to extract realistically shaped ballast stones from the granular solid is proposed. With this novel approach it is possible to obtain irregular, polyhedral stones made of breakable material. A number of tangent planes are created with a well defined degree of maximal irregularity on ellipsoids of matching dimensions. The volume enclosed by all of these planes is defined as the stone. The created stones show planar faces and feature edges, whose sharpness is only limited by model resolution, i.e. particle size.

Several stones comprising different numbers of particles are compressed diametrically between parallel platens to determine single particle crushing strength. Statistical evaluation reveals very good qualitative and reasonable quantitative agreement with measurements from literature. Different measures for single particle strength are investigated with respect to the loading state, which causes failure. While this test gives an estimate of the tensile strength of spherical agglomerates, it is not obvious if this is also true for stones of irregular shape that are compressed with larger contact areas at the loading platens. It is found that at least in these simulations compressive stresses and strength are important for the failure of the stones.

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