On the breakage function for constructing the fragment replacement modes

The fragment replacement method (FRM), a particle breakage simulation method, is often used in discrete element simulations to investigate the particle breakage effect on the mechanical behavior of granular materials. The fragment size distribution of the fragment replacement mode of FRM, which is generally generated based on the fragmentation characteristics of single particles after uniaxial compression, affects the breakage process and the mechanical behavior of the particle assembly. However, existing fragment replacement modes are seldom generated based on experimental data analysis. To capture the fragmentation process and investigate the breakage function for the construction of the fragment replacement mode, 60 numerical single particle compression tests were implemented by DEM. The bonded-particle model was applied to generate the crushable rock particles. The numerical simulations were qualitatively validated by experimental results, and the fragment size of broken single particles was analyzed. The fractal dimension was used to describe the fragmentation degree of single particles after compression. The fragmentation degree was random, and the fractal dimensions of the 60 tests at the same loading displacement fit the Weibull distribution well. The characteristic fractal dimension increased with increasing loading displacement, indicating that the fragmentation of single particles is a gradual process. According to the overall breakage function of the 60 tests at the first bulk breakage, a two-stage distribution model with 4 parameters was proposed and validated by the numerical and experimental results. The various fracture patterns of a single particle at the first bulk breakage under compression tests were well captured by the two-stage distribution model. Finally, an initial application strategy using the two-stage distribution model to construct fragment replacement modes was discussed and presented.