Numerical Study of Effect of Input Energy on Dynamic Rock Fragmentation using SHPB Test

In mechanics of rock fracture and comminution, researchers have always been looking for a relationship between the consumed energy and the particle size distribution of the disintegrated rock specimen. This relationship has important industrial applications considering the fact that comminution of rock is a very energy demanding process and its efficiency is very low. Furthermore, investigating the damage evolution of rock under different loading rates, helps to better understand and more accurately design rock structures such as tunnels, rock slopes and foundations subjected to dynamic loading. In this work, a hybrid finite-discrete element numerical model was used to simulate rock disintegration under different loading rates in the Split Hopkinson Pressure Bar (SHPB) system. The rock and the steel bars in the SHPB apparatus were simulated by the Bonded Particle Model (BPM) and finite element model, respectively. BPM is a simplified version of the discrete element method in which the discrete particles are spherical in shape. Spherical particles or balls in the BPM are very useful in reducing the computational time; the contact detection of the spherical particles is computationally very fast. The computer program CA3, which is a 3D code for static, dynamic and nonlinear simulation of geomaterials was used for the numerical analysis. To capture the rate dependent behavior of rock, a micromechanical model was utilized in which the bond strength at a contact point increases as a function of relative velocity of involved particles. The numerical model was calibrated to mimic the mechanical behavior of Masjed Soleyman sandstone. To facilitate and expedite the calibration process of the BPM system, the curves and dimensionless parameters introduced in the literature were used. Input pulses with different intensities were applied to the specimen in the numerical modeling of the SHPB system. The input energy and the energy consumed to disintegrate the numerical rock specimen were evaluated by the numerical integration. Different particle sizes in the BPM system were used to investigate the impact of combined particle size and input energy on the rock disintegration. The results suggest that the energy consumption density for rock crushing changes linearly with the stress rate. Furthermore, it is shown that the dynamic strength of the rock increases with the increase in the consumed energy density. The disintegrated numerical specimen was carefully inspected and its particle size distribution was obtained. This was achieved by using a searching algorithm to identify the clusters in the damaged specimen; each cluster was made of one or several spherical particles. The volume of each cluster was calculated by finding the volume of its constituent particles and the porosity of the specimen. This volume was used to obtain the equivalent radius of the cluster; the cluster shape was imagined as a sphere to identify the equivalent particle or cluster size. The mean particle size (D50) of the damaged numerical specimen shows a linear relationship with the stress rate in a logarithmic coordinate system, which is consistent with the physical test results reported in the literature.