An estimation model for the fragmentation properties of brittle rock block due to the impacts against an obstruction

Mountain hazards with large masses of rock blocks in motion – such as rock falls, avalanches and landslides – threaten human lives and structures. Dynamic fragmentation is a common phenomenon during the movement process of rock blocks in rock avalanche, due to the high velocity and impacts against obstructions. In view of the energy consumption theory for brittle rock fragmentation proposed by Bond, which relates energy to size reduction, a theoretical model is proposed to estimate the average fragment size for a moving rock block when it impacts against an obstruction. Then, different forms of motion are studied, with various drop heights and slope angles for the moving rock block. The calculated results reveal that the average fragment size decreases as the drop height increases, whether for free-fall or for a sliding or rolling rock block, and the decline in size is rapid for low heights and slow for increasing heights in the corresponding curves. Moreover, the average fragment size also decreases as the slope angle increases for a slidingrock block. In addition, a rolling rock block has a higher degree of fragmentation than a sliding rock block, even for the same slope angle and block volume. Finally, to compare with others' results, the approximate number of fragments is estimated for each calculated example, and the results show that the proposed model is applicable to a relatively isotropic moving rock block.

Numerically investigating the crushing of sandstone by a tooth hob

To investigate the mechanical process that occurs between rocks and tooth hobs,the crushing of sandstone with a tooth hob was simulated using reconstructed multi-mineral mesoscopic numerical models of various grain-sized sandstone samples.When a piece of sandstone is crushed by the tooth of a hob rolling at a constant speed,the resultant reaction forces of the sandstone on the tooth first hinder and then contribute to the rolling of the hob.The absolute value of the longitudinal reaction force is significantly higher than that of the lateral reaction force.Because the tooth was subjected to reaction forces from the sandstone,forces and moments were applied to the hob in order to keep the hob rolling.The applied forces were equal in value and opposite in direction to the reaction forces of the sandstone on the tooth.Three typical curves of the work done by the applied forces and moment were obtained,and the contribution of the applied lateral force and moment to the total work done for crushing sandstones was variable;however,no work was done by the applied longitudinal force.Moreover,the applied longitudinal force and total work were positively correlated with the strength of sandstone samples.The total work,applied forces,and moment increased with the maximum penetration depth of the tooth in the sandstone.