Analysis of impact-induced rock fragmentation using a discrete element approach

Rockfalls involving abrupt movements of rock masses detached from steep slopes or cliffs 1 are widely observed in mountainous areas. These events can cause significant hazards to human lives and lifeline facilities.2,3 Among various types of rock block motion (e.g. freefall, bouncing, and rolling), bouncing (impact) is the most complex, uncertain, and poorly understood one.4,5 During impacting, the kinetic energy dissipates and the direction of motion changes. Depending on the mechanical properties of the terrain and the rock block, the impact angle, and the block shape, mass, and velocity, the impact process can vary from the elastic to plastic.5,6 In addition, during impact, the rock block tends to break, this is especially true for weak rocks.4 After fragmentation, the trajectories of rock fragments are very difficult to predict, increasing the probability of damage to human lives and properties.7 In this process, the position and the extent of the debris accumulation zone are strongly affected by rock fragmentation. This phenomenon has been observed by Crosta et al.,8 and they concluded that rock fragmentation influences the runout extent and trajectory of rockfall. Several parameters can influence the fragmentation process,9,10 namely, the pre-existing joints and micro-fractures, the ground conditions, the impact energy and angle. Through numerical analyses and laboratory tests, several researchers11–13 have investigated the impactinduced fragmentation for granular agglomerates, concluding that the breakage intensity of agglomerates mainly depends on the normal component of the impact velocity. Wang and Tonon9 analysed the effect of impact angle on the rock fragmentation using discrete element method (DEM), and their results indicate that the magnitude of the normal velocity is the main factor influencing the rock fragmentation. Paluszny et al. 14,15 employed the combined finite element method and impulse-based discrete element method to study rock fragmentation. They concluded that the impacting velocity strongly controls the final fragment size distribution. De Blasio and Crosta 16 point out that the fragmentation is mainly due to the effect of normal stress acting on the impacting plane. Consequently, it can be concluded that the normal component of the impact velocity plays an important role in rock fragmentation. This paper presents a model of the fragmentation induced by normal impact of a synthetic spherical rock block under different impact loading rates, using the open source DEM code ESyS-Particle.17,18 It is true that a spherical rock block is not commonly found in nature. However, the block shape has a significant influence on the rock fragmentation due to impact induced stress concentration,19,20 and the spherical block can effectively avoid this effect.20 Therefore, this model is considered as a reasonable initial proxy to study impact-induced rock fragmentation. The paper is organized as follows: in Section 2, the DEM model configurations of impact-induced rock fragmentation are presented. In Section 3, the obtained numerical results are illustrated with respect to the fragmentation process, the fragmentation intensity, the fragment number, and the fragment size distribution. Finally, in Section 4, some conclusions reached in this study are provided.