Numerical Study of Damage Accumulation in Brittle Spheres During Repeated Impacts and Development of a Conceptual Model for Rocks

Rock fragmentation upon impact during a rockfall event is a very challenging phenomenon to predict. To estimate the likelihood of breakage upon impact, one needs the survival probability of the rock. Recently, a survival probability model was proposed and validated for brittle spheres. The model was later extended to irregular shapes under colinear impact with promising preliminary experimental validation. These two models rely on the mechanical properties of the intact material prior to any impact, and as such, these models are only applicable to the very first impact. However, it is very likely for a rock to sustain some damage during a fall and only fragment after several impacts, in which case the survival probability cannot be predicted by the aforementioned models. This numerical study provides new insight into damage accumulation upon multiple impacts in free fall. The study systematically investigates how the work required to achieve failure in quasistatic compression (referred to as work at failure) is affected by prior impacts. Attention is focused on the work at failure because it is one of the key inputs of the survival probability models developed by one of the authors, and tracking its evolution with the number of impacts could allow one to adjust the survival probability with impact history. The simulations show that the governing mechanism for the loss of strength following multiple impacts is the interaction among different damage zones and that there exists no unique relationship between damage accumulation and work at failure. The paper concludes with a conceptual model based on the findings of this study and statistical considerations that can be used to predict the evolution of critical work with the impact velocity for different impact scenarios, which in turn can be used to predict the evolution of the survival probability of brittle spheres or rocks during a fall.