Numerical modeling of the coupled effect of specimen size and loading rate on the dynamic tensile strength of rock

The loading rate and specimen size are two main influential factors which control the tensile and compressive strengths of Quasi-brittle materials such as concrete, ceramic and rock. Most of the studies in the past have been focused on the size effect in the static loading situations i.e. in situations in which the effect of the loading rate and inertia can be ignored. In particular, fracture mechanics size effect have received substantial attention both with respect to the physical testing and the numerical modeling. On the other hand, combined effect of the specimen size and loading rate on the rock strength has received little attention in the literature. Understanding the dynamic size effect of Quasi-brittle materials such as rock is essential for better analysis and design of rock structures. This is particularly the case when rock is subjected to the blasting loads or when it is prone to the strain bursting. Studies on the failure of rock under the coupled effect of specimen size and loading rate are far from sufficient. Due to the limitations of the laboratory test devices, limited research efforts have been conducted on the size effect of materials under dynamic loading. In this study, a 3D hybrid finite-discrete element code called CA3 was used to simulate the Split Hopkinson Pressure Bar test. The Incident and Transmitted bars were modeled by the finite element method while the Brazilian specimen was simulated using a Bonded Particle Model (BPM). The bars were assumed to beave elastically while the simulated specimen could develop micro and macro cracks which eventually could end up to complete disintegration and failure. Brazilian specimens with different sizes were numerically modeled. The specimen contained a vertical notch so that fracture mechanics size effect under high strain loading rate could be studied. The samples were subjected to different loading rate by adjusting the incoming wave in the incident bar. A micromechanical model in which the contact bond strength was allowed to vary in proportion to the relative velocity at the contact point of the involved particles was employed to capture the loading rate effect. The effect of sample size on the dynamic tensile strength of rock was explored and compared with the static size effect. The results were analyzed and discussed using the dimensional analysis approach. The numerical results suggest that the dynamic size effect on tensile strength of rock is different from the static size effect. While for small loading rates, the rock strength reduces as the specimen size increases, this is not the case when high loading rates are involved. For high loading rates, with the increase in the specimen size, the tensile strength initially increases. However, with further increase in the specimen size and the increase in the distance between the notch tips and the impact points, it appears that the inertia and loading rate effects reach to a stable situation, i.e. with further increase in the specimen size, the material strength remains constant. This interesting observation is discussed and compared with the published data in the literature.