Dynamic tensile strength of rock specimens with different defect lengths

Rock masses contain defects at various scales. The presence of these defects and imperfections must be considered in the design of rock structures particularly when dynamic loading due to earthquake or rock blasting is involved. The role of an existing defect or notch on the tensile strength of a synthetic rock under static and dynamic loads is examined in this study. Brazilian specimens with diameter = 50 mm and thickness = 10 mm were prepared from molded gypsum to represent the synthetic rock. Both intact and notched specimens were tested. The mode I loading was applied to the specimens; the notch was aligned with the applied diametric line load. The Split Hopkinson Pressure Bar (SHPB) equipment was utilized for the dynamic testing. Different notch lengths of 10 to 40 mm were considered. The Bonded Particle Model (BPM) was employed to identify the crack formation and evolution in the specimens for the numerical analysis. The numerical simulation was performed by employing the CA3 finite element - bonded particle software. The whole SHPB device was modeled, including the incident and transmission bars, together with the rock specimen. The physical and numerical data suggest that specimens with notches demonstrate stronger responses to the stress rate compared to the intact specimens. In particular, the fracture toughness increases substantially as the loading rate is intensified. Furthermore, it is shown that while the physical and numerical static tensile strengths decrease as the notch length increases, the dynamic tensile strength remains unchanged with increasing the notch length when loading rates of high intensity are applied. The reason for this observation is scrutinized and it is shown that the crack tip opening velocity is responsible for this peculiar finding. The numerical model is able to capture this phenomenon due to the appropriate rate dependent micromechanical model used in this study. Finally, based on the published studies and the results of this work, an equation is derived which suggests a linear relationship between the rock tensile strength and the strain rate. This equation is valid for the physical and numerical specimens with different notch lengths.