Investigation into size and strain rate effects on the strength of rock-like materials

• Obtained the relationship of spatial & temporal properties of deformation & fracture.
• Determined one-to-one relation between characteristic length scale and strain rate.
• Size effect is the realization of structural surface strength at given scale level.
• High strain rate activates smaller elements due to the finite crack growth speed.
• Dynamic strength reflects the size effect at activated smaller scale level of solid.

Based on a relaxation model, the relationship between spatial and temporal properties of deformation and fracture of rock-like materials is established, the essence of which lies in the finiteness of crack propagation speed and the complex internal structural hierarchy. There exists one-to-one correlation between characteristic length scale and characteristic strain rate, i.e., in order to fracture a sample of size L or activate structural elements of size L  , definite strain rate ε̇L must be applied, below which a sample of size L would not fracture or structural elements of size L would not be activated. From the viewpoint of structural hierarchy, the size effect may be considered as the realization of the structural surface strength of smaller scale structural elements with the decrease of the sample size. The essence of strain rate effect is that because of the finiteness of crack propagation speed, the increase of strain rate activates the deformation and fracture process of smaller scale elements before the complete fracture of the sample. The dynamic strength of material is the realization of size effect on strength at the activated smaller scale level of solid. Based on one-to-one correlation between characteristic scale level and characteristic strain rate, size effect equation is transformed into strain rate effect equation. This investigation examines the size and strain rate effects on strength of rock-like materials, which would give better understanding of dynamic phenomena of deformation and fracture of rock mass, including the Earth's crust.