A damage-based constitutive model for rock under impacting load

Using the Splitting Hopkinson Pressure Bar (SHPB) experimental system, investigations were made into the dynamic mechanical performances of underground soft rocks. The experiments proved that the measured stress–strain curves display the characteristics of plastic deformation. By making use of a revised overstress constitutive formula for the stress model and by taking into account that the strain rate and strain are a function of 1 − E(t)/E0, a revised overstress constitutive formula for the stress model was simplified by applying dimensional analysis and consequently, a simplified overstress formula was obtained for the stress model. Then, by taking into consideration the effects of damage under a dynamic load on the dynamic loading strength of the rock, the continuous damage theory and the statistical strength theory were introduced into the development of the simplified overstress constitutive formula for the stress model. Hence, a damage-based constitutive formula for an overstress model, which can be appropriately applied to the analysis of full dynamic stress–strain curves, was developed. By using the simplified damage-based constitutive formula for an overstress model, the actually measured curves are fitted, indicating that the fitting curves and those actually measured are in good agreement.