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This paper develops a new statistic damage model for rock to mainly study the effect of a loading rate on its mechanical behaviours. The proposed model adopts a new loading rate-dependent damage density function and is capable of describing the macroscopic damage accumulation process for rock samples subjected to external high-speed dynamic loadings. The proposed model can also account for the residual strength of rocks by introducing a modified equivalent strain principle, which considers the contribution of the friction force to the strength of rocks. The friction force is generated by the movements of the nearby microcracks. The predicted stress-strain curves by the proposed model agree with the measured data of salty rock under the conditions of various confining pressures and loading rates. It can be found that both the peak strength and the corresponding axial strain are increased at high-speed loading conditions. At the same time, a transition from ductile failure to brittle failure can be observed in rock samples.