This paper derives the integrated constitutive relation at the singular point theoretically by using Hyushin's postulate in the the strain space, and gives an example applicable to the rock cap model.

At the same time, some scientific hypotheses of the damage evolution equations and stress-strain relationship as well as the failure mechanism of rock mass are also proposed.

This provides a feasible testing method for studying the behavior and constitutive relation of rock failure with medium stain rate under dynamical loading or static and dynamical combination loading.