Based on damage mechanics and the concept of damage threshold

rock behaves elastically at the beginning of loading

and successive damage is followed when the stress reaches the yield state. Until rock is completely damaged

the stress-strain curve shows deformation characteristics of residual strength. In this study

three-parameter Weibull distribution function is adopted to describe the evolution of rock damage. Meanwhile

the Lemaitre strain equivalence hypothesis is modified by considering the friction force caused by the relatively slipping deformation of rock along pre-existing local cracks. Finally

a new constitutive damage model is proposed to precisely describe deformation characteristics of residue strength and the elastic deformation at the low confining pressure. Furthermore

the proposed model is also verified by experimental results

which indicates that the model can be widely applied to practical engineering projects.