A discrete viscoplastic damage model is proposed for the description of time-dependent behaviour of quasi-brittle rocks. This model is inspired by micromechanical considerations. Rocks are considered as quasi-brittle materials containing a spatial distribution of microcracks. Viscoplastic strains of rocks are generated by the time-dependent frictional sliding of microcracks surfaces while the damage of rocks is related to the growth of microcracks. The two inelastic mechanisms are coupled. The model is formulated in the framework of discrete thermodynamics of irreversible processes. The local strains and stresses applied to microcracks are related to the macroscopic counterparts through appropriate kinematic and static conditions. Specific viscoplastic flow rule as well as damage evolution law is defined for each family of microcracks. The validity of proposed model is verified through comparisons between numerical results and experimental data in triaxial compression tests and creep tests for sandstone.
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