A New Constitutive Model for the Time-dependent Behavior of Rocks With Consideration of Damage Parameter

Deformation and time-dependent behavior of rocks are closely related to the stability and safety of underground structures and mines. In this paper, a numerical-analytical model is presented to investigate time-dependent damage and deformation of rocks under creep. The proposed model is obtained by combining the elastic-visco-plastic model based on the theory of over-stress and stress hardening law with the sub-critical crack growth model. The advantage of this model is that it is in incremental form and therefore can be implemented numerically. First, the governing equations of the model and its numerical computational algorithm are described. The proposed constitutive model is then implemented in the FLAC code using the FISH function. Determination of model parameters and calibration is done by various laboratory tests performed on a type of gypsum. The creep test was performed on gypsum under a stress of 13 MPa, which is equal to 70% of its compressive strength. After determining the parameters, by fitting the creep curve of the presented analyticalnumerical model, a good agreement is observed with the creep curve obtained from the laboratory data. It is also observed that during creep, the damage parameter and wing crack length increase.