A model for describing and predicting the creep strain of rocks from the primary to the tertiary stage

Abstract

Rocks under applied stresses can exhibit more or less degree of creep. Over the years, a large number of creep models have been proposed for rocks. However, few models account for friction angle and time to failure. In most cases, curve fitting technique is applied to all of the available experimental results to obtain the required model parameters. The ability of the calibrated model (i.e. the model with the obtained model parameters) to predict the rheological behavior under untested stress conditions remains unknown. In this paper, a new model, called ubiquitous-corrosion-Coulomb (UCC) creep model, is proposed. Distinction is made between reversible and irreversible creep strains. Subcritical crack growth is related to the irreversible creep strain and delayed failure of rocks. The effect of friction angle and confining stresses on the rate of irreversible creep strain and time to failure has been considered. With the UCC model, the failure plane in creep tests making an angle of 45°−ϕ/2 with the major principal stress σ1 is explained by the fact that among the numerous micro cracks, the cracks along this orientation are the first ones becoming unstable. To test the capability of the UCC creep model against experimental results available in the literature, the required model parameters are first obtained by applying the curve-fitting technique on a part of the available experimental results. The predictability of the calibrated model is then tested against another part of the available experimental results, which are not used in the previous curve-fitting process. The results showed that the proposed UCC creep model can be used to describe and predict the creep strain and time to failure of rocks.