Impact of the intermediate principal stress on the strength of heterogeneous rock

Abstract

A numerical model simulating a granular material has been used to study the impact of the intermediate principal stress on rock strength. While maintaining the minimum principal stress at zero, the model predicts strength to increase with increasing constant ratios of σ2/σ1. This trend was found to reverse as the stress ratio exceeded 0.5, and for the case of σ2 = σ1 the predicted compressive strength nearly equaled the one obtained under uniaxial loading conditions. This impact of the intermediate principal stress indicates that not only the stress level but also the stress symmetry has an impact on the rock strength. If the rock is heterogeneous, which rocks always are at some scale, there is a different probability for failure at different orientations of the sample, relative to the orientation of the stresses (irrespective of any anisotropy effects). If σ2 = σ3 or σ2 = σ1, there are many equivalent orientations of the macroscopic failure plane once the failure criterion is fulfilled, and the failure plane will take the orientation for which the rock fails most easily. If σ2 is truly intermediate, only two potential orientations of the failure plane fulfils the failure criterion initially. As a consequence, the expectation value for the rock strength is higher when σ2 is truly intermediate. A numerical model has been developed, which incorporates rock heterogeneity through a smoothened failure criterion. The model quantitatively couples the impact of the intermediate principal stress on rock strength to the natural variation in experimental tests results.