A Generalized Unified Strength Theory for Rocks

The unified strength theory (UST) has been widely applied in engineering. It includes many well-known strength criteria as its special or asymptotic cases. However, the UST predicts the same strength at σ2 = σ3 and σ2 = σ1, which contradicts with the test results of some rock types and limits its application. In this study, the effect of σ2 on rock strength is investigated. The contribution of σ2 in the UST is identified and re-interpreted. By introducing a mobilized factor χ to characterize the weakening effect of σ2 on rock strength at high σ2 values, a generalized unified strength theory (GUST) is proposed. The proposed criterion is validated using the true triaxial test data of the fourteen rock types reported in the literature. The results show that the GUST achieves better fits to all rocks than the UST. Some existing three-dimensional strength criteria are piecewise linear approximations of the proposed criterion, implying that the GUST is more versatile. A substantial relationship between the intermediate principal stress coefficient and the unconfined compressive strength is obtained and approximated by a hyperbola function, ensuring that the GUST can still function effectively even in the absence of true triaxial test data.