Abstract: An anisotropic failure criterion is proposed to present anisotropic failure behaviors for different kinds of sand, which can be employed to simulate both isotropic and anisotropic strength behaviors of granular materials. The model parameters can be determined by the strength ratios based on the triaxial compression and extension tests in different stress areas. Concepts and expressions are put forward for the generalized intermediate principal stress parameter and the generalized internal friction angle, respectively. The generalized expression of the internal friction angle influenced by the intermediate principal stress parameter is deduced based on the proposed anisotropic failure criterion. This generalized explicit expression is available for different soil strength criteria to establish the relationship between the internal friction angle and the intermediate principal stress parameter. Comparisons between simulations and test results show that this general expression of the internal friction angle can well reproduce the true triaxial test results of soils in all stress areas.