One kind of transverse isotropic strength criterion and the transformation stress space

The geomaterials with original anisotropic properties formed in the natural process are usually simplified as a kind of cross-anisotropic material. The spatial location of the depositional plane (DP) and the effective spatial mobilized plane (ESMP) in physical space is closely related to anisotropic properties; thus, the inclined angle between DP and ESMP is taken as a primary parameter governing the strength degree of geomaterial anisotropy. According to the concept of ESMP, the frictional capacity can be more effectively mobilized when the inclined angle between DP and ESMP is larger, inducing a higher stress strength. In this study, a new stress strength formula is proposed for geomaterials, which takes the cross-anisotropic properties into account. The transformation strategy can be regarded as a strength criterion describing the convert of transversely isotropic behavior formula into an isotropic von Mises criterion formula. Based on the cross-anisotropy strength criterion, the transformed stress (TS) equation can be derived by transforming the cross-anisotropy stress space to the isotropic stress space. By using the proposed TS method, it is convenient to convert the traditional two-dimensional (2D) constitutive models on the basis of the Von-Mises criterion to the general three-dimensional (3D) models considering cross-anisotropy. Comparing the predicted and the tested results of strength and stress-strain relationship tests for geomaterials under the true triaxial loading condition, the validity and the applicability of the proposed TS method with related criterion can be ensured.