Modeling Cross Anisotropy in Granular Materials

A constitutive model has been developed to capture the behavior of cross-anisotropic frictional materials. The elastoplastic, single hardening model for isotropic materials serves as the basic framework. Based on the experimental results of cross-anisotropic sands in isotropic compression tests, the principal stress coordinate system is rotated such that the model operates isotropically within the rotated framework. Experimental plastic work contours on the octahedral plane are plotted for a series of true triaxial tests on dense Santa Monica Beach sand to study the effects of cross anisotropy on the evolution of yield surfaces. The amount of rotation of the yield and plastic potential surfaces decreases to zero (isotropic state) with loading. The model is constructed for cases where the principal stress and material symmetry axes are collinear and no significant rotation of principal stresses occur. The model incorporates fourteen parameters that can be determined from simple experiments, such as isotropic compression, drained triaxial compression, and triaxial extension tests. A series of true triaxial and isotropic compression tests on dense Santa Monica Beach sand are used as a basis for verification of the capabilities of the proposed model.