Elastoplastic constitutive model and parameter determination for transversely isotropic rocks

Layered rocks are widely distributed in formations. The macro-structure of the layered rocks is characterized with transversely isotropy, which will induce the transverse isotropy in deformation and strength. Based on the basic theory of elasticity and generalized plastic mechanics, an elastoplastic constitutive model for transversely isotropic rock is proposed. In the model, the generalized Hooke's law is adopted for the elastic behavior. For the plastic behavior, the yield criterion and potential function formulated as a function of the generalized octahedral shear stress, the non-associated flow rule and the stress-dependent hardening criterion are used. The yield surface of the model is convex with non-equal intercept elliptical cross-section pyramid, which can be simplified under isotropic condition as that for the Mises yield criterion. A method for determination of the model parameters is proposed, that is, the elastic parameters are obtained by combining the triaxial compression tests with a torsion test. The plastic parameters are obtained by using the triaxial compression tests on samples with different bedding directions. Taking the carbonaceous slate as an example, the proposed transversely isotropic elastic-plastic model and the parameter determination method are verified. The results show that the proposed model can reflect the transversal isotropy of the rock well, and the parameter determination method is simple and effective. The direction of plastic potential and the coupling between elastic and plastic behaviors of carbonaceous slate are also discussed according to the test data. This research provides a theoretical basis for enriching the basic theory of rock mechanics and solving engineering problems.