Shear hyperbolic-type equivalent-time rheological model

In order to predict the rheological deformation under variable shear loadings, the Yin-Graham's equivalent-time method is used to derive a shear rheological model in the framework of continuum mechanics with thermodynamic internal variables. Firstly, the Mesri's hyperbolic creep expression is generalized into dissipative space, and the equivalent-time lines between viscoplastic shear strain and shear stress are plotted in the dissipative space. Secondly, the relationship equation between shear viscoplastic strain rate and equivalent time is established using the Yin-Graham's equivalent-time method, and the function expression among shear viscoplastic strain rate, stress level and shear viscoplastic strain is obtained. Finally, after using the mechanical formula that dissipative stress is equal to the true stress and combining the expression for viscoplastic strain rate with linear elastic constitutive equation, a one-dimensional elasto-viscoplastic shear rheological model is formulated, and the expressions for rheological model are studied in terms of the absolute equivalent time and the relative equivalent time, respectively. Based on this rheological model, the analytical solutions of shear rheology are obtained for single-stage and multi-stage loading in drained triaxial shear creep tests. The case study shows that the shear rheological model can relatively well fit the test data of drained triaxial shear creep tests.