Constitutive Modeling of Kinematic Hardening Behavior of Saturated Anisotropic Soils

A new three-dimensional cone-cap limit-state surface (LSS) model is proposed for cross-anisotropic, saturated, cohesionless, or cohesive remolded soils in consideration of anisotropic yielding and kinematic hardening. Matsuoka-Nakai failure criterion equations are adopted as the cone yield functions, and a new ellipse cap associated with Matsuoka-Nakai cone is developed. The anisotropic vertical and horizontal yield stresses (${\sigma }_{\text{aL}}^{\prime }$ and ${\sigma }_{\text{rL}}^{\prime }$) are used as hardening variables to describe evolution of the fabric anisotropy. A smart kinematic hardening law is suggested without any addition of material parameters. With a nonassociated flow rule and because of the cone-cap connection on a constant $p\prime$ critical state plane, a smooth transition of a plastic strain increment vector at the cone-cap intersection points is ensured for the convenience of numerical calculation. There are very few parameters involved in the proposed model, and they are the same as those in the Cam-clay model, except one parameter for cross-anisotropy [slope of the anisotropic line (AL) $K_{\text{AL}}$ or horizontal yield stress ${\sigma }_{\text{rL}}^{\prime }$]. They can be simply determined from conventional laboratory odometer and undrained triaxial compression experiments. The soil sample is simplified as a stress element, and the element numerical analysis results validate the test data very well. The model-predicted results well illustrate the size and shape modification of the cone-cap LSS of isotropic and cross-anisotropic soils as well as the kinematic hardening effect on the stress-strain behavior. Based on this model, other important features of natural soils, such as viscosity, microstructure, and partial saturation, can be further incorporated by extending the vertical and horizontal yield stresses (${\sigma }_{\text{aL}}^{\prime }$ and ${\sigma }_{\text{rL}}^{\prime }$) in consideration of the effect of viscosity, microstructure, and partial saturation, respectively.