Simple Yield Surface Expressions Appropriate for Soil Plasticity

Abstract

The objective of this paper is to present a number of simple, practical, and useful analytical expressions of a yield surface for geomaterials. In classical plasticity, the analytical expression of a yield surface defines the locus of points in stress space at which plastic flow initiates, and the corresponding function must depend on direct and mixed invariants of stress and tensor-valued internal variables. One single function describes a yield surface in order to avoid singularities and computational difficulties arising from the use of multiple functions representing intersecting surfaces in stress space that are often used for cap-type models in soil plasticity. The presented functions are conveniently subdivided in three main categories depending on the type of analytical expression used, and they all describe properly closed yield surfaces which are continuous and convex. The internal variables in these functions can be used in order to address classical plasticity features such as isotropic and kinematic hardening, the latter in the form of rotational hardening. The effects of parameters on the shape of yield surfaces are clearly demonstrated and illustrated for all functions in triaxial stress space. The generalization of these functions to the multiaxial stress space is presented using a consistent method such that if one applies triaxial loading conditions on the multiaxial expressions, the triaxial ones are retrieved. Finally, the appropriateness of the yield functions in regards to the soil type is discussed.