NOR-SAND - A SIMPLE CRITICAL STATE MODEL FOR SAND

A generalized Cambridge-type constitutive model for sand is developed from the fundamental axioms of critical state theory. An infinity of normal consolidation loci for sand prevents the direct coupling of yield surface size (hardness) to void ratio. Therefore, the second axiom of critical state theory is used as the basis of an incremental hardening rule by defining an image of the critical state on the yield surface and requiring that the image state become critical with shear strain. The proposed representation of sand behaviour has the attribute of normality and yet realistic dilation rates are obtained; this duality is achieved by defining limiting hardening loci proportional to the state parameter psi at the image stress. A range of models can be developed within the general scheme. A simple rigid-plastic variant is presented and shown to capture the constitutive behaviour of sand in drained triaxial tests; a single set of material parameters models sand behaviour regardless of initial density or confining stress, initial density being introduced through psi. The approach is not limited to dilatant (dry) soils and smoothly represents soil behaviour from very loose to very dense states. The simple rigid-plastic model is called Nor-Sand and requires two additional parameters to the normal suite for a critical state model. Nor-Sand appears to meet the need for a simple and enlightening representation of sand.