An investigation on the uniqueness of the incremental response of elastoplastic models for virgin sand

The paper investigates the possibility of the occurrence of a multiplicity of homogeneous responses of soil specimens under the same incremental loading, and the associated non-controllability of the imposed loading path. It is shown that for non-associated elastoplastic strain-hardening constitutive laws, such a possibility exists even in the hardening regime. Only when the stiffness matrix is positive-definite is the incremental solution unique for any loading programme. A particular constitutive model is chosen and the shape of the loci of non-uniqueness is calculated for various loading programmes. It is shown that the conditions for the occurrence of a shear band and of a peak of the deviator stress in a triaxial undrained test can be seen as special cases of the theory presented. Accordingly, the so-called ‘instability line’ concept in undrained conditions is generalized.