A new hyper-elastic law for single yield surface constitutive models for clays

The elasticity law is a great challenge in soils, due to the well-known non-linear, anisotropic, pressure-dependent soil response even at negligibly small strains. A new hyper-elastic formulation is proposed, based on a polynomial expression (including a fabric tensor defining the elastic anisotropy) with two branches, one for the negligibly small stresses, ensuring good convergence properties at low confining pressure, and one for the soil response at intermediate strains, corresponding to stress states inside a single large-sized, yield surface defining the occurrence of large irreversible strain. Typical numerical simulations are discussed for isotropic and oedometric compression and swelling tests, and for undrained triaxial compression tests. The results are compared with those obtained with similar hyper-elastic models proposed in the literature. A comparison with experimental oedometric and drained and undrained triaxial tests on undisturbed samples of London clay is provided, revealing that the proposed model has great flexibility in selecting both the shear stiffness and the evolution of elastic anisotropy, which can be chosen independently, thus providing a general applicability. For instance, the great flexibility of the proposed hyper-elastic formulation can be exploited to model the non-linear swelling curves typically observed in oedometric swelling tests of structured clays or active clays.