Refinement of the Hardening Soil model within the small strain range

Abstract The popularity of the elasto-plastic Hardening Soil (HS) model is based on simple parameter identification from standard testing and empirical formulas. The HS model is implemented in many commercial FE codes designed to analyse geotechnical problems. In its basic version, the stress–strain behaviour within the elastic range is subject to the hypoelastic power law, which assures the barotropy of the elastic stiffness. However, a proper modelling within the small strain range, i.e. strain-induced stiffness degradation and correct reproduction of the hysteretic behaviour, was one of the most important drawbacks in the HS formulation. The first small strain stiffness extension to the HS model was proposed by Benz (Small strain stiffness of soils and its numerical consequences, 2007), and the new model was called Hardening Soil Small (HSS). Despite the simple isotropic formulation, its applicability was proved in various numerical simulations in geotechnics. However, the HSS formulation exhibits a serious fault known in the literature as overshooting, i.e. uncontrolled reset of the loading memory after tiny unloading–reloading cycles. The authors' main aim was to retain the set of material parameters for the HSS formulation and to propose a new small strain extension to the HS model without overshooting. The new proposal is based on the Brick model which represents the concept of nested yield surfaces in strain space. The implementation aspects of the new HS-Brick model are described, and its performance is presented in some element tests and selected boundary value problems by comparisons with the HSS formulation.