Incorporation of cross-anisotropic small-strain stiffness into the Hardening Soil model

The Hardening Soil model and its refinements are formulated under the assumption of isotropic mechanical characteristics. This choice is driven both by the feasibility of robust FE implementations for isotropic formulations and by practical considerations regarding the availability of material parameters. However, the literature clearly demonstrates that incorporating anisotropy into constitutive models enables FE simulations of soil–structure interaction that align more closely with field measurements. In this paper, inherent cross-anisotropy is introduced into the recently proposed small-strain HS-Brick refinement of the Hardening Soil model, where the Brick-type approach is used to control the degradation and recovery of the current reference hypoelastic stiffness. In the examined version of the new model, cross-anisotropy is incorporated only within the small-strain range through a specialized scaling of the isotropic hypoelastic stiffness matrix. The model is primarily designed for simulating the mechanical pre-failure behaviour of cross-anisotropic, stiff, fine-grained soils. Details of the FE implementation are provided, along with selected element tests. Finally, the model’s performance is evaluated in an exemplary boundary value problem involving tunnelling-induced deformations. The obtained results are analysed and discussed.