Influence of Stress-Dependent Small-Strain Stiffness and Threshold Strain in the HS-Small Model

Soil stiffness at very small strains exhibits strong stress dependency and nonlinearity with strain amplitude, influencing the accuracy of numerical predictions in geotechnical analyses. Benz (2007) formulated analytical relationships describing the stress dependency of the small-strain shear modulus (𝐺0) and threshold strain (𝛾0.7), but his implementation—using Mohr–Coulomb (MC) and Matsuoka–Nakai (MN) yield criteria—did not fully represent their impact on numerical predictions. In this study, the current PLAXIS Hardening Soil–Small (HS-Small) model, which combines the Hardening Soil elastoplastic framework with the small-strain overlay, is employed to evaluate the influence of these stress-dependent formulations. Element tests and boundary-value simulations (anchored excavation and tunnel) are conducted using the HS-Small model and compared with results from earlier HS-Small formulations using MC and MN yield criteria. The results of the stress-dependent HS-Small formulation show excellent agreement with experimental stiffness–strain relationships and measured boundary deformations. Incorporating stress-dependent stiffness and threshold strain leads to 5–40% reductions in computed deformations and reproduces realistic stiffness–strain behavior observed in laboratory and field data. At a broader level, the results demonstrate that constitutive models incorporating stress dependency of stiffness and strain at small strains more accurately reproduce ground response, while conventional models such as Mohr–Coulomb and Hardening Soil lack this capability and may underestimate soil stiffness in the working strain range.