Calibration and Evaluation of a Stress-Dependent Extended Hypoplastic Small-Strain Model

Accurate prediction of soil deformations in geotechnical engineering requires a reliable representation of stiffness at very small strain levels, where experimental evidence shows a pronounced dependency on stress state. Although extended hypoplastic models with intergranular strain can reproduce strain-dependent stiffness degradation, their standard formulations do not explicitly account for the stress dependency of small-strain stiffness and the associated strain evolution. This limitation can lead to unrealistic deformation predictions in numerical analyses of soil–structure interaction problems. In this study, a stress-dependent extension of the hypoplastic model with intergranular strain is proposed by introducing a confining-stress-dependent formulation for the parameter governing small-strain stiffness degradation. The modified model is calibrated using reference results from the HS-Small model and analytical considerations, and its performance is evaluated through element-level triaxial simulations and several boundary-value problems, including deep excavations and tunnel construction. Numerical results demonstrate that the proposed formulation successfully captures the experimentally observed increase in small-strain stiffness with confining pressure and yields systematically improved predictions of wall deflection, surface settlement, and heave compared with the original hypoplastic formulation. The results indicate that incorporating stress dependency into the small-strain framework of Hypoplasticity significantly enhances the physical realism and predictive capability of the model, while remaining compatible with standard finite-element workflows. The proposed approach provides a practical improvement for deformation analysis in excavation and tunneling applications.