Small Strain Path-Dependent Stiffness of Toyoura Sand: Laboratory Measurement and Numerical Implementation

Although Toyoura sand has been widely used as a standard material for physical model tests (particularly centrifuge model tests), its path-dependent stiffness degradation curves are rarely reported in the literature. This leads to difficulties in back-analyzing and understanding the physical tests involving significant changes in the direction of stress paths (such as unloading problems). In this study, path-dependent stiffness degradation curves of medium-dense Toyoura sand were determined by carrying out a series of stress-path triaxial tests, with local strain measurements. In the triaxial tests, four typical recent stress histories (changes of path direction = 0, 90, –90, and 180°) were simulated. The measured small strain stiffnesses of Toyoura sand were then used to calibrate an advanced hypoplastic model that accounts for path-dependent soil stiffness at small strains. To justify the validity of the calibrated hypoplastic model and model parameters, a Type A numerical prediction and a centrifuge model test were carried out to simulate a typical unloading problem (i.e., excavation) in medium-dense Toyoura sand. Triaxial test results show that a 180° reversal in the direction of the stress path increased the initial secant modulus of Toyoura sand by eight times. The path dependency of soil stiffness, however, vanished when the deviatoric strain exceeded 0.3%. The ground deformations (resulting from excavation) predicted by the numerical analysis show reasonable agreement with the measured data from the centrifuge test. This suggests the potential applicability of the calibrated soil model and its model parameters in predicting or back-analyzing other physical model tests in Toyoura sand.