Constitutive modelling of a dry sand–structure interface under high-frequency vibration with a constant normal load

Sand–structure interfaces undergo strength loss and volume contraction under high-frequency vibration, potentially compromising the performance of underground structures in high-speed railway engineering. However, an appropriate method for quantitatively characterizing the behaviour of the sand–structure interface under high-frequency vibration is currently lacking, impeding the advancement of related design methods. In this work, the primary deformation and strength characteristics, such as the evolution of shear stress and volumetric strain, of the dry sand–structure interface under high-frequency vibration are summarized via a modified direct shear apparatus under a constant normal load. The concept of “vibro-induced virtual pore pressure” is subsequently introduced to modify the expressions of the critical state, yield, and bounding surfaces. The relationships between vibro-induced volume contraction and the vibration stress amplitude and state parameters are also established. Ultimately, a constitutive model describing the behaviour of the dry sand–structure interface under high-frequency vibration is formulated within the frameworks of critical state soil mechanics and bounding surface plasticity. The model comprises 14 parameters, all of which can be calibrated via laboratory experiments. Through comparison with experimental observations, the model is found to accurately simulate the key behaviours of the dry sand–structure interface under both static and high-frequency vibration conditions with a constant normal load, effectively reflecting the influence of the density, normal stress, and vibration stress amplitude of the sample.