Theoretical closure model for rock joints considering interaction of deformations of substrate deformation and asperity

The closure behavior of rock joints remains a problem of interest with applications in many practical engineering cases. Based on a comprehensive assessment of realistic closure behavior, a Hertz-based theoretical model is proposed to predict the closure behavior of a rock joint under compressive loading. In the present study, special attention is focused on the role of mechanical interaction of asperities during the closure process. The vertical positions (perpendicular to the least square plane) of asperities are adjusted by using the discrete methodology based on the Hertz solution of substrate deformation outside the contact region. The factors influencing the closure behavior of rock joints can be considered by the model, namely (1) the surface morphology component, (2) the contact state between the upper and lower blocks (or the composite topography), and (3) the deformation due to asperity itself, the substrate deformation due to the deformed asperity and the deformation caused by the mechanical interaction due to the adjacent deformed asperities. The validity is demonstrated by comparing the experimental results with the curves predicted by Xia model, Tang model and the proposed model. The results show that the closure behavior predicted by the proposed model is in good agreement with experimental data, with small discrepancies between the predicted and the measured values. A preliminary explanation for the discrepancies of contact stiffness predicted by Xia model, Tang model and the proposed model associated with different underlying principles is also put forward.