Theoretical model with multi-asperity interaction for the closure behavior of rock joint

The closure behavior of rock joints remains a problem of interest with applications in many practical engineering problems. Based on a comprehensive assessment of realistic closure behavior, we developed a Hertz-based theoretical model 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 of rock joint under compressive loading. The factors influencing the closure behavior of rock joint can be considered by the model, namely (1) surface morphology component, (2) contact state between the upper and lower rock blocks (or the composite topography), and (3) deformation due to asperity itself substrate deformation due to the deformed asperity and deformation caused by the mechanical interaction due to the adjacent deformed asperities. In the model, the vertical position (perpendicular to the least square plane) of asperities are adjusted by using a discrete methodology based on the Hertz-solution of substrate deformation outside the contact region. The applicability is demonstrated by comparing the experimental results with the curves predicted by the Tang model,20 and the model proposed in this paper. The results show that the closure behavior predicted by the proposed model is in good agreement with experimental test data, with small discrepancies between the predicted and the measured values.