An excess stress model for capturing rate-dependent compressive behavior of rock joint and its validation and applications

The deformational and mechanical behavior of rock masses is determined by discontinuities at different scales, e.g., rock joints. The discontinuous rock masses are often subjected to dynamic loads, e.g. blasts and earthquakes. Therefore, understanding dynamic response of rock joints is crucial. However, the dynamic compressive characteristics of rock joints have not been well understood yet. In this study, an excess stress model, employing the mechanical conceptual models based on the Hooke, the modified Saint Venant and the Newton elements, was developed. It is capable of capturing the nonlinear compressive processes of joints at different loading rates. This new model was validated by the comparison between model predictions and laboratory measurements obtained at loading rates ranging from approximately 200 GPa/s to 600 GPa/s. It was found that certain of rate-dependent compressive characteristics of rough joints can be successfully quantified with the proposed joint model. Compressive strength can be approximately predicted on the assumption that the peak-stress displacement is independent of the loading rate. Both the peak-stress secant stiffness and tangent stiffness predicted by the new joint model increase linearly with the loading rate. The wave energy dissipation at joints calculated by the proposed model decreases with increasing loading rate. Based on this model, the underlying mechanisms responsible for loading rate effects were related to the rate-dependency of crack propagation. Two hypotheses have been proposed: 1)the amount of cracking decreases with the increase of loading rate before the peak stress, causing 'apparent' hardening effects; 2) crack propagation velocity is relatively steady under static/quasi-static conditions, but becomes increasingly unstable when the loading rate is higher than the critical transition value. The present findings potentially provide a mechanically sound frame for the rate-dependent characteristics of joints, and have important implications for explicating the rate-dependent phenomena of fracturing, such as crack branching and fracture smoothening.