Probabilistic-based contact modeling of sand particles

Granular materials though very common in everyday experience are poorly understood from a theoretical perspective. This may be attributed to the fact that they exhibit surprisingly complex behavior even in the simplest of the situations. The discrete-based numerical tools have been proven to provide interesting insights into the complex behavior of granular materials, however, their accuracy depends primarily on the chosen contact parameters. Recent literature on particle scale experiments reveals that there are significant discrepancies of the contact parameters of granular systems, adding significant uncertainties in contact mechanics modeling and the selection of input parameters. Hence, a probabilistic-based approach in the analysis of grain-scale experimental data provides an invaluable solution to address these high discrepancies. In this study, we present a new probabilistic-based approach illustrated in Figure 1 in the analysis and identification of the best-suited models to fit the tangential stiffness reduction-displacement curves of granular contacts (after Reddy et al., 2022). For this purpose, three different hyperbolic models and the Mindlin and Deresiewicz model were accordingly adjusted with respect to their original versions to be suitable for analysis of non-conforming contacts employing the concept of secant stiffness rather than tangent stiffness. Bayesian probabilistic optimization and model selection was employed for each individual experimental curve analysed in the present study. Through this study, we demonstrate that the new approach outperforms that of traditional methods used in contact mechanics modeling.