Basal force distribution from steady fully-developed granular flows

Understanding the impact of geophysical flows on the channel bed is essential for assessing erosion processes of bed material. In this study, the discrete element method (DEM) is used to simulate idealized, steady-state, fully-developed granular flows impacting the channel bed with systematically varying total particle number (1000-30000), grain size (2-16mm), and slope angle (28-34°) to investigate the probability distributions of the basal force. The probability density functions of the basal force, normalized to the mean force, were calculated and fitted with ten probability distributions. Four indices, namely R², Residual Sum of Squares (RSS), Wasserstein distance, and information entropy, are introduced to evaluate the goodness of fit for each probability density distribution. By comparison, the broad probability density distribution of normalized basal force can be well-described by Gamma distributions (GD) with its shape and scale parameters. The shape parameter of the Gamma distribution is positively correlated with the total particle number and grain size, but negatively correlated with the slope angle. An opposite relationship is revealed in the scale parameter of the Gamma distribution. Additionally, we analyzed flow kinematics by calculating the coordination number, dimensionless velocity, shear rate, inertial number, and volume fraction, and linking these variables to the shape and scale parameters. The coordination number, shear rate, inertial number, and volume fraction serve as effective proxies for the shape and scale parameters, enabling interpretation of the statistical characteristics of monitored basal forces in geophysical mass flows.