Basal Force Probability Distributions in Thin-Layer Granular Flows

Abstract

Extreme geophysical flows, such as granular and debris flows, can significantly shape the landscape in steep lands and generate seismic signals that can be recorded over long distances. However, direct field measurements needed to constrain the granular physics remain difficult due to the damage potential of those flows. Here, we investigate how the granular flows impact the bedrock channel using a computational fluid dynamics model coupled with the discrete-element method, systematically varying the grain size, discharge, and water content for two flow regimes: unsteady and steady flows. These numerical experiments allow us to quantify the basal forces as probability density functions (PDFs). We test those PDFs based on several evaluation metrics, such as determination coefficient, residual sum of squares, Wasserstein distance, and information entropy for 12 selected probability distributions. We find that the t Location-Scale and lognormal distributions are best-performing among the tested distributions for unsteady and steady flows, respectively, rather than the exponential and generalized Pareto distributions in previous studies. Our results demonstrate that grain size, discharge, and water content strongly influence the basal-force distribution. Furthermore, we established the relationships between flow kinematics and basal force statistics. Results indicate that compared to effective friction coefficient and volume fraction, the fitted parameters of the probability distributions exhibit monotonic relationships with Froude number, granular temperature, and dimensionless velocity. These results provide empirical constraints for modeling extreme geophysical flow incision and inversion of seismic signals generated by such flows.