The Statistical Mechanical Model of Sediment Transport Capacity and Scour-and-Silt volume in Wide and Shallow Rivers

Abstract

This study aims to develop a universal, parameter-free model for sediment transport and riverbed evolution using a rigorous statistical physics framework. It seeks to overcome the limitations of traditional deterministic and empirical approaches by establishing formulas with general applicability. The river channel is conceptualized as an isothermal-isobaric ensemble containing numerous non-identical sediment particles. The macroscopic state of the system, defined by the scour-and-silt volume, is derived from the statistical mechanics of particle distributions. The Gibbs free energy and partition function for the ensemble are formulated, considering the two primary states of particles (suspended load and bed load) and the transitions between them. This theoretical framework yields a universal formula for the number of particles in transport and the consequent volumetric change. The model was applied to six reaches of the Lower Yellow River from 2000-2001. Calculations revealed a seasonal pattern in the number of transported particles, higher in winter and lower in summer. The results showed an alternation between scour (January-July) and siltation (July-January), with a net scour volume over the 24-month period. The magnitude of scour-and-silt volume decreased from upstream to downstream, findings that are consistent with independent observational records following the operation of the Xiaolangdi Reservoir. The model successfully simulates riverbed evolution without empirical parameters, demonstrating that statistical physics provides a robust framework for predicting complex fluvial processes. Its general formulation suggests potential applicability to other similar multi-particle systems.