# Theoretical impulse threshold for particle dislodgement

## TL;DR

This paper derives a theoretical impulse threshold for sediment particle dislodgement using the work-energy principle, aligning well with experimental data and offering a new framework for understanding flow-induced particle motion.

## Contribution

It introduces a novel theoretical expression for the impulse threshold based on particle size and mass, enhancing the predictive understanding of sediment dislodgement.

## Key findings

- Derived an explicit impulse threshold formula
- Excellent agreement with existing experimental data
- Provides a robust framework for future research

## Abstract

The problem of determining the threshold of motion of a sediment particle resting on the bed of an open channel has historically been dominated by an approach based on the time-space-averaged bed shear stress (i.e. Shields criterion). Recently, experimental studies have promoted an alternative approach to predict the dislodgement threshold, which is based on the impulse of the flow-induced force. Nonetheless, theoretical analyses accompanying these studies result in complex expressions that fail to provide a direct estimate of said impulse threshold. We employ the work-energy principle to derive a prediction of the fundamental impulse threshold that the destabilising hydrodynamic force must overcome in order to achieve full particle dislodgement. For the bed configuration studied, which is composed of spheres, the proposed expression depends on the mobile particle's size and mass, and shows excellent agreement with experimental observations previously published. The derivation presented in this paper may thus represent a robust theoretical framework that aids in the re-interpretation of existing data, as well as in the design of future experiments aimed at analysing the importance of hydrodynamic impulse as criterion for prediction of particle dislodgement.