Reliability-Based Analysis of Initiation of Sediment Motion on Movable Bed

Sediment transport dynamics are of great importance in understanding geophysical flows, where determining the threshold conditions for the initiation of sediment motion presents a complex challenge. In a pioneering work, Shields (1936) established the Shields’ criterion to assess the critical shear stress (τ_c) required for sediment motion in non-turbulent flows. Although this approach has significant advantages, including a robust empirical foundation and the implementation of non-dimensional critical shear stress, it is valid for limited conditions since it oversimplifies vital aspects such as sediment heterogeneity and complex flow interactions.

In turbulent flows, the effective critical shear stress acting on a grain may become higher than that measured in the case of laminar flows (i.e., the average critical stress, τ_c, defined by Shields, 1936) as a result of fluctuations in the shear stress (τ′). Owing to this, in geophysical turbulent flows near the threshold of motion, neither the driving nor the resisting parameters of sediment motion have crisp values; instead, they may be considered probabilistic parameters. The reliability-based approach is applied here in to handle the complex nature of the initiation of sediment motion.

This study aims to present preliminary results of research that aims to enhance the knowledge of incipient motion by applying a reliability-based analysis of Shields’ criterion based on the theory and empirical equations adopted by Zanke (2003). In this analysis, the turbulence parameter (n) and angle of repose (ϕ) are introduced as key parameters regarding the initiation of sediment motion. These parameters are generated as random variables by means of Monte Carlo Simulations, introducing various probabilistic distributions (e.g., normal, log-normal, triangular, gamma) and statistical moments (e.g., mean, standard deviation).

By simulating a wide range of angles of repose and turbulence parameters with Monte Carlo Simulations, the inherent uncertainties in sediment transport and the complexity of hydrodynamic models are incorporated. In this work critical shear stresses of thousands of grains are assessed for different grain Reynolds numbers. As a result, threshold of motion curves are probabilistically derived, indicating confidence for grain entrainment, and establishing a model that enables risk assessment and decision-making for a wide range of scenarios. Comparisons of model results with empirical data show that the model captures the complex physical process.