Open-channel flow of Bingham fluids: Applications in debris-flow research

The results of a numerical simulation of open-channel flow of Bingham fluids provide improved capabilities for analyzing muddy debris flows and their deposits, and for routing debris flows. Because of limitations of the phenomenonological Bingham model, results are deemed applicable to mud-rich debris flows only. Most published field estimates of debris-flow rheological (Bingham) properties depend on application to natural channels of analytical solutions for flow through channels with either circular or very wide channel cross-sections. Lack of a general solution for flow of Bingham fluids in channels with realistic shapes has restricted capabilities in debris-flow modeling and field data analysis. Numerical solutions permit generalization and extension of analytical solutions to channels of arbitrary cross-sectional form without loss of accuracy. The numerical model (FIDAP) utilizes a well established finite-element formulation of the non-Newtonian fluid flow problem and reproduces available analytical solutions nearly exactly. A regression analysis of model results constrains general, easily applied equations that give discharge and plug velocity as functions of channel geometry, channel slope, debris bulk density, viscosity, and yield strength. These empirical equations are suitable for back-calculation of debris-flow viscosity from field data, engineering analysis, and for incorporation into one- and two-dimensional debris-flow routing models. An analysis of debris-flow rheology on the basis of new field observations in Owens Valley, California, utilizing this method yields the most reliable field estimates of debris-flow yield strength-viscosity pairs to date. These new field estimates corroborate trends seen in recent laboratory studies and suggest that these trends may be extrapolated to field scale.