Transport velocities of bedload particles in rough open channel flows

Abstract

This dissertation aims at defining the bedload particle velocity in smooth and rough open channels as a function of the following variables: bed slope Sf, flow depth y, viscosity of the fluid v, particle size ds, bed roughness ks, particle specific gravity G, and gravitational acceleration g.

Sets of aluminum plates were placed on the bottom of an experimental plexiglass-tilting flume, with trapezoidal cross-section, to form a smooth bed. A layer of sand or gravel was glued onto aluminum plates to form bed roughness. Bedload particles used in the experiments were stainless steel ball bearings, glass marbles, and natural quartz particles. The experiments were performed to provide 529 average bedload particle velocities. The analysis of the laboratory measurements showed that: (1) for a smooth bed (ks = 0), the rolling bedload particle velocity Vp increases with particle sizes ds; (2) for a rough bed (ks > 0), particle velocity decreases with particle density G, thus lighter particles move faster than heavier ones; and on a very rough boundary Vp decreases with particle sizes; (3) bedload particles move at values of the Shields parameter τ*ds = u*2/(G-1) gds below the critical Shields parameter value of τ*dsc = 0.047; (4) few of the observed particles moved at values of Shields roughness parameter τ*ks = u*2/(G-1)gks less than 0.01; (5) particles are observed to move at values of the Shields roughness parameter 0.01 < τ*ks < 0.15; (6) the ratio of particle velocity Vp to mean flow velocity Uf lies in the range of 0.2 to 0.9, while Kalinske (1942) suggested 0.9 to 1.0; and (7) the ratio of particle velocity Vp to shear velocity u* lies in the range of 2.5 to 12.5, compared to the values cited in the literature 6.0 < Vp/u* < 14.3.

New methods for predicting transport velocity of bedload particles in rough and smooth open channels are examined. Two approaches for transport velocities of bedload particles were considered. The first approach combines dimensional analysis and regression analysis to define bedload particle velocity as a power function of the Shields parameter τ*ds, boundary relative roughness ks/ds, dimensionless particle diameter d*, and excess specific gravity (G-1). The second approach considers the transport velocity of a single particle on a smooth bed. The reduction in particle velocity due to bed roughness is then examined through a theoretical and empirical analysis. Results show that the bedload particle velocity on smooth beds is approximately equal to the flow at the center of the particle; and the bed roughness gradually decreases the transport velocity of the rolling bedload particles. Comparatively, [t]he first approach gives satisfactory results, except when ks equals 0, then Vp goes to ∞; and when ks is large, Vp does not stop (unbounded); for the second approach Vp = Vpmax when ks equals 0, and when Vp equals 0 (no motion), then ks follows the criteria a and b described in Chapter 5 (section 5.4).

The analysis shows that the proposed formula, Eq. (5.34) provides much better predictions than the existing formulas. The discrepancy ratio distributions using Eq. (5.34) are normally distributed and have higher density (close to perfect agreement) than all other formulas. In addition, the proposed formula, Eq. (5.34) is also verified with the devastating flood of the Avila Mountain in Venezuela in December 1999. The results give realistic estimates of particle velocities.