| 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. Particles used in the experiments were stainless steel, glass, and natural particles. The analysis of the laboratory measurements showed that: (1) for a smooth bed (ks = 0), Vp increases with ds; (2) for a rough bed (ks > 0), Vp decreases with G, thus lighter particles move faster than heavier ones; and on a very rough boundary Vp decreases with ds; (3) 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) 0.2 < Vp/uf < 0.9; and (7) 2.5 < Vp < 12.5.; 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 τ*ds, ks/ds, d*, and (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.; The analysis shows that the proposed formula, Eq. (5.34) provides much better predictions than the existing formulas. In addition, the proposed formula was also verified with the devastating flood of the Avila Mountain in Venezuela in December 1999. The results give realistic estimates of particle velocities. |
