Velocity of Rolling Bed Load Particles

Experimental measurements of the reach-averaged bed-load particle velocity V-p on smooth and rough plane surfaces were analyzed for particles of different shape, size d(s), and density G. Particle types included natural quartz particles (1.2 mm < d(s) < 13.6 mm at G = 2.65), spherical glass marbles (14.5 mm < d(s) < 29.3 mm at G = 2.6), and spherical steel ball bearings (1.6 mm < d(s) < 19 mm at G = 8.02). The velocity of 9,739 individual bed load particles continuously rolling on aluminum plates coated with a layer of sand/gravel (roughness 0 < k(s) < 3.4 mm) was measured for 356 different conditions. For each flow condition, the reach-averaged particle velocity measurements over a 2 m test reach were repeated at least 15 times to provide mean values and standard deviations. For bed load particles rolling on smooth surfaces (k(s) = 0), it was concluded that (1) V-p is within +/- 30% of the calculated flow velocity from the vertical velocity profile at the top of the particle; (2) V-p for spheres does not vary much with particle density; and (3) V-p increases slightly with particle size d(s), up to approximately 20u(*). On rough surfaces (k(s) > 0), for particles of diameter d(s) continuously rolling on a stationary bed of roughness k(s), it was concluded that (1) bed load particles roll in continuous motion in the range 2.5 < V-p/u(*) < 12.5; (2) steel particles are much slower than spherical marbles (G = 2.6); and (3) the particle velocity increases primarily with a new parameter tau(*ks) RhSf/(G - 1)k(s) in the range 0.008 < tau(*ks) < 0.2 up to a maximum V-p approximate to 12u(*). Spherical particles roll slightly faster than natural particles. In a comparison with a large data set that included 1,018 measurements, the analysis of discrepancy ratios showed that the proposed formula was in good agreement with other measurements from the literature. DOI: 10.1061/(ASCE)HY.1943-7900.0000657. (C) 2013 American Society of Civil Engineers.