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 ($1.2\mathrm{mm}<d_s<13.6\mathrm{mm}$ at $G=2.65$), spherical glass marbles ($14.5\mathrm{mm}<d_s<29.3\mathrm{mm}$ at $G=2.6$), and spherical steel ball bearings ($1.6\mathrm{mm}<d_s<19\mathrm{mm}$ 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 $0<k_s<3.4\mathrm{mm}$) 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 $\pm 30\%$ 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 ${\tau }_{*ks}=R_h{S}_f/(G-1)k_s$ in the range $0.008<{\tau }_{*ks}<0.2$ up to a maximum $V_p\approx 12u_{*}$. 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.