The Beginning of Bedload Movement of Mixtures Investigated as Natural Armoring in Channels

Abstract

Beginning of bedload transport in channels, whose beds are formed by gravel-sand mixtures, is theoretically and experimentally investigated. In order to make a theoretically approachable treatment to the problem two assumptions are made: 1. the turbulent fluctuations of the bottom shear stress are statistically describable by a Gaussian distribution; 2. a grain starts in motion when the effective (instantaneous) eroding bottom shear stress on a grain exceeds a critical value, which is a function of the grain size and Reynolds number of the grain. On the basis of these assumptions the probability of remaining still (or being eroded) for a certain grain under given hydraulic conditions is calculated (equation 8; this probability is independent of the grain size distribution of the gravel-sand mixture). During the work a feasible way was found to determine the critical shear stress by a basically new method: the average bottom shear stress was defined as equal to the control shear stress, when for the grain in question, the probability for remaining still and being eroded are equal. To supplement and verify the theory, natural armoring of channel bottoms consisting of gravel-sand-mixtures was investigated in the laboratory. On the basis of these experiments the dimension- less critical shear stress can be determined as a function of the Reynolds number of the grains (Fig. 8), and the distribution function of the fluctuation of the bottom shear stress (Fig. 9); in doing so it was confirmed that the distribution function can be approximated by the Gaussian distribution with a standard deviation of σ = 0.57. The laboratory experiments were supplemented by observations in the field.