PARTIAL BED LOAD TRANSPORT OF NONUNIFORM SEDIMENT

Abstract

^onuniformity of the bed material is one of the variables that affects bed load transport in an alluvial stream. The transport rate of any fraction of a sediment is strongly affected by the presence of the other fractions. Shielding- of finer sizes by the coarser ones and exposure of the coarser sizes in a mixture to larger forces than in case of uniform materials make the formulation of a bed load transport model for nonuniform sediments rather complicated. Einstein's bed load function is the only available tool that takes the nonuniformity of sediment into consideration by explicitly determining the transport rates of different fractions of a mixture. The total transport rate is obtained as the sum of the individual rates. The method involves the use of a number of empirical correction factors. Many previous investigations have been aimed at checking the correctness of Einstein's procedure only at a macroscopic level, i.e. by comparing the computed and observed transport rates of the mixture as a whole. The agreement has, in many instances not been satisfactory. It is in this background that the present investiga tion was taken up. An extensive series of experiments was conducted on four coarse uniform and nine nonuniform sediments in a laboratory flume of 16 m length, 0.75 m width and 0.35 m Ill depth under controlled conditions. A relationship for trans port and flow parameters was established for uniform sediments as a first step towards studying the effects of nonuniformity in mixtures. The standard deviation and the median size were varied in the experiments on mixtures. The transport rates of all the fractions were measured under different flow condi tions. The number of fractions used in these mixtures varied from two to fifteen, the size of individual fractions ranging from 0.5 mm to 51.5 mm. A large range of shear stresses yielding transport of a few fractions as well as of all fractions was used. Data on uniform sediments have shown that the trans port parameter <p~ is uniquely related to x#« Here t; = Yf . 1 VYf *d YfRbs (Ys -Y )d (D (2) The data of other investiga.tors using coarse uniform sediment are in agreement with the author's data on this relationship. Data on nonuniform sediments have been used to check some of the bed load transport relationships using a diameter like d as the representative size of the mixture. As expec ted the agreement has not been encouraging over the entire IV range of flow and transport parameters due to the omission of nonuniformity effects. •The data on nonuniform sediments have first been used to check Einstein's procedure at the microscopic level. Ana lysis of the data has shown that the sheltering effect is not fully taken into account by Einstein's ^-parameter. "While the finer fractions in a mixture show a smaller transport than that corresponding to the case of uniform sediment - indicative of the well known sheltering effect, - the coarser fractions move at a much faster rate compared to the case of uniform sediment. Apparently, the coarser sizes experience a larger force when they are scattered on the bed than when they are closely packed. In the light of the above differences, the data have been analysed from a different standpoint to provide a satisfactory tool for the computation of sediment loads of mixtures. A simple conceptual model is proposed for the trans port of sediment mixtures with a large spread. It is visuali sed that lift is the predominant force influencing the motion of particles smaller than the arithmetic mean size d since these particles are hidden in the wakes of the larger parti cles. The effective shear stress on the finer particles is hence obtained by assuming (i) a constant pressure in the wake of the particles of size d0, SI (ii) a suitable reduction in lift force after the particle is lifted up from the bed, and that (iii) the effective shear stress for particles of size d a is the grain shear stress t'. The correction for sheltering so determined indicates fair agreemejnt with theory. Without explicitly specifying which force is predomi nant, it is hypothesised that the force on a particle coarser than d„ is represented by Foc *l , (3) in which u^ is the velocity at the top of the grain of size d.. Since the velocity at the top of a particle ooarser than d increases with increase in d /d , the effective shear a i a stress for such particles will be greater than x1 as indicated o by the data. A model based on sheltering caused by all the coarser fractions of a mixture- recognised in terms of area covered by the wakes - was extensively investigated, but did not yield very encouraging results. For the purpose of evolving an accurate method of computation of sediment load, a more complex relationship (than indicated by the model) was required to be written down considering all relevant parameters. Such a relationship vi is f e = f ( T oc 'Fy~d. , M ) (4) si Here "3* = ratio of effective shear stress to grain shear + /Teff \ stress I-—-— ;. To The functional relationship between the foregoing parameters was obtained by detailed analysis of data as t' °'75 0.038 K2(—a ) Te tI 1.2 1 + 3.125x10-3 - AY d,' s 1 where F? = f(M) (^rd7} s i T« 2.1 -» 1/3 (5) Use of the above equation alongwith the transport law for uniform sediments enables determination of the transport rates of the different fractions in a mixture. The appli cability of the method has been tested using flume and field data.