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. 2048 NOVEMBER 1973 HY11 aI., 1937(13); USWES,1935, 1936 (17,18); Murphy, 1914 (8); Brooks and Nomicos, 1957(3); Stein, 1965 (16); Casey, 1935 (5); Barton and Lin, 1955 (2); and Haywood, 1940 (10)]. In general, each data set represented a series of tests, (19 on the average) which were carried out with a single sediment over a range of transport rates. Certain USGS data (21,22) which consisted of 98 indIvidual measurements all with the same sediment size, were split into groups according to water temperature. The value of D gr is constant throughout a series of experiments with one size of sediment at constant temperature. Data/sets can therefore be considered separately. and Eq. 15 can be used to evaluate optimum values of C, A, m, and n for one particular D value. Consideration of results from all the data " sets then shows how these parameters vary with D gr' A computer program was written that obtained best-fit values of A, C, m, and n. All four coefficients were allowed to vary and the results were plotted. The relationships between A, n, and D gr were better defined than those between C, rn, and D" and are shown in Figs. 3(a) and 3(h). For thc transition, 1.0 < Dgr:5 60 n~ 1.00 - 0.56 log D" . 0.23 A= VD + 0,14. . . " (16) ,.. ....,.. ............. (17) For coarse sediments, Dgr > 60 n= 0.00 . A~ 0.17 (18) (19) Next, valucs of n and A wcre inserled using Eqs. (16--19), and resultant best-fit values of C and m were determined and plotted against D gr' Of the two graphs, the variation of m with Dgr [Fig. 3(d)] showed the clearer trend 9.66 m~-+ 1.34 D" Transition: (20) Coarse: m = 1.50 . . . . . . (21) In the final stage of optimization, best-fit values of the values of n, A, and m defined by the preceding are shown in Fig. 3(c). Thus Transition: log C = 2.86 log D" - (log D,,)' - 3.53 Coarse: C = 0.025 C were obtained using equations. The results (22) (23) ANALYSIS OF RESULTS Range of Transitional Sizes.- The limits of the transition zone were determined after the first optimization. A clear variation of n with D gr has been shown. The data confirms the anticipated trend, from n = 1.0 at a D g, of 1 to a value of n = 0.0 at a D /lr of 60. Particle sizes for sand in water at about 150 C corresponding to these limiting DRr values arc 0.04 mm and 2.5 mm, respectively. HYll SEDIMENT TRANSPORT . 2049 None of the flume data were in the fine range although some (12) were very close to the D = 1 limit. These indicated an n value of 1.0 and confirmed the hypothesis thatSthe movement of fine sediments is best described in terms of total bed shear. At the coarse end of the scale there is scatter in the flume data. Certain data for Dgr = 35 (20,21) gave an optimum n value that was less than 0 (i.e., negative), though with very little internal scatter. On the other hand, some data for D r ~ 100 produced unexpectedly high optimum values of n (8,13,18). There is ~ need for further investigation in this area. The data for lightweight materials (17) are remarkably consistent and show no systematic variations from the results of experiments with sand. Thus !he form of the D /I' parameter properly takes into account the effect of partIcle specific gravity. The lower limit of the transitional sizes, Dgr = 1, is very close to the point at which sediments exhibit cohesive properties and the laws of erosion and accretion arc far more complex. Thus, as far as the present theory is concerned, predictive equations for the fine range are meaningless and no attempt has been made to extend curves below a D sr value of 1.0. . Initial Motion of Sediment.-From Eq. 15, A represents the Fgr value at which transport of sediment begins. The present theory thus predicts initial movement criteria based on the analysis of experiments with established motion of sediment. Also shown in Fig. 3(b) is the usual version of the Shields curve (4), curves proposed by recent experimenters (9,19) and three individual results for coarse materials (14). In the range, 4 < D gr < 60, the results are comparable. At low~r D gr values, i.e., with finer sediments, the present work agrees more closely With the results presented by Grass (9), and lies midway between thc Shields (15) and White (19) data. At the coarse grain end of thc scale, the present results agree WIth Neill's findings (14) and cast further doubts upon the rise in the Shields curve in this region. Established Motion.- The variation of the exponent, m, with D gr is shown in Fig. 3(d). An exponent of 1.5 is indicated at the coarse end of the transitional zone and the curve rises with increasing steepness as particle size diminishes. Thus' for fine sediments the theory indicates very large changes in transport rates for small changes in shear, and this is consistent with the view that the transport of fine sediments traveling mainly as suspended load is very sensitive to stream power, a small increase in power rapidly bringing more layers of bed material into suspension. Fig. 3(c) shows the variation of the coefficient, C, withD". There is noticeably more scatter on this plot. The predictive equation in the coarse range is shown dOlled because of the scalier within the small amount of data available at the present time. This may be due to particle shape, sediment grading, Of possibly a Froude number effect, since most experimenters have had to work with steep slopes in order to produce significant rates of transport of coarse material. More data are required. The results for the lightweight materials follow the general trends and this has particular significance in hydraulic modeling. Correlation of Transport Rates.- The authenticity of the general function in providing a description of available laboratory scale data is demonstrated in Fig. 4(b). This compares predicted and observed velocities (mean velocities I i I I I i i i .J " ~ 41 '~ i ; "j " ....\ 1 ,j ~Ii I ,}{ " ~ H .~Ii 1 '~ ~1 .: ~ . ! 1 Ii ~. \' 1,1 n ',\ ~ ii' ~ l ~ji :~~ ,~~- M ,:\ "I . ;'! ~I d ';1