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<br />
<br />2044
<br />
<br />NOVEMBER 1973
<br />
<br />FIRST PHASE OF ANALYSIS
<br />
<br />Because a much simpler relationship was expected for coarse sediment than
<br />for intermediate sizes, this zone was examined first.
<br />Evaluation of a.-Although F Ilr is not strongly dependent upon 0., a suitable
<br />value had to be assessed. As Q: allows for the relative depth, data covering
<br />a wide range of dj D are required. Most test series with well-established motion
<br />cover a rather narrow range of depths, so data on the initial motion of gravels
<br />in the range 6.2 mm < D < 28.1 mm wcre utilized (14). These cover a 200,fold
<br />range of dl D.
<br />
<br />3
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<br />la) 'I
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<br />v
<br />JgIs-II0
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<br />\~ \~ ~
<br />O....a'l \" \~, \':'"
<br />---..:..', 1/1 ~q ~ ~
<br /><:lr~J~_ '.!! \".?--, \\1-
<br />-~C'O' "-~'" \~.
<br />O:9s -+- ;--.fI~_ -+- . \.
<br />'l><3 o-.i!.._",. \..,.
<br />-+- M'~-,-y ,.~
<br />.. ,,'-. 'tbc~....." .OQ
<br />'0 . . --...a_~ .
<br />;c, " . ~""'Q---'
<br />....... " " ...........-~--
<br />'" ... ~--'O
<br />""" '....... ..C'.,.
<br />......... ...... c,:-o
<br />,....... "6S
<br />.... .... '"
<br />',""" ""
<br />
<br />r
<br />
<br />KEY
<br />+ 6.22mm 9ra~
<br />I 8'Smm
<br /><<:> lO'6mm
<br />L: ~:g~:;;
<br />. 29.'mm
<br />,
<br />0'0'
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<br />"0
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<br />z
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<br />0"
<br />O/d
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<br />'9Is..liO
<br />
<br />\
<br />\
<br />.............. ~"" \ 5<;p..- -critical flow
<br />.'~~ '~GG GG
<br />
<br />KEY e '-
<br />
<br />e 6"mm c~lulo$r ac<<at.
<br />. 5.0mm glass sph<ros
<br />4) '6mm glass ~ V
<br />
<br />{" I }' =Clog.l><cVO)
<br />~g s-liO '"
<br />
<br />(6)
<br />
<br />z
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<br />/
<br />O'Ot
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<br />0./
<br />%
<br />
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<br />
<br />FIG. 1.-EvlluBtion of Coefficient from Initial Movement of Coerse Sediment
<br />
<br />By Eq. 10, in the coarse zone where viscous effects (and thus D r) are not
<br />relevant, initial motion is defined by 0 = !(FCg); Le.: 8
<br />
<br />v
<br />\l'32g(, I)D
<br />
<br />constant x log (" :) . , . . , . . . . . . . . . . . . . (12)
<br />
<br />This is plotted in Fig, !(a), on a long linear basis.
<br />The data form two groups depending on whether the sediment considered
<br />
<br />HY11
<br />
<br />HYll
<br />
<br />2045
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<br />::
<br />
<br />SEDIMENT TRANSPORT
<br />
<br />is above or below 15 mm. Although there is appreciable scatter, each group
<br />approximates to
<br />
<br />V = constant x log (lOd) . . . . , . . . . . . . . . . . . . (13)
<br />V32g(s - I)D D
<br />
<br />(the lincs go through thc point Did = 10; V/~)D = 0).
<br />The constant varies from 0.19 to 0.23, depending on whether the gravel is
<br />fine or coarse, but there is not a systematic variation with diameter. An interaction
<br />between the bed roughness and the free-surface could change the apparent
<br />mobility of a sediment. Lines denoting F values of 0.8, 1.0, and 1.25 have
<br />been added to Fig. I(a) tn demonstrate this factor.
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<br /> 10" , 10'
<br /> ",.1 F. y
<br /> gr. iJ1g0(s-1} IOg,O(!ffJ
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<br />b-fGg" O.56(Fg,..O.17/
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<br />,
<br />
<br />10"
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<br />
<br />10.J
<br />
<br />,
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<br />10~0'J
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<br />.5 ro'}
<br />
<br />.s 10"
<br />F9r - A
<br />
<br />.5 100
<br />
<br />
<br />FIG. 2.-flume Transport Data (Ref. 211
<br />
<br />Fig. I(b) relating to glass spheres and cellulose acetate balls lends support
<br />to a value of 10, but again there is some variation of the coefficient for supercritical
<br />flow. In view of the closeness of the a value in Eq. 13 to the usual value
<br />of 12.3 in the rough turbulent equation, the round figure, a == to, was accepted.
<br />Transport of Coarse Scdiment.- The D ler- value that separates coarse sediment
<br />from transitional sizes was at this stage unknown. Based on previous treatments
<br />of sediment transport, and boundary friction on immobile surfaces, a median
<br />sand diameter of between I mm and 2 mm appeared appropriate, i.e., a D
<br />"
<br />value between 25 and 50 (for sand in water at 150 C, D = 25 D with D in
<br />millimeters). sr-
<br />
<br />In order to avoid an upper phase of sediment transport, which the present
<br />theory is not intended to cover, no flume data for channel Froude numbers
<br />
<br />i-
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