FLOOD03637

• County: Statewide
• Basin: Statewide
• Title: Incipient Motion and Sediment Transport
• Date: 10/1/1973
• Prepared By: Journal of the Hydraulics Division
• Floodplain - Doc Type: Educational/Technical/Reference Information

1694 OCTOBER 1973 HY10

of them can be applied only to some special laboratory conditions. When those
equations arc applied to field studies, the chance of success is slim. Encouraged
by the good correlation between total sediment concentration and the dimension-
less effective unit stream power for all the applicable data, an attempt is made
herein to develop a generalized equation from Eq. 23 with I and J relatcd
to some fluid and sediment properties such that the resulting equation may
satisfy the above five requirements. Gilbert's (6) data are not used in obtaining
the general equation because of the lack of temperature measurements. The
general equation is derived from the remaining 463 ..sets of laboratory data shown
in Table 2. '
From Eq. 22, C, is rclatcd to wd/v and V./w. Combinations of different
forms of w d/v and U./w were tried for the determination of I and J in Eq.
23. Eqs. 24 and 25 were selected as the final form to be used for I and J
in Eq. 23:

I = a I + a,log (Wvd) + o,log ( ~,) ........"......... (24)

J=bl+b210g(Wvd)+b,IOg(~') .,.............,.,. (25)

in which G1, G2, u3, b1, b2, and b) are coefficients.
The coefficients in Eqs. 24 and 25 can be dctermined by considcring log
C,as the depcndcnt variable, and log (wd/v), log (V./w), log (VS/w - V <,S/w),
log (wd/v) log (VS/w - V<,S/w), and log (V./w) log (VS/w - V"S/w)
as independent variables, and running a multiple regression analysis for the
463 sets of data. The equation thus obtained is

wd V. (. wd
log C, = 5.435 - 0.286 log - - 0.457 log - + 1.799 - 0.409 log -
v w v

U,) (VS V"S)
- 0.314 log - log - - - ..................... (26)
W it) W

Eq. 26 has a correlation coefficient of 0.971, and a standard error of estimate
of 0.188 in terms of logarithmic units for the 463 sets of laboratory data. The
absolute values of the standard regression coefficients, which indicate the relative
importance of the independent variables involved (25), are used to compare
the relative importance of log (wd/v), log (V./w), log (VS/w - V"S/w),
log (wd/v) log (VS/w - V"S/w), and log (V./w) log (VS/w - V"S/w).
The standard regression coefficients have a value of -0.191, -0.165, 1.526,
-0.831, and -0.225 for log (wd/v), log (U./w), log (VS/w - V"S/ w), log
(wd/v) log (VS/w - V"S/w), and log (V./w) log (VS/w - V"S/w),
respectively. These statistical results clearly indicate that the dimensionless
effective unit stream power plays a very important role in the determination
of total sediment concentration. The student T-test is used to check the significance
of each regression coefficient in Eq. 26. The value of T is defined as the I
ratio of regression coefficient to its standard error. The T values for the
independent variables log (wd/v), log (V./w), log (VS/w - V"S/w), log (wd/v)
log (VS/w - V"S/w), and log (V./ w) log (VS/w - V"S/ w) are -3.552,

INCIPIENT MOTION

,~~'---'-",,'-rr------'---'----'-;-T~
,.,.~ I . ,/
, I: !'[ I ("
~, ~
~" .. 1".
~ ,,'-- -.,-.---'1(-----
. r 1'.)/"1
'.', ,,: ~;;>'- [-

V"~I'
. . . 'I I: ::::'.:::;:;.....

.. _.. ",,,I. u,J.""'~''''

",[",.,.",-".",,,,.,,,,

FIG. 5.-Comparison Between Measured and Predicted Total Sediment Concentra~
tioos by Eq. 26

IOS

'" \O~

'" 103

UPLANI\TlON

Q'O.2ft
T-20'C
.d-O.]"'"
od_O.51lYTl
to. d _ 0.7 or..
. d < 1.0 mill
" rl _ 1.~ ",11
.d-1.B,OOl

\07 . 1
10-) 10.2 10
UNIT STRLAM rOWER, VS. IN FOOT_~OUNOS PER POlINO Pf_R 5[[mIO

FIG. 6.-Etfect of Variation of Particle Size on Predicted Total Sediment Concentration
by Eq. 26