pdf, 12 MiB - Infoscience - EPFL
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Bed topography in the bend<br />
3.5.3 Comparison of the scour formulae<br />
The authors of the scour formulae used different approaches which are based on:<br />
1. momentum considerations on banks and bed (Fargue),<br />
2. equilibrium considerations of the forces acting on a sediment grain (van Bendegom, Engelund,<br />
Bridge and Kikkawa et al, Reindl with a different velocity distribution),<br />
3. considerations based on forces acting on a control volume (Zimmermann, Falcon &<br />
Kennedy, Odgaard and Bazilevich) and finally<br />
4. empirical formulae (Peter).<br />
The characteristics of the different scour formulae are summarized in Table 3.5 (see also HERS-<br />
BERGER & SCHLEISS, 2002).<br />
AUTHOR<br />
YEAR<br />
EQ<br />
NO<br />
K<br />
=<br />
fct<br />
USED<br />
DATA<br />
*<br />
ESTABLISHMENT<br />
OF EQUATION<br />
REMARKS<br />
Fargue 1868 3.56 R c<br />
⁄ B , roughness,<br />
V<br />
F<br />
analytical,<br />
momentum on<br />
bank and bed<br />
formula for max.<br />
scour only<br />
van Bend. 1)<br />
Engelund 2)<br />
Bridge<br />
1947<br />
1974<br />
1976<br />
3.62<br />
3.67<br />
3.72<br />
Fr d<br />
7 ⋅ tanφ<br />
11 ⋅ tanφ<br />
= cst<br />
= cst<br />
analytical, equilibrium<br />
of a grain<br />
1) valid for small<br />
slopes, big B⁄ h,<br />
r » h<br />
2) not established for<br />
fully dev. flow<br />
Kik et al. 1976<br />
Reindl 3) 1994<br />
3.91<br />
3.<strong>12</strong>2<br />
Fr d<br />
, V∗ ⁄ V , n<br />
Fr d<br />
, V∗ ⁄ V , n,<br />
Gs<br />
L<br />
L<br />
analytical, equilibrium<br />
of a grain;<br />
velocity distribution<br />
3) introduced sed. saturation<br />
parameter<br />
Zimmerm.<br />
Falc.&Ken.<br />
Odgaard<br />
1978<br />
1983<br />
1986<br />
3.103<br />
3.105<br />
3.106<br />
Fr2<br />
d<br />
, n<br />
Fr d<br />
, n, θ , p<br />
Fr d<br />
, n, θ<br />
L+F<br />
L+F<br />
L+F<br />
analytical, equilibrium<br />
of control<br />
volume<br />
established for sand<br />
bed rivers<br />
Bazilevich 1982 3.116 h m<br />
⁄ h max<br />
L+F control volume quite sensitive to chosen<br />
values<br />
Peter 1986 3.118 R c<br />
⁄ B , σ, h m<br />
⁄ B , L empirical, dimension<br />
analysis R c<br />
valid for<br />
Fr ⁄ B = 2 ÷ 6; use<br />
with care since d not<br />
in formula<br />
Table 3.5:<br />
Comparison of characteristics of discussed scour formulae<br />
* F = Field data, L = Lab data<br />
a) Formulae based on momentum considerations<br />
The oldest examined scour formula of FARGUE considered the momentum equation on the bank<br />
and on the river bed. He simplified the scour process, assuming that the near bed velocity is submitted<br />
to little changes with varying discharge. Therefore the scour depth depends essentially on<br />
the river geometry and the computed value for a given river reach is almost constant.<br />
<strong>EPFL</strong> Ph.D thesis 2632 - Daniel S. Hersberger November 9, 2002 / page 57
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