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Summary and conclusions
scour, was also enhanced. The correlation for the maximum scour depth can be increased to 0.82
and the predicted cross-section shape fits quite well to the measured one (without macro-roughness).
A new way was explored to establish a formula based on the shape of the cross-section (§ 7.3.3).
Assuming that the maximum bed slope in a radial direction is limited to a maximum value corresponding
to the friction angle of the bed material, different polynomial functions (Table 7.6) of
the third and fifth degree were tested. The best correlation ( R 2 = 0.856 )was obtained with a
polynome of the third degree (equation 7.31), fitting well to the measured cross-section. But the
application to results of scale model tests and field measurements showed a significant underestimation
of the maximum scour depth. Therefore the modified formula of Bridge (eq. 7.7) is proposed
for the scour depth computation for the configuration without macro-roughness. This
equation showed a good agreement with field data (§ 7.5)
sinβ
0.394 11 23 h m
= ⋅ ⎛ – ⋅ ----- ⎞ -----
⎝
, (7.7)
B ⎠
⋅ ⋅ tanφ
⋅ ---- R
B r
2 = 0.817
Another approach, inspired by the similitude and approximation theory of KLINE (1965) was
investigated (§ 7.3.4), resulting in physically based dimensionless parameters. Unfortunately the
resulting correlations are quite low.
Finally a genetic algorithm written by KEIJZER & BABOVIC (1999) was used to search for a function
fitting well to the measured data (§ 7.3.5). Without ribs, the previously obtained results could
not be enhanced. The search for an equation predicting the scour locations was more successful,
resulting in two formulae with good correlations.
Finally a formula was established, allowing for the prediction of the maximum scour depth in the
presence of macro-roughness with an excellent result ( R 2 = 0.876 ):
R c
h s
h
---------- max
7.7 e s
= ⋅ ----- ⋅ Fr ⋅( 0.001 + ( θ–
θ
h m
R cr ) 2 ) + 1.7
h
(7.63)
Enhancing the results obtained with the genetic algorithm, the following equations were established
for the determination of the location of the scour holes without macro-roughness:
B S
α 1 σ 0.58 -----
e
= ⋅ ⎛ ⋅ + 12.7 ⋅ ---------------- ⎞
⎝
, (7.54)
h m σ – Fr d
⎠
+ 1.4 ⋅Fr V
d ⋅ ------ – 6.6 R 2 = 0.829
V∗
R c
α 2 12.6 ⋅ Fr d 0.9 ⎛-----
⎞ 2
= – ⋅ + 91.6 , R (7.57)
⎝ B ⎠
2 = 0.602
For the second scour, a slightly better correlation can be obtained with equation (7.56) but which
is much more complicated and quite sensitive to the choice of the used parameters.
EPFL Ph.D thesis 2632 - Daniel S. Hersberger November 9, 2002 / page 197