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7.3 Establishment of the scour formula
Establishment of the scour formula
7.3.1 Introduction
The following possibilities were explored to establish a new formula:
• Enhance existing scour formulae,
• Approach based on the geometry of the cross-section profile,
• Approach based on the Pi-theorem,
• Genetic algorithm.
In order to compare the measured to the computed results, different criteria can be applied. The
most important one for engineering concerns is the maximum scour depth. A second one can be
of interest: the fit to the bed topography in the cross section at the maximum scour locations
(radial direction). In the present section, both criteria were used to establish new formulae.
7.3.2 Enhancement of existing scour formulae
a) Kikkawa, Ikeda & Kitagawa (1976)
Since the formula of KIKKAWA ET AL. (1976) is quite frequently used, a first optimization had the
aim to increase the prediction capability of this formula by adjusting its parameters. If Kikkawa’s
equation is used in its originally published form (see § 3.5.2/5), the correlation between measured
and computed max. scour is only R 2 = 0.35 . To increase the prediction quality of this formula,
equations 3.91 and 3.93 were parametrized in the following way:
h
----- s
h m
=
exp A
--- ⎛----- r 2
– 1⎞
⎝
⎛ ⋅
2 ⎝ ⎠⎠
⎞
where A c 1
1.8955 3.0023 V ∗
= ⋅ – ⋅ ------
(7.3)
⎝
⎛ V ⎠
⎞ ⋅ Fr d
The difficulty mainly consists in the fact that either the maximum scour or the bed topography in
radial direction can be fitted to the measured data.
• If the above equation is adjusted to the max. scour depth, correlations of R 2 = 0.60 (for
the maximum scour depth over both holes) can be obtained by using a coefficient
c 1
= 0.689 . The problem is that the obtained equation gives a much too flat cross-section
profile, since the maximum bed slope is located at the outer side wall. The correlation
between measured and computed maximum transversal bed slope is only 0.25.
• If the data is adjusted to fit the transversal bed topgraphy, the correlation with the bed slope
can be increased to 0.36, which is by far not satisfying. But, the maximum scour prediction
becomes completely useless ( R 2 = 0.04 ).
c 2
Even if a factor is added to the first term in the parenthesis in equation 7.3, the scour depth
correlation is not modified in a significant manner.
EPFL Ph.D thesis 2632 - Daniel S. Hersberger November 9, 2002 / page 155
R c
2
(7.2)