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Analysis of the final scour
Max. rel. scour (h s /h m ) [-]
8
6
4
2
First scour
Second scour
supercritical
tests
0
0 5 10 15 20 25
B/h m [-]
Figure 6.3: Relative scour depth as a function of the width to depth ratio (without macro-roughness tests, with
Peters tests)
Furthermore, the channel geometry influences the scour. With increasing radius of curvature to
width ratio ( R c ⁄ B ), the relative scour reduces. If the width to flow depth ratio ( B ⁄ h m , Figure
6.3) is increased, the relative scour also increases. But this tendency does not seem to continue
without limit; probably the relative scour stabilizes at a value between 3 and 5 if the width to depth
ratio becomes greater than about 10. This can be explained in the following way. If we approach
the real cross-section (Figure 6.4) with two straight lines, we see that the radial bed slope tanβ in
the outer half of the cross-section gets close to the maximum possible bed slope of tanφ . Lets
consider a cross-section with B⁄ h m = 10 and compare the maximum scour depth to the mean
water depth. If we simplify and assume that h m is located on the axis of the channel, we can write:
h ⁄ h m ≅ ( 4 ⁄ 6 ⋅ B) ⁄ ( 1⁄ 6⋅
B)
= 4 . The bed slope in radial direction can now be determined:
tanβ
≅ h m ⁄ ( B ⁄ 6)
. Knowing that h m ⁄ B = 1 ⁄ 10, finally yields
tanβ
≅0.6 ≅ tanφ
.
This “demonstration” is very approximative and one can reply that the separation point S does
not need to be on the axis of the channel. But the cross-sections in Appendix 7, show that S is
located somewhere in the central one third of the channel width. If S shifts towards the inner
bank, the cross-section profile becomes s-shaped with an almost horizontal bed slope at the outer
bank. In this case the maximum scour as well as the mean water depth increase only little. Therefore
the ratio ⁄ is not submitted to a big influence due to the radial shift.
h s
h m
EPFL Ph.D thesis 2632 - Daniel S. Hersberger November 9, 2002 / page 117