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Comparison with scale model tests and field data
The macro-rougness related characteristics are the rib-spacing
e d = 0.6 m, the rib-length e θ
= 1.8 m
The scour depth is computed based on equation 3.55:
h s = h m ⋅ ⎛1
B
⎝
+ ------------
2 ⋅ R ⎠ c
⎞ K
e s = 10
m, the rib-depth
(7.64)
Different scour formulae lead to a set of scour depth for these characteristics:
• The modified formula of Bridge (eq. 7.7) gives the exponent K and the maximum scour depth
h smax , with:
K 0.394 ⎛ 5
11 – 23 ⋅ ---- ⎞ 110
= ⋅ -------
⎝
, m.
30⎠
⋅ ⋅ tan38
= 8.1 h
30
smax ,
= 14.1
• Peter’s equation for rectangular cross sections (eq. 3.117) results in:
K = 5.23 – 13 ⋅ ----
5
– 0.379 ⋅ 10 + 68.4 ⋅ 0.026 =
30
1.05 , h smax ,
= 5.7 m
which occurs to be a significant underestimation.
His equation for trapezoidal cross sections (eq. 3.118) gives:
K = 4.2 , h smax ,
= 8.6 m.
• The formula fitted to the cross-section shape (eq. 7.31 and 7.32) leads to:
c 290⎛ 5
1 – 3.2 ⋅ ---- ⎞ 4 ⋅ 4.3
= ------------------------- = 4.5 , h
⎝
m
30⎠
smax ,
= 18.7
9.81 ⋅ 30 3
• Equation 7.63 (GPKernel), taking into account the influence of the macro-roughness results in a maximum
scour depth of:
,
= 5 ⋅ ⎛7.7 ⋅ ------ 10 ⋅ 0.7 ⋅ ( 0.001 + ( 0.110 – 0.047) 4.3
2 ) + 1.7⎞
= 8.8
⎝
⎠
h smax
Comparing the obtained results, it can be seen that the computed scour depths show a big scatter.
Without macro-roughness, the formulae of Peter for rectangular and for trapezoidal cross sections
(3.117 and 3.118) underestimate the scour depth. The formula established in the present
work, fitted to the cross-section profile (7.31) may lead to a somewhat overestimated scour depth.
The best results are obtained with the modified equation of Bridge (7.7) with a computed scour
depth which is about 30% bigger than the scour depth measured with ribs 1 .
Compared to a measured scour depth (with vertical ribs) of 10.9 m, the computed water depth
taking into account the macro-roughness of the banks is underestimated. But if we take into
account the insecurity of the formula (Fig. 7.12 on page 181), the computed results are within the
interval of ±20 %. Furthermore, the scale model tests rather overestimated the scour depth.
m
1. Since the scour depth without ribs was not determined for the same configuration without ribs,
it is assumed that the reduction of the scour depth is of the same order of magnitude as observed
in this study.
EPFL Ph.D thesis 2632 - Daniel S. Hersberger November 9, 2002 / page 185