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Bed topography in the bend
The superelevation of the free water surface is computed with:
R o
∆z = L⋅
S b ⋅ ⎛-----⎞
⎝ ⎠
R c
(3.115)
Based on the analysis of field data with h smax ,
⁄ h m
= 1.03 ÷ 3 , BAZILEVICH established the following
equation for the lateral bed slope. If the value of h smax ,
is not known, he proposed to use
h smax ,
= 1.6 · ⋅ h m for mountain rivers (leading to a β = 1.09 = 62° ).
β 0.155 h s,
max
= ⋅ -------------- + 0.845
(3.116)
Finally, BAZILEVICH compared his formula against a small set of laboratory (TALMAZA & KROSH-
NIN, 1968 and VLASENKO 1 ) and field data (Tisa River near Khust, Ukraine, below the mouth of
the Boroyavka River). The configuration of all data sets was a 180° meander. The results of the
comparison are satisfying. PETER (1985) indicated that BAZILEVICH’S formula is quite sensitive to
numerical instability and to the choice of the bed roughness. 2
h m
10) Peter (1986)
PETER (1986) compared different scour formulae. He performed a large series of laboratory tests
in a 135° bend with rectangular and trapezoidal cross-sections on a mobile bed. He varied the
radius of curvature, the width of the channel, the discharge, the sediment mixture and the bed
slope. Based on a dimensional analysis of his test data, PETER established an empirical formula for
channels with a rectangular cross-section. The following equation gives the maximum scour
depth, which can be located either at the first or second scour:
h
-------------- smax ,
= 5.23 – 13.0
h m
h
⋅ ----- m
–
B
0.379 ⋅ σ + 68.4 ⋅ S e
(3.117)
Since the parameter R c
⁄ B is not a part of this equation, the application has to be limited to examined
ratios of R c
⁄ B = 2 ÷ 6. Furthermore, this equation does not take into account the grain
size diameter; therefore a critical attitude towards this formula is necessary.
For channels with a trapezoidal cross-section, PETER found:
sinβ
2.95 R c
----- 0.7 ⋅ σ 29.3 h m
= ⎛
⋅ -----
⎝
⋅ – – + 2.7 ⋅ Fr + 3.4⎞
B
B
⎠
(3.118)
PETER also established formulae to locate the position of the first and the second scour, yet with a
rather poor correlation ( r2 α1
= 0.55 and r2 α2
= 0.12 ):
α 1
= 20 ⋅ σ – 0.138 ⋅ d∗ + 28
(3.119)
α 2
= 104 + 5.66 ⋅ σ
h s
⋅ ----
r
1. Bazilevich does not give any reference for this data set.
2. Bazilevich based the determination of the bed roughness on the work of Altunin & Kurganovich,
which could not be found in any library.
EPFL Ph.D thesis 2632 - Daniel S. Hersberger November 9, 2002 / page 55