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discharge in comparison to nature and a falsification of the sediment transport
occurs. Moreover, by scaling grain sizes, bed forms could be generated which in
nature would not occur and thus form roughness and the total resistance would be
increased in the physical model.
3.2 Conversion of the Grain Size Distribution into Model Scale
In order to avoid the above-mentioned scale effects and thus to achieve a similar
transport rate at similar discharges, Zarn ( 1992 ) suggests an adjustment of the
scaling. His approach assures that the reduction of the shear velocity from nature
into model scale is consistent with the velocity scale 1/ p l according to Froude:
u nature
l
p
u model ¼
(2)
The suggested conversion of the grain size distribution from nature to model
scale takes place in three steps:
1. Conversion of the grain size distribution into model scale by the multiplication
with the scale 1:l, according to d model ¼
d nature /l
2. Coarsening of the grain sizes with Re *d cr ¼
2-200, belonging to d
¼
0.22-
4 mm. According to ( 1 ) and ( 2 ), the following relation is valid:
1
l
Y cr nature
Y cr model
d model ¼
d nature
(3)
with Y cr nature being 0.047 and Y cr model being between 0.03 and 0.047, depend-
ing on the grain size.
3. Elimination of the grain sizes with Re *d cr <
2, belonging to d
<
0.22 mm, as
cohesive properties of the material might play a role.
Figure 5 shows the resulting coarser grain size distribution following the three
steps from the Zarn's approach. Principally, the elimination of the fraction of grains
with d
0.22 mm leads to a strong coarsening of the grain size distribution. In the
actual case, the eliminated fine grain fraction amounted to 40%. The medium grain
size has been increased from 51 to 105 mm. This effect inhibits the false generation
of bed forms, but it implies an adjustment of the sediment input in order to avoid an
overestimation of the coarse fraction.
<
3.3 Adaptation of the Sediment Input
The coarser the sediment, the smaller the transport capacity. Therefore, the coarsen-
ing of the grain size distribution according to Zarn ( 1992 ) would result in a smaller
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