Geoscience Reference
In-Depth Information
different research objectives regarding flood safety, the effect of backwater, and the
function of the confluence and the dam, a lot of relevant processes take place at the
same time at different locations in the model and require the constant observation of
more than one person as well as installed monitoring cameras. Because of the
relevance of the sediment processes for the research objectives, the correct simula-
tion of the grain size distribution is important. From conventional, geometrical
scaling by the multiplication with the scale factor 1/
p
l, model effects emerge and,
unfortunately, there is no other proved practice for simulating bed load transport in
physical models. The approach of Zarn (
1992
) - as applied in this chapter - is based
on a correct simulation of initial motion of all grain fractions. It is composed of
three steps (Fig.
5
). By step 1, the natural grain size distribution is geometrically
scaled. By step 2, the grains of
d
0.22-4 mm are coarsened to get Froude-scaled
shear velocity, and by step 3, the grains of
d
ΒΌ
<
0.22 mm are eliminated in order to
avoid cohesive effects. Steps 2 and 3 coarse the grain size distribution. In the actual
case of Meiringen, the eliminated fine fraction of step 3 amounted to 40% involving
a strong coarsening on the grain size distribution. As the transport capacity of
coarse material is smaller, a lower transport rate would occur in the model using the
coarsened material and deposition would be overestimated compared to nature. To
gain a correct simulation of the transport processes in the model, a reduction of the
sediment input is consequently implied. The reduction is proposed in a way that the
use of the theoretical maximum transport capacity is equal in model and nature
scale (
4
). This leads to a sediment input that is not Froude-scaled (Fig.
6
). If no
further correction would be conducted, less sediment would be added in total and an
underestimation of the deposition height and likewise of the bed level and the water
level would occur. Therefore, the model hydrograph is extended in time by the
extension factor g (
5
). The extension guarantees correct bed load input per time step
and total volume and thus, a simulation of deposition height, slope, and water level
as well as a bed load balance which is concordant in the nature and model (Fig.
7
).
Converting the model results to natural scale, the extension of the hydrograph
must be considered by multiplying the model time both by the Froude factor
p
l
and by the inverse extension factor 1/g.
Using the extension factor g based on the sum of the bed load of the Alpbach and
Milibach, two simplifications are made. It is first assumed that the relation of the
input at each time step is equal to the relation of the total input and second that the
Milibach and Alpbach exhibit the same extension factor. Due to these simplifica-
tions, the sediment input per time step is finally simulated with an accuracy of 5%.
Taking into account the overall uncertainties of the model with respect to input data,
e.g., expected hydrograph or sediment sizes, and other model inaccuracies, it can be
concluded that the proposed methodology of the grain size conversion (Sect.
3.2
)
and the adaptation of the sediment input (Sect.
3.3
), including the reduction of the
input and the extension of the flood hydrograph, leads to reasonable results.
However, it must be considered that the proposed method is only valid for
systems exhibiting turbulent flow in each zone of interest. The proposed method
is not valid for systems composed of different kind of flow, e.g., flow with low
Reynolds number in basins.
