As shown in Table 10.1, the average Froude number is approximately 0.74, which implies the
maximum local Froude number in the center of the flow could be on the order of 1.0 to 1.2.
According to Simons and Richardson (1963, 1966), these flow conditions should be in the
upper regime with antidunes with breaking or nonbreaking waves. The estimated Manning's
coefficient of 0.023 is correct for these flow conditions. In addition, the backwater effects are
negligible because the flows are in the upper regime. The normal depth as computed should
be satisfactory for design purposes.
There are many methods for determining riprap size (Simons and Senturk 1977). Among
them, the method developed by Stevens et al. (1984) may be the most comprehensive and
appropriate method to use. In applying their method, the depth of flow, the flow velocity and
the angle between the horizontal and the velocity vector in the plane of the side slope are
necessary as discussed in Chapter 6.
As mentioned in Chapter 3, the bed forms of antidunes or standing waves constitute a series of
inphase symmetrical sand and water waves. These waves are in the center of the channel.
Thus, the depth of flow at the bank for designing riprap sizes is taken to be the sum of the
normal depth from thalweg level and the superelevation (yo = yn + ∆z). The flow velocity for
designing riprap size is computed by utilizing Manning's equation:
1.486 2 / 3 1/ 2
Vo =
yo Sf
n
in which Sf is the energy slope. The angle between the horizontal and the velocity vector in the
plane of the side slope is assumed to be negligible.
Three design alternatives based on different radii of curvature are considered in this phase of
the study. Different hydraulic designs result for each of the three design alternatives and each
of three different design floods. The hydraulic design includes the determination of the total
length of bank protection, the minimum buffer strip distance between the railroad and the river
bank, the estimated volume of earthwork, the side slope of riprapped bank, the sizes of riprap
material, the thickness of riprap, the size of the gravel filters, the thickness of the gravel filters,
the height of riprap protection above the existing bed level, and the depth the riprap should
extend below thalweg level. Using the hydraulic data, all these values can be computed.
Table 10.2 provides a summary of the hydraulic designs for different design conditions. The
methods of design are described in the following sections.
From Figures 10.6, 10.7, and 10.8 the length of bank protection, minimum buffer strip distance
between the railroad and the river bank, and the excavation volumes for three different design
alternatives can be estimated. The minimum buffer strip distance is a measure of how far the
river bank must migrate due to bank erosion to endanger the railroad. A wider minimum buffer
strip distance between Bijou Creek and the railroad will provide a larger factor of safety for the
railroad. However, the length of bank protection and excavation volumes increase accordingly,
which in turn increase the cost of construction.
10.9
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