design charts that could be applied to estimate embankment erosion caused by a range of
overtopping depths and tailwater conditions.
When a bare soil embankment fails, it is often directly related to the bed shear stress that is
applied as the flow accelerates over and down the embankment. Clopper and Chen (1988)
describe a computational approach to calculating the bed shear stress. Using the principle
of the conservation of momentum, the following equation was developed for non-uniform
flow on the downstream embankment slope.
(
)
γ
(d1 + d2 ) sinθ + 1 γ d1 - d2 cos θ - ρq2 1 - 1
2
τo =
(6.29)
d
2
2
L 2
2 d2
where γ is the unit weight of water, ρ is the unit mass of water, q is the volumetric discharge
per unit width, and the remaining parameters are presented in Figure 6.27.
Figure 6.27. Definition sketch for application of the momentum equation
for embankment overtopping flow.
If uniform flow is assumed, Manning's equation can be used to estimate the depth of flow,
and shear stress calculated by
τo = γ d S f
(6.30)
It should be noted that when using Manning's equation, the assumption is made that the
high estimate of bed shear stress, unless the combination of slope length and unit discharge
result in conditions which approach uniform flow.
6.47
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