Figure 6.14. Stability numbers for a 1.5 stability factor for horizontal flow along a side slope.
The curves in Figure 6.14 are computed in the following manner: (1) Select an angle of repose
φ. For example φ = 45; (2) Select a side slope angle. For example θ = 25; (3) Compute Sm
from Equation 6.11:
tan 45
Sm =
= 2.14;
tan 25
Compute η from Equation 6.12 with S. F. = 1.5
(4)
(2.14)2 - (1.5)2
η=
cos 25 = 0.31
(1.5) (2.14)2
Repeat the above steps for the full range of interest for φ and θ.
(5)
If the shear stress τo on the side slope is known, then, from Equation 6.5, the riprap size
required is obtained from:
21τo
Dm =
(6.13)
(S s - 1) γ η
where the stability number η is obtained from Figure 6.14.
6.5.3 Velocity Profile and Tractive Force
In riprap design, it is often desirable to relate the tractive force (shear stress) acting on the
riprapped bed or bank to the fluid velocity in the vicinity of the riprap. For fully turbulent flow,
the reference velocity Vr at a distance D50 above the bed is determined from Equation 6.14.
6.24
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