incipient motion; if S.F. is less than unity, the riprap is unstable. Problem F.1 in Appendix F
illustrates how to determine the stability of riprap.
Simplified Design Aid For Side Slope Riprap. When the velocity along a side slope has no
downslope component (i.e., the velocity factor is along the horizontal), some simple design aids
can be developed.
For horizontal flow along a side slope, the equations relating the stability factor, the stability
number, the side slope angle, and the angle of repose for the rock are obtained from
Equations 6.4 and 6.6 with λ = 0.
η tan φ
β = tan -1
2 sin θ
(6.7)
and
1 + sin β
η′ = η
(6.8)
2
When Equations 6.7 and 6.8 are substituted into Equation 6.3, the expression for the stability
factor for horizontal flow on a side slope is:
{ζ
}
Sm
2
S.F. =
+4 -ζ
(6.9)
2
in which
ζ = Sm η sec θ
(6.10)
and
tan φ
Sm =
(6.11)
tan θ
If we solve Equations 6.9 and 6.10 for η, then:
Sm - (S.F.)2
2
η=
cos θ
(6.12)
2
(S.F.)
Sm
The interrelation of the variables in these two equations is represented in Figure 6.14. Here,
the specific weight of the rock is taken as 2.65 and a stability factor of 1.5 is employed. This
recommended stability factor for the design of riprap (S.F. = 1.5) is the result of studies of the
riprap embankment model data obtained by Lewis. These studies were reported by Simons
and Lewis (1971).
6.23
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