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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