1 + sin 90 + 0
η′ = η
It follows from Equation 6.3 that the stability factor is
cos θ tan φ
η tan φ + sin θ
Alternatively, solving for η yields
^ 1 - tan
η = cos θ
Figure. 6.36. Definition sketch for riprap on a channel bed.
Using this information we wish to calculate (if the angle of repose, φ = 40), what is the
maximum bed angle θ at which η will be 5 percent different from that of a horizontal bed.
Solving for θ with η = 0.95, S.F. = 1 and φ = 40 yields θ = 2.35 or 4.1 percent.
6.12.2 PROBLEM 2 Riprap Design on Embankment Slopes
In a design situation water flows parallel to an embankment built of crushed rock riprap, (Ss =
2.65), at a sloping angle θ = 20.
(a) If the design shear stress is τo = 2.0 psf, calculate the riprap size that gives a stability factor
equal to 1.5.