1 + sin 90 + 0

η′ = η

=η

2

It follows from Equation 6.3 that the stability factor is

^

cos θ tan φ

S.F. =

^

η tan φ + sin θ

Alternatively, solving for η yields

^

θ

^ 1 - tan

η = cos θ

φ

S.F. tan

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.

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.

6.65

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