Figure. 6.32. Definition sketch for riprap on a channel bed.
6.10.2 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.
2
(a) If the design shear stress is τo = 95.8 N/m , calculate the riprap size that gives a stability
factor equal to 1.5.
Assuming angle of repose φ = 40, the stability number η is obtained from Equation 6.3 or
Figure 6.14 for θ = 20 (η = 0.36). The stone size is then calculated from Equation 6.13.
21τo
21 x 95.8
Dm =
=
= 0.35 m
(S s - 1) γη (2.65 - 1) 9800 x 0.36
2
(b) For the same design shear stress τo = 95.8 N/m , determine the stability factor of particle
sizes Dm = 0.15 m. From Equation 6.5
21τ o
21 x 95.8
η=
=
= 0.83
(S s - 1) γDm (2.65 - 1) 9800 x 0.15
Then, Equations 6.11, 6.10, and 6.9 are used to calculate the stability factor
tan φ tan 40
Sm =
=
= 2.31
tan θ tan 20
ζ = Sm η sec θ = 2.31 x 0.83 sec 20 = 2.04
6.56
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