Figure. 6.32. Definition sketch for riprap on a channel bed.

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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