1 + sin (20 + 32.8)

η′ = 0.68

= 0.61

2

From Equation 6.3,

cos 18.5 tan 40

S.F. =

= 1.02

0.61 tan 40 + sin 18.5 cos 32.8

The procedure is repeated with increasing stone size until S.F. = 1.5. A riprap size of 9 inches

would give a S.F. slightly over 1.5.

fps and an angle with the horizontal λ of 0 degrees. Determine the size of riprap to protect

the toe of the abutment.

The riprap size is determined either by the same iterative procedure used in a or by using

Equations 6.11, 6.12, and 6.16.

Using the latter method:

Equation 6.11

Sm = tanφ/tanθ = tan 40/tan 18.5 = 2.51

Equation 6.12

Sm - S.F.2

(2.5)2 - 1.5 2

2

cos θ =

η=

cos 18.5 = 0.40

1.5 x 2.5 2

S.F. S 2

m

Riprap size is obtained from Equation 6.16

0.3 Vr2

0.3 x (9.45)2

=

=

= 1.26 ft

Dm

(S s - 1) g η (2.65 - 1) x 32.2 x 0.4

This is the size recommended.

The requirements for a gravel filter are given in Section 6.7. The gradation of a filter should be

such that

D50 (Filter )

< 40

(6.24)

D50 (Base)

6.70

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