These factors for determining the value of the safety factor coefficient must be considered

and the largest value used as the safety factor. The Corps manual (1994) provide the

following additional guidance.

If the riprap design is for a channel bottom, use the local depth-averaged velocity and local

depth in Equation 6.18. Determining the depth-averaged velocity to design riprap to protect

side slopes is more difficult because the velocity varies greatly form the toe to the top of the

bank. The Corps manual EM 1110-2-1601 uses the depth-averaged velocity at a point 20

percent up slope from the toe. This velocity can be determined by physical or computer

models, empirical equations or methods, and prototype data. The Corps manual EM 1110-

2-1601 gives the following equation for estimating the side slope riprap design velocity.

Vss

R

= 1.74 - 0.52 Log

(6.19)

Vavg

W

Note that the value of Vss / Vavg rarely exceeds 1.6 in alluvial or man made channels for large

discharges for which riprap is designed.

K1, the side slope correction factor in Equation 6.18, is taken from the Carter et al. (1953)

relation in the Corps manual EM 1110-2-1601. The relationship is:

1/ 2

Sin 2 θ

K 1 = 1 -

(6.20)

Sin 2 φ

where:

θ

=

Angle of side slope with horizontal

o

φ

=

Angle of repose of the riprap (normally 40 )

The Corps manual ME 1110-2-1601 gives an equation to determine riprap size for steep

slopes (2 to 20 percent) where the unit discharge is low. A typical application is a rock-lined

chute. The equation is:

1.95 S 0.555 q2 / 3

=

D30

(6.21)

g1/ 3

EM 1110-2-1601 states Equation 6.21 is applicable for thickness = 1.5 D100, angular rock,

3

unit weight of 167 lb/ft , D85/ D15 from 1.7 to 2.7, slopes from 2 to 20 percent and uniform flow

with no tailwater. Also, q is determined using the bottom width of the chute.

The Corps manual 1110-2-1601 gives charts and figures as design guides and guidance for

toe scour, toe scour protection, quality control, revetment top protection and revetment end

protection (see also HEC-23). Termination of riprap bank protection often leads to the

formation of an eddy (wake vortex) that erodes the bank. This erosion is undesirable and

can initiate failure of the riprap. For this reason, end protection is needed. Maynord (1996)

also gives equations and methods for toe scour estimation and toe scour and end section

protection. He describes a computer program "CHANLPRO" available from the U.S. Army

Engineer Waterways Experiment Station that incorporates the above riprap design and

scour depth procedures as well as sizing gabion mattresses.

6.27

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