FLOOD00950

• County: Statewide
• Title: Rock Riprap Design for Protection of Stream Channels near Highway Structures volume 2
• Date: 1/1/1986
• Prepared By: USGS
• Floodplain - Doc Type: Educational/Technical/Reference Information

Other analytical procedures (Chow, 1959) derive the
force per unit of wetted area) for gradually varied flow
is replaced by the energy slope S , giving the equation:
e

shear stress (tractive
conditions in which So

to = yRS
e

(3)

In uniform flow, the energy slope (Se) and water-surface or bed slope (So) are
equal; in gradually varied flow, the difference between the energy and water-
surface slopes is generally small and either value can be used in estimating
shear stress. The energy slope is less than the water-surface slope when flow
is contracting. Thi. suggests that use of the water-surface slope will give
larger than actual values of energy slope when estimating the shear stress
unless the reach is expanding or is at a bend. In an expanding reach, energy
losses are usually assumed to be 50 percent of the change in velocity head.

For wide channels, where the mean depth (da) is approximately equal to the
hydraulic radius, the average shear stress may be determined by the equation
from Chow (1959):

to = yd So
a

(4)

To determine the maximum stress at a cross section, the
substituted for mean depth, Equation 4 may then be
critical shear stress needed for rip rap design procedures

maximum depth (dm) is
modified to estimate
by HEC-15.

to = )'dmSo

(5)

Boundary shear is also a function of channel velocity, and equation 4 may
be expressed in terms of mean velocity (Val and Manning's roughness coefficient
n. Using the following procedure, the Chezy equation Va = c,JRS; may be
rearranged and modified for bed slope so that RS = RSo = (V /C)2 and substitut-
e a
ing in equation 3 gives:

to = y(V /C)2
a

(6)

The relationship between Manning's n and the Chezy C can be expressed by the
equation:

C =

1. 486 Rl/6
n

(7)

where C is a coefficient that varies with the hydraulic radius (R) and rough-
ness (n) of the channel. The boundary shear on the wetted perimeter is given by
the equation:

to =

yV 2n2
a

(8)

2.21Ro.333

For wide channels, the hydraulic radius and mean depth are assumed to be approx-
imately equal (table 2). Grouping constants and simplifying yields:

to =

28.2 V 2n2
a
d 0.333
a

(9)

8