Environmental Engineering Reference
In-Depth Information
The tractive force concept primarily originates from work carried out
by the U.S. Bureau of Reclamation (USBR) under the direction of Lane
(Raudkivi, 1990 and HR Wallingford, 1992). This method considers the
balance of forces acting on sediment grains and is only used to evaluate the
erosion limits. Since the method assumes no suspended or bed material
transport, it is only relevant for canals with coarse bed material and zero
or very small bed material input (HR Wallingford, 1992). Breusers (1993)
also supported the statement that the tractive force method is only suitable
when the water transports very little or no sediment.
The distribution of the shear stress in narrow and trapezoidal canals
is not uniform and the maximum shear stress is smaller than the one
predicted by Equation 4.13. Lane (1953) determined experimentally that
the adjustment factor for both the bed and side slopes largely depends
on the width to depth ratio B/y and side slope m (Figure 4.4). Based on
extensive work and field data of the U.S. Bureau of Reclamation, Lane
(1955) established a critical tractive force diagram that relates the critical
force value with the mean diameter of the bed material for canals carrying
water with different amounts of sediment.
1.0
Trapezoids,
m = 2 and 1.5
0.9
Trapezoids, m = 2
0.8
0.7
0.6
0.5
Trapezoids, m = 1.5
Rectangles
Rectangles
0.4
0.3
0.2
0.1
Trapezoids, m = 1
0
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
Figure 4.4. Maximum shear
stress in a canal (Lane, 1953)
(adapted from Chow (1983)).
b/y
On side slope channels
b/y
On bed of channels
These diagrams together with the uniform flow equation (Manning or
de Chézy) can be used to design a stable canal. Normally the grain size
( d 50 ) of the bed material is known, so the design process involves the
assumption of any three of the side slope, bed slope, bed width, water
depth and B - y ratio to find the remaining two. The merits and limitations
of this method have been discussed by Simons and Albertson (1963).
The tractive force method was developed for the threshold condition
of sediment transport, which occurs for the critical boundary shear stress
along the canal's perimeter. Field studies on very coarse material showed
that the 'critical shear stress', above which motion would start, is approx-
imately 0.94 * D 75 (N/m 2 ). For the canal design a boundary shear stress
 
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