Page 239 - Soil and water contamination, 2nd edition

226 Soil and Water Contamination
C C 2 C J s
u x D x (12.1)
t x x 2 H

-1
-2
where J = net sediment flux from the water to the bottom [M L T ], and H = water depth
s
[L]. As mentioned above, the erosion and sedimentation rate are governed by the shear stress
at the soil–water interface. If this bottom shear stress τ exceeds a certain critical value τ ,
b b,e
then net erosion occurs. If the shear stress drops below another critical value τ , then net
b,d
sedimentation occurs. In general, there are four situations:

1. erosion (τ > τ ; J < 0);
b b,e s
2. neither erosion nor sedimentation (τ ≤ τ ≤ τ ; J = 0);
b,d b b,e s
3. hindered sedimentation (τ < τ ; J > 0);
b b,d s
4. free sedimentation (τ = 0; J > 0).
b s
For cohesive sediment s, i.e. fine sediments or a mixture of fine and coarse sediments
in which the particles adhere to each other, the critical bottom shear stress for erosion τ

b,e
is larger than the critical shear stress for deposition τ . This implies that deposition and
b,d
erosion of cohesive sediments do not occur simultaneously (Parchure and Mehta, 1985). For
non-cohesive sediments, the critical bottom shear stress for erosion τ may be equal to or less
b,e
than the critical shear stress for deposition τ . In this case, deposition and erosion may occur
b,d
simultaneously and situation 2 (neither erosion nor sedimentation ) does not occur.
12.3 BOTTOM SHEAR STRESS
In turbulent flow ing waters the bottom shear stress is given by:
g H S u 2 (12.2)
b w w *
-1
-3
-2
where τ = the bottom shear stress [M L T ], ρ = the density of water [M L ], g = the
b w
-2
-2
gravitational acceleration constant (= 9.8 m s ) [L T ], S = the river slope [-], H = the depth
-1
of the river channel [L], and u = the shear velocity [L T ] (see also Equation 11.34).
*
Example 12.1 Critical shear stress es for erosion and deposition in rivers
A river has a channel 10 m wide that is uniformly rectangular in cross-section. The river
has the following stage–discharge rating curve that gives the relationship between channel
depth and river discharge:
Q = 3.0 x H 1.6
3 -1
where Q = the discharge (m s ) and H = the water depth (m). The critical shear stress for
-2
-2
deposition = 0.45 N m and the critical shear stress for erosion = 0.95 N m . Calculate
the discharge below which deposition occurs and the discharge above which erosion
occurs.
Solution
The bottom shear stress τ is given by Equation (12.2):

b
2
u 1000 u 2
b w * *
The shear velocity u can be estimated using Equation (11.35):

*
u . 0 10 u x
*
Hence,

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