1078 SEDIMENT TRANSPORT AND EROSION

over the N year period. Some typical^8 averaged values of

–*for various time periods are:

N^  10 years, gg**^10 = T=^1 0 675. K

N  50 years, gg** 50  T= 1 1 298. K

N  100 years, gg** 100    T= 1 1 588..K

The decrease in storage (in acre-ft) during an N year

period is given by:

v





TE SY DA N

(^100) N
2000
43 560
⎛
⎝⎜
⎞
⎠⎟
⎛
⎝⎜
⎞
⎠⎟
()( )
g ,
(59)
in which
TE
__
 average trap efficiency in percent;
SY
—
 average annual sediment yields in tons
sq. mile;
( DA )  drainage area in sq. miles;
– (^) N  average bulk specific weight for the N -year com-
putation period in lbs
ft^3.
A typical distribution of reservoir sediments is shown in
Figure 16. The coarse sediments (sands and gravels) form a
delta at the upstream section of the pond. Finer sediments
are deposited downstream from the delta. Very fine sediment
(clay particles) may pass through the reservoir or be depos-
ited in the downstream portion of the pond.
THE DEGRADATION PROBLEM
The response of a stream to changes in its sediment load was
described qualitatively in Section 6. The problem of comput-
ing the probable rate and extent of degradation downstream
from a proposed reservoir has recently received the attention
of a number of researchers. 15,49,50
Numerical estimates of the degrading channel profiles
may be obtained by solving, simultaneously, the following
equations (see Gessler, Ref. 15):

1. the equation of sediment continuity—
   ∂
   ∂

• 
  

  −
  ∂
  ∂

  
  

  z
  tb m
  qb
  x
  (^1) TB
  1
  0
  ()
  ()
  (60)

  
  

2. the bed material transport equation which may
   have the form—
   q TB  C ′ (  o –  c )^ P^ (61)


3. the bed shear equation—
    o  RS e (62)


4. a friction equation, e.g. the Chézy equation—
   v  C ( RS e )^1
   ^2 , (63)
   0.001 0.01 0.1 1.0 10.0
   0
   20
   40
   60
   80
   100
   CAPACITY-INFLOW RATIO (cap.acre ft./acre ft. annual inflow)
   SEDIMENT TRAPPED %
   ENVELOPE CURVES FOR NORMAL
   PONDED RESERVOIR
   MEDIAN CURVE FOR NORMAL
   PONDED RESERVOIR
   FIGURE 15 Trap efficiency curve (after Brune).
   TABLE 7
   Constants for Eq. (59) (after Lane and Koelzer)
   Reservoir operation Sand Silt Clay
   gKgKg*K
   Normally submerged 93 0 65 5.7 30 16.0
   Moderate reservoir drawdown 93 0 74 2.7 46 10.7
   Considerable reservoir
   drawdown
   93 0 79 1.0 60 6.0
   Reservoir normally empty 93 0 82 0.0 78 0.0
   C019_001_r03.indd 1078C019_001_r03.indd 1078 11/18/2005 11:06:02 AM11/18/2005 11:06:02 AM