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OCR for page 66

66
Users of Equations 7.17 and 7.18 should be aware that the and soil strength. In the front part of the scour hole, the flow
velocity VHec also has its limitations. These limitations are tied vortex can generate a steep slope that stresses the soil beyond
to the ability of the program HEC-RAS to simulate the flow its shear strength. Therefore, it is the soil strength that controls
at the contraction. As an illustration, the water surfaces and the front slope of the scour. At the back of the scour hole, the
velocity distributions measured and predicted by different slope is usually gentle and slope stability is not a problem.
means along the centerline of the channel are compared for Based on these and other observations, the following steps
Test 2 in Figure 7.23. As can be seen, the HEC-RAS gener- are recommended to draw the full contraction scour profile
ated velocity profile cannot give the peak velocity value in the (Figure 7.24):
contracted channel. Instead, HEC-RAS gives a step function
that parallels the bank contraction profile. 1. Plot the position of the bridge contraction, especially
the start point of the full contraction;
7.10 CONSTRUCTING THE COMPLETE 2. Calculate Xmax by Equations 7.13, 7.14, and 7.15, and
CONTRACTION SCOUR PROFILE mark the position where the maximum contraction
scour happens in the figure;
Three characteristic dimensions of the contraction scour 3. Calculate Zmax by Equations 7.10, 7.14, and 7.15, draw a
profile have been determined by the flume tests Zmax, Zunif, and horizontal line at this depth and extend it 0.5 Zmax on both
Xmax. Additional information was obtained from the tests in sides of the location of Zmax (B and C on Figure 106);
order to develop a procedure to draw the complete contraction 4. Plot A, the starting point of the contraction scour pro-
scour profile. It was found that the contraction scour hole, file at a distance equal to Zmax from the starting point of
much like the pier scour hole, is determined by both the flow the full contraction;
5. Connect A and B as the slope of the contraction scour
profile before the maximum scour;
180
6. Calculate Zunif by Equations 7.11, 7.14, and 7.15, and
draw a line with an upward slope of 1 to 3 from Point
C to a depth equal to Zunif (D on Figure 106); Line CD
Water Surface Elevation (mm)
is the transition from the maximum contraction scour
120 depth to the uniform contraction scour depth.
7. Draw a horizontal line downstream from Point D to
Before
After
represent the uniform contraction scour.
HEC-RAS
60
7.11 SCOUR DEPTH EQUATIONS
FOR CONTRACTION SCOUR
The following equations summarize the results obtained in
0 this chapter.
-1000 -500 0 500 1000 1500
X(mm)
Zmax (Cont ) = K K L × 1.90
0.5
1.38 V1 1 c
90 B
B2
- H1 0 (7.19)
gH1 gnH11 3
60
Velocity (cm/s)
Contraction a =Z max/2
Before
After
Flow
30 X max
HEC-RAS Original Soil
Z max Bed
Nominal
A Z max
a a 3 Z unif
0 1 D
-1000 -500 0 500 1000 1500 B C
X(mm)
Figure 7.23. Comparison of water depth and velocity
between HEC-RAS simulations and measurements for Figure 7.24. Generating the complete contraction scour
contraction Test 2. profile.

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67
Zmax (Cont ) = K K L × 1.90 depth of scour along the centerline of the contracted channel,
Xmax is the distance from the beginning of the fully contracted
c
0.5
section to the location of Zmax, V1 is the mean velocity in the
1.49VHec approach channel, VHec is the velocity in the contracted chan-
- H1 0 (7.20)
gH1 gnH11 3 nel given by HEC-RAS, B1 is the width of the approach chan-
nel, B2 is the width of the contracted channel, c is the critical
Z unif (Cont ) = K K L × 1.41 shear stress as given by the EFA, is the mass density of
water, n is Manning's Coefficient, H1 is the water depth in the
0.5
1.31 V1 1 c
B approach channel, K is the correction factor for the influence
B2
- H1 0 (7.21) of the transition angle as given by Equation 7.24 below, and
gH1 gnH11 3 KL is the correction factor for the influence of the contraction
length as given by Equation 7.25 below.
Z unif (Cont ) = K K L × 1.41
c K Z max = 1.0
0.5
1.57 Hec
- H1 0 (7.22) K Z unif = 1.0 (7.24)
gH1 gnH11 3
K X max = 0.48 tan + 0.95
= K K L × 2.25 2 + 0.15
Xmax B
( 7.23)
B2 B1 K L Z max = 1.0
where Zmax(Cont) is the maximum depth of scour along the K L Z unif = void (7.25)
centerline of the contracted channel, Zunif (Cont) is the uniform K L X max = 1.0