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TABLE 5.8 Transition of the location of maximum
scour depth
Attack Angle (°) Location of the maximum scour depth 2.5cm
0 (1), (4) 5.5cm
0<<45 (1) (4) (4)
45 (1), (3) 6cm
7cm(1)
45<<90 (3)
90 (1), (2), (3), (4) (1)
14cm 8cm
10cm
the location of the maximum scour depth will either happen
at Corner 1 or Corner 3. When the attack angle increases, the (3) 6cm
location of the maximum scour depth gradually moves from (3)
3cm (2)
Corner 1 to Corner 3, and this transition is documented in (2)
Table 5.8. It also was noted that the scour hole in the tested
cohesive soil (Figure 5.27) was much smaller than the scour Figure 5.27. Shape of scour around a skewed pier in a
hole in sands sketched by Raudkivi (1991). cohesive soil (left: attack angle = 15 degrees, right: attack
angle = 30 degrees).
5.21 MAXIMUM SCOUR DEPTH EQUATION
FOR COMPLEX PIER SCOUR
In the previous sections, individual effects on the maximum
pier scour depth were studied by flume testing. A series of (1) (1)
15° 15° (1) 45° (1) 45°
figures and equations are given to quantify the corresponding
correction factors. However, bridge piers are likely to exhibit (3) (3) (3) (3)
a combination of these effects and recommendations are
needed to combine these effects in the calculations. It is rec-
ommended that the correction factors be multiplied in order to 0.5m 0.5m 0.5m 0.5m 0.5m 0.5m
represent the combined effect:
Figure 5.28. Configuration of the flume tests to verify the
( BvV )
0.635 superposition rule.
Zmax ( mm ) = 0.18 K w K sp K sh (5.7)
where Zmax is the maximum depth of scour (mm); V is depth vidual effects described in previous sections were expected
average velocity at the location of the pier if the pier or to happen simultaneously. The main parameters and results
bridge was not there (m/s); B is the projection width of are summarized in Table 5.9, and the time history of the
the pier (m); v is the kinematic viscosity of water (10E-6 scour development is plotted in Figure 5.29. The final
(m2/s) at 20°C); Kw is the correction factor for shallow water maximum scour depth was obtained by using the hyper-
effect (Equation 5.2), Ksp for pier spacing effect (Equation bola model.
5.3), and Ksh for pier shape effect (1.1 for rectangular piers); The maximum scour depths for the two tests were calcu-
and B is the pier projection width (Equation 5.4 for rectan- lated according to Equation 5.7. The calculations are detailed
gular pier). This is a common approach that implies that the in Table 5.10, and the measured results also are listed at the
effects are independent and has been used in many instances bottom of that table which shows that the difference between
before (HEC-18, Melville [1997]). the predictions and measurements is remarkably small (less
Two complex pier flume tests were conducted with the than 5%). This tends to indicate that the chosen superposition
configuration shown in Figure 5.28 where all of the indi- law works well for complex pier scour predictions.
TABLE 5.9 Parameters and results for the complex pier flume tests
Test
H V L B C g Time Zmax
No. (mm) (mm/s) (mm) (mm) (mm) (°) (h) (mm)
Cp-1 375 330 244 61 500 15 115.32 175.4
Cp-2 375 330 244 61 500 45 150.67 285.7
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200
160
Scour Depth (mm)
120
80 CP-1
CP-2
40
0
0 50 100 150 200
Time (Hr)
Figure 5.29. Scour development curves for the complex
pier flume tests.
TABLE 5.10 Comparison of calculated and measured maximum pier
scour depths
PARAMETERS Cp - 1 Cp - 2 CALCULATION NOTE
Primary Inputs
B (mm) 61 61 Pier width
L (mm) 244 244 Pier length
H (mm) 375 375 Water depth
(°) 15 45 Attack angle
V (mm/s) 330 330 Mean approaching velocity
C (mm) 500 500 Center to center pier spacing
Attack Angle Effect
B' (mm) 122.07 215.67 Projection width following Eq. (5.4)
Basic Scour Depth
Z1 (mm) 151.19 217.01 SRICOS: simple pier Eq. (5.6)
Water Depth
H/B' 3.07 1.74
Kw 1.00 1.00 Shallow water effect, Eq. (5.1)
Contraction Effect
C/B' 4.10 2.32
Ksp 1.0 1.233 Interpolated from Fig. 5.7
Pier Shape Effect
Ksh 1.1 1.1 Calculated from Fig. 5.11
Composite Effect
K 1.16 1.36 K= Kw·Ksp·Ksh
Final Scour Depth
Zcal(mm) 174.63 294.33 Zcal=K·Z1
Comparison
Ztest (mm) 175.44 285.71
(Zcal-Ztest)/Ztest - 0.46 3.02
(%)
