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the two previous models, this model must be programmed Initial Screening of Scour Evolution
in order to produce scour depth time histories. Chang et al. Predictive Methods
(2004) provided the computer program for this model, but it
yielded unreasonable results for a number of conditions in the An initial assessment of the selected scour evolution
data sets and, therefore, was eliminated in the final analysis. equations was performed to see if any of the methods yielded
results that were clearly unreasonable. All of the methods
were evaluated for combinations of values of the pertinent
Yanmaz (2006) independent variables (and dimensionless groups).
Yanmaz's (2006) method for temporal variation of clear- This analysis showed that the methods do not yield consis-
water scour depth at cylindrical bridge piers is based on a tent results, leading to a wide range of predictions of scour
common assumption that the shape of the scour hole can be depth development with time. The comparison yielded several
approximated by an inverted cone having a circular base and interesting results. The method by Shen et al. (1966) can
slope equal to the angle of repose of the bed sediment. In give very high, or very low, predictions relative to the other
applying the method, Yanmaz used initial measured scour methods. The methods of Kothyari et al. (1992, 2007) lead to
depths as the starting point for the integration of Equation 37. very large scour depths under live-bed conditions. Similarly,
The resulting equation has the form the methods of Oliveto et al. (2007) and Oliveto and Hager
(2002, 2005) yield relatively deep scour predictions. At this
yst t 0.05 , (28) point in the study, the various predictive methods were not
tested for the conditions of the laboratory and field data, thus
only those producing unrealistically large or small scour values
which renders the results very sensitive to the choice of initial
conditions. If the equation is integrated from time equals zero, were eliminated from further consideration. The methods
the results are quite different from those presented by Yanmaz eliminated were Shen et al. (1966), Yanmaz (2006), Chang
(2006), which started the integration from measured values in et al. (2004) and Sumer et al. (1992) due to their unrealistic
his experiments. predictions.
Kothyari et al. (2007) Modifications of Scour Evolution
Predictive Methods
Kothyari et al. (2007) undertook additional experiments to
extend the methods of Oliveto and Hagar (2002, 2005) for evo- The possibility of improving the accuracy of the better
lution of clear-water scour at bridge piers. They developed a performing predictive equations was investigated. Some of
new relationship for the temporal scour evolution at piers based the methods, such as the Miller and Sheppard (2002) model,
on the similitude of Froude by relating the scour depth to the are complex and modifications would require significant effort.
difference between the actual and the entrainment densimetric The Melville and Chiew (1999) model is less complex and easy
particle Froude numbers. The new relationship is validated by to use and modify. By adjusting the coefficients in Melville and
the complete ETH Zurich data set and verified using data from Chiew's model and replacing the equilibrium scour depth
Chabert and Engeldinger (1956), Ettema (1980), and Melville equation with the S/M equation, its accuracy was improved.
and Chiew (1999). An expression is given for the time to "end The recommended equation is given as Equation 39
scour," which is equivalent to time to equilibrium scour. (Table 13) with ys being evaluated using the S/M equation.
Table 13. Modified Melville and Chiew equation (M/S equation).
Reference Equations Notes No.
ys t (t) = K t ys yst = time-dependent scour
1.6
Vc t ys = S/M equilibrium scour
Kt exp C1 ln equation
V1 te
C1 = 0.04
Melville/ a V1 y1 V1
t e (days) C2 - 0.4 6, 0.4 C2 = 200 days/sec 39
Sheppard V1 Vc a Vc
(Recommended) C3 = 127.8 days/sec
0.25
a V1 y1 y1 V1 te = reference time
t e (days) C3 - 0.4 6, 0.4
V1 Vc a a Vc
t90 = time to reach 90% of
V1 equilibrium scour
t 90 (days) exp( 1.83 )t e
Vc depth