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Publication Number: FHWA-HRT-07-026
Date: February 2007

Bottomless Culvert Scour Study: Phase II Laboratory Report

Chapter 4: Results

The results presented in this section reflect the experiments described in the “Experimental Approach” section. The first subsection shows how these experiments compared with theoretical predictions of scour at the inlet of bottomless culverts. The second subsection presents scour maps that illustrate the scour that occurred at the culvert outlet. And the third subsection shows how the experiments relate to different scour countermeasures.

CLEAR WATER SCOUR EXPERIMENTS

This subsection presents the result of using laboratory experiments to determine the actual form of equations 4 and 11–13.

Representative Velocity

This section focuses on the calibration of VRM. The representative velocities in the vicinity of the upstream corners of culverts were measured during fixed-bed experiments as prescour conditions. The measured VRM values were then compared to the VRP values from the potential flow theory to derive a multiplier, C, in equation 4, as illustrated in figure 10.

Figure 10. Graph. Calibration of C in equation 4. The y-axis is measured representative velocity, V subscript R M, and ranges from 0 to 5 feet per second. The x-axis is potential representative velocity, V subscript R P, and ranges from 0 to 5 feet per second. The plotted data points fall between x-axis coordinates of 1 and 3 and y-axis coordinates of 1 and 3.7. A regression line through the data points rises from left to right. The regression equation of the line is y equals 1.2781 times x; R squared equals 0.7299. One foot equals 0.305 meters.

Figure 10. Graph. Calibration of C in equation 4.

A linear regression of the results shows that VRM for bottomless culvert applications is 1.28 times VRP. Thus, equation 4 can now be rewritten as equation 22.

22. V subscript R M equals the product of two terms. The first term is the sum of 1.28 plus the product of 1.024 times the quotient to the 1.5 power of lowercase q subscript 1 divided by lowercase q subscript 2. The second term is the quotient of uppercase Q divided by the product of y subscript 0 times w subscript C U L V. (22)
Spiral Flow Adjustment Factors

Experiments were used to determine the form of the 12 different expressions for ks. Two examples are given.

The first example is the calibration and validation of ks as a function of VRA, VCL, and the Froude number. In this combination, y2 was calculated from equation 1 using the approach velocity, VRA (equation 2), and Laursen’s critical velocity, VCL (equation 5). Figure 11 shows the regression of ks versus the Froude number in the approach as the independent variable for bottomless culverts with and without wingwalls.

Figure 11. Graph. Calibration of k subscript s as a function of V subscript R A, V subscript C L, and F subscript 1. The y-axis is the dimensionless coefficient k subscript s as a function of V subscript R A, V subscript C L, and F subscript 1, and ranges from 0 to 3. The x-axis is the Froude number, which is dimensionless and the quotient of Q divided by the product of y subscript 1 times w subscript a times the square root of the product of g times y subscript 1. The x-axis ranges from 0 to 0.4. Two sets of data points are plotted, one for bottomless culverts with wingwalls and one for bottomless culverts without wingwalls. The data points are widely scattered in the upper portion of the graph. The regression equation for a line through the no wingwalls data points is y equals 2.2658 minus the product of 0.7411 times x; R squared equals 0.0327. The regression equation for a line through the with wingwalls data points is y equals 1.7613 minus the product of 0.0176 times x; R squared equals 0.00001.

Figure 11. Graph. Calibration of ks as a function of VRA, VCL, and F1.

Figure 12 is a plot of ymax that was calculated using the regression equation from figure 11 versus the measured ymax.

Figure 12. Graph. Validation of y subscript max using k subscript s as a function of V subscript R A, V subscript C L, and F subscript 1. The y-axis is the calculated y subscript max and ranges from 0 to 0.9 meters. The x-axis is the measured y subscript max and ranges from 0 to 0.9 meters. Two sets of data points are plotted, one for bottomless culverts with wingwalls and one for bottomless culverts without wingwalls. The data points are scattered about a line that rises from the origin to the right at an angle of 45 degrees. The mean squared error of the no wingwalls data points is 0.00394 meters. The mean squared error of the with wingwalls data points is 0.00758 meters. One meter equals 3.28 feet.

Figure 12. Graph. Validation of ymax using kS as a function of VRA, VCL, and F1.

The second example is the calibration and validation of ks as a function of VRM, VCN, and the Qblocked ratio. In this combination, y2 was calculated from equation 1 using the approach velocity, VRM (equation 22), and Neill’s critical velocity, VCN (equations 7 and 8). Figure 13 shows the regression of ks versus the Qblocked ratio as the independent variable for bottomless culverts with and without wingwalls.

Figure 13. Graph. Calibration of k subscript s as a function of V subscript R M, V subscript C N, and Q subscript blocked. The y-axis is the dimensionless coefficient k subscript s as a function of V subscript R M, V subscript C N, and Q subscript blocked, and ranges from 0 to 2. The x-axis is the dimensionless quotient of Q subscript blocked divided by the product of the square root of g times the five-seconds power of y subscript 2, and ranges from 0 to 1.6. Two sets of data points are plotted, one for bottomless culverts with wingwalls and one for bottomless culverts without wingwalls. Most of the data points are located in the upper left quadrant of the graph. The regression equation for a line through the no wingwalls data points is y equals the product of 1.4456 times the 0.2332 power of x; R squared equals 0.6112. The regression equation for a line through the with wingwalls data points is y equals the product of 1.5149 times the 0.0602 power of x; R squared equals 0.0607.

Figure 13. Graph. Calibration of ks as a function of VRM, VCN, and Qblocked.

Figure 14 is a plot of ymax that was calculated using the regression equation from figure 13 versus the measured ymax.

Figure 14. Graph. Validation of y subscript max using k subscript s as a function of V subscript R M, V subscript C N, and Q subscript blocked. The y-axis is the calculated y subscript max and ranges from 0 to 0.9 meters. The x-axis is the measured y subscript max and ranges from 0 to 0.9 meters. Two sets of data points are plotted, one for bottomless culverts with wingwalls and one for bottomless culverts without wingwalls. The data points are scattered about a line that rises from the origin to the right at an angle of 45 degrees. The mean squared error of the no wingwalls data points is 0.00758 meters. The mean squared error of the with wingwalls data points is 0.00228 meters. One meter equals 3.28 feet.

Figure 14. Graph. Validation of ymax using ks as a function of VRM, VCN, and Qblocked.

Similar calculations and plots were obtained for the other ten ks combinations. Table 2 summarizes the scour equation for each scenario for unsubmerged bottomless culverts, and some calibration and validation statistics. The Froude numbers in the experiments did not cover the full range that is expected in the field, and the negative slopes presented in table 2 are probably not realistic. For this reason, we recommend changing the Froude number multiplier to zero for equations in table 2 with negative slopes.

Table 2. Unsubmerged scour equations.
Equation 1 Parameters Unsubmerged Scour Equation Calibration R2 Validation (Mean Error)2 (m)
y2 = f(VRA,VCL) no ww: ks = (-0.7411 F1 + 2.2658) 0.0327 0.00394
w/ww: ks = (-0.0176 F1 + 1.7613) 0.00001 0.00758
y2 = f(VRA,VCL)
no ww: ks = (2.1389 R 0.1197 )
Qblocked
0.2948 0.0148
no ww: ks = (1.7273 R 0.2779 )
Qblocked
0.7764 0.00460
y2 = f(VRA,VCN) no ww: ks = (-0.956 F1 + 2.0758) 0.0834 0.00394
w/ww: ks = (-0.0456 F1 + 1.5235) 0.00002 0.00758
y2 = f(VRA,VCN)
no ww: ks = (1.9458 R 0.0693 )
Qblocked
0.0799 0.00402
no ww: ks = (2.1389 R 0.2345 )
Qblocked
0.6251 0.000838
y2 = f(VRP,VCL) no ww: ks = (-0.6555 F1 + 2.0041) 0.0327 0.00394
w/ww: ks = (-0.0155 F1 + 1.5579) 0.00001 0.00758
y2 = f(VRP,VCL)
no ww: ks = (1.5883 R 0.1197 )
Qblocked
0.2948 0.00916
no ww: ks = (1.3465 R 0.2779 )
Qblocked
0.7764 0.00361
y2 = f(VRP,VCN) no ww: ks = (-0.8535 F1 + 1.8643) 0.0837 0.00284
w/ww: ks = (-0.031 F1 + 1.3696) 0.0001 0.00365
y2 = f(VRP,VCN)
no ww: ks = (1.7777 R 0.066 )
Qblocked
0.0726 0.00231
no ww: ks = (1.56 R 0.234 )
Qblocked
0.62 0.00754
y2 = f(VRM,VCL) no ww: ks = (-0.5305 F1 + 1.6219) 0.0327 0.00394
w/ww: ks = (-0.0126 F1 + 1.2608) 0.00001 0.00781
y2 = f(VRM,VCL)
no ww: ks = (1.6921 R 0.1197 )
Qblocked
0.2948 0.00916
no ww: ks = (1.5597 R 0.2779 )
Qblocked
0.7764 0.00361
y2 = f(VRM,VCN) no ww: ks = (-0.7025 F1 + 1.5491) 0.0842 0.00239
w/ww: ks = (-0.0114 F1 + 1.1399) 0.00002 0.00359
y2 = f(VRM,VCN)
no ww: ks = (1.5149 R 0.0602 )
Qblocked
0.0607 0.00228
no ww: ks = (1.4456 R 0.2332 )
Qblocked
0.6112 0.00758

Note: As discussed in the text, the Froude number multiplier should be changed to zero for equations with negative slopes.

Pressure Flow Adjustment Factors

Although future experiments eventually will expand the range of the submerged flow conditions presented here, this section shows preliminary results for scour in a submerged bottomless culvert. These preliminary experiments were also used to determine the form of the 12 different expressions for kp that correspond to the 12 different ks equations in the previous section. Recall also that y0 in equation 1 for pressure flow is equal to the hydraulic grade line at the inlet (HGLo in figure 8). Two examples, similar to the ks section, are given.

The first example is the calibration and validation of kp as a function of Ak when ks is a function of VRA, VCL, and F1 (equations 13 and 14). In this combination, y2 was calculated from equation 1 using the approach velocity, VRA (equation 2), and Laursen’s critical velocity, VCL (equation 5). Figure 15 shows the regression of kp versus Ak as the independent variable for bottomless culverts with wingwalls.

Figure 15. Graph. Calibration of k subscript p when k subscript s is a function of V subscript R A, V subscript C L, and F subscript 1. The y-axis is the dimensionless coefficient k subscript p when k subscript s is a function of V subscript R A, V subscript C L, and F subscript 1, and ranges from 0 to 1.4. The x-axis is the dimensionless submerged area ratio, A subscript k, and ranges from 0 to 0.12. With two exceptions, the plotted data points are clustered in the upper right corner of the graph. The approximate x-axis and y-axis coordinates of the two exceptions are: 0 and 1 for the first, and 0.08 and 1.25 for the second. The regression equation for a line through the data points is y equals 1.0284 plus the product of 1.6923 times x; R squared equals 0.2927.

Figure 15. Graph. Calibration of kp when ks is a function of VRA, VCL, and F1.

Figure 16 is a plot of ymax that was calculated using the regression equation from figure 15 versus the measured ymax.

Figure 16. Graph. Validation of y subscript max using k subscript p when k subscript s is a function of V subscript R A, V subscript C L, and F subscript 1. The y-axis is calculated y subscript max and ranges from 0 to 0.45 meters. The x-axis is measured y subscript max and ranges from 0 to 0.45 meters. The data points are in the upper right quadrant of the graph. The mean squared error of the data points is 0.000336 meters. One meter equals 3.28 feet.

Figure 16. Graph. Validation of ymax using kp when ks is a function of VRA, VCL, and F1.

The second example is the calibration and validation of kp as a function of Ak when ks is a function of VRM, VCN, and Qblocked (equations 13 and 14). In this combination, y2 was calculated from equation 1 using the approach velocity, VRM (equation 22), and Neill’s critical velocity, VCN (equations 7 and 8). Figure 17 shows the regression of kp versus Ak as the independent variable for bottomless culverts with wingwalls.

Figure 17. Graph. Calibration of k subscript p when k subscript s is a function of V subscript R A, V subscript C L, and Q subscript blocked. The y-axis is the dimensionless coefficient k subscript p when k subscript s is a function of V subscript R A, V subscript C L, and Q subscript blocked, and ranges from 0 to 1.8. The x-axis is the dimensionless submerged area ratio, A subscript k, and ranges from 0 to 0.12. With two exceptions, the plotted data points are clustered in the upper right corner of the graph. The approximate x-axis and y-axis coordinates of the two exceptions are: 0 and 1 for the first, and 0.08 and 1.55 for the second. The regression equation for a line through the data points is y equals 1.0555 plus the product of 3.8411 times x; R squared equals 0.5693.

Figure 17. Graph. Calibration of kp when ks is a function of VRM, VCN, and Qblocked.

Figure 18 is a plot of ymax that was calculated using the regression equation from figure 17 versus the measured ymax.

Figure 18. Graph. Validation of y subscript max using k subscript p when k subscript s is a function of V subscript R M, V subscript C N, and Q subscript blocked. The y-axis is measured y subscript max and ranges from 0 to 0.45 meters. The x-axis is calculated y subscript max and ranges from 0 to 0.45 meters. The data points are in the upper right quadrant of the graph. The mean squared error of the data points is 0.000335 meters. One meter equals 3.28 feet.

Figure 18. Graph. Validation of ymax using kp when ks is a function of VRM, VCN, and Qblocked.

All of the kp equations derived in the preceding discussion can be substituted into equation 13 to obtain equations for the maximum scour depth in a submerged bottomless culvert. Table 3 summarizes the scour equation for each scenario. The Froude numbers in the experiments did not cover the full range that is expected in the field, and the negative slopes presented in table 3 are probably not realistic. For this reason, we recommend changing the Froude number multiplier to zero for equations in table 3 with negative slopes.

Table 3. Submerged scour equations for culverts with wingwalls.
Equation 1 Parameters Submerged Scour Equation Calibration R2
(Mean Error)2
y2 = f(VRA,VCL) kp = (-0.0176 F1 + 1.7613)(1.6923 Ak + 1.0284) 0.2927
0.000336 m
y2 = f(VRA,VCL)
kp = (1.7273 R 0.0279 )(4.2862 Ak + 1.0737)
Qblocked
0.5653
0.00539 m
y2 = f(VRA,VCN) kp = (-0.0456 F1 + 1.5235)(2.0225 Ak + 1.10183) 0.3896
0.000307 m
y2 = f(VRA,VCN)
kp = (1.63 R 0.2345 )(3.1353 Ak + 1.0481)
Qblocked
0.5092
0.00149 m
y2 = f(VRP,VCL) kp = (-0.0155 F1 + 1.5579)(1.6923 Ak + 1.0284) 0.2927
0.000336 m
y2 = f(VRP,VCL)
kp = (1.3465 R 0.2779 )(4.0963 Ak + 1.0714)
Qblocked
0.5536
0.00456 m
y2 = f(VRP,VCN) kp = (-0.031 F1 + 1.3696)(2.0082 Ak + 1.0182) 0.3869
0.000307 m
y2 = f(VRP,VCN)
kp = (1.56 R 0.234 )(2.6483 Ak + 1.0427)
Qblocked
0.4554
0.00146 m
y2 = f(VRM,VCL) kp = (-0.0126 F1 + 1.2608)(1.6923 Ak + 1.0284) 0.2927
0.000336 m
y2 = f(VRM,VCL)
kp = (1.5597 R 0.2779 )(3.7757 Ak + 1.0676)
Qblocked
0.5316
0.00417 m
y2 = f(VRM,VCN) kp = (-0.0114 F1 + 1.1399)(1.9836 Ak + 1.018) 0.3823
0.000307 m
y2 = f(VRM,VCN)
kp = (1.4456 R 0.2332 )(3.8411 Ak + 1.0555)
Qblocked
0.5693
0.000335 m

Note: As discussed in the text, the Froude number multiplier should be changed to zero for equations with negative slopes.

OUTLET SCOUR EXPERIMENTS

The bottomless culvert outlet scour experiments were completed in accordance with the test matrix (table 1). Specifically, the following results are presented and discussed:

  • Fixed-bed prescour conditions, including velocity distributions analyzed using particle image velocimetry (PIV), for rectangular culverts with 45-degree wingwalls.

  • Submerged entrance conditions for both fixed and movable bed conditions.

  • Effects of various inlet and outlet wingwall configurations on resulting scour patterns (including location, lateral extent, and maximum depth of scour).

  • Preliminary test of pile dissipator design to reduce outlet scour.

  • Effectiveness of MDSHA Standard Plan to reduce scour.

  • Revised stability coefficients and regression equations for sizing and placing riprap at entrances to bottomless culverts (originally presented in Phase I of this study) (discussed in a separate section).

  • Performance of Rosgen-type cross vanes near bottomless culvert entrances, in the approach flow, as countermeasures to reduce culvert scour and channel instability (discussed in a separate section).

A sample of the resulting scour maps is given in appendix A. A table that summarizes the parameters for each experiment in appendix A is given in appendix B.

Flow Conditions
Fixed Bed

Fixed-bed tests were conducted to measure prescour conditions, which are the conditions best suited for the methodology proposed in Phase I to predict scour (figure 19). Detailed velocity distributions were measured at the culvert entrance using advanced techniques. A display of velocity distributions is provided in figure 20.

Figure 19. Photo. Outlet prior to scour test. The photo shows the model of the rectangular bottomless culvert. Made mostly of Plexiglas, the model is centered in the flume. The model’s entrance is to the front. The model’s back is to the right rear. The bottom of the flume is a sand and epoxy paint mix on plywood. Models of wingwalls are on each side of the entrance.

Figure 19. Photo. Outlet prior to scour test.

Figure 20. Image. Velocity distribution for unsubmerged culvert with 45-degree wingwalls at entrance. The figure is a plan, or overhead, view, using a laser distance sensor, of the velocity of the flow in the culvert model. The culvert entrance, which is 110 millimeters wide, is to the left. The culvert barrel is in the center. The bed beyond the culvert exit is to the right. The bed is wider than the culvert barrel, extending an equal distance to the top and bottom of the diagram, or to the left and right of the culvert exit. Within the culvert barrel, the velocity of the flow is 70 centimeters per second. In the wider area beyond the culvert exit, a lighter shading in the center indicates the area of greatest velocity, which is 55 centimeters per second. Darker shading on the top and bottom indicates less or no velocity. One millimeter equals 0.0394 inch. One centimeter equals 0.394 inch.

Figure 20. Image. Velocity distribution for unsubmerged culvert with 45-degree wingwalls at entrance.

From the fixed-bed experiments, it is clear that the vorticity increases as flow moves away from the culvert exit. The turbulent shear stress map in figure 21 shows very high shear stress at two locations a distance beyond the culvert outlet. These high shear stresses explain why scour holes are created in a moveable bed (figure 22). As shown in figure 23, adding wingwalls at the outlet reduces the shear stress, and thus reduces the outlet (downstream) scour hole depth (figure 24).

Figure 21. Image. Turbulent shear map for outlet with no wingwalls. The figure is a plan, or overhead, view of the turbulent shear forces caused by flow in the culvert model. The culvert entrance is to the left and is 110 millimeters wide. The culvert barrel is in the center, and the bed beyond the culvert exit is to the right. The bed is wider than the culvert barrel, extending an equal distance to the top and bottom of the diagram, or to the left and right of the culvert exit. Shear forces are indicated by lighter shading. Small forces are found at the corners to the culvert entrance. Two areas of more pronounced forces are found beyond each side of the culvert exit. Before the culvert entrance, a shear stress of 5.0 pascals is indicated. Beyond the culvert exit, a shear stress of minus 2.9 pascals is indicated. One millimeter equals 0.0394 inch. One pascal equals 0.000145 poundforce per square inch.

Figure 21. Image. Turbulent shear map for outlet with no wingwalls.

Figure 22. Image. Scour map for outlet with no wingwalls. The figure is a plan, or overhead, view of the scour caused by flow in the culvert model. The culvert entrance is to the left and is 600 millimeters wide. The culvert barrel is in the center, and the bed beyond the culvert exit is to the right. The bed is wider than the culvert barrel, extending an equal distance to the top and bottom of the diagram, or to the left and right of the culvert exit. Areas of scour are indicated by darker shadings. The areas of scour roughly match the areas of shear forces in figure 21. Before the culvert entrance, a scour depth of 138 millimeters is indicated. Beyond the culvert exit, a scour depth of 107 millimeters is indicated. One millimeter equals 0.0394 inch.

Figure 22. Image. Scour map for outlet with no wingwalls.

Figure 23. Image. Turbulent shear map for outlet with streamlined wingwalls. The figure is a plan, or overhead, view of the turbulent shear forces caused by flow in the culvert model. The culvert entrance is to the left and is 110 millimeters wide. The culvert barrel is in the center, the culvert exit has streamlined wingwalls, and the bed beyond the culvert exit is to the right. The bed is wider than the culvert barrel, extending an equal distance to the top and bottom of the diagram, or to the left and right of the culvert exit. No shear force readings are indicated in the culvert barrel. Shear forces in the bed beyond the culvert exit are indicated by lighter shading. An area of strong shear forces is found on one side of the bed. A force of minus 2.9 pascals is indicated. One millimeter equals 0.0394 inch. One pascal equals 0.000145 poundforce per square inch.

Figure 23. Image. Turbulent shear map for outlet with streamlined wingwalls.

Figure 24. Image. Scour map for outlet with streamlined wingwalls. The figure is a plan, or overhead, view of the scour caused by flow in the culvert model. The culvert entrance is to the left and is 600 millimeters wide. The culvert barrel is in the center, the culvert exit has streamlined wingwalls, and the bed beyond the culvert exit is to the right. The bed is wider than the culvert barrel, extending an equal distance to the top and bottom of the diagram, or to the left and right of the culvert exit. The areas of scour are indicated by darker shadings. The principal area of scour is on the opposite side of the culvert bed from the area of strong shear forces indicated in figure 23. A scour depth of 59 millimeters is indicated. One millimeter equals 0.0394 inch.

Figure 24. Image. Scour map for outlet with streamlined wingwalls.

Movable Bed

Movable bed tests were conducted to measure scour conditions at the outlet for a variety of wingwall configurations (figure 25).

Figure 25. Photo. Outlet scour after test. The photo shows the model of the rectangular bottomless culvert with a movable bed after a test. The model’s exit is to the front. The model’s entrance is to the right rear. Scour is evident at the corners of the culvert’s exit.

Figure 25. Photo. Outlet scour after test.

Submerged and Unsubmerged Conditions

Various inlet and outlet wingwall configurations were investigated under both submerged and unsubmerged flow conditions to determine the overall effects of the flow conditions on scour hole formation. The results show that submerged flow conditions induce greater inlet scour depths, while unsubmerged flow conditions induce greater outlet scour depths.

Wingwalls

Wingwalls have traditionally been constructed with highway culverts to increase flow capacity (for culverts operating in inlet control) and reduce the severity of erosion and scour of both the channel and adjacent banks at both the inlet and outlet. Various inlet and outlet wingwall configurations were investigated under both submerged and unsubmerged flow conditions to determine the overall effects of wall shape, length, and orientation on scour hole formation. The results from the experimental wingwall studies are covered in the following paragraphs. Maps for all of the resulting scour profiles can be found in appendix A.

Inlet Wingwalls

While the study focused on outlet scour, inlet wingwalls and their impacts on the scour at the inlet were also investigated. The experimental culvert setup was used to model a square culvert inlet with and without wingwalls for both submerged and unsubmerged flow conditions. Wingwalls were built with a 45-degree and an 8-degree flare.As demonstrated by the inlet experiments, upstream scour is deeper in submerged, pressure flow conditions. The results also show that 45-degree inlet wingwalls are effective at reducing inlet scour, whereas 8-degree inlet wingwalls are not effective. See table 4 and related figures 26 through 29.

Table 4. Inlet wingwall test configurations.
Inlet Wingwall Type Experiment Photos Submerged/
Unsubmerged
Representative Inlet Scour
Map (see Appendix A)
45-degree flare Figures 26, 27 Submerged Figure 62
Unsubmerged Figure 63
8-degree flare (smooth joint) Figures 28, 29 Submerged Figure 71
Unsubmerged Figure 70

Figure 26. Photo. 45-degree inlet wingwalls before scour. The photo shows the bottomless culvert model with 45-degree wingwalls before scour. The model’s entrance is in the approximate center of the photo. The model’s back is to the left rear. The bed is in the foreground.

Figure 26. Photo. 45-degree inlet wingwalls before scour.

Figure 27. Photo. 45-degree inlet wingwalls after scour. The photo shows the bottomless culvert model with 45-degree wingwalls after scour. The model’s entrance is in the approximate center of the photo. The model’s back is to the left rear. The bed is in the foreground. Scour is evident where the wingwalls join the culvert entrance.

Figure 27. Photo. 45-degree inlet wingwalls after scour.

Figure 28. Photo. 8-degree inlet wingwalls before scour. The photo shows the bottomless culvert model with 8-degree wingwalls before scour. The model’s entrance is in the approximate center of the photo. The model’s back is to the left rear. The bed is in the foreground.

Figure 28. Photo. 8-degree inlet wingwalls before scour.

Figure 29. Photo. 8-degree inlet wingwalls after scour. The photo shows the bottomless culvert model with 8-degree wingwalls after scour. The model’s entrance is in the approximate center of the photo. The model’s back is to the left rear. The bed is in the foreground. Scour is evident where the wingwalls join the culvert entrance.

Figure 29. Photo. 8-degree inlet wingwalls after scour.

Outlet Wingwalls

As demonstrated by the outlet experiments, downstream scour is deeper in unsubmerged conditions (table 5). However, scour in unsubmerged conditions can be substantially reduced by the use of outlet wingwalls with a streamlined shape (compare figures referenced in table 5). Experimental results indicate that turbulence is reduced and “vortex shedding” caused by abrupt changes in pressure is almost eliminated by use of this shape. In other words, the streamlined wall eliminates flow separation and decreases turbulence.(10) Hence, with the streamlined bevel, vortices do not propagate downstream and the resulting turbulence is more evenly distributed—not concentrated in a single location. Conversely, the abrupt change in pressure that results from a square exit shape (as found in culverts without wingwalls at the outlet) induces vortex shedding and increased scour depths.

Table 5. Outlet wingwall test configurations.
Outlet Wingwall Type Experiment Photos Representative Outlet Scour Map
(see Appendix A)
No wingwall Figure 30 Figure 63
Truncated, circular Figures 31, 32 Figure 64
Elongated, streamlined Figures 33, 34 Figure 65
Short bevel Figure 35 Figure 66
8-degree flare (rough joint) Figures 36, 37 Figure 68
8-degree flare (smooth joint) Figures 38, 39 Figure 69
45-degree flare Figure 40 Figure 67

Figure 30. Photo. No wingwalls. The photo shows the exit of the bottomless culvert model with no wingwalls. The culvert exit is to the right of the center of the photo. The bed beyond the culvert exit is in the foreground. The bed shows substantial scouring at the corners of the culvert’s exit, and downstream from those corners.

Figure 30. Photo. No wingwalls.

Figure 31. Photo. Truncated, circular wingwalls before scour. The photo shows the bottomless culvert model with truncated, circular wingwalls at the exit, before scour. The culvert exit is in the upper center of the photo. The culvert entrance is to the right rear. The bed is in the foreground.

Figure 31. Photo. Truncated, circular wingwalls before scour.

Figure 32. Photo. Truncated, circular wingwalls after scour. The photo shows the bottomless culvert model with truncated, circular wingwalls at the exit, after scour. The culvert exit is in the upper center of the photo. The culvert entrance is to the right rear.

Figure 32. Photo. Truncated, circular wingwalls after scour.

Figure 33. Photo. Elongated, streamlined wingwalls before scour. The photo shows the bottomless culvert model with elongated, streamlined wingwalls at the exit, before scour. The culvert exit is in the upper center of the photo. The culvert’s entrance is to the right rear. The bed is in the foreground.

Figure 33. Photo. Elongated, streamlined wingwalls before scour.

Figure 34. Photo. Elongated, streamlined wingwalls after scour. The photo shows the bottomless culvert model with elongated, streamlined wingwalls at the exit, after scour. The culvert exit is in the upper center of the photo. The culvert’s entrance is to the right rear. The bed is in the foreground.

Figure 34. Photo. Elongated, streamlined wingwalls after scour.

Figure 35. Photo. Short, streamlined bevel wingwalls after scour. The photo shows the bottomless culvert model with short, streamlined wingwalls at the exit. The culvert exit is in the upper center of the photo. The culvert’s entrance is to the right rear. The bed is in the foreground.

Figure 35. Photo. Short, streamlined bevel wingwalls after scour.

Figure 36. Photo. Wingwalls with 8-degree flare (rough joint) before scour. The photo shows the bottomless culvert model with wingwalls with an 8-degree flare and a rough joint with the culvert exit, before scour. The culvert exit is in the upper center of the photo. The culvert’s entrance is to the right rear. The bed is in the foreground.

Figure 36. Photo. Wingwalls with 8-degree flare (rough joint) before scour.

Figure 37. Photo. Wingwalls with 8-degree flare (rough joint) after scour. The photo shows the bottomless culvert model with wingwalls with an 8-degree flare and a rough joint with the culvert exit, after scour. The culvert exit is in the upper center of the photo. The culvert’s entrance is to the right rear. The bed is in the foreground.

Figure 37. Photo. Wingwalls with 8-degree flare (rough joint) after scour.

Figure 38. Photo. Wingwalls with 8-degree flare (smooth joint) before scour. The photo shows the bottomless culvert model with wingwalls with an 8-degree flare and a smooth joint with the culvert exit, before scour. The culvert exit is in the upper center of the photo. The culvert’s entrance is to the right rear.

Figure 38. Photo. Wingwalls with 8-degree flare (smooth joint) before scour.

Figure 39. Photo. Wingwalls with 8-degree flare (smooth joint) after scour. The photo shows the bottomless culvert model with wingwalls with an 8-degree flare and a smooth joint with the culvert exit, after scour. The culvert exit is in the upper center of the photos. The culvert’s entrance is to the right rear. The bed is in the foreground.

Figure 39. Photo. Wingwalls with 8-degree flare (smooth joint) after scour.

Figure 40. Photo. 45-degree wingwalls after scour. The photo shows the bottomless culvert model with 45-degree wingwalls at the exit. The culvert exit is in the upper center of the photo. The culvert’s entrance is to the right rear. The bed is in the foreground. Scour is discernable in the vicinity of the culvert exit.

Figure 40. Photo. 45-degree wingwalls after scour.

Scour Countermeasures

Four scour countermeasures were evaluated other than wingwalls: riprap, cross vanes, pile dissipators at the outlet, and the MDSHA Standard Plan combination of countermeasures. The results of the riprap and cross vane analyses are presented later in this report.

Outlet Scour Control Using Pile Dissipators

Chang at MDSHA designed a series of group piles herein called pile dissipators (cylindrical pegs, 25 mm (0.975 inch) in diameter and 12 cm (4.68 inches) in height, mounted on a board) to reduce scour at the culvert outlet.(2) Table 6 lists the three tests used to evaluate this type of countermeasure, and the scour maps presented in appendix A that illustrate their effect. Figure 41 shows a photo of the pile dissipators used in the experiments, and figure 42 shows the position of the dissipators. Figure 43 shows the culvert prior to scour, while the last two photos show the resultant scour both without (figure 44) and with (figure 45) pile dissipators. The maximum scour depth without pile dissipators was 110 mm (4.29 inches), while the scour with dissipators ranged from 84 to 91 mm (3.28 to 3.55 inches). In other words, the pile dissipators decreased the scour depth by 17 to 26 percent.

Table 6. Tests using pile dissipators.
Inlet/Outlet Wingwall Type Submerged/Unsubmerged Representative Outlet Scour Map (see Appendix A)
Inlet/outlet walls with 45-degree flare; pile dissipators not used Submerged Figure 72
Inlet/outlet walls with 45-degree flare; pile dissipators used Submerged Figure 73

Figure 41. Photo. Pile dissipators. The figure is a photo of the culvert model with pile dissipators beyond the culvert exit. The photo is from a raised angle. The culvert model is in the background, and the pile dissipators are in the foreground. The dissipators are in ten parallel horizontal rows of five each.

Figure 41. Photo. Pile dissipators.

Figure 42. Diagram. Plan view of pile dissipators. The culvert exit is to the right. The arrangement of the pile dissipators is in the center. The dissipators are in five horizontal rows of ten each. The length of the dissipator arrangement is 1.2 meters. The width of the dissipator arrangement is 0.6 meters. The distance from the dissipators to the culvert exit is 0.3 meters. The distance from the center of the dissipator arrangement to the top edge of the area covered by the figure is 0.91 meters. One meter equals 3.28 feet.

Figure 42. Diagram. Plan view of pile dissipators.

Figure 43. Photo. Culvert outlet prior to pile dissipator test. The photo shows the model of the rectangular bottomless culvert prior to testing. The model’s exit is to the front. The model’s entrance is to the right rear.

Figure 43. Photo. Culvert outlet prior to pile dissipator test.

Figure 44. Photo. Outlet scour area without protective pile dissipators. The photo shows the model of the rectangular bottomless culvert without dissipators after testing. The model’s exit is to the front. The model’s entrance is to the right rear. Areas of scour are evident in the bed in the foreground.

Figure 44. Photo. Outlet scour area without protective pile dissipators.

Figure 45. Photo. Outlet scour area with protective pile dissipators. The photo shows the model of the rectangular bottomless culvert with dissipators after testing. The model’s exit is to the front. The model’s entrance is to the right rear. Dissipators are in the bed in the foreground. Areas of scour are evident in the bed and around the dissipators.

Figure 45. Photo. Outlet scour area with protective pile dissipators.

Scour Control Using MDSHA Standard Plan Methods

The MDSHA Standard Plan was tested as a scour countermeasure design. This design employs wingwalls at the inlet and outlet of the culvert and lines the wingwalls and the inside walls of the culvert with riprap (D50 equals 25 mm (0.975 inches); see figures 46 and 47). The plan was tested under submerged conditions with 45-degree inlet wingwalls and both 45-degree and streamlined beveled outlet wingwalls. Figures 48 to 50 show the tests prior to scour with the riprap positioned along the corners of the culvert. The plan was tested with a flow depth of 23 cm (8.97 inches) and a velocity of 13 cm/s (5.07 inches/s). When the plan was tested, the riprap moved and fell into the scour holes, after which the riprap stabilized (figures 51 and 52). Table 7 shows the results. Since these results are still preliminary, this report does not make any recommendations about sizing or placing riprap for this design.

Table 7. Tests using MDSHA Standard Plan methods.
Inlet/Outlet
Wingwall Type
Submerged/
Unsubmerged
Representative Outlet Scour Map
(see Appendix A)
Inlet/outlet walls with 45-degree flare Submerged Figure 74

Figure 46. Diagram. Countermeasure installation for M D S H A Standard Plan, top view. The culvert entrance is to the left, and the exit is to the right. One side of the culvert is to the top of the figure, and the other side is to the bottom. A band of fixed bed is on the left edge of the figure. Both the culvert entrance and exit have 45-degree wingwalls behind each of which is an embankment with a 2 to 1 slope. On each side of the culvert between the embankments at each end and behind the culvert barrel is a fixed bed. The approach bed to the culvert, the bed inside the culvert, and the exit bed consist of 2-millimeter sand. On each side of the culvert, a band of riprap 0.42 feet wide stretches along the base of the entrance wingwall, the culvert barrel, and the exit wingwall. The width of the culvert barrel is 2 feet. The length of the culvert barrel is 6 feet. The width of the carved main channel is 0.8 feet. The distance from the fixed bed on the left to the culvert entrance is 2 feet. The distance from the fixed bed on the left to the outer point on each of the two wingwalls at the culvert entrance is 1 foot. On each side of the culvert barrel, two arrows labeled A mark a cross section that is the subject of figure 39. One foot equals 0.305 meters.

Figure 46. Diagram. Countermeasure installation for MDSHA Standard Plan (top view).

Figure 47. Diagram. Countermeasure installation for M D S H A  Standard Plan, section A dash A from figure 46. This figure is a cross section of the culvert in figure 38. The culvert barrel is in the center of the figure, and a fixed bed 0.5 feet in height extends from each side of the barrel to the edge of the figure. The top of the figure is the top embankment. The culvert barrel is 2 feet wide. The riprap band on the inner wall of each side of the culvert barrel is 0.42 feet wide and 0.33 feet high. The top of the riprap is even with the fixed bed outside the culvert. The distance from the top of the riprap to the top of the culvert is 0.5 feet. The bed inside the culvert is 2-millimeter sand. The top of the bed inside the culvert is 0.1 feet below the top of the riprap. A dotted horizontal line labeled contraction scour is near the bottom of the bed in the culvert. The vertical distance from the contraction scour line to the top of the riprap is labeled y subscript c and is 0.4 feet. A horizontal water line is above the top of the culvert. The distance from the water line to the top of the fixed bed outside the culvert and the top of the riprap inside the culvert is labeled y subscript 1 and is 0.75 feet. The velocity inside the culvert is labeled V subscript c and is 1.9 feet per second. One foot equals 0.305 meters.

Figure 47. Diagram. Countermeasure installation for MDSHA Standard Plan (Section A-A from figure 46).

Figure 48. Photo. Culvert inlet before Standard Plan test. The photo shows the riprap along the edges and corners of the culvert inlet.

Figure 48. Photo. Culvert inlet before Standard Plan test.

Figure 49. Photo. Culvert barrel before Standard Plan test. The photo shows the riprap along the edges of the culvert barrel.

Figure 49. Photo. Culvert barrel before Standard Plan test.

Figure 50. Photo. Culvert outlet before Standard Plan test. The photo shows the riprap along edges and corners of the culvert outlet.

Figure 50. Photo. Culvert outlet before Standard Plan test.

Figure 51. Photo. Shifted riprap in culvert inlet after Standard Plan test. The photo shows that the flow has moved some of the riprap into the scour holes created by the flow.

Figure 51. Photo. Shifted riprap in culvert inlet after Standard Plan test.

Figure 52. Photo. Shifted riprap in culvert barrel after Standard Plan test. The photo shows that the flow has moved some of the riprap into the scour holes created by the flow.

Figure 52. Photo. Shifted riprap in culvert barrel after Standard Plan test.

RIPRAP STABILITY DESIGN COEFFICIENTS

The data collected were the local bed velocity (VLB) and the average contraction velocity (VAC), the ratio of which is plotted versus the Froude number in the contraction zone in figure 53.

Figure 53. Graph. Calibrated function for K subscript V M. The y-axis is the dimensionless K subscript V M and ranges from 0 to 1.2. The x-axis is the dimensionless Froude number, which is the quotient of V subscript A C divided by the square root of the product of g times y subscript o, and ranges from 0 to 2. The data points are in the upper center and upper right of the graph. The regression equation for the line through the data points is K subscript V M equals the product of 0.9362 times F subscript o to the negative 0.2476 power; R squared equals 0.6078.

Figure 53. Graph. Calibrated function for KVM.

Figure 53 reveals that the equation for KVM takes the form of equation 23.

23. Uppercase K subscript V M equals the quotient of V subscript L B divided by V subscript A C. That quotient in turn equals the product of 0.94 times, to the negative 0.25 power, uppercase F subscript o. (23)

Data collected for different riprap sizes (for which Veff was calculated using equation 19) by measuring the local velocity prior to movement were used to calibrate KRIP, which is plotted versus the Froude Number at the contraction in figure 54.

Figure 54. Graph. Calibrated function for K subscript R I P. The y-axis is the dimensionless K subscript R I P and ranges from 0 to 1.6. The x-axis is the dimensionless Froude number, which is the quotient of V subscript A C divided by the square root of the product of g times y subscript o, and ranges from 0 to 2. The data points are in the upper center and upper right of the graph. The regression equation for the line through the data points is K subscript R I P equals the product of 1.1192 times F subscript o to the negative 0.4237 power; R squared equals 0.6093.

Figure 54. Graph. Calibration function for KRIP.

The fitted relationship in figure 54 reveals that the equation for KRIP takes the form of equation 24.

24. Uppercase K subscript R I P equals the quotient of V subscript e f f divided by V subscript L B. This quotient in turn equals the product of 1.12 times, to the negative 0.42 power, uppercase F subscript o. (24)

Rewriting equation 17 by inserting equations 18 and 19 in terms of D50 produces equation 25.

25. D subscript 50 equals the product of 0.69 times the quotient of the square of V subscript e f f divided by the product of 2 times lowercase g times the difference of S G minus 1. V subscript e f f in turn equals the product of uppercase K subscript R I P times V subscript L B. V subscript e f f also equals the product of uppercase K subscript R I P times uppercase K subscript V M times V subscript A C. (25)

Substituting equations 23 and 24, dividing both sides by yo, and collecting similar terms yields equation 26.

26. The quotient of D subscript 50 divided by y subscript o equals the product of two quotients. The numerator of the first quotient is 0.69 times the square of the product of four terms: 1.12, the negative 0.42 power of uppercase F subscript o, 0.94, and the negative 0.25 power of uppercase F subscript o. The denominator of the first quotient is the product of 2 times the difference of S G minus 1. The numerator of the second quotient is the square of V subscript A C. The denominator of the second quotient is the product of lowercase g times y subscript o. The product of two quotients simplifies to the product of the square of uppercase F subscript o times the quotient of the product of 0.76 times the negative 1.34 power of uppercase F subscript o divided by the product of 2 times the difference of S G minus 1. (26)

Thus, the final dimensionless equation calculating D50 from yo and Fo is equation 27.

27. The quotient of D subscript 50 divided by y subscript o equals the quotient of the product of 0.38 times the 0.66 power of uppercase F subscript o divided by the difference of S G minus 1. The quotient of D subscript 50 divided by y subscript o also equals the product of two quotients. The first quotient is 0.38 divided by the difference of S G minus 1. The second quotient is the 0.33 power of the square of V subscript A C divided by the product of lowercase g times y subscript o. (27)

To validate the results, VAC measurements and Froude number measurements were used to calculate the design D50 using equation 27. Figure 55 shows that the calculated D50 matches the D50 of the riprap used in the experiments very well.

Figure 55. Graph. Validation of D subscript 50 for riprap sizing. The y-axis is measured D subscript 50 size and ranges from 0 to 0.06 meters. The x-axis is calculated D subscript 50 size and ranges from 0 to 0.06 meters. Six data points are in the approximate center of the graph, and a seventh is in the upper right corner. The mean squared error is 0.0000228 meters. One meter equals 3.28 feet.

Figure 55. Graph. Validation of D50 for riprap sizing.

USE OF CROSS VANES FOR INLET SCOUR CONTROL

Rosgen-type cross vanes, used near the modeled culvert entrance in the approach flow, were tested as a countermeasure for mitigation of inlet culvert scour and channel instability. The original intent of this set of experiments was to optimize cross vane geometry and location to minimize the amount of inlet scour. After determining that the cross vanes promoted more scour, the listed cross vane experiments were replaced with experiments using streamlined wingwalls at the exit. Figures 56 and 57 show the configuration and dimensions of the cross vanes, and figure 58 shows the fabrication of the cross vane. Figure 59 shows a photo of the culvert and cross vane before the experiment was run.

Figure 56. Diagram. Culvert with a cross vane. The figure is a three-dimensional view of a cross vane at a culvert entrance. The entrance is to the left rear. The cross vane is in the foreground. The vane is partially in the shape of the letter V; instead of the two sides coming to a point at the bottom of the V, the sides meet a third small cross piece. The cross piece is toward the flow. Each side of the other end of the cross vane meets a wingwall at the culvert entrance. The base of the cross vane is wider than the top.

Figure 56. Diagram. Culvert with a cross vane.

Figure 57. Diagram. Experimental arrangement of culvert with a cross vane. The figure is a two-dimensional diagram. A culvert entrance with 45-degree wingwalls is at the top of the figure. The direction of flow is from the bottom of the figure to the top. The cross vane’s cross piece is at the bottom of the figure. The ends of the sides of the vane are flush with the wingwalls. The width of the culvert entrance is 609 millimeters, or 24.00 inches. The distance from the center of the culvert entrance in a direction perpendicular to a side of the culvert and to a point that is even with the center of the side of the cross vane where the side meets the wingwall is 367 millimeters, or 15.62 inches. The distance from the center of the culvert entrance to the far side of the cross vane’s cross piece is 747 millimeters, or 29.42 inches. The inside width of the vane’s cross piece is 152 millimeters, or 6.0 inches. The outside width of the cross piece is 327 millimeters, or 12.87 inches. The sides of the cross vane are at an angle of 25 degrees to the vane’s cross piece. The distance from the outside of the cross piece in a direction perpendicular to the cross piece and to a point even with the center of the end of one of the cross vane’s sides is 657 millimeters, or 25.87 inches. The distance from the outside of the cross piece in a direction perpendicular to the cross piece and to a point even with the end of the inside edge of one of the cross vane’s sides is 724 millimeters, or 28.50 inches.

Figure 57. Diagram. Experimental arrangement of culvert with a cross vane.

Figure 58. Photo. Fabrication of the cross vane. The figure shows that the cross vane consists of riprap held between large boards at the bottom and small boards on top.

Figure 58. Photo. Fabrication of the cross vane.

Figure 59. Photo. Cross vane installed at inlet of experimental culvert. The culvert entrance is to the left rear. The cross vane is in the foreground and partially buried in the approach bed.

Figure 59. Photo. Cross vane installed at inlet of experimental culvert.

The cross vane contributed to, rather than diminished, the effect of scour at the inlet. The cross vane creates a spiral current on each side of the cross vane and excavates the corners, the opposite of its desired intent. The flow field was measured at the entrance with PIV and the results show the spiral current effect (figure 60). Figure 61 shows that scour is increased when the cross vane is added.

Figure 60. Image. P I V image of flow field at culvert entrance showing spiral current in corners. The figure is a particle image velocimetry image. The image shows the effect of adding a cross vane to a culvert entrance. The effect is increased scour because the vane creates spiral currents. Particle image velocimetry shows the spiral currents as lighter shaded areas in the bottom corners of the image.

Figure 60. Image. PIV image of flow field at culvert entrance showing spiral current in corners.

Figure 61. Graph. Cross vane results. The y-axis is scour depth, y subscript s, and descends from 0 to minus 200 millimeters. The x-axis is distance along fume and ranges from 600 to 1200 millimeters. Six sets of data points are plotted. Three sets are for scour with a cross vane at the culvert entrance, and three sets are for scour without a cross vane. Each of the three-set groups has a plot for flows of three lengths: 23 minutes, 24 hours, and 48 hours. The three plots for the culvert entrance with the cross vane show greater scour than the three plots for the culvert entrance without the cross vane. Within each three-set group, the depth of scour increased with the length of flow. In general, the scour for each plot reached its greatest depth at an approximate distance from the flume of 800 to 1000 millimeters. One millimeter equals 0.0394 inch.

Figure 61. Graph. Cross vane results.

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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). The hydraulics and hydrology research program at the TFHRC Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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United States Department of Transportation - Federal Highway Administration