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Publication Number: FHWAHRT07026 Date: February 2007 
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.
This subsection presents the result of using laboratory experiments to determine the actual form of equations 4 and 11–13.
This section focuses on the calibration of V_{RM}. The representative velocities in the vicinity of the upstream corners of culverts were measured during fixedbed experiments as prescour conditions. The measured V_{RM} values were then compared to the V_{RP} 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.
A linear regression of the results shows that V_{RM} for bottomless culvert applications is 1.28 times V_{RP}. Thus, equation 4 can now be rewritten as equation 22.
(22) 
Experiments were used to determine the form of the 12 different expressions for k_{s}. Two examples are given.
The first example is the calibration and validation of k_{s} as a function of V_{RA}, V_{CL}, and the Froude number. In this combination, y_{2} was calculated from equation 1 using the approach velocity, V_{RA} (equation 2), and Laursen’s critical velocity, V_{CL} (equation 5). Figure 11 shows the regression of k_{s} versus the Froude number in the approach as the independent variable for bottomless culverts with and without wingwalls.
Figure 11. Graph. Calibration of k_{s} as a function of V_{RA}, V_{CL}, and F_{1}.
Figure 12 is a plot of y_{max} that was calculated using the regression equation from figure 11 versus the measured y_{max}.
Figure 12. Graph. Validation of y_{max} using kS as a function of V_{RA}, V_{CL}, and F1.
The second example is the calibration and validation of k_{s} as a function of V_{RM}, V_{CN}, and the Q_{blocked} ratio. In this combination, y_{2} was calculated from equation 1 using the approach velocity, V_{RM} (equation 22), and Neill’s critical velocity, V_{CN} (equations 7 and 8). Figure 13 shows the regression of k_{s} versus the Q_{blocked} ratio as the independent variable for bottomless culverts with and without wingwalls.
Figure 13. Graph. Calibration of k_{s} as a function of V_{RM}, V_{CN}, and Q_{blocked}.
Figure 14 is a plot of y_{max} that was calculated using the regression equation from figure 13 versus the measured y_{max}.
Figure 14. Graph. Validation of y_{max} using k_{s} as a function of V_{RM}, V_{CN}, and Q_{blocked}.
Similar calculations and plots were obtained for the other ten k_{s} 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.
Equation 1 Parameters  Unsubmerged Scour Equation  Calibration R^{2}  Validation (Mean Error)^{2} (m)  

y_{2} = f(V_{RA},V_{CL})  no ww: k_{s} = (0.7411 F_{1} + 2.2658)  0.0327  0.00394  
w/ww: k_{s} = (0.0176 F_{1} + 1.7613)  0.00001  0.00758  
y_{2} = f(V_{RA},V_{CL}) 

0.2948  0.0148  

0.7764  0.00460  
y_{2} = f(V_{RA},V_{CN})  no ww: k_{s} = (0.956 F_{1} + 2.0758)  0.0834  0.00394  
w/ww: k_{s} = (0.0456 F_{1} + 1.5235)  0.00002  0.00758  
y_{2} = f(V_{RA},V_{CN}) 

0.0799  0.00402  

0.6251  0.000838  
y_{2} = f(V_{RP},V_{CL})  no ww: k_{s} = (0.6555 F_{1} + 2.0041)  0.0327  0.00394  
w/ww: k_{s} = (0.0155 F_{1} + 1.5579)  0.00001  0.00758  
y_{2} = f(V_{RP},V_{CL}) 

0.2948  0.00916  

0.7764  0.00361  
y_{2} = f(V_{RP},V_{CN})  no ww: k_{s} = (0.8535 F_{1} + 1.8643)  0.0837  0.00284  
w/ww: k_{s} = (0.031 F_{1} + 1.3696)  0.0001  0.00365  
y_{2} = f(V_{RP},V_{CN}) 

0.0726  0.00231  

0.62  0.00754  
y_{2} = f(V_{RM},V_{CL})  no ww: k_{s} = (0.5305 F_{1} + 1.6219)  0.0327  0.00394  
w/ww: k_{s} = (0.0126 F_{1} + 1.2608)  0.00001  0.00781  
y_{2} = f(V_{RM},V_{CL}) 

0.2948  0.00916  

0.7764  0.00361  
y_{2} = f(V_{RM},V_{CN})  no ww: k_{s} = (0.7025 F_{1} + 1.5491)  0.0842  0.00239  
w/ww: k_{s} = (0.0114 F_{1} + 1.1399)  0.00002  0.00359  
y_{2} = f(V_{RM},V_{CN}) 

0.0607  0.00228  

0.6112  0.00758 
Note: As discussed in the text, the Froude number multiplier should be changed to zero for equations with negative slopes.
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 k_{p} that correspond to the 12 different k_{s} equations in the previous section. Recall also that y_{0} in equation 1 for pressure flow is equal to the hydraulic grade line at the inlet (HGL_{o} in figure 8). Two examples, similar to the k_{s} section, are given.
The first example is the calibration and validation of k_{p} as a function of A_{k} when k_{s} is a function of V_{RA}, V_{CL}, and F_{1} (equations 13 and 14). In this combination, y_{2} was calculated from equation 1 using the approach velocity, V_{RA} (equation 2), and Laursen’s critical velocity, V_{CL} (equation 5). Figure 15 shows the regression of k_{p} versus A_{k} as the independent variable for bottomless culverts with wingwalls.
Figure 15. Graph. Calibration of k_{p} when k_{s} is a function of V_{RA}, V_{CL}, and F1.
Figure 16 is a plot of y_{max} that was calculated using the regression equation from figure 15 versus the measured y_{max}.
Figure 16. Graph. Validation of y_{max} using k_{p} when k_{s} is a function of V_{RA}, V_{CL}, and F1.
The second example is the calibration and validation of k_{p} as a function of A_{k} when k_{s} is a function of V_{RM}, V_{CN}, and Q_{blocked} (equations 13 and 14). In this combination, y_{2} was calculated from equation 1 using the approach velocity, V_{RM} (equation 22), and Neill’s critical velocity, V_{CN} (equations 7 and 8). Figure 17 shows the regression of k_{p} versus A_{k} as the independent variable for bottomless culverts with wingwalls.
Figure 17. Graph. Calibration of k_{p} when k_{s} is a function of V_{RM}, V_{CN}, and Q_{blocked}.
Figure 18 is a plot of y_{max} that was calculated using the regression equation from figure 17 versus the measured y_{max}.
Figure 18. Graph. Validation of y_{max} using k_{p} when k_{s} is a function of V_{RM}, V_{CN}, and Q_{blocked}.
All of the k_{p} 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.
Equation 1 Parameters  Submerged Scour Equation  Calibration R^{2} (Mean Error)^{2} 


y_{2} = f(V_{RA},V_{CL})  k_{p} = (0.0176 F_{1} + 1.7613)(1.6923 A_{k} + 1.0284)  0.2927 0.000336 m 

y_{2} = f(V_{RA},V_{CL}) 

0.5653 0.00539 m 

y_{2} = f(V_{RA},V_{CN})  k_{p} = (0.0456 F_{1} + 1.5235)(2.0225 A_{k} + 1.10183)  0.3896 0.000307 m 

y_{2} = f(V_{RA},V_{CN}) 

0.5092 0.00149 m 

y_{2} = f(V_{RP},V_{CL})  k_{p} = (0.0155 F_{1} + 1.5579)(1.6923 A_{k} + 1.0284)  0.2927 0.000336 m 

y_{2} = f(V_{RP},V_{CL}) 

0.5536 0.00456 m 

y_{2} = f(V_{RP},V_{CN})  k_{p} = (0.031 F_{1} + 1.3696)(2.0082 A_{k} + 1.0182)  0.3869 0.000307 m 

y_{2} = f(V_{RP},V_{CN}) 

0.4554 0.00146 m 

y_{2} = f(V_{RM},V_{CL})  k_{p} = (0.0126 F_{1} + 1.2608)(1.6923 A_{k} + 1.0284)  0.2927 0.000336 m 

y_{2} = f(V_{RM},V_{CL}) 

0.5316 0.00417 m 

y_{2} = f(V_{RM},V_{CN})  k_{p} = (0.0114 F_{1} + 1.1399)(1.9836 A_{k} + 1.018)  0.3823 0.000307 m 

y_{2} = f(V_{RM},V_{CN}) 

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.
The bottomless culvert outlet scour experiments were completed in accordance with the test matrix (table 1). Specifically, the following results are presented and discussed:
Fixedbed prescour conditions, including velocity distributions analyzed using particle image velocimetry (PIV), for rectangular culverts with 45degree 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 Rosgentype 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.
Fixedbed 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.
Figure 20. Image. Velocity distribution for unsubmerged culvert with 45degree wingwalls at entrance.
From the fixedbed 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.
Figure 22. Image. Scour map for outlet with no wingwalls.
Figure 23. Image. Turbulent shear map for outlet with streamlined wingwalls.
Figure 24. Image. Scour map for outlet with streamlined wingwalls.
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.
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 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.
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 45degree and an 8degree flare.As demonstrated by the inlet experiments, upstream scour is deeper in submerged, pressure flow conditions. The results also show that 45degree inlet wingwalls are effective at reducing inlet scour, whereas 8degree inlet wingwalls are not effective. See table 4 and related figures 26 through 29.
Inlet Wingwall Type  Experiment Photos  Submerged/ Unsubmerged 
Representative Inlet Scour Map (see Appendix A) 

45degree flare  Figures 26, 27  Submerged  Figure 62 
Unsubmerged  Figure 63  
8degree flare (smooth joint)  Figures 28, 29  Submerged  Figure 71 
Unsubmerged  Figure 70 
Figure 26. Photo. 45degree inlet wingwalls before scour.
Figure 27. Photo. 45degree inlet wingwalls after scour.
Figure 28. Photo. 8degree inlet wingwalls before scour.
Figure 29. Photo. 8degree inlet wingwalls after scour.
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.
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 
8degree flare (rough joint)  Figures 36, 37  Figure 68 
8degree flare (smooth joint)  Figures 38, 39  Figure 69 
45degree flare  Figure 40  Figure 67 
Figure 30. Photo. No wingwalls.
Figure 31. Photo. Truncated, circular wingwalls before scour.
Figure 32. Photo. Truncated, circular wingwalls after scour.
Figure 33. Photo. Elongated, streamlined wingwalls before scour.
Figure 34. Photo. Elongated, streamlined wingwalls after scour.
Figure 35. Photo. Short, streamlined bevel wingwalls after scour.
Figure 36. Photo. Wingwalls with 8degree flare (rough joint) before scour.
Figure 37. Photo. Wingwalls with 8degree flare (rough joint) after scour.
Figure 38. Photo. Wingwalls with 8degree flare (smooth joint) before scour.
Figure 39. Photo. Wingwalls with 8degree flare (smooth joint) after scour.
Figure 40. Photo. 45degree wingwalls after scour.
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.
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.
Inlet/Outlet Wingwall Type  Submerged/Unsubmerged  Representative Outlet Scour Map (see Appendix A) 

Inlet/outlet walls with 45degree flare; pile dissipators not used  Submerged  Figure 72 
Inlet/outlet walls with 45degree flare; pile dissipators used  Submerged  Figure 73 
Figure 41. Photo. Pile dissipators.
Figure 42. Diagram. Plan view of pile dissipators.
Figure 43. Photo. Culvert outlet prior to pile dissipator test.
Figure 44. Photo. Outlet scour area without protective pile dissipators.
Figure 45. Photo. Outlet scour area with protective pile dissipators.
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 (D_{50} equals 25 mm (0.975 inches); see figures 46 and 47). The plan was tested under submerged conditions with 45degree inlet wingwalls and both 45degree 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.
Inlet/Outlet Wingwall Type 
Submerged/ Unsubmerged 
Representative Outlet Scour Map (see Appendix A) 


Inlet/outlet walls with 45degree flare  Submerged  Figure 74 
Figure 46. Diagram. Countermeasure installation for MDSHA Standard Plan (top view).
Figure 47. Diagram. Countermeasure installation for MDSHA Standard Plan (Section AA from figure 46).
Figure 48. Photo. Culvert inlet before Standard Plan test.
Figure 49. Photo. Culvert barrel before Standard Plan test.
Figure 50. Photo. Culvert outlet before Standard Plan test.
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 data collected were the local bed velocity (V_{LB}) and the average contraction velocity (V_{AC}), the ratio of which is plotted versus the Froude number in the contraction zone in figure 53.
Figure 53. Graph. Calibrated function for K_{VM}.
Figure 53 reveals that the equation for K_{VM} takes the form of equation 23.
(23) 
Data collected for different riprap sizes (for which V_{eff} was calculated using equation 19) by measuring the local velocity prior to movement were used to calibrate K_{RIP}, which is plotted versus the Froude Number at the contraction in figure 54.
Figure 54. Graph. Calibration function for K_{RIP}.
The fitted relationship in figure 54 reveals that the equation for K_{RIP} takes the form of equation 24.
(24) 
Rewriting equation 17 by inserting equations 18 and 19 in terms of D_{50} produces equation 25.
(25) 
Substituting equations 23 and 24, dividing both sides by y_{o}, and collecting similar terms yields equation 26.
(26) 
Thus, the final dimensionless equation calculating D_{50} from y_{o} and F_{o} is equation 27.
(27) 
To validate the results, V_{AC} measurements and Froude number measurements were used to calculate the design D_{50} using equation 27. Figure 55 shows that the calculated D_{50} matches the D_{50} of the riprap used in the experiments very well.
Figure 55. Graph. Validation of D_{50} for riprap sizing.
Rosgentype 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.
Figure 57. Diagram. Experimental arrangement of culvert with a cross vane.
Figure 58. Photo. Fabrication of the cross vane.
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. PIV image of flow field at culvert entrance showing spiral current in corners.
Figure 61. Graph. Cross vane results.
Topics: research, infrastructure, hydraulics Keywords: research, infrastructure, hydraulics, Scour, culverts, hydraulics, physical model TRT Terms: research, hydraulics, hydrology, fluid mechanics, earth sciences, geophysics Updated: 04/23/2012
