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Publication Number: FHWARD99156 Date: August 2004 
Enhanced Abutment Scour Studies for Compound Channels508 Compliance Captions for Enhanced Abutment Scour Studies for Compound ChannelsFIGURESFigure 1. Diagram. Compoundchannel configurations used in scour experiments. The figure shows the cross sections of the compound channels A and B, which are used in the scour experiments. Compound channel A has a total width of 2.13 meters with a rectangular main channel 0.152 meters deep, and a B subscript lowercase M, which is the width of main channel, of 0.267 meters, which produces a B subscript lowercase F, which is the width of the floodplain, of 0.933 meters on either side of the main channel. The slope of compound channel A is 0.005. Compound channel B has a total width of 4.21 meters, with the main channel on the right side of the compound channel. The main channel has a depth of 0.154 meters and a B subscript lowercase M of 0.158 meters with a 0.393meter transition grade to the floodplain elevation. The B subscript lowercase F is 3.66 meters. The slope of compound channel B is 0.0022. Figure 2. Diagram. Abutment shapes used in scour experiments. The figure shows three abutment shapes arranged longitudinally with the vertical wall shape on top, spillthough in the middle, and wingwall on the bottom. The vertical wall, or VW, is rectangular in nature and has a width of 0.15 meters and a length of L subscript lowercase A, which is the abutment length. The spillthrough, or ST has a center section width of 0.15 meters that is extended by side slopes of 2:1 and rounded side slope transition corners between the length and width of the abutment. The wingwall, or WW has a center section width of 0.15 meters that is extended by side slopes of 2.1 and a wingwall angle of 30 degrees producing a raked leading edge side slope transition between the length and width. Each of the abutment shapes has the same overall length, or L subscript lowercase A. Figure 3. Graph. Sediment grain size distributions. This graph plots grain size distribution data for sediments A, B, and C. The Xaxis shows sieve size in millimeters from 0.1 to 10 on a logarithmic scale, and the Yaxis shows percent passing from 0 to 100. This graph shows the relative grain size for each of the sediments examined. Sediment A has the largest overall particle size with 100 percent passing at 4.8 millimeters, 50 percent passing at 3.2 millimeters, 16 percent passing at 2.2 millimeters, and zero percent passing at 1.2 millimeters. Sediment B has a slightly smaller particle size with 100 percent passing at 4.8 millimeters, 50 percent passing at 2.8 millimeters, 16 percent passing at 2.1 millimeters, 10 percent passing at 2 millimeters, and zero percent passing at 1.5 millimeters. Sediment C has the smallest overall particle size with 100 percent passing at 2.4 millimeters, 50 percent passing at 1.2 millimeters, 16 percent passing at 0.9 millimeters, and 12 percent passing at 0.85 millimeters. Figure 4. Graph. Manning's N in the mainchannel and floodplain for compound channel B. This graph plots experimental results for Manning's N for the floodplain and main channel. The Xaxis shows R divided by lowercase K subscript lowercase S, which is the channel hydraulic radius divided by the equivalent sandgrain roughness, from 1 to 100 on a logarithmic scale. The Yaxis shows lowercase N divided by lowercase K subscript lowercase S, which is Manning's N divided by the equivalent sandgrain roughness raised to the onesixth power to the onesixth power, from 0.01 to 0.10 on a logarithmic scale. The floodplain data are in a relatively linear grouping parallel to the Xaxis, with Xaxis values ranging from 5.6 to 18.5, and consistent Yaxis values of 0.4. The main channel data are also in a relatively linear grouping parallel to the Xaxis, with Xaxis values ranging from 22 to 30, and consistent Yaxis values of 0.7. Values determined by using equation 17 produce linear trendlines through each of the floodplain and main channel data point groupings. Both the main channel and floodplain are reported to have KS values of 0.004 meters. Figure 5. Graph. Measured and computed normal depth for compound channel B. This graphs plots normal depth, measured depth, and critical depth as a function of flow. The Xaxis shows Q, which is the total discharge in compound channel in cubic meters per second from zero to 0.2. The Yaxis shows depth in meters from 0.15 to 0.25. The computed normal depth data begins with a depth of 0.178 meters at 0.055 cubic meters per second, and follows an approximately linear trend to a depth of 0.228 meters at 0.19 cubic meters per second. The measured normal depth data follows this same trend, which confirms that the computed values are correct. The critical depth is less than the measured and computed normal depth at each flow value, and begins with a depth of 0.174 meters at 0.055 cubic meters per second, and follows an approximately linear trend to a depth of 0.25 meters at 0.19 cubic meters per second. So, at the highest flow on the graph, or 0.19 cubic meters per second, the critical depth is 0.054 meters less than the computed and measured normal depth. Figure 6. Graph. Ratio of mainchannel discharge to total discharge as a function of relative normal depth in the floodplain. This graph plots the ratio of main channel to total discharge as a function of relative normal depth in the floodplain for measured compound channel A, measured compound channel B, calculated A and B with variable lowercase N, and calculated A with constant lowercase N. The Xaxis shows Q subscript lowercase Mzero, which is the discharge in the main channel for uniform flow in a compound channel, divided by Q, which is the total discharge in compound channel, from 0.0 to 1.0. The Yaxis shows lowercase Y subscript lowercase Fzero, which is the normal depth in the floodplain, divided by lowercase Y subscript Mzero, which is the normal depth in the main channel, from 0.0 to 0.5. Measured compound channel A begins at coordinates 0.35, 0.3, and ends at coordinates 0.06, 0.89. The values for lowercase Y subscript lowercase Fzero divided by lowercase Y subscript Mzero decrease as the values for Q subscript lowercase Mzero divided by Q increase. The curves for calculated A with variable lowercase N, and calculated A with constant lowercase N follow approximately the same data pattern. The curve for measured compound channel B is slightly lower than for compound channel A. Compound channel B begins at coordinates 0.33, 0.3, and ends at coordinates 0.13, 0.63. The values for lowercase Y subscript lowercase Fzero divided by lowercase Y subscript Mzero decrease as the values for Q subscript lowercase Mzero divided by Q increase. The curves for calculated B with variable lowercase N, and calculated A with constant lowercase N follow approximately the same data pattern. Figure 7A. Graph. Dependence of M on approach depth and abutment length. This graph plots the M, or discharge distribution factor for various L lowercase a divided by B lowercase F, which is the abutment length divided by width of the floodplain, for an assortment of twelve theoretical compound channel cases. The Xaxis shows lowercase Y subscript lowercase F 1 divided by lowercase Y subscript lowercase M 1, which is the bridge approach depth in the floodplain channel divided by the bridge approach depth in the main channel, from zero to 0.5. The Yaxis is M, which is the discharge distribution factor in the approach section ranging from zero to 1. There are three compound channel A, vertical wall cases with L lowercase A divided by B lowercase F values of 0.17, 0.33, and 0.5. The remaining 12 cases are compound channel B with either vertical wall or spillthrough shapes, and L lowercase A divided by B lowercase F values ranging from 0.22 to 1.0. For all cases, the value of M decreases as the lowercase Y subscript lowercase F 1 divided by lowercase Y subscript lowercase M ratio increases. Of the 15 groups of data plotted, the highest values of the discharge distribution factor, M, occurred for compound channel A with vertical wall abutment and L lowercase A divided by B lowercase F equal to 0.17 where M varied from 0.98 to 0.95 as the Xaxis varied from 0.13 to 0.31. The lowest values of the discharge distribution factor, M, occurred for compoundchannel B with a vertical wall abutment and L lowercase A divided by B lowercase F equal to 1.0 where M varied from 0.51 to 0.29 as the Xaxis varied from 0.20 to 0.42. Figure 7B. Graph. Use of M to reflect mainchannel discharge ratio. This graph plots the M, which is the discharge distribution factor in the approach section by Q lowercase M 1 divided by Q lowercase M 2, which is the flowrate per unit width in the main channel divided by flowrate per unit width in the contracted section, for three cases, compound channel B with vertical sidewall, compound channel B with spillthrough, and compound channel A with vertical sidewall. The X and Yaxis range from zero to 1. Both compound channel B cases begin at coordinates of 0.69, 0.67, and follow an approximately linear trend upwards to a coordinates of 0.88, 0.9. The compound channel A case follows the same pattern except shifted slightly upward beginning at coordinates of 0.74, 0.74 and following an approximately linear trend upwards to the coordinates 0.94, 0.97. Figure 8A. Graph. Compound channel B: watersurface profiles for abutment VW. This graph plots the depth in meters for three different L lowercase A divided by B lowercase F, which is the abutment length divided by width of the floodplain, for a vertical wall type abutment with a constant flow of 0.085 cubic meters per second. The three cases of L lowercase A divided by B lowercase F ratios are 0.22, 0.44, and 0.66. The Xaxis is Xstation distance in meters ranging from 0 to 20. The Yaxis is depth in meters ranging from 0.15 to 0.3. The position of the abutment is in the approximate center of the Xaxis at the 10meter mark. In each case, there is a rise in depth approaching the abutment, followed by a steep drop in depth as the water passes through the abutment, and then a gradual rise in depth after the abutment. The case with an L lowercase A divided by B lowercase F ratio of 0.66 has the greatest depth prior to the abutment with a value of 0.22 meters. The case with an L lowercase A divided by B lowercase F ratio of 0.22 has the lowest depth prior to the abutment with a value of 0.19 meters. The longer the abutment is in relation to the width of the floodplain, the greater the depth of water prior to the abutment. After the abutment the three cases have approximately the same depth, 0.18 meters. Figure 8B. Graph. Compound channel B: Approach velocity distributions, station 7.3; abutment VW. This graph plots a cross section of depth across compound channel upstream of the abutment for different L lowercase A divided by B lowercase F, which is the abutment length divided by width of the floodplain, for a vertical wall type abutment with a constant flow of 0.085 cubic meters per second. The four cases of L lowercase A divided by B lowercase F ratios are zero or no abutment, 0.22, 0.44, and 0.66. The Xaxis represents transverse station distance in meters ranging from 0 to 4.5. The Yaxis is velocity in meters per second ranging from zero to 0.6. The lower velocities are found in the floodplain and the higher velocities are found in the main channel on the right side of the cross section. The highest velocities are for the no abutment case with an average floodplain velocity of 0.3 meters per second, and a main channel velocity of 0.55 meters per second. The lowest velocities are for the case with an L lowercase A divided by B lowercase F ratio of 0.66 and are approximately 0.2 meters per second for the floodplain section and 0.4 meters per second for the main channel section. The longer the abutment is in relation to the width of the floodplain, the lower the velocity of water prior to the abutment. Figure 9A. Graph. Compound channel B: watersurface profiles for abutment VW. This graph plots the depth in meters for three different flow values for a vertical wall type abutment with a L lowercase A divided by B lowercase F, which is the abutment length divided by width of the floodplain, of 0.44. The three cases of flow values are 0.0708, 0.0850, and 0.0991 cubic meters per second. The Xaxis represents Xstation distance in meters ranging from 0 to 20. The Yaxis is depth in meters ranging from 0.15 to 0.3. The position of the abutment is in the approximate center of the Xaxis at the 10meter mark. In each case, there is a rise in depth approaching the abutment, followed by a steep drop in depth as the water passes through the abutment, and then a gradual rise in depth after the abutment. The case with a flow value of 0.0991 cubic meters per second has the greatest depth prior to the abutment with a value of 0.211 meters. The case with a flow value of 0.0708 cubic meters per second has the lowest depth prior to the abutment with a value of 0.195 meters. The greater the flow of water in the channel, the greater the depth of water prior to the abutment. After the abutment the case with a flow value of 0.0991 cubic meters per second has a depth of 0.19 meters. The case with a flow value of 0.0708 cubic meters per second has a depth of 0.18 meters. The values after the abutment then rise gradually. Figure 9B. Graph. Compound channel B: Approach velocity distributions, station 7.3; abutment VW. This graph plots a cross section of depth across compound channel upstream of the abutment for different flow values for a vertical wall type abutment with a L lowercase A divided by B lowercase F, which is the abutment length divided by width of the floodplain, of 0.44. The three cases have flows of 0.0708, 0.0850, and 0.0991 cubic meters per second. The Xaxis represents transverse station distance in meters ranging from 0 to 4.5. The Yaxis is velocity in meters per second ranging from zero to 0.6. The lower velocities are found in the floodplain and the higher velocities are found in the main channel on the right side of the cross section. The highest velocities are for the case with a flow of 0.0991 cubic meters per second and have velocities of around 0.3 meters per second in the floodplain and 0.45 meters per second in the main channel. The lowest velocities are for the case a flow value of 0.0708 cubic meters per second and have a velocity of approximately 0.45 meters per second for the floodplain section and 0.4 meters per second for the main channel section. The graph shows that the greater the flow in the channel, the higher the velocity of water prior to the abutment. Figure 10A. Graph. Compound channel B: watersurface profiles for abutment VW. This graph plots depth in meters for three different tailwater depth values for a vertical wall type abutment with a L lowercase A divided by B lowercase F, which is the abutment length divided by width of the floodplain, of 1, and a flow of 0.0567 cubic meters per second. The three different tailwater depths are 0.262, 0.210, and 0.194 meters. The Xaxis represents Xstation distance in meters ranging from 0 to 20. The Yaxis is depth in meters ranging from 0.15 to 0.3. The position of the abutment is in the approximate center of the Xaxis at the 10meter mark. In each case, there is a rise in depth approaching the abutment, followed by a steep drop in depth as the water passes through the abutment, and then a gradual rise in depth after the abutment. The case with a tailwater depth of 0.262 meters has the greatest depth prior to the abutment with a value of 0.275 meters. The case with a tailwater depth of 0.194 meters has the lowest depth prior to the abutment with a value of 0.235 meters. After the abutment the case with a tailwater depth of 0.262 meters has a depth of 0.245 meters. The case with a flow value of 0.194 meters has a depth of 0.178 meters. The values after the abutment then rise gradually. The higher the tailwater depth, the less impact the abutment contraction has on flow characteristics in terms of depth change through the contraction and floodplain depth differential between upstream and approach. Figure 10B. Graph. Compound channel B: Approach velocity distributions, station 7.3; abutment VW. This graph plots a cross section of depth across compound channel upstream of the abutment for three different tailwater depth values for a vertical wall type abutment with a L lowercase A divided by B lowercase F, which is the abutment length divided by width of the floodplain, of 1, and a flow of 0.0567 cubic meters per second. The three different tailwater depths are 0.262, 0.210, and 0.194 meters. The Xaxis represents transverse station distance in meters ranging from 0 to 4.5. The Yaxis is velocity in meters per second ranging from zero to 0.6. The lower velocities are found in the floodplain and the higher velocities are found in the main channel on the right side of the cross section. The highest velocities are for the case with a tailwater depth of 0.194 meters and have velocities of around 0.149 meters per second in the floodplain and 0.19 meters per second in the main channel. The lowest velocities are for the tailwater depth of 0.262 meters and have a velocity of approximately 0.09 meters per second in the floodplain section and 0.125 meters per second for the main channel section. The higher the tailwater depth in the channel, the lower the velocity of water prior to the abutment. The presence of a tailwater after the abutment also reduces the depth differential between the floodplain channel and the main channel, with the highest tailwater depth having the smallest depth differential. Figure 11A. Graph. Tailwater equal to normal depth, compound channel B: watersurface profiles for abutment VW. This graph plots depth in meters for flow before and after scour has occurred for a vertical wall type abutment with a L lowercase A divided by B lowercase F, which is the abutment length divided by width of the floodplain, of 0.44, and a flow of 0.085 cubic meters per second. In this example the tailwater depth is equal to normal depth. The Xaxis represents Xstation distance in meters ranging from 0 to 20. The Yaxis is depth in meters ranging from 0.15 to 0.3. The position of the abutment is in the approximate center of the Xaxis at the 10meter mark. The normal depth is plotted as a straight line at a depth of 0.192 meters. In both cases, there is a rise in depth approaching the abutment, followed by a steep drop in depth as the water passes through the abutment, and then a gradual rise in depth after the abutment. In both cases depth prior to the abutment rises to 0.23 meters. After the abutment the before scour case drops to a depth of 0.185 meters, and the after scour case drops to a depth of 0.189 meters. The depth values after the abutment then rise gradually back to normal depth. In this example the flow characteristics of the channel before and after scour closely match each other, with a slightly higher postabutment depth after scour has occurred. Figure 11B. Graph. Tailwater greater than normal depth, compound channel B: watersurface profiles for abutment VW. This graph plots depth in meters for flow before and after scour has occurred for a vertical wall type abutment with a L lowercase A divided by B lowercase F, which is the abutment length divided by width of the floodplain, of 0.88, and a flow of 0.0567 cubic meters per second. In this example the tailwater depth is greater than normal depth. The Xaxis represents Xstation distance in meters ranging from 0 to 20. The Yaxis is depth in meters ranging from 0.15 to 0.3. The position of the abutment is in the approximate center of the Xaxis at the 10meter mark. The normal depth is plotted as a straight line at a depth of 0.178 meters. In both cases, there is a rise in depth approaching the abutment, followed by a steep drop in depth as the water passes through the abutment, and then a gradual rise in depth after the abutment. Prior to the abutment the before scour case rises to a depth of 0.218 meters, and the after scour case rises to a depth of 0.21 meters. After the abutment the before scour case drops to a depth of 0.185 meters, and the after scour case drops to a depth of 0.187 meters. In this example the depth approaching the abutment is reduced after scour has occurred. Figure 12A. Graph. Tailwater equal to normal depth, compound channel B: watersurface profiles for abutment VW. This graph plots depth in meters for flow before and after scour has occurred for a vertical wall type abutment with a L lowercase A divided by B lowercase F, which is the abutment length divided by width of the floodplain, of 0.97, and a flow of 0.0567 cubic meters per second. In this example the tailwater depth is equal to normal depth. The Xaxis represents Xstation distance in meters ranging from 0 to 20. The Yaxis is depth in meters ranging from 0.15 to 0.3. The position of the abutment is in the approximate center of the Xaxis at the 10meter mark. The normal depth is plotted as a straight line at a depth of 0.178 meters. In both cases, there is a rise in depth approaching the abutment, followed by a steep drop in depth as the water passes through the abutment, and then a gradual rise in depth after the abutment. Prior to the abutment the before scour case rises to a depth of 0.22 meters, and the after scour case rises to a depth of 0.194 meters. After the abutment the before scour case drops to a depth of 0.162 meters, and the after scour case drops to a depth of 0.162 meters. The depth values after the abutment then rise gradually back to normal depth. In this example, the depth approaching the abutment is reduced and the depth leaving the abutment is increased after scour has occurred. Figure 12B. Graph. Tailwater greater than normal depth, compound channel B: watersurface profiles for abutment VW. This graph plots depth in meters for flow before and after scour has occurred for a vertical wall type abutment with a L lowercase A divided by B lowercase F, which is the abutment length divided by width of the floodplain, of 1, and a flow of 0.0567 cubic meters per second. In this example the tailwater depth is greater than normal depth. The Xaxis represents Xstation distance in meters ranging from 0 to 20. The Yaxis is depth in meters ranging from 0.15 to 0.3. The position of the abutment is in the approximate center of the Xaxis at the 10meter mark. The normal depth is plotted as a straight line at a depth of 0.178 meters. In both cases, there is a rise in depth approaching the abutment, followed by a steep drop in depth as the water passes through the abutment, and then a gradual rise in depth after the abutment. Prior to the abutment the before scour case rises to a depth of 0.24 meters, and the after scour case rises to a depth of 0.21 meters. After the abutment the before scour case drops to a depth of 0.195 meters, and the after scour case drops to a depth of 0.195 meters. In this example the depth approaching the abutment is reduced by 0.03 meters after scour has occurred, and the depth before and after scour are the same leaving the abutment. Figure 13A. Graph. Mainchannel centerline velocityX for abutment VW. This graph plots relative depth, or Y prime divided by Y subscript lowercase M, by velocity in the X direction in cubic meters per second for five stations downstream of the channel entrance. This example has an L lowercase A divided by B lowercase F, which is the abutment length divided by width of the floodplain, of 0.88, and a flow of 0.0567 cubic meters per second. The stations are at 6.1, 7.3, 8.5, 9.8 and 10.9 meters. The centerline of the abutment is located at station 9.8. The Xaxis represents the velocity in the X direction in centimeters per second ranging from zero to 90. The Yaxis represents lowercase Y prime divided by lowercase Y subscript lowercase M, which is the ratio of distance above the main channel bed to depth of flow in the main channel, ranging from zero to 1. Stations 6.1 and 7.3 have velocities of 10 centimeters per second at a relative depth of zero, and the velocities increase steeply to approximately 23 centimeters per second and stay constant through the relative depth range of 0.3 through 0.65. Station 9.8 has a constant velocity of approximately 55 centimeters per second throughout the relative depth range from 0.1 to 0.65. The curve for station 10.9 begins with a velocity of 46 centimeters per second at a relative depth of 0.03 and increases gradually to a velocity of 65 centimeters per second at a relative depth of 0.65. As the flow approaches the abutment, the velocity throughout the depth increases, with the highest velocities immediately following the abutment. Figure 13B. Graph. Mainchannel centerline velocityZ for abutment VW. This graph plots relative depth, or lowercase Y prime divided by lowercase Y subscript lowercase M, which is the ratio of distance above the main channel bed to depth of flow in the main channel, by velocity in the Z direction in cubic meters per second for five stations downstream of the channel entrance. This example has an L lowercase A divided by B lowercase F, which is the abutment length divided buy the width of the floodplain, of 0.88, and a flow of 0.0567 cubic meters per second. The stations are at 6.1, 7.3, 8.5, 9.8 and 10.9 meters. The centerline of the abutment is located at station 9.8. The Xaxis represents the velocity in the Z direction in centimeters per second ranging from zero to 90. The Yaxis represents lowercase Y prime divided by lowercase Y subscript lowercase M ranging from zero to 1. Stations 6.1, 7.3, 8.5, and 10.9 have velocities of approximately 4 centimeters per second at throughout the relative depth range from zero to 6.5. Station 9.8 has a constant velocity of approximately 7.5 centimeters per second throughout the relative depth range from 0.1 to 0.65. The transverse flow positive to the right when looking down stream is highest at the location of the abutment, indicating higher scour potential. Figure 14A. Graph. Mainchannel centerline velocityX for abutment VW. This graph plots relative depth, or lowercase Y prime divided by lowercase Y subscript lowercase M, which is the ratio of distance above the main channel bed to depth of flow in the main channel, by velocity in the X direction in cubic meters per second for four stations downstream of the channel entrance. This example has an L lowercase A divided by B lowercase F, which is the abutment length divided buy the width of the floodplain, of 0.97, and a flow of 0.0567 cubic meters per second. The stations are at 6.1, 7.3, 8.5, and 10 meters. The centerline of the abutment is located at station 9.8. The Xaxis represents the velocity in the X direction in centimeters per second ranging from zero to 90. The Yaxis represents lowercase Y prime divided by lowercase Y lowercase M ranging from zero to 1. Stations 6.1, 7.3, and 8.5 have velocities of 12.5, 17.5, and 27.5 centimeters per second, respectively, at a relative depth of 0.05. The velocities increase to 24, 28, and 37.5 centimeters per second, respectively, at a relative depth of 0.65. As the flow approaches the abutment, the velocity throughout the depth increases. Figure 14B. Graph. Mainchannel centerline velocityZ for abutment VW. This graph plots relative depth, or lowercase Y prime divided by lowercase Y subscript lowercase M, which is the ratio of distance above the main channel bed to depth of flow in the main channel, by velocity in the Z direction in cubic meters per second for four stations downstream of the channel entrance. This example has an L lowercase A divided by B lowercase F, which is the abutment length divided buy the width of the floodplain of 0.97, and a flow of 0.0567 cubic meters per second. The stations are at 6.1, 7.3, 8.5, and 10 meters. The centerline of the abutment is located at station 9.8. The Xaxis represents the velocity in the Z direction in centimeters per second ranging from zero to 90. The Yaxis represents lowercase Y prime divided by lowercase Y subscript lowercase M ranging from zero to 1. Stations 6.1, 7.3, and 8.5 have velocities of 1, 2, and 3 centimeters per second, respectively, throughout the relative depth range from 0.1 to 0.65. The transverse flow positive to the right when looking down stream increases slightly as the flow moves downstream towards the abutment. Figure 15A. Graph. Mainchannel centerline velocityX for abutment VW. This graph plots relative depth, or lowercase Y prime divided by lowercase Y subscript lowercase M, which is the ratio of distance above the main channel bed to depth of flow in the main channel, by velocity in the X direction in cubic meters per second for four stations downstream of the channel entrance. This example has an L lowercase A divided by B lowercase F, which is the abutment length divided buy the width of the floodplain, of 1, and a flow of 0.0567 cubic meters per second. The stations are at 6.1, 7.3, 8.5, and 9.8 meters. The centerline of the abutment is located at station 9.8. The Xaxis represents the velocity in the X direction in centimeters per second ranging from zero to 90. The Yaxis represents lowercase Y prime divided by lowercase Y subscript lowercase M ranging from zero to 1. Stations 6.1, 7.3, and 8.5 have velocities of 11, 13, and 21 centimeters per second, respectively, at a relative depth of 0.05. The velocities increase to 18, 20, and 28 centimeters per second, respectively, at a relative depth of 0.65. Station 9.8 has a constant velocity of approximately 64 centimeters per second throughout the relative depth range from 0.05 to 0.65. As the flow approaches the abutment, the velocity throughout the depth increases, with the highest flow values occurring at the abutment itself. Figure 15B. Graph. Mainchannel centerline velocityZ for abutment VW. This graph plots relative depth, or lowercase Y prime divided by lowercase Y subscript lowercase M, which is the ratio of distance above the main channel bed to depth of flow in the main channel, by velocity in the Z direction in cubic meters per second for four stations downstream of the channel entrance. This example has an L lowercase A divided by B lowercase F, which is the abutment length divided buy the width of the floodplain, of 1, and a flow of 0.0567 cubic meters per second. The stations are at 6.1, 7.3, 8.5, and 9.8 meters. The centerline of the abutment is located at station 9.8. The Xaxis represents the velocity in the Z direction in centimeters per second ranging from zero to 90. The Yaxis represents lowercase Y prime divided by lowercase Y subscript lowercase M ranging from zero to 1. Stations 6.1, 7.3, and 8.5 have velocities of 2, 3, and 4 centimeters per second, respectively, throughout the relative depth range from 0.1 to 0.65. Station 9.8 has a constant velocity of approximately 10 centimeters per second throughout the relative depth range from 0.1 to 0.65. The transverse flow positive to the right when looking down stream is highest at the location of the abutment, indicating higher scour potential. Figure 16. Graph. Measured and calculated critical velocities at incipient motion. This graph plots the critical value of sediment number on the Yaxis by the median sediment grain diameter divided by flow depth. Data plotted includes measured critical velocities for sediments A, B, and C with a vertical wall, a spill through with sediment A, as well as calculated critical velocities using one Parola, two Laursen, and a Keulegan equations. The Laursen equations utilized shields parameters of 0.039 and 0.035. The Keulegan equation utilized a shields parameter of 0.047. The Xaxis measures lowercase D subscript 50 divided by lowercase Y, which is median diameter of sediment divided by depth of flow in the main channel, ranging from 0.01 to 1 on a logarithmic scale. The Yaxis measures N subscript lowercase SC, which is the critical value of sediment number, from 1 to 10 on a logarithmic scale. The calculated data produce approximately linear plots beginning at coordinates 3, 0.016, and ending at coordinates 1.8, 0.3. The measured data are represented by a few scattered points around the cluster of calculated data lines. The critical value of the sediment number gets smaller as the ratio of sediment grain diameter to flow depth gets larger. Figure 17A. Diagram. Bed elevations for shorter VW abutments after scour. This diagram shows contour elevations of the channel bed for a verticalwall abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.44, and a flow value of 0.0992 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 16 centimeters at the center. The decrease in elevation begins where the abutment ends, and is aligned with it longitudinally. The area of the depression is about 0.7 meters in the Z plane by 0.9 meters in the X plane. Figure 17B. Diagram. Bed elevations for shorter VW abutments after scour. This diagram shows contour elevations of the channel bed for a verticalwall abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.44, and a flow value of 0.117 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 8 centimeters at the center. The lowest elevation occurs directly adjacent to the end of the abutment. The area of the depression is about 1 meter in the Z plane by 1 meter in the X plane. Figure 17C. Diagram. Bed elevations for shorter VW abutments after scour. This diagram shows contour elevations of the channel bed for a verticalwall abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.66, and a flow value of 0.0994 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 6 centimeters at the center. The decrease in elevation begins where the abutment ends, and is aligned with it longitudinally. The area of the depression is about 1.1 meters in the Z plane by 1.3 meters in the X plane. Figure 18A. Diagram. Bed elevations for longer VW abutments after scour. This diagram shows contour elevations of the channel bed for a verticalwall abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.88, and a flow value of 0.0567 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 12 centimeters at the center. The decrease in elevation begins where the abutment ends, and is aligned with it longitudinally. There is also a slight decrease in elevation across the main channel going from the end of the abutment to the channel wall. The elevation of the main channel profile downstream of the abutment is slightly more varied than the elevation profile found upstream of the abutment. Figure 18B. Diagram. Bed elevations for longer VW abutments after scour. This diagram shows contour elevations of the channel bed for a verticalwall abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.97, and a flow value of 0.0567 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. The main channel has a reduced elevation in the proximity of the end of the abutment. The decrease in elevation begins where the abutment ends, and has a minimum elevation of 14 centimeters, and is aligned with it longitudinally. There is also a slight decrease in elevation across the main channel going from the end of the abutment to the channel wall. The elevation of the main channel profile downstream of the abutment is slightly more varied, specifically a small increase in elevation, than the elevation profile found upstream of the abutment. Figure 18C. Diagram. Bed elevations for longer VW abutments after scour. This diagram shows contour elevations of the channel bed for a verticalwall abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 1, and a flow value of 0.0567 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. The main channel has a reduced elevation located primarily at the end of the abutment. The decrease in elevation begins where the abutment ends, and has a minimum elevation of 14 centimeters. There is also a slight decrease in elevation across the main channel going from the end of the abutment to the channel wall. The elevation of the main channel profile downstream of the abutment is slightly more varied, specifically a small increase in elevation, than the elevation profile found upstream of the abutment. Figure 19A. Diagram. Bed elevations for shorter ST abutments after scour. This diagram shows contour elevations of the channel bed for a spillthrough abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.65, and a flow value of 0.085 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 16 centimeters at the center. The decrease in elevation begins where the abutment ends, and is aligned with it longitudinally. The area of the depression is about 1 meter in the Z plane by 1.1 meters in the X plane. Figure 19B. Diagram. Bed elevations for shorter ST abutments after scour. This diagram shows contour elevations of the channel bed for a spillthrough abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.65, and a flow value of 0.0983 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the upstream corner of the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 10 centimeters at the center. The lowest elevation occurs directly adjacent to the abutment. The area of the depression is about 1 meter in the Z plane by 1 meter in the X plane. Figure 19C. Diagram. Bed Elevations for shorter ST abutments after scour. This diagram shows contour elevations of the channel bed for a spillthrough abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.88, and a flow value of 0.085 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the upstream corner of the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 4 centimeters at the center. The lowest elevation occurs directly adjacent to the abutment. The area of the depression is about 1 meter in the Z plane by 1 meter in the X plane. The elevation of the main channel profile downstream of the abutment is slightly more varied, specifically a slightly reduced in elevation, than the elevation profile found upstream of the abutment. Figure 20A. Diagram. Bed elevations for longer ST abutments after scour. This diagram shows contour elevations of the channel bed for a spillthrough abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.88, and a flow value of 0.0708 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 2 centimeters at the center. The decrease in elevation begins where the abutment ends, and is aligned with it longitudinally. There is also a slight decrease in elevation across the main channel going from the end of the abutment to the channel wall. The elevation of the main channel profile downstream of the abutment is slightly more varied than the elevation profile found upstream of the abutment. Figure 20B. Diagram. Bed elevations for longer ST abutments after scour. This diagram shows contour elevations of the channel bed for a spillthrough abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.97, and a flow value of 0.0697 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. The main channel has a reduced elevation in the proximity of the end of the abutment. The decrease in elevation begins where the abutment ends, and has a minimum elevation of 4 centimeters, and is aligned with it longitudinally. There is also a slight decrease in elevation across the main channel going from the end of the abutment to the channel wall. The elevation of the main channel profile downstream of the abutment is slightly more varied, specifically a small increase in elevation, than the elevation profile found upstream of the abutment. Figure 20C. Diagram. Bed elevations for longer ST abutments after scour. This diagram shows contour elevations of the channel bed for a spillthrough abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 1, and a flow value of 0.0697 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. The main channel has a reduced elevation located primarily at the end of the abutment. The decrease in elevation begins where the abutment ends, and has a minimum elevation of 4 centimeters. There is also a slight decrease in elevation across the main channel going from the end of the abutment to the channel wall. The elevation of the main channel profile downstream of the abutment is slightly more varied, specifically a small increase in elevation, than the elevation profile found upstream of the abutment. Figure 21A. Diagram. Bed elevations for a VW abutment after scour. This diagram shows contour elevations of the channel bed for a verticalwall abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.66, and a flow value of 0.0994 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 6 centimeters at the center. The decrease in elevation begins where the abutment ends, and is aligned with it longitudinally. The area of the depression is about 1 meter in the Z plane by 1.1 meters in the X plane. Figure 21B. Diagram. Bed elevations for a ST abutment after scour. This diagram shows contour elevations of the channel bed for a spillthrough abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.65, and a flow value of 0.0983 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the upstream corner of the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 10 centimeters at the center. The lowest elevation occurs directly adjacent to the corner of the abutment. The area of the depression is about 1 meter in the Z plane by 1 meter in the X plane. Figure 21C. Diagram. Bed elevations for a WW abutment after scour. This diagram shows contour elevations of the channel bed for a wingwall abutment with an L lowercase A divided by B lowercase F value of 0.61, and a flow value of 0.0992 cubic meters per second. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the upstream corner of the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 10 centimeters at the center. The area of the depression is about 1 meter in the Z plane by 1 meter in the X plane. The elevation of the main channel profile downstream of the abutment is slightly more varied, specifically a slightly reduced in elevation, than the elevation profile found upstream of the abutment. Figure 22A. Diagram. Bed elevations for a VW abutment after scour with sediment A. This diagram shows contour elevations of the channel bed for a verticalwall abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.44, a flow value of 0.085 cubic meters per second, and sediment A. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 20 centimeters at the center. The decrease in elevation begins where the abutment ends, and is aligned with it longitudinally. The area of the depression is about 0.6 meters in the Z plane by 0.5 meters in the X plane. Figure 22B. Diagram. Bed elevations for a VW abutment after scour with sediment B. This diagram shows contour elevations of the channel bed for a verticalwall abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.44, a flow value of 0.085 cubic meters per second, and sediment B. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 18 centimeters at the center. The decrease in elevation begins at the end of the abutment, and is aligned with it longitudinally. The area of the depression is about 0.7 meters in the Z plane by 0.6 meters in the X plane. Figure 22C. Diagram. Bed elevations for a VW abutment after scour with sediment C. This diagram shows contour elevations of the channel bed for a verticalwall abutment with an L lowercase A divided by B lowercase F value, which is the abutment length divided buy the width of the floodplain, of 0.44, a flow value of 0.085 cubic meters per second, and sediment C. The Xaxis is the width of the channel, or Zplane ranging from zero to 4.2 meters. The Yaxis represents the length of channel, or Xplane ranging from 8.5 to 12.8 meters. The abutment is located at 9.8 meters. The channel bed has an average elevation of approximately 32 centimeters. A depression is delineated at the end of the abutment by a series of concentric elevation rings with lower and lower values that reach a minimum elevation of 10 centimeters at the center. The lowest elevation occurs directly adjacent to the upstream corner of the end of the abutment. The area of the depression is about 1.1 meters in the Z plane by 1.3 meters in the X plane. Figure 23. Diagram. Definition sketch for idealized floodplain contraction scour in a laboratory compound channel, compound channel A. This diagram details three views of an idealized compound channel A, a plan view, section AA, and section BB. The plan view shows the main channel and floodplain, approach point defined as number 1, bridge abutment location defined as number 2, direction of flow, section AA and BB location, and assorted variables such as B subscript lowercase M, Q, and L subscript lowercase A. Section AA is a longitudinal cross section of the channel along axis of the floodplain with a theoretical flow, abutment location, and assorted variables such as lowercase Y subscript lowercase F zero, lowercase Y subscript lowercase F 2, and lowercase D subscript lowercase SC. Section BB is a cross section of the width of the channel downstream of the abutment with a theoretical flow, and the variables lowercase Y subscript lowercase F zero and lowercase Y subscript lowercase M zero. Figure 24. Diagram. Definition sketch for idealized mainchannel contraction scour in a laboratory compound channel, compound channel B. This diagram details two views of an idealized compound channel B, a plan view, and section AA. The plan view shows the main channel and floodplain, approach point defined as number 1, bridge abutment location defined as number 2, direction of flow, section AA, and assorted variables such as B subscript lowercase M, Q, and L subscript lowercase A. Section AA is a longitudinal cross section of the channel along axis of the main channel with a theoretical flow, abutment location, and assorted variables such as lowercase Y subscript lowercase F zero, lowercase Y subscript lowercase F 2, lowercase Y subscript lowercase M zero, and lowercase D subscript lowercase SC. The water surface, floodplain, and main channel elevations are also defined. Figure 25. Graph. Scourdepth relationship based on approach hydraulic variables for VW abutments with L subscript A divided by B subscript F values greater than or equal to 0.17 and less than or equal to 0.66. This graph plots data for compound channel A with L Subscript A divided by B subscript F, which is the abutment length divided buy the width of the floodplain, values of 0.17, 0.33, 0.5, and sediment size lowercase D 50, which is the median diameter of sediment, values of 1.1, 2.7, and 3.3 millimeters. The graph also plots data for compound channel B with L Subscript A divided by B subscript F values of 0.22, 0.44, 0.66, and sediment size lowercase D 50 values of 1.1, 2.7, and 3.3 millimeters. The Xaxis is lowercase Q subscript lowercase F 1 divided by M lowercase Q subscript FOC, which is the flow rate per unit width in the approach section of the floodplain divided by the discharge distribution factor multiplied by the critical flow rate per unit width in the floodplain at normal depth, ranging from zero to 3. The Yaxis is the normalized scourdepth, or lowercase D subscript lowercase S divided by lowercase Y subscript lowercase F zero ranging from zero to 12. The data points are in a linear grouping beginning at coordinates 1, 0.7 and ending at coordinates 9, 1.4. The majority of the data points are centered around the coordinates 4, 0.8. A bestfit trendline is plotted through the data points that plateaus at a normalized scourdepth value of 10. Another data line is plotted in approximately the same location that is based on the Strurm and Janjua equation. Figure 26. Graph. Scourdepth relationship based on approach hydraulic variables in main channel for VW and ST abutments with L subscript A divided by B subscript F values greater than or equal to 0.88 and less than or equal 1.0. This graph plots data for verticalwall and spillthrough abutments with L Subscript A divided by B subscript F values, which is the abutment length divided buy the width of the floodplain, of 0.88, 0.97, and 1. The Xaxis is lowercase Q subscript lowercase M 1 divided by the quotient M multiplied by V subscript M zero C multiplied by Y subscript lowercase F zero, which is the flow rate per unit width in the approach section of the floodplain divided by the discharge distribution factor multiplied by the critical velocity for the unconstricted depth in the main channel multiplied by normal depth in the floodplain, ranging from zero to 10. The Yaxis is the normalized scourdepth, or lowercase D subscript lowercase S divided by lowercase Y subscript lowercase F zero ranging from zero to 12. The data points for the VW abutments with L Subscript A divided by B subscript F values of 0.88 and 1 are in an approximately linear grouping beginning at coordinates 1.5, 0.7 and ending at coordinates 9, 5.2. The data points for the VW abutment with an L Subscript A divided by B subscript F value of 0.97 are in a grouping around the coordinates 8, 5.5. The data points for the ST abutments with L Subscript A divided by B subscript F values of 0.97 and 1 are in an approximately linear grouping beginning at coordinates 10, 5.5 and ending at coordinates 10, 7.8. A regression trendline is plotted through the data points that begins at coordinates 0,0.5, and rises linearly to a plateau point at coordinates 10, 5.5. The overall picture of the graph is that the normalized scourdepth increases linearly as the QM quotient increases until at plateau at a normalized scourdepth value of 10. Figure 27. Graph. Scourdepth relationship based on approach hydraulic variables in floodplain for all abutments and sediments for compound channel B. This graph plots data for verticalwall, spillthrough, and wingwall abutments with assorted L Subscript A divided by B subscript F value, which is the abutment length divided by the width of the floodplain, ranging from 0.22 to 1. The Xaxis is lowercase Q subscript lowercase F 1 divided by the quotient M multiplied by V subscript XC multiplied by lowercase Y subscript lowercase F zero which is the flow rate per unit width in the approach section of the floodplain divided by the discharge distribution factor multiplied by the critical velocity multiplied by normal depth in the floodplain, ranging from zero to 10. The Yaxis is the normalized scourdepth, or lowercase D subscript lowercase S divided by lowercase Y subscript lowercase F zero ranging from zero to 12. The data points are in an approximately linear grouping beginning at coordinates 0.3, 0.7, and ending at coordinates 10, 1.4. The data points for the spillthrough abutment with L Subscript A divided by B subscript F values of 0.88, 0.97, and 1 are in a grouping around the coordinates 10, 1.5 to 2.25. The data points for the VW abutment with an L Subscript A divided by B subscript F value of 0.97 are in a grouping around the coordinates 8, 5.5. The data points for the ST abutments with L Subscript A divided by B subscript F values of 0.97 and 1 are in an approximately linear grouping beginning at coordinates 10, 5.5, and ending at coordinates 10, 7.8. A regression trendline is plotted through the data points and it has a forked appearance at the bottom of the graph. The best fit line for the verticalwall begins at coordinates 0, 0.54, and the best fit line for the spillthrough begins at coordinates 0, 0.65. Both lines increase linearly to the coordinates 6.5, 1.2 where they then merge into one and rise linearly to a plateau at coordinates 10, 1.2. The overall picture of the graph is that the standard error of estimate increases linearly as the QM quotient increases until at plateau at a normalized scourdepth value of 10. The overall picture of the graph is that the normalized scourdepth increases linearly as the QM quotient increases until at plateau at a normalized scourdepth value of 10. Figure 28. Graph. Scourdepth relationship based on local hydraulic variables for VW abutments with L subscript A divided by B subscript F values less than or equal to 0.66 and lowercase D subscript 50 equal to 3.3, 2.7, and 1.1. This graph plots data for compound channel A with L Subscript A divided by B subscript F values, which is abutment length divided by the width of the floodplain of 0.17, 0.33, 0.5, and sediment size lowercase D 50 values of 1.1, 2.7, and 3.3 millimeters. The graph also plots data for compound channel B with L Subscript A divided by B subscript F values of 0.22, 0.44, 0.66, and sediment size D 50 values of 1.1, 2.7, and 3.3 millimeters. The Xaxis is the quotient of V subscript lowercase AB divided by V subscript lowercase C, which is the maximum resultant velocity at the upstream abutment corner divided by the critical velocity for initiation of motion, minus 1 ranging from 0.1 to 10 on a logarithmic scale. The Yaxis is the standard normalized scourdepth, or lowercase D subscript lowercase S divided by lowercase Y subscript lowercase F zero ranging from 0.1 to 100 on a logarithmic scale. The data points are in a linear grouping beginning at coordinates error 0.38, 0.015 and ending at coordinates 10, 1.6. The majority of the data points are centered about the coordinates 4, 0.6. A bestfit trendline is plotted through the data points and it plateaus at a normalized scourdepth value of 10. Figure 29. Graph. Scourdepth relationship based on local hydraulic variables for VW and ST abutments with L subscript A divided by B subscript F values greater than or equal to 0.88 and lowercase D subscript 50 equal to 3.3 mm. This graph plots data for verticalwall and spillthrough abutments with L Subscript A divided by B subscript F values, which is the abutment length divided by the width of the floodplain, of 0.88, 0.97, and 1. The Xaxis is the quotient of V subscript lowercase AB divided by V subscript lowercase C, which is the maximum resultant velocity at the upstream abutment corner divided by the critical velocity for initiation of motion, minus 1 ranging from 0.1 to 10 on a logarithmic scale. The Yaxis is the normalized scourdepth, or lowercase D subscript lowercase S divided by lowercase Y subscript lowercase F zero ranging from 0.1 to 100 on a logarithmic scale. The data points for the VW abutment with an L Subscript A divided by B subscript F value of 0.97, and all of the data points for the ST abutment are in a tight grouping around the coordinates 9, 5.5. The data points for the VW abutments with L Subscript A divided by B subscript F values of 0.88 and 1 appear in a grouping at coordinates 1.4, 0.4. A bestfit trendline is plotted on the graph and begins at coordinates 0.35, zero, and rises linearly to a normalized scourdepth plateau point of 10 that begins at coordinates 10, 2. Only a couple of the data points are intersected by the bestfit line, with the majority of points clustered in groups with normalized scourdepth values higher than those of the bestfit line. Figure 30A. Graph. Relationship between local and approach hydraulic variables. This graph plots data for three cases, verticalwall compound channel A and B, and spillthrough compound channel B with L Subscript A divided by B subscript F values, which is the abutment length divided by the width of the floodplain, less than or equal to 0.66. The Xaxis is lowercase Q subscript lowercase F 1 divided by M multiplied by lowercase Q subscript lowercase F zero lowercase C, which is the flow rate per unit width in the approach floodplain divided by the discharge distribution factor multiplied by the critical flow rate per unit width in the floodplain at normal depth, minus 0.4 ranging from 0.1 to 10 on a logarithmic scale. Yaxis is the quotient of V subscript lowercase AB divided by V subscript lowercase C, which is the maximum resultant velocity at the upstream abutment corner divided by the critical velocity for initiation of motion, minus 1 ranging from 0.1 to 10 on a logarithmic scale. The data points for the three cases are in a linear grouping that begins at coordinates 0.5, 0.25, and ends at coordinates 1.5, 1. A bestfit equation trendline is plotted on the graph and begins at coordinates zero, 0.12, and ends at coordinates 1.9, 1.2. The data points correlate very well with the bestfit equation trendline. Figure 30B. Graph. Relationship between local and approach hydraulic variables. This graph plots data for two cases, verticalwall and spillthrough wall for compound B with L Subscript A divided by B subscript F values which is the abutment length divided by the width of the floodplain, greater than or equal to 0.88. The Xaxis is the quotient of lowercase Q subscript lowercase F 1 divided by M multiplied by lowercase Q subscript lowercase F zero C, which is the flow rate per unit width in the approach floodplain divided by the discharge distribution factor multiplied by the critical flow rate per unit width in the floodplain at normal depth, minus 0.4 ranging from 0.1 to 10 on a logarithmic scale. The Yaxis is the quotient of V subscript lowercase AB divided by V subscript lowercase C, which is the maximum resultant velocity at the upstream abutment corner divided by the critical velocity for initiation of motion, minus 1 ranging from 0.1 to 10 on a logarithmic scale. The data points for the two cases appear somewhat scattered on the graph. There is a grouping of several points about the coordinates 1, 1.5. A bestfit equation trendline is plotted on the graph and begins at coordinates zero, 0.12, and ends at a coordinates 1.9, 1.2. The data points do not correlate very well with the bestfit equation trendline. Figure 31. Graph. Livebed contraction scour coefficient for L subscript lowercase A divided by B subscript lowercase F equal to 1. This graph plots the live bed coefficient for a range of approach to critical sheer stress ratios at 5 different approach to main channel width ratios, 0.25, 0.5, 1, 2, and 3. The Xaxis represents the approach to critical sheer stress ratio or tau subscript lowercase 1 divided by tau subscript lowercase C, which is the Shields' parameter in the approach section divided by the Shields' parameter, ranging from 1 to 5. The Yaxis represents the livebed scour coefficient or C subscript LB ranging from zero to 3. The line plotted for the channel width ratio of 0.25 has a relatively flat C subscript LB value across the range of sheer stress values, going from coordinates 0.3, 1, to coordinates 0.4, 5. The line plotted for the channel width ratio of 0.5 also has a relatively flat C subscript LB value across the range of sheer stress values, going from coordinates 0.55, 1, to coordinates 0.65, 5. The line plotted for the channel width ratio of 1 has a perfectly flat C subscript LB value of 1 across the range of sheer stress values. The line plotted for the channel width ratio of 2 begins at coordinates 1.8, 1, with a gradual transition to a relatively flat line that ends at coordinates 1.55, 5. The line plotted for the channel width ratio of 3 begins at coordinates 2.55, 1, with a transition to a relatively flat line that ends at coordinates 1.9, 5. The higher the channel width ratio, the higher the livebed scour coefficient. Figure 32. Graph. Calculated and measured watersurface profiles for compound channel A. The graph plots the measured surface water profile and those that are determined by a 2D model, and a WSPRO model for a compound channel A with a verticalwall abutment, a L lowercase A divided by B lowercase F value, which is the abutment length divided by the width of the floodplain, of 0.33, and a flow of 0.0567 cubic meters per second. The Xaxis represents the longitudinal station points in meters ranging from zero to 18, with the abutment located at station 9.8. The Yaxis is depth in meters ranging from 0.15 to 0.25 meters. The normal depth is plotted as a straight line at a depth of 0.183 meters. The plot of the data from the WSPRO model shows a rise in depth to 0.197 meters just before the abutment and then a steep drop to a depth of 0.187 meters exiting the abutment. The plot of the data from the 2D model shows a rise in depth to 0.195 meters just before the abutment and then a steep drop to a depth of 0.176 meters exiting the abutment. The plot of the measured data shows a rise in depth to 0.194 meters just before the abutment and then a steep drop to 0.176 meters exiting the abutment. Of the two models, the 2D model appears to correlate best with the measured surface water profile. Figure 33. Graph. Calculated and measured approach velocity distributions for compound channel A. The graph plots the measured velocity profile and those that are determined by a 2D model, and a WSPRO model for a compound channel A with a verticalwall abutment, a L lowercase A divided by B lowercase F value, which is the abutment length divided by the width of the floodplain, of 0.33, and a flow of 0.0567 cubic meters per second. The Xaxis represents the transverse station points in meters ranging from zero to 2.2. The Yaxis is longitudinal velocity ranging from zero to 1 meter per second. The BED and WSE elevation in meters are also plotted on a secondary Yaxis that ranges from zero to 1 meter. The plot of the data from the WSPRO model shows a velocity of 0.35 meters per second across the left floodplain, then drops to 0.2 meters per second at the main channel wall, rises to 0.7 meters per second across the main channel, then drops back to 0.2 meters per second at the other main channel wall, and then rises to 0.35 meters per second across the right floodplain. The plot of the data from the 2D model shows a velocity of 0.35 meters per second across the left floodplain, then rises to 0.5 meters per second at the main channel wall, then rises to 0.7 meters per second across the main channel, then drops back to 0.5 meters per second at the other main channel wall, and then drops to 0.35 meters per second across the right floodplain. The plot of the measured data shows a velocity of 0.35 meters per second across the left floodplain, then rises to 0.5 meters per second at the main channel wall, then rises to 0.65 meters per second across the main channel, then drops back to 0.5 meters per second at the other main channel wall, and then drops to 0.38 meters per second across the right floodplain. Both models correlate reasonably with measured velocities in the approach section. The WSE elevation is constant at 0.25 meters across the compound channel. Figure 34. Graph. Calculated and measured resultant velocity distributions for the contracted section for compound channel A. The graph plots the measured velocity profile and those that are determined by a 2D model for a compound channel A with a verticalwall abutment, a L lowercase A divided by B lowercase F value, which is the abutment length divided by the width of the floodplain, of 0.33, and a flow of 0.0567 cubic meters per second. The Xaxis represents the transverse station points in meters ranging from zero to 2.2. The Yaxis is resultant velocity ranging from zero to 1 meter per second. The BED and WSE 2D model elevation in meters are also plotted on a secondary Yaxis that ranges from zero to 1 meter. The plot of the data from the 2D model shows a velocity of 0.54 meters per second at the edge of the left abutment, which then slopes down to 0.44 meters per second at the main channel wall, then rises to 0.78 meters per second at the center of the main channel, then slopes downward to 0.44 meters per second at the other main channel wall, and then slopes back up to 0.54 meters per second at the edge of the right abutment. The plot of the measured data shows a velocity of 0.54 meters per second near the edge of the left abutment, which then slopes down to 0.46 meters per second approaching the main channel wall, then rises to 0.75 meters per second at the center of the main channel, then slopes downward to 0.46 meters per second just past the other main channel wall, and then slopes back up to 0.55 meters per second at the near the edge of the right abutment. The 2D model appears to correlate well with the measured resultant velocity profile even at the end of the abutment. The WSE elevation is constant at 0.29 meters across the contraction section. Figure 35. Graph. Calculated and measured watersurface profiles for compound channel B. The graph plots the measured surface water profile and those that are determined by a WSPRO model for a compound channel B with a verticalwall abutment, a L lowercase A divided by B lowercase F value, which is the abutment length divided by the width of the floodplain, of 0.44, and a flow of 3 cubic feet per second. The Xaxis represents the longitudinal station points in feet ranging from zero to 60, with the abutment located at station 33. The Yaxis is depth in feet ranging from 0.5 to 0.85 meters. The normal depth is plotted as a straight line at a depth of 0.63 feet. The plot of the data from the WSPRO model starts at a depth of 0.66 feet and station 4, and then rises to a depth of 0.68 feet at station point 22, and then the plot stops and reappears at station 44 at the normal depth line 0f 0.63 feet. There is no WSPRO model depth data around the abutment. The plot of the measured data starts at a depth of 0.64 feet and then shows a rise in depth to 0.67 feet just before the abutment, and then a steep drop to 0.6 feet exiting the abutment, and then a gradual rise back up to normal depth downstream of the abutment. Figure 36. Graph. Calculated and measured approach velocity distributions for compound channel B. The graph plots the measured velocity profile and a 2D model for a compound channel A with a verticalwall abutment, a L lowercase A divided by B lowercase F value, which is the abutment length divided by the width of the floodplain, of 0.44, and a flow of 0.085 cubic meters per second. The Xaxis represents the transverse station points in meters ranging from zero to 4.2. The Yaxis is resultant velocity ranging from zero to 1 meter per second. The BED and measured WSE elevation in meters are also plotted on a secondary Yaxis that ranges from zero to 1 meter. The plot of the data from the WSPRO model shows a velocity of about 0.25 meters per second at the left edge of the floodplain channel, which then gradually slopes up to a velocity of 0.3 meters per second at the beginning of the main channel, and then rises to 0.49 meters per second at the center of the main channel. The plot of the measured data shows a velocity of about 0.25 meters per second at the left edge of the floodplain channel, which then gradually slopes up to a velocity of 0.31 meters per second at the beginning of the main channel, and then rises to 0.48 meters per second at the center of the main channel. The WSPRO model appears to correlate well with the measured resultant velocity profile in the approach section. The measured WSE elevation is constant at 0.29 meters across the approach section. Figure 37. Graph. Comparisons of approach floodplain velocities for a compound channel. The graph plots the calculated approach velocity, or V lowercase F 1 determined by 2D and WSPRO models by the measured approach velocity V lowercase F1 for compound channel A and B, with a verticalwall abutment and spillthrough abutment. The Xaxis represents the measured approach velocity in meters per second ranging zero to 0.6. The Yaxis is calculated approach velocity ranging from zero to 0.6 meters per second. The graph is dissected diagonally by a Y equals X line. The plot of the data from the WSPRO model for a compound channel B, with verticalwall and spillthrough wall cases matches up well with the measured data, with almost all of the points on, or close to the diagonal Y equals X line. Both the WSPRO and 2D model data for a compound channel A, verticalwall abutment scenarios are somewhat scattered around the Y equals X line, with the 2D model data being much closer, and thus a better model in this scenario. Figure 38. Graph. Comparisons of approach floodplain depths for a compound channel. The graph plots the calculated approach depth, or Y lowercase F 1 determined by 2D and WSPRO models by the measured approach depth Y lowercase F1 for compound channel A and B, with a verticalwall abutment and spillthrough abutment. The Xaxis represents the measured approach depth in meters ranging zero to 0.1. The Yaxis is calculated approach depth ranging from zero to 0.1 meters. The graph is dissected diagonally by a Y equals X line. The majority of the plotted data from the WSPRO and 2D models is consistently higher than the diagonal Y equals X line. The modeled data plots are all relatively parallel to the Y equals X line, but are on average shifted up by 0.01 meters. However, the plotted 2D model data is just slightly below the Y equals X line. Figure 39. Graph. Comparisons of discharge Distribution factor for a compound channel. The graph plots the calculated discharge distribution factor, or M determined by 2D and WSPRO models by the measured discharge distribution factor, or M for compound channel A and B, with a verticalwall abutment and spillthrough abutment. The Xaxis represents the measured M ranging zero to 1. The Yaxis is calculated M ranging from zero to 1. The graph is dissected diagonally by a Y equals X line. The plot of the data from the WSPRO and 2D models for a compound channel A, with verticalwalls matches up well with the measured data, with almost all of the points slightly higher than the diagonal Y equals X line. The WSPRO model data for a compound channel B, with verticalwall and spillthrough abutment scenarios are plotted lower than the Y equals X line by about 0.05 on average. Figure 40. Graph. Comparisons of maximum velocity at abutment face for a compound channel. The graph plots the calculated maximum velocity at abutment face, or V lowercase AB determined by a WSPRO model by the measured maximum velocity at abutment face, or V lowercase AB for compound channel B, with a verticalwall abutment and spillthrough abutment. The Xaxis represents the measured maximum velocity at abutment face ranging zero to 1.2. The Yaxis is calculated maximum velocity at abutment face ranging from zero to 1.2. The graph is dissected diagonally by a Y equals X line. The plot of the data from the WSPRO models for verticalwall and spillthrough abutments are significantly lower than the diagonal Y equals X line, and relatively scattered, which give the appearance of poor correlation between the calculated and measured data. Figure 41. Graph. Dimensionless representation of time development of scour. This graph plots data for V lowercase R values of 1.25, 1.5, 2, and 2.5, and assorted sediment size D 50 values of 1.1, 2.7, and 3.3 millimeters. V lower case R is defined as the resultant velocity at the abutment face divided by the critical velocity for the initiation of motion. The Xaxis is the quotient of V subscript lowercase C multiplied by lowercase T, or critical velocity at time T, divided by Y subscript lowercase F zero, or normal floodplain depth ranging from 1 times 10 to third power to 1 times 10 to the seventh power on a logarithmic scale. The Yaxis is the normalized scourdepth, or D subscript lowercase S T, or unsteady scour depth at time T, divided by Y subscript lowercase F zero, or normal floodplain depth, ranging from zero to 10. The data points for the V lowercase R value of 1.25 begin around the coordinates1.5, 0.0012 and rise in an approximately linear fashion to the coordinates 3.5, 0.000001. The data points for the V lowercase R value of 1.5 begin around the coordinates 2, 0.0012 and rise in an approximately linear fashion to the coordinates 4.5, 0.000001. The data points for the V lowercase R value of 2 begin around the coordinates 2.5, 0.0012 and rise in an approximately linear fashion to the coordinates 7, 0.000001. The data points for the V lowercase R value of 2.5 begin around the coordinates 3, 0.0012 and rise in an approximately linear fashion to the coordinates 9.5, 0.000001. A bestfit regression trendline is plotted through the data points of each four cases. Each of the four cases has relative plateaus in the trendlines where the maximum Yvalues are reached. Figure 42. Graph. Comparisons of measured and predicted scour depths using the Melville formula. The graph plots the calculated scour depth, or DS, determined by the Mellville model by the measured scour depth. The Xaxis represents the measured scour depth ranging zero to 50 in centimeters. The Yaxis is calculated scour depth ranging from zero to 50 centimeters. The graph is dissected diagonally by a Y equals X line, and there are lines extending out from the origin delineating the plus or minus 30 percent range. The plot of the data from the Melville model is relatively scattered with most of the points above the diagonal Y equals X line. Approximately half of the points fall within the plus or minus 30 percent lines, with the other half falling above the plus 30 percent line. Figure 43. Graph. Comparisons of measured and predicted scour depths using the Froehlich clearwater scour formula. The graph plots the calculated scour depth, or DS, determined by the Froehlich CWS model by the measured scour depth. The Xaxis represents the measured scour depth ranging zero to 50 in centimeters. The Yaxis is calculated scour depth ranging from zero to 50 centimeters. The graph is dissected diagonally by a Y equals X line, and there are lines extending out from the origin delineating the plus or minus 30 percent range. The plot of the data from the Froehlich CWS model is relatively scattered with most of the points above the diagonal Y equals X line. Approximately half of the points fall within the plus or minus 30 percent lines, with the other half falling above the plus 30 percent line. There are also several points with larger measured scour depths that are greatly underestimated by the model. Figure 44. Graph. Comparisons of measured and predicted scour depths using the Froehlich livebed scour formula. The graph plots the calculated scour depth, or DS, determined by the Froehlich LBS model by the measured scour depth. The Xaxis represents the measured scour depth ranging zero to 50 in centimeters. The Yaxis is calculated scour depth ranging from zero to 50 centimeters. The graph is dissected diagonally by a Y equals X line, and there are lines extending out from the origin delineating the plus or minus 30 percent range. The plot of the data from the Froehlich LBS model is relatively scattered with most of the points above the diagonal Y equals X line. Approximately a third of the points fall within the plus or minus 30 percent lines, with most of the remaining points falling above the plus 30 percent line. Figure 45. Graph. Comparisons of measured and predicted scour depths using the G.K. Young (GKY) formula. The graph plots the calculated scour depth, or DS, determined by the GKY model by the measured scour depth. The Xaxis represents the measured scour depth ranging zero to 50 in centimeters. The Yaxis is calculated scour depth ranging from zero to 50 centimeters. The graph is dissected diagonally by a Y equals X line, and there are lines extending out from the origin delineating the plus or minus 30 percent range. The plot of the data from the GKY model is slightly scattered with almost all of the points falling below the minus 30 percent line. Figure 46. Graph. Comparisons of measured and predicted scour depths using the Maryland formula. The graph plots the calculated scour depth, or DS, determined by the MD model by the measured scour depth. The Xaxis represents the measured scour depth ranging zero to 50 in centimeters. The Yaxis is calculated scour depth ranging from zero to 50 centimeters. The graph is dissected diagonally by a Y equals X line, and there are lines extending out from the origin delineating the plus or minus 30 percent range. The plot of the data from the MD model is slightly scattered with most of the points falling below the minus 30 percent line, and approximately 30 percent falling within the plus or minus 30 percent range. Figure 47. Graph. Comparisons of measured and predicted scour depths using the formula from the present study. The graph plots the calculated scour depth, or DS, determined by the present study model by the measured scour depth. The Xaxis represents the measured scour depth ranging zero to 50 in centimeters. The Yaxis is calculated scour depth ranging from zero to 50 centimeters. The graph is dissected diagonally by a Y equals X line, and there are lines extending out from the origin delineating the plus or minus 30 percent range. The data plotted using this model almost completely falls within the plus or minus 30 percent lines, and is distributed about 5050 above and below the Y equals X line. There are only a few points located above the plus 30 percent line, and these are found primarily at the lowest scour depth. Figure 48. Graph. Cross sections and watersurface elevation for Burdell Creek bridge. This graph details the cross section and water surface elevations for the Burdell creek bridge, which has a drainage area of 971 square miles and 100year flow of 397 cubic meters per second. The bottom chord and bridge roadway are detailed on the graph at elevation of 5.5 and 6.7 meters, respectively. The Manning's N values are 0.032 for the floodplains and 0.042 for the mainchannel. The water surface elevation at the bridge abutment is given as 3.8 meters. The Xaxis is the transverse station in meters ranging from zero to 800. The Yaxis is the elevation in meters ranging from zero to 8. The left hand edge of the channel starts with an elevation of 5.8 meters and then drops to a floodplain elevation of about 3.2 meters, the central main channel then drops to an elevation of 1 meter, and the right side floodplain elevation rises again to 3.2 meters. Figure 49. Graph. Design 100year hydrograph for Burdell Creek. This graph plots the design 100year hydrograph for Burdell creek. The Xaxis is time in hours ranging from zero to 40. The Yaxis is flow in cubic meters per second ranging from zero to 600. The curve begins at coordinates 50, 4, and follows a bell shaped rise to a peak at coordinates 390, 14, and the falls at a slightly elongated bell shaped path to the coordinates 50, 35. Figure 50. Graph. Cross sections for Highway 22 over the Pomme de Terre River for the flood of April 9, 1997. This graph details the cross section of highway 22 over the Pomme de Terre River during the flood of April 9, 1997. The elevations for the upstream edge of the bridge, the Full Valley, highway 22, and the upstream water surface are given. The Xaxis is station in meters from minus 700 to minus 300. The Yaxis is elevation in meters from 305 to 330. The Full Valley is shown to have a minimum elevation of 313.8 meters in the channel between the two bridge piers of the abutment contraction. After the scour event, the minimum elevation of the channel on the upstream side of the bridge is 311.3 meters between the two bridge piers, and the overall depth of the channel in the abutment contraction is lower than the channel elevation given for the Full Valley. The water surface elevation between the abutment contraction on the upstream side is shown to be about 317.3 meters at the time of the flood, and the road surface elevation is about 319 meters. Figure 51. Graph. Cross sections for Highway 12 over the Pomme de Terre River for the flood of April 9, 1997. This graph details the cross section of highway 12 over the Pomme de Terre River during the flood of April 9, 1997. The elevations for the upstream edge of the bridge before scour, the upstream edge of the bridge after scour, the Full Valley, highway 12, contraction exit, contraction approach, and the upstream water surface are given. The Xaxis is station in meters from 100 to 700. The Yaxis is elevation in meters from 290 to 315. The upstream edge of the bridge is shown to have a minimum elevation of 298.5 meters in the channel next the right abutment before scour. After the scour event, the minimum elevation of the channel on the upstream side of the bridge is 293.5 meters next to the right abutment, and the overall depth of the channel in the abutment contraction appears to be reduced by about 4 meters. The water surface elevation between the abutment contraction on the upstream side is shown to be about 302.6 meters at the time of the flood, and the road surface elevation is about 304.5 meters. 
Topics: research, infrastructure, hydraulics Keywords: research, infrastructure, hydraulics, Bridge scour, abutment scour, compound channels TRT Terms: research, hydraulics, hydrology, fluid mechanics, earth sciences, geophysics Updated: 07/09/2014
