Figure 1.
Graphical representation of the variables, hu, hb, and s, used in Equations (1) and (2).
Figure 1.
Graphical representation of the variables, hu, hb, and s, used in Equations (1) and (2).
Figure 2.
Schematic of forces on the bridge deck. FR,bear is bearing (friction) force. Fz,d is weight. FB,d is buoyancy. FL,d is lift. FD,d is drag. Mcg,d is the centroidal moment.
Figure 2.
Schematic of forces on the bridge deck. FR,bear is bearing (friction) force. Fz,d is weight. FB,d is buoyancy. FL,d is lift. FD,d is drag. Mcg,d is the centroidal moment.
Figure 3.
Yabitsu bridge before flood (upper) and after (lower).
Figure 3.
Yabitsu bridge before flood (upper) and after (lower).
Figure 4.
Laboratory setup, including debris damming on the upstream face of decks. The far deck is outfitted with the load cell, while the other two decks are free standing.
Figure 4.
Laboratory setup, including debris damming on the upstream face of decks. The far deck is outfitted with the load cell, while the other two decks are free standing.
Figure 5.
Laboratory setup with one pier connected to the load cell, and the other pier and abutments free standing.
Figure 5.
Laboratory setup with one pier connected to the load cell, and the other pier and abutments free standing.
Figure 6.
1:37 scale model of the Yabitsu Bridge.
Figure 6.
1:37 scale model of the Yabitsu Bridge.
Figure 7.
Self-standing pier failure without the deck.
Figure 7.
Self-standing pier failure without the deck.
Figure 8.
Laboratory setup showing the rigidly connected deck-pier system with excessive debris damming.
Figure 8.
Laboratory setup showing the rigidly connected deck-pier system with excessive debris damming.
Figure 9.
Self-weight restoring moment of the deck-pier system (about the heel of the pier) minus the hydrodynamic overturning moment, as measured by the load cell.
Figure 9.
Self-weight restoring moment of the deck-pier system (about the heel of the pier) minus the hydrodynamic overturning moment, as measured by the load cell.
Figure 10.
Results of the free standing deck experiments. Green cells indicate that no deck failure was observed, while red cells mean that failure occurred consistently across repeated tests. Yellow cells indicate critical conditions, i.e., the deck would be stable for some time (a few tens of seconds), but then collapse. Grey cells represent conditions that were above the maximum achievable Froude number or above a realistic inundation ratio. The number in each cell corresponds to the Froude number of that test. Light green and light yellow colors indicate that no specific experiments were conducted at these conditions, but an outcome was predicted based on the outcomes of neighboring experiments.
Figure 10.
Results of the free standing deck experiments. Green cells indicate that no deck failure was observed, while red cells mean that failure occurred consistently across repeated tests. Yellow cells indicate critical conditions, i.e., the deck would be stable for some time (a few tens of seconds), but then collapse. Grey cells represent conditions that were above the maximum achievable Froude number or above a realistic inundation ratio. The number in each cell corresponds to the Froude number of that test. Light green and light yellow colors indicate that no specific experiments were conducted at these conditions, but an outcome was predicted based on the outcomes of neighboring experiments.
Figure 11.
Drag coefficients measured with the load cell, compared with those of the three girder deck of Kerenyi et al. [
6]. The dashed line corresponds to the values of Kerenyi et al. [
6]. Note that C
D values at h* = 0.13 are based on forces close to the resolution limit of the load cell.
Figure 11.
Drag coefficients measured with the load cell, compared with those of the three girder deck of Kerenyi et al. [
6]. The dashed line corresponds to the values of Kerenyi et al. [
6]. Note that C
D values at h* = 0.13 are based on forces close to the resolution limit of the load cell.
Figure 12.
Pier drag coefficients. It can be seen that the values approach the canonical value of 0.7 [
14] as the flow depth, h
u, keeps increasing. However, blockage and free surface effects are clearly visible at low flow depths where the pier is not fully submerged.
Figure 12.
Pier drag coefficients. It can be seen that the values approach the canonical value of 0.7 [
14] as the flow depth, h
u, keeps increasing. However, blockage and free surface effects are clearly visible at low flow depths where the pier is not fully submerged.
Figure 13.
Self-weight restoring moment of the pier (about the heel of the pier) minus the hydrodynamic overturning moment, as measured by the load cell. The only observed failure in the free standing experiments is indicated by the green circle.
Figure 13.
Self-weight restoring moment of the pier (about the heel of the pier) minus the hydrodynamic overturning moment, as measured by the load cell. The only observed failure in the free standing experiments is indicated by the green circle.
Figure 14.
Boundary conditions of the numerical simulation.
Figure 14.
Boundary conditions of the numerical simulation.
Figure 15.
Mesh distribution around the deck. Fine mesh resolution is used near the bridge and at the free surface elevation. Coarser mesh resolution is defined above the free surface where only air exists. Mesh resolution becomes coarser moving away from the deck towards the inlet and outlet. Near the deck, the mesh is flexible quadrilateral, while it is rectangular elsewhere. The inset shows a magnified view of the flexible quadrilateral mesh for the case of the three-girder bridge used in
Section 3.2.5 below.
Figure 15.
Mesh distribution around the deck. Fine mesh resolution is used near the bridge and at the free surface elevation. Coarser mesh resolution is defined above the free surface where only air exists. Mesh resolution becomes coarser moving away from the deck towards the inlet and outlet. Near the deck, the mesh is flexible quadrilateral, while it is rectangular elsewhere. The inset shows a magnified view of the flexible quadrilateral mesh for the case of the three-girder bridge used in
Section 3.2.5 below.
Figure 16.
Comparison of numerical and experimental results in terms of force coefficients on the submerged rectangular cylinder.
Figure 16.
Comparison of numerical and experimental results in terms of force coefficients on the submerged rectangular cylinder.
Figure 17.
Bridge and water depth configurations. Scenario1 (left picture): Fixed proximity ratio, pr = 2.5. Scenario 2 (middle picture): Constant Blockage ratio, Br = 0.17. Scenario 3 (right picture): Constant inundation ratio, h* = 2.
Figure 17.
Bridge and water depth configurations. Scenario1 (left picture): Fixed proximity ratio, pr = 2.5. Scenario 2 (middle picture): Constant Blockage ratio, Br = 0.17. Scenario 3 (right picture): Constant inundation ratio, h* = 2.
Figure 18.
Drag coefficient versus inundation ratio for different upstream velocities.
Figure 18.
Drag coefficient versus inundation ratio for different upstream velocities.
Figure 19.
(Top left) Hydraulic jump downstream of the bridge, h* = 2, Frs = 0.97. (Top right) Total pressure (Pa) in the flow around the deck. (Bottom left) Pressure coefficient on upstream and downstream faces of the deck. (Bottom right) Pressure coefficient on upper and lower faces of the deck.
Figure 19.
(Top left) Hydraulic jump downstream of the bridge, h* = 2, Frs = 0.97. (Top right) Total pressure (Pa) in the flow around the deck. (Bottom left) Pressure coefficient on upstream and downstream faces of the deck. (Bottom right) Pressure coefficient on upper and lower faces of the deck.
Figure 20.
Effect of boundaries (free surface and bottom channel) on the lift coefficient for hu/s = 6.
Figure 20.
Effect of boundaries (free surface and bottom channel) on the lift coefficient for hu/s = 6.
Figure 21.
Streamlines of mean velocities around the deck for different inundation ratios, Frs = 0.24.
Figure 21.
Streamlines of mean velocities around the deck for different inundation ratios, Frs = 0.24.
Figure 22.
Drag coefficient (left) and lift coefficient (right) versus the blockage ratio. Based on the two scenarios of undisturbed upstream velocity and local velocity (dotted lines). h* = 2.
Figure 22.
Drag coefficient (left) and lift coefficient (right) versus the blockage ratio. Based on the two scenarios of undisturbed upstream velocity and local velocity (dotted lines). h* = 2.
Figure 23.
Pressure coefficient in the upstream and downstream side of the deck for different blockage ratios.
Figure 23.
Pressure coefficient in the upstream and downstream side of the deck for different blockage ratios.
Figure 24.
Comparison of contour lines of the threshold of deck failure between the Eurocode (C
D = 1.44) [
5] and this research for a box deck. Numbers on the figure demonstrate the blockage ratio (Br) for each failure point. To the right of each line is the unstable region, and the stable region is to the left. These stability curves hold for a comcrete box girder with a 48% void ratio, an aspect ratio (height:width) of 0.27, and a bearing friction coefficient of 0.25.
Figure 24.
Comparison of contour lines of the threshold of deck failure between the Eurocode (C
D = 1.44) [
5] and this research for a box deck. Numbers on the figure demonstrate the blockage ratio (Br) for each failure point. To the right of each line is the unstable region, and the stable region is to the left. These stability curves hold for a comcrete box girder with a 48% void ratio, an aspect ratio (height:width) of 0.27, and a bearing friction coefficient of 0.25.
Figure 25.
Drag coefficient for box deck based on the proximity ratio (Pr—1.5,2,2.5,3), inundation ratio (h*—0.5,1,2,3), and Froude number (Fr—0.30,0.45,0.65,0.80). These drag coefficients hold for a rectangular deck with an aspect ratio (height:width) of 0.27.
Figure 25.
Drag coefficient for box deck based on the proximity ratio (Pr—1.5,2,2.5,3), inundation ratio (h*—0.5,1,2,3), and Froude number (Fr—0.30,0.45,0.65,0.80). These drag coefficients hold for a rectangular deck with an aspect ratio (height:width) of 0.27.
Figure 26.
Schematic shape of the deck using end caps for flood force mitigating effect. Displayed on the left are Scenario 6 (top), Scenario 5 (middle), and Scenario 4 (bottom).
Figure 26.
Schematic shape of the deck using end caps for flood force mitigating effect. Displayed on the left are Scenario 6 (top), Scenario 5 (middle), and Scenario 4 (bottom).
Figure 27.
(Left) Lift coefficient versus h* for six different end caps. (Pr = 3, Fr = 0.3). (Right) Drag coefficient versus h* for six different end caps. (Pr = 3, Fr = 0.3).
Figure 27.
(Left) Lift coefficient versus h* for six different end caps. (Pr = 3, Fr = 0.3). (Right) Drag coefficient versus h* for six different end caps. (Pr = 3, Fr = 0.3).
Figure 28.
Contour lines of the threshold of failure for Scenario 5 end caps attached to the deck.
Figure 28.
Contour lines of the threshold of failure for Scenario 5 end caps attached to the deck.
Figure 29.
Dimensions of three girder deck in mm.
Figure 29.
Dimensions of three girder deck in mm.
Figure 30.
Comparison of force and centroidal moment coefficients between the box deck and three girder deck.
Figure 30.
Comparison of force and centroidal moment coefficients between the box deck and three girder deck.
Figure 31.
Streamlines of mean velocities around the box deck and three girder deck, Fr = 0.32, Pr = 1.5, h* = 2.
Figure 31.
Streamlines of mean velocities around the box deck and three girder deck, Fr = 0.32, Pr = 1.5, h* = 2.
Figure 32.
Comparison of the pressure coefficient between the box deck and three girder deck, Fr = 0.32, h* = 2.
Figure 32.
Comparison of the pressure coefficient between the box deck and three girder deck, Fr = 0.32, h* = 2.
Table 1.
Dimensions of the scale bridge model (Colors refer to
Figure 6).
Table 1.
Dimensions of the scale bridge model (Colors refer to
Figure 6).
Bridge Deck (Yellow) | Laboratory Model | Yabitsu Bridge (Actual) |
---|
Length (along road axis) | 254 mm | 9.4 m |
Width (along river axis) | 142 mm | 5.3 m |
Height | Girders: 19 mm Deck: 11 mm | Girders: 700 mm Deck: 410 mm |
Base of the pier (red) | | |
Length (along river axis) | Bottom:127 mm Top: 113 mm | Bottom: 4.7 m Top: 4.2 m |
Width (along road axis) | Bottom: 41 mm Top: 49 mm | Bottom: 1.5 m Top: 1.8 m |
Height | 129 mm | 4.8 m |
Pier foundation (brown) | | |
Length (along river axis) | 147 mm | 5.4 m |
Width (along road axis) | 61 mm | 2.3 m |
Height | 22 mm | 814 mm |
Abutment (green) | | |
Length (along river axis) | 96 mm | 3.6 m |
Width (along road axis) | 76 mm | 2.8 m |
Height | 151 mm | 5.6 m |
Table 2.
Dimensions of debris used for damming the pier.
Table 2.
Dimensions of debris used for damming the pier.
| Wet Weight (g) | Volume (cm3) | Frontal Area (cm2) |
---|
Debris shape XXL | 382 | 545 | 100 |
Debris shape XL | 292 | 417 | 83 |
Table 3.
Flow conditions investigated.
Table 3.
Flow conditions investigated.
Hypothesis 1—deck—without debris | hu = 12.0 cm to 20.0 cm | Fr = 0.33 to 0.52 |
Hypothesis 1—deck—with debris | hu = 13.0 cm to 19.0 cm | Fr = 0.10 to 0.52 |
Hypothesis 1—pier—without debris | hu = 8.0 cm to 21.0 cm | Fr = 0.40 to 0.62 |
Hypothesis 1—pier—with debris | hu = 8.0 cm to 17.0 cm | Fr = 0.34 to 0.52 |
Hypothesis 2—combination—without debris | hu = 12.0 cm to 21.0 cm | Fr = 0.52 |
Hypothesis 2—combination—with debris | hu = 16.0 cm to 21.0 cm | Fr = 0.52 |
Table 4.
Summary of the experimental conditions used for Fluent model validation.
Table 4.
Summary of the experimental conditions used for Fluent model validation.
Flume Length (m) | Deck Length (m) | Deck Thickness, S (m) | hb (m) | hu (m) | Fr (−) |
---|
5 | 0.18 | 0.06 | 0.14 | 0.1–0.4 | 0.1–0.15 |
Table 5.
Summary of the numerical configuration.
Table 5.
Summary of the numerical configuration.
Time step size (s) | 0.005 |
Iteration per time step | 20 |
Multiphase model | Volume Of Fluid (VOF) |
Pressure—velocity coupling scheme | Simple |
Spatial discretization of momentum, turbulent kinetic energy, and specific dissipation rate | Second order upwind |
Under relation factor for pressure | 0.3 |
Under relaxation factors for remaining parameters | 0.7 |
Mesh method/size | Multi-block technique/1 mm–1 cm |
Table 6.
Comparison of drag coefficients between AS5100 [
7] and this study. Red numbers indicate situations when AS5100 [
7] fails to be conservative.
Table 6.
Comparison of drag coefficients between AS5100 [
7] and this study. Red numbers indicate situations when AS5100 [
7] fails to be conservative.
Pr | h* | CD—AS5100 | CD—Numerical |
---|
1.5 | 3 | 3.35 | 2.49 |
2 | 3 | 2.9 | 2.26 |
2.5 | 3 | 2.5 | 2.14 |
3 | 3 | 2.35 | 2.06 |
1.5 | 2 | 3.35 | 2.85 |
2 | 2 | 2.9 | 2.5 |
2.5 | 2 | 2.5 | 2.31 |
3 | 2 | 2.35 | 2.2 |
1.5 | 1 | 2.1 | 2.7 |
2 | 1 | 1.93 | 2.3 |
2.5 | 1 | 1.8 | 2.09 |
3 | 1 | 1.65 | 1.94 |
Table 7.
Dimensions of the end caps.
Table 7.
Dimensions of the end caps.
| Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | Scenario 5 | Scenario 6 |
---|
| 1 | 0.5 | 0 | 1 | 0.5 | 0 |
| 0.5 | 0.5 | 0.5 | 1 | 1 | 1 |