Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, Japan

CFD ANALYSIS OF BRIDGE DECK FAILURE DUE TO
TSUNAMI
Jeremy D. BRICKER1, Kazuhiko KAWASHIMA2, and Akihiko NAKAYAMA3
1

Visiting Associate Professor, Department of Civil Engineering, Tokyo Institute of Technology,
Tokyo, Japan, Jeremy.bricker@gmail.com
2
Professor, Department of Civil Engineering, Tokyo Institute of Technology,
Tokyo, Japan, kawashima.k.ae@m.titech.ac.jp
3
Professor, Department of Civil Engineering, Kobe University,
Kobe, Japan, nakayama@kobe-u.ac.jp
ABSTRACT: The Tsunami resulting from the Great East Japan Earthquake caused failureof many bridges in Miyagi and Iwate Prefectures. Field surveys and numerical modelingwere carried out to evaluate possible mechanisms of failure of these bridges. The
OpenFOAM Computational Fluid Dynamics package was used to determine the effects oflift, drag, and moment on a typical bridge deck based on two-dimensional
Reynolds-averaged simulations. Results show that deck inclination, flow speed, trapped
air, entrained sediment, and tsunami surge all contribute to deck failure.
Key Words: Tsunami, bridge deck, lift, moment, CFD, surge, trapped air, inclination

INTRODUCTION
The Tsunami resulting from the Great East Japan Earthquake of March 11, 2011 caused failure of many
bridges along the coast in Iwate and Miyagi Prefectures. Field surveys and numerical modeling werecarried out to evaluate the mechanisms of failure of a typical bridge, using the Utatsu highway bridge in
Minamisanriku town, Miyagi Prefecture (Figures 1 and 2) as a model for structure scale and shape.

Figure 1. Google Earth map of Japan, with the location of the Utatsu Bridge indicated.
The Utatsu highway bridge was a concrete girder bridge about 8 m above water level, spanning a
fishing port and river mouth. Due to the horizontal curve in the highway at this location, the bridge
deck was inclined up to 3° (seaward side upward). In order to prevent deck displacement, unseating
prevention devices (UPD's) were installed between girders (Figures 3 and 4).
A field survey after the tsunami showed that despite the UPD's, the inclined sections of the bridge

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deck were lifted off their piers and deposited landward of the bridge in an inverted position (Figure 2,
decks C, D, and E). The bridge piers and UPD's themselves incurred almost no damage (Figure 4),
indicating that these deck sections experienced a large lift force or/and overturning moment. In anotherlocation, level sections of bridge deck whose UPD's were destroyed were deposited landward of thebridge in an upright position (Figure 2, decks F, G, H, I, and J), indicating they were pushed off thebridge by the drag force resulting from the flow, but this could not have been the case for the sections
with undamaged UPD’s.

Figure 2. Google Earth image of the Utatsu Bridge on April 6, 2011. Place-marks enumerate individual
deck segments.

Figure 3. Photo of Utatsu Bridge east abutment (east end of deck A) showing steel and concrete
unseating prevention devices (UPD's).

Figure 4. Photo of Utatsu Bridge pier cap between decks B (intact) and C (failed), showing intact
unseating prevention devices (UPD's).
Lifting or overturning of the inclined deck sections could be a result of either (or a combination of)1399

hydrostatic forces (buoyancy of the deck enhanced by air trapped between the girders; i.e. Chen et al,2005) or hydrodynamic forces (lifting or overturning of the deck like an airfoil; i.e. Kerenyi et al, 2009,
and Patil et al, 2009). The OpenFOAM (2011) Computational Fluid Dynamics (CFD) package wasused to determine the effects of buoyancy, lift, drag, and moment on such a bridge deck based on
two-dimensional Reynolds-averaged simulations. Results show that deck inclination, flow speed,
trapped air, tsunami impact, and entrained sediment could all contribute to deck failure.
TSUNAMI BEHAVOIRIn Tohoku, two types of tsunami behavior were observed. In regions of shallow offshore bathymetry(such as southern Miyagi Prefecture), the tsunami approached shore as a surge or bore (a turbulent
wall of water). In areas with deeper offshore bathymetry, such as Iwate and northern Miyagi
Prefectures, the tsunami appeared as a smoothly rising water surface. This paper investigates both ofthese situations.
Based on video taken by a local resident, the tsunami at Utatsu can be seen rising gradually, though
the instant when the water submerged the bridge deck is not captured on the video. Flow near thebridge appears subcritical in the video, with a speed between 3 m/s and 5 m/s based on visual trackingof floating debris. The following simulations are based on these flow speeds.
MODEL SETUP
Fluid forces on the model bridge deck were evaluated using the OpenFOAM (Open source Field
Operation And Manipulation) computational fluid dynamics (CFD) software. Simulation was carriedout using a two-dimensional grid. Figure 5 shows detail of the grid near the bridge. The full domainspans 110 m in the horizontal and either 20 m (for rising free surface simulations) or 30 m (for surge
and steady flow simulations) in the vertical. The bridge itself is inclined 3° upward on the seaward(left) side. Bridge deck width is 7.9 m and deck thickness is 0.5 m. Girder height is 2 m and girder
thickness is 0.6 m, spaced 1.9 m on center. Curbs on the edges of the deck are 0.2 m tall by 0.4 m wide.
The landward edge of the landward girder is located 8 m above the ground.

Figure 5. Detail of OpenFOAM mesh near the Utatsu Bridge.
Grid cell size is 0.2 m x 0.2 m on average, though this varies slightly due to non-orthogonality
introduced by the inclined bridge (the grid follows the surface of the bridge as well as the model domainboundaries, so non-orthogonality is introduced because these surfaces are oblique to each other).
Boundary conditions used in the simulations are shown in Table 1.
The model was run as a Reynolds Averaged Navier Stokes (RANS) simulation, using the standardk-ε turbulence closure model. Within OpenFOAM, the interFOAM module was used, in order tosimulate two-phase (air and water) flow. The PIMPLE (merged PISO/SIMPLE) algorithm was used
for transient Navier-Stokes solution. Interface compression (anti-diffusion) was enacted in order tomaintain a sharp air-water interface. An iterative correction for grid non-orthogonality was also

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activated to enhance model stability and accuracy. The model time step was variable, to keep the
Courant number below 0.5. Typically, this resulted in a time step between 0.001 sec and 0.01 sec.
Table 1. Boundary and initial conditions used in the OpenFOAM model.
Location
Ground (bottom
surface) and Bridge
Atmosphere (uppersurface)
Inlet (left surface)
Outlet (right surface)
Initial condition

Boundary Condition for surge
simulation
No-slip, with physical roughness
height 1 mm
Constant pressure (atmospheric)Boundary Condition for rising
surface and steady simulations
No-slip, with physical roughness
height 1 mm
Constant pressure (atmospheric)Constant (specified) water level;velocity calculated from pressure
gradient
Outflow
Specified water surface and flow
velocity

Time-varying (specified) waterlevel;
constant (specified) velocity
Outflow
Specified water surface and flow
velocity

MODEL SCENARIOSThe model was run to investigate two situations, both of which were experienced by bridges in Tohoku:
1. The bridge is struck by a tsunami surge (i.e., southern Miyagi Prefecture).
2. The bridge is engulfed by a smoothly rising water surface (as was the case at Utatsu).
Boundary conditions are detailed in Table 1, and example time series for both cases are shown in
Figures 6 and 7.
As Figure 6 shows, the surge scenario is not the case of a turbulent bore (a wall of water)
impacting the structure; rather, it is the case of a sloping water surface surging into the structure. The
surge begins as a 3-m high step in the free surface located 10 m upstream of the bridge, but relaxes
into the sloping surface shown before impacting the bridge.
Baseline surge simulations were run with a water density of 1030 kg/m3, which represents
seawater. As a conservative sensitivity analysis, additional simulations were run with a water densityof 1200 kg/m3, which assumes that 10% of the flow volume consisted of entrained sediment and debris(Applied Technology Council, 2008).
Simulations assumed that the air which became trapped between girders could not escape upward(air trapped between girders is visible in Figures 6 and 7). Furthermore, air was assumed to beincompressible, which is a conservative assumption, as in reality trapped air would be compressed andthus occupy a smaller volume (and cause less buoyancy) than here modeled.
Video of the tsunami indicates the water level rose 3 m to 4 m above the bridge deck elevation, andthe flow appears to have been subcritical, meaning the flow speed was less than 12 m/s for an
approximately 15 m deep flood. Simulations were thus carried out for initial flow speeds of 3 m/s, 5m/s, 7 m/s, and 9 m/s.
As a final sensitivity analysis, the above cases were also analyzed for the case of a level bridgedeck. This is to determine what effect the 3°deck inclination had on the deck failure. For the level
bridge deck simulations, the grid of Figure 5 was modified to remove the bridge inclination, resulting
in an orthogonal grid for these simulations.
In addition to the surge simulations, smoothly rising surface simulations (Figure 7) were carriedout with the initial free surface located 8 m above ground level (at the bottom of the bridge girders),
then rising up to a maximum elevation of 15 m above ground level (4 m above the bridge deck).
However, due to an upstream instability (Figure 7, t=801 sec) in the rising surface simulation for waterlevels higher than approximately 12 m above ground (1 m above the bridge deck), a separate
steady-state simulation was carried out for the case of a water level of 15 m above ground (4 m above1401

the bridge deck), for each horizontal flow speed case. An example of this steady-state simulation isshown in Figure 8, after 29 sec of spin-up from an initial condition of a level free surface and uniform
flow speed.
Arrow length for 8 m/s flowt = 0.1 sec

t = 0.6 sec

t = 1.6 sec

t = 2.6 sec

Figure 6. Phase (blue=water and red=air) and flow velocity for the bridge being submerged by atsunami surge. For this case, initial flow speed is 3 m/s, and water density is 1030 kg/m3.
RESULTS
Calculation of forces
Pressure along the bridge surface (Figure 9) was extracted from the model runs in order to calculate
lift, drag, and moment on the bridge deck under all scenarios. These quantities were calculated via
equations (1) – (4):
(1)
(2)
(3)
(4)
in which : force per unit length of bridge acting on the kth cell along the deck surface, : pressure
acting on the kth cell along the deck surface,: width of the kth cell along the deck surface,:
unit vector normal to the kth cell along the deck surface,: total drag force per unit length acting
on the bridge deck, : horizontal unit vector,: total lift force per unit length acting on the bridge
deck, : vertical unit vector,: overturning moment per unit length acting about thebottom of the landward-most girder, and : vector pointing from the bottom of the landward-mostgirder to the kth cell along the deck surface.
To determine whether the bridge deck would be displaced by the lift or moment that it is exposed1402

to, the bridge’s weight per unit length was calculated assuming a density of 2600 kg/m3, which isstandard for concrete. The Utatsu Bridge has a cross-sectional (concrete) area of approximately 8.91
m2, resulting in a weight per unit bridge length of 227 kN/m and a restoring moment per unit bridge
length about the landward girder of 716 kNm/m.
Arrow length for 8 m/s flowt = 1 sect = 201 sec

t = 401 sec

t = 801 sec

Figure 7. Phase (blue=water and red=air) and flow velocity for the bridge being engulfed by a risingwater surface with ambient flow speed 3 m/s. Water density is 1030 kg/m3.
Arrow length for 8 m/s flow

Figure 8. Phase (blue=water and red=air) and flow velocity vectors at t=29 sec for the bridge subject
to steady flow of speed 3 m/s and depth 15 m. Water density is 1200 kg/m3.
Example timeseries of forces
Figure 10 shows a time series of total lift, drag, and moment for the example case corresponding to theflow shown in Figure 6 (surge case, inclined deck, flow density 1030 kg/m3, flow speed 3 m/s). For
the first 2 seconds of the simulation, lift and moment are both positive, as the approaching flow surges
up against the seaward side of the bridge deck. At t=1.1 sec, the moment is even large enough toovercome the bridge’s weight and cause the deck to tilt upward on the landward side and begin to
overturn. After t=2.6 sec, the wave which had surged up above the bridge deck, now comes crashingdown onto the top of the deck, causing a negative lift and moment.
Figure 11 shows a similar timeseries of forces, corresponding to the flow shown in Figure 7(rising surface case, inclined deck, flow density 1030 kg/m3, flow speed 3 m/s). At t=0, flow begins1403

with a level free surface. However, the bridge acts as an obstacle to the flow and has two effects.
One effect is that the flow under the bridge accelerates, lowering the pressure under the bridge andcausing a negative lift and moment. This effect continues throughout the simulation period. The
second effect is that the rising free surface causes a gradual increase in lift and moment due tobuoyancy of the bridge (the static buoyant force on the deck including the effect of incompressible aircompletely filling the spaces between girders is 169 kN/m, and the overturning moment due to thisbuoyancy is 532 kNm/m). After submergence, the lift and moment due to buoyancy remain relatively
constant, while the accelerated flow under the bridge continues to hold the deck down. Toward theend of the simulation, lift and moment both begin to increase again, as the higher water level allows
more flow to pass over the bridge; this reduces the negative lift compared to that experienced at lower
water levels when all the flow had to pass (and accelerate) under the bridge.
Figure 12 shows a timeseries of forces corresponding to the steady flow simulation of Figure 8(inclined deck, flow density 1200 kg/m3, flow speed 3 m/s). The first few seconds of this simulation
can be considered a spin-up from initial conditions of uniform flow and a level free surface. At
t=16-17 sec and t=28-30 sec, the overturning moment is large enough to displace the deck.
(Pa)

Figure 9. Example of pressure calculated by OpenFOAM on each cell along the bridge deck section
surface, at 29 sec into the simulation of the “steady, 3 m/s, inclined deck, water density 1200 kg/m3”
case (Figure 8). The deck section is shown skewed for clarity of the colors on the surface.
Mechanisms causing deck failure
Deck failure can be a result of both lift force and overturning moment. These processes work
together to cause failure, but they are analyzed separately here for simplicity. In the following results,
failure due to overturning moment is much more readily achieved than failure due to lift force alone.
Lift
Figures 13 and 14 show the maximum (in time) lift force and overturning moment on the bridge deckfor each simulation. Figure 13 shows the lift force for the smoothly rising surface and steady flow
cases simulated is never large enough to cause deck failure via upward translation.
The surge simulations in Figure 13 show that at initial flow speeds greater than about 6 m/s, atsunami surge generates enough lift to cause failure of the inclined bridge deck. The level bridge
deck, however, does not fail due to lift alone at any speed. This shows that the bridge deck
inclination angle has a substantial effect on the stability of the deck during tsunami surge; a deck
inclined on the seaward side experiences substantially more lift than a level deck does.
Figure 13 also shows that the density of water has a significant effect on lift force during thesurge simulations. Turbid flow with specific gravity (SG) of 1.2 generates more lift than standard
seawater (SG=1.03) does. However, this effect is secondary to the effect of the inclined deck in thesurge cases investigated.
Another item that has a substantial effect on lift is trapped air. However, it does not add enoughlift to overcome the weight of the bridge for any of the rising surface or steady flow cases investigated.
For the surge cases, trapped air could have been responsible for pushing the lift force above that1404

required to move the deck. At an initial flow speed of 7 m/s, for example, the lift force for the “surge,
SG=1.03, inclined” case is about 30 kN/m greater than the weight of the deck. If trapped air wereallowed to escape, however, the lift force could decrease by as much as 79 kN/m (this is the static
buoyant force due to incompressible air completely filling the spaces between girders). In this case,removal of trapped air could reduce the lift force to a magnitude below that which would cause deck
failure.

Figure 10. Example time series of fluid forces on bridge deck for the bridge being impacted by atsunami surge. For this case, initial flow speed is 3 m/s, and water density is 1030 kg/m3. This
corresponds to the flow shown in Figure 6.

Figure 11. Example time series of fluid forces on bridge deck for the bridge subject to a smoothly
rising free surface with ambient speed 3 m/s. Water density is 1030 kg/m3. This corresponds to theflow shown in Figure 7.
MomentFigure 14 shows that a smoothly rising surface at subcritical flow speeds does not cause a large

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enough overturning moment to cause bridge deck failure (these simulations are valid for flow depths
up to about 12 m). The steady flow simulations with flow depth 15 m (4 m above the bridge deck),
however, cause inclined deck overturning failure for the seawater case (SG=1.03) at a flow speed of 9
m/s.

Figure 12. Example time series of fluid forces on bridge deck for the bridge subject to a free surfaceof elevation 15 m and speed 3 m/s. Water density is 1200 kg/m3. This corresponds to the steady flowcase shown in Figure 8.
For the turbid water (SG=1.2) case, steady flow causes inclined deck failure for flow of 3 m/s,
which is close to that seen in the video from Utatsu. Figure 8 shows that for this case, the free surface
experiences a slight dip over the bridge, as is expected for subcritical flow over an obstacle. Figure 9shows the pressure distribution along the surface of the bridge deck at the time of greatest overturning
moment (t=29 sec in the timeseries of Figure 12). Vortex shedding in the lee of the bridge deck isapparent in Figure 15. Vortex shedding, together with migration of the dip in the free surface over thedeck, cause fluctuations in the overturning moment experienced by the deck.
To explain vortex shedding, the Strouhal number S=nL/U where n is the frequency of vortex
shedding, L is the length scale of the bridge deck, and U is the mean flow speed. For a cylinder in aflow, it’s known that S=0.21 for a wide range of Reynolds numbers (Kundu, 1990). In the case of thebridge deck of height L=2.7 m in a flow of speed U=3 m/s, the resulting rate of vortex shedding is
n=0.23 cycles/sec, which corresponds to a shedding period of about 4 sec, as is seen to be the period of
the lift and moment signals in Figure 12. At speeds higher than 3 m/s, vortex shedding from the deck
is replaced with a turbulent wake. Without the fluctuations of vortex shedding, maximum lift andmoment at speeds higher than 3 m/s are reduced. At near-critical speeds (i.e., 9 m/s), however,overturning moment again increases, this time due to the behavior of the free surface downstream ofthe deck, where critical flow and a hydraulic jump periodically exist.
Unlike the steady flow cases, the surge cases induce a large enough overturning moment to cause
failure of the inclined deck at all speeds modeled (3 m/s and greater). The presence of air trapped
between girders is essential to inclined deck failure at low initial flow speeds though, as the static
overturning moment due to air occupying the full space between girders is 248 kNm/m. Without air
trapped between girders, the inclined deck (with SG=1.03) could have been stable for flow speeds up
to 5 m/s, and the level deck up to 7 m/s. For the steady-flow scenarios, removal of trapped air would
have prevented deck instability in all cases.
Figure 14 shows that for all scenarios, deck inclination is important in causing deck failure. The
inclined deck is unstable at surge-case flows as slow as 3 m/s, while the level deck is stable at flows up

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to 5 m/s. In the turbid (SG=1.2) steady-flow scenarios, the inclined deck fails at 3 m/s flow speed,
while the level deck is marginally stable at this flow speed.

Lift force, kN/m

350.00300.00surge SG=1.2 inclined

250.00steady SG=1.2 inclined

200.00surge SG=1.03 inclined

150.00steady SG=1.03 inclined

100.00surge SG=1.03 level
50.00
steady SG=1.2 level

0.00-50.00rising surface SG=1.03
inclined-100.00

Deck weight in air
0

1

2

3

4

5

6

7

8

9

Mean flow speed, m/s

Figure 13. Summary of maximum (in time) lift force on the bridge deck in each scenario. The thickblack line indicates the weight of the bridge. Liftoff of the deck can occur when lift force exceeds
the bridge weight.
Another item of importance to the overturning moment is flow density. For the surge cases, thedifference in moment between the SG=1.03 case and the SG=1.2 case is as large as approximately 250
kNm/m. This is the same order as the static contribution of air trapped between girders. For thesteady-flow cases, deck failure at low speeds does not occur for the SG=1.03 case, indicating thatentrained sediment might have been essential for causing deck failure at Utatsu.
CONCLUSIONS
Smoothly rising water surface, steady-flow, and surge simulations were carried out to investigate thecause of deck failure of a typical bridge of the size and shape of the Utatsu Bridge during the 2011
Tohoku Tsunami. Simulation results indicate that surge, where present, could cause deck failure. In
lieu of surge, at subcritical flow speeds a smoothly rising water surface would not cause bridge deck
failure, because accelerated flow under the bridge deck causes a negative lift. However, once the flow
significantly submerges the bridge deck so that flow accelerates as much over the deck as it does under
the deck, vortex shedding and free-surface fluctuations can cause the deck to overturn.
At Utatsu, surge was not evident in the video. The bridge appeared to be submerged by three tofour meters, and the flow speed appeared to be between 3 m/s and 5 m/s based on a fishing boat seendrifting over the bridge site. Furthermore, at this high water level, the water surface over the bridge
site experienced only small fluctuations. These conditions are similar to those modeled in the 3 m/s
steady flow case. The model only shows deck overturning for the case of a sediment-laden flow, butwhether this was the case at Utatsu could not be determined from the video. Also undetermined is1407

whether the seawall located landward of the Utatsu bridge could have contributed to deck failure; thiswill be the subject of further investigation.
2000.00
1800.00

surge SG=1.2 inclined

Clockwise moment, kNm/m

1600.00

steady SG=1.2 inclined

1400.00
surge SG=1.03 inclined

1200.00
1000.00

steady SG=1.03 inclined

800.00surge SG=1.03 level

600.00steady SG=1.2 level

400.00rising surface SG=1.03
inclined

200.00
0.00
0

1

2

3

4

5

6

7

8

9

Deck moment fromweightMean flow speed, m/s

Figure 14. Summary of maximum (in time) overturning moment (upward on the seaward edge of thebridge deck) about the landward edge of the landward-most girder, for each scenario. The thickblack line indicates the counterclockwise moment due to the weight of the bridge deck. Overturningof the deck can occur when the clockwise moment due to fluid forces exceeds the counterclockwise
moment due to bridge deck weight.

(m/s)

Figure 15. Flow velocity magnitude and vectors at t=29 sec for the bridge subject to steady flow of
speed 3 m/s and depth 15 m. Water density is 1200 kg/m3.
For a bridge subjected to either a subcritical steady flow or a surge, the combination of two
actions could prevent deck failure:
1. Construction of an escape path for trapped air that is large enough to allow air to evacuate
quickly during the approach of a surge or flood, and
2. Replacement of the inclined deck with a level deck.

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In addition to this, UPD’s must be strong enough to withstand the drag force of the flood (Figure 16).
350.00Drag force, kN/m

300.00surge SG=1.2 inclined

250.00steady SG=1.2 inclined

200.00surge SG=1.03 inclined

150.00steady SG=1.03 inclined
surge SG=1.03 level

100.00steady SG=1.2 level

50.00

rising surface SG=1.03
inclined

0.00
0

1

2

3

4

5

6

7

8

9

Mean flow speed, m/s

Figure 16. Summary of maximum (in time) drag force on bridge deck in each scenario.
ACKNOWLEDGMENTS
The authors are grateful to Mr. Katsuya Oikawa and the citizens of Minamisanriku for providing videoof the tsunami and first-hand accounts of the event.
REFERENCES
Applied Technology Council. (2008). “Guidelines for Design of Structures for Vertical Evacuationfrom Tsunamis.” Report FEMA P646 of the Federal Emergency Management Administration.
Chen, G., Emitt, C.W. III, Hoffman, D., Luna, R., and Sevi, A. (2005). “Analysis of the Interstate 10
Twin Bridge's Collapse During Hurricane Katrina.” Science and the Storms: the USGS Response to
the Hurricanes of 2005, pp 35-42.
Kerenyi, K., Sofu, T., and Guo, J. (2009). “Hydrodynamic Forces on Inundated Bridge Decks.” Report
No. FHWA-HRT-09-028 of the Federal Highway Administration.
Kundu, P.K. (1990). Fluid Mechanics. Academic Press. San Diego. p 323.
OpenFOAM (2011). OpenFOAM version 2.1.0 User Guide. www.openfoam.org.
Patil, S., Kostic, M., and Majumdar, P. (2009). “Computational Fluid Dynamics Simulation ofOpen-Channel Flows Over Bridge-Decks Under Various Flooding Conditions.” Proceedings of the
6th WSEAS International Conference on Fluid Mechanics (FLUIDS'09), pp 114-120.

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