Mitsubishi Heavy Industries Technical Review Vol. 51 No. 3 (September 2014)21

Clarification of Behavior ofHuge Tsunami Action on Bridges- Hydraulic Model Experiment andSimulation Technology TOSHIMITSU SUZUKI*1 RIKUMA SHIJO*2

KAORU YOKOYAMA*3SYUNICHI IKESUE*4

HIROFUMI YAMASAKI*2

JUNICHIRO MOTOYAMA*5

In the Tohoku-Pacific Ocean Earthquake that occurred in 2011, many social infrastructure
facilities suffered significant damage from resulting tsunami. For disaster recovery, bridges are an
important lifeline, and therefore it is necessary to prevent loss of their functionality when adisaster such as a tsunami occurs. In conventional designs, however, it was not assumed thatbridge girders or other bridge elements would be carried away by tsunami wave forces, andestimations of tsunami wave force were difficult because no load calculations or design methods
had been established. The authors are working on hydraulic model experiments andtwo-dimensional and three-dimensional numerical simulations to clarify the behavior of tsunami
and their wave forces acting on the upper structure of a bridge1-3. This report presents a generaloverview.

|1. Introduction
In the past, many examinations were performed to research tsunami wave forces acting on abridge5-8. However, no calculation methods of tsunami wave forces acting on bridge girders thathave complex cross sectional shapes have been established in current design standards. The
consideration of tsunami wave forces in the design process requires an understanding of thebehavior and wave force characteristics of tsunami acting on the object, in addition to accurate
tsunami simulation. The authors are working on various experiments and analyses in order toclarify this behavior and calculate the wave forces. Specifically, the following examinations wereperformed.
(1) Experiments using a miniature model of a bridge in the see-through hydraulic waterway
owned by the Nagasaki Research and Development Center(2) Reproduction through numerical analysis of the results of hydraulic model experiment(3) Understanding the behavior of tsunami acting on a certain range of structures and anestimation of their safety through a combination of two-dimensional tsunami propagation
simulation and three-dimensional numerical simulation
It is difficult to uniquely determine tsunami wave force in detail because its estimation varies
depending on the shape of the structure, the terrain of the location where the bridge is constructed
and the seismic source. However, it is believed that the methods shown in this document allow for
the estimation of the wave forces of tsunami acting on a structure. The following chapters describe
the investigation and the results.
*1

Manager, Brige Headguarters, Mitsubishi Heavy Industries Bridge & Steel Structures Engineering Cｏ., LTD.

*2

Nagasaki Research & Development Center, Technology & Innovation Headquarters*3

Brige Headguarters, Mitsubishi Heavy Industries Bridge & Steel Structures Engineering Cｏ., LTD.

*4

Chief Staff Manager, Nagasaki Research & Development Center, Technology & Innovation Headquarters*5

Brige Headguarters, Mitsubishi Heavy Industries Bridge & Steel Structures Engineering Cｏ., LTD.

Mitsubishi Heavy Industries Technical Review Vol. 51 No. 3 (September 2014)22|2. Hydraulic model experiment and numerical simulation
2.1

Hydraulic model experimentThis experiment employed the visualized hydraulic waterway owned by the Nagasaki
Research and Development Center, which uses a glass wall on one side and is 20 meters long, has across-sectional width of 0.7 meters and a cross-sectional height of 1.0 meters (Figure 1). Waves
are generated by the sliding wave generation plate shown at the far left of Figure 1. The height,
flow velocity and period of the waves to be generated can be adjusted by setting the moving
distance/speed and static depth of the wave generation plate. The bridge model is connected to theforce meter fixed on the beam above the hydraulic model through the supporting beam of themodel, and therefore the wave forces acting on the model can be measured directly. For thisexperiment, the following analogy using Froude number Fr was applied because the effects offrictional resistance and surface tension of water are small and the viscosity effect is sufficiently
smaller than the gravity effect in a typical hydraulic experiment for the reproduction of tsunami.

Fr =vpgH p=vmgH m(1)

where v is tsunami flow velocity, g is gravity acceleration, H is immersion depth, and thesubscripts p and m represent the actual bridge and the girder model respectively.

Figure 1 Schematic diagram of hydraulic modelThis figure illustrates an overview of the entire hydraulic model, the measurement positions, and the settings ofthe model.

2.2

Numerical simulation

If the hydraulic model experiment described above can be reproduced by numericalsimulation, the reproduction of various tsunami characteristics and the calculation of tsunami force
can be performed efficiently. Therefore we tried to reproduce the hydraulic model experimentthrough numerical simulation (CFD: Computational Fluid Dynamics). ANSYS FLUENT, a general
purpose fluid analysis code, was used for the simulation, and a VOF (Volume of Fluid) method,
one of the interface capturing methods, was used to determine the free surface of the tsunami. Fluid
was modeled as water-air two-phase flow. The VOF method defines a function for representing therate of fluid to the analyzed cell and tracks changes in the water surface by solving the advection
equation of the function. The two-phase flow fluid model was employed in order to accurately
estimate the generation of the lift force with buoyancy that is expected to occur due to the air layer
confined in the space between the free surface of a wave, the extending part of the floor slab andthe girder, when tsunami waves act on the bridge. The governing equations are equations ofcontinuity and an equation of motion (Navier-Stokes equation), and LES (Large-Eddy Simulation)
was used as the turbulent flow model.

Mitsubishi Heavy Industries Technical Review Vol. 51 No. 3 (September 2014)23

2.3

Results of experiment and simulation

An example of the results of the experiment and simulation that were performed for isolatedwave tsunami is described below. The experiment and its tsunami height settings are shown in
Table 1 and Figure 2. This experiment was implemented with the assumption of a maximum
tsunami height of 10 m (20 cm in the actual experiment) and a flow velocity of 6.4 m/s (0.91 m/s inthe actual experiment). These settings were based on the fact that the predicted tsunami heightcaused by the Nankai Trough Earthquake at the target bridges was 5 to 10 meters4 and the flow
velocity of tsunami caused by the Tohoku-Pacific Ocean Earthquake was estimated at
approximately 6 m/s from image analysis of drifting articles5. In the experiment, isolated waves
with these specified height and flow velocity were generated by adjusting the operating speed,
stroke and static water depth of the wave generation plate. In addition, this experimental device canalso reproduce long-period waves and more waves (with or without breaking waves) by controllingthe sliding wave generation plate and setting the model scale.
Table 1 Experiment cases
Case1234567891011

Tsunami height (cm)20131120Flow velocity (m/s)

Cross grade of
the bridge model (%)

0.91
0.83
0.80
0.88
0.78
0.60
0.79
0.59
0.53

00.91

2.5
5.0

Figure 2 Settings of tsunami height, flow velocity and cross grade inexperimentThis figure illustrates the relationship between the three types of wave height and thebridge position set in the experiment.

As another example, Figure 3 compares the obtained results of flow around a cross section
periphery between the experiment and a simulation of case 1. The following features of flow
around a cross section periphery are shown: (a) first, a wave contacts the front stream edge of thelower flange, (b) the wave enters the underside of the lower flange and the front stream extending
part of the floor slab and simultaneously crashes on the web side face and the front stream
balustrade side face, and then is thrown up over the bridge, (c) the thrown water drops onto theupper face of the floor slab, and (d) the dropped water flows over the rear stream balustrade, whileat the underside of the girder the wave flows off of the underside of the lower flange. Thesebehaviors generally correspond to the flow pattern observed in the experiment and reproduce theexperimental results qualitatively.

Mitsubishi Heavy Industries Technical Review Vol. 51 No. 3 (September 2014)
24

Figure 3 Flow state at cross section periphery in case 1

This figure compares the experiment and the analysis. (The values in parentheses represent the time from thestart of operation of the wave generation plate. The start of operation is defined as zero.)Figure 4 compares the obtained results of the horizontal wave force, the vertical wave force
and the flow force moment between the experiment and the simulation. The wave forces obtainedby the experiments are values directly measured by the component force meter fixed above themodel, and the wave forces obtained by the simulation are an integration value of the pressure
acting on the surface of the bridge model by the tsunami. Before the comparison, smoothing ofeach wave force was performed using a 10-Hz low pass filter to remove model vibration in theexperiments and analytic noise in the calculation of numerical values. The vertical axis of Figure 4
represents the measured value and the analyzed value of the wave force, while the horizontal axis
represents the time from start of operation of the wave generation plate (the start of operation isdefined as zero). Figure 4 indicates that this simulation method can well reproduce the tendency of
the time-history of the wave forces such as the existence of multiple peaks on the wave shape of thewave force and the acting direction.

Figure 4

Comparison of waveform of wave force between experiment and analysis (case 1)

This figure compares the obtained horizontal wave force, vertical wave force, and flow force moment between
the experiment and the analysis.

|3. Three-dimensional numerical simulation at bridge point
There are a variety of tsunami incursion patterns, and therefore actual tsunami assumptions
require the identification of the seismic source fault and the bridge point. Typical tsunami
simulation uses an initial water level obtained from the crustal movement amount of the assumed
seismic source fault model to analyze the propagation and run up of the tsunami from the seismic
source to the target coast area based on a two-dimensional nonlinear long wave (shallow-watertheory). However, when a tsunami runs up onto the land, its flow becomes complicated under theinfluence of terrain and structures. Therefore the accurate estimation of the tsunami wave forces
acting on a bridge structure requires a reproduction of three-dimensional fluid phenomena
including the throwing up of the tsunami at the front face of the bridge and wraparound to the backface. Accordingly, two-dimensional analysis cannot accurately reproduce wave forces acting on
complicated terrain and three-dimensional structures.

Mitsubishi Heavy Industries Technical Review Vol. 51 No. 3 (September 2014)25

The authors therefore used three-dimensional numerical simulation in order to reproduce indetail the tsunami behavior at bridge points within a specific area and the tsunami wave forces
acting on the target bridge. For this simulation, the wave height, speed and flow direction of thetsunami at the vicinity of a bridge point were calculated through two-dimensional tsunami
propagation simulation, and the results were applied to the boundary of a three-dimensional
analysis model around the bridge point. Specifically, the wave height and flow speed of the tsunami
obtained through the propagation tsunami simulation were entered for each mesh of thethree-dimensional analysis model boundary after linear interpolation, and convergence calculationof the water amount and the momentum within the three-dimensional area was performed for eachtime step to calculate the tsunami behavior. The pressure acting on the target bridge surface wasobtained through three-dimensional simulation and the tsunami wave forces acting on the bridge
were estimated by integrating the obtained pressure. The software, turbulent flow model and otherfactors used for three-dimensional simulations were the same as those described in Chapter 2.
In this way, the tsunami wave forces acting on structures within a specific area could besimulated. Figure 5 shows the results of tsunami propagation simulation and Figure 6 shows anexample of the three-dimensional numerical simulation results. For the simulation of tsunami
running up a river, there remain issues that should be considered such as a method to create
detailed terrain data (analysis mesh) and consideration of the normal water flow of the river.

Figure 5

Results of wide range tsunami propagation simulation

This figure illustrates the tsunami propagation at the time points five, fifteen, and twenty five minutes after theoccurrence of an earthquake obtained by tsunami propagation simulation.

Figure 6 Results of three-dimensional numerical simulation
This figure illustrates the run up of a tsunami around a bridge at the time points fifteen, twenty, twenty five,twenty seven, thirty, thirty five minutes from the occurrence of an earthquake obtained by three-dimensional
numerical simulation.

Mitsubishi Heavy Industries Technical Review Vol. 51 No. 3 (September 2014)26|4. Conclusion
In this report, a hydraulic model experiment and its simulation, as well as a numericalsimulation method that combines two-dimensional tsunami propagation simulation andthree-dimensional numerical simulation for the calculation of wave forces used for theunderstanding, clarification and design of behaviors of tsunami acting on a bridge, were presented.
These methods enable the estimation of wave forces acting on a bridge that can be used for theunderstanding of assumed damage and the consideration of countermeasures.
Although the numerical simulation itself is one of the analysis methods that have been
established to some extent, accurate reproduction of behaviors in analysis imperatively requires anunderstanding of the actual behaviors and the tsunami generation mechanism through a hydraulicmodel experiment, etc. Furthermore, the implementation of such analysis should be conductedusing an appropriate model. We are willing to continue the consideration of these tsunami-related
technologies to further improve accuracy and to develop other applications.
Acknowledgment: The technologies presented in this report are a summary of some of theresults of business operation commissioned by Nippon Expressway Research Institute Company
Limited. Prof. Koshimura (International Research Institute of Disaster Science, Tohoku University)
provided us with advice on the development of these technologies. We would like to express oursincere gratitude.

References
1.

2.
3.

4.
5.
6.

7.
8.

Shijo，Aoki，Hayashi，Suzuki，Yokoyama，Koshimura：Numerical Analysis Study on Tsunami Wave
Force Acting on a Bridge Superstructure using VOF Method ， Journal of JSCE B2 (CoastalEngineering），Vol.69，No.2，pp.801-805，2013.11.
Hayashi ， Aoki ， Shijo ， Suzuki ， Koshimura ， Study on tsunami wave force acting on a bridge
superstructure，Journal of Structural Engineering Vol. 60（2014.3）, pp.45-58.
Shijo，Tsukuda，Sato，Ikesue，Higuchi，Kudo，Ishizaki，Shimizu：3D Simulation of Tsunami Caused by
Tohoku-Pacific Ocean Earthquake in the Power Plant ， Transactions of the Japan society ofmechanical engineers series B., Vol. 79, No. 801, pp.980-991, 2013.5.
Cabinet Office, Government of Japan：Estimation of Tsunami wave height, inundation area (SecondReport) and disaster assumption (First Report) due to Nankai Trough giant Earthquake, 2012.8.
Shimizu，Kosa，Sasaki，Takehira：Tsunami damage analysis in highway bridges，Journal of StructuralEngineering Vol.58A，pp.366-376，2012.3.
Kosa：”Damage of Structure due to Great East Japan Earthquake”,The International Workshop on
Advances in Seismic Experiments and Computation (ASEC2012), Advanced Research Center for
Seismic Experiments and Computations (ARCSEC), 2012.3.
Nakao，Izuno，Kobayashi：Study on relation of velocity and wave height to hydrodynamic force on
bridges by tsunami，Journal of Structural Engineering Vol.56A，pp.564-575,2010.3.
Ikari，Gotoh：Numerical Simulation of Washed Process of Girder Bridge by Tsunami Run-up，Journal ofJSCE (Coastal Engineering），Vol.54，pp.211-215，2007.10.