1 Copyright © 2011 by ASME

Proceedings of the ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering OMAE2011

June 19-24, 2011, Rotterdam, The Netherlands

OMAE2011-49487

TSUNAMI BORE FORCES ON WALLS

I.N. Robertson Dept. of Civil and Environmental Engineering

H.R. Riggs

Dept. of Civil and Environmental Engineering

K. Paczkowski Dept. of Civil and Environmental Engineering

A. Mohamed

Dept. of Civil and Environmental Engineering

University of Hawaii at Manoa Honolulu, Hawaii 96822

ABSTRACT A series of experiments have been carried out at Oregon

State University to quantify tsunami bore forces on structures. Phase 1 of the tests was carried out in the Tsunami Wave Basin (TWB), while Phase II of the tests were carried out in the Large Wave Flume (LWF) at approximately twice the scale of the Phase I tests. These latter tests included ‘offshore’ solitary waves, with heights up to 1.3 m, that traveled over a flat bottom, up a sloping beach and breaking onto a flat ‘fringing reef’. Standing water depths on the reef varied from 0.05 m to 0.3 m. Resulting bores on the reef measured up to approximately 0.8 m. After propagating along the reef, the bores struck a vertical wall. The resulting forces and pressures on the wall were measured.

The test setup for the Phase II tests in the LWF is described and the experimental results are reported. The results include forces and pressure distributions. Results show that the bores propagated with a Froude number of approximately 2, and that the forces follow Froude scaling. Finally, a design formula for the maximum impact force is given. The formula is shown to be an improvement over existing formulas found in the literature. The lateral forces are shown to be quite significant compared to traditional lateral loads on vertical wall elements.

INTRODUCTION Coastal buildings, bridges, highways, and harbor facilities

that are at risk of tsunami inundation may suffer significant damage if the structures are not adequately designed for the fluid loading. Ref. [1, 2] document damage from fluid loading during the 2004 Great Indian Ocean Tsunami. The structural damage is strikingly similar to what can happen from hurricane storm surge and waves [3, 4]. Damage to walls during the 2009 tsunami in Samoa (Figure 1) [5] and 2010 tsunami in Chile

demonstrate the potential for large hydrodynamic forces on vertical walls.

Figure 1: Failure of reinforced masonry wall in Tula,

Samoa

The quantification of wave impact forces on structures has received significant attention over the years. The work can be categorized into three areas. Probably one of the most studied is the issue of storm wave impact on offshore platforms. A sampling of work, spanning experimental and numerical attempts to develop design formulas for the loads, can be found in [6-9]. The second area is storm wave breaking on coastal structures, especially seawalls and breakwaters [10-19]. Much less studied are the forces resulting from tsunami bores/surges hitting coastal structures [20-25].

Tsunami engineering, the focus of a 2007 special issue of the ASCE Journal of Waterway, Port, Coastal and Ocean Engineering, was defined therein as ‘those activities that are significant for the engineering goal of designing and protecting the built environment and the people that dwell therein, with

2 Copyright © 2011 by ASME

regard to potential tsunami hazards’ [26]. While this has received more attention recently, designers of onshore facilities typically have very little experience and receive very little guidance in tsunami induced loads that should be considered for bridge and building design [27, 28]. In addition, the simulation of these loads is very complex and it pushes the state-of-the-art in computational fluid dynamics (CFD).

The US National Science Foundation (NSF) has funded a program to improve the understanding of tsunamis and their threat to the built environment. One aspect of this initiative is the funding of the NSF Network for Earthquake Engineering Simulation (NEES), which includes Oregon State University’s (OSU) Large Wave Flume (LWF). The LWF is 104 m long, 3.7 m wide and 4.57 m deep. The wavemaker is a piston-type hydraulic actuator capable of producing regular, irregular, and solitary (tsunami-like) waves. The wave periods range from 0.5 s to 10 s. The piston has a maximum stroke of 4 m and a maximum velocity of 4 m/s. More information on the facility can be found on the web [29].

The authors were investigators on an NSF-funded project that utilized the LWF. The project was titled ‘Development of Performance-Based Tsunami Engineering, PBTE’, and its goal was to contribute to the methodology and validated simulation tools for implementation of site specific PBTE for use in the analysis, evaluation, design and retrofit of coastal structures and facilities, as well as the development of code-compatible provisions for tsunami-resistant structural design.

The project’s experimental component focused on tsunami 1) run-up and inundation, including fluid velocities and energy dissipation; 2) fluid loading on structural elements; and 3) sediment transport and scour as a result of inundation and drawdown.

The primary objective of the experimental component of the project was to provide data to validate numerical models for each of these 3 areas. This paper focuses on the fluid forces of a bore impacting a vertical wall. The experimental setup will be described and force results will be presented. The experimental results are useful to validate simulation of bore impact with CFD models. The data were also used to develop a design equation for the maximum impact forces from bore impact on a wall.

EXPERIMENTAL SETUP As illustrated in Figure 2, the experiments involved a

solitary wave propagating ‘offshore’ over a flat bottom, running up a 1:12 beach slope and onto a ‘fringing reef’, i.e., a flat section. A solid wall was located on the reef, 83 m from the wave maker. The beach slope terminated 2.36 m above the flume bottom. The beach and reef were smooth concrete though some experiments included a bedform on the beach slope as part of a parallel study on the effect of bottom roughness. The wave flume is 3.7 m wide.

A tsunami impacting a shoreline consists of several long period waves, and the largest wave is not necessarily the first wave. Hence, there is a good chance that there will be standing water on-shore from a previous wave when a large wave hits.

As a result, the water level in the wave flume was varied from 2.36 m to 2.66 m so as to change the still water level on the flat reef. For a water level of 2.36 m, there was no water on the flat reef. For the maximum water level of 2.66 m the still water on the flat reef was 30 cm deep.

The incoming solitary wave transforms to a turbulent bore/surge at the transition between the beach slope and the fringing reef. This bore/surge then impinges the structural test specimen, i.e., the wall. The characteristics of this bore were captured using a high resolution video camera filming an 8 m length of flume in front of the test wall at 60 frames per second. The side wall of the flume was painted black for improved contrast with the turbulent bore. Post-processing of the video capture was used to determine bore height and velocity at midheight of the leading edge. These results were validated by comparison with resistance wave gages and ultrasonic wave gages located along the side wall of the flume (Figure 3).

Figure 3 shows the instrumented wall installed in the wave flume. The bottom 1.83 m height of wall was constructed using a 6mm thick aluminum plate reinforced by 200mm deep aluminum I-beams spanning across the flume. The wall is attached to brackets mounted on the side walls of the flume by means of four load cells, identified as LC1 to LC4 in Figure 4. A flexible rubber seal was installed around the edge of the wall to prevent water from passing behind the wall. The seal does not provide any resistance against lateral loads on the wall. A 2.44 m high plywood extension was attached to the top of the aluminum wall to prevent any overtopping. All lateral load applied to both aluminum and plywood walls is measured by the four load cells behind the wall. Plywood splash guards were also fitted to the top of the flume side walls in front of the test specimen to prevent water from exiting the flume.

Thirteen FPG pressure sensors were installed along the vertical centerline of the wall as shown in Figure 4. Four Druck pressure sensors were installed adjacent to selected FPG sensors for the purpose of validating the pressure readings. The load cells and pressure sensors were monitored at 1000 Hz throughout each wave impact. Further details on the experimental setup and instrumentation are presented by Santo and Robertson [30].

Figure 5 shows a schematic of a bore propagating on the reef. The bore depth, hb, is the sum of the initial standing water level, ds, and the jump height, hj. For future reference, vs and vj are the assumed-uniform velocities in these two layers.

Solitary waves with heights varying from 0.10 to 0.50 times the offshore water depth were generated by the wave maker. Solitary wave heights used in these experiments are listed in Table 1, together with the number of times each case was repeated (in parentheses). Each wave configuration was run between 2 and 4 times to ensure repeatability and quantify any variation in loading on the wall.

Although the dry bed case was also considered, the bore/surge is qualitatively different than when there is initial standing water. Therefore, the focus herein is on the cases with initial standing water.

3 Copyright © 2011 by ASME

Figure 2 : Beach slope and fringing reef with solid wall specimen

Figure 3 View of instrumented aluminum wall and plywood

extension to prevent overtopping

Figure 4 Wall instrumentation

Figure 5 Tsunami bore characteristics

Table 1: Wave heights in cm and number of trials

Still water depth

on reef, ds (cm)

Water depth

in flume (m)

Ratio of wave height to water depth

0.10 0.15 0.20 0.25 0.30 0.40 0.45 0.50

0 2.36 23.6 (4)

35.4 (2)

47.2 (4)

59 (2)

70.8 (4)

94.4 (4)

106.2 (2)

118 (4)

5 2.41 24.1 (4)

36.15 (2)

48.2 (4)

60.25 (2)

72.3 (4)

96.4 (4)

108.45 (2)

120.5 (4)

10 2.46 24.6 (4)

36.9 (2)

49.2 (4)

61.5 (2)

73.8 (4)

98.4 (4)

110.7 (2)

123 (4)

20 2.56 25.6 (4)

38.4 (2)

51.2 (4)

64 (2)

76.8 (4)

102.4 (4)

115.2 (2)

128 (4)

30 2.66 26.6 (4)

39.9 (2)

53.2 (4)

66.5 (2)

79.8 (4)

106.4 (4)

119.7 (2) -

EXPERIMENTAL RESULTS Figure 6 and Figure 7 show time histories of the total

lateral force on the wall specimen, as measured by the load cells, from four bores produced by 24.1 cm and 120.5 cm high solitary waves, respectively, over a reef with 5 cm standing water. The time scale starts shortly prior to the first measurement of load on the wall. Note that the vertical scales differ to increase plot clarity. Wave trials designated with BS1 and BS2 involved different bedform roughness on the beach slope leading up to the reef. These bedforms were part of a parallel study investigating the effect of bottom roughness on wave breaking and bore formation. Bedform BS2 was a more pronounced roughness than BS1, leading to slightly lower wall forces, particularly for smaller incoming waves. The variation in time history between nominally identical incoming waves is also related to the turbulent nature of the leading edge of the bore as it propagates over the flat reef.

BO

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jh

sdbh jv

vs

Black wall for video capture FPG pressure

sensors

Resistance and Ultrasonic wave gages

4 Copyright © 2011 by ASME

Each time history is characterized by a steep loading ramp to approximately 2/3 of the peak load, which coincides with the incident bore being redirected up the face of the wall. The load increases more slowly until reaching a peak when the run-up collapses onto the incoming flow. The peak load is followed by a rapid decrease to a sustained, though fluctuating, residual lateral load. A reflective bore has now formed travelling away from the wall over the incoming flow. This residual load dissipates with time as the incoming flow decreases due to the relatively short wave length of the solitary waves generated in the laboratory flume. During a tsunami this residual load would be expected to continue for a longer duration.

Figure 8 and Figure 9 show the pressure sensor readings up the centerline of the wall at the peak lateral load for a typical 24.1 cm and 120.5 cm wave trial, respectively. The linear

regression lines are shown for all sensors measuring significant pressure. Integration of the pressures gave good comparison with the load cell measurements.

Figure 10 and Figure 11 show time histories of the total lateral force induced on the wall specimen for four bores produced by 53.2 cm and 106.4 cm high solitary waves, respectively, over 30 cm of standing water on the reef. The time histories show a similar trend to that observed for the 5 cm standing water condition.

Figure 12 and Figure 13 show the pressure sensor readings up the centerline of the wall at the peak lateral load for a typical 53.2 cm and 106.4 cm wave trial, respectively. Linear regression lines are shown for all sensors measuring significant pressure.

Figure 6: Force time history for 24.1 cm waves with 5 cm

standing water on reef

Figure 7: Force time history for 120.5 cm waves with 5 cm

standing water on reef

Figure 8: Typical wall pressure distribution at peak lateral

load for 24.1 cm wave with 5 cm standing water on reef

Figure 9: Typical wall pressure distribution at peak lateral

load for 120.5 cm wave with 5 cm standing water on reef

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Vb

5 Copyright © 2011 by ASME

Figure 10: Force time history for 53.2 cm waves with 30 cm

standing water on reef

Figure 11: Force time history for 106.4 cm waves with 30

cm standing water on reef

Figure 12: Typical wall pressure distribution at peak lateral

load for 53.2 cm wave with 30 cm standing water on reef

Figure 13: Typical wall pressure distribution at peak lateral

load for 106.4 cm wave with 30 cm standing water on reef

FROUDE SCALING Because a tsunami bore behaves as a gravity wave, it is

commonly assumed that scaling from model to prototype follows Froude scaling. Defining the Froude number in terms of the height of the incoming jump, hj, and the jump velocity, vj, gives:

!" =!!!!!

(1)

Figure 14 shows the resulting Froude numbers for all wave trials over the reef with 5, 10, 20 and 30 cm standing water. The inset in Figure 14 shows the mean as well as the minimum and maximum values for all waves at each of the standing water levels. Although there is some scatter in the data, it would appear that the incoming hydraulic jump has a Froude number of approximately 2.0 for all standing water depths.

Froude scaling implies that the force on a prototype

structure, Fp, can be determined from the force on the model structure, Fm, using

!! = !!!! (2a)

where λ is the dimensional scale between prototype and model. For the two-dimensional condition tested in this study, the out-of-plane dimension was not scaled. Therefore Froude scaling reduces to

!! = !!!! (2b)

All relevant dimensions must change by the same ratio, λ, for Froude scaling to apply. Hence λ is given by

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6 Copyright © 2011 by ASME

! =!!"!!"

= !!"!!"

(3)

where subscripts p and m refer to prototype and model respectively. This means that both the standing water depth and jump height have to change by the same ratio. Given that the standing water depths were 5, 10, 20 and 30 cm, this implied available λ values of 1.5, 2, 3, 4 and 6. All jump heights were compared to find those that matched one of these λ values within 5%. Matches were only found for λ values of 1.5, 2 and 3. Figure 15 shows the relationship between the ratio of maximum forces and λ2 for these matching conditions. Although there is scatter about the one-to-one match line, these data appear to confirm that Froude scaling is appropriate for the maximum force applied by a tsunami bore to a solid wall.

Figure 14: Froude number for all wave trials. Inset plot

shows average values for each standing water depth.

Figure 15: Froude scaling verification.

DESIGN EQUATION FOR MAXIMUM FORCE The data for the wet bed case have been used to develop a

design equation for the maximum bore impact force on a wall. The equation is based on the simplified model shown in Figure 16. In addition to ds and hj, hr is defined as the height of the

reverse flow that results from the rebound of the incoming fluid. The sum of the heights defines the total ponding height, hp. It is assumed that each of the three fluid layers has a uniform velocity, vs, vj and vr, respectively.

Figure 16. Schematic of bore impacting wall

Conservation of Mass It is reasonable to assume that the velocity in the initial

standing water layer is some fraction of the incoming jump velocity, i.e.,

!! = !!!! (4)

From the conservation of mass inside the control volume indicated by the fluid boundaries shown in Figure 16, and assuming an incompressible fluid,

  !! ℎ! + !!!! = !!ℎ! (5)

The reverse velocity vr can be expressed in terms of the Froude number as

!! = !"! !ℎ! (6)

Substitution of eq. (6) into eq. (5) results, after some manipulation, in the following expression for hr:

ℎ!!/! =

!! ℎ!+!!!!!"! !

(7)

Momentum Equation Assuming momentum accumulation within the control

volume is zero, the one dimensional momentum flux can be written as

! = (!!)!" − !! !"# − !  !  !" −!" !  !  !"!"# (8)

where ! is the force per unit width on the wall, ! is the mass flow rate per unit width, ! is the velocity, ! is pressure, and ! is the sign of the normal to the control surface. If it is assumed that the pressure on the inflow boundary is hydrostatic and on the outflow boundary is atmospheric, eq. (8) can be written as

! = !ℎ!!!! + !!!!!! + !ℎ!!!! +!!!!ℎ!! (9)

where ℎ! = ℎ! + !!. Substituting eq. (4) and rearranging gives

! = !!!!ℎ!! + ! ℎ! + !!!!! !!! + !ℎ!!!! (10)

Using eqs. (6) and (7), the last term of eq. (10) can be written as

0

1

2

3

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Frou

de n

umbe

r

h /d

d = 30 [cm]d = 20 [cm]d = 10 [cm]d = 5 [cm]

0123

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50

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N]

h / d

d [cm]

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ss

ss

j s

ssss s

j s

0

50.0

100.0

150.0

200.0

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erro

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d [cm]s

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12

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F /

F

!2

pm

IN

FL

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vr

jh

sdbh jv

vs

hr

hp

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7 Copyright © 2011 by ASME

!ℎ!!!! = !!! ℎ!+!!!!

!

!/!!  !"!

!/! (11)

The expression for force involves the parameters, vj, αs, Frr, ds and hj. Jump velocity

The bore front velocity was measured by processing video of the moving front captured by a high-resolution camera. Mohammed [31] showed that hydraulic jump theory provides a good estimate for the incoming bore velocities. From hydraulic jump theory,

!! = !!!!!

!!!!

!+ !

!!!!!

(12)

An advantage of using eq. (12) for design is that it removes the jump velocity, vj, as an unknown. Design Equation

It can be assumed that a designer will be able to specify ds and hj as part of the design condition. Knowing what to use for αs and Frr is more difficult. Considering all the data sets for ds = 5, 10, 20, and 30 cm, we used the method of least–squares to obtain values for αs and Frr. These values were 0.0 and 0.96, respectively. For simplicity and practical application we use the values of αs = 0.0 and Frr = 1.0. The first value implies that as the jump portion of the water enters the domain, the still water velocity will always be “zero”. Substituting the values for αs and Frr, and using eq. (11), eq. (10) simplifies to

! = !!!!ℎ!! + !ℎ!!!! + !!!/! ℎ!!!

!/! (13)

Alternative Equations

Results from eq. (13) will be compared to several previously proposed equations. Cross [32] proposed

! = !!!!ℎ!! + !ℎ!!!! (14)

Eq. 14 results from the present approach if αs = 1.0 and Frr = 0.0 (no reverse flow). Asakura et al. [33] proposed

! = !!!!(3ℎ!)! (15)

based on experiments with a similar beach slope and flat reef configuration, but adding a vertical seawall a short distance in front of the test specimen. Fujima et al. [34] recently published an approach, which is similar to the one introduced by Yeh [35], however, omitting the drag coefficient, CD, and introducing instead a constant coefficient. The experimental setup was similar to Asakura et al. [33]. The final form involves two equations, based on the maximum water inundation level and structure distance from the reef break. The equation used here is

! = 1.3!ℎ!!!! (16)

RESULTS In this section the comparison between the different impact

force equations is presented based on the data obtained in our experiments.

Figure 17 shows the predicted force from the proposed approach (eq. 13), Cross (eq. 14), Asakura (eq. 15), and Fujima (eq. 16). The solid black line defines the ideal trend on which the points would lie if the predicted results equaled the experimental results. For points below the line, the force is underestimated; for points above the line, the force is overestimated. Visually, it appears that the proposed approach in general lies most closely to the ideal trend line.

Figure 17. Predicted force versus experimental force.

Figure 18. Percentage error versus initial standing water

level for results in Figure 17.

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8 Copyright © 2011 by ASME

The percentage error is calculated for each data point. The values plotted in Figure 18 are the averages of the percentage errors for all the data points for each initial water level. In general, the proposed method gives smaller average errors.

Another comparison of the predicted force from eq. 13 and the experimental result is presented in Figure 19. The experimental data points are represented by symbols, whereas the curves are the predicted values. The predictions are quite good. Figure 19 also illustrates the variability in the experimental data. Although the incoming solitary waves were dimensionally very consistent, the transformation to a broken bore and the turbulence inherent in the bore resulted in variability in the force measured on the wall for nominally identical test conditions. For each of the still water depths, ds, identified by the symbols in Figure 19, the vertical scatter indicates the variability in resulting peak wall force for bores with a similar jump height, hj.

Figure 19. Variability and proposed approach match to

experimental data.

CONCLUSIONS This paper presents results of an experimental laboratory

study to quantify the lateral load applied to a vertical wall when subjected to different size tsunami bores. A method is proposed to predict the peak lateral force on the vertical wall given only the incoming jump height, hj, and the standing water depth, ds. Based on these results, the following conclusions are made:

• The hydrodynamic forces on the wall are much larger than

typical lateral design forces resulting from wind or seismic loading. Non-structural walls will likely break away under these loads, thereby reducing the tsunami load on the structural frame. However, structural walls must be able to resist the tsunami loads so that they continue to support the building gravity loads.

• The proposed design equation provides a good estimate of the experimental force for various bore heights and

standing water depths. The average error for a particular standing water level is generally around 10%. This is an improvement over prior expressions found in the literature.

• Although the design equation was developed for scaled model results, it can be used for prototype scale following Froude scaling.

• The proposed design equation assumes that the main impact force comes from the incoming jet of water, described here as a ‘jump height’. While such an approach might not resemble the actual impact phenomena, for design purposes it appears to be sufficient. Further investigation using computational fluid dynamics can be performed to verify fluid flow mechanics within the fluid.

• The proposed design equation is only valid for wet bed cases. For bores traveling on top of a dry bed, the impact forces are generally smaller than for wet beds, for the same jump height. However, the dry bed condition should be investigated further.

ACKNOWLEDGMENTS Funding for this research was provided by the National

Science Foundation through the NSF George E. Brown, Jr. Network for Earthquake Engineering Simulation (grants #0530759 and CMMI-1041666). This funding is gratefully acknowledged. In addition, the authors would like to acknowledge the important contributions to the experiments of Geno Pawlak, graduate student Jillian Santo, and the OSU staff of the TWB.

REFERENCES [1] Saatcioglu, M., Ghobarah, A., Nistor, I., 2005, ‘Reconnaissance Report on The December 26, 2004 Sumatra Earthquake and Tsunami,’ Report The Canadian Association for Earthquake Engineering, 21 pp. [2] Yeh, H., Francis, M., Peterson, C., Katada, T., Latha, G., Chadha, R.K., Singh, J.P., Rahghuraman, G., 2007, ‘Effects of the 2004 Great Sumatra Tsunami: Southeast Indian Coast,’ Journal of Waterway, Port, Coastal, and Ocean Engineering, 133, pp. 382-400. [3] Robertson, I., Riggs, H.R., Yim, S., Young, Y.L., 2006, ‘Lessons from Katrina,’ ASCE Civil Engineering magazine, April, pp. 56-63. [4] Robertson, I.N., Riggs, H.R., Yim, S.C.S., Young, Y.L., 2007, ‘Lessons from Hurricane Katrina storm surge on bridges and buildings,’ Journal of Waterway, Port, Coastal, and Ocean Engineering, 133, pp. 463-483. [5] Robertson, I.N., Carden, L., Riggs, H.R., Yim, S., Young, Y.L., Paczkowski, K., and Witt, D., 2010, 'Reconnaissance Following the September 29, 2009 Tsunami in Samoa', Research Report UHM/CEE/10-01, University of Hawaii, http://www.cee.hawaii.edu/reports/UHM-CEE-10-01.pdf [6] Bea, R.G., Iverson, R., Xu, T., 2001, ‘Wave-in-deck forces on offshore platforms,’ Journal of Offshore Mechanics and Arctic Engineering, 123, pp. 10-21.

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9 Copyright © 2011 by ASME

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