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Chapter 11

Tsunami-Induced Forces on Structures

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Ioan Nistor∗ , Dan Palermo, Younes Nouri, Tad Murty

and Murat Saatcioglu
Department of Civil Engineering, University of Ottawa
by KAINAN UNIVERSITY on 02/15/17. For personal use only.

161 Louis Pasteur, CBY, A115, Ottawa, Canada

∗
inistor@uottawa.ca

This chapter deals with the estimation of tsunami-induced hydrodynamic forces

on infrastructure located in the vicinity of the shoreline. While extensive research
has been conducted on the impact of hydrodynamic forces on classical coastal
protection works (breakwaters, seawalls, reefs, etc.), there is limited research on
their impact on structures such as buildings and bridges located inland. The dev-
astation brought by the 26 December 2004 Indian Ocean Tsunami on coastal com-
munities in Indonesia, India, Sri Lanka, Thailand, and other countries outlined
the urgent need for research on the evaluation of structural resilience of infras-
tructure located in tsunami-prone areas. This chapter summarizes the state-of-
the-art knowledge with respect to forces generated by tsunami-induced hydraulic
bores, including debris impact. Further, sample calculations of tsunami loading
on a prototype structure are presented.

11.1. Introduction

Tsunami waves represent extreme, often catastrophic events, which significantly and
adversely impact coastal areas. In spite of the lower frequency of occurrence com-
paring to storms and storm-induced surges, tsunami-induced coastal flooding often
leads to massive casualties and tremendous economic losses.1–3 Hence, tsunamis are
rare events, high-impact natural disasters.
The devastating effects of the 26 December 2004 Tsunami on many coun-
tries bordering the Indian Ocean raised public concern and revealed existing defi-
ciencies within the current warning and defense systems against tsunamis. One of
the important elements that needs significant improvement is the estimation of
forces generated by tsunami-induced bores, as well as water-borne debris. Before
the 2004 Indian Ocean Tsunami, the design of structures against tsunami-induced
forces was considered of minor importance when compared to the attention given
to tsunami warning systems. This was due to the assumption that tsunamis are

261
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262 I. Nistor et al.

(a) (b)
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(c) (d)

Fig. 11.1. Tsunami damage in Thailand and Indonesia (December 2004 Indian Ocean Tsunami):
(a) severe structural damage, Khao Lak, Thailand; (b) column failure of a reinforced con-
crete frame, Phuket, Thailand; (c) column failure due to debris impact, Banda Aceh, Indonesia;
(d) punching failure of infill walls, Banda Aceh, Indonesia.4

rare events, with significantly high return periods (sometimes more than 500 years).
Reconnaissance missions of the December 2004 Indian Ocean Tsunami disaster
revealed that tsunami-induced forces can lead to severe damage or collapse of struc-
tures as shown in Fig. 11.1.3–11 Therefore, these forces should be properly accounted
for in the design of infrastructure built within a certain distance from the shoreline
in tsunami-prone areas.
The design of coastal structures such as breakwaters, jetties, and groins against
waves is typically based on considering the effect of breaking waves and their asso-
ciated forces, and is well established. Unlike coastal structures, the evaluation of
tsunami-induced hydrodynamic forces on structures used for habitation and/or eco-
nomic activity, received little attention by researchers and engineers.
Results of field surveys conducted in the aftermath of the December 2004 Indian
Ocean Tsunami in Indonesia and Thailand showed that poorly detailed concrete
structures experienced severe damage.3,4 This highlighted the fact that the current
structural design codes do not account for tsunami-induced forces and the impact
of associated debris. Reinforced concrete structures have been observed to with-
stand tsunamis with acceptable low levels of damage.12 However, as shown in
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Tsunami-Induced Forces on Structures 263

: The 2004 Indian Ocean Tsunami

: Past Tsunamis

Damage

Partial Damage

Withstand

0 1 2 3 4 5 6 7 20
Lack of data
Inundation Depth (m)
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Fig. 11.2. Relation between the inundation depth and degree of damage to reinforced concrete
buildings.13
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Fig. 11.2, inundation depths of more than 5 m can induce partial damage to concrete
structures.
Currently, there are no clearly established procedures to address the aforemen-
tioned forces. Moreover, significant disagreement on existing empirical formulae fos-
tered new research interest in an effort to properly address the inclusion of both
tsunami-induced forces and the impact of debris into design codes. Aspects related
to these forces are discussed in this chapter. Some of the shortcomings and incon-
sistencies of existing codes are also highlighted.

11.2. Literature Review

11.2.1. Tsunami-induced hydraulic bores

As tsunami waves advance toward the shoreline and water depth decreases, their
wave height increases while celerity decreases. Tsunami waves may break offshore or
at shoreline, inundating low-lying coastal areas in the form of a hydraulic bore. On
the other hand, tsunami inundation can also occur as a gradual rise and recession
of the sea level for the case of nonbreaking tsunami waves. The width of the conti-
nental shelf, the initial tsunami wave shape, the beach slope, and the tsunami wave
length are the parameters which govern the breaking pattern of tsunami waves.2,15
Figure 11.3 shows a tsunami wave approaching the Khao Lak Beach in Thailand
during the December 2004 Indian Ocean Tsunami.
Tsunami waves have a larger horizontal length scale compared to the vertical.
Consequently, implementing shallow water wave theory (i.e., depth-integrated equa-
tions of momentum and mass conservation with the assumption of a hydrostatic
pressure field) seems to be a reasonable method for representing tsunami wave prop-
agation. Using these equations, it has been shown that the behavior and runup of
nonbreaking tsunami waves can be predicted with acceptable accuracy. However,
disagreement has been observed between experiment and prediction, in terms of
behavior and runup of breaking waves and the resulting bore.16,17
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264 I. Nistor et al.

(a) (b)
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(c) (d)

Fig. 11.3. Tsunami wave in Khao Lak, Thailand (December 2004 Indian Ocean Tsunami):
(a) water recedes; (b) waves approach the shoreline; (c) tsunami waves break close to the shoreline;
(d) tsunami waves inundate the shoreline.14

Significant efforts were directed toward the experimental investigation of the

mechanisms of tsunami bore runup.2,18,19 Although a two-dimensional dam-break
phenomenon was used in the experiments, the bore motion was observed to be fully
three-dimensional and highly turbulent. This is in agreement with other observa-
tions regarding the irregularity of the bore front in transverse direction and the
noticeable fluctuation of the front propagation.19
The onshore propagation of the tsunami wave is similar to the classical dam-
break problem. Chanson20 compared the instantaneous free surface flow profiles
of a tsunami-induced bore with floating bodies to a dam-break flow on a hori-
zontal bed. A frame-by-frame analysis of a video recording taken during the Indian
Ocean Tsunami in Banda Aceh, Indonesia was used to obtain the flow profile of
the tsunami-induced bore. The agreement between the tsunami field data and the
dam-break analytical formulation demonstrated the analogy between propagation
of tsunami-induced bores and dam-break flow.
Direct estimation of tsunami inundation bore velocities is limited. Tsutsumi
et al.21 estimated the nearshore flow velocity of the tsunami caused by the Southwest
Hokkaido Earthquake of 12 July 1993. Forces exerted on a bent iron handrail and
an iron guardrail were estimated using in situ strength tests. Then, the velocity of
the tsunami flow was calculated from the forces using Morison’s equation.22
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Tsunami-Induced Forces on Structures 265

Matsutomi et al.13 and Chanson20 estimated inundation flow velocities in terms

of inundation depth. Frame-by-frame analysis of video recordings from the 2004
Indian Ocean Tsunami in Banda Aceh was conducted. The videos showed that
the inundation flow carried numerous floating bodies with approximately the same
speed as that of the bore. This may have influenced the bore characteristics. Fur-
thermore, Matsutomi et al.13 developed an empirical model that predicts the bore
front velocity. Also, surveyed data were used to improve the criterion for estimating
the degree of structural damage.

11.2.2. Tsunami-induced forces on structures

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Snodgrass et al.23 noticed that broken waves induced larger hydrodynamic hori-
zontal forces on a test pile compared to waves breaking at the pile location. As
previously mentioned, broken tsunami waves inundate shoreline in the form of a
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hydraulic bore, which is a fast moving body of water with an abrupt front. However,
mechanisms of impingement of broken tsunami waves on structures located inland
are not yet well understood.
Pioneering analytical and experimental attempts to quantify forces due to bores
date back to Stoker,24 Cumberbatch,25 Fukui,26 Cross,27 and Dames and Moore.28
Comprehensive experimental investigation of the interaction of bores and dry-
bed surges with a vertical wall was performed by Ramsden and Raichlen29 and
Ramsden.30,31 In these experiments, three flow conditions were analyzed: (1) tur-
bulent bores (initial still water downstream of the gate); (2) dry-bed surges (no
initial water depth downstream of the gate); and (3) solitary waves. Forces and over-
turning moments due to bores and dry-bed surges were recorded and calculated,
respectively. The results of Ramsden’s studies are not applicable to the estimation
of impulsive forces.31 It was observed that the pressure distribution during impact
is essentially nonhydrostatic. The experiment also demonstrated that the transition
from undular to turbulent bores led to a discontinuous increase in water-surface
slope, followed by an increase in measured runup, pressure head, and exerted forces
and moments. Figure 11.4 shows the difference between a strong turbulent bore and
a dry-bed surge with approximately the same celerity.
It was shown that recorded forces gradually increased to an approximately con-
stant value for both the case of a surge and a bore. No impulsive (shock) force
exceeding the hydrodynamic force was observed. However, an initial impulsive
pressure equal to three times the pressure head, corresponding to the mea-
sured runup, was recorded. Ramsden31 further derived empirical formulae for the
maximum force and moment exerted on a vertical wall due to the bore impact
[Eqs. (11.1) and (11.2)].




3 2
F H 1 1 H H
= 1.325 + 0.347 ++ , (11.1)
Fl h 58.5
7160 h h


2
3
M H 1 H 1 H
= 1.923 + 0.454 + + , (11.2)
Ml h 8.21 h 808 h
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266 I. Nistor et al.

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Fig. 11.4. Comparison of: (a) wave profile; (b) runup; (c) pressure head; (d) force due to a strong
turbulent bore and a dry-bed surge.31

where F is the force on the wall; Fl is the force on the wall due to a runup equal to
twice the wave height, assuming hydrostatic pressure; H is the wave height at the
wall; h is still water depth; M is the moment on the wall; and Ml is the moment
corresponding to Fl .
Okada et al.32 conducted a survey of previous studies on tsunami wave forces
and pressures, and identified five empirical formulae for tsunami-induced forces or
pressures. It was found that calculation of tsunami load on structures using these
formulae would result in approximately the same magnitude of load. These formulae
are as follows:

• Tsunami wave pressure without soliton breakup,33

• Tsunami wave pressure with soliton breakup,33
• Tsunami wave pressure without soliton breakup,34
• Tsunami-induced wave forces on houses,35
• Tsunami force exerted on houses.36
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Tsunami-Induced Forces on Structures 267

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Fig. 11.5. Measured and nondimensional force history for a square column.37

Arnason37 measured forces exerted on rectangular, rhomboidal, and circular

structures due to a hydraulic bore on a dry bed. It was observed that the surge
force overshot the hydrodynamic force in the case of a square column for small bore
heights (Fig. 11.5). However, no overshoot was recorded for the case of circular
and rhomboidal columns. This is in agreement with the results obtained by Nouri
et al.,38 where similar experiments with larger bore heights, up to three times those
of Arnason,37 were performed (Fig. 11.6).
Nouri et al.38 conducted experiments with the objective of estimating bore-
induced forces on free-standing structural components. The effect of other param-
eters such as upstream obstacles, flow constrictions, and debris impact was also
investigated. The structural components were subjected to a dam-break flow gen-
erated by impoundment depths of 0.5, 0.75, and 0.85 m.
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268 I. Nistor et al.

350

250
Force (N)

150
h0 = 1.00 m
h0 = 0.85 m
50
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-50
10 12 14 16 18 20 22
Time (s)
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Fig. 11.6. Time history of exerted forces on a circular structure38 ; h0 is the impoundment depth.

60 60
Height of the structure (cm)

Height of the structure (cm)

50 50

40 t=0.000 s 40
t=0.160 s
t=0.006 s t=0.170 s
30 t=0.006 s 30 t=0.180 s
t=0.009 s t=0.190 s
20 20

10 10

0 0
-2 3 8 13 18 -2 3 8 13 18
P (kPa) P (kPa)

Fig. 11.7. Variation of pressure distribution on the front face — circular structure38 ; t = 0.0 s is
the instant when the bore impacts the structure.

The variation of the vertical distribution of pressure was measured. Selected

snapshots from the variation of pressure distribution due to bore impact generated
by an impoundment depth of 1.0 m are shown in Fig. 11.7.

11.2.3. Debris impact force

Matsutomi39 performed small- and full-scale experiments on impact forces gen-
erated by driftwood on rigid structures. Dam-break waves generated in a small
flume carried pieces of lumber to the point of impact on a downstream wall. Also,
full-scale experiments in which wooden logs impacted a frame were conducted in
open air, and impact forces were measured. An empirical formula for estimating the
impact force, F , was derived using regression analysis of collected data [Eq. (11.3)].

1.2
0.4
F u σf
= 1.6CM √ , (11.3)
γw D2 L gD γw L
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Tsunami-Induced Forces on Structures 269

Fm/γ D2L

σf / γL = 2000

1500
120
1000

500
80

200
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100
40
20
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0
0.0 1.0 2.0 3.0 VA0/(gD)0.5

Fig. 11.8. Impact forces of wood logs for bores and surges.39

where γw is the specific weight of wood, D is the diameter of the log, L is the
length of the log, CM is a coefficient which depends on the flow passing around the
receiving wall (≈ 1.7 for bore or surge, and 1.9 for steady flow), u is the velocity of
the log at impact, and σf is the yield stress of the log. Figure 11.8 shows the design
chart based on Eq. (11.3).
Currently, three basic models are proposed for estimating the forces due to the
impact of debris on structures, which are used by a few design codes. In these
models, the impact force is calculated based on the mass and velocity of debris,
while ignoring the mass and rigidity of the structure. However, other than the mass
and velocity of debris, each model needs an additional parameter. The three models
and their corresponding additional parameters are

• Contact stiffness — stiffness between debris and structure,

• Impulse–momentum — stopping time of debris after impact and time history of
impact,
• Work energy — distance traveled from where initial contact occurs, to where
debris stops.

Haehnel et al.40,41 used a single-degree-of-freedom model with effective collision

stiffness as an additional parameter. They reviewed the current models discussed
above and demonstrated that none of the additional parameters are independent.
Hence, the three models are equivalent, provided that additional parameters are
appropriately selected. Further, small- and large-scale experiments were performed
in order to develop the single-degree-of-freedom model. Small-scale tests were per-
formed in a flume where wooden logs were released into the flow and impacted a
load frame located further downstream. Large-scale experiments were performed in
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270 I. Nistor et al.

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Fig. 11.9. Effect of impact orientation on force.40

a large basin where water was stationary and logs were placed on a movable car-
riage. The effect of parameters such as added mass of the water and the eccentricity
and obliqueness of the collision were also considered. Figure 11.9 shows the effect of
impact orientation on the measured force. It was found that the maximum impact
force, Fi,max , can be calculated using Eq. (11.4).

Fi,max = Maxk̂x = u k̂m1 , (11.4)

where u is the impact velocity of the log, k̂ is the constant effective stiffness between
the log and the structure, and m1 is the mass of the log. Based on experiments,
Haehnel et al.40 found the value of k̂ = 2.4 MN/m to be the representative for the
upper envelope of the collected data.

11.3. Existing Design Codes

The design of structures in flood-prone areas has previously been investigated.

However, few existing codes specifically address the design of onshore structures
built in tsunami-prone areas. Design codes that specifically address tsunami-induced
forces were introduced in order to suggest provisions for designing infrastructure
in tsunami-prone areas. Post-tsunami field investigations of the December 2004
Indian Ocean Tsunami are indicative of the extreme loads generated by tsunami-
induced floods,3,4 and have outlined the need for developing new design guidelines.
Recent research work42 indicated that tsunami-induced loads are comparable or can
exceed earthquake loads. Tsunami-induced forces and the impact of debris are not
properly accounted for in the current codes, and significant improvement is needed.
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Tsunami-Induced Forces on Structures 271

At present, only four design codes and guidelines specifically account for tsunami-
induced loads as listed below:

• FEMA 55: The code is adopted by the Federal Emergency Management Agency,
the United States, and recommends formulae for tsunami-induced flood and wave
loads.43
• The City and County of Honolulu Building Code (CCH): The code, developed
by the Department of Planning and Permitting of Honolulu, Hawaii, United
States, makes provisions for regulations that apply to districts located in flood
and tsunami-risk areas.44
• Structural Design Method of Buildings for Tsunami Resistance (SMBTR): The
code is proposed by the Building Center of Japan32 and outlines the structural
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design for tsunami refuge buildings.

• Development of Guidelines for Structures that Serve as Tsunami Vertical Evacu-
ation Sites: The guidelines were prepared by Yeh et al.45 for estimating tsunami-
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induced forces on structures for the Washington State Department of Natural

Resources.

There are several other design codes (sometimes country-specific) which contain
prescriptions and design guidelines for flood-induced loads. Examples of widely used
codes are indicated below:

• 1997 Uniform Building Code, Appendix 33, proposed by the International

Conference of Buildings Officials (ICBO),47
• ASCE 7-05 of the American Society of Civil Engineers,48
• 2006 International Building Code by the International Code Council.49

However, none of the above codes address directly the tsunami-induced forces,
which represent the focus of this chapter. The reader is advised to refer to these
codes when seeking guidance for the design of structures subjected to flood-induced
loads other than tsunamis: coastal flooding due to storm surges, flooding of river
banks above bank-full conditions, etc.

11.3.1. Tsunami-induced forces

A broken tsunami wave running inland generates forces which affect structures
located in its path. Three parameters are essential for defining the magnitude and
application of these forces: (1) inundation depth, (2) flow velocity, and (3) flow
direction. The parameters mainly depend on: (a) tsunami wave height and wave
period; (b) coast topography; and (c) roughness of the coastal inland. The extent
of tsunami-induced coastal flooding, and therefore the inundation depth at a spe-
cific location, can be estimated using various tsunami scenarios (magnitude and
direction) and modeling coastal inundation accordingly. However, the estimation of
flow velocity and direction is generally more difficult. Flow velocities can vary in
magnitude from zero to significantly high values, while flow direction can also vary
due to onshore local topographic features, as well as soil cover and obstacles. Forces
associated with tsunami bores consist of: (1) hydrostatic force, (2) hydrodynamic
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272 I. Nistor et al.

(drag) force, (3) buoyant force, (4) surge force, and (5) impact of debris. A brief
description of these forces is further presented.

11.3.1.1. Hydrostatic force

The hydrostatic force is generated by still or slow-moving water acting perpen-
dicular onto planar surfaces. The hydrostatic force per unit width, FHS , can be
calculated using Eq. (11.5), where ρ is the seawater density, g is the gravitational
acceleration, ds is the inundation depth, and up is the normal component of flow
velocity. Equation (11.5) is proposed by CCH and accounts for the velocity head.
Alternatively, FEMA 55 does not include the velocity head in its formulation since
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it is assumed to be a negligible component of the hydrostatic force:

 2
1 u2p
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FHS = ρg dS + . (11.5)
2 2g

The point of application of the resultant hydrostatic force is located at one-third

distance from the base of the triangular hydrostatic pressure distribution. In the
case of a broken tsunami wave, the hydrostatic force is significantly smaller than the
drag and surge forces. Conversely, Dames and Moore28 noted that the hydrostatic
force becomes important when tsunami is similar to a rapidly-rising tide.

11.3.1.2. Buoyant force

The buoyant force is the vertical force acting through the center of mass of a sub-
merged body. Its magnitude is equal to the weight of the volume of water displaced
by the submerged body. The effect of buoyant forces generated by tsunami flooding
was clearly evident during post-tsunami field observations.1,5,6 Buoyant forces can
generate significant damage to structural elements, such as floor slabs, and are cal-
culated as follows:

FB = ρgV, (11.6)

where V is the volume of water displaced by submerged structure.

11.3.1.3. Hydrodynamic (drag) force

As the tsunami bore moves inland with moderate to high velocity, structures are
subjected to hydrodynamic forces caused by drag. Currently, there are differences in
estimating the magnitude of the hydrodynamic force. The general expression for this
force is shown in Eq. (11.7). Existing codes use the same expression, but different
drag coefficient values (CD ). For example, values of 1.0 and 1.2 are recommended
for circular piles by CCH and FEMA 55, respectively. For the case of rectangular
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Tsunami-Induced Forces on Structures 273

piles, the drag coefficient recommended by FEMA 55 and CCH is 2.0:

ρCD Au2
FD = , (11.7)
2
where FD is the drag force acting in the direction of flow, A is the projected area
of the body normal to the direction of flow, and u is the tsunami-bore velocity.
The flow is assumed to be uniform, and therefore, the resultant force will act at
the centroid of the projected area. As indicated, the hydrodynamic force is directly
proportional to the square of the tsunami-bore velocity. The estimation of the
bore velocity remains one of the critical elements on which there is significant dis-
agreement in literature. A brief discussion on the tsunami-bore velocity is presented
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below.
Tsunami-bore Velocity. Previous research shows that significant differences in esti-
mating forces exerted on structures by tsunami bores, as well as impact of debris,
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are due to differences in estimating bore velocity. Since the hydrodynamic force is
proportional to the square of the bore velocity, uncertainties in estimating veloc-
ities induce large differences in the magnitude of the resulting hydrodynamic force.
Tsunami-bore velocity and direction can vary significantly during a major tsunami
inundation. Current estimates of the velocity are crude; a conservatively high flow
velocity impacting the structure at a normal angle is usually assumed. Also, the
effects of runup, backwash, and direction of velocity are not addressed in the current
design codes.
Although there is certain consensus in the general form of equation for the
hydrodynamic force, several researchers proposed different empirical coefficients.
The general form of the bore velocity is shown below [Eq. (11.8)]:

u = C gds , (11.8)
where u is the bore velocity, ds is the inundation depth, and C is a constant
coefficient.
Various formulations were proposed by FEMA 55 (based on Dames and
Moore28 ), Iizuka and Matsutomi,35 CCH,44 Kirkoz,50 Murty,51 Bryant,52 and
Camfield53 for estimating the velocity of a tsunami bore in terms of inundation
depth (Fig. 11.10). Velocities calculated using CCH and FEMA 55 represent a lower
and upper boundary, respectively.

11.3.1.4. Surge force

The surge force is generated by the impingement of the advancing water front of a
tsunami bore on a structure. Due to lack of detailed experiments specifically appli-
cable to tsunami bores running up the shoreline, the calculation of the surge force
exerted on a structure is subject to substantial uncertainty. Accurate estimation of
the impact force in laboratory experiments is a challenging and difficult task. CCH
recommends using Eq. (11.9), based on Dames and Moore28 :
FS = 4.5ρgh2 , (11.9)
where FS is the surge force per unit width of wall and h is the surge height.
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274 I. Nistor et al.

16
CCH: u=h
FEMA 55: u=2(gh)^0.5
Iizuka: u=1.1(gh)^0.5
12 Kirkoz: u=(2gh)^0.5
Murty: u=1.83(gh)^0.5
Bryant: u=1.67h^(0.7)
V (m/s)

4
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0
0 2 4 6
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d S (m)

Fig. 11.10. Comparison of various tsunami-bore velocities as a function of inundation depth.42

building
qx
3h
Design inundation depth
z
h
z
3ρgh

Fig. 11.11. Tsunami wave pressure for structural design recommended by SMBTR.32

The point of application of the resultant surge force is located at a distance h

above the base of the wall. This equation is applicable to walls with heights equal
to, or greater than 3h. Structural walls with height less than 3h require surge forces
to be calculated using an appropriate combination of hydrostatic and drag force for
each specific situation.
SMBTR recommends using the equation for tsunami wave pressure without
soliton breakup derived by Asakura et al.33 [Eq. (11.10)]. The equivalent static
pressure resulting from the tsunami impact is associated with a triangular dis-
tribution where water depth equals three times the tsunami inundation depth
(Fig. 11.11):

qx = ρg(3hmax − z), (11.10)

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Tsunami-Induced Forces on Structures 275

where qx is the tsunami wave pressure for structural design, z is the height of the
relevant portion from ground level (0 ≤ z ≤ 3h), ρ is the mass per unit volume of
water, and g is the gravitational acceleration.
Integration of the wave pressure formula for walls with heights equal to or greater
than 3h results in the same equation as the surge force formula recommended by
CCH [Eq. (11.9)]. The magnitude of the surge force calculated using Eqs. (11.9)
and (11.10) will generate a value equal to nine times the magnitude of the hydro-
static force for the same flow depth. However, a number of experiments31,37 did not
capture such differences in magnitude. Yeh et al.45 commented on the validity of
Eq. (11.9) and indicated that this equation gives “excessively overestimated values.”
On the other hand, Nakano and Paku46 conducted extensive field surveys in order
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to examine the validity of the proposed tsunami wave pressure formula [Eq. (11.10)].
The coefficient 3.0 in Eq. (11.10) was taken as a variable, α, and was calculated
such that it could represent the boundary between damage and no damage in the
surveyed data. A value of α equal to 3.0 and 2.0 was found for walls and columns,
by KAINAN UNIVERSITY on 02/15/17. For personal use only.

respectively. The former is in agreement with the proposed formulae by both CCH
and SMBTR [Eqs. (11.9) and (11.10)].
The tsunami wave force may be composed of drag, inertia, impulse, and
hydraulic gradient components. However, SMBTR does not specify different compo-
nents for the tsunami-induced force, and the proposed formula presumably accounts
for other components.

11.3.1.5. Debris impact force

A high-speed tsunami bore traveling inland carries debris such as floating automo-
biles, floating pieces of buildings, drift wood, boats, and ships. The impact of floating
debris can induce significant forces on a building, leading to structural damage or
collapse.5,6
Both FEMA 55 and CCH codes account consistently for debris impact forces,
using the same approach and recommend using Eq. (11.11) for the estimation of
debris impact force:

dub ui
Fi = mb =m , (11.11)
dt ∆t
where Fi is the impact force, mb is the mass of the body impacting the structure,
ub is the velocity of the impacting body (assumed equal to the flow velocity), ui is
approach velocity of the impacting body (assumed equal to the flow velocity), and
∆t is the impact duration taken equal to the time between the initial contact of the
floating body with the building and the instant of maximum impact force.
The only difference between CCH and FEMA 55 resides in the recommended
values for the impact duration which has a noticeable effect on the magnitude of
the force. For example, CCH recommends the use of impact duration of 0.1 s for
concrete structures, while FEMA 55 provides different values for walls and piles for
various construction types as shown in Table 11.1.
According to FEMA 55, the impact force (a single concentrated load) acts hor-
izontally at the flow surface or at any point below it. Its magnitude is equal to
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276 I. Nistor et al.

Table 11.1. Impact duration of floating

debris (FEMA 55).

Impact duration (s)

Type of construction Wall Pile

Wood 0.7–1.1 0.5–1.0

Steel N.A. 0.2–0.4
Reinforced concrete 0.2–0.4 0.3–0.6
Concrete masonry 0.3–0.6 0.3–0.6
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the force generated by 455 kg (1000-pound) of debris traveling with the bore and
acting on a 0.092 m2 (1 ft2 ) surface of the structural element. The impact force is
to be applied to the structural element at its most critical location, as determined
by the structural designer. It is assumed that the velocity of the floating body goes
by KAINAN UNIVERSITY on 02/15/17. For personal use only.

from ub to zero over some small finite time interval (∆t). Finding the most critical
location of impact is a trial and error procedure that depends, to a large extent, on
the experience and intuition of the engineer.

11.3.1.6. Breaking wave force

Tsunami waves tend to break offshore and approach shoreline as a broken hydraulic
bore or a soliton, depending on the wave characteristics and coastal bathymetry.
Consequently, classic breaking wave force formulae are not directly applicable to
the case of tsunami bores. Hence, this chapter does not discuss the estimation of
breaking wave forces.

11.3.2. Loading combinations for calculating

tsunami-induced forces
Based on the location and type of structural elements, appropriate combinations
of tsunami-induced force components (hydrostatic, hydrodynamic, surge, buoyant,
and debris impact force) should be used in calculating the total tsunami force.
This is due to the fact that a certain element may not be subjected to all of these
force components simultaneously. Loading combinations can significantly influence
the total tsunami force and the subsequent structural design. Unlike the case of
tsunami waves, loading combinations for flood-induced surges are well-established
and have been included in design codes. The literature review revealed that proposed
tsunami loading combinations must be significantly improved and incorporated into
new design codes. Tsunami-induced loads are different from flood-induced loads.
Therefore, load combinations based on flood surges are not directly applicable to
tsunamis. Loading combinations proposed in the literature are as follows:

(i) FEMA 55 does not provide loading combinations specifically for calculation
of tsunami force. However, flood load combinations can be used as guidance.
Flood load combinations for piles or open foundations, as well as solid walls
(foundation) in flood hazard zones and coastal high hazard zones are presented
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Tsunami-Induced Forces on Structures 277

as follows:
Pile or open foundation:
Fbrkp (on all piles) + Fi (on one corner or critical pile only), or
Fbrkp (on front row of piles only) + Fdyn (on all piles but front row) +
Fi (on one corner or critical pile only).
Solid (wall) foundation:
Fbrkw (on walls facing shoreline, including hydrostatic component) +
Fdyn (assumes one corner is destroyed by debris),
where Fbrkp , Fi , Fdyn , and Fbrkw refer to breaking force on piles, impact force,
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hydrodynamic force, and breaking force on walls, respectively. The reader can
refer to FEMA 5543 for more details.
(ii) Yeh et al.45 modified flood load combinations provided by FEMA 55 and
adapted them for tsunami forces as follows:
by KAINAN UNIVERSITY on 02/15/17. For personal use only.

Pile or open foundation:

Fbrkp (on column) + Fi (on column), or
Fd (on column) + Fi (on column),
where Fd is the drag force.
Solid (wall ) foundation (perpendicular to flow direction):
Fbrkw (on walls facing shoreline) + Fi (on one corner), or
Fs (on walls facing shoreline) + Fi (on one corner), or
Fd (on walls facing shoreline) + Fi (on one corner),
where Fs is the surge force on walls.
(iii) Dias et al.54 proposed two load combinations called “point of impact” and
“post-submergence/submerged” (Fig. 11.12). These load combinations are
based on two conditions: (i) the instant that tsunami bore impacts the
structure, and (ii) when the whole structure is inundated.
Point of impact:
Fd (on walls facing shoreline) + Fs (on walls facing shoreline),
where Fs is defined as the hydrostatic force by Dias et al.54
Post-submergence/submerged:
Fd (on walls facing shoreline) + Fb (on submerged section of the structure).
The net hydrostatic force is zero and Fb (γV) is the buoyant force.

(a) (b)

Fd Fd
Fs Fs Fs
W W- V

Fig. 11.12. Loading combinations: (a) point of impact/not submerged; and (b) post-submergence/
submerged.54
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278 I. Nistor et al.

(a)

Fi

h FS

(b)
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Fi
dS Fd
by KAINAN UNIVERSITY on 02/15/17. For personal use only.

FHS FHS
Fig. 11.13. Proposed loading conditions: (a) point of impact; and (b) post-impact.42

(iv) Nouri et al.42 proposed two new load combinations based on the two condi-
tions considered by Dias et al.,54 as shown in Fig. 11.13. The proposed load
combinations by Nouri et al.42 are adapted to follow a consistent format as the
above combinations:
Columns:
Fs (on front row of piles only) + Fi (on one corner or critical column in the
front row only), or
Fd (on all piles) + Fi (on one corner or critical column only),
where Fs is the surge force on walls.
Solid (wall) foundation:
Fs (on walls facing shoreline) + Fi (on walls facing shoreline), or
Fd (on walls facing shoreline) + Fi (on one critical wall facing shoreline) +
Fb (on submerged section of the structure).

11.4. Design Example

Building codes provide guidance for the design of lateral force resisting systems
subjected to wind and seismic excitations. Tsunami-induced loading is normally
not considered. The objective of this example is to demonstrate the levels of
lateral loading associated with tsunamis for a prototype reinforced concrete building
located in a tsunami-prone area. Specifically, the loads generated by a tsunami
bore are addressed. Other researchers have provided comparisons between tsunami
loading and other lateral loads (Okada et al.,32 Pacheco and Robertson,55 Nouri
et al.,42 and Palermo et al.56 ).
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Tsunami-Induced Forces on Structures 279

6.0 6.0 6.0 m 6.0 6.0

6.0
B
Tsunami

6.0
C

6.0
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1 2 3 4 5 6
by KAINAN UNIVERSITY on 02/15/17. For personal use only.

Fig. 11.14. Plan view of structural layout of reinforced concrete moment-resisting frame.56

The following example consists of a moment-resisting frame with simple

geometry, as shown in Fig. 11.14. The thickness of the slab is assumed to be
200 mm, and the beams are 450 mm deep (including the thickness of the slab) and
300 mm wide. The exterior and interior columns are 450 mm and 500 mm square sec-
tions, respectively. The center-to-center storey heights are 3.65 m, and a 10-storey
structure is considered.
The components of the tsunami-induced forces are calculated based on CCH,
FEMA 55, and SMBTR. The calculation of tsunami-induced loads require a number
of assumptions, together with engineering judgment and lessons from reconnaissance
missions in regions affected by tsunamis. The authors assume that the net hydro-
static force exerted on the lateral system is zero in calculating the base shear. The
surge and drag forces require an effective area for load transfer to the lateral force
resisting system. In this example, two scenarios are considered: (1) 100% breakaway
walls, which expose the structural elements; and (2) nonbreakaway walls. In the
latter, the exterior nonstructural elements remain intact. For breakaway walls, the
external elements will be damaged and all the columns of the structure will be
subjected to drag force. The forces are calculated for inundation depths of 1–5 m,
and the structure is oriented with its short side parallel to the shoreline. When
designing structures located in tsunami-prone areas, the inundation depth at a
specific location should be obtained from tsunami inundation hazard maps, when
available. Otherwise, numerical modeling based on various tsunami scenarios should
be conducted in order to estimate the tsunami inundation depth.

11.4.1. Hydrodynamic (drag) forces

For the case where 100% breakaway walls are assumed and the columns are exposed
to the hydraulic bore, the drag forces are based on a drag coefficient of 2.0 for
square columns, as recommended by CCH and FEMA 55. For the second case,
nonbreakaway walls are assumed to remain intact and the hydraulic bore impacts
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280 I. Nistor et al.

the entire surface of the building. In this situation, the drag coefficients are taken
as 1.5 and 1.25 for CCH and FEMA 55, respectively.

11.4.2. Debris impact forces

To calculate debris impact, a mass of 455 kg is used to represent a floating object at
the water surface. The mass used is consistent with the recommendations of CCH
and FEMA 55. In this example, it is assumed that the debris will impact a single
reinforced concrete column. CCH assumes a duration of 0.1 s for concrete structures.
FEMA 55 recommends an impact duration ranging from 0.3 to 0.6 s for reinforced
concrete piles or columns. Hence, impact duration of 0.3 s is assumed in the design
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example.

11.4.3. Surge forces

by KAINAN UNIVERSITY on 02/15/17. For personal use only.

In this example, the surge force is applied over the full length of the building in the
direction of the tsunami for nonbreakaway walls. For the case of 100% breakaway
walls, it is assumed that the surge force will develop on the four exterior columns
which face the hydraulic bore. Note that the surge force is not applicable for FEMA
55 and that SMBTR assumes a different surge force per unit width for columns and
walls, as mentioned in Sec. 11.3.1.4.

11.4.4. Sample calculation: Breakaway walls

The following is a sample calculation for breakaway walls for the given structure
subjected to a tsunami inundation depth of 5 m:
m kg
g = 9.81 ; ρ = 1030 ; ds = 5 m.
s2 m3
Surge Force:


2 kg  m
FS = 2.0ρgh = 2.0 1030 3 9.81 2 (5 m)2
m s
N
= 0.505 × 106
; SMBTR
m


6N
FS × width = 0.505 × 10 (4(0.45 m)) = 909 × 103 N = 909 kN;
m


2 kg  m
FS = 4.5 ρgh = 4.5 1030 3 9.81 2 (5 m)2
m s
N
= 1.14 × 106
; CCH
m


6N
FS × width = 1.14 × 10 (4(0.45 m)) = 2046 × 103 N = 2046 kN.
m
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Tsunami-Induced Forces on Structures 281

Drag Force:

ρCD Au2
FD =
2


 m m
u = C gds = 2 9.81 2 (5 m) = 14 ; FEMA 55
s s

m
u = ds = 5 ; CCH
s
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CD = 2.0 Rectangular columns;

by KAINAN UNIVERSITY on 02/15/17. For personal use only.

A = (5 m)((16 × 0.45 m) + 8(0.50 m)) = 56 m2 ;

 2
1030 kg/m3 (2)(56 m2 ) (14m/s)
FD = = 11,317 × 103 N = 11,317 kN; FEMA 55
2

 2
1030 kg/m3 (2)(56 m2 ) (5 m/s)
FD = = 1442 × 103 N = 1442 kN. CCH
2
Debris Impact Force:


ui 14m/s
Fi = m = 455 kg = 21.2 × 103 N = 21 kN; FEMA 55
∆t 0.3 s


5 m/s
Fi = 455 kg = 22.8 × 103 N = 23 kN. CCH
0.1 s

11.4.5. Sample calculation: Nonbreakaway walls

The following is a sample calculation for nonbreakaway walls for the given structure
subjected to a tsunami inundation depth of 5 m.

m kg
g = 9.81 ; ρ = 1030 ; ds = 5 m
s2 m3
Surge Force:


N
FS = 1.14 × 106 (18 m + 0.45 m)
m

= 20,973 × 103 N = 20,973 kN SMBTR/CCH

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282 I. Nistor et al.

Drag Force:
ρCD Au2
FD =
2
CD = 1.25 Walls FEMA 55
CD = 1.5 Walls CCH

A = (5 m)(18 m + 0.45 m) = 92 m2 ;


1030 kg/m3 (1.25)(92 m2 ) (14 m/s)2
FD =
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2
= 11,652 × 103 N = 11,652 kN; FEMA 55


 2
1030 kg/m3 (1.5) 92 m2 (5 m/s)
by KAINAN UNIVERSITY on 02/15/17. For personal use only.

FD = = 1782 × 103 N = 1782 kN. CCH

2
Debris Impact Force:


ui 14 m/s
Fi = m = 455 kg = 21.2 × 103 N = 21 kN; FEMA 55
∆t 0.3 s


5 m/s
Fi = 455 kg = 22.8 × 103 N = 23 kN. CCH
0.1 s

11.4.6. Results
Tables 11.2 through 11.7 provide the results for the calculation of the individual
force components for the structure considered using CCH, FEMA 55, and SMBTR,
respectively.
Given the force components, a loading combination must be specified in order
to evaluate the maximum tsunami load that would be used for either design or
analysis purposes. Yeh et al.45 suggested loading combinations that are applicable
for tsunami loading. CCH does not specifically provide guidance to evaluate the
maximum tsunami load. Nouri et al.42 proposed a two-part loading combination:
Initial impact and Post-impact flow. For this example, these loading combinations
are similar to those of Nouri et al.42 Table 11.8 provides the results of the tsunami

Table 11.2. Tsunami-induced force components based on CCH for

breakaway walls.

Inundation depth Velocity Surge Drag Debris impact

Code (m) (m/s) (kN) (kN) (kN)

CCH 1 1 82 12 5
2 2 327 92 9
3 3 737 311 14
4 4 1310 738 18
5 5 2046 1442 23
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Tsunami-Induced Forces on Structures 283

Table 11.3. Tsunami-induced force components based on CCH for non-

breakaway walls.

Inundation depth Velocity Surge Drag Debris impact

Code (m) (m/s) (kN) (kN) (kN)

CCH 1 1 839 14 5
2 2 3356 114 9
3 3 7550 385 14
4 4 13,423 912 18
5 5 20,973 1782 23
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Table 11.4. Tsunami-induced force components based on FEMA 55

for breakaway walls.

Inundation depth Velocity Drag Debris impact

by KAINAN UNIVERSITY on 02/15/17. For personal use only.

Code (m) (m/s) (kN) (kN)

FEMA 55 1 6 453 10
2 9 1811 13
3 11 4074 16
4 13 7243 19
5 14 11,317 21

Table 11.5. Tsunami-induced force components based on FEMA 55

for nonbreakaway walls.

Inundation depth Velocity Drag Debris impact

Code (m) (m/s) (kN) (kN)

FEMA 55 1 6 466 10
2 9 1864 13
3 11 4195 16
4 13 7457 19
5 14 11,652 21

load calculation for CCH, FEMA 55 and SMBTR for an inundation depth of 5 m
based on loading combinations of Nouri et al.42
For the prototype moment-resisting frame structure with the short side per-
pendicular to the advancing bore, it is apparent that nonbreakaway walls or rigid
exterior nonstructural components can lead to large design base shears. CCH and
SMBTR estimate significantly larger base shears relative to FEMA 55 due to the
omission of a surge component in FEMA 55. It is evident that the width of exposed
surfaces affects the magnitude of total forces exerted on a structure. Therefore, it
would be prudent to orient buildings such that the short side is placed parallel to the
shoreline. Furthermore, using breakaway or flexible walls at the lower level would
reduce the lateral force that is transmitted to the lateral force resisting system. Note
that although the debris impact force is a negligible component in the base shear,
 July 31, 2009 8:18 9.75in x 6.5in b684-ch11 FA

284 I. Nistor et al.

Table 11.6. Tsunami-induced force components

based on SMBTR for breakaway walls.

Code Inundation depth (m) Surge (kN)

SMBTR 1 36
2 146
3 327
4 582
5 909

Table 11.7. Tsunami-induced force components

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based on SMBTR for nonbreakaway walls.

Code Inundation depth (m) Surge (kN)

SMBTR 1 839
by KAINAN UNIVERSITY on 02/15/17. For personal use only.

2 3356
3 7550
4 13,423
5 20,973

Table 11.8. Tsunami-induced load based on CCH, FEMA 55, and SMBTR for
5 m inundation depth.

Surge + Impact Drag + Impact Tsunami load

Standard Case (kN) (kN) (kN)

CCH Breakaway 2069 1465 2069

CCH Nonbreakaway 20,995 1804 20,995
FEMA 55 Breakaway N.A. 11,338 11,338
FEMA 55 Nonbreakaway N.A. 11,673 11,673
SMBTR Breakaway 909 N.A. 909
SMBTR Nonbreakaway 20,973 N.A. 20,973

it could be critical in the design of individual structural components subjected to

the debris impact.

Acknowledgment

Special thanks to Dr Andrew Cornett, Group Leader — Coastal, Ports and

Offshore at the Canadian Hydraulics Centre, National Research Council of Canada
in Ottawa, Canada, for his valuable advice.

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