Understanding the Generation, Propagation, Near- and Far-Field Impacts of TSUNAMIS
and Planning Strategies to Prepare for Future Events
Chapter 5
CHAPTER 5. IMPACT ASSESMENT
5.1. PALEOTSUNAMI STUDIES; CONTRIBUTION TO MITIGATION AND RISK
ASSESMENT
The study of paleotsunami traces is typically conducted by geologists--in particular by
stratigraphers and sedimentologists. Answers to s number of questions are looked for during
paleotsunami studies. They are
1. Do tsunamis leave deposits?
2. Where do tsunamis leave deposits, and where are they most likely preserved?
3. Are tsunami deposits distinctive? For example, how can we tell them from storm
deposits? flood deposits?
4. Can we distinguish locally generated from distally generated tsunami deposits?
5. How well can we date & correlate (paleo-)tsunami deposits?
6. Can we quantify run-up (or tsunami amplitude) from tsunami deposits?
7. If so, can we quantify paleo-seismic events from paleo-tsunami deposits?
The basic activity of paleotsunami studies is the identification, mapping, correlation and dating
of tsunami deposits. Each of these steps requires careful attention. The fundamental goal of
such work is to reconstruct past and pre-historic tsunamis, including a determination of
recurrence interval. Ideally, these reconstructions would include quantified estimates of
tsunami size and extent, as well as of earthquake size. These attempts to quantify
paleotsunami frequency and size can contribute directly to tsunami-mitigation and riskassessment programs.
Key problems in paleotsunami studies include the very basic issue of positive identification of
such deposits--for example, can we distinguish them from storm and flood deposits? Recent
studies of historic tsunami deposits have contributed to our understanding, and some criteria
have been developed for identifying tsunami deposits. However, it is known that tsunami
deposits are quite variable in character, and limited in geographic extent; for these reasons we
must be careful to realize that non-occurrence, or non-recognition of tsunami deposits at a
given locality does not mean, positively, that tsunamis did not occur at that locality.
Another key problem in paleotsunami studies is the dating and correlation of events. When we
go from one locality to another, are we looking at the same tsunami deposit, or at deposits
from separate events? Even with key marker horizons, such as distinctive ash layers,
correlation of tsunami deposits, which helps us estimate the size (and frequency) of
paleoevents, can be problematic. For example, some subduction zones are known to rupture
in segments, at close time intervals, followed by long intervals of low seismicity. Numerical
dating of prehistoric tsunami deposits is also difficult, at a time-scale accuracy of decades.
The standard dating technique is radiocarbon, and sampling of appropriate material (i.e., alive
during and then killed by the event, as opposed to transported or older/younger material) can
be problematic, as can contamination and correction issues. New techniques of surface
dating, such as thermoluminescence, and chlorine-36 dating, are promising, but still in the
development stage.
The third key problem is the quantification of paleotsunami events--how well can we calculate
wave size or paleorunup, for example? A few pioneering studies have been done in this realm,
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Chapter 5
but until some of the recent events have been used to test them, paleotsunami models remain
tentative. Thus paleotsunami researchers and others are called upon to conduct careful posttsunami surveys of recent tsunamis, paying particular attention not only to runup
measurements and damage, but also to geomorphic and sedimentologic effects.
5.2. POST TSUNAMI SURVEYS AND ASSESMENT
Tsunami leave traces on the shoreline and some of them can be measured bur some of them
can be obtained by interviews with eyewitnesses.
Near the source, the arrival of a local tsunami resembles the concurrence of several
phenomena running together (a syndrome), whose noticeable effects may happen almost
simultaneously. The main effects of the interaction of this tsunami syndrome with the coast
are (Farraras, 2000)












Sinking or rising sea-level and/or land-level in short term (hours) or long term (years),
Inundation and currents,
Uplifting or subsidence of the ground,
Earth landslides and/or submarine slumps,
Soil deformation and/or liquefaction,
Sediment: erosion-transport-deposition,
Vegetation: uprooting-destruction-immersion,
Exposure of the subaqueous (below inter-tidal level) marine life,
Salt water penetration into the inland soil,
Shoreline alteration,
Destruction and damage to human life, man-made structures and infrastructure, and
Inland and seaward transport of objects (ships, vehicles, houses, structures, etc)
Post-Tsunami Field Survey
At least, three basic elements are needed for the successful performance of a post-tsunami
field survey: trained personnel, adequate equipment, and standard procedures. Through
observation of the evidence (marks) left by the coastal interaction effects listed above, the
surveyors must be able to adequately identify and quantitatively evaluate the following
parameters at all coastal locations by measurements and/or eyewitness interviews.
1. The maximum horizontal extension of the inundation (for several transects), This data
provides estimating the height of initial wave.
2. The vertical reach of the inundation (maximum runup and maximum water level), This
data provides estimating the height of initial wave.
3. The period of the wave. This data provides estimating the width of the fault.
4. The arrival time, This data provides estimating the distance of the soıurce from shore
5. Shape of the wave such as leading deprpression or leading elevation wave. This data
provides estimating the location of the subsidence and uplift segments of the fault
and/or initial wave
6. Sudden erosion, transport, and deposition of sediments (volume, type, and rate),
7. Ground uplifting and/or subsidence (size and shape), and
8. Landslides and/or slumps (volume, rate, direction, orientation, type and size of
material).
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Chapter 5
9. Photographs from all conditions (surface and aerial with the footnotes of GPS
coordinate and date/time of the photo.
5.3.IMPLICATIONS of TSUNAMIS ON COASTAL and MARINE STRUCTURES
5.3.1. Added Mass Concept
Let us consider the motion of two dimensional objects in a fluid which is otherwise at
rest.
SWL
z
f
y
x
U
V
Assume the fluid is ideal (i.e. fluid viscocity,   0 ).
The motion of the object will result the flow of the fluid. The fluid motion can be
described by a velocity potential function,  .
Example:
Cylinder
a
U
Stream lines
 U
a2

Cos
  (y2  z2)
1
2
z
y
  tan 1 ( )
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Chapter 5
The kinetic energy which will be possessed by the moving fluid is equal to:
1
Tf   f
2
2
2

      



A  y    z  dA


The result of this integral can be written for any shape of the object (i.e. cylinder,
paralelopide, etc.) as:
Tf 
1 ' 2
MU
2
where M’ is a “mass term” which depends on the volume and shape of the object, on the
density of the fluid, and on the direction in which the object moves.
The kinetic energy of the object is equal to:
T0 
1
MU 2
2
M=mass of the object
Then, the total kinetic energy is:
TT  T f  T0 
1
( M  M ' )U 2
2
Consider that the force, F is acting on the object to accelarate it. The power which is
applied to change the kinetic energy of the system is, by definition:
d
(T0  T f )
dt
1
d (U 2 )
F .U  ( M  M ' )
2
dt
Power  F .U 
dU
dt
dU
F  (M  M ' )
dt
 ( M  M ' )U
This equation shows that, if you want to give the acceleration
should exert a force F which is greater than M .
dU
to the object, you
dt
dU
(the force which will be necessary in
dt
vacuum).
This is because, while accelerating the object, you would also give acceleration to the
surrounding fluid particles. One may say that an object accelating in a fluid, behaves as
if it has an apperent mass (M+M’) which is in excess of its real mass (M).


M’ is called the ADDED MASS
M+M’ is called the VIRTUAL MASS
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Chapter 5
CONCLUSION: The presence of the fluid creates a ‘resistance’ against the acceleration
of the body.The added mass is conventinally expressed in terms of a coefficient as:
M’=k (mass of the fluid replaced by the object)
 k f V
k=added mass coefficient
5.3.1.1. Added Masses Moment of Inertias of Some Two Dimensional Shapes
z
Cylinder
y
Plate
a
x
a
b
a
M yy' : a 2
added moment
M zz' : a 2
I xx' : 0
of inertia
O' 0
M
yy
M yy' : b 2
I xx'
M zz' : a 2
1
 (a 2  b 2 ) 2
8
cross
b
a
a
M zz' : a 2
1
I xx'  a 4
8
prism
a
2a
2a


 
M yy' : a 2
M yy' : 4.754 a 2
M yy' :  a 2  b 2  a 2 / b 2
M zz' : a 2
M zz' : a 2
M zz' : 4.754 a 2
I xx' 
2

a 4
I xx'  0.725 a 4
1
1

 
I xx' : a 4  Csc 4 2 2  Sin 4  Sin 2 2   
2

 2

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Sin  
where

2
2ab
a  b2
Chapter 5
2
complicated!
 
2
M xx'  M yy'  M zz'  a 3
Sphere with radius “ a ”
3
'
I 0
5.3.2. FORCES on an OBJECT
Morrison approach
A formula which fills in the gap between large objects in small waves and small objects
in a steady current is Morison's equation. The idea with this equation is to split the force
on a body in one linear acceleration term and one quadratic velocity term. The
acceleration and velocity should be evaluated from the undisturbed fluid motion as it
would have been if the body does not present. The magnitude of the force terms is
adjusted by dimensionless coefficients which are mainly depending on the geometry of
the body.
If the body in the fluid has length L, the net force the force on the body of volume V will
have the form
V/L is a characteristic cross sectional area. V is submerged Volume and the
characteristic length of the object. This force formula is rather close to what is called
Morison's equation.
F = FI + FD


inertia drag
force force
5.3.2.1. Drag Forces on the Objects in Fluids
Force in the direction of flow exerted by the fluid on the solid is called drag.
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Chapter 5
Figure shows a stationary smooth sphere of diameter DP situated in a stream, whose
velocity far away from the sphere is uµ to the right. Except at very low velocities,
when the flow is entirely laminar, the wake immediately downstream from the sphere
is unstable, and turbulent vortices will constantly be shed from various locations
round the sphere. Because of turbulence, the pressure on the downstream side of
the sphere will never fully recovered to that on the upstream side, and there will be a
form drag to the right of the sphere. (For purely laminar flow, the pressure recovery is
complete, and the form drag is zero.)
In addition, because of the velocity gradients that exist near the sphere, there will
also be a net viscous drag (also called as wall drag) to the right (In potential flow
there is no wall drag). The sum of these two effects is known as the (total) drag force,
FD. A similar drag occurs for spheres and other objects moving through an otherwise
stationary fluid - it is the relative velocity that counts.
Form drag can be minimized by forcing separations toward the rear of the body. This
is accomplished by stream lining (see figure below).
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The experimental results of the drag on a smooth sphere may be correlated in terms
of two dimensionless groups - the drag coefficient CD and particles Reynolds number
Re:
Re = u D/υ
In which A = П D2/4 is the projected area of the sphere in the direction of motion, and
υ is the kinematic viscosity of the fluid.
The subscript denote particle, NRe denotes Reynold’s number simply as Re
There are at least three distinct regions, for flow around a sphere.
1. For Re less than 1 (laminar), CD vs. Re is a straight line, and is given by the
relation
CD = 24/Re (given by Stoke's law, FD = 3pm uµ DP)
2. 1 < Re < 1000 , CD = 18 NReP-0.6 (transition)
3. 1000 < Re < 2 x 105 , CD = 0.44 (turbulent)
For cylinders and disks, for Re up to 1, CD = 24/Re and in other regimes CD varies
with ReP in the manner as shown in figure. Here the flow orientation is much
important. Drag coefficients varies with orientation of solid to the flow direction.
In all these curves the transition from laminar to turbulent flow is more gradual than
that for pipe flow (f vs. Re curve).
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FD=
1
CD f A U2
2
Chapter 5
CD=CD(Re , ks/D) ,drag coefficient
Raughness parameter (ks=raughness height)
The drag force FD is generated by the squared velocity component normal to the
element and normal to the lift force. The magnitude is adjusted by a drag coefficient
CD depending on the geometry.
5.3.2.2. Inertia Forces on the Object in the Fluid
FI=CM  f V
dU
where, V= immersed volume of the object
dt
The inertia force (FM is oriented along the acceleration vector component normal to
the member. The magnitude is proportional to the acceleration component and is
adjusted by a dimensionless inertia coefficient CM.

4
FI  Force/m
V= D 2 x1 m3/m
D
1
CM=k (if the object is moving relative to the fluid)
CM=1+k (if the fluid is moving around the object)
Directions of FD and FI
a)Flow past a fixed object
U
FD
FI

dU
dt
U,
dU
, FI, FD are vectors
dt
1
2
FD= C D  f AU U
Wave motion (periodic wave) past a fixed object:
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CI
U
dU
0
dt
FD 
FI 
Chapter 5
CII
U
dU
0
dt
FD 
FI 
U
U
dU
0
dt
FD 
FI 
dU
0
dt
FD 
FI 

1
2
1
dU
FI=  f C m V
2
dt
FD=  f C D AU U
b)Object moving in an otherwise still fluid
FD
FI
U
dU
dt
c)Both object and the fluid are in motion
u
I)
1
2
d ( u  U)
1
FI= C m  f V
2
dt
FD= C D  f SA u  U (u  U)
FD
U

d (u  U )
dt
II)
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Chapter 5
III)
FD
u
FI  d(u  U)
dt
U
5.3.2.3. Lift Forces on the Objects in Fluids
Force on Slender Elements
Morison's equation is of special importance - sometimes even the only tool available for evaluation of forces on framework structures. Piled offshore platforms, which exist
in great number, belong to this class. In such constructions tubular elements are
jointed together, pointing in almost any direction. To treat such members in general, it
may sometimes be difficult to decompose the forces in well-defined components. For
this reason it is convenient to write Morison's equation on a vectorial form which
automatically takes care of the orientation of structural elements and force
components.
Consider a segment of a long, slender structural element submerged into the water.
The element may presently have arbitrary cross section and is oriented along a unit
vector l with directional cosines (l, m, n), that is
(i, j, k) are the unit vectors of the global system of axes. The instantaneous, local
fluid velocity vector v may be written in component form as
The acceleration vector a is correspondingly
The force per unit length on the element may in general be written as a vector sum of
the inertia or mass force FM the drag force FD and a transversal lift force FL, that is
The formulation of the force should agree with the following empirical properties of
the force components:
The lift force FL is oriented normal to the velocity vector and normal to the axis of the
element. The force is proportional to the velocity squared and is tuned by a lift
coefficient CL. (See Equation below)
Lift is one of the most important forces in moving fluid. It is a result of pressure
differences around the particle.
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Lift
Chapter 5
maximum velocity,
minimum pressure
u
Sketch Showing Lift Force
The mathematical expression for the lift force is :
1
FL=
CL f A U2
2
where A is the surface area of the particle, cL is the coefficient of lift (highly particle
and flow dependent) and U is the velocity perpendicular to particle.
We can write the force components explicitly in quite general cases for the object,
that is, when the vectors l, v and a are introduced without restrictions. Presently,
however, we will rather consider three special cases which cover the slender
members.
1.a circular tube in the vertical yz-plane transverse to the wave propagation direction,
2.a circular tube in the vertical xz-plane longitudinal to the wave propagation
direction,
3.a circular tube in the horizontal plane.
References
Farreras S. F., (2000), “Post Tsunami Field Survey Procedures an Outline, Natıural Hazards
Journal, 21, 207-214, Kluwer Academic Publishers.
Bourgeous J., and Minoura K., Paleotsunami Studies; Contribution to Mitigation and Risk
Assesment, http://omzg.sscc.ru/tsulab/paper1.html
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