Tsunami Effects on Coastal Infrastructures
and How to Evaluate Them
Harry Yeh
Oregon State University
Northwest Transportations Conference 2010
April 1, 1946 Aleutian Tsunami
Nagappattinam (N10º45.785, E79º50.928)
Evaluations for Tsunami Forces
• June 2008: Guidelines for Design of Structures for Vertical
Evacuation from Tsunamis.
FEMA P646
Tsunami Inundation Map
Tsunami inundation area and the
maximum runup elevations are
readily available from a tsunami
evacuation map.
Can we estimate tsunami
forces from the maximum
runup height found in the
tsunami inundation map?
Hydrodynamic and Surge Forces
1
FD = ! C D b h u 2
2
h u2
z
" z%
=
0.125
!
0.235
+
0.11
$# '&
g R2
R
R
2
based on the elevation
Impact Force
FI = C M umax
kˆ m
m = mass of the debris
k = effective stiffness
umax = max. flow speed with
the debris draft depth, d
R = max. runup elevation.
z = ground elevation
d = draft depth
η = d/R
Example
•
Maximum runup height R ≈ 19.5 m
•
Location of a structure at z ≈ 10 m, and the column breadth 0. 76 m
(30”).
•
ρ = 1200 kg/m3 for sediment laden sea water.
•
Driftwood – mass = 450 kg; effective stiffness k = 2.4 × 106 N/m; draft
depth = 0.25 m
hmax
R
z
datum
x
l
Example
•
Hydrodynamic and surge forces:
(h u )
2
2
"
z
" z% %
= g R $ 0.125 ! 0.235 + 0.11$ ' ' = 124.6 m 3 sec 2
# R& &
R
#
2
max
(
)
1
! Cd B h u 2 max
2
1
= 1200 kg m 3 ( 2.0 ) ( 0.76 m ) 124.6 m 3 sec 2
2
= 114 kN
Fd =
(
•
)
(
)
Impact forces (drift wood):
umax = 0.334 2 g R = 6.53m sec.
Fi = Cm umax
km
= 2.0 ( 6.53m sec )
= 429 kN
•
( 2.4 !10
6
)
N m ( 450 kg )
ζ = z/R = 0.5; η = d/R = 0.013
Design forces on a column:
Fd + Fi = 114 + 429 = 543 kN (122 kips).
What do we need to do to evaluate tsunami forces
on bridges and other infrastructures?
• The foregoing methods were developed to provide
design guidelines for Tsunami Evacuation Buildings
(TEB) that are usually constructed at inshore (initially
dry) locations.
• Coastal bridge piers are located at low elevations and
initially wet; tsunamis will first propagate against the
river flow prior to striking the bridge piers.
• The existing methods developed for TEB can be
modified for evaluation of tsunami forces on bridges,
based on the existing tsunami inundation maps.
Tsunami Scour Problems
Bridges
Kalpakkom, India, 2004
Tsunami Scour Problems
Roads
The 2004 Indian Ocean Tsunami:
Chennai
1
Quay-wall collapse
Konakano, Japan: the 1960 Chilean Tsunami.
4
2
5
3
Scour Formation
Kesen-numa, Japan: the 1960 Chile Tsunami
Scour hole more than 8 m deep at the entrance to the port.
After Takahashi et al. (1992)
Scour Formation
Capsized breakwater due to
foundation failure at Aonae
Port, Japan
Scour depth: 4 m
Foundation Failure: the 1993 Okushiri Tsunami
Scour Formation
Runup height 4.1 m
Inundation depth 0.95 m above the floor;
Scour depth 1.2 m
Scour span 5.0 m.
Sri Lanka: photo by Patrick Lynett
Scour depth ≈ 2.0 m
2004 Indian Ocean Tsunami
Tsunami Scours
FEMA55: Coastal Construction Manual
Approach
1.
Compute hypothetical but typical runup flows for
idealized beach condition, viz. tsunami runup onto a plane
beach with a uniform slope and uniform sediments.
–
Use the analytic-numeric hybrid solution given by Carrier et al.
(2003) to calculate tsunami flow velocities and depths.
2.
Compute the Shields parameter θ and the Rouse number
Ro for this hypothetical tsunami runup.
3.
Compute the analytic predictions for pore-pressureinduced scour depths (momentary-liquefaction-like
scour).
–
Use the 1-D solution given by Tonkin et al. (2003).
Model Tsunami
Long-Wave Runup on a Plane Beach: Nonlinear Problem
Carrier, Wu, and Yeh (2003) -- Analytic-Numeric Hybrid Approach
[u' (! x' + "' )]
x'
+ "' t ' = 0,
u' t' + u' u' x' + g "' x' = 0,
Nonlinear Shallow-Water-Wave Equations
⇒
4 ! " ## $ (! "! )! = 0
Linear Cylindrical Wave Equation
Initial Tsunami Form used in this Study
Leading Depression N-Wave
α= 1/250.
Maximum positive displacement a0 = 1.4 m
Breadth of approximately 60 km
Resulting Flow Depth and Velocity
α= 1/250.
Maximum inundation distance 1160 m
Maximum runup height 4.6 m
Runup/drawdown process takes 16 minutes
Water depth
Flow velocity
A very realistic runup condition of a locally generated tsunami
Shields Parameter
!=
"0
(
)
#gd s $1
=
f u2
(
)
8g d s $ 1
f = 0.01
ds = 0.35 mm
s = ρs/ρ = 2.64
α = 1/250
Suspension sheet flow: θ > 2.0
Threshold of sediment motion : θc = 0.04 ~ 0.06
Rouse Number
RO =
ws =
ws
!" u*
8! #
%
d s %$
s " 1) g d
(
1+
72 ! 2
3
s
&
" 1(
('
ws = 52 mm/sec
ds = 0.35 mm
κ = 0.4
β = 1.0
u* = ! 0 "
Possible sediment suspension: Ro < 2.5
Full sediment suspension:
Ro < 1.0
• Tsunami runup is an “unsteady” flow phenomenon.
– Typically tsunamis have one or a few cycles with a
period in minutes or tens of minutes.
– Storm waves have many cycles with a period of less than
tens of seconds.
– Slope instability problems associated with rapid
drawdown in reservoirs and tidal inlets have a time scale
of hours to days.
Tsunami Tank at PWRI (NILIM) - 135 m long
Cylinder embedded in gravel
Scour Mechanisms
• Shear stress due to water motion –
Shields model
• Low effective stress between sand
particles



Dependent on pore pressure gradient
Sediment liquefies if effective stress
disappears
Pore pressure gradients can enhance
scour due to shear stress
Momentary Liquefaction
Linear fit to the drawdown portion of the pressure
head at the back of the cylinder
60
50
Pressure head (cm)
40
ΔT
30
20
Δp
10
0
-5
0
5
10
-10
-20
Time (s)
15
20
25
Back to Model Tsunami
f = 0.01
ds = 0.35 mm
s = ρs/ρ = 2.64
α = 1/250
Water-surface elevation
Flow velocity
Scour Enhancement Parameter Λ(0)
!(0) =
2
#p
.
" $ b c v#T
total liquefaction
enhanced scour
• The region where Λ > 0.5 is –300 m < x < 1200 m
• At x = 450 m, the value of Λ(0) exceeds unity, i.e. total liquefaction.
Spatial variation of scour depth
+
% d
(.
"p
2
s
*0 .
- 1 $ 4i erfc '
! ds =
# b ds -,
' 2 cv "T *0/
&
)
( )
• The maximum scour depth in the onshore area is less than 3 m.
• Pore-pressure driven scour does not occur farther inland than x = –300 m.
• The maximum scour depth is found to be 6.2 m deep at 450 m offshore
Observed Scour Depths
Scour depth 1.2 m
Scour depth: 4 m
Scour depth: 8 m
Scour depth 2.0 m
Summary for this Example
α= 1/250.
Maximum inundation distance: 1160 m
Maximum runup height: 4.6 m
Runup/drawdown process:16 minutes
• This implies that offshore coastal structures (breakwaters,
oil/gas berth terminals) could be vulnerable from
liquefaction-induced scours.
• The pore pressure effect remains important more than 1.2 km
offshore from the shore.
Tsunami Runup on the Tokachi River, Japan:
The 2003 Tokachi-Oki Earthquake
Comments
We demonstrated that momentary liquefaction is
important for tsunami scour during the drawdown
process.
It appears that when a pier is embedded in gravel,
liquefaction might be suppressed.
We’ve just seen the video of the tsunami runup
along the river. Because of the formation of
undular bore, residual liquefaction could play a
role in scour during the river runup process? ?
Remarks and Research Directions
• Recently developed guidelines (FEMA p646) for tsunami
evacuation buildings can be modified for evaluation of
tsunami forces on coastal bridges and other infrastructures
– prediction of the force from a given inundation map.
• Likewise, tsunami induced scour and foundation failures
due to momentary liquefaction can be estimated using the
similar approach, i.e. based on a given inundation map.
• Once estimation of tsunami effects were made, more
detailed predictions for critical and vulnerable coastal
infrastructures should be made with numerical simulations.