PBTE
Harry Yeh & Dylan Keon
Oregon State University
Tsunami Forces – FEMA P646
Pre 2011 Tsunami Event
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2
Hydrostatic Forces: Fh = pc Aw = ρ s gbhmax
2
Buoyant Forces: Fb = ρ s gV
Hydrodynamic Forces: Fd =
1
ρ sCd B(hu 2 )max
2
Impulsive Forces: Fs = 1.5Fd
Debris Impact Forces: Fi = 1.3umax k md (1+ c)
Damming of Accumulated Debris: Fdm =
1
ρ s Cd Bd (hu 2 )max
2
Many different types of forces must be considered because there are
a variety of tsunami loading patterns depending on many factors.
What flow parameters do we need to know?
•  Hydrostatic Forces
–  Max. Inundation Depth, hmax
•  Hydrodynamic Forces
–  Drag Coefficient CD; Max. Momentum Flux ρu2h
•  Impulsive Forces
–  Empirical but could relate it to Hydrodynamic Forces
•  Debris Impact Forces
–  Effective Stiffness k for the Combination of Debris and Structure;
Impact Speed uI. Validity of the simplified formula is questionable.
•  Damming of Waterborne Debris
–  Drag Coefficient CD; Max. Momentum Flux ρ u2h
•  Moment
–  Max. Moment ρ u2h2
Substantial Uncertainties: although some are more than the others.
Remaining Issues for FEMA P646.
•  People tends to use this sort of
documentation as a strict rule to
follow.
•  Conservatism of FEMA P646
may cause a problem. Some of
the recommendations make the
building design and construction
so unrealistic.
•  How conservative do we need to
be for the design “guideline?”
Design criteria must be different for each bridge
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Due to advance in computational power, it is possible
to apply simulation-based designs for critical coastal
facilities performing probabilistic tsunami hazard
analysis quantifying its uncertainty.
The following is our attempt by developing a portal
for this purpose.
http://isec.nacse.org/pbte/
Performance-Based Tsunami Engineering: Data Explore
Performance-Based Tsunami Engineering: Data Explore
Select from multiple
tsunami cases: each case
may be identified with its
occurrence probability.
Note that one of them is
a case of an artificially
enhanced tsunami based
on the Alaska scenario.
Performance-Based Tsunami Engineering: Data Explore
Provide a map to select
a location of interest.
Performance-Based Tsunami Engineering: Data Explore
Retrieve the metadata.
Performance-Based Tsunami Engineering: Data Explore
Provide a map to select
a location of interest.
Performance-Based Tsunami Engineering: Data Explore
View the bathymetry
and topography.
Performance-Based Tsunami Engineering: Data Explore
Select a location of
interest and the date to
be download.
Performance-Based Tsunami Engineering: Data Explore
Plot the data.
And download the data
of interest.
Performance-Based Tsunami Engineering: Data Explore
Plot the zoom-in data
by selecting the time
interval of interest.
Example: Port Hueneme, CA
Example 1: Hypothetical Coastal Bridge
For uncertainty analysis, we take data from five spatially adjacent locations for
the case of a fictitiously beefed-up tsunami originated from Alaska.
Example 1: Hypothetical Coastal Bridge
Case of a fictitiously beefed-up tsunami originated from Alaska Inundation elevations for the five adjacent locations
Example 1: Hypothetical Coastal Bridge
Case of a fictitiously beefed-up tsunami originated from Alaska Inundation Elevations for the five adjacent locations
Example 1: Hypothetical Coastal Bridge
Case of a fictitiously beefed-up tsunami originated from Alaska Flow speeds at the five adjacent locations
Example 1: Hypothetical Coastal Bridge
Case of a fictitiously beefed-up tsunami originated from Alaska Flow speeds at the five adjacent locations
Example 1: Hypothetical Coastal Bridge
Bridge Cross Section -- Assumed
W=
h0 =
Example 1: Hypothetical Coastal Bridge
Force Estimates
1
ρ sCd B(hu 2 )max (W h ) when h > h0 + W
2
1
= ρ sCd B(hu 2 )max (1− h0 h ) when h0 + W > h > h0
2
= 0 when h < h0
Fd =
W=
h0 =
Example 1: Hypothetical Coastal Bridge
Case of a fictitiously beefed-up tsunami originated from Alaska Computed forces exerted on the bridge girder.
force/unit bridge span
Example 1: Hypothetical Coastal Bridge
Case of a fictitiously beefed-up tsunami originated from Alaska Computed forces exerted on the bridge girder near t = 80 min.
See the substantial variations in such a close vicinity
Example 1: Hypothetical Coastal Bridge
Case of a fictitiously beefed-up tsunami originated from Alaska Computed forces exerted on the bridge girder near t = 80 min.
Example: Port Hueneme, CA
Example 2: Soil Instability in Port Quay Walls
For uncertainty analysis, we take data from five locations along the quay walls for
four realistic tsunami scenarios: Cascadia, Alaska, Japan (2011), Chile (2010).
The Port of Soma, Fukushima
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Quay-wall collapse
Konakano, Japan: the 1960 Chilean Tsunami.
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2
5
3
Example 2: Port Quay Walls
Five location we examined for uncertainty analysis for the cases of Cascadia,
Regular Alaska, Beefed-up Alaska, Japan (2011), and Chile (2010).
Tsunami Induced Liquefaction
Example 2: Port Quay Walls
Alaska Case
Methodology by Yeh and Mason (2014)
Flow Depth (cm)
300
200
Variation of Flow Depth
100
2000
4000
6000
8000
10 000
time (sec)
-100
-200
Depth (cm)
-200
-150
-100
H (cm)
-50
-100
Variation of Pore-Water
Pressure Profiles in the soil.
-200
-300
-400
Δt = 100s
-500
Example 2: Port Quay Walls
Alaska Case
dH/dz
1.0
Methodology by Yeh and Mason (2014)
0.5
Variation of Pore-Water-Pressure Gradient
at the seabed
2000
4000
6000
8000
10 000
time (sec)
-0.5
Depth (cm)
-1.0
-0.8
-0.6
-0.4
0.2
-0.2
-100
Variation of the Profile of the PoreWater-Pressure Gradient in the Soil.
-200
Total liquefaction: dH/dz < − 1.0
Likely Liquefaction: dH/dz < − 0.5
-300
-400
Δt = 100s
-500
dH/dz
Example 2: Port Quay Walls
Example 2: Port Quay Walls
Cascadia and Japan events unlikely induce severe soil instability.
Alaska and Chile events can create soil instability up to the soil depth
of 2 m and 1 m respectively.
A similar PBTE system can be made for a real bridge
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