Risks Projects - Hazard Maps
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Hazard Maps
Fragility and Shake Maps
HONDURAS
- Risk Projects -
Presented by:
David Gutirrez Rivera
101082
January/2014
NHRE- Natural Hazards and Risks in Structural Engineering
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CONTENTS
Page
Introduction----------------------------------------------------------------------- 4
Preliminaries--------------------------------------------------------------------- 5
1. Fundamentals---------------------------------------------------------------- 71. Fragility2. Performance
i. Capacityii. Demand
3. Probability4. Simulation
2. Fragility Maps---------------------------------------------------------------- 141. Fragility Curves2. Building Stock
3. Construction
3. Shake Maps------------------------------------------------------------------ 191. Ground Motion Prediction Equation (GMPE)2. Sensors Data3. Construction
4. Case Study Honduras----------------------------------------------- 241. Building Stock
i. Fragility Curves2. GSHAP Map3. Fragility Maps4. Shake Maps
References----------------------------------------------------------------------- 33
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LIST OF FIGURES
Page
Fig.1.1 Seismic Hazard Map----------------------------------------------------------------- 5
Fig. 1.2 Loss Estimation---------------------------------------------------------------------- 5
Fig. 1.3 2011 Japan Earthquake ShakeMap--------------------------------------------- 6
Fig. 1.4 Hammurabi, King of Babylon------------------------------------------------------ 8
Fig. 1.5 Damage States---------------------------------------------------------------------- 9
Fig. 1.6 Pushover Analysis------------------------------------------------------------------ 9
Fig. 1.7 Seismic Response Spectra Equations---------------------------------------- 10
Fig. 1.8 EC Seismic Response Spectra------------------------------------------------- 10
Fig. 1.9 Performance Point----------------------------------------------------------------- 11
Fig. 1.10 Normal Probability Distribution------------------------------------------------ 12
Fig. 1.11 Cumulative Probability Distribution------------------------------------------- 12
Fig. 1.12 Numerical Simulation------------------------------------------------------------ 13
Fig. 1.13 Monte-Carlo Simulation--------------------------------------------------------- 13
Fig. 2.1 Fragility Curves-------------------------------------------------------------------- 14
Fig. 2.2 Building Stock Classification--------------------------------------------------- 14
Fig. 2.3 Fragility Curve Construction----------------------------------------------------- 15
Fig. 2.4 Fragility Curve Construction Flow Chart------------------------------------- 16
Fig. 2.5 Fragility Map Construction Flow Chart--------------------------------------- 16
Fig. 2.6 GSHAP MAP----------------------------------------------------------------------- 17
Fig. 2.7 Fragility Curve Adobe Building------------------------------------------------- 17
Fig. 2.8 Table Fragility Data for Adobe Buildings------------------------------------- 18
Fig. 2.9 Fragility Map Adobe Buildings------------------------------------------------- 18
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Page
Fig. 3.1 GMPE (Attenuation Relation)------------------------------------------------- 19
Fig. 3.2 Dahles Attenuation Relation (Depth=30Km)----------------------------- 20
Fig. 3.3 Seimics Sensors LocationsMap---------------------------------------------- 20
Fig. 3.4 Shake Map Construction Flowchart----------------------------------------- 21
Fig. 3.5 Shake Map Earthquake Coordinates--------------------------------------- 22
Fig. 3.6 PGA Calculation using GMPE----------------------------------------------- 22
Fig. 3.7 Honduras Shake Map---------------------------------------------------------- 23
Fig. 4.1 Honduras Building Stock Map------------------------------------------------ 24
Fig. 4.2 Honduras Brick Building Fragility Curve------------------------------------ 25
Fig. 4.3 Honduras Masonry Building Fragility Curve------------------------------- 25
Fig. 4.4 Honduras Concrete Building Fragility Curve------------------------------ 26
Fig. 4.5 Honduras Timber Building Fragility Curve-------------------------------- 26
Fig. 4.6 Honduras Adobe Building Fragility Curve--------------------------------- 26
Fig. 4.7 Honduras GSHAP Map------------------------------------------------------- 27
Fig. 4.8 Honduras Brick Buildings Fragility Map----------------------------------- 28
Fig. 4.9 Honduras Masonry Buildings Fragility Map------------------------------ 28
Fig. 4.10 Honduras Timber Buildings Fragility Map------------------------------ 29
Fig. 4.11 Honduras Adobe Buildings Fragility Map------------------------------- 29
Fig. 4.12 Honduras Overall Fragility Map------------------------------------------- 30
Fig. 4.13 Honduras South Coast Collapsed Buildings--------------------------- 31
Fig. 4.14 Honduras South Coast Shake Map-------------------------------------- 31
Fig. 4.15 Honduras North Coast Collapsed Buildings---------------------------- 32
Fig. 4.16 Honduras North Coast Shake Map--------------------------------------- 32
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INTRODUCTION
In this project we study the theory behind the development of Hazard Maps, specifically
Fragility Maps and Shake Maps. We delve first on the fundamentals we need to know for the
generation of this maps, then we study the theory of Fragility Curves and Fragility Maps and
the theory behind Shake Maps, and finally we apply this knowledge to our Home Country
and develop its respective maps.
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PRELIMINARIES
Hazard Maps
A Hazard Map highlights areas that are
affected or vulnerable of a particular
hazard. They help use describe
qualitatively and quantitatively a specific
area in order to assess its vulnerability toa particular hazard.
The first type of Hazard Map well be studying are the so called Fragility Maps.
Fragility Maps show the vulnerability of
areas in the map with respect to a given
hazard.
Some applications for Fragility Curves and
Fragility Maps are:
Probabilistic Risk Assessment
Construction Code Development
Urban Planning
Loss Estimation Retrofitting
Shake Maps
With Fragility Curves at your disposal for each of this building types and damages states, and
also knowing the expense for repairing this damages on the buildings, we can estimate the
expected annual or monthly loss.
Fig 1.1 Seismic Hazard
Fig 1.2 Loss Estimation
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The other Hazard Map well be studying are Shake Masp.
Shake Maps are a representation of ground shaking produced by an earthquake. Shake Maps
focuses on the ground-shaking produced by the earthquake, rather than the parameters
describing the earthquake source.
Some applications of ShakeMaps are:
Seismological Research
Earthquake Scenarios Preparedness
Emergency Response Loss Estimation
Fig. 1.3 2011 Japan Earthquake ShakeMap
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FUNDAMENTALS
Fragility
It is a measure of part of the Vulnerability of a structure to loads induced by a hazard.
Mathematically, fragility can expressed by:
Where:
Pf is the failure probability for a specific damage state
Sd is the structural demand, and
Sc is the structural capacity.
Fragility of a Structure can be affected by the following aspects:
Type of Hazard (EQ, Wind, Flood,...)
Strength of Hazard
Structural Type
Construction Materials
Soil-Structure Interaction
Risk = Fun ( Hazard, Vulnerability, Cost )
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Performance
Hammurabi, King of Babylon once said:
Article 229: The builder has built a house for a man and his
work is not strong and if the house he has built falls in and
kills a householder, that builder shall be slain.
This is a performance statement. He addressed structural
safety entirely in terms of user requirements, did not statehow to construct the building, and did not refer to building
structure or building materials.
Performance-Based Design
The Performance approach consists of working in terms of Ends rather than Means. It isconcerned with what a building is required to do, and not with how it is to be constructed.
The two main important ingredients in a performance-based design are:
- Capacity
Performance-Based Design Ingredients:
- Demand
With this two parameters we follow with the determination of thePerformance Point.
The we proceed with the check of Structural Behavior under the defined Seismic Action and
your Defined Limit States.
Fig 1.4 Hammurabi, King of Babylon
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Capacity
Is a measure of the maximum load, or any other parameter, a structure can sustain for it to
achieve a predefined damage state. This will depend on the structural system, materials and
other structural attributes that affect the resistance of a structure.
Using Pushover Analysis we can obtain the Capacity of a Structure. The procedure consists on
applying either a small lateral displacement or force to the structure, iteratively increasingthis amount, re-analizing the structure at each step, until the predefined damage state is
obtained.
Fig. 1.5 Damage States
Fig. 1.6 Pushover Analysis
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Demand
Its a measure of the loads, or any other parameter, that a structure would be subjected to by
a given hazard. It will depend on characteristics of the hazard and site conditions, which
affect the overall effect on the structure. Seismic Demand is represented by using Response
Spectra.
A Response Spectra is a plot of the peak or steady-state response (displacement, velocity or
acceleration) of a series of buildings of varying Natural Frequency or Period, forced into
motion by the same base Ground Motion.
Fig. 1.8 EC Seismic Response Spectra
Fig. 1.7 Seismic Response Spectra Equations
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Performance Point
The performance point is the intersection between the capacity and demand
Fig. 1.9 Performance Point
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Probability
Inprobability theory,a probability density function (pdf), or density of acontinuous random
variable,is afunction that describes the relative likelihood for this random variable to take on
a given value.
In probability theory and statistics, the cumulative distribution function (CDF), or just
distribution function, describes the probability that a real-valuedrandom variable X with a
givenprobability distribution will be found at a value less than or equal to x. Intuitively, it is
the "area so far" function of the probability distribution.
Fig. 1.10 Normal Probability Distribution
Fig. 1.11 Cumulative Probability Distribution
http://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Continuous_random_variablehttp://en.wikipedia.org/wiki/Continuous_random_variablehttp://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Continuous_random_variablehttp://en.wikipedia.org/wiki/Continuous_random_variablehttp://en.wikipedia.org/wiki/Probability_theory -
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FRAGILITY MAPS
Fragility Curves
By assuming material properties and certain other structural attributes that affect the overall
Capacityof a structure, and with additional assumptions about the ground motion and site
conditionsboth factors that affect the seismic Demand,we can deterministically calculate
the performance of a structure.
Naturally, values of these parametersare not exact they invariably have a
measure of both randomness and
uncertaintyassociated with them.
When we take into account this
probabilistic characteristics we generate
what we know as Fragility Curves.
Building Stock
A Classification of the Building Stock
needs to be made in order to develop
their respective fragility curves.
Classification can be made according to:
Structural Type
Building Purpose
Building Quality
Fig. 2.2 Building Stock Classification
Fig. 2.1 Fragility Curves
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Construction
Now well see the process on developing a Fragility Curve and finally getting to the Fragility
Maps. First lets take a look at a Building stock and what data is important to collect from
them in order to develop fragility curves and get to the final destination of a fragility map.
To begin with we need an area of study with a population of buildings.
Then we need to classify these buildings according to some standardized classification
and collect the data from the Building Stock. This classification can be the buildings
general geometry (like in Fig.2.3), number of stories, building materials, quality or age,
usage or purpose etc.
With this a Fragility Curve is developed for each of this type of buildings, by using
simulation procedures like the Monte-Carlo Simulation.
Having the fragility curves we can obtain probability of occurrence of specific damage
state for a specific hazard event, and therefore asses the vulnerability of the area for a
specific hazard, like an earthquake or flooding.
Fig. 2.3 Fragility Curve Construction
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The process of developing a fragility curve generally
involves the following steps:
1) Building Properties Selection2) Structure Idealization3) Inclusion of Structural Variability
4) Pushover Analysis and Limit States Definitions5) Structural Analysis Numerical Simulation Run6) Data Fit to a Probability Distribution Function7) Which becomes the Fragility Curve
The Numerical Simulation run of the Structural Analysis is an iterative procedure were the
input of the structure is randomly generated according to stochastic parameter know of the
hazards and construction materials of the building, like described on section1.4 of Numerical
Simulation.
Fig. 2.4 Fragility Curve Construction Flow Chart
Fig. 2.5 Fragility Map Construction Flow Chart
___________
___________
___________
___________
___________
___________
___________
_________
____
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Now well explain step by step the construction procedure for a Fragility Curve and the Map,
specifically considering a Seismic Hazard for my Home Country.
1) Generate GSHAP Map
Map containing probability of PGA occurrence in a site
2) DefineFragility Curvesfor each of the differentBuilding Types
Fig. 2.6 GSHAP MAP
Fig. 2.7 Fragility Curve Adobe Buiding
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SHAKE MAPS
Shake Maps are a representation of ground shaking produced by an earthquake. Shake Maps
focuses on the ground-shaking produced by the earthquake, rather than the parameters
describing the earthquake source.
Depending on distance from the earthquake, depth, rock and soil conditions at sites, and
variations in the propagation of seismic waves from the earthquake due to complexities in
the structure of the Earth's crust, it produces a range of ground shaking levels at sitesthroughout the region.
Some areas of application for Shake Maps are:
Seismological Research - Calibration of GMPE
Earthquake Scenarios Preparedness
Emergency Response
Loss Estimation
Ground Motion Prediction Equation (Attenuation Relation)
Ground motion prediction equations are statistical models to predict ground shaking on a
site. They can be developed for different tectonic regions (shallow crustal regions,
subduction zones, intra-plate).
Fig. 3.1 GMPE (Attenuation Relation)
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The Attenuation Relation used in our region is the one proposed by Dahle.
DAHLE
Ycan be Peak Ground Acceleration (PGA).
This model is the one applied for the stable tectonic region in Europe.
According to some studies this Dahle model is the most adequate model to predict ground
motion for the Central America region, therefore is the one we will be using.
0.001
0.01
0.1
1
1 10 100
PGA-
g
Distance - Km
Attenuation Relation, Dahle's (depth=30km)
Mw=5.5
Mw=6.0
Mw=6.5
Mw=7.0
Mw=7.5
Mw=8.0
Fi . 3.2 Dahles Attenuation Relation De th=30Km
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Sensors Data
Sensors Data is prioritize over GMPE when
calculating site Ground-Shaking (PGA), IF there is
enough data available.
Interpolation and Extrapolation Schemes must be
implemented to calculate interior and exterior
PGA values, respectively.
Interpolation Methods
Uni-Dimensional
- Linear
- Polynomial
- Spline , others ...
Multi-Dimensional, Spatial
Bilinear
Natural & Nearest Neighbor
Kriging , others ...
Construction
Fig. 3.4 Shake Map Construction Flowchart
_____ ___________
______
__________________
_____
_____
___________
__________
Fig. 3.3 Seimics Sensors Locations Map
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Now well explain the step by step procedure for generating a Shake Map using critical
earthquake scenarios for my Home Country.
1) Earthquake Coordinates and Magnitude
This would mean to locate and determine the Earthquakes Magnitude and Coordinates, if it
event has just occurred, or to decide on the location and magnitude of the earthquake we
would like to study.
2) Calculate Sites PGA using aGMPE
This would mean to locate and determine the Earthquakes Magnitude and Coordinates, if it
event has just occurred, or to decide
Fig. 3.5 Shake Map Earthquake Coordinates
Fig. 3.6 PGA Calculation using GMPE
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3) CalculateProbability of Exceedancefor each and every Site
In the same way it is done for Fragility Maps we calculate the Probability of Exceedance of
each site, using the sites PGA calculate in the previous step.
4) Compile Data and Generate Shake Map
Fig. 3.7 Honduras Shake Map
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CASE STUDY HONDURAS
Building Stock
The Building Stock of my Home Country comprises the following building types:
Concrete
Brick
Masonry
Timber
Adobe
Fig. 4.1 Honduras Building Stock Map
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Fragility Curves
For each of this building types we generated their fragility curves, we used an European
database of Fragility Curves for different Types of Buildings as base to work on, this database
is called SynerG -http://www.vce.at/SYNER-G/.
Fig. 4.2 Honduras Brick Building Fragility Curve
Fig. 4.3 Honduras Masonry Building Fragility Curve
http://www.vce.at/SYNER-G/http://www.vce.at/SYNER-G/http://www.vce.at/SYNER-G/http://www.vce.at/SYNER-G/ -
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Fig. 4.5 Honduras Timber Building Fragility Curve
Fig. 4.6 Honduras Adobe Building Fragility Curve
Fig. 4.4 Honduras Concrete Building Fragility Curve
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GSHAP Map
The GSHAP map was used to obtain the PGA for the sites in order to evaluate the fragility of
the sites.
Fig. 4.7 Honduras GSHAP Map
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Timber Building Collapse Damage State
Adobe Building Collapse Damage State
Fig. 4.10 Honduras Timber Buildings Fragility Map
Fig. 4.11 Honduras Adobe Buildings Fragility Map
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Overall Fragility Map Collapse Damage State
Fig. 4.12 Honduras Overall Fragility Map
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SHAKE MAPS
Fig. 4.13 Honduras South Coast Collapsed Buildings
Fig. 4.14 Honduras South Coast Shake Map
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Fig. 4.15 Honduras North Coast Collapsed Buildings
Fig. 4.16 Honduras North Coast Shake Map
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REFERENCES
Seismic Hazard Study Hidroelectric Dam Project Site Tornillito
Eurocode 8 - Design of structures for earthquake resistance
Fragility Curve Development for Assessing the Seismic Vulnerability of Highway
Bridgeshttp://mceer.buffalo.edu/publications/resaccom/99-sp01/ch10mand.pdf
http://www.vce.at/SYNER-G/
Seismic Risk Assessment and Loss Estimation
http://web.mit.edu/istgroup/ist/documents/earthquake/Part1.pdf
Performance-based design NHRE 3rd Course Lecture: Risk Projects
Seismic Risk Assessment and Loss Estimation
http://web.mit.edu/istgroup/ist/documents/earthquake/Part1.pdf
Application of the Applied Element Method to the Seismic Vulnerability Evaluation of
Existing Buildings
http://www.extremeloading.com/upload/Karbassi%20et%20Nollet_CSCE2008_withou
t%20logo.pdf
Determination of Fragility Curves-http://www.merci.ethz.ch
http://www.seismo.ethz.ch/static/GSHAP/
http://earthquake.usgs.gov/earthquakes/shakemap/
http://en.wikipedia.org/wiki/Normal_distribution
http://references/Fragility%20Curve%20Development%20for%20Assessing%20%20the%20Seismic%20Vulnerability%20of%20Highway%20Bridges.pdfhttp://references/Fragility%20Curve%20Development%20for%20Assessing%20%20the%20Seismic%20Vulnerability%20of%20Highway%20Bridges.pdfhttp://mceer.buffalo.edu/publications/resaccom/99-sp01/ch10mand.pdfhttp://www.vce.at/SYNER-G/http://references/Summary%20%20-%20Seismic%20Risk%20Assessment%20and%20Loss%20Estimation.pdfhttp://web.mit.edu/istgroup/ist/documents/earthquake/Part1.pdfhttp://references/NHMSE_Performance-based-design_II_pushover.pdfhttp://references/Summary%20%20-%20Seismic%20Risk%20Assessment%20and%20Loss%20Estimation.pdfhttp://web.mit.edu/istgroup/ist/documents/earthquake/Part1.pdfhttp://references/Application%20of%20the%20Applied%20Element%20Method%20to%20the%20Seismic%20Vulnerability%20Evaluation%20of%20Existing%20Buildings.pdfhttp://references/Application%20of%20the%20Applied%20Element%20Method%20to%20the%20Seismic%20Vulnerability%20Evaluation%20of%20Existing%20Buildings.pdfhttp://references/Application%20of%20the%20Applied%20Element%20Method%20to%20the%20Seismic%20Vulnerability%20Evaluation%20of%20Existing%20Buildings.pdfhttp://references/Application%20of%20the%20Applied%20Element%20Method%20to%20the%20Seismic%20Vulnerability%20Evaluation%20of%20Existing%20Buildings.pdfhttp://www.extremeloading.com/upload/Karbassi%20et%20Nollet_CSCE2008_without%20logo.pdfhttp://www.extremeloading.com/upload/Karbassi%20et%20Nollet_CSCE2008_without%20logo.pdfhttp://references/Jens_MERCI_ISPRA_workshop_20_05_2005.pdfhttp://www.merci.ethz.ch/http://www.seismo.ethz.ch/static/GSHAP/http://earthquake.usgs.gov/earthquakes/shakemap/http://en.wikipedia.org/wiki/Normal_distributionhttp://en.wikipedia.org/wiki/Normal_distributionhttp://en.wikipedia.org/wiki/Normal_distributionhttp://earthquake.usgs.gov/earthquakes/shakemap/http://www.seismo.ethz.ch/static/GSHAP/http://www.merci.ethz.ch/http://references/Jens_MERCI_ISPRA_workshop_20_05_2005.pdfhttp://www.extremeloading.com/upload/Karbassi%20et%20Nollet_CSCE2008_without%20logo.pdfhttp://www.extremeloading.com/upload/Karbassi%20et%20Nollet_CSCE2008_without%20logo.pdfhttp://references/Application%20of%20the%20Applied%20Element%20Method%20to%20the%20Seismic%20Vulnerability%20Evaluation%20of%20Existing%20Buildings.pdfhttp://references/Application%20of%20the%20Applied%20Element%20Method%20to%20the%20Seismic%20Vulnerability%20Evaluation%20of%20Existing%20Buildings.pdfhttp://web.mit.edu/istgroup/ist/documents/earthquake/Part1.pdfhttp://references/Summary%20%20-%20Seismic%20Risk%20Assessment%20and%20Loss%20Estimation.pdfhttp://references/NHMSE_Performance-based-design_II_pushover.pdfhttp://web.mit.edu/istgroup/ist/documents/earthquake/Part1.pdfhttp://references/Summary%20%20-%20Seismic%20Risk%20Assessment%20and%20Loss%20Estimation.pdfhttp://www.vce.at/SYNER-G/http://mceer.buffalo.edu/publications/resaccom/99-sp01/ch10mand.pdfhttp://references/Fragility%20Curve%20Development%20for%20Assessing%20%20the%20Seismic%20Vulnerability%20of%20Highway%20Bridges.pdfhttp://references/Fragility%20Curve%20Development%20for%20Assessing%20%20the%20Seismic%20Vulnerability%20of%20Highway%20Bridges.pdf