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In this project we study the theory behind the development of Hazard Maps, specificallyFragility Maps and Shake Maps. We delve first on the fundamentals we need to know for thegeneration of this maps, then we study the theory of Fragility Curves and Fragility Maps andthe theory behind Shake Maps, and finally we apply this knowledge to our Home Countryand develop its respective maps.
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Slide 1
Presented by: David Gutierrez RiveraHazard MapsFragility Maps & Shake Maps
Project Rainbow IIIntroductionMotivationFundamentalsFragilityPerformance: Capacity & DemandProbabilitySimulationsFragility MapsFragility CurvesBuilding StockShake MapsGround Motion Prediction Equation (GMPE)Sensors Data
Hazard Maps: ContentsHazard 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 to a particular hazard.
Hazard Maps: Introduction3Introduction: Seismic Hazard Map
http://www.seismo.ethz.ch/static/GSHAP/Ref. http://www.seismo.ethz.ch/static/GSHAP/
Introduction: Fire Hazard MapRef. http://www.battle-creek.net/docs/fire/fire_hazard_map_final.jpg
Introduction: Tsunami Vulnerability MapRef. Tsunami fragility curves and tsunami vulnerability - http://bymur.bo.ingv.it/frames/wg4.html Introduction: Building Stock Vulnerability Map
Ref. Determination of Fragility Curves - http://www.merci.ethz.ch Fragility Maps: MotivationApplications of Fragility Maps & Fragility Curves are:
Probabilistic Risk AssessmentConstruction Code Development Urban PlanningLoss EstimationRetrofittingShake Maps
Fragility Maps: Loss EstimationA group of buildings of different types subjected to a hazard may experience damage states of different types.
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. 3,000 1,000 500 1,500 2,500Fragility
It is a measure of part of the Vulnerability of a structure to loads induced by a hazard.
Risk = Fun ( Hazard, Vulnerability, Cost )
Fundamentals: Fragility
10
Fundamentals: FragilityMathematically, a fragility relationship can be defined as:
Where: Pf is the failure probability for a specific damage state Sd is the structural demand, and Sc is the structural capacity.
Fragility
Fragility of a Structure is affected by:Type of Hazard (EQ, Wind, Flood,...)Strength of HazardStructural TypeConstruction MaterialsSoil-Structure Interaction
Fundamentals: Fragility
12Fundamentals: CapacityCapacity
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.
Capacity: Pushover AnalysisPushover Analysis
Using this method we can obtain the Capacity of a Structure. The Procedure consists on applying either a small lateral displacement or force to the structure, iteratively increasing this amount, re-analizing the structure at each step, until the predefined damage state is obtained.
Fundamentals: DemandDemand
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 commonly represented by using Response Spectra.
Demand: Seismic Response SpectraSeismic 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.
Ground Motion Data Using the available Ground Motion Data from a region a general Seismic Response Spectra can be develop for use in this region.Demand: Seismic Response SpectraSeismic Response Spectra
Fundamentals: PerformancePerformance
Hammurabi, King of Babylon once said: Article 229: The builder has built a housefor 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 state how to construct the building, and did not refer to building structure or building materials.
Performance: Performance-Based DesignPerformance-Based Design
The Performance approach consists of working in terms of Ends rather than Means. It is concerned with what a building is required to do, and not with how it is to be constructed.
- CapacityPerformance-Based Design Ingredients: - Demand
-> Determination of the Performance Point
-> Check Structural Behavior under Defined Seismic Action with your Defined Limit States.
Performance: Performance PointPerformance PointCapacity CurveBase Shear Roof DisplacementCapacity CurveSa SdResponse SpectrumSa PeriodResponse SpectrumSa Sd
Performance: ComparisonFragility Maps: Fragility CurvesFragility Curves
By assuming material properties and certain other structural attributes that affect the overall Capacity of 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 parameters are not exact they invariably have a measure of both randomness and uncertainty associated with them.
When we take into account this probabilistic characteristics we generate what we know as Fragility Curves.
Fragility Curves: ShapeFragility Curves: Normal (Gaussian) Distribution Normal (Gaussian) Distribution
d d c c Fragility Curves: Normal (Gaussian) Distribution Probability Density Function
Fragility Curves: Normal (Gaussian) Distribution Cumulative Distribution Function
Normal Distribution: Parameter Estimation Maximum Likelihood Method
For the Normal Distribution:
Normal Distribution: Parameter Estimation
Normal Distribution: Parameter Estimation
For Civil Engineering Structures:
Newton-Cotes Integration Trapezoidal Rule Simpson Rule
Gaussian Quadratures Gauss-Legendre Gauss-Hermite
Normal Distribution: Cumulative Distribution Function Numerical Integration Methods
Building Stock: Building CategoriesBuilding Categories
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
Building Stock: Structural Type IBC Building Occupancy ClassificationsAssembly (Group A) - places used for people gathering for entertainment, worship, and eating or drinking. Examples: churches, restaurants (with 50 or more possible occupants), theaters, and stadiums.Business (Group B) - places where services are provided (not to be confused with mercantile, below). Examples: banks, insurance agencies, government buildings (including police and fire stations), and doctor's offices.Educational (Group E) - schools and day care centers up to the 12th grade.Factory (Group F) - places where goods are manufactured or repaired.High-Hazard (Group H) - places involving production or storage of very flammable or toxic materials. Includes places handling explosives and/or highly toxic materials.Institutional (Group I) - places where people are physically unable to leave without assistance. Examples: hospitals, nursing homes, and prisons. In some jurisdictions, Group I may be used to designate Industrial.Mercantile (Group M) - places where goods are displayed and sold. Examples: grocery stores, department stores, and gas stations.Residential (Group R) - places providing accommodations for overnight stay (excluding Institutional). Examples: houses, apartment buildings, hotels, and motels.Storage (Group S) - places where items are stored (unless considered High-Hazard). Examples: warehouses and parking garages.Utility and Miscellaneous (Group U) - others. Examples: water towers, barns, towers.
Building Stock: Building Purpose
Fragility Curves: Construction
Fragility Curves: ConstructionNumerical Simulation
Determine Site-Specific Seismic Ground Motion
Construct Numerical Model accounting for Soil-Structure Interaction
Definition of failure criteria
Uncertainty quantification, Modeling and PropagationFragility Curves: Construction
Monte Carlo Simulation
Fragility Curves: Construction
E, I
Load
Monte Carlo Simulation
Fragility Curves: Construction
Retrofitting Effects on Fragility of Structures
Ref. Deterministic and Probabilistic Evaluation of Retrofit Alternatives for a Five-Story Flat-Slab RC Building - https://www.ideals.illinois.edu/bitstream/handle/2142/8784/Deterministic%20and%20Probabilistic%20Evaluation%20of%20Retrofit%20Alternatives%20for%20a%20Five-Story%20Flat-Slab%20RC%20Building.pdf?sequence=2 Shake Maps: MotivationApplication of Shake Maps are:
Probabilistic Seismic Hazard AssessmentCalibration of GMPESeismic Hazard Scenarios PreparednessEmergency Response
Shake Maps: Emergency Response
Shake Map: Construction
Shake Map: ShakeCast
Shake Map: GMPEShake Map: Sensors DataShake Map: Sensors Data Interpolation and Extrapolation
MATLAB Commands Used:
interp ( , ) ; interp2d( , , , , ) TriScatteredInterp( , , )
Fragility MapBuilding StockFragility CurvesPGA GSHAPData HandlingMasonry Fragility MapConcrete Fragility MapAdobe Fragility MapOverall Fragility MapShake MapGMPEInterpolation & ExtrapolationShakeMap EQ1ShakeMap EQ2
Case Study: ContentsCase Study: HondurasSoftware Tools Used:- MapInfo- Matlab- Excel
47Honduras: Building Stock
~ 300 Data PointsHonduras: Fragility Curves
Brick Building TypeMasonry Building Type
Honduras: Fragility CurvesConcrete Building Type
Honduras: Data HandlingTimber Building TypeAdobe Building TypeHonduras: PGA - GSHAP
Honduras: Data Handling Interpolation and Extrapolation
MATLAB Commands Used:
interp ( , ) ; interp2d( , , , , ) TriScatteredInterp( , , )
Honduras: Masonry Fragility Map
Honduras: Concrete Fragility Map
Honduras: Adobe Fragility Map
Honduras: Overall Fragility Map
Shake Map: Honduras South Coast
Shake Map: Honduras South Coast
Shake Map: Honduras North Coast
Shake Map: Honduras North Coast
Thank You Sheet1CapacityDemandC(x)D(x)C1D1C2D2C3D3......CnDn