Fragility & ShakeMaps

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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.

Transcript of Fragility & ShakeMaps

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 U