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SEISMIC STRUCTURALSEISMIC STRUCTURALVULNERABILITY

A Presentation to the Global Earthquake Model Workshop

Trinidad

By R. Clarke, Dept Civil & Environmental Engineering, UWI

11(3 May 2011)

Dept Civil & Environmental Engineering, The University of the West Indies

PRESENTATION OUTLINEPRESENTATION OUTLINE

A. DEFINITION AND ASSOCIATED TERMINOLOGY

B. HOW IS A STRUCTURAL VULNERABILITY CURVE USED

C. HOW IS VULNERABILITY INFORMATION DEVELOPED

D EXAMPLE: VULBERABILITY ANALYSIS OF T&T HOUSINGD. EXAMPLE: VULBERABILITY ANALYSIS OF T&T HOUSING

E. POSSIBLE STRUCTURAL VULNERABILITY ANALYSIS STRATEGY FOR GEM‐CARIBBEAN

2Dept Civil & Environmental Engineering,

The University of the West Indies

A. DEFINITION OF SEISMIC STRUCTURAL VULNERABILITYSTRUCTURAL VULNERABILITY

The term “Seismic Structural Vulnerability” does not follow the dictionary definition ofdoes not follow the dictionary definition of “vulnerability”. If so, the term would mean something like The lack of structural safetysomething like – The lack of structural safety under earthquakes (due to unsuitable design or construction)construction).

Maybe a better term than “StructuralMaybe, a better term than Structural Vulnerability” for describing what it is about, is “Dynamic Damageability”

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Dynamic Damageability .Dept Civil & Environmental Engineering,


A. DEFINITION OF SEISMIC STRUCTURAL VULNERABILITY (cont’d)VULNERABILITY (cont d)

The term “Structural Vulnerability” is technical jargon within the field of “Seismic Risk Assessment” orwithin the field of “Seismic Risk Assessment” or “Earthquake Loss Estimation” and is therefore fundamentally due to the inherent randomness hencefundamentally due to the inherent randomness hence uncertainty of the seismic loading on a structure.

Seismic Risk Assessment (SRA) is the quantitative evaluation of the likelihood of failure, expressed as a

b bili N d h l f f ilprobability. Nowadays, there are several types of failure. For example, the inability to provide: collapse prevention (CP) life safety (LS) immediate occupancy (IO) and

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(CP), life safety (LS), immediate occupancy (IO), and operationality(O).


A. DEFINITION OF SEISMIC STRUCTURAL ( ’d)VULNERABILITY (cont’d)

E th k L E ti ti (ELE) i t i fEarthquake Loss Estimation (ELE) is an extension of Seismic Risk Assessment. It is the quantitative evaluation of the consequences of failure expressed in terms thatof the consequences of failure, expressed in terms that are of direct social interest. For example: number of persons killed, number of persons injured, the repair p , p j , ptime, the cost of repair, the number of persons to be accommodated elsewhere, the impact on a country’s annual budget, etc.




SRA and ELE can be undertaken for individual structures, or for an entire region. For example, the GEM project is ELE for the whole world.

Seismic Structural Vulnerability is the probability of at least a certain type of failure, given the seismic intensity. It is part of the overall SRA or ELE calculation (in modern frameworks).




The Vulnerability data is fundamentally necessaryb f i f f h k lbecause of a certain fact of earthquake structural engineering: F1a: For the same structure identical in all physicalF1a: For the same structure identical in all physical

respects, the same extent of damage will be causedby a set of earthquakes each with a different seismicy qpeak intensity.

F1b: Conversely, the same structure subjected to different earthquakes of the same peak intensity, will experience a different extent of damage for

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will experience a different extent of damage for each earthquake. Dept Civil & Environmental Engineering,



Thi i d t th i h t d f i iThis is due to the inherent randomness of seismic loading, called “record‐to‐record variability”. It is

i f t i t i th ka primary source of uncertainty in earthquake structural engineering (of the class called “ l t ” t i t )“aleatory” uncertainty).



A. DEFINITION OF SEISMIC STRUCTURAL VULNERABILITY (cont’d)VULNERABILITY (cont d)

Vulnerability is expressed using the language of statistics/probability as a set of data points or more ideally as a function (i e theas a set of data points, or, more ideally, as a function (i.e. the cumulative distribution function, CDF). Being a function, it can be expressed graphically. It is then called a vulnerability curve (VC).

Probability that damage is at least = DS

1

β = Dispersion of intensities that give same damage (expresses

0.5

give same damage (expresses fact F1a)

C^ M di l f I t iti th t

0VC for Damage State (DS) =

Earthquake Intensity

C = Median value of Intensities that give same damage

0Slight Damage = Operational LS EXAMPLE OF A VULNERABILITY CURVE FOR

SLIGHT DAMAGE 9Dept Civil & Environmental Engineering,


DEFINITION OF SEISMIC STRUCTURAL VULNERABILITYIn the modern trend of Performance‐Based Seismic Design, for

complete definition of the vulnerability, it is typical to have a vulnerability curve for each limit (i.e. damage) state.y ( g )

Probability that damage 1

Probability ofExtensive Damage

gis at least = DS

SLIGHT DAMAGE

E th k

MODERATE DAMAGE

EXTENSIVE DAMAGE

COMPLETE DAMAGE

Expresses fact F1b:At any one intensity level, there is uncertainty about

0Earthquake Intensity

EXAMPLE OF A COMPLETE SET OF VULNERABILITY

which DS the structure is in.

10CURVES FOR A STRUCTURE



It is noteworthy to mention that authors frequently use the terms Vulnerability and Fragility as synonyms. But this is not always the case. For current studies in the USA in particular (i.e. the PEER methodology), the fragility is the probability of failure,the PEER methodology), the fragility is the probability of failure, but conditioned on a structural response variable (e.g. interstory‐drift ratio, etc), and not on the earthquake intensity.



B. HOW IS VULNERABILITY INFORMATION USED

In the most common current frameworks for the probabilistic calculation of risk or loss, the vulnerability information is used as follows:

Multiply this way (and)

HAZARD ANALYSIS DAMAGE ANALYSIS LOSS ANALYSIS

y (o

r)

Probabilistic Hazard VulnerabilityFunctions

ConsequenceFunctions

his

wayINCREMENTAL

QUANTUM OFLOSS

Intensity Extent of eachtype of damage

Add

tLOSS

TOTAL LOSS

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TOTAL LOSS(OVER ALLINTENSITIES)Dept Civil & Environmental Engineering,


C. HOW IS VULNERABILITY INFORMATION DEVELOPED

The technical aim is to collect the damage statisticsg

There are 3 approaches for determining seismicvulnerability:

‐ empirical: observation of tests or after earthquakes;typically expressed as tabular data that cantypically expressed as tabular data that canbe converted to closed‐form (i.e. formulae);Example – ATC 13 Earthquake Damagexample ATC 3 arthquake amageEvaluation Data for California (1985)

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‐judgment: based on the opinions of suitably qualified individuals (ASTM E2026 for qualifications)

C. HOW IS VULNERABILITY INFORMATION DEVELOPED (cont’d)( )

‐ analysis: requires simulation or sampling to generatey q p g gthe statistics. Common methods are:

‐Monte Carlo simulation (many thousands of runs;typically used with NSP CSM or N2)CSM or N2)

‐ Response Surface (sophisticated, compact MCS)‐ Latin hypercube (Experiment Design)atin hypercube ( xperiment esign)‐ Incremental Dynamic Analysis (Dynamic Pushover)



C. HOW IS VULNERABILITY INFORMATION DEVELOPED (cont’d) ‐

INCREMENTAL DYNAMIC ANALYSISINCREMENTAL DYNAMIC ANALYSIS 4:-Dynamic pushover

Base Shear Dynamic pushover

curves-1 for each record-Say 12 records in

h l di ti

Shear

5: each plan direction of structure = 24 curves

Required PDF;convert base

2: Each record scaled Incrementally to

Drift

base shear to intensity

cover the intensity range

O IO LS CPDrift

1: Limit state drift l f t ti

3: Each point is from a nonlinear dynamic

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values from static pushover analysis

yanalysis with max. drift and corresponding base shear recorded


D. EXAMPLE OF VULNERABILITY ANALYSIS – T&T HOUSING

At least 75% of all structures in T&T are URM single-story or two story with URM top

16Dept Civil & Environmental Engineering, The University of the West Indies

D. EXAMPLE OF VULNERABILITY ANALYSIS –T&T HOUSING ( ’d)T&T HOUSING (cont’d)

TYPICAL LAYOUTOF HOUSEOF HOUSE

17Dept Civil & Environmental Engineering, The University of the West Indies


STRUCTURAL BEHAVIOUR AND MODELINGBased on near full‐scale reversed cyclic lateral load wall testingBased on near full scale reversed cyclic lateral load wall testingUnder significant lateral load the “toothed” connection of the internal toexternal walls will cause a vertical line of weakness in the external wallsand separate them into a set of vertical elements, from ground level toa d sepa a e e o a se o e ca e e e s, o g ou d e e othe top of the wall, interconnected at the top by the ring beam. Pier regions at the sides of openings in the walls are also modeled in this manner since it is typically the case that one vertical edge of a piercoincides with an internal partition.The bearing stress on any wall element, and its self-weight, are sufficiently low that any element loaded in-plane will respond in a lidi d i t d d t l t l l d f 0 13 kN/ 2sliding-dominated mode at a lateral load of 0.13 kN/m2

The sliding in-plane load-displacement response is nonlinear andassumed to be of elastic-perfectly plastic form with initial stiffness of

10 7 kN/mm

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10.7 kN/mmA wall element is susceptible to out-of-plane dynamic instability due to its thinness and low self-weight/bearing stress


D. EXAMPLE OF VULNERABILITY ANALYSIS –T&T HOUSING (cont’d)T&T HOUSING (cont d)

MECHANICAL MODEL OF TYPICAL PIER




BEARING WALL MODELOF HOUSE FOR ANALYSIS



D. EXAMPLE OF VULNERABILITY ANALYSIS –T&T HOUSING ( ’d)T&T HOUSING (cont’d)IDA METHODOLOGY SPECIFICS

Computer program ZEUS NL by A S Elnashi of MidComputer program = ZEUS‐NL by A.S. Elnashi of Mid‐America Earthquake Center, U.S.AIntensity measure = Sa (T1, 5%)Intensity measure Sa (T1, 5%)Ground motion records = 10 arbitrarily selected from PEER database; converted to spectrum‐compatible records based on UWI/SRC data and IBC 2006 Spectrum for Site Class DN f i t d 24No. of increments per record = 24Limit states = HAZUS Low‐code URM drift values (i.e.slight; moderate; extensive complete damage)

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slight; moderate; extensive, complete damage) plus Priestley et al out‐of‐plane dynamic instability(DI) displacement

D. EXAMPLE OF VULNERABILITY ANALYSIS –T&T HOUSING ( ’d)

VULNERABILITY CURVES FOR LOCAL HOUSES (1‐STORY)T&T HOUSING (cont’d)



E. POSSIBLE STRUCTURAL VULNERABILITY ANALYSIS STRATEGY FOR GEM CARIBBEANSTRATEGY FOR GEM‐CARIBBEAN

Construction in the English‐speaking Caribbean probably consistent with HAZUS building taxonomy (except for Trinidad andconsistent with HAZUS building taxonomy (except for Trinidad andTobago)HAZUS structure classification (128 types):‐ 36 Structural Types‐ 4 Design/Construction Grade types = pre‐code;

low‐code; medium‐code; high‐code; ; g‐ 3 building height types = low‐rise; mid‐rise; high‐riseHAZUS has a published vulnerability function for each of the128 building types128 building types HAZUS technical challenge:‐ Structural vulnerability conditioned on drift, hence damage not


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directly tied to seismic hazard


BUILDING TYPES HAZUS RISE VOLUME HAZUS CLASS HAZUS GRADE

URM1 – 100mm Clay NIL 70% NIL NILURM1 – 100mm Clay tile/100mm Concrete Blk.

NIL 70% NIL NIL

URM2 – 100mm Clay NIL 10% NIL NILURM2 100mm Clay tile/100mm Concrete Blk

NIL 10% NIL NIL

Conc. Frame w/URM LOW 8% C3L PRE‐CODEInfill

Concrete Moment Frame

LOW 5% C1L LOW‐CODE

Concrete Moment Frame

MID 3% C1M MEDIUM‐CODE


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EXAMPLE OF HAZUS CLASSIFICATION – PORT-OF-SPAIN BUILDING STOCK


BUILDING TYPES HEIGHT(m) VOLUME HAZUS CLASS HAZUS GRADE

Steel Moment Frame MID RISE 2% S1M PRE CODESteel Moment Frame MID‐RISE 2% S1M PRE‐CODE

Reinforced Masonry LOW‐RISE 1% RM1L LOW‐CODE

Other 1% Can be handled separately

EXAMPLE OF HAZUS CLASSIFICATION – PORT-OF-SPAIN BUILDING STOCK (cont’d)


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1. Convert HAZUS vulnerability functions from “conditioned d if ” “ di i d S ” b i h PORTERon drift” to “conditioned on Sa”, by using the PORTER

method2 If the desired Intensity Measure is not S but PGA:2. If the desired Intensity Measure is not Sa, but PGA:

‐ use a compatible response spectrum to convert3. If the desired Intensity Measure s not Sa, but Sd:y a, d

‐ use simple dynamics relations to convert4. For non‐English‐speaking territories:

‐ use the Syner‐G methodologies (apparently conditioned on PGA; OpenQuake documentation/ WP3 documentation)


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WP3 documentation)

THE ENDthank you for your time



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