u, kadakal, n. g. kishi, j. song, j. byeon · 2014. 5. 18. · steel moment resisting frame or...

An objective methodology for the assessment of

building vulnerability to earthquakes and the

development of damage functions

U, Kadakal, N. G. Kishi, J. Song, J. ByeonApplied Insurance Research, Inc., Boston, Massachusetts

Abstract

This paper describes a new objective methodology for modeling buildingvulnerability. The methodology called Advanced Component Method (ACM™)is a major attempt to replace the conventional loss estimation procedures, whichare based on subjective measures and the opinions of experts, with one thatobjectively measures both earthquake intensity and the physical and monetarydamage to buildings. First, response of typical buildings (for example, mid-risesteel moment resisting frame or low-rise concrete frame with shear wall) isobtained analytically by nonlinear seismic, (pushover), analysis. Spectraldisplacement is used as a measure of earthquake intensity. Damage functions foreach building component, both structural and non-structural, are developed as afunction of component deformation. Examples of components include columns,beams, floors, partitions, glazing, etc. A cost model is developed that bridges thegap between the physical and monetary damage for each component. Finally,building response, component damage functions, and cost model were combinedprobabilistically, using Monte Carlo simulation techniques, to develop the finaldamage functions for each building type. Uncertainty in building responseresulting from variability in material properties, loads, etc. as well as componentdamage functions and cost model were incorporated in the Monte Carlosimulation. The developed damage functions are calibrated with actual observeddamage and loss data. The paper also presents and compares damage functionsdeveloped for several building types.

Risk Analysis II, C.A. Brebbia (Editor) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-830-9

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1 Introduction

Last year, earthquakes in Turkey, Taiwan, and elsewhere refocused attention onthe ability of catastrophe modelers to estimate, more reliably and accurately,building damage and corresponding monetary losses in the face of future events.As becomes immediately apparent in any post-earthquake field investigation, theintensity of earthquakes, as measured by the damage that results, is not uniformbut spotty, even for locations with similar soil conditions and at equal distancefrom the rupture. In order to better understand this phenomenon, to model it, tomake more reliable estimates of building damage, a new methodology, calledAdvanced Component Method (ACM), has been developed [1].This paper describes the ACM. Existing vulnerability assessment

methodologies are revisited first. Their advantages and shortcomings arecompared. The advantages of ACM to address the potential shortcomings ofexisting methodologies are discussed. ACM methodology of developingbuilding damage functions is described. The methodology has several stagesincluding building design, push-over analysis, component damage functions,cost model and calibration. Each stage is described separately. Finally, some ofthe damage functions obtained from ACM are presented.

2 Existing methodologies

The science of vulnerability assessment, that is, of estimating the probability andextent of earthquake damage before an earthquake occurs, is still very young.Most attempts have been based on simple extrapolations from observed damagein the aftermath of earthquakes or, given their relative infrequency, on theopinion of experts as to what might result were an earthquake to occur. Twomost notable attempts to address vulnerability assessment were ATC-13 andHAZUS studies. Following section describes both methodologies and comparestheir advantages as well as shortcomings.

2.1 ATC-13

One of the first systematic attempts to quantify building vulnerability toearthquakes came from the Applied Technology Council in a report to theSeismic Safety Commission of the State of California, ATC-13 [2]. ATC-13essentially derived damage functions by asking experts to estimate the expectedpercentage of damage that would result to a typical building of a specificconstruction type were that being subjected to a given MMI. Based on theirpersonal knowledge and experience, the experts responded to a formalquestionnaire with their best estimates of damage ratios.Because it was the first systematic attempt to develop damage functions,

ATC-13 quickly became the standard reference for earthquake vulnerabilityassessment. Catastrophe modelers adopted the ATC-13 damage curves virtuallyunaltered until the 1994 Northridge earthquake. After that event, an attempt tomodify the ATC-13 curves was made using actual claims data from Northridge.


Risk Analysis II

2.2 HAZUS

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A second major effort to develop a methodology for vulnerability assessmentwas undertaken by the National Institute of Building Sciences (NIBS), andfunded by FEMA. The result, HAZUS, was released in 1997 as a riskassessment interactive software [3]. In HAZUS, spectral displacements andspectral accelerations replaced MMI as the measure of seismic intensity, Thefocus shifted from ground motion to the individual building's response toground motion. This objective measure of earthquake intensity allowed for finergradations in estimating the potential damage to a structure. However, theHAZUS study continues to rely on expert opinion and engineering judgement toestimate the state of damage that would result from a given spectraldisplacement and acceleration. While HAZUS represent a significant advance,the difficulties surrounding reliance on expert opinion remain.

3 ACM™

Considering the shortcomings of both ATC-13 and HAZUS methodologies,ACM attempts to provide a major improvement on the existing vulnerabilityassessment techniques. ACM replaces the subjective measures and opinions of

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Figure 1 A flow chart of ACM compared with traditional vulnerabilityassessment methodologies


86 Risk Analysis II

experts about how building damage relates to earthquake intensity with anobjective and scientific methodology. Being an objective model, ACM is fully atransparent method. Because the underlying parameters are accessible and thesignificance of each is well understood, ACM can be easily calibrated. Likewise,it can be easily modified to incorporate the results of new research andexperimentation. It can be extended to include new building types and newregions. It can be updated as repair costs change and new repair strategies areintroduced. Figure. 1 describes a general flow-chart of developing ACM damagefunctions as compared to traditional methods, such as ATC-13, of developingdamage functions.ACM replaces earthquake intensity of MMI with spectral displacements.

Spectral displacement is the maximum horizontal displacement experienced bythe equivalent SDOF system of the building during an earthquake. The buildingdamage is calculated from the spectral displacement. Existing methods estimatebuilding damage from MMI or PGA which are not a measure of buildingresponse rather a measure of ground motion. Because each building has adifferent natural period, each will be subjected to a different seismic intensity(spectral displacement) and, hence, a different damage state. For example, anearthquake of magnitude 8.0 occurring at a distance of 50km and an earthquakeof magnitude 5.0 at a distance of 5 km may well produce the same PGA at acertain location. Using the conventional method for assessing vulnerability,these two earthquakes will subject a building to the same intensity and willtherefore result in the same level of damage. But the spectral ordinates of thesetwo earthquakes may be quite different and, accordingly, the building's responsewill be quite different. The use of MMI or PGA as the measure of intensity willresult in a relatively narrow distribution of damage, which will not reflect thespottiness of damage that is actually observed. Because of using spectraldisplacements as a measure of earthquake intensity, ACM can capture thisspottiness of damage.

4 Developing ACM damage functions

Second breakthrough of ACM is the way it develops building damage functions.As pointed out earlier, existing methodologies rely on damage functionsdeveloped based on expert opinions. ACM uses totally objective analytical andexperimental tools to develop building damage functions. Following sectiondescribes different stages of developing these damage functions.

4.1 Building design and modeling

The first step in developing ACM damage functions is to identify buildingstypical of the modeled region and define general configuration andcharacteristics. Actual design plans are created for each building type. Designdocuments include the physical dimensions of each component, as well as their


Risk Analysis 11 87

axial, bending, moment and shear capacities, yield strength and othermechanical properties. Each building type is to be as representative of theaverage of its type in the modeled region as possible.

In order to incorporate the variation from the typical building, a number ofparameters of the building are assumed to be random variables. Table 1 shows acomplete list of parameters considered as random variables. Table 1 also showstheir means and coefficient of variables with corresponding distributions. As aresult, a number of buildings were created from a single design. Then a finiteelement model of each building was developed.

Table 1 Random variable and their distributions

Random VariableRoof mass at edge (kips/in/ŝ )Roof mass in middle (kips/in/ŝ )Typical floor mass at edgeTypical floor mass in middleTypical Roof dead load at edge (kips/in)Typical Roof dead load in middle (kips/in)Typical Roof live load at edge (kips/in)Typical Roof live load in middle (kips/in)Typical Floor dead load at edge (kips/in)Typical Floor dead load in middle (kips/in)Typical Floor live load at edge (kips/in)Typical Floor live load in middle (kips/in)Modulus of elasticity of steel (ksi)Modulus of elasticity of concrete (ksi)Steel yield strength (ksi)Concrete strength (ksi)Yield strength of reinforcing bars (ksi)

Mean0.03130.0530.07010.13780.03780.01830.00420.0030.08360.04790.01040.0075290003605393.467

cov0.180.180.180.180.10.10.60.60.10.10.60.60.050.050.140.110.11

DistributionNormalNormalNormalNormalNormalNormal

Type I LargestType I Largest

NormalNormal

Type I LargestType I Largest

NormalNormal

LognormalNormal

Lognormal

Latin Hypercube sampling is chosen to represent uncertainties in structuralparameters in calculating the response statistics by simulation [4]. It is astratified sampling method, and is comparatively efficient for estimating theresponse statistics when no closed-form relationship between structural responseand variables (material strength and loading) is available, and when the numberis samples is limited.

4.2 Calculating building deformations

Once a three-dimensional model of each building was built, a three dimensionalpush-over analysis was performed to calculate building deformations. Push-overanalysis was performed by applying the building a lateral load along its height.SAP 2000 software [5] was used to perform the analysis. The lateral load isproportional to the first mode shape of the building. The load is applied


88 Risk Analysis II

incrementally until the building collapses. As connections and members fails,the force is redistributed to the elements that remain functional. Lateral forcesare applied in two directions, separately, and the effects are combined torepresent the three-dimensional analysis that captures the building's dominantmodes of vibration and approximates the results of a time history analysis.

First product of push-over analysis is building capacity curves. Buildingcapacity curves describe the relationship between the building displacement andthe force applied. Building displacements are calculated based on an equivalentSingle-Degree-of-Freedom-System (SDOF). Figure 2 illustrates a series ofcapacity curves developed for the five story Steel Moment Resisting Frame(SMRF) building. Due to the inherent uncertainty in both material strength and

co

V(1)ou

Spectral Displacement (in)

Figure 2 Set of capacity curves obtained from five story Steel Moment Frame

loading process, one would also expect uncertainty in the behavior of thebuilding response to dynamic loading. The variability in the capacity curves is agood measure of the uncertainty. It is captured here for further uncertaintyconvolution in vulnerability estimation.

The second product of push-over analysis is floor deformations. As the lateralforce applied, building deforms proportionally. For each incrementaldisplacement of the building, the amount by which components at each of thefloors are deformed will determine the interstory drift. Interstory drift ratios arecalculated and used to calculate component damage ratios as will be explainedin the following section. As in the case of capacity curves, uncertainties are alsocaptures in drift ratios.


RiskAnalvsis II 89

as

story drift

Figure 3 Selected component damage functions

4.3 Calculating component damage

Historically, problem of estimating building vulnerability has been approachedas a whole. In other words, damage to a building was calculated at once. Thisestimation was usually achieved by means of expert opinion because of thecomplexity of the problem. However, ACM approaches the problem in a totallydifferent way in order to solve it objectively. ACM, first, breaks the buildinginto its components of manageable portions. Those components includecolumns, beams, partitions, etc. Criteria for selecting each component was thatone should be able to obtain an individual function describing damagability ofeach component. These individual damage functions were developed bycombining the data obtained from the experimental studies conducted at variousuniversities and research organizations in a probabilistic manner. Figure 4 showssome of these individual damage functions.Damage on each component under a given earthquake intensity, described by

the spectral displacements, can be calculated from the individual componentdamage functions. These damage rations are then summed over each floor andcomponents to obtain building damage ratio. Hence the final number, obtainedthrough an objective methodology, is much more reliable compared to existingmethodologies.

4.4 Cost model

Previous section describes the calculation of physical damage ratios. However,monetary losses, defined by the repair cost of the damage caused by the givenearthquake is calculated differently. ACM estimates monetary damage at thecomponent level and the component damages are subsequently aggregated toproduce building monetary damage curves.


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The first step in developing the cost model is to estimate the total cost ofbuilding that is the cost of constructing the building as a new project. Totalreplacement cost is then calculated by adding the cost of demolishing the oldbuilding. The total cost of the building is calculated by estimating the cost ofeach individual component including the ones that individual damage functionswere developed in the previous section. All cost related information wasobtained from the data published yearly by R. S. Means [6].Given the damage state, that was described by the physical damage ratios

obtained in the previous section, the next step is the calculation of repair cost.This is achieved by developing a repair strategy for each damage state andbuilding type. Five damage states of negligible, slight, moderate, extensive andcomplete were used. In the case of a reinforced concrete column, for example, ifdamage is negligible or slight with minor deformations in connections orhairline cracks in a few welds, the recommended action may be a minimal repairor even to do nothing and, hence, the repair cost itself is negligible or zero.There may be alternative methods of repair, each associated with a differentcost; the appropriate method may depend on the degree of damage andaccessibility. At high levels of damage, replacing the affected member may beconsidered. (Note that the cost of replacing a damaged component may be asmuch as two times higher than the cost of the original placement. The "cost ofreplacing" should therefore not be confused with "replacement cost" as used ininsurance terminology.)The cost of repair also depends on the story on which the damaged

component resides. In the case of a moment resisting frame building, interstorydrift and, therefore, deformation, damage and the cost of repair are all higher athigher stories. Reinforcing this relationship, the conveyance of tools andmaterials to upper stories may be hampered by damage to lower stories or thelack of an operating elevator, thus, again, making repairs at higher stories moreexpensive.Other costs including the cost of inspections, set up costs, demolition and

removal of debris are also considered. Economies of scale exist, too; that is, theaverage per unit cost of small jobs will be higher than that of large jobs, as thefixed costs are spread over a larger volume. Correlation between cost of repairmust also be taken into account. A given contractor may be equipped to performrepairs on a number of different component types. But a contractor hired torepair beams and columns is unlikely to perform repairs on dry wall, orelectrical equipment. As the number of contractors goes up, so, too, do costs.

4.5 Final damage functions

So far, given the intensity of earthquake, described by spectral displacements,calculation of building deformations, component damages and finallyreplacement costs has been described. However, the analysis has been for asingle case. In order to incorporate the uncertainty, a crude Monte Carlosimulation has been performed. Initially, given the spectral displacement, anumber of simulations based on assumptions regarding probability distributions


Risk Analysis II 91

derived from pushover analysis and literature were performed to calculateinterstory drift ratios. For each interstory drift ratio, a number of simulationswere performed to calculate component damage ratios. Finally, same number ofsimulations were performed for each physical damage ratio to calculate repaircost. Figure 4 illustrates this procedure. As a result, a distribution of repair costswas obtained for each value of spectral displacement. Then one can produce adamage function by calculating mean damage ratios from the repair costdistributions. Figure 5 compares such damage functions developed for severalconstruction types.

5 Conclusion

The advantages of ACM are many. Earthquake intensity is directly linked toindividual building performance, rather than to ground shaking or theperformance of the "average" building within a large portfolio of buildings.ACM captures the unique structural system of a building, as well as the seismicperformance characteristics of its non-structural components. One implication ofthis is that damage patterns, as simulated by ACM, will much more closelyresemble the pattern and spottiness of damage that is observed after actualearthquakes.

damageabilityvariability

deformationvariability

Figure 4 Illustration of the Monte Carlo simulation performed to obtainbuilding damage functions

ACM damage functions are far more realistic than those of existing methods.Other damage functions treat buildings as a single, unified component, which isdamaged smoothly and proportionally as it is subjected to increasing levels ofintensity. But glass, for example, is not damaged smoothly. It undergoes stressuntil it breaks. While this example is perhaps extreme, most building elementsand materials exhibit discontinuities in their capacity to withstand deformation.Because ACM models damage at the component level, it is able to capture suchdiscontinuities.


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References

Risk Analvsis II

/TM[1] AIR (2000) "ACM'™ Advanced Component Method: A Breakthrough inVulnerability Assessment Technology", Technical Report (www.air-worldwide.com/Publications/PDF/acm.pdf)

[2] ATC-13, (1985) "Earthquake damage evaluation data for California",Report no. ATC-13, Applied Technology Council, 1985.

[3] HAZUS, (1997) "Earthquake loss estimation methodology", Vol.1, NationalInstitute of Building Sciences, 1997

[4] Song, J. and Ellingwood, B.R. (1999), "Seismic Reliability of SpecialMoment Steel Frames with Welded Connections: I and II," Journal of Structural

mg, ASCE, 125(4) 357-384.

[5] Computer and Structures, Inc. (2000), SAP 2000 Nonlinear Version 7.21,Structural Analysis Program, Berkeley, CA.

[6] R.S. Means (1999), "Square foot cost data", R.S. Means, Inc. Kingston,Mass.

0)o>OSCO

spectral displacement

Figure 5 Final damage functions calculated for several building types


u, kadakal, n. g. kishi, j. song, j. byeon · 2014. 5. 18. · steel moment resisting frame or...

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