NAVAL FACILITIES ENGINEERING SERVICE CENTERPort Hueneme, California 93043-4370

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TECHNICAL REPORTTR-2055-SHR

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ECONOMIC ANALYSIS PROCEDURE FOREARTHQUAKE HAZARD MITIGATION

by

J. M. Ferritto

February 1997

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Report Date 01FEB1997

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Title and Subtitle Economic Analysis Procedure for Earthquake Hazard Mitigation

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Supplementary Notes

Abstract The 1990s represents a period in which both government and industry are attempting to reduce expenditures,focusing on economics of operation as a priority problem. Both are undergoing a downsizing to eliminateunnecessary functions and personnel with an increased emphasis on cost effectiveness and maximization ofreturn on investment. All construction has a purpose and the economics of use is involved in the decisionprocess to build or upgrade. Commercial and industrial construction are categories of investment whichgenerally are designed to serve in an income producing role. The user commits to the expenditure of anamount of resources to establish an operating environment to meet a specific objective. In the corporateworld, the objective may be an office complex designed for administrative or sales functions, or the objectivemay be an industrial complex designed to produce a product. It may be a hospital designed to assist thecommunity by offering medical services. In the government sector, the objective might be an office complexto administer a state or federal program. In the Department of Defense, small self-contained cities areoperated to meet the military needs for ports, airfields, industrial facilities, administration and personnelhousing. Executive Order 12911 directs a screening program to quantify the numbers of federal buildingsrequiring seismic upgrade and an estimate of the cost to bring these deficient buildings up to currentrequirements. The expected costs of upgrade are huge and economics plays a central role in the decisionprocess.

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Executive Summary

While previous research by others has dealt with the subject of economics ofseismic design, none has provided a framework to examine a single building in detail; thatis why this report has been written. There is an increased emphasis on post-earthquakebuilding functionality by the engineering community. In this light, it is essential to be ableto evaluate the extent and location of expected building damage. Are there any weak linksin the building system design which will preclude operability? Operability demands that thebuilding be viewed as a total system not just a structural system. Utilities and the otherelements must function to have operability. We need to know what building systemelements are damaged in addition to the damage to the lateral force resisting system. Thisreport presents a detailed analysis procedure which can evaluate the economics of seismicdesign for a building system.

The purpose of this analysis procedure is to perform an economic comparison ofalternative designs of a structure considering initial construction expenditures andexpected earthquake induced damage over the life of the structure. It may comparedifferent types of construction or different design levels. It is thus intended to assist theuser and the design engineer in obtaining cost effective seismic construction. The Navyseismic economic analysis procedure is a process of estimating earthquake damage basedon both interstory drift (displacement) and floor acceleration. As such it recognizes thatthe building system is composed of components, some structural, some nonstructural andsome mechanical and electrical, which are affected by displacement or drift. It alsorecognizes that damage is induced in some building system components which aremounted to floors or ceilings by the transmitted story accelerations. The procedure ofincluding both drift and acceleration is a significant factor in this procedure which is animprovement over other techniques which focused only on drift. Failure to include theacceleration induced damage leads to erroneous conclusions that mere stiffening whichreduces drift is fully effective. For every dollar that is invested in stiffening a structure, aportion of it may be wasted because stiffening results in increased floor accelerationswhich can cause additional damage to acceleration sensitive components like contents.

This report defines the steps in the procedure for conducting an economic analysis.The initial step is to establish the seismic exposure of the building site. The building isdivided into components based on function and damage mechanism Some components aredrift sensitive while others are acceleration/force sensitive. The cost of buildingcomponents must be identified to distinguish variations in cost of alternatives. A series ofanalyses are conducted for the range of expected site ground motion for each alternativeconcept to determine interstory drift and floor acceleration. Damage functions arepresented in the report to determine component damage. Since the damage can occur atany time over the life of the structure, the present value of the damage cost is determined.Loss-of-use costs may be included. Damage costs are combined with initial strengtheningcosts to determine total expected cost for comparison of alternatives.

Table of ContentsPage

Introduction................................................................................................................1

Seismic Exposure (Step 1)..........................................................................................3

Seismic Cost of Alternatives (Step 2)..........................................................................4

Damage Evaluation (Step 3).......................................................................................5

Illustrative Example....................................................................................................8

Simplification of General Approach.............................................................................9

Conclusion..................................................................................................................10

Acknowledgment........................................................................................................10

References..................................................................................................................10

APPENDIX

A - Proposed Criteria for Economic Analysis of Seismic Design Alternatives..............A-1

Seismic Exposure (Step 1)....................................................................................A-3Seismic Cost of Alternatives (Step 2)....................................................................A-3Damage Evaluation (Step 3)..................................................................................A-4Simplification of General Approach.......................................................................A-6

Introduction

The 1990’s represents a period in which both government and industry areattempting to reduce expenditures, focusing on economics of operation as a priorityproblem. Both are undergoing a downsizing to eliminate unnecessary functions andpersonnel with an increased emphasis on cost effectiveness and maximization of return oninvestment. All construction has a purpose and the economics of use is involved in thedecision process to build or upgrade. Commercial and industrial construction arecategories of investment which generally are designed to serve in an income producingrole. The user commits to the expenditure of an amount of resources to establish anoperating environment to meet a specific objective. In the corporate world, the objectivemay be an office complex designed for administrative or sales functions, or the objectivemay be an industrial complex designed to produce a product. It may be a hospitaldesigned to assist the community by offering medical services. In the government sector,the objective might be an office complex to administer a state or federal program. In theDepartment of Defense, small self-contained cities are operated to meet the military needsfor ports, airfields, industrial facilities, administration and personnel housing. ExecutiveOrder 12911 directs a screening program to quantify the numbers of federal buildingsrequiring seismic upgrade and an estimate of the cost to bring these deficient buildings upto current requirements. The expected costs of upgrade are huge and economics plays acentral role in the decision process.

In the 1980’s the Naval Civil Engineering Laboratory, now named the NavalFacilities Engineering Service Center, developed a procedure for the economic analysis ofseismic design levels and lateral force resisting systems, Ferritto (1982, 1983, 1984a and1984b). That work lead to the development of Chapter 7 of NAVFAC P355.2, SeismicDesign Guidelines For Upgrading Existing Buildings. The procedures have been adoptedfor use by the engineering community and used to analyze the seismic upgrade of severalhospitals. Recently the State of California passed SB920 which mandates an economicanalysis be conducted when new earthquake hazard mitigation technology such as baseisolation or viscoelastic dampers are proposed for use in State construction projects. TheState of California has adopted for use the economic analysis procedures developed by theNavy referenced above. New data on damage was added. The State of Californiaprocedures for conducting an economic analysis are contained in “Earthquake HazardMitigation Technology Guidelines”, Way (1995). This report will present the standardizedprocedure and the new damage data.

Economic analysis techniques have been used extensively in business andengineering. There has been investigation of the cost of seismic construction upgrading ina number of documents such as FEMA 157 (1988). FEMA 228 (1992) and 229 (1992)discuss a benefits-cost model for the rehabilitation of buildings. A significant study wasperformed by the Applied Technology Council, ATC-13 (1985). These studies took amacroeconomics perspective looking at the decision process for large inventories of

buildings, expressing costs on a per square foot basis, and developing guidelines forapplication to classes of construction. The models for estimating cost and damage focusedonly on evaluating the lateral force resisting system. Harris and Harmon (1986)performed an economic analysis using techniques very similar to those outlined in Ferritto(1984a), but the work was unfortunately oversimplified to the point where its results arelimited. They related damage only to drift and failed to include story force/acceleration asa separate damage mechanism. Ductility demand alone can not represent all damage sincedirect force/acceleration effects on elements mounted to floors or ceilings and damage tobuilding contents would not be included. One would erroneously conclude that simplystiffening a building would reduce all damage when in effect we find that induced flooraccelerations are increased by stiffening. One would never be able to completely assess thecost - benefits of base isolation if acceleration damage were omitted. Their damagefunction for the total building consisted of interpolating between yield and collapseductility levels for only the lateral force resisting element neglecting the possibilities ofdifferent level of damage to the other building elements and subsystems.

While previous papers have dealt with the subject of economics of seismic design,none has provided a framework to examine a single building in detail which is why thisreport has been written. There is an increased emphasis on post-earthquake buildingfunctionality by the engineering community. In this light, it is essential to be able toevaluate the extent and location of expected building damage. Are there any weak links inthe building system design which will preclude operability? Operability demands that thebuilding be viewed as a total system not just a structural system. Utilities and the otherelements must function to have operability. We need to know what other building systemelements are damaged in addition to the damage to the lateral force resisting system. Thisreport presents a detailed analysis procedure which can evaluate the economics of seismicdesign for a building system.

The purpose of this analysis procedure is to perform an economic comparison ofalternative designs of a structure considering initial construction expenditures andexpected earthquake induced damage over the life of the structure. It may comparedifferent types of construction or different design levels. It is thus intended to assist theuser and the design engineer in obtaining cost effective seismic construction. The Navyseismic economic analysis procedure referenced above is a process of estimatingearthquake damage based on both interstory drift (displacement) and story acceleration.As such it recognizes that the building system is composed of components, somestructural, some nonstructural and some mechanical and electrical, which are affected bydisplacement or drift. It also recognizes the damage induced in some building systemcomponents which are mounted to floors or ceilings are damaged by the transmitted storyaccelerations. The procedure of including both drift and acceleration is a significant factorin this procedure which is an improvement over other techniques which focused only ondrift. As noted above, failure to include the acceleration induced damage leads toerroneous conclusions that mere stiffening which reduces drift is fully effective. For everydollar that is invested in stiffening a structure, a portion of it may be wasted because

stiffening results in increased floor accelerations which can cause additional damage toacceleration sensitive components like contents.

This Navy technique utilized available structural data correlating structuralcomponent member damage to measured drift levels. Additional data relating accelerationsensitive components to damage was compiled. The technique referenced above usedavailable data at the time of its writing; since then the Loma Prieta earthquake of 1989 andthe Northridge earthquake of 1994 coupled with extensive university testing have greatlyincreased the damage data base. In the process of developing the State of Californiaguideline, the original damage estimation tables were updated to include the new data.This new data base is now available and was used to update damage relationships, Way(1995). The procedure for conducting an economic analysis is applicable to both new andexisting structures. The procedure is appropriate for larger projects which can justify asite seismicity study and the additional steps involved. The procedure is not meant forstructures where the building code is design is adequate, but rather for those structureswhere post-earthquake performance is under consideration. It is best applied during thedesign process when cost estimates of the proposed structure are usually made and theperformance of the structure analyzed. When only relative performance of alternatives isrequired, the general procedure may be shortened as will be described in followingsections.

Seismic Exposure (Step 1)

Fundamental to evaluating the potential for seismic damage is quantifying of thehazard exposure. This is accomplished by a site seismicity study which determines theintensity and characteristics of ground motion shaking which pose a risk to a specificlocation. The method of performing a site seismicity study has become standard practiceand is used by many geotechnical firms. In general, an historical epicenter data base isused in conjunction with available geologic data to compute the probability distribution ofsite ground motion. The process of quantifying the level of hazard involves building amathematical model of the region. The controlling elements of seismic sourcecharacterization depend on the tectonic environment. In the Western United States, thetectonic environment is such that earthquakes are associated with known faults. However,in the Eastern United States, the causative geologic structures are generally not as welldefined. The seismic model must be based on the knowledge of the local area in sufficientdetail to yield results appropriate to estimate site motion for events with return times onthe order of 1,000 years. The results of a seismicity study are presented in an engineeringreport which gives a discussion of the results, the site acceleration probability distribution,and the determination of specific site acceleration levels to be used for building design.Figure 1 illustrates a typical non-exceedance probability ground acceleration distributionfor a site for a given exposure period. The word “total” is used because it represents thecombined effects of all seismic source zones acting on the site. A histogram can beconstructed showing the expected probabilities of various levels of ground shaking, Figure2. Development of Figures 1 and 2 are the first steps in the economic analysis and areusually part of a routine seismicity study for a large facility.

The structural design engineer may use either a response spectra or earthquaketime history in the analysis of a structure. The data base of available recordedaccelerograms is routinely used to generate a series of spectra or time histories for use bythe structural and geotechnical engineers in further assessment of the site.

Seismic Cost of Alternatives (Step 2)

The economic analysis may be applied to new construction to evaluate:

• alternative structural systems such as moment frame vs. braced frame or shear wall• alternative materials, concrete vs. steel• alternative concepts such as conventional construction vs. new earthquake hazard

mitigation technology such as base isolation• alternative seismic design load levels such as various acceleration levels• alternative earthquake return time design levels

For existing construction, economic analysis may be applied to evaluate:• alternative seismic upgrade levels• alternative concepts of upgrade including conventional construction vs. new

earthquake hazard mitigation methods

When an economic analysis is applied to a design project considering alternative concepts,it is necessary to evaluate the cost of each alternative. A preliminary structural design mustbe performed to determine structural member sizes for each alternative. Additionallynonstructural items affected by the seismic forces must be designed to the extent that theyrepresent significant cost factors which vary among the alternatives. For special structuressuch as base isolated buildings, special requirements such as building clearance, flexibleutility connections, isolator design, etc. must be included to be able to define the structure.Once the structure is defined a detailed cost estimate can be completed. This is a veryimportant step in the economic analysis and one which determines the level of accuracy.As is usual practice in preparing a cost estimate, the structure should be broken down intomajor components and the cost of each component noted separately. The division of thebuilding into components is an important step since each component will be later analyzedfor damage. As will be shown later, it is important to separate out components which aredrift sensitive from those that are force/acceleration sensitive. Equipment mounted onfloors will be sensitive to the acceleration levels it receives; while, items such as verticalplumbing risers spanning between floors will be drift sensitive. Some items will fall intoboth categories. As a minimum, the major components should include the structuralsystem, non structural partitions, exterior walls, floors, foundations, ceiling lights andfixtures, mechanical equipment, electrical equipment, and building contents. Wheredesired, a component may be subdivided into elements for a more detailed evaluation. It isrequired that a detailed cost estimate be compiled for each alternative being evaluated.There may significant portions of the cost estimate which do not vary among thealternatives. The amount of work involved is not as great as it might appear. Once a

routine detailed cost estimate is prepared for the basic structure concept, as is standardpractice, only those elements which change among alternatives need be evaluated. Use ofindividual components has the added benefit of showing where the damage occurs andwhether there are any weak links in the building system. This is especially important forbuildings which are expected to remain operational after an earthquake.

To illustrate the process, a study was performed in which a 185-foot square three-story building was designed for various steel and concrete lateral force resistingalternatives. Five lateral force resisting alternatives were evaluated for six designacceleration levels. Figure 3 shows the cost increase of seismic design as a function of thedesign acceleration level for the various alternative lateral force resisting systems. For thisillustration, the structure was designed to be at the elastic limit at the design accelerationlevel to facilitate comparison. It is interesting to note that in this case, the cost of seismicstrengthening is a relatively minor part of the structure’s total cost.

Damage Evaluation (Step 3)

Earthquake induced structural damage is caused principally by two mechanisms:interstory drift and story forces/accelerations. Drift is the mechanism usually causingdamage to structural systems. There have been numerous tests conducted of lateralstructural resisting systems which show the strength of these elements under cyclic loadreversal. Building elements anchored to floors or suspended from ceilings feel the flooracceleration and respond as substructures. Depending upon the natural period of thestructure, floor accelerations can be significantly higher than surface ground motion levelsand tend to increase with height within the structure. The original Navy work, Ferritto(1984a), presented data tables relating damage of various components to drift and toacceleration. Way (1995) has updated this information based on experience over the lastdecade. Figure 4 gives the most current damage estimate data.

For each alternative it is necessary to conduct a series of dynamic analyses tocompute damage over a range of possible ground motion levels. Looking at the histogramin Figure 2, it can be seen that the bins cover increments of 0.1 g from a range of 0 to 1.0g for the particular site. A set of ten dynamic analyses starting at 0.05g to 0.95g wouldbe appropriate for this case to cover the range of possible accelerations which couldproduce expected damage of significance. For a specific alternative, a basic finite elementmodel would be constructed; then, the ten analyses of the model would be performed inwhich the applied load level was increased from 0.05 g to 0.95g. The author has foundthat performing a nonlinear time history analyses using programs like theDRAIN2DX/DRAIN3DX computer program to be highly efficient. The amount of effortinvolved is not increased significantly beyond the basic analysis since repeated analyses atdifferent load levels only involve adjusting a few parameters to change or scale theacceleration load record and the structure damping level. The topic of damping will bediscussed below. No changes need be made to the structure geometry model. The resultsof the analysis are used to establish the interstory drifts and floor accelerations at eachapplied load increment. These are used to compute the damage ratio for each component

by using Figure 4, examining the individual component elements and their appropriatedrift and/or floor acceleration. The damage evaluation process is repeated for each of theten applied load levels from 0.05g to 0.95g for each alternative. This part of the analysiscan be automated by a program which post-processes the output from the finite elementprogram and computes damage to all components and then sums component damage foroverall building damage at that level of applied loading. Thus to summarize:

Alternatives 1... i

Acceleration Increments 1... j

For each dynamic analysis for a given alternative, i, and applied load level, j, each of theidentified components such as structural frame, mechanical equipment etc. is evaluated fordamage using the drift and floor acceleration response data

The element damage relationship expressed in Figure 4 is in terms of a damageratio; the actual element damage cost is obtained by multiplying the damage ratio fromFigure 4 times the element cost from the cost estimate. Alternatively the element damagecan be summed to a component level based on average damage ratios and then expressedas a component damage cost based on the average damage ratio times the componentcost. Experience has shown that the cost of repair is greater than the original costbecause elements must first be removed before the damaged component can be repaired orreplaced. A component repair multiplier, R, is used to account for this increase. Therepair multipliers are based on GSA data obtained from actual experience. For example,when a lateral force element is damaged the level of damage is first computed from thedrift data. This level of damage is then multiplied by 1.5 to take into account that therepair process requires more work than the initial installation. Specifically, a given level ofdrift may represent 10 percent damage to the element which would become 15 percent ofthe dollar cost of the element ( 10% times 1.5 ). The following repair multipliers aresuggested to increase the component costs:

Lateral force resisting system 1.5Other structural components 1.5Mechanical equipment 1.25Electrical equipment 1.25Architectural elements 1.25Elevators 1.25Contents 1.05

The Total Building Damage for a given iteration of acceleration load level can beexpressed as:

Total Building Damage = Σ ( Damage Ratio ) * (Component Cost)*(Component Repair Multiplier)

Additional cost factors can be included in the Total Building Damage at this point, such asloss of life, injury and down time. Loss of functionality can be a very significant costfactor for certain types of facilities. It can be estimated in terms of lost revenue forincome producing facilities or in terms of the work-force salaries for service facilities. Theowner/user is willing to pay an aggregate salary to have a work-force perform a set offunctions. The inclusion of these indirect costs are significant and can shape the results ofan analysis. The users can in most cases express the loss of use of the structure and thisinformation should be included.

The Expected Building Damage Cost is computed by multiplying the probabilitythat the acceleration increment from the histogram will occur, such as Figure 2, times thedamage or damage ratio for the building evaluated at that acceleration increment, andsummed over all acceleration loading increments. The Expected Building Damage Cost forthe specific alternative concept over the range of possible accelerations is given by:

Expected Building Damage = Σ ( Total Building Damage for increment “bin” ofacceleration ) * (Acceleration “bin” Probability)

Since the damage will occur some time in the future it must be expressed in terms of thepresent value (PV) to relate it to the current costs of seismic strengthening or remediation.

Current Expected Damage Costs = PV( Expected Building Damage Cost)

In most cases, we do not have data which defines the temporal sequence of expected earthquakesover the life of the structure. It may be assumed that the risk is uniform over the exposure period.The present worth can be determined by dividing the exposure time into segments and then takingthe present value of each segment or more simply by using a single average exposure time equal tohalf the total exposure time.

The life cycle cost of this alternative is the sum of the initial construction cost plusthe present value of the expected damage.

Alternative Cost = Initial Construction Cost + PV( Expected Damage Costs)

Engineers have used two forms of structural dynamic analysis: response spectraprocedures and time history solutions. A nonlinear time history solution is preferredbecause it directly computes displacements and floor accelerations taking into accountstructure yielding. Since there is substantial variation among earthquake records evenwhen scaled to the same nominal peak acceleration value, the selection of an accelerationrecord can be a factor in establishing the maximum response of the structure. The choiceof records should be examined to quantify variation in response and a series of threeacceleration time histories is typically used to cover a range of response. It is important tonote that as the ratio of applied loading to design load increases, the structure undergoesincreased deformation and possible nonlinear behavior. As the level of deformationincreases, an increase in damping occurs which must be included in the analysis. Values

for damping as a function of inelastic deformation have been discussed in the literature andare presented in Ferritto (1984a). Care must be taken at each load level iteration to selectthe appropriate damping for that load increment.

Illustrative Example

To illustrate the economic analysis of alternative concepts, the building discussedabove will be used. The structure is a proposed three-story square building 185 feet on aside.

Problem: Consider for a new building the alternative designs of• Steel frame and concrete shear wall• Steel braced frameThe alternatives of frame/shear wall design and braced frame design will be compared fora 0.2g elastic design acceleration. The building is shown in plan view in Figure 5a and thetwo lateral force resisting alternatives are shown in Figure 5b. The components identifiedfor analysis, their costs and repair multipliers are shown in Table 1. The components havebeen divided based on their susceptibility to drift or acceleration. The initial constructiontotal costs for each alternative are

Steel Frame and Concrete Shear Wall $5876,700

Steel Braced Frame $5,928,800

For each increment in acceleration between 0.05g and 0.95g a nonlinear analysis wasperformed and the interstory drift and floor accelerations determined. Using drift andacceleration damage data from Figure 4, damage ratios were computed and are shown inFigure 6. The data in Figure 6 was combined with the data in Figure 2 to compute TotalBuilding Damage. The calculations are shown in Table 2. The present worth of the futuredamage which can occur any time in the 50 year exposure period is determined based onthe average present worth factor for increments of time using a 7 percent interest rate. Theinterest rate was based on the approximate rate of return on long term federal bonds and isthought appropriate for federal construction. The expected damage is:

Steel Frame and Concrete Shear Wall $206,000

Steel Braced Frame $96,000

The loss of building function from an earthquake can be a significant factor and can beincluded at this point. Here the user develops a value for the operation of the building interms of the value of the product produced in the building. For administrative buildingsthe value of the salaries paid to the occupants can be an approximate indication of thevalue of the operation. As an illustration consider that the out of service lost time mightbe estimated as follows based on the dollar value of the damage and the time to repair:

Steel Frame and Concrete Shear Wall 10 weeks

Steel Braced Frame 5 weeksIf the building housed 200 people with a total annual payroll of $10 million, one week oflost productivity would be about $200,000 times the present value factor 0.28 or$56,000.

The total cost of the two alternatives involves summing the initial constructioncosts plus the present worth of the total damage and lost time costs expected. In thisexample they are:

Steel Frame and Concrete Shear Wall $5,876,700 + $206,000 + $560,000 = $6,642,700

Steel Braced Frame $5,928,800 + $96,000, + $280,000 = $6,304,800

Up to this point the interest rate and the life of the structure have not beendiscussed. Both of these can affect the life cycle cost and influence the choice of options.It is up to the building owner/user to select these values based on the value of money tohim/her and the projected useful life of the structure. For federal construction the value ofborrowed money such as long term Treasury Bonds is a good indication of what money iscosting. Increasing the value of the interest rate makes the present value of future lossesless and reduces the economic worth of damage prevention over initial savings. It becomesharder to justify seismic damage reduction technology. Conversely if borrowed moneywere without cost, seismic improvements would be very attractive. Buildings tend toremain in service for long periods of time. Fifty years has been used as the economic lifefor federal construction. Increasing the life of the structure increases its exposure todamage but also increases the time factor in present value calculations which reduces thepresent worth of future damage. The specifics of the problem determine the net effect. Ingeneral the life of the structure has less effect than the interest rate.

Simplification of General Approach

The above procedure involves three main steps: the quantification of the seismichazard in probabilistic terms, the determination of the initial costs of seismic strengtheningor remediation, and the determination of the expected damage. It was proposed to use anincremental approach in which the ground motion acceleration probability distribution isexpressed as a histogram composed of incremental “bins” of acceleration and theirassociated probabilities of occurrence. This produces a full and complete analysis of thebest estimate of the seismic exposure. However, a site seismicity study may not always beavailable. The engineer is free to substitute a set of earthquake events of design interest.This set is not a complete risk assessment but rather is a comparison of the proposedstructural design alternatives under an assigned set of design load conditions. Havingdone this, the designer may choose to consider the average performance of the structureunder the assigned set of events, or perhaps the worst case event, or perhaps thecumulative effect of all the events. Again it is important to note that this approach is not a

total risk analysis but only a relative comparative performance of the alternatives under aset of design conditions. It was suggested that nonlinear time history finite elementmodels of the structure be used to estimate drift and floor accelerations using sets of timehistories. The engineer may substitute elastic response spectra techniques if he chooses aslong as the results are adjusted for yielding.

Conclusion

This report has presented a procedure for economically comparing alternativeseismic designs. The focus should be on the general procedure discussed and the choiceof components and damage data should be adjusted for the specifics of the application.The data shown has evolved and will continue to evolve as the engineering communityperforms more earthquake case studies. The approach is a systematic method forestimating life cycle costs and calculating expected damage. The level of effort involved inthis approach is greater than that of a single alternative design, but not enormously so.The procedure should be applied to significant structures where alternatives for designexist and the tradeoff costs are significant enough to justify the added analyses. Generallya site seismicity study is required for these structures of significance. Automated softwarein use at many geotechnical firms simplifies the preparation of a site study to produce therequired histogram of site acceleration probability. The design of alternative must becarried to a level to identify the major cost differences. The automated nonlinear analysisis not significantly more complex that response spectra techniques in current use. Therequirement for repeated analysis at increasing load levels requires that only minorchanges be made to the input data files for the structural model. Most of the analysis canbe automated.

Acknowledgment

The data in Figure 4 is based on the work of Mr. Douglas Way, Base IsolationConsultants, Inc. His work has added significantly to the methodology presented hereinand is acknowledged.

References

Applied Technology Council, ATC-13 “Earthquake Damage Evaluation Data forCalifornia, Redwood City CA 1985

FEMA 157 “Typical Costs of Seismic Rehabilitation of Existing Buildings” Sept. 1988

FEMA 227 “A Benefit Cost Model For the Seismic Rehabilitation of Buildings” Volume1 A User’s Manual April 1992

FEMA 228 “A Benefit Cost Model For the Seismic Rehabilitation of Buildings” Volume2 , Supporting Documents April 1992

Ferritto, J (1982) Technical Note N1640, "An Economic Analysis of Earthquake DesignLevels", July 1982

Ferritto, J. (1983) Technical Note N 1671, "An Economic Analysis of Earthquake DesignLevels For New Construction", July 1983

Ferritto, J (1984a) "Economics of Seismic Design for New Building", American Societyof Civil Engineers Journal of the Structures Division, ASCE Journal of StructuralEngineering Vol. 110 No. 12 Dec. 1984

Ferritto, J (1984b) "Economics, Expected Damage and Costs of Seismic Strengthening",8th World Conference on Earthquake Engineering, San Francisco July 1984

Harris J. L. and T. G. Harmon “ A Procedure For Applying Economic Analysis ToSeismic Design Decisions” Engineering Structures Vol. 8 Oct. 1986

Way, D (1995) “Earthquake Hazard Mitigation Technology Guidelines” prepared forDivision of the State Architect, State of California, by Base Isolation Consultants, SanFrancisco (in publication).

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Braced Frame Frame & Shear Wall

For 50 years of equal exposure the average Present Worth factor is 0.28

The present value of the damage costs are:

Braced Frame 0.28 * 0.1241 * $5,928,800 = $206,000

Shear Wall 0.28 * 0.0584 * $ 5,876,700 = $96,000

13

Table 2. Damage Ratio and present value calculation

Braced Frame Frame & Shear Wall

Acceleration Increment

(9's)

(1) Probability

(2) Damage

Ratio Braced Frame

(1)x(2) Probable Damage

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0-.1 0.34 0.03 0.0102 0.015 0.0051 .1-.2 0.35 0.11 0.0385 0.05 0.0175 .2-.3 0.16 0.175 0.028 0.08 0.0128 .3-.4 0.07 0.25 0.0175 0.11 0.0077 .4-.5 0.02 0.305 0.0061 0.14 0.0028 .5-.6 0.02 0.335 0.0067 0.17 0.0034 .6-7 0.01 0.365 0.00365 0.19 0.0019 7-.8 0.01 0.41 0.0041 0.22 0.0022 .8-. 9 0.01 0.45 0.0045 0.24 0.0024

.9-1.0 0.01 0.485 0.00485 0.26 0.0026

Total Damage Ratio

BF = 0.1241 SW = 0.0584

For 50 years of equal exposure the average Present Worth factor is 0.28

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Braced Frame 0.28 * 0.1241 * $ 5,928,800 = $206,000

Shear Wall 0.28 * 0.0584 * $ 5,876,700 = $96,000

13

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Proposed Criteria

for

Economic Analysis Of Seismic Design Alternatives

Seismic Exposure (Step 1)

Fundamental to evaluating the potential for seismic damage is quantifying of thehazard exposure. This is accomplished by a site seismicity study which determines theintensity and characteristics of ground motion shaking which pose a risk to a specificlocation. The method of performing a site seismicity study has become standard practiceand is used by many geotechnical firms. In general, an historical epicenter data base isused in conjunction with available geologic data to compute the probability distribution ofsite ground motion. The process of quantifying the level of hazard involves building amathematical model of the region. The seismic model must be based on the knowledge ofthe local area in sufficient detail to yield results appropriate to estimate site motion forevents with return times on the order of 1,000 years. The results of a seismicity study arepresented in an engineering report which gives a discussion of the results, the siteacceleration probability distribution, and the determination of specific site accelerationlevels to be used for building design.

The structural design engineer may use either a response spectra or earthquaketime history in the analysis of a structure. The data base of available recordedaccelerograms is routinely used to generate a series of spectra or time histories for use bythe structural and geotechnical engineers in further assessment of the site.

Seismic Cost of Alternatives (Step 2)

When an economic analysis is applied to a design project considering alternativeconcepts, it is necessary to evaluate the cost of each alternative. A preliminary structuraldesign must be performed to determine structural member sizes for each alternative.Additionally nonstructural items affected by the seismic forces must be designed to theextent that they represent significant cost factors which vary among the alternatives. Forspecial structures such as base isolated buildings, special requirements such as buildingclearance, flexible utility connections, isolator design, etc. must be included to be able todefine the structure. Once the structure is defined a detailed cost estimate can becompleted. This is a very important step in the economic analysis and one whichdetermines the level of accuracy. As is usual practice in preparing a cost estimate, thestructure should be broken down into major components and the cost of each componentnoted separately. The division of the building into components is an important step sinceeach component will be later analyzed for damage. As will be shown later, it is importantto separate out components which are drift sensitive from those that are force/accelerationsensitive. Equipment mounted on floors will be sensitive to the acceleration levels itreceives; while, items such as vertical plumbing risers spanning between floors will be driftsensitive. Some items will fall into both categories. As a minimum, the major componentsshould include the structural system, non structural partitions, exterior walls, floors,foundations, ceiling lights and fixtures, mechanical equipment, electrical equipment, andbuilding contents. Where desired, a component may be subdivided into elements for amore detailed evaluation. It is required that a detailed cost estimate be compiled for each

Performance Objective

Navy waterfront facilities fall into the category of essential construction. There isan increased emphasis on post-earthquake functionality of essential construction. In thislight, it is important to be able to evaluate the extent and location of expected buildingdamage. Are there any weak links in the building system design which will precludeoperability? Operability demands that the building be viewed as a total system not just astructural system. Utilities and the other elements must function to have operability.Additionally a procedure is required to evaluate alternative seismic designs and select themost effective choice. This guidance presents a detailed analysis procedure which canevaluate seismic strengthening, expected damage and the economics of seismic design fora building system.

The purpose of this procedure is to perform an economic comparison of alternativedesigns of a structure considering initial construction expenditures and expectedearthquake induced damage over the life of the structure. It may compare different typesof construction or different design levels. It is thus intended to assist the user and thedesign engineer in obtaining cost effective seismic construction. The Navy seismiceconomic analysis procedure is a process of estimating earthquake damage based on bothinterstory drift (displacement) and floor acceleration. As such it recognizes that thebuilding system is composed of components, some structural, some nonstructural andsome mechanical and electrical, which are affected by displacement or drift. It alsorecognizes that damage is induced in some building system components which aremounted to floors or ceilings by the transmitted story accelerations. The procedure ofincluding both drift and acceleration is a significant factor in this procedure which is animprovement over other techniques which focused only on drift. Failure to include theacceleration induced damage leads to erroneous conclusions that mere stiffening whichreduces drift is fully effective. For every dollar that is invested in stiffening a structure, aportion of it may be wasted because stiffening results in increased floor accelerationswhich can cause additional damage to acceleration sensitive components like contents.

This criteria defines the steps in the procedure for conducting an economicanalysis. The initial step is to establish the seismic exposure of the building site. Thebuilding is divided into components based on function and damage mechanism Somecomponents are drift sensitive while others are acceleration/force sensitive. The cost ofbuilding components must be identified to distinguish variations in cost of alternatives. Aseries of analyses are conducted for the range of expected site ground motion for eachalternative concept to determine interstory drift and floor acceleration. Damage functionsare used to determine component damage. Since the damage can occur at any time overthe life of the structure, the present value of the damage cost is determined. Loss-of-usecosts may be included. Damage costs are combined with initial strengthening costs todetermine total expected cost for comparison of alternatives.

alternative being evaluated. There may significant portions of the cost estimate which donot vary among the alternatives. The amount of work involved is not as great as it mightappear. Once a routine detailed cost estimate is prepared for the basic structure concept,as is standard practice, only those elements which change among alternatives need beevaluated. Use of individual components has the added benefit of showing where thedamage occurs and whether there are any weak links in the building system. This isespecially important for buildings which are expected to remain operational after anearthquake.

Damage Evaluation (Step 3)

Earthquake induced structural damage is caused principally by two mechanisms:interstory drift and story forces/accelerations. Drift is the mechanism usually causingdamage to structural systems. There have been numerous tests conducted of lateralstructural resisting systems which show the strength of these elements under cyclic loadreversal. Building elements anchored to floors or suspended from ceilings feel the flooracceleration and respond as substructures. Depending upon the natural period of thestructure, floor accelerations can be significantly higher than surface ground motion levelsand tend to increase with height within the structure. Damage relationships are shown inFigure 1.

For each alternative it is necessary to conduct a series of dynamic analyses tocompute damage over a range of possible ground motion levels. Typically the distributionis broken into increment bins of 0.1 g size covering a range of 0 to 1.0 g for the particularsite. A set of ten dynamic analyses starting at 0.05g to 0.95g would be appropriate tocover the range of possible accelerations which could produce expected damage ofsignificance. For a specific alternative, a basic finite element model would be constructed;then, the ten analyses of the model would be performed in which the applied load levelwas increased from 0.05 g to 0.95g. The results of the analysis are used to establish theinterstory drifts and floor accelerations at each applied load increment. These are used tocompute the damage ratio for each component by using Figure 1, examining theindividual component elements and their appropriate drift and/or floor acceleration. Thedamage evaluation process is repeated for each of the ten applied load levels from 0.05gto 0.95g for each alternative.

The element damage relationship expressed in Figure 1 is in terms of a damageratio; the actual element damage cost is obtained by multiplying the damage ratio fromFigure 1 times the element cost from the cost estimate. Alternatively the element damagecan be summed to a component level based on average damage ratios and then expressedas a component damage cost based on the average damage ratio times the componentcost. Experience has shown that the cost of repair is greater than the original costbecause elements must first be removed before the damaged component can be repaired orreplaced. A component repair multiplier, R, is used to account for this increase.

Lateral force resisting system 1.5Other structural components 1.5Mechanical equipment 1.25Electrical equipment 1.25Architectural elements 1.25Elevators 1.25Contents 1.05

The Total Building Damage for a given iteration of acceleration load level can beexpressed as:

Total Building Damage = Σ ( Damage Ratio ) * (Component Cost)*(Component Repair Multiplier)

Additional cost factors can be included in the Total Building Damage at this point, such asloss of life, injury and down time. Loss of functionality can be a very significant costfactor for certain types of facilities. It can be estimated in terms of lost revenue forincome producing facilities or in terms of the work-force salaries for service facilities. Theowner/user is willing to pay an aggregate salary to have a work-force perform a set offunctions. The inclusion of these indirect costs are significant and can shape the results ofan analysis. The users can in most cases express the loss of use of the structure and thisinformation should be included.

The Expected Building Damage Cost is computed by multiplying the probabilitythat the acceleration increment from the histogram will occur times the damage or damageratio for the building evaluated at that acceleration increment, and summed over allacceleration loading increments. The Expected Building Damage Cost for the specificalternative concept over the range of possible accelerations is given by:

Expected Building Damage = Σ ( Total Building Damage for increment “bin” ofacceleration ) * (Acceleration “bin” Probability)

Since the damage will occur some time in the future it must be expressed in terms of thepresent value (PV) to relate it to the current costs of seismic strengthening or remediation.

Current Expected Damage Costs = PV( Expected Building Damage Cost)

The present worth can be determined by dividing the exposure time into segments and then takingthe present value of each segment or more simply by using a single average exposure time equal tohalf the total exposure time.

The life cycle cost of this alternative is the sum of the initial construction cost plusthe present value of the expected damage.

Alternative Cost = Initial Construction Cost + PV( Expected Damage Costs)

Engineers have used two forms of structural dynamic analysis: response spectraprocedures and time history solutions. A nonlinear time history solution is preferredbecause it directly computes displacements and floor accelerations taking into accountstructure yielding. Since there is substantial variation among earthquake records evenwhen scaled to the same nominal peak acceleration value, the selection of an accelerationrecord can be a factor in establishing the maximum response of the structure. The choiceof records should be examined to quantify variation in response and a series of threeacceleration time histories is typically used to cover a range of response. It is important tonote that as the ratio of applied loading to design load increases, the structure undergoesincreased deformation and possible nonlinear behavior. As the level of deformationincreases, an increase in damping occurs which must be included in the analysis. Care mustbe taken at each load level iteration to select the appropriate damping for that loadincrement.

Simplification of General Approach

The above procedure involves three main steps: the quantification of the seismichazard in probabilistic terms, the determination of the initial costs of seismic strengtheningor remediation, and the determination of the expected damage. An incremental approach isused in which the ground motion acceleration probability distribution is expressed as ahistogram composed of incremental “bins” of acceleration and their associatedprobabilities of occurrence. This produces a full and complete analysis of the bestestimate of the seismic exposure. However, a site seismicity study may not always beavailable. The engineer is free to substitute a set of earthquake events of design interest.This set is not a complete risk assessment but rather is a comparison of the proposedstructural design alternatives under an assigned set of design load conditions. Havingdone this, the designer may choose to consider the average performance of the structureunder the assigned set of events, or perhaps the worst case event, or perhaps thecumulative effect of all the events. Again it is important to note that this approach is not atotal risk analysis but only a relative comparative performance of the alternatives under aset of design conditions. It was suggested that nonlinear time history finite elementmodels of the structure be used to estimate drift and floor accelerations using sets of timehistories. The engineer may substitute elastic response spectra techniques if he chooses aslong as the results are adjusted for yielding.

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i i » ' u t ' i i ' ' ' "1 i 1 i ; i i i il

-

10 -1 10

Average Displacement (m)

Figure 1. Earthquake Magnitude versus average surface displacement (from Coppersmith, Proceedings Fourth International

Conference on Seismic Zonation, 1991)

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Mw = 5.00 + 1 .ZO*log(Rupture Length)

10 100

Surface Rupture Length (km)

Figure 2. Earthquake magnitude versus fault surface rupture length. (from Coppersmith, Proceedings Fourth International

Conference on Seismic Zonation, 1991)

A-29

8 -

a> 1 7

c CD (0

6 -

-

'1 1

o Strike Slip

£ Reverse Slip

; !—, ! : . 1 1

— <r Normal Slip »*/ -

- 60 Oata Points ö / o

— —■

— —

m

m Mw = 5.00 + 1.20*!og(Rupture Length) -

Ill ! ! t 1

10 100

Surface Rupture Length (km)

10

Figure 2. Earthquake magnitude versus fault surface rupture length. (from Coppersmith, Proceedings Fourth International

Conference on Seismic Zonation, 1991)

A-29

I I I

-ti Am'

f I

m' Magnitude,m

I

mu

Figure 3. Generalized frequency magnitude density function.

A-30

• c o

n(mc)

m Magnitude, m

Figure 3. Generalized frequency magnitude density function.

A-30

I I I

(a) M6

P 1 1

JR __I____ C 1

Figure 4. Comparison of different relationship for peak horizontal acceleration at Magnitude 6.5 and 7.5

Reprinted from Joyner and Boore (1988) with permissioa from Americlan Society df Civil Engineers

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1.0

0.1

o 2* o <

LÜ _-' LJ u o <

2 o jsj 0.01

o X

0.001

i i mi| 1—i i i mi| iiM 11111 r—r

(a) M 6.5 -=

5 z - V^ - ■*■ V^ ™

■■* Ys\ - —

wm DB Mi _ ^™*™" M

:,

i

.1 i . I Mill! - t .„! t

IB

c

1 1 III' i t J lim!—

1.0

0.1

o

< u o o <

2 O M 0.01

o x

0.001

OB

JB C

limit I III! III! L 1 10

DISTANCE, KM

Ltil I L-L 100

Figure 4. Comparison of different relationship for peak horizontal acceleration at Magnitude 6.5 and 7.5

Reprinted from Joyner and Boore (1988) with permission from American Soeiety of Civil Engineers

A-31

, I

pi-32

»If u y> JJ 3; £ »■ < 2i in

1/5

% ä -o 2 "2

in < i/) tA a

P 2.5 < l/i Ä v-.

, i

c c « u

i/i c >» « *g-

- < i7> <

i k

.* 8 .H

a: 0 c <« VI o « M

? 5 u E

.2

•s t: « ■S

I IT)

E

A-32