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Application of decision analysis to seismic rehabilitation of historic buildings : a case study of rehabilitation… Kwan, Joanna 1993

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APPLICATION OF DECISION ANALYSISTO SEISMIC REHABILiTATION OF HISTORIC BUILDINGS:A CASE STUDY OF REHABILITATION OFSTANFORD UNiVERSITY MEMORIAL CHURCHbyJOANNA KWANB.A.Sc. (Hons.), The University of British Columbia, 1991A THESIS SUBMITTED IN PARTiAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF CIVIL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIANovember 1993©JoannaKwan, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of L v’L. élThe University of British ColumbiaVancouver, CanadaDate N c V & 3DE-6 (2/88)ABSTRACTThe construction of an expected value decision model for selecting seismic retrofit schemes for ahistoric building is demonstrated through a case study. Net Present Costs (NPC) are used to rank theretrofit options. NPC is defined as the sum of the initial investment cost and the present expected value ofthe total future damage costs.Four options are assumed to be proposed to upgrade the Stanford Memorial Church in 1980.Option 1 is to do nothing in terms of seismic strengthening, whereas options 2 to 4 are seismicstrengthening the Church with increasing level of safety and costs. Seismic data are selected to derive aset of earthquake probabilities. Damage probabilities and damage costs, including direct costs, indirectcosts, and costs of life, are estimated. A discount rate and a life span are chosen to discount the futuredamage costs to present expected values.Option 3, strengthening the Church to building integrity standard without removing theunreinforced masomy (URM) walls, has the lowest NPC and is considered as the optimal option. If it hadbeen recommended and adopted in 1980, about 40% of the accumulative expense from 1980 to 1990would have been saved.A sensitivity analysis is carried out in order to determine the importance of variables that areonly crudely estimated. In general, the outcome is insensitive to changes in seismic data, damage costs,discount rates and life spans when the changes are within reasonable ranges. To obtain higher accuracy,attention should be paid to estimating the probabilities and damage costs of moderate to large earthquakes(MIvil V to IX) rather than that of great earthquakes (MIvil X and above). The outcome is sensitive to theexpected reduction in damage due to retrofits. Better methods for predicting structural behavior is needed.More research in developing guidelines for estimating future damages and social impacts isrecommended.IITABLE OF CONTENTSABSTRACTTABLE OF CONTENTS iiiLIST OF TABLES vLIST OF FIGURES viiiACKNOWLEDGEMENT ixCHAPTER 1 iNTRODUCTION 1CHAPTER 2 THE MEMORIAL CHURCH AT STANFORD UNIVERSITY 52.1 Brief History of The Memorial Church 52.2 The Original Structure 62.3 Reconstruction After the 1906 San Francisco Earthquake 102.4 Renovation in 1980 and 1985 142.4.1 New Organ Installation and Partial Strengthening in 1980 142.4.2 Roof Strengthening in 1985 152.5 The Loma Prieta Earthquake in 1989 162.5.1 Damage Assessment 172.5.2 Fund Raising and Planning 202.5.3 Analysis and Design 202.5.4 Building Strengthening Schemes 212.5.5 Final Design and Construction Major Structural Strengthening Miscellaneous Non-structural Repairs 302.5.5.3 Facilities Improvements 32CHAPTER 3 RETROFIT OPTIONS AND COST ESTIMATES 333.1 Do Nothing Option 343.2 Life-Safety Option 343.3 Building Integrity A Option 373.4 Building Integrity B Option 393.5 Summary 40CHAPTER 4 SEISMIC DATA 424.1 Definitions 434.2 Ground Motion Parameter: Intensity Scale 444.3 Seismic Data 464.3.1 Location of Stanford University 474.3.2 Maximum Probable Earthquake 494.3.3 Annual Occurrence Rates 524.4 Derivation of Earthquake Probabilities 534.5 Local Site Effects 544.6 Discussion 55111CHAPTERS LOSS ESTIMATE 575.1 Damage Assessment 585.1.1 Damage Probability Matrices (DPM) 585.1.2 Establishing the Basic DPM for the Memorial Church 615.1.3 Expected Reduction in Damage (ERD) 635.1.3.1 Past Performance of the Memorial Church 635.1.3.2 Effectiveness of the Retrofit Schemes 645.1.3.3 ERDFactorsfortheFourOptions 655.1.3.4 Summaxy of ERD Factors 665.2 Damage Cost Estimate 675.2.1 Direct Costs: Repair and Replacement Costs 685.2.1.1 Inventory List 685.2.1.2 Replacement Cost 705.2.1.3 Repair Cost For 50% Damages 715.2.1.4 Assigning Damage Costs to Damage States 725.2.2 Costs of Deaths and Injuries 745.2.3 Indirect Costs 775.2.4 Summaiy of Damage Cost Estimates 79CHAPTER 6 DECISION ANALYSIS 826.1 Definition of Variables 826.2 Decision Tree 836.3 Initial Investment of Retrofit Options (1NV) 856.4 Time Conversion Factor (TCF) 856.4.1 Life SpanT 866.4.2 Discount Rate 1 876.5 Calculation of Net Present Costs (NPC) 886.6 Results 896.7 Cost Comparison 91CHAPTER 7 SENSITIVITY ANALYSIS 947.1 Seismic Data 947.2 ERD Factors 977.3 Damage Costs 1007.3.1 Direct Costs 1007.3.2 Indirect Costs 1047.4 Time Conversion Factors: Discount Rate and Life Span 1057.4.1 Discount Rate 1057.4.2Life Span 1067.5 Conclusion of Sensitivity Analysis 106CHAPTER 8 CONCLUSION 109REFERENCES 112ivLIST OF TABLES3.1 Cost of Life-Safety Strengthening (In 1990 Dollars) 363.2 Cost of Building Integrity A Retrofit (In 1990 Dollars) 383.3 Cost of Building Integrity B Retrofit (In 1990 Dollars) 403.4 Summary of Investment Costs (In 1980 Dollars) 414.1 Modified Mercalli Intensity Scale 454.2 Conversion Between Intensities and Magnitudes Using Equation (4.2) 474.3 Annual Occurrence Rate for Zone 24 524.4 Probabilities of Earthquake Intensity I. 535.1 Definition of Damage States and Corresponding Damage Factors 595.2 a Damage Probability Matrix For Type 75: Unreinforced Masonry (Bearing Wall, LowRise) Buildings 595.2 b Damage Probability Matrix For Type 78: Unreinforced Masonry (Load BearingFrame, Low Rise) Buildings 605.3 The Basic Damage Probability Matrix For The Memorial Church 625.4 Important Earthquakes Near Stanford, 1917 - 1980 645.5 Expected Rehabilitation Effectiveness of Life Safety Retrofit 645.6 Expected Reduction in Damage (ER])) of Each Retrofit Option 675.7 Summary of Estimated Repair Costs For 50% Damage (In 1980 Dollars) 725.8 Direct Costs: Facilities Repair and Replacement For Each Damage State (In 1980Dollars) 745.9 Expected Death and Injury Rates For Existing Vulnerable Buildings 755.10 Expected Death and Injury Rates For Life-Safety Rehabilitated Buildings 765.11 Expected Cost of Life For Each Damage State (In 1980 Dollars) 775.12 Indirect Costs (In 1980 Dollars) 795.13 Case 1: Direct Costs and Case 2: Direct Costs Plus Indirect Costs, For All RetrofitOptions (All Costs in 1980 Dollars) 805.14 Case 3: Direct Costs with Costs ofLife (All Costs in 1980 Dollars) 80v5.15 Case 4: Direct Costs with Costs of Life Plus Indirect Costs (All Costs in 1980 81Dollars)6.1 Retrofit Options and Investment Costs 856.2 Results of Decision Analysis (All Costs in 1980 Dollars) 906.3 The Description of the Two Cases 916.4 Accumulative Expense from 1980 to 1990 of Case 1: Actual Case 916.5 Accumulative Expense from 1980 to 1990 of Case 2: Decision Analysis Suggestion 927.1 Example of Data Set 1 & 2, Varying Annual Occurrence Rate of MMI VBy ±25% 957.2 Data Sets for Variation in Annual Occurrence Rate of Each MN’ll Level 957.3 Net Present Costs By Vaiying Annual Occurrence Rate of Each MMI Level (AllCosts in Thousand and in 1980 Values) 967.4 The Percentage Change from the Original NPCs Due to Changes in AnnualOccurrence Rates 967.5 The Original ER]) Factors 977.6 Data Sets for Variation in ER]) Factors of Each Retrofit Option 987.7 Net Present Costs By Varying the ER]) Factors of Each Retrofit Option (All Costs inThousand and in 1980 Values) 997.8 Net Present Costs of Option 3 by Using Different ERD Factors (All Costs inThousand and in 1980 Values) 997.9 Net Present Costs of Option 4 by Using Different ER]) Factors (All Costs inThousand and in 1980 Values) 1007.10 Data Sets for Direct Costs (All Costs in Thousand and in 1980 Values) 1017.11 Net Present Costs By Using Different Direct Costs (All Costs in Thousand and in1980 Values) 1017.12 Data Sets for Variation in Damage Cost of Each Damage State (All Costs inThousand and in 1980 Values) 1027.13 Net Present Costs By Changing Damage Cost of Each Damage State (All Costs inThousand and in 1980 Values) 1027.14 The Percentage Changes From the Original NPCs Due to Changes in Damage Cost ofEach Damage State 1037.15 Data Sets of Indirect Costs (All Costs in Thousand and in 1980 Values) 104vi7.16 Net Present Costs By Using Different Indirect Costs (AU Costs in Thousand and in1980 Values) 1047.17 Effect of Discount Rate on the Net Present Costs (AU Costs in Thousand and in 1980Values) 1057.18 Effect of Life Span on the Net Present Costs (AU Costs in Thousand and in 1980Values) 106vuLIST OF FIGURES2.1 Map of Stanford University Showing Location of the Memorial Church 52.2 The Original Memorial Church in 1904 72.3 Floor Plan of the Memorial Church 72.4 The Original Facade in 1904 82.5 One of the Arch Mosaic Angels 92.6 a Front View of the Memorial Church after 1906 Earthquake 112.6 b Side View of the Memorial Church after 1906 Earthquake 112.6 c Interior Damage of the Memorial Church after 1906 Earthquake 122.7 The Memorial Church after 1913 Reconstruction 132.8 Map of Affected Regions and Epicenter of Loma Prieta Earthquake in 1989 162.9 a Damage to Mosaic Angel Uriel 172.9 b Damage to Stone Veneer at Apex of Crossing Arches 182.9 c Damage to Plaster Frieze at Crossing Drum 182.9 d Damage to the Organ Loft Balcony Railing 192.9 e Cracking in the Stone Cross above North Wall 192.10 Strengthening of Arches, New Crossing Diaphragm System and Addition of 25Collectors2.11 a RoofDiaphragm Strengthening: Key Plan 262.11 b Roof Diaphragm Strengthening: Connection of Roof Trusses to Walls 272.12 Addition of Roof Diaphragm in Nave Arcades 282.13 Addition of Roof Diaphragm in Gallery Stair Towers 292.14 Repair of Non-Structural Elements 314.1 Location of Major Faults in San Francisco Bay Region 484.2 Seismogenic Zones in Coastal and Offshore California 504.3 Estimated Maximum Magnitude for Each Seismogenic Zone 516.1 Decision Tree 84viiiACKNOWLEDGEMENTI would like to thank my supervisors Prof. R.G. Sexsmith and Prof. R.O. Foschi for their timeand effort in helping me to develop a thesis out of my own interest. This thesis would not be madepossible without their support and advice.I would also like to thank Mr. F. Bendimerad, Manager of Seismic Engineering, Facilities ProjectManagement of Stanford University for granting me permission to obtain information on therehabilitation project of Stanford Memorial Church and Mr. C. Poland, President of H.J. DegenkoibAssociates in San Francisco, for releasing the documentation. I am in debt to Mr. Evan Reis of H.J.Degenkolb Associates, who has been a great help for providing me with information, organizing thedocuments I needed and sending them to me.Special thanks to those who have assisted me in gathering information or given me valuableadvice: Ms. P. Ehret of Facilities Project Management at Stanford; Prof. C. Thiel of Civil Engineering atStanford; Prof. A. Kiremidjian of Earthquake Engineering at Stanford; Mr. 3. McDonald of Green Libraryat Stanford; Ms. K. Frohmberg of EERC at University of Berkeley; Ms. 3. Kawaguchi of DPRC at UBC;Ms. J. Bruun in Victoria; Mr. Brian Folz of UBC; and Mr. Edmond Chow.I deeply appreciate my parents for their support and encouragement throughout my studies inUBC. Last but not least, I would like to express my gratitude towards Kenny Lam who has always beenthere for me.ixChapter 1 IntroductionC11APTER 1INTRODUCTIONIn recent decades, there has been an increased awareness of seismic hazards throughout theworld. This has raised concerns regarding seismic retrofit of existing buildings located in seismicallyactive areas. The conununities in the west coast of the United State of America, located in high seismiczones, are exposed to the possibility of a major earthquake at any moment. The US government hascharged a variety of agencies for preparation of guidelines for seismic rehabilitation and investigatingmethodology for testing and retrofitting existing buildings for seismic safety.The primaiy goal of seismic retrofitting for existing buildings is to ensure life safety and preserveconununity functions. For public institutions, such as govenunent buildings, emergency facilities, andschools, an operational level is required to be maintained after an earthquake. If a building has specialhistoric or architectural value, preservation of the structure and its content is also a concern in theretrofitting program.Among various types of existing buildings, historic buildings are among the most vulnerable toearthquakes. Historic buildings are generally built in unreinforced masomy, which may not havesufficient lateral strength to withstand seismic motion. The buildings may also be deteriorated due to age,pollution, man-made damages or natural damages. Furthermore, they may have been upgradedincorrectly in the past. Even though a historic building may have survived past earthquakes, it may not beable to withstand further future earthquakes.According to the Seismic Safety Commission of California (1987), it is recommended that hazardmitigation of historic buildings should follow the State Historical Building Code which contains Sections18950 through 18961 of the Health and Safety Code, and Part 8 of Title 24 of the CaliforniaAdministrative Code. The basic requirement in these codes is to provide for building integrity andcontinued operation of a facility after a major earthquake. However, there is no specific rule as to what1Chapter 1 Introductionextent the strengthening is really required. In general, it is up to the engineer to suggest and the owner todecide. The main factor in affecting the decision is whether the cost of the strengthening is worthwhile.A computer program was developed by Federal Emergency Management Agency (FEMA) tocompare the benefit and cost of rehabilitation projects. The documents of the program are referred asFEMA-227 (VSP Associates, 1992a) and FEMA-228 (VSP Associates, 1992b). There are otherdocuments which address the issues of typical costs or financial incentives for seismic rehabilitation ofexisting buildings, such as: FEMA-156 (Englekirk and Hart Consulting Engineers, 1988a) and FEMA157 (Englekirk and Hart Consulting Engineers, 1988b), FEMA-198 (Building Technology Inc., 1990a)and FEMA-199 (Building Technology Inc., 1990b), FEMA-174 (Building Systems Development Inc. etal., 1989).The aim of the FEMA Benefit Cost Model computer program is to calculate the benefit-cost ratioof a life-safety seismic rehabilitation program applied to groups of ordinary residential or commercialbuildings. It was not recommended to be applied on an individual basis or to special buildings.Furthermore, it does not explicitly allow the user to compare the benefit-cost ratio between differentretrofit schemes. The other documents mentioned above are intended for ordinary buildings as well andthus, cannot be applied to seismic rehabilitation of historic buildings directly.Decision analysis is a useful approach for selection of a seismic retrofit scheme for individualhistoric buildings. It offers an effective way of comparing different seismic retrofit options. The objectiveis to select the retrofit option which has the lowest total cost, i.e. the sum of the initial retrofit cost and theexpected value of the future damage cost. The cost of retrofit will usually be more expensive if higherlevel of safety is to be achieved and less severe future earthquake damage is to be expected. However,future damages can only be predicted but not determined and the future damage cost can only be estimatedin a probabilistic manner.The Bayesian statistical decision theory provides a mathematical model for making decisions inthe face of uncertainty (Benjamin and Cornell, 1970). The theory suggests the use of expected values torank the available alternatives. The decision maker has to identify the possible events, assign probabilitiesand estimate the consequences related to these events. The expected value is the sum of the products of2Chapter 1 Introductionprobability and consequence of each possible event. In other words, the expected value is the weightedaverage of the possible outcomes of an alternative.For selecting seismic retrofit scheme for historic buildings, net present costs are recommended inthis thesis for ranking the alternatives. The net present cost is the sum of the initial investment of aretrofit scheme and the present expected value of the future consequence as a result of adopting thatretrofit scheme. The future consequence is the total earthquake damage cost expected to accrue over thelife span of the historic building. It depends on the frequencies and the sizes of future earthquakes at thesite, the predicted performance of the structure, the possible damage states and the damage costs. Bothearthquake probabilities and damage probabilities are taken into account in calculating the expected valueof the future consequence.In order to illustrate an actual application of decision analysis to seismic retrofit selection,information on the Stanford University Memorial Church is used to construct a case study. The MemorialChurch was built in 1899. In 1980, the Church was partially upgraded to support the excessive load of anew organ. The Loma Prieta earthquake in 1989 caused substantial damage to the Church which lead to acomprehensive seismic rehabilitation program, designed by H.J. Degenkolb Associates, in 1990. Thehistory of the Church is described in Chapter 2.In this thesis, the seismic retrofit decision that could have been made in 1980, prior to the partialupgrade, is examined. Three seismic retrofit schemes are developed according to the strengtheningproposal by Degenkoib (1990). The details of the retrofit schemes are described in Chapter 3. Thederivation of the seismic data is explained in Chapter 4 and the future earthquake damages are estimatedin Chapter 5. In Chapter 6, the data are used to carry out a decision analysis. Since the input data involveuncertainty, a sensitivity analysis is done in Chapter 7 to assess the sensitivity of the outcome of thedecision to the variation in the input data.In constructing the expected value decision model, there are difficulties in the selection ofseismic data and the derivation of earthquake probabilities. Estimating the performance of the retrofits,the extent of damages and the related costs involves many uncertainties. A document called ATC-13(Applied Technology Council, 1985) is particularly useful in loss estimate and its content is often referred3Chapter 1 Introductionby other documents, such as FEMA-227 (VSP Associates, 1992a) and FEMA-174 (Building SystemsDevelopment Inc. et a!., 1989). Furthermore, the time effect on the future costs has to be taken intoaccount properly.The main objective of this thesis is to point out what data are needed, and how they can beobtained and organized for decision analysis in the selection of a seismic retrofit scheme for historicbuildings. Effort is put into making a reasonable choice or a fair estimate of the required data. Therationale for obtaining each set of data is discussed in each chapter accordingly. The purpose is to providea logical yet simple tool on making comparison of different retrofit options for decision makers.The second objective is to compare the expense of the actual case with the projected expense ofthe hypothetical case in this thesis. If a decision analysis had been carried out to recommend a seismicretrofit scheme in 1980 and the recommendation had been adopted, what would be the difference in thetotal expense on the Church between 1980 and 1990, after the Loma Prieta earthquake? It is believed thatthe accumulative cost of the hypothetical case will be less then that of the actual case.Many people may have the notion that seismic retrofitting historic buildings is a “luxurious”thing to do. Yet most people will agree that if a historic building were to be damaged in an earthquake, itshould be repaired and restored to its original form as much as possible. It is hoped that this thesis willprovide some hindsight on the advantage of seismic rehabilitation of historic buildings prior to damagingevents.4Chapter 2 The Memorial Church at Stanford UniversityCHAPTER 2TN1 MEMORIAL CE[URCH AT STANFORD UNiVERSITY2.1 BRIEF HISTORY OF THE MEMORIAL CHURCHThe Memorial Church was built by Jane Stanford (1828 - 1905) as a memorial to her husbandLeland Stanford (1824- 1893) who was the founder of Stanford University (Allen, 1980). It was intendedto be one of the most beautiful and imposing structures in the United States. “The interior will be therichest that perfect taste can devise,” said Mrs. Stanford (The Stanford Alumnus, 1899). It was notdedicated for any one particular faith or denomination but for emphasizing the importance of seekingspiritual truth and offering a sanctuary to people of eveiy persuasion (Taylor, 1990). The Church islocated in the center of the campus in Stanford University facing north to the Main Quad (See Figure 2.1).FIGURE 2.1 Map of Stanford University Showing Location of the Memorial Church5Chapter 2 The Memorial Church at Stanford UniversityThe excavation was started in May 1899 and the cornerstone was laid on January 29, 1900. Theconstruction was completed in 1902 (The Stanford Alumnus, 1905-1906). The Church was dedicated onSunday, Januaiy 25, 1903 (The Stanford University News, 1953). Work on some of the decorationcontinued until 1905 (Stockholm, 1980). The Round room, located in the southwest corner of the Church,was built between 1902 and 1906.2.2 TUE ORIGINAL STRUCTUREArchitect Charles A. Coolidge worked on the project in the 1880’s. In 1899, when theconstruction finally began, the contract was granted to architect Clinton Day of San Francisco and thearchitect on the premises to supervise workmen was Charles Hodges of Palo Alto (Stockholm, 1980). Theoriginal budget was over $250,000 (The StanfordAlumnus, 1899) in 1899 dollars (i.e. about $6 million in1980 dollars).The architectural style of the Church is a combination of Moorish and Richardson Romanesque(See Figure 2.2). The building plan is a cruciform (See Figure 2.3). The material used is buff sandstone.The dimension of the church is: exterior 190 ft long and 150 ft wide; interior 152 ft long and 98 ft longdown the main aisle; center of nave is 50 ft across (Stockholm, 1980). The building area is 28,000 sq. ftapproximately (Smith and Reitherman, 1984).The basic elements of the original Church are listed as follows:• foundation: plain concrete or brick footings;• floor: concrete slab supported on footings;• wall: unreinforced masonry walls along the church perimeter;• roof: wood and Spanish tile roof supported on steel trusses which were supported by walls.6Chapter 2 The Memorial Church at Stanford University-4 4-FIGURE 2.3 Floor Plan of the Memorial Church(From p.2 of Taylor, 1990)FIGURE 2.2 The Original Memorial Church in 1904(From Figure 32, p.43 of Turner et at., 1976).(Gallery Above)STAIRSEAST.CROSSING1rAlRSNAVE VESTVESTIBULE—— .ARCADE7Chapter 2 The Memorial Church at Stanford UniversityAs for the Round Room, there is no floor plan available. According to inspection, the wall isunreinforced masonry covered with wood paneling or stone veneer. The roof consists of straight-sheathedboards supported on steel trusses, covered with wood finishes. (Degenkolb, 1990)The three most important features of the original structure were the Facade, the Crossing and theClock Tower.The Facade was located at the north entrance above the North Arcade (See Figure 2.4). It was a2-foot thick brick wall, 84 feet across the base and 86 feet in height, with mosaics and stained glasswindows. The mosaic, showing Christ welcoming the righteous into the Kingdom of God (Matthew25:34), was the largest in America at that time. It took 12 men two years to complete. Below the mosaic,across in carved stone is the inscription: “Erected to the Glory of God and in Loving Memory of MyHusband Leland Stanford.” (Taylor, 1990)II1FIGURE 2.4 The Original Facade in 1904(From Figure 39, p. 50 of Turner etal., 1976)8Chapter 2 The Memorial Church at Stanford UniversityThe Crossing consisted of four 73-foot tall brick arches on each side, supporting a circularpainted frieze, called the Drum. There were four large mosaic angels in the corner pendentives. Themosaic angels were 16 feet tall with a 22-foot wingspan (Bartholomew, 1992a). The name of the angelsare Michael, Gabriel, Raphael and Uriel. (See Figure 2.5)The Clock Tower was a 80-foot tall steel frame, masonry and wood tower set atop the crossingarches (Degenkolb, 1990).Other features of the original structure are listed below:• A basement and a fhrnace room were located under the Chancel area.• Mosaic tiles covered much of the interior wall, illustrating Bible stories. The mosaic were producedby Salviati & Co. in Venice, Italy and shipped to California to install. More than 20,000 differentshades of tesserae were used and it took about five years to complete (Taylor, 1990).• Some parts of the wall were covered by wood finished done by E.A. Hettinger, P.A.. There were alsothick stone veneer attached to the walls with metal anchors.• The stone work was by The McGilvray Stone Co., San Francisco.• Intricate stained glass windows, about 50 of them, throughout the church, were made by Frederick S.N-FIGURE 2.5 One of the Arch Mosaic Angels(From p. 3 of Taylor, 1990)9Chapter 2 The Memorial Church at Stanford UniversityLamb of J.& R. Lamb, New York.• The organ was constructed by Murray M. Harris Organ Co., LA. The total weight of the organ was25 tons and worth $15,500 in 1903 dollars (i.e. about $318,000 in 1980 dollars). (The Daily PaloAlto, 1903)• The chimes were built by McNeely Foundry, Troy, NY.• The sitting capacity was about 1700.(The above information are based on the StanfordAlumnus, 1905-1906, unless otherwise stated.)The total cost of construction was $623,000 (The Stanford University News, 1953) in 1903dollars (about $12,766,000 in 1980 dollars). About 60% of the total construction cost was spent on theinterior decoration.No particular seismic design criteria was used at that time. Effort was made to take earthquakeprotection into consideration during the first phase of the construction of the buildings on campus. Yet,due to limited budget, the buildings constructed in the second phase were of poorer quality. TheMemorial Church, unfortunately, was built in the second phase. (Smith and Reitherman, 1984)2.3 RECONSTRUCTION AFTER THE 1906 SAN FRANCISCO EARTHQUAKEThe epicenter of the San Francisco earthquake on April 18, 1906 was near the north coast of theSan Andreas Fault. The magnitude was estimated to be about 8 on the Richter Scale (Working Group OnCalifornia Earthquake Probabilities, 1990). The intensity was estimated to be MN’II XI in San Francisco(Bolt, 1988) and MMI VIII- IX at Stanford University. The earthquake caused severe damage to theChurch (See Figure 2.6), The roofs collapsed, the Facade and the upper portion of the Clock Tower weredestroyed and portions of the brick walls was damaged. The Crossing and the Round Room sufferedminimal damage. The organ and the stained glass windows were only slightly damaged. Nearly allbuttresses and ornamental supports were demolished. (The Daily Palo Alto, 1906a & b)10Chapter 2 The Memorial Church at Stanford UniversityFIGURE 2.6a Front View of the Memorial Church after 1906 Earthquake(From Plate 103 B of Lawson et al., 1908)FIGURE 2.6b Side View of the Memorial Church after 1906 Earthquake(From Plate 102 B of Lawson et al., 1908)11Chapter 2 The Memorial Church at Stanford University[1*.IiH-,FIGURE 2.6c Interior Damage of the Memorial Church after 1906 Earthquake(From Figure 46, p. 56 of Turner et al., 1976)12Chapter 2 The Memorial Church at Stanford UniversityAccording to the engineers report in The Daily Palo Alto (1906b), “the damage sustained by thechurch was due chiefly to the crash of the falling clock-tower, which tumbled northward, carrying the roofthrough near the dome. The sides of the transept were broken away from the church by the force of theearthquake. When the crash of the clock-tower came, timbers, bricks, mortar and stones weighinghundreds of pounds were hurled into the body of the church, smashing windows, statuary, and woodwork,wrecking pews and ornaments, and littering the interior of the church with debris The arches withinthe church remain whole, indicating that the lower part of the walls of the building suffered little.”In 1909, the entire structure except the Crossing and the Round Room was demolished. A newsteel frame was erected to support gravity loads from the roofs and reinforced concrete walls were castaround the frame where the unreinforced brick walls once were. The stone, wood and stained glass werereset and a new wood roof added. The Facade was rebuilt in concrete. The Clock Tower was replacedwith a small pyramid-shaped hipped roof over the crossing. (See Figure 2.7)FIGURE 2.7 The Memorial Church after 1913 Reconstruction(From Bartholomew, 1992a)13Chapter 2 The Memorial Church at Stanford UniversityThe total reconstruction cost was $399,000 in 1909 dollars (Green Library) which is about$6,462,000 in 1980 dollars. According to the original contracts found in Special Collection of GreenLibrary, the cost of producing the mosaic was about $97,000 in 1909 dollars ($1,571,000 in 1980 dollars)and repairing the stained glass window was about $6,600 in 1909 dollars ($107,000 in 1980 dollars). Themarble apostles were not replaced. The cost would have been around $740 to $1340 in 1909 dollars foreach (i.e. $12,000 - $22,000 in 1980 dollars). The marble altar was replaced at the original cost in year1901 plus $200. Plumbing cost about $700 in 1909 dollars ($11,300 in 1980 dollars). At that time one ofthe engineers suggested laying steel bars in the floor for about $4000 in 1909 dollars ($65,000 in 1980dollars). This was almost rejected by the University officials for economic reasons, but the plan waspassed at last and the floor has been very effective since then. (Reis, 1993) Roughly speaking, a quarter(about $110,000 in 1909 dollars or $1,781,000 in 1980 dollars) of the total reconstruction cost was spenton the architectural elements and the other three quarters (about $289,000 in 1909 dollars or $4,680,000in 1980 dollars) were spent on structural elements.After being closed for 7 years for reconstruction, the Church was reopened in October 5, 1913,just 4 days after the inauguration of John Casper Branner as second president (The Stanford UniversityNews, 1953). Minor repairs lasted until 1917.2.4 RENOVATION IN 1980 AND 19852.4.1 New Organ Installation And Partial Strengthening In 1980A new Baroque tracker-type organ was to be purchased and installed in the choir loft over thefoyer at the north end of the Church. Due to the inadequate capacity of the existing structure, a newstructural system was needed to carry the weight, over 20,000 pounds, of the organ. The project wasapproved by the Board of Trustees in June, 1980.14Chapter 2 The Memorial Church at Stanford UniversityA structural box” frame was designed to provide vertical and lateral support to the organplafform and the Facade. New steel columns would be installed at the arcade level and connected withhorizontal steel beams at the floor and ceiling levels of the arcade. Vertical steel trusses in the choir loftwould be extended and new concrete walls would be poured around the base of the north wall in order toprovide lateral support of the Facade.The original budget was $1,632,000 with fimding from gifts and the Facilities Reserve.Additional funds of $292,000 were authorized in the summer of 1979 and another $37,000 wereauthorized in February 1980 for organ enhancements. The total budget was $1,961,000, among whichabout $1,095,000 was for construction and management and $866,000 was for the new organ and voiceimprovements. (All these costs are in 1980 dollars.)The construction started in April, 1981 and was completed in May, 1982 which was 4 monthslater than planned. The delay was due to serious structural problems uncovered during demolition. Theproblems included: insufficient anchorage of structural beams to walls, inadequate structural connectionsof some members and discontinuous foundations. They were corrected accordingly during theconstruction.The organ builder, C.B. Fisk, started the organ construction in July, 1982 and delivered theorgan in September, 1983. Completion of the whole project, including the organ installation and voicing,was in May, 1984. (Facilities Project Management of Stanford University, 1980)2.4.2 Roof Strengthening In 1985In 1985, the hipped roof above the Crossing was strengthened with plywood when the skylightand roofing was replaced to eliminate a leakage problem. It is assumed that the strengthening wasseismic strengthening and the cost was about $1,750,000 in 1985 dollars. (Facilities Project Managementof Stanford University, 1980)15Chapter 2 The Memorial Church at Stanford University2.5 THE LOMA PRIETA EARTHQUAKE IN 1989In October 17, 1989, the Loma Prieta Earthquake caused substantial damage to the Church. Theearthquake was centered along the San Andreas Fault east of Santa Cruz (Figure 2.8) and measured. 7.1on the Richter Scale. The MMI level was estimated to be VIII and the ground motion was 0.29g with aduration of 10-15 seconds at the Stanford Campus. (EERI and NRC, 1990)OUNA$‘I .r ismIcr •Ik TSANt.ANO• Cls ccCTfl 11*01 \1’ SANS?ATI 11*01pr. ..oI — —-. I UndslideSanClBOCldaJIS‘S\€mcetr\ ®..,..‘ I5’ I—$1_lIF?O2•.S4 UCl.ilClOft GfQ.21Cl P*1.. sSo*i. . 41.10wFIGURE 2.8 Map of Affected Regions and Epicenter of Loma Prieta Earthquake in 1989(From Figure 3.1, p.24 of EERI and NRC, 1990)16Chapter 2 The Memorial Church at Stanford UniversitySince then, funds were raised and a seismic rehabilitation program was carried out. Therehabilitation program not only included repairing the damaged portion of the structure, but also includedimproving the seismic resistance of the structure and updating the electrical and mechanical features.2.5.1 Damage AssessmentAccording to the damage assessment report done by H. J. Degenkolb Associates (1989), majordamage was in the masorny arches supporting the central portion of the church below the dome. Cracksand displacement of some of the sandstone elements of the arches were observed. Since the masonry wallwas not braced by horizontal stiffening elements, it could not gain lateral support from the adjacent roofs.Therefore, the damage was due to excessive lateral motion of the structure caused by extremely heavymass and inadequate horizontal bending capacity of the brittle masonry work.An 8-foot portion of the wing of the mosaic angel in the northeast corner of the Crossingdislodged and fell. Portions of the railing of the organ loft balcony were dislodged as well. Thechandelier and a portion of the ballery in the east transept were damaged by the falling stone of theeasterly arch. The stone cross on top of the Facade was severely cracked. (See Figure 2.9 a - e)FIGURE 2.9a Damage to Mosaic Angel Uriel(From Bartholomew, 1992a)17Chapter 2 The Memorial Church at Stanford UniversityFIGURE 2.9b Damage to Stone Veneer at Apex of Crossing Arches(From Figure 5a of Degenkoib, 1990)FIGURE 2.9c Damage to Plaster Frieze at Crossing Drum(From Figure 5b of Degenkolb, 1990)18Chapter 2 The Memorial Church at Stanford UniversityFIGURE 2.9d Damage to the Organ Loft Balcony Railing(Froml’ 5dofDe enkolb, 1990)FIGURE 2.9e Cracking in the Stone Cross above North Wall(From Figure 5c of Degenkolb, 1990)19Chapter 2 The Memorial Church at Stanford UniversitySchweinlChristensen Laboratories, Inc. carried out a detailed investigation on the interior stonearch and made a report (SchweinlChristensen, 1989) outlining test methods, dimensions and constructionmethod of the arches.2.5.2 Fund Raising and PlanningThe fund raising committee was established in the Spring of 1990 with Melvin B. Lane as thechair person. Together with the effort of the Dean of the Chapel Robert Gregg and other members of thecommittee, the committee raised 10 million dollars by the end of 1991. The donations came from majorcorporations, Stanford alumni, and individual undergraduate students.One unique characteristic of this rehabilitation project was that fund raising and constructionproceeded simultaneously in early 1990. This was due to the support of William Hewlett of HewlettPackard.Initially, the Stanford University officials planned to limit the rehabilitation to the extent ofrepairing earthquake damage and bracing the structure against future earthquake. But Mr. Lanedeveloped additional projects, including reopening the balconies, renovating basement into office space,re-establishing the Round Room as a reception area, establishing a small chapel in the west transept, andupgrading light and sound systems. (Bartholomew, 1992a)2.5.3 Analysis And DesignIn 1990, Stanford University retained H.J. Degenkolb Associates, a San Francisco structuralengineering firm, to analyze the structure and to design and oversee execution of a seismic retrofit plan.Chris Poland, the president and senior principal of Degenkolb, was the project manager and Evan Reiswas the project engineer.The evaluation carried out by the consultant was based on Evaluating the Seismic Resistance ofExisting Buildings (ATC-14) by Degenkolb Associates, Engineers (1987). ATC-14 is a consensus20Chapter 2 The Memorial Church at Stanford Universitydocument which provides a consistent procedure for the life safety seismic evaluations of existingbuildings in the United States. At the request of the Stanford Seismic Evaluation Committee, theminimum base shear coefficient used for the evaluation was increased to 13.3%g from 8.0%g required byATC-14. In addition the building was checked for conformance to the Santa Clara County OrdinanceNumber 1100.78.Further evaluation was also done based on Essential Building Provisions of Title 24 of theCalifornia Adminisfrative Code for Hospital Construction. This requirement is intended to provide forbuilding integrity and continued operation of a facility after a major earthquake.The detaiLed seismic analysis of the Memorial Church consisted of performing calculations todetermine the areas of potential weakness in the structural and non-structural systems of the building.The analysis was based on information contained in the original 1899-1902 plans, drawings of the re-builtChurch dated 1909-1913, plans of the subsequent additions in 1980 and 1985 and results of exploratorytests performed on the Church. (Degenkoib, 1990)2.5.4 Building Strengthening SchemesAccording to the strengthening proposal dated by H. 3. Degenkolb Associates, Engineers (1990),two levels of strengthening schemes to mitigate the damage were considered:a. Life-Safety: A minimum strengthening scheme which would mitigate the potential hazard whichmight cause death, serious injury or entrapment of building occupants. This scheme was developedbased on the evaluation done according to ATC-14 (Degenkolb, 1987).b. Building Integnty: A higher level of strengthening which would mitigate life-safety hazards andadditionally limit damage to the structural and non-structural elements of the building to a levelwhich would require minimal repair. This scheme was developed based on the evaluation doneaccording to Title-24.For each level of strengthening the following options were considered:1. Minimal Disruption: Strengthening schemes which would not temporarily or permanently alter21Chapter 2 The Memorial Church at Stanford Universityarchitectural features of the building including the overall building plan, stone, wood and mosaicfinishes and other historical elements of the Church.2. Without Regard: Strengthening schemes which allow for the possibility of significant, temporary orpermanent alternations to the building’s architectural features.Due to the important historic value of the Church, the strengthening scheme of either life safetyor building integrity adopted the minimum disruption option. The unreinforced masonry (URM) walls inthe crossing area were the biggest problem in developing the strengthening scheme since URM is notacceptable under the current building code. Dismantling the URM and rebuilding with reinforcedconcrete would be very expensive and would also damage the mosaic, plaster drum and stone arches.During the exploration work by the workers of Dinwiddie Construction, a 20-inch void space wasdiscovered between the brick walls above the crossing arches. The void space ran full length of the archwalls, and ranged from about 6 feet high at the arch apex to 15 feet in the corners. The discovery of thevoid space allowed the engineers to develop an effective strengthening system for the crossing, whichserved as an alternative to the dismantling scheme. The fact that the strengthening system could behidden behind the original architectural elements satisfied the minimal disruption goal.The two strengthening schemes are briefly outlined as follows:(a) Life Safety Strengthening Scheme:1. In the Crossing area, pour reinforced concrete frame inside the arches and dowel to bricks to increaselateral stability.2. Add steel bracing system of “strong-back” columns and girders and new roof diaphragm above thearches to provide perpendicular bracing of the four arches.3. Add collector at each corner of the Crossing to transfer forces to the walls.4. Replace sheathed boards on roof with plywood and strengthen connections to the walls to increaselateral resistance.5. Strengthen connection of the roof to the brick walls in the Round Room.6. Place reinforced concrete slab above the ceiling between the interior and exterior arcade walls toreduce forces on the interior walls.22Chapter 2 The Memorial Church at Stanford University7. Repair non-structural elements to avoid falling, e.g. stone cross, balcony railings, stone veneer,chandeliers, mosaics.The expected damage are cracks and spalling in the arch area, the walls and the windows, and damage toarchitectural finishes.(b) Building Integrity Strengthening Scheme:In addition to the seven points of the life safety strengthening scheme listed above, otherstrengthening required to achieve the building integrity level are listed below:8. Increase member sizes of the “strong-back” columns and girders of new crossing roof diaphragm toprevent cracking.9. Place reinforced concrete slab between the discontinuous wall of the Gallery Stair Towers and thelower parallel wall which extents to the foundation to transfer load away from the perpendicularwalls.10. Provide gap between window frames and glasses.11. Remove and replace all unreinforced masonry in the Crossing area and in the Round Room.The expected damage are cracks in piers, isolated damage to arch finishes, organ loft, and transeptgalleries.Preliminary cost estimate was done by Dinwiddie Construction Company (1990). The cost of thelife safety scheme was estimated to be $4,792,000 and the building integrity scheme was $13,000,000 to$15,000,000 (in 1990 dollars), The costs were estimated with 20% contingency.2.5 5 Final Design And ConstructionAccording to the structural drawings by Degenkolb Associates, Engineers dated May 15, 1991,“It is the intent of these strengthening measures to significantly improve the earthquake resistance of thestructure in an attempt to prevent a major collapse or other catastrophic damage which could lead toconsiderable loss of life.”“The level of strengthening used ... represented essential compliance with the lateral force requirements ofthe current Ca1fornia Administrative Code for Hospital Construction and County of Santa ClaraRegulations.”23Chapter 2 The Memorial Church at Stanford University“The specific criteria is based on a design base shear of 18.6%g in both the E-W (transverse) and N-S(longitudinal) directions. It is the magnitude of lateral force defined by the 1988 CaliforniaAdministrative Code.” Major Structural Strengthening1. Strengthening of Arches: Reinforced concrete infihled inside existing 20-inch-wide cavity betweenthe bricks above the arches. (See Figure 2.10)2. New Crossing Diaphragm System: A steel frame was added to the top of the crossing arches, with asteel beam anchored diagonally at each corner to interconnect the four walls. Extended from the twoends of each diagonal steel beam were two W14 x 193 strongback columns anchored to the face of thebricks to further stabilize the brick walls. A 18” x 54” concrete perimeter cap beam was doweled intothe bricks which constituted a lid for the steel frame. (See Figure 2.10)3. Addition of Collectors in Crossing Arches: Steel and Concrete collectors reached out 20 feet from thecrossing arches to anchor the top of the nave, chancel and transept walls. (See Figure 2.10)4. Roof Diaphragm Strengthening: Spanish tiles and 7/8” board sheaths were removed and replacedwith 3/4” structural I plywood diaphragm on straight roofs or with two sheets of flexible 3/8” plywoodon curve roofs. Connection of roof trusses and plywood diaphragms to arches, the north wall and theconcrete walls around the perimeter of the Church were strengthened. Spanish tiles were placed backon to the roof by hand. (See Figure 2.11)5. Round Room Diaphragm Strengthening: The roof and 1 x 4 T&G sheathing were removed andreplaced with 3/4” structural plywood. Connection of roof diaphragm to Round Room walls wasstrengthened.6. Addition of New Roof Slabs at Arcades: A 6” reinforced concrete slab was added under the roof ofeach of the nave arcades. Each end of the concrete slab was doweled into the existing concrete wall.(See Figure 2.12)7. Addition of New Roof Slabs at Gallery Stair Towers: A 6” reinforced concrete slab was added underthe roof of the gallery stair towers. (See Figure 2.13)24Chapter 2 The Memorial Church at Stanford UniversityFIGURE 2.10 Strengthening of Arches,New Crossing Diaphragm System and Addition of Collectors(From Figure 11, p.5346 of Poland and Reis, 1992)(N) I rxz4 CONCRETE CAP BEAMDOWELED 1(10 BRICK(N)RE4FORCED CONCRETEI’FLL. NSIDE )WAU. VITYBETWEEN BRICKI I(N)CONCRETE ANOSTEEL25p CD 1W CDC’U ii rI1I 0 E-C’ 0-nC-) •1 IChapter 2 The Memorial Church at Stanford UniversitycCTIO CCF IC L-.JALLFIGURE 2.1 lb Roof Diaphragm Strengthening: Connection of Roof Trusses to Walls(From Figure lOb of Degenkoib, 1990)X1i9e OC WAt.-L.JUNC.TiQIir4 cMpPL.4AL.. Lc EL-AMA9..Ae27Chapter 2 The Memorial Church at Stanford UniversityADI1CN C WOr IAHIAM1r4 NAVE AR.CAEFIGURE 2.12 Addition of Roof Diaphragm in Nave Arcades(From Figure 11 of Degenkoib, 1990)() COr4.wrfl4 rot4V28Chapter 2 The Memorial Church at Stanford UniversityA1ITICr4 C CF ‘14PHRAfr1IN LLY eTAR TcWRFIGURE 2.13 Addition of Roof Diaphragm in Gallery Stair Towers(From Figure 13 of Degenkoib, 1990)(H) &?_i’w..etfr.y4e.B” t...NalEI-Iep Ir4T )EMOV(ZTft.aF(9) Pt44TZ C.IL’(7%K-r PLAN t4WIN29Chapter 2 The Memorial Church at Stanford University2.5.5.2 Miscellaneous Non-structural Repairs1. Facade cross was rebuilt with sand stone instead of rebuilding with cast-concrete replica.2. Balcony railing was strengthened by inserting 1/2” diameter stainless steel through balusters to stonepanel below. In the horizontal direction, the railing was doweled to arch columns to strengthen theconnection.3. Crossing arch stone repair: The horizontal cracks on the faces of the outer voussoir stones wereepoxied and doweled together. The stones that had slipped, maximum about 2 inches, out of placewere jacked up into position and long dowels were installed horizontally from both sides, anchoringeach voussoir to the brick arch in between. The voussoir stones that needed to be replaced werereplaced by the same material as the original.4. Chandelier anchorages were strengthened by attaching cable to roof truss above and replacing theexisting 1/2” bolts by 1/2” A325 x bolts.5. Mosaic angels strengthening: Threaded robs were bolted through concrete and limestone beneath themosaic to metal T-bars behind each angel. After cleaning, three layers of epoxy and fiberglass clothwere applied on the back of each angel. Dislodged mosaic tiles were glued back on to the mosaic andthe remaining gaps were filled with epoxy-putty, colored carefully and scored to resemble mosaics.6. Stained glass windows: Both the protective screens installed in 1960s and acrylic plaster covers onthe west transept windows done in 1988 were removed. The glasses were cleaned. The windowswere considered structurally safe for earthquake because the stained glass could move and shift andyield to the motion induced by an earthquake. Some frame separated slightly from the sandstonesettings around but did not impose any danger.7. Round Room parapet strengthening8. Reinforcement of pedestal9. Murray-Harris Organ Bracing(See Figure 2.14)30Chapter 2 The Memorial Church at Stanford Universityuj 002 >.. Z+4is\ ,—2/- 1of777\ LiSi-N_—1I-‘ . 4UI____ ______çIc 1I izi uJ i.-.:111FIGURE 2.14 Repair of Non-Structural Elements(From Figure 12 b of Degenkolb, 1990)LUJU’II31Chapter 2 The Memorial Church at Stanford University2.5.5.3 Facilities Improvements All costs quoted below are in 1992 dollars.1. New Sound System: Speakers were installed on the back of the pews. The speakers haveprogrammed delay which could make it easier for the human ears to comprehend what is being said.The new sound system cost about $300,000.2. New Lighting System: Modified theatrical lighting was installed. Higher-wattage, long-life bulbswere put in the large nave chandelier.3. Reopening of Transept Balconies: The fake double doors on the south side of each transept weretransformed into real doors for the reopening of the 2 transept balconies. The stone and brick wallswere cut through in order to make connections in each transept to the existing hidden staircase. Thecost was about $500,000.4. Fire Protection: Fire sprinklers were installed around the ceiling. In order to protect the Fisk-Nanneyorgan from accidental water breakout, a dry-pipe system which holds water in reserve was used and atwo-step system was chosen to detect both smoke and heat before sending water into the sprinklerpipes. Furthermore, to satis1’ fire code, an emergency exit from the west balcony had to be cutthrough the back exterior wall not far from the Round Room.5. New Floor and Carpet: New cork flooring and new red carpet were placed.6. Pews: About 100 pews were refinished and reinstalled.7. New Chapel in the West Transept: A small new chapel in the west transept was reopened.(The information in Section is from Bartholomew, 1992)The final total rehabilitation cost was not the same as the preliminary cost estimate due to certainchanges in the retrofit scheme. The total amount of the rehabilitation cost was $8.5 million, in which$6.5 million was spent on structural strengthening and repair, $2 million was spent on repair andstrengthening architectural elements and improving other facilities (Reis, 1993). The remaining portionof the fund, about $1.5 millions, was saved as a preservation fund and would be used for maintenance andfuture upgrading. Three years after the earthquake, Memorial Church was reopened on November 1,1992. (Bartholomew, 1992)32Chapter 3 Retrofit Options and Cost EstimatesCHAPTER 3RETROFIT OPTIONS AND COST ESTIMATESIn this chapter, four retrofit options are defined and the investment of each option is estimated, interms of a decision considered in 1980, before the new organ installation and structural upgrade in thefoyer area. AU the costs in this chapter are quoted in 1980 dollars unless otherwise stated.The structural upgrade purposed for the new organ installation is considered as the “Do Nothing”option, i.e. the basic one. The other retrofit options are seismic strengthening in addition to the structuralupgrade for supporting the new organ. The seismic retrofit options are defined based on “SeismicEvaluation and Strengthening Proposals for The Stanford University Memorial Church, Stanford,California” by H.J. Degenkoib Associates (1990).Some of the documents referred to in the proposal were not yet available in 1980. Constructiontechnology may have changed quite a bit in the decade in between. However, it is assumed that a similarset of safety levels would still be defined and the essence of the retrofit schemes would also be similar. Itis also assumed that technology available in 1980 would be sufficient to achieve the defined goals.The investment estimates are based on the preliminary cost estimates by Dinwiddie ConstructionCompany (1990). The costs given by that report included both damage repair costs and strengtheningcosts. The costs related to damage repair are taken out and certain adjustment are made to constructestimates of the investment of each retrofit option. The investment costs are then converted to 1980dollars by assuming discrete compounding and using a discount rate i of 4%, i.e.,Total Cost Estimates— Repair CostInvestment= 10(1—i)The choice of the discount rate I will be discussed in Chapter 6. All the investments areestimated based on preliminary values. Effort is put into making consistent and reasonable estimates but33Chapter 3 Retrofit Options and Cost Estimatesit is not guaranteed that these data could accurately represent the actual case. However, the estimates doreflect the relative extent and expense among the options.3.1 DO NOTHING OPTIONThe “Do Nothing” option refers to the addition of a new structural system required to support theweight, over 20,000 pounds, of the new Baroque tracker-type organ. The details of the new structuralsystem are described in Section 2.4.1.Even though the new structural system may contribute to a certain degree of seismicstrengthening to the Church, especially for the foyer area, it is still considered as the “Do Nothing” option.It is the basic requirement for the installation of the new organ and cannot be avoided. The other threeretrofit schemes will have this basic requirement plus different levels of seismic strengthening.The budget for this option is $1,961,000 in 1980 dollars, including $866,000 for purchasing thenew Baroque tracker-type organ and voice improvement and $1,095,000 for management andconstruction of the new structural system. (Facilities Project Management, 1980)3.2 LIFE-SAFETY OPTIONThe purpose of the life-safety scheme is to strengthen the structure to provide sufficient lateralresistance for preventing catastrophic damage or collapse which would cause death, serious injury, orentrapment of occupants in a major earthquake.This scheme is developed based on the evaluation done according to Evaluating the SeismicResistance ofExisting Buildings (ATC-14) by Degenkoib Associates, Engineers (1987). ATC-14 provides34Chapter 3 Retrofit Options and Cost Estimatesprocedures for the life safety seismic strengthening evaluations of existing building in the United States.Presented in the document is the general methodology for:• data collection: existing reports & drawings, field investigation, test methods, etc.;• building type identification;• structural analysis: member capacity, rapid analysis procedure, equivalent lateral force procedure,dynamic lateral force procedure, and special procedure for wood diaphragms.Besides the general methodology, ATC-14 also provides specific procedures for evaluatingdifferent type ofbuildings. This document is widely recognized in the engineering conununity both in theUnited States and Canada. It is currently being used as the basis for the development of a nationalstandard in the United States for the seismic evaluation of existing buildings.This strengthening scheme will meet the minimum standard regarding the safety of theoccupants as required by ATC-14 but will not fully confonu to the current code requirements for newbuildings. The strengthened structure may not be usable immediately after a moderate or majorearthquake. Moreover, the damage, especially to the architectural elements, may not be recoverable.The life-safety strengthening scheme includes the following works:1. Increase the lateral stability of the Crossing arches with a reinforced concrete frame poured inside thevoid space and doweled to the brick, thus interconnecting the arch walls and giving themsignificantly more bending strength perpendicular to their plane.2. Provide perpendicular bracing of the four arches to each other with a new steel bracing system androof diaphragm. This is accomplished by removing the lipped roof dropping a steel frame system of“strong-back” columns and girders into the Crossing, and anchoring the columns to the arches withbolts.3. Transfer the forces generated in the Crossing arches into the stronger concrete walls by addingcollectors at each corner of the Crossing.4. Improve the lateral resisting strength of the roofs of the Nave, Chancel and Transepts, by temporarilyremoving the Spanish tile roof and replacing the straight sheathed boards underneath with plywood.35Chapter 3 Retrofit Options and Cost EstimatesAdditionally, to provide an adequate transfer of forces from the plywood to the concrete walls,strengthen the connection of the roofs and walls.5. Improve the connection of the roof of the Round Room to its brick walls with a detail similar to theprevious point.6. Reduce the forces in the interior walls of the West and East Arcades by temporarily removing theroofs of the arcades and placing a six-inch reinforced concrete slab above the plaster ceiling betweenthe interior and the exterior Arcade walls.7. Avoid falling hazards by repairing several non-structural elements, such as: stone cross, balconyrailings, stone veneer, chandeliers, mosaics.(Note: Points ito 6 are directly extracted from the proposal by Degenkolb, 1990.)Table 3.1 is a sununaiy of the cost estimates. All the costs in the table are in 1990 dollars.TABLE 3.1Cost of Life-Safety Strengthening(In 1990 Dollars)Work Number Cost Estimate Repair Cost Retrofit only1,2,3 2,164,000 327,000 1,837,0004 720,000 0 720,0005 54,480 0 54,4806 157,000 0 157,0007 898,000 305,000 593,000Total 3,993,480 632,000 3,361,480The first colunm indicates the work number which corresponds to the description above. Thesecond column is the original cost estimate, including material and labor of the repair and seismicstrengthening of each work item, given by Dinwiddie Construction (1990). A 20% contingency cost forlabor and material has been included in the total cost for each work item. The third column is the costs,including material and labor, allocated for damage repair within each work item. This repair cost alonedoes not represent the damage cost if no seismic strengthening work is required. It is the cost of materialand labor spent on repairing damages, and it does not include the cost of construction facilities, such as36Chapter 3 Retrofit Options and Cost Estimatestemporary protection, scaffolding, hoisting, electricity, etc., which will be required if the repair is donealone. There is no repair related work stated explicitly in work item 4 to 6. Hence, the repair costs forthese three items are all assumed minimal. The fourth column is the difference between the secondcolumn and the third column, i.e. the cost of seismic strengthening only.According to the preliininaiy cost estimate (Dinwiddie Construction, 1990), an extra 20% overalldesign and construction contingency fee is added to the final total cost. This 20% contingency fee isconsidered redundant in this study and will be ignored.The cost of retrofit is converted back to 1980 dollars by using a discount rate of 4%:Retrofit Cost = $3,361,480 = $2,725,000.(1+0.04)’°In addition to the retrofit cost, the cost of the new structural system at the foyer area to supportthe new organ and the cost of the new organ should be included. Note that the cost of constructing thenew structural system at the foyer area should be less than that in option 1 since construction facilities areset up for the retrofit. It is assumed that the cost of construction of the new structural system at the foyerarea is reduced by two third, i.e.Cost of foyer new structure = . x $1,095,000 = $365,000.Therefore, the total cost of option 2, which equals to the sum of the costs of the new organ, the newstructural system at the foyer area and life-safety strengthening for the whole Church, is (in 1980 dollars)$866,000+$365,000+$2,271,000 = $3,502,000.3.3 BUILDiNG INTEGRITY A OPTIONThe purpose of the building integrity A scheme is to strengthen the structure not only to providesufficient lateral resistance for preventing catastrophic damage or collapse which would cause death,serious injury, or entrapment of occupants in a major earthquake, but also to limit damage to the37Chapter 3 Retrofit Options and Cost Estimatesarchitectural elements to a level which would require minimal repair and to ensure continued operation ofthe facility after a major earthquake.The scheme is developed based on the Essential Building Provisions of Title-24 of the CalforniaAdministrative Code for Hospital Construction. This code has stricter criteria on the evaluation andstrengthening requirement than ATC-14 (Degenkoib, 1987). The minimal damage goal in Title-24 issuitable for evaluating the vulnerability of the special architectural and structural features of the Church.The required strengthening work for this scheme included the 7 work items described in theprevious option, with increased member sizes of the “strong-back” columns and girders of the newCrossing roof diaphragm in work item #2 to prevent cracking of the arches and damage to the drum.Another three additional works required are listed as follows (extracted from the proposal by Degenkoib,1990.):8. Remove the roof and pour a new slab from the discontinuous wall of the Gallery Stair Towers to alower parallel wall which extends to the foundation, in order to transfer loads away from theperpendicular walls.9. Remove the stained glass windows and retrofit the frames to provide a gap, isolating the windowsfrom the movement expected in the walls.10. For the Round Room: temporarily remove the wood paneling around the inside of the entire room,dowel into the exposed brick and gunite an eight-inch layer of reinforced concrete against the walls.The cost estimates are listed in Table 3.2.TABLE 3.2Cost of Building Integrity A Retrofit(In 1990 Dollars)Work Number Cost Estimate Repair only Retrofit only1,2,3 2,172,000 327,000 1,845,0004 720,000 0 720,0005 54,480 0 54,4806 157,000 0 157,0007 898,000 305,000 593,0008 108,000 0 108,0009 2,500,000 0 2,500,00010 455,500 0 455,500Total 7,065,000 632,000 6,433,00038Chapter 3 Retrofit Options and Cost EstimatesThe retrofit cost is then converted back to 1980 dollars by using a discount rate of 4%:$6 433 000Retrofit Cost= 10 =$4,346,000.(1+0.04)Therefore, the total cost of option 3, including the new organ, the new structural system at the foyer areaand the building integrity strengthening cost for the whole Church is (in 1980 dollars)$866,000 +$365,000+$4,346,000 = $5,577,000.Current Title-24 prohibits the use of unreinforced masonry construction because it is brittle andmay suffer significant damages during an earthquake. The walls of the Crossing arches and the walls ofthe Round Room are unreinforced masomy. The strengthening of the wails of the Round Room byreinforced concrete is considered sufficient. But the strengthening of the walls of the Crossing arches willnot be. Hence, this strengthening scheme is not considered fully compliant with the Essential BuildingProvisions of Title-24.3.4 BUILDING INTEGRITY B OPTIONThe Building Integrity B option is essentially the same as the Building Integrity A option, exceptfor the Crossing area. The work listed for item 1 - 3 will be replaced by the following:• Dismantle the arches and replace with reinforced concrete to match. This involves removing the roofof and taking down the drum, mosaic angels and stone veneer in the Crossing, demolishing the brickarches and pouring new reinforced concrete arches in their place. All the architectural elementswould then be replaced.As mentioned in the previous section, Title-24 prohibits the use of unreinforced masonryconstruction. By removing the unreinforced masonry in the Crossing arches and reconstructing withreinforced concrete, there will be a higher confidence in achieving the desired safety level. However, the39Chapter 3 Retrofit Options and Cost Estimatescost associated with this is very high compared to the previous option. The extra cost can be seen as theinvestment on purchasing lower risk. The cost estimates are listed in Table 3.3.TABLE 3.3Cost of Building Integrity B Retrofit(In 1990 Dollars)Work Number Cost Estimate Repair only Retrofit only1 - 3 10,158,000 0 10,158,0004 720,000 0 720,0005 54,480 0 54,4806 157,000 0 157,0007 898,000 305,000 593,0008 108,000 0 108,0009 2,500,000 0 2,500,00010 455,500 0 455,500Total Cost 15,051,000 305,000 14,746,000The retrofit cost is then converted back to 1980 dollars by using a discount rate of 4%:Retrofit Cost= $14,746,000= $9,962,000.(1+0.04)Therefore, the total cost of option 4, including the new organ, the new structural system at the foyer areaand the building integrity strengthening cost for the whole Church is (in 1980 dollars)$866,000+$365,000+$9,946,000 = $11,193,000.3.5 SUMMARYThe cost of the new organ and the structural upgrade to support the new organ is about $2million. The church can be upgraded to life safety standard at a cost of $3.5 million, about 75% higherthan the previous option. In order to minimize the damage to architectural elements, about $5.6 million isneeded for option 3. To be in full compliance with Title-24, i.e. to remove all URM walls, the cost of the40Chapter 3 Retrofit Options and Cost Estimatesretrofit is estimated to be $11.2 million, which is two times the cost of option 3. A summary of the costsof the four retrofit options is listed in Table 3.4.TABLE 3.4Summaiy of Investment Costs(In 1980 Dollars)Option Description Investment1 Do Nothing 1,961,0002 Life-Safety 3,502,0003 Building Integrity A 5,577,0004 Building Integrity B 11,193,00041Chapter 4 Seismic DataCHAPTER 4SEISMIC DATATo estimate building damages and calculate expected damage costs, the size and the frequency offuture earthquakes at the site are needed.Ideally, to evaluate the seismicity of a site, the first step is to identii the location of all thepotential faults around the site and collect the frequency of different magnitudes of earthquakes alongeach fault. Then, the impact of earthquakes along each fault on the site should be studied. In particular,the distance of each fault from the city and the attenuation of intensity away from the faults should beconsidered. Combining the information collected, a site-specific ground-shaking versus hazard curve,giving the probability of exceedence of each ground-motion level, can be produced. This method requiresa lot of mathematical and statistical computation. Furthermore, detailed local geologic information isoften not completely available at the present time. (VSP, 1992)A less complete but acceptable method is to use the seismic data provided by the United StatesGeological Survey. In FEMA-227 (VSP, 1992), the seismic data are based on Algermissen et a!. (1982).In this study, the seismic data in another report by Algermissen et a!. (1980) are used. The seismic datagiven by this report are more specific and refined for areas within the coastal California than the reportused by FEMA-227 (VSP, 1992). Moreover, the year that this report (Algermissen et a!., 1980) wasprepared, i.e. 1980, is the same as the assumed present time for the decision analysis.In this chapter, the seismic data selected are discussed and the derivation of earthquakeprobabilities to be used for calculating expected values are explained. Some of the terms used in thischapter are defined in Section 4.1.42Chapter 4 Seismic Data4.1 DEFINITIONSSeismic data refers to the expected “frequency” as a function of the “size” of future earthquakes ata “location”.“Frequency” is a general term which can be referring to either one of the below:• Annual Occurrence Rate (r): number of occurrence of a particular level of earthquake per year. It isthe reciprocal of return period and it can be greater than 1.• Annual Probability of Occurrence (P0): the probability that one or more earthquakes of a particularlevel or range of levels will occur per year. It is calculated by using a Poisson Process assumption andthe annual occurrence rate. It is generally expressed in percentage and must be less than 1.• Probability of Earthquake (F): the probability that the earthquake is of a particular intensity levelgiven that an earthquake occurs. It is the ratio between the number of occurrences of that particularlevel per year and the total number of events per year.“Size” is a general term which can be referring to either the magnitude or the intensity:• Magnitude: the measure of an earthquake’s total size, the energy release at its source as estimatedfrom instrumental observations. One commonly used parameter is Richter Magnitude. (Coburn andSpence, 1992)• Intensity: the measure of severity of the shaking of the ground at a particular site. One commonlyused parameter is Modified Mercalli Intensity (Mtvil). (Coburn and Spence, 1992)The “location” can be referring to one of the below:• Source: location where the earthquake originated, or where the fault was located.• Site: city or area where the building under consideration is located.• Seismogemc zones: areas not defined solely on the spatial distribution of seismicity but also ontectonic and geologic setting. They are not equivalent to “tectonic province” nor “seismotectonicprovince” which refer to the siting of critical facilities. (Algermissen et a!., 1980)43Chapter 4 Seismic Data4.2 GROUND MOTION PARAMETER: INTENSITY SCALEIntensity is the most commonly used parameter to measure seismic hazard in loss estimationstudies. Intensity of an earthquake is the measure of severity of the shaking of the ground at a particularlocation. Intensity scales are essentially site-specific and non-quantitative. There are usually 12 levelsand stated in Roman numerals to differentiate from magnitude. The assessment of level depends on thebehavior of the people and animals, the response of facilities and the observation of the ground in thelocation considered. (Coburn and Spence, 1992)There are different kinds of Intensity Scales used in different countries. The first Intensity Scalewas developed by M.S. de Rossi of Italy and F.A. Forel of Switzerland at the end of the nineteenthcentury. The Rossi-Forel Intensity Scale (RF) has 10 levels and was used for about two decades. In 1902,a Italian seismologist, Mercalli, devised a new scale on a Ito XII range to keep up with the advancementof the science of seismology.The Mercalli Scale was then modified and revised in 1931 by American seismologists Hany 0.Wood and Frank Neumann to take into account modern structural features. The Modified MercalliIntensity Scale (MIV[I) became the most commonly used Intensity Scale in the United States. A briefsummary of the Modified Mercalli Intensity Scale is listed in Table 4.1.Since level assessment involves subjective evaluation and interpretation, the data should be usedin conjunction with the original damage descriptions. There is also a tendency to overestimate intensitylevel especially for large earthquakes (Coburn and Spence, 1992). Therefore, the use of high intensityvalues, such as MIvil level XI and XLI, should provide explicit explanation to avoid misunderstandingsince the high intensity levels emphasize ground failure, not shaking severity which differ from thecriteria of lower levels (Panel On Earthquake Loss Estimation Methodology et a!., 1989).44Chapter 4 Seismic DataTABLE 4.1Modified Mercalli Intensity ScaleFrom Appendix B, p.66 of Holden and Real (1990)MMI DescriptionLevelI Not felt except by a very few under especially favorable circumstances.II Felt only by a few persons at rest, especially on upper floors of buildings.Delicately suspended objects may swing.III Felt quite noticeably indoors, especially on upper floors of buildings, butmany people do not recognize it as an earthquake. Standing motor cars mayrock slightly. Vibration like passing of truck. Duration estimated.IV During the day felt indoors by many, outdoors by few. At night someawakened. Dishes, windows, doors disturbed; walls make cracking sound.Sensation like heavy truck striking building. Standing motor cars rockednoticeably.V Felt by nearly everyone, many awakened. Some dishes, windows, etc.,broken; a few instances of cracked plaster; unstable objects overturned.Disturbances of trees, poles and other tall objects sometimes noticed.Pendulum clocks may stop.VI Felt by all, many frightened and run outdoors. Some heavy furniture moved;a few instances of fallen plaster of damaged chimneys. Damage slight.VII Everybody runs outdoors. Damage negligible in building of good design andconstruction; slight to moderate in well-built ordinary structures;considerable in poorly built or badly designed structures; some chimneysbroken. Noticed by persons driving motor cars.VIII Damage slight in specially designed structures; considerable in ordinarysubstantial buildings, with partial collapse; great in poorly built structures.Panel walls thrown out to frame structures. Fall of chimneys, factory stacks,columns, monuments, walls. Heavy furniture overturned. Sand and mudejected in small amounts. Changes in well water. Persons driving motorcars disturbed.IX Damage considerable in specially designed structures; well-designed framestructures thrown out of plumb; great in substantial buildings, with partialcollapse. Buildings shifted off foundations. Ground cracked conspicuously.Underground pipes broken.X Some well-built wooden structures destroyed; most masonry and framestructures destroyed with foundations; ground badly cracked. Rails bent.Landslides considerable from river banks and steep slopes. Shifted sand andmud Water splashed (slopped)_over banks.XI Few, if any, (masonry) structures remain standing. Bridges destroyed.Broad fissures in ground. Underground pipelines completely out of service.Earth slumps and land slips in soft ground. Rails bent greatly.XII Damage total. Practically all works of construction are damaged greatly ofdestroyed. Waves seen on ground surface. Lines of sight and level aredistorted._Objects are thrown upward into the air.45Chapter 4 Seismic Data4.3 SEISMIC DATAThe coastal area of California is divided into 41 seismogenic zones, which are areas of similartectonic and geologic settings. The annual occurrence rates are calculated for “those zones that have asufficient number of earthquakes to make possible a judgment on the period of time for which eachmagnitude level is complete.” (Algermissen et aL, 1980)The annual occurrence rates are estimated by annual averages over the time of completeness foreach magnitude level and by the method shown by Stepp (1973) (as mentioned in Algermissen et a!.,1980). The historic data are fitted into the Richter Law of Occurrence Frequencies,logN=a+(bxM) (4.1)where a and b are constants given or calculated from tables of seismic parameters for each earthquakesource zone. N is the expected number of earthquakes per year which equals to or exceeds magnitude Mat the zone.(Algermissen et a!., 1980) This equation is a variation of the Gutenberg-Richter relationshipwhich has been verified from worldwide observations of seismicity. This relationship quantifies theobservation that the smaller earthquakes are more frequent than larger ones and hence, makes it possibleto estimate the frequency of larger earthquakes from the observed data of the smaller earthquakes.(VSP,1992)The historic data are based on the earthquake catalogue compiled by Algermissen and Rothmanand partially listed in Hays and others (1975) (as mentioned in Algernussen et a!., 1980). The historicand instrumental seismicity contained in the catalogue are dated from 1796 to 1974 (a period of 178years) in the coastal area of California (Algermissen et a!., 1980). Many of the earthquakes in thecatalogue are recorded in intensity level. Intensity level attenuates as the distance from the sourceincreases. Magnitude represents the energy release at its source which is not related to distance. Ingeneral, the distance between the source and the site where the intensity is recorded has to be taken intoaccount in the conversion between intensity and magnitude. However, the intensity in the catalogue is46Chapter 4 Seismic Dataassumed to be the epicentral intensity, i.e. the intensity at the source, hence it can be converted tomagnitude without taking distance into account. The relationshipM=O.6x1+L3 (4.2)is used to convert epicentral intensities (1) to magnitudes (M). (Algermissen eta!., 1980)Since intensity levels are defined in discrete intervals, only one magnitude is directly related toeach intensity level by using the equation. For each intensity level, a range of magnitude is defined usingthis magnitude as the center point. The data are listed in the following table.TABLE 4.2Conversion Between Intensities and MagnitudesUsing Equation (4.2)Intensity, I Magnitude, M Range of MV 4.3 4.0 - 4.6VI 4.9 4.6- 5.2VII 5.5 5.2 - 5.8VIII 6.1 5.8-6.4IX 6.7 6.4 - 7.0X 7.3 7.0 - 7.6XI 7.9 7.6 - 8.2XII 8.5 8.2 - Location of Stanford UniversityStanford University is located in Palo Alto, Santa Clara County, near the western shore of theSan Francisco Bay. The San Andreas fault and the San Gregono fault lie on the west side whereas theHayward fault and the Calaveras fault lie on the east side of this area. (See Figure 4.1)47Chapter 4 Seismic DataSanaRosa -A—38‘\Oakland.7San Francisco\-\P SanJose‘TAc*J7 J, ‘\\t.OMAPRIETA 7c.EARThQUAKE_‘ISanta Ctuz___37_ ___San JuanI I I Il4oister123 122FIGURE 4.1 Location of Major Faults in San Francisco Bay Region(From Figure 2, p.9 of Working Group On California Earthquake Probabilities, 1990)48Chapter 4 Seismic DataReferring to the zoning map (Figure 4.2), Stanford is located on the boundary of zone 24 andzone 38. The seismic data for zone 24 is used since ills more likely to be the zone containing Stanford.Zone 24 contains the entire San Andreas fault. Numerous historic earthquakes have occurredalong this fault and the entire zone shows evidence of Holocene movement. There are substantialdifferences in activity rates and style of deformation along segments of the fault. There are alsosignificant differences in interpretation by different experts. Despite the controversy, Algermissen andothers believed that the central creeping section of the fault is capable of generating a large magnitudeearthquake in the future. (Algermissen et a!., 1980)4.3.2 Maximum Probable EarthquakeZone 24 is assigned the highest maximum magnitude among other zones in western California(see Figure 4.3). The great 1906 San Francisco earthquake with magnitude 8.3 occurred in this zone.Thus, a maximum probable magnitude of 8.5 is assigned for this zone.(Algermissen et a!., 1980) Byusing equation (4.2) to convert magnitude to intensity, the maximum probable intensity is XII, which isthe maximum on the MMI scale.The maximum probable earthquake is estimated based on the historical maximum magnitudeexperienced in that zone. This historical largest earthquake could be less than the potential maximumand is likely to be, especially if the period of record is less than the return period of the potentialmaximum earthquake.(Algermissen eta!., 1980) The earthquake record of United States does not exceed500 years and is around 150 years for parts of the western United States (VSP, 1992). The catalogue usedby Algermissen et at. (1980) contains record from 1796 to 1974, which is 178 years long. Therefore,earthquakes greater than the estimated maximum probable are still possible in zone 24. However, theassigned maximum probable intensity for zone 24 is already the highest on the intensity scale. The factthat the worst scenario is expected suggests that no adjustment for the maximum probable intensity isnecessary.49Chapter 4 Seismic Data-SEISMOGENIC ZONES IN COASTAL AND OFFSHORE•V CALIFORNIAL•• r•*4ti•i .e*IIt* .d i.t..., V)h sub hi...-, d.hd Ii,.ifl n.e ,nfl, — this .5. .1e ..fl i.dt..i...i.t in. Inst. ci hfl.,s4. fl..,r. st*d- I ld.,t (tenS. ....C.frS..%..Ie.,...,..i... fence Jn inn.., na inSt. I• V., ••(. .‘ I - —••t.•_.,,.V •• V\ • •3g . .. -V\\. F . S I\ .:..\\r •.• .\ \\\\ •V • V3e• 1___. . . ... -V •\\c •.. ... . .V•• :, :.:. . .- ..— — — — ——.1• \ •.I. •V\ \‘L :\\V•, .31.\ ‘-... • V V ••S•i._Ii•••_ . • .-• . ..•\./• 25 ).30 . . . • V\\1N\ :• -•20 .-AF’\\2V.1’• •••.S • ‘...‘.N \\•V • •. V••.SSr\10&FIGURE 4.2 Seismogenic Zones in Coastal and Offshore California(From Plate 1 of Algermissen eta!., 1980)50Chapter 4 Seismic DataFIGURE 4.3 Estimated Maximum Magnitude for Each Seismogenic Zone(From Figure 3, p.40 of Algermissen et aL, 1980)51Chapter 4 Seismic Data4.3.3 Annual Occurrence RatesThe annual occurrence rate for each range of magnitudes for each seismogemc zone is tabulatedin Table 1, p.30 of Algermissen eta!. (1980). The data for zone 24 is selected from this table and listed inTable 4.3.TABLE 4.3Annual Occurrence Rate for Zone 24Intensity, I Magnitude, M Range of M AnnualOccurrence RateV 4.3 4.0 - 4.6 1.9700VI 4.9 4.6 - 5.2 0.7400VII 5.5 5.2 - 5.8 0.2810VIII 6.1 5.8-6.4 0.1060IX 6.7 6.4 - 7.0 0.0400X 7.3 7.0 - 7.6 0.0150Xl 7.9 7.6 - 8.2 0.0057XII 8.5 8.2 - 8.8 0.0021Z = 3.1598As mentioned in Section 4.1, the annual occurrence rate is the number of occurrence of aparticular level of earthquake per year. Note that in FEMA-227 (VSP, 1992), the annual occurrence ratesare used directly to calculate the expected cost, i.e.EC=> xcwhich is, in fact, the total damage cost in a year. According to the definition in Bayesian Theory, theexpected value should be calculated byEV=Fxqwhere probabilities are used instead of occurrence rates. The basic requirement for P is that the events bemutually exiusive and exhaustive, i.e. the sum of all P• equals to one. The value of EV will always be lessthan BC since P, cannot be greater than 1.0 but r• can be greater than 1.0.52Chapter 4 Seismic Data4.4 DERiVATION OF EARTHQUAKE PROBABILITIESThe conditional probability of earthquake intensity 1 is defined as the probability that theintensity level is I• given that an earthquake of intensity greater than Mlvii V occurs. It is the ratiobetween the number of events of that particular intensity level per year (the annual occurrence rate, r) andthe total number of events from Mlvii level V to XII per year:Note thatP(”IQ)—---I-8i=1=3.16(4.3)which means, on average, there are 3.16 earthquakes with intensities ranging from Ivilvil V to XII in oneyear. The conditional probabilities are calculated and listed in the following table.TABLE 4.4Probabilities of Earthquake Intensity IThe probability of occurrence of one or more earthquakes with intensity between V and XII(inclusive) in time t can be calculated by using a Poisson process:1 Intensity, I Annual Probability,Occurrence Rate, P( I, I Q)r1 V 1.97 0.62352 VI 0.74 0.23423 VII 0.28 1 0.088934 VIII 0.106 0.033555 IX 0.040 0.012666 X 0.015 0.0047477 XI 0.0057 0.0018048 XII 0.002 1 0.0006646=3.1598 z=1.053Chapter 4 Seismic DataP0(IV)=l—e (44)where r is the occurrence rate and (is the time span. Substituting r = 3.16 and t 1 year into the aboveequation,P,(I V) = 1—0.0424 = 0.9576i.e., the probability of occurrence of at least one earthquake with intensity between V and XII, inclusively,is about 0.9576 per year. In other words, there is a 96% chance that one or more earthquakes withintensity between V and XII will occur in one year.The conditional probabilities listed in Table 4.4 are measures on a set of mutually excluive andexhaustive events, hence they may be used in the decision tree. Being mutually exclusive means that eachevent does not “intersect” with each other. The MMI levels are considered as individual events. Beingcollectively exhaustive implies that the union of the set of events exhausts the sample space and the sumof the probabilities of all events equals to one. The sample space is defined as earthquake with intensitylevel between V and XII, inclusively. The intensity levels lower than V are ignored since the damageassociated with these intensities are minimal. The damage associated with level V is veiy small already.The probability of each level, from V to XII, is calculated and the sum of these probabilities equals to one.So, it can be concluded that the sample space is valid and the set of events exhausts the sample space.4.5 LOCAL SITE EFFECTSIn general, local site conditions have to be taken into account in conjunction with the intensity ofground motion to estimate earthquake losses. Unfavorable soil or topographic conditions may amplifyground motion which increases intensity of shaking and induces greater losses.It is important to make sure whether the intensity in a scenario earthquake applies to the localground condition or to some standard ground conditions. If a standard ground condition is used, thenmodification may be needed.54Chapter 4 Seismic DataTwo different adjustment procedures are described in FEMA-227 (VSP, 1992): one method issuggested by ATC-13 and one is by FEMA-227 itself The method introduced by ATC-13 is morecomplex than that by FEMA-227. In the former one, the user identifies the soil type from the five soiltypes defined in Table 8.4 in ATC-13 and adjusts the damage probability matrix for the type of buildingunder consideration using Table 8.4 again and Equation 8.2a in ATC-13. In the later method, there areonly two soil types: either poor or firm. If the site has poor soil, then the mean damage factor is adjustedupward by one IvIMI level. For example, the expected damage for an MIvil VIII earthquake at a firm soilsite will be assigned as the expected damage for an MMI VII event at a poor soil site.The methodology suggested by FEMA-227 would have been adopted in this project, if the soiltype was poor. Since the soil underlying Stanford University is not poor soil type, no adjustment isnecessary.4.6 DISCUSSIONThe annual occurrence rates derived by Algermissen et at. (1980) using historic data “may notfairly represent the probability of the next large earthquake in a zone where it is possible to invoke astatistical time-dependent or geophysical predictive model.”The rates could be overestimated or underestimated for a site depending on the distance betweenthe site and the nearby source zones of future earthquakes. If the source is far away from the site, theintensity experienced by the site will be lower and the occurrence rates could be overestimated. On theother hand, if the source is closer to the site, the intensity experienced by the site will be higher and theoccurrence rates could be underestimated.(VSP, 1992)The uncertainty in the annual occurrence rates estimated for zone 24 is relatively low comparedto other zones. Since the San Andreas fault is a seismic active area, more research activities have been55Chapter 4 Seismic Dataconcentrated in this zone. The tectonics and seismicity of this zone are better understood than many otherzones. Thus, the seismic data are considered more reliable than that of the other zones.To predict the location, time and intensity of a specific future earthquake is not yet possiblenowadays. However, effort has been made to understand and evaluate the average, long-term seismicity ofseismically active zones in the United States (VSP, 1992). The average, long-term seismic data areconsidered sufficient for decision analysis in general. In fact, “correct” infonnation is not the mainconcern in making rational decisions. It is making decisions consistent with the best availableinformation that matters. Sensitivity studies can always be used to decide when it is necessary to obtainbetter information. And when further information is obtained, a new decision can be considered.56Chapter 5 Loss EstimateCHAPTER 5LOSS ESTIMATEThere are risk analysis computer programs available in California, as reviewed in Holden andReal (1990). The user can input the structural type, the year built, the address, and the replacement costof the buildings and the programs will generate annual loss or average loss over a specific time span. Thetwo major methods of loss estimate involved in these computer programs are:1. the Probable Maximum Loss (PML) method developed by Karl Steinbrugge and Ted Algermissen forthe Insurance Services Office (ISO) in California. It includes 21 building categories based on theinformation that is readily available to insurance companies. The method are developed based onexperience with California earthquakes and expert judgment.2. the ATC-13 method developed by the Applied Technology Council. It includes 41 building types andother classes for structures such as bridges, pipelines, dams, tunnels, etc. The data in ATC-13 arealso developed based on experience with California earthquakes and expert opinions.Both methods are based on the propositions that:• earthquake magnitudes and fault rupture lengths may be effectively converted into Modified MercalliIntensity (Mlvii) patterns;• Mlvii attenuates as the distance from the causative fault increases;• monetary losses are directly related to Mlvii and the type and value of structure.Given the MMJ, the building type and the value of the structure, the average monetary loss of aset of structures can be estimated. Both the ISO and ATC methods yield similar results for similarstructure types. These methods are mainly designed for analyzing groups of ordinary buildings and theyare not suitable for application on an individual basis or for special structures. So they can not be applieddirectly in this study. However, the basic method and data in ATC-13 (ATC, 1985)will be used as themain reference.57Chapter 5 Loss EstimateThe process of loss estimate can be divided into two main components: damage assessment anddamage cost estimate. The procedures and rationales behind the development of these two componentsare discussed in this chapter.5.1 DAMAGE ASSESSMENTDamage assessment is estimating damages of a structure depending on the severity of the groundmotion and the vulnerability of the structure itself Given a certain earthquake intensity, the extent ofdamage that the structure may suffer and the probability of occurrence of that extent of damage are neededto be estimated. The estimates require information on the performance of similar type of buildings in pastearthquakes and prediction of structural behavior of that particular building. Knowledge in damageassessment is rare and the data that has been widely accepted are the Damage Probability Matrix (DPM)provided by ATC-13 (ATC, 1985).5.1.1 Damage Probability Matrices (DPM)Surveys have been done on structural damage states at different earthquake intensity levels fordifferent types of existing building in California. The results are statistically organized and tabulated inmatrix forms in ATC-13 (ATC, 1985). The damage probability is the conditional probability that abuilding will suffer a certain damage state if an earthquake with certain intensity occurs. Seven buildingdamage states are defined, ranging from none to destroyed. For each damage state, a range of damagefactors and a central damage factor (CDF) are assigned. Damage factors are defined as percentage ofbuilding replacement value which reflect the percentage of physical damage to the structure. The centraldamage factor is defined as the midpoint of the range. The damage states and damage factors are listed inTable 5.1.58Chapter 5 Loss EstimateTABLE 5.1Definition of Damage States and Corresponding Damage FactorsFrom Table 3-4, p. T3-7 of FEMA-227 by VSP (1992)(Original From Table 2.1, p.45 of ATC-13)Damage State Description Damage CentralFactor Damage_______________________________________Range (%) Factor (%)1 - None No damage. 0 02 - Slight Limited localized minor damage not requiring 0 - 1 0.5repair.3 - Light Significant localized damage of some 1 - 10 5components generally not requiring repair.4 - Moderate Significant localized damage of many 10 - 30 20components warranting repair.5 - Heavy Extensive damage requiring major repairs. 30 - 60 456 - Major Major widespread damage that may result in 60 - 100 80the facility being razed, demolished, orrepaired.7 - Destroyed Total destruction of the majority of the facility. 100 100There are different DPMs for different types of structures. The general form of DPM is shown inthe following tables. They are the DPMs for unreinforced masomy (URM) low rise buildings withbearing wall (in Table 5.2 a) and with load bearing frame (Table 5.2 b).TABLE 5.2 aDamage Probability MatrixFor Type 75: Unreinforced Masomy (Bearing Wall, Low Rise) BuildingsFrom Table 3-5, p. T3-8 of FEMA-227 by VSP (1992)(Original from ATC-13, Table 7.10, pp. 198 - 217)Modified Mercalli IntensityCDF VI VII VIII IX X Xl X[I0.000.50 9.1 0.65.00 90.5 55.5 10.9 0.520.00 0.4 43.4 66.0 22.4 2.0 0.1 0.145.00 0.5 22.9 65.9 35.0 10.1 3.480.00 0.2 11.2 62.5 83.1 50.4100.0 0.5 6.7 46.1MDF 4.7 11.7 24.2 43.1 66.7 77.7 88.059Chapter 5 Loss EstimateTABLE 5.2 bDamage Probability MatrixFor Type 78: Unreinforced Masomy (Load Bearing Frame, Low Rise) BuildingsFrom Table 3-5, p. T3-9 of FEMA-227 by VSP (1992)(Original from ATC-13, Table 7.10, pp. 198 - 217)_____Modified Mercalli IntensitCDF VI VII VIII IX X Xl XII0.00 5.20.50 38.8 3.2 0.75.00 55.9 84.1 37.9 5.5 0.8 0.2 0.120.00 0.1 12.7 55.4 52.6 20.6 6.9 2.545.00 6.0 40.4 60.8 40.2 17.780.00 1.5 17.8 51.7 62.8100.0 1.0 16.9MDF 3.0 6.8 15.7 30.2 45.8 61.8 75.6At the bottom of each table, a MDF is calculated for each column. MDF represents meandamage factor. It is the expected value of the CDFs at a particular MIvil level. For example, at MMI VIof Table 5.2a,MDF = (0.5 x 9.1%÷5.0 x 90.5%+20.0 x 0.4%)+ 100 = 4.7%.How accurate are the DPM? According to FEMA-174 (Building Systems Development et al,1989), for most building types, the accuracy should be assumed as within a 100% accuracy envelope.That is, a given damage factor can be considered as a number midway between a 2:1 range of accuracy.For example, a damage probability of 66% represent an actual range between 44 and 88%. The damageinformation for IJRM buildings is superior to all other structural types therefore, it would be valid toassume that the accuracy is about 25%.The DPMs given in ATC-13 are developed based on California data. For cities outsideCalifornia, adjustment has to be made to account for the difference in building practices and the probableabsence of seismic provisions in codes. Local DPMs could also be developed based on consensus opinionof well-informed engineers. (VSP, 1992) Since Stanford University is located in California, the DPMscan be used as references directly without adjustment for location.60Chapter 5 Loss Estimate5.1.2 Establishing The Basic DPM for the Memorial ChurchAlthough the data in the DPMs given in ATC-13 (ATC, 1985) do not needed to be adjusted forlocation, they should not be applied directly to damage estimates for the Memorial Church. These DPMsare evaluated for typical building types but the structure of the Church is quite different from typicalresidential or commercial buildings.Among various structure types, URM structures are considered as the most hazardous typebecause they are brittle and would suffer significant damages in an earthquake. Most URM bearing wallstructures in California were built before 1933. They are usually one to six stories high. In the tables,“low rise” refers to one to three stories high. The usage of the URM buildings includes commercial,residential or industrial. Construction components vaiy depending on the size and usage of the building.Smaller commercial and residential buildings usually have light wood floor I roof joists supported on aperimeter URM wall and interior wood load bearing partitions. Larger URM buildings, such aswarehouses, have heavier wood floors and interior columns, and thick bearing walls which are about 24inches or more at the base. (Building Systems Development et cii., 1989)The Church is a combination of URM and reinforced concrete. The crossing arches and theRound Room were built in URM whereas the walls along the perimeter of the nave, the transepts and thechancel were built in concrete. The two major types of URM buildings are bearing wall and load bearingframe. The URM portions of the Church neither completely belongs to the URM bearing wall type northe URM load bearing frame type. The reinforced concrete walls constructed in the early 1900’s could notbe considered as having the same quality as the reinforced concrete walls built in recent years. There arealso considerable doubts about the connections between the URM and the reinforced concrete walls.There are DPMs for concrete frame or precast concrete buildings, but the DPMs for URM lowrise buildings with bearing wall and load bearing frame are used to establish a basic DPM for the Church.It is because the performance of the whole Church depends mainly on the perfonnance of the URM archesat the crossing.61Chapter 5 Loss EstimateThe basic DPM for the Church is calculated by taking the average of the DPMs of the URM lowrise buildings with bearing wall and load bearing frame listed in Table 5.2 a & b. For example, at MM[level VIII, the damage probability of damage state 4 for the Church is calculated by66.0÷55.4=60.72where 66.0 is selected from MMI VIII and damage state 4 in Table 5.2 a and 55.4 is selected from thesame location in Table 5.2 b.Note that MMI V is not included in the DPMs because it is suggested by ATC-13 that damagesare ignorable at this Mlvfl level. In this study, it is assumed that there is a 90% chance that the Churchwill have no damage and 10% chance that minor damage will occur for this level of earthquakes.TABLE 5.3The Basic Damage Probability Matrix For The Memorial Church(Without retrofit, in 1980)Damage CDF Modified Mercalli IntensityState (%) V VI VII VIII IX X XI XII1 0.00 90.00 2.60 0 0 0 0 0 02 0.05 10.00 23.95 1.90 0.35 0 0 0 03 5.00 0 73.20 69.80 24.40 3.00 0.40 0.10 0.054 20.00 0 0.25 28.05 60.70 37.50 11.30 3.50 1.305 45.00 0 0 0.25 14.45 53.15 47.90 25.15 10.556 80.00 0 0 0 0.10 6.35 40.15 67.40 56.607 100.0 0 0 0 0 0 0.25 3.85 31.50MDF 0.5 3.85 9.22 19.94 36.65 56.21 69.79 81.79The damage that the Church suffered in the Loma Prieta Earthquake in 1989 was approximately10 to 20%, around the lower end of damage state 4. The intensity of the earthquake was estimated to beMIvil Vifi at Stanford. In the DPM above, the probability of damage state 4 is about 60% and the MDF isabout 20% for Mtvil VIII. The probability should have been higher for damage states 3 and 4, and lowerfor damage state 5 which will then reduce the predicted MDF slightly. This DPM is considered slightlyover-estimating the damages of the Church without retrofit in 1980. The adjustment of the DPM for theChurch is discussed in the following section.62Chapter 5 Loss Estimate5.1.3 Expected Reduction inDaniage (ER]))In FEMA-227 (VSP, 1992), a factor called Expected Rehabilitation Effectiveness (ERE) isintroduced to adjust the expected damages of unrehabilitated buildings. The effectiveness is defined as thepercentage reduction in expected damages in the seismically strengthened facility compared to theexpected damages in the unstrengthened facility. It varies depending on the rehabilitation techniquesused, on the standard, code, or safety level to which seismic rehabilitation is carried out, and on thedesign, construction, and condition of the building before rehabilitation.In this project, a similar factor called Expected Reduction in Damage (ERD) is used to adjust theaverage damage cost for each intensity level, which in effect modifies the basic DPM for each option. TheERD factors are basically the same as the effectiveness of seismic retrofit defined in FEMA-227 (VSP,1992) except that the ER]) factors will also take into account the past performance of the Church.For the convenience of discussion, MMI levels are divided into three groups:Group MIvil RangeModerate V - VILarge VII -IXGreat X - XII5.1.3.1 Past Performance of the Memorial Church The original Church, built in 1899 and finished in1903, was constructed with unreinforced masomy. It suffered severe damages in the 1906 earthquake.The intensity of the earthquake was estimated to be about Mlvll level VIII to IX. The roofs collapsed, theGable Wall and the upper portion of the Clock Tower were destroyed and portions of the brick walls wasdamaged.Yet the Crossing and the Round Room suffered minimal damages. The Church was thendemolished and reconstructed except for the Crossing and the Round Room. This suggests that the URMin the Crossing area and the Round Room might be able to withstand significant amount of earthquakeshaking. It could be assumed that the URM of the Church is stronger than the URM of typical buildingsby 5% in large earthquakes.63Chapter 5 Loss EstimateThe Church was reopened in 1913. There was neither major damage recorded nor structuralupgrade done along the years until 1980, the assumed present time. There were some major earthquakeswhich could have affected the Stanford area in this period of time (from 1917 to 1980). They are listed inthe following table.TABLE 5.4Important Earthquakes Near Stanford, 1917 - 1980Extracted from Appendix B of Bolt (1988)Time Place MMI RemarksApril 7, 1957 San Francisco Vifi Damage in West lake and Daly City area.Aug. 6, 1979 Coyote Lake VII $500,000 property damage; 16 injuries; grounddisplacement along Calaveras fault. Maximumhorizontal displacement was 5 to 6 mm.Jan. 24, 26, Livermore VII $11.5 million damage; 50 injured; felt over 75,000 sq.1980 km; 1500 m of discontinuous surface rupture showinga maximum of 5 to 10 mm of right lateraldisplacement.The earthquakes listed above were very close to Stanford and could have affected the Stanfordarea. Since earthquake intensities attenuate as the distance from the epicenter increases, Stanford couldhave experienced several moderate earthquakes along the years. Yet no structural damage was recorded.The reconstruction in the early 1900 was considered quite effective. From this observation, it is assumedthat the Church, at its present (1980) unrehabilitated condition, is about 20% stronger than typical URMbuildings. Effectiveness of the Retrofit Schemes The suggested values of ERE are listed in Table 3-6a, p.T3-14 in FEMA-227 (VSP, 1992). These estimates were based on engineering experience and judgment,assuming that life safety was the principal objective of the retrofit. The ERE of life-safety retrofit fortypical URM buildings are extracted as follows.TABLE 5.5Expected Rehabilitation Effectiveness of Life Safety RetrofitExtracted From Table 3-6a, p. T3-14 of FEMA-227 (VSP, 1992)Building Type Percentage Reductionin Damage (%)Unreinforced Masonry (bearing wall, low rise) 50-30Unreinforced Masonry (load bearing frame, low rise) 40 -2564Chapter 5 Loss EstimateNote that the high end of the range is estimated for Mlvii VI and the low end of the range is forMIvil XII. As the Mlvii level increases, the effectiveness of the retrofits is expected to be lower. Based onthese values, it can be deduced that, on average, the ERE is about50% ÷ 40%= 45% for moderate earthquakes;50%÷30% + 40%+25%J÷2 35% for large earthquakes;30% ÷ 25%= 27% or about 25% for great earthquakes. ERD Factors for the Four Ontions The ER]) factors will be the sum of the reduction due to thepast performance and the adjusted effectiveness of the retrofit The four options are:1. Do Nothing: strengthening the foyer area to support the excessive weight of a new organ. It isconsidered as do nothing in terms of seismic strengthening.2. Life-Safety Option: strengthening the structure to provide sufficient lateral resistance for preventingdeath, serious injury, or entrapment of occupants in a major earthquakes.3. Building Integrity A Option: strengthening the structure not only to ensure life safety, but also tolimit damage to the architectural elements to a level which will require minimal repair and to ensurecontinued operation of the facility after a major earthquake.4. Building Integrity B Option: similar goal as Building Integrity A, except the URM in the Crossingarea has to be removed and reconstructed with reinforced with reinforced concrete.Option 1: Do Nothing. For the existing Church without retrofit, the ER]) factors are assignedaccording to the discussion in Section, the past performance of the Church. A 20% reduction indamages in moderate earthquakes and a 5% reduction in large earthquakes are expected. In greatearthquakes, there will be no reduction expected.65Chapter 5 Loss EstimateOption 2: “Life-Safety” Retrofit The ER]) is the sum of the ER]) of option 1 and the EREdiscussed in Section, i.e.20% +45% = 65% for moderate earthquakes;5% +35% = 40% for large earthquakes;0% + 25% = 25% for great earthquakes.Option 3 & 4: Basically, both option 3 “Building Integrity A” and option 4 “Building Integrity B”are designed to the same level of safety, i.e. the damage to both the structural and architectural elementsshould be minimal and the building should be able to remain functional after a great earthquake.Therefore, a 100% reduction in damage is expected for moderate earthquakes. A 99% is assigned insteadjust to be conservative. The retrofits are expected to perform well even for large earthquakes. The maindifference between the two options is that there is a greater uncertainty in the effectiveness of option 3than the effectiveness of option 4. It is because in option 4, the URM in the Crossing arches has to beremoved and the walls will be reconstructed in reinforced concrete. The uncertainty is reflected in thelower expected effectiveness estimated for option 3 than that for option 4. For option 3, the ER]) isestimated to be 90% for large earthquakes and 80% for great earthquakes. For option 4, the ER]) is 95%for large earthquakes and 90% for great earthquakes. The assessment of these factors are deduced fromthe discussion in the strengthening proposal by H.J. Degenkoib Associates (1990). Summary of ER]) Factors The ER]) factors will be used in Chapter 6 to modify the expecteddamage costs for each intensity level for different retrofit options. For example, the adjusted expecteddamage cost for lvll41 Viii is(1-ERD)xZP(DIVJII)xC,where P(D1 I VIII) is the damage probability and C is the damage cost of damage state D1. Details of theapplication will be explained in Chapter 6. The assessment of ER]) factors in this study is quite66Chapter 5 Loss Estimatesubjective. Better methods of predicting structural behavior will improve the accuracy of the assessmentand thus the result of the analysis. The ERD factors are summarized in Table 5.6 below.TABLE 5.6Expected Reduction in Damage (ERD) of Each Retrofit OptionOption Description Expected Reduction in Damage (%)V-V1 Vil-IX X-Xfl1 DoNothing 20 5 02 Life-Safety 65 40 253 Building Integrity A 99 90 804 Building Integrity B 99 95 905.2 DAMAGE COST ESTIMATEDamage costs can be classified into two categories:1. Direct Costs:Facilities repair and replacement: They are solely related to the physical damages to the structure andits contents. They are usually estimated by joint effort of engineering firms and constructioncompanies.• Deaths and injuries: The estimate depends on the social function and occupancy of the structure, andthe value of life. The methodology provided by ATC-13 is generally adopted as discussed in FEMA174 (Building Systems Development et aL, 1989) and FEMA-227 (VSP, 1992).2. Indirect Costs:• Economic impacts: In general, they are referred to business interruption, unemployment and taximpact. Since the structure of concern is a church, those impacts are less relevant here. One possibleeconomic impact could be the tourist businesses on campus. Since the Church is the symbol ofStanford University and has special architectural elements (namely, the mosaic and the stained glass67ChapterS Loss Estimatewindows), it is the major attraction of the university. If it were damaged, tourist related businesseswould be affected.• Social impacts: For most cases, they are the loss and pain experienced by individuals and thedisruption of the community as a whole. The social impacts are usually intangible, yet substantialand long term. For historic buildings, the historic value of the architectural elements and the culturalimportance represented by the buildings themselves are the main concern. Damages to them areusually irreparable. Interruption to the Church’s normal operations, such as Sunday services,religious activities and weddings, will also cause inconvenient to the community.While researches and statistics provide sufficient information for estimating direct costs, theknowledge on the nature of indirect costs is scarce and assessing monetary values on economic and socialimpacts is veiy difficult. Yet, indirect costs are very significant, especially when historic buildings are ofconcern. Most researchers agree that, in general, indirect costs are at least equal to the direct costs ofrepair and replacement, and they are long term in their effect (Building Systems Development et a!.,1989).5.2.1 Direct Costs: Repair and Replacement CostsThe goal is to restore the Church back to its pre-damage condition but not necessary to upgradethe structure to satis1 current building codes. The damage is referred to the physical damage to thestructure and to the architectural elements. The first step is to establish an inventory list of the elementsof the church. Then, a replacement cost will be estimated. Costs for repairing 50% damages will also beestimated. Finally, a direct cost related to repair or replacement will be assigned for each damage level. Inventory List In order to estimate the repair cost, an inventory of the Church and possibleexpense categories related to each item are developed. The categories are stated in general terms toprovide a basis for evaluating costs of the 50% damage. The inventory and possible expense categoriesare listed in the following.68Chapter 5 Loss EstimateStructural Elements:1. Crossing area• replace / repair dislodged or cracked arch-stones• plaster cracks on veneer on spandrel and ring• repair cracks and spalllng of supporting columns• repair damaged roof elements• basic cost: scaffolding, demolition, temporary protection, hoisting, electrical, etc.2. South & West Transept Galleries• repair damaged railings• patch cracked or damaged balcony floor3. Organ loft balcony• repair damaged railings• patch cracked or damaged balcony floor4. Wall• repair cracks and spalling on concrete walls around the perimeter• repair cracks and spalling on narrow piers in arcade and transepts area• repair cracks and spalling on wall perpendicular to Gallery Stair Towers5. Nave, Channel & Transepts’ roof• repair damaged roof elements• repair wood finishes around roof truss• basic cost6. Round Room• repair or replace damaged unreinforced masonry wall• repair roof parapet• repair damaged roof• basic cost7. Floor69Chapter 5 Loss Estimatepatch cracks and damages due to falling objectsArchitectural Elements:1. Mosaic: repair I replace cracks and dislodged elements of the mosaic on the facade, the interior wallsand the crossing arches;2. Stained glass windows: repair cracks or replace broken portions;3. Stone Cross: repair cracks or reattach if fallen;4. Chandeliers: tighten loosen anchorage, repair if damaged due to falling objects, reattach if fallen;5. Organ: repair damages due to falling objects;6. Marble Altar: repair damages due to falling objects;7. Furniture (e.g. pews): repair damages due to falling objects. Replacement Cost “Replacement” refers to replacing the function of a demolished buildingserved. The replacing structure could be of different construction type as the original one (VSP, 1992). Itis absolutely applicable for URM buildings because URM is not acceptable under current building codes.Even though the construction type will be different, it may still be desirable to reconstruct theChurch according to its original floor plan. The architectural elements could be replaced by replicas toresemble the originals. The replicas do not have to be exactly the same as the originals in aspects such as:workmanship, material and construction method. The mosaic could be replaced by similar painting if thecost of mosaic is out of budget. There is no need to reproduce the decorative elements in an exact mannersince the value of the original is already lost and the loss is irreparable.The typical replacement costs of buildings are listed in Table 3-10, p. T3-21 of FEMA-227 (VSP,1992) (original from Table 4.6, pp. 91 -92 of ATC-13). For churches, the cost is $75, in 1985 dollars, persquare foot of floor space, which is about $62 in 1980 dollars. This cost is too low considering the specialstructure of the original Church. It is assumed that the replacement cost is double of the typicalreplacement cost, i.e. $124 in 1980 dollars. Therefore, for the 28,000-square-foot Memorial Church , thetypical cost is70Chapter 5 Loss Estimate$124 /sqft x 28,000sqft $3,500,000.This cost can be used as the basic replacement cost of the structure. For the architecturalelements such as the mosaic and the stained glass windows, the production cost varied. It depends on thedelicacy of the work required and the available budget. One reasonable estimate is to assume the cost ofproducing the architectural elements equal to the basic cost of the structure, i.e. about $3,500,000. Hence,the replacement cost of the Church is $7,000, Repair Cost For 50% Damages In FEMA-227 (VSP, 1992), the repair cost is defined as theproduct of the central damage factor (CDF) from the Damage Probability Matrix (DPM) and thereplacement value of the building. This method is not applicable for the Church. The main reason is thatrepairing historic buildings with special architectural elements is much more expensive than replacingthem.The difficulties, the excessive time and effort required to repair the damaged wing of the mosaicangels in the restoration following the 1989 Loma Prieta Earthquake are described in different articles(Bartholomew, 1992a; Bone, 1993; Kreysler, 1993). In the preliminary construction cost estimate byDinwiddie Construction (1990), about $350,000 was allocated for repairing and reinforcing the damagedmosaic angel, and $50,000 was allocated for reinforcing each undamaged mosaic angel. The two costs donot include basic cost such as scaffolding and temporary protection which are standard costs in both cases.The difference, $300,000, is the cost of repair which is 6 times of the strengthening cost. Thereplacement cost varies depending on the delicacy of the workmanship and material required but would bemuch less than the repair cost stated above.Although the cost of repair is always more expensive than the cost of replacement, repair is still apriority due to the special historic value of the Church itself Especially for damaged architecturalelements, the originals are expected to be preserved and restored as much as possible. Only if the damageto a particular piece is beyond repairable, replacement could be made for resemblance of the original.The repair cost for each item is estimated based on the preliminary cost estimate by DinwiddieConstruction (1990). The costs given by the report included both damage repair costs, for 10 to 20%71Chapter 5 Loss Estimatedamages, and life-safety strengthening costs. The labor and material costs related to strengthening, thelabor and material costs related to repairing and the basic construction costs are separated for each workcategory. Considerable adjustments in the labor and material costs for repairing are made to account forestimating repair costs for 50% damage in this section. The adjusted labor and material costs for repairare then added to the basic construction costs to give the overall repair costs. The estimated overall repaircosts are then converted back to 1980 dollars by assuming discrete compounding and a discount rate I of4%:Cost(1980$) = Cost(1990$)(1 j)10In the cost estimate (Dinwiddie, 1990), a 20% general conditions fee and a 20% contingencyfund are added to the total of the estimates. Adding a 20% contingency fund is considered redundantwhen calculating expected values and may cause overestimation in the final results. Hence, the 20%contingency fund will be ignored in this project. A summary of the estimated repair cost is in Table 5.7.TABLE 5.7Summary of Estimated Repair Costs For 50% Damage (In 1980 Dollars)Structural Architectural TotalEstimated Repair Cost 4,668,000 12,066,000-20% G.C./Fee 934,000 2,413,000 -Total 5,602,000 14,479,000 20,081,000Cost per square ft 200 517 717Note that the cost of architectural repair is almost three times of the cost of structural repair dueto the special architectural features, i.e. the mosaic, the stained glass windows, etc. Assigning Damage Costs to Damage States The repair cost and replacement cost will be usedas references to estimate damage costs of different damage states. It is assumed that all damages will berepaired each time after an earthquake, regardless of the size of the damages. The following is therationale on assigning damage costs to each state.State 1: Damage Factor: 0%. The associated damage cost is $0.72Chapter 5 Loss EstimateState 2: Damage Factor 0 - 1%, CDF = 0.5%. There will be no structural damage but someminor architectural damages. According to the definition of this damage state, no repair is required. Thedamage cost associated with this state could be $0. However, it is assumed that the minor architecturaldamage is visible and repair is desired. The repair cost will be linearly proportional to the 50%architectural repair cost in Section, i.e.x $14,479,000 = $145,000.50State 3: Damage Factor 1 - 10%, CDF = 5%. Similar to state 2, there will be no structural repaircost but architectural repair cost which is proportional to the 50% case, i.e.$14,479,000 =$1,448,000.50State 4: Damage Factor 10 - 30%, CDF = 20%. The Church suffers moderate damage on bothstructural and architectural elements, and the repair cost is 2/5 of the total cost of the 50% damage case,x $20,081,000 = $8,032,000.State 5: Damage Factor 30 - 60%, CDF = 45%. There will be extensive damage on the structuraland architectural elements. The cost associated with this state is equal to the 50% damage cost discussedin section, despite the difference of 5% to the CDF. Therefore, the damage cost is $20,081,000.In general, for any damage below damage state 5, or damage factor of 60%, the repair costs canbe assumed to vary linearly with respect to the repair costs estimated for 50% structural and/orarchitectural damage estimated.State 6: Damage Factor 60 - 100%, CDF = 80%. According to FEMA-227 (VSP, 1992), if abuilding suffers more than 60% damage, then demolition and replacement will be considered. In thiscase, due to the importance and historic value of the building, this may not be applicable. Repair is still apriority over replacement. The practical concern is whether the damage is repairable. For example, givena 80% damage, the structure may still be repairable at high cost, however, it may be impossible to put thebroken pieces of the mosaic or stained glass windows together again. Therefore, it can be assumed that73Chapter 5 Loss Estimatethe cost is a combination of repair cost of the structural elements and the replacement cost of thearchitectural elements. The costs of repairing structural elements are estimated in the same manner asthat for 50% damage. The repair cost is about $8,074,000. The costs of replacing the architecturalelements will be $3,500,000 according to Section The total damage cost is therefore,$11,574,000.State 7: Damage Factor 100%. This damage suggests totally destruction of the Church. The costrelated to this level is the replacement cost, $7,000,000, discussed in Section following table listed a summary of the damage costs associated with each damage state.The total damage cost increases from damage state 1 to 5 and then decreases. This is mainly due to thechange in architectural damage cost from damage state 5 to damage state 6. In damage state 5, thearchitectural damage cost is associated with repair whereas in damage state 6, the architectural damagecost is associated with replacement.TABLE 5.8Direct Costs: Facilities Repair and ReplacementFor Each Damage State (In 1980 Dollars)Damage Damage CDF Structural Architectural TotalState Factors1 0 0 0 0 02 0 - 1 0.5 0 145,000 145,0003 1 - 10 5 0 1,448,000 1,448,0004 10 - 30 20 2,241,000 5,791,000 8,032,0005 30 - 60 45 5,602,000 14,479,000 20,081,0006 60- 100 80 8,074,000 3,500,000 11,574,0007 100 100 3,500,000 3,500,000 7,000,0005.2.2 Costs of Deaths and InjuriesThe factors involved in estimating the costs of deaths and injuries include: the occupancy rate ofthe building, the expected death and injury rates, and the value of human lives.74Chapter 5 Loss EstimateThe typical number of occupants for buildings with different social functions is listed in Table 3-8, p. T3-19 of FEMA-227 (VSP, 1992) (original from Table 4.12, p.126 - 127 of ATC-13). The typicaloccupancy for religion and non-profit groups is 65 people per 1000 square feet in the day time (3:00 p.m.)and 0 people in the night time (3:00 am). The area of the Church is 28,000 square feet. Therefore,• Number of occupants in the Church in day time:28,000sqft x 65people/l000sqft = l82Opeople.• Number of occupants in the Church in night time is:28,000sqft x Opeoplel l000sqft = Opeople.• Average number of occupants in the Church is:1820 + 02= 9lopeople.Death and injury rates increase with increasing damage states. They also depend on the structuretype and condition of individual buildings. Consensus values of expected death and injury rates for theseven damage states are given in FEMA-227 (VSP, 1992) (original from ATC-13) and listed in Table 5.9.TABLE5.9Expected Death and Injury Rates For Existing Vulnerable BuildingsFrom Table 3-9, p. T3-20 of FEMA-227 (VSP, 1992)(Original from Table 9.3, p 266 of ATC-13)Damage CDF Injury DeathState (%) Minor Serious1 0 0 0 02 0.5 0.000030 0.000004 0.00000 103 5 0.000300 0.000040 0.0000 1004 20 0.003000 0.000400 0.00010005 45 0.030000 0.004000 0.00 100006 80 0.300000 0.040000 0.01000007 100 0.400000 0.400000 0.2000000These rates represent reasonable estimates for vulnerable structure types, such as IJRM buildings,but may be overestimated for less vulnerable structure types, such as ductile steel or ductile concrete framebuildings.(VSP, 1992)75Chapter 5 Loss EstimateThe estimated death and injury rates for rehabilitated buildings are given by FEMA-227 (VSP,1992). These estimates are based on the expected death and injuiy rates given by ATC-13 and adjustedwith engineering experience and judgment. It is assumed that “the strengthening rehabilitation lowers thedeath and injury rates to those that would be expected if the building damage states were three stateslower.”(VSP, 1992) Strengthening programs are expected to reduce the death and injury ratessignificantly since increasing life safety is the prime objective. The expected rates are listed in Table 5.10.TABLE 5.10Expected Death and Injury Rates For Life-Safety Rehabilitated BuildingsFrom Table 3-9, p T3-20 of FEMA-227 (VSP, 1992)Damage CDF Iniury DeathState (%) Minor Serious1 0 0 0 02 0.5 0 0 03 5 0 0 04 20 0 0 05 45 0.000030 0.000004 0.00000106 80 0.000300 0.000040 0.00001007 100 0.003000 0.000400 0.0001000The cost of life used in different studies varies from few thousand dollars to over a hundredmillion. FEMA-174 (Building Systems Development et al., 1989) suggests using the Nuclear RegulatoryCommission’s standard as a reference. The cost of life is estimated to be about $5 million in 1975 dollars(i.e. about $6.1 million in 1980 dollars).FEMA-227 (VSP, 1992) suggests the value ranged from $1.1 million per life (by Dept. ofAgriculture) to $8 million per life (by Enviromnental Protection Agency) in 1990 dollars (i.e. about $0.7million and $5.4 million in 1980 dollars, respectively). Keech (1989), as mentioned in FEMA-227 (VSP,1992), reviewed 25 updated studies for the Federal Aviation Administration and obtained a consensusvalue of $1,740,000 per life in 1989 dollars (i.e. about $1,250,000 in 1980 dollars). FEMA-227 (VSP,1992) adopted this value as the value of life for cost/benefit analysis. The value of life will assumed to be$1,250,000 in 1980 dollars in this project.76Chapter 5 Loss EstimateSo far only the cost of life is discussed. The cost of injury could be greater than the cost of life.It is complicate to estimate and not mentioned in all the documents reviewed. Due to the lack ofinformation in estimating injury cost; it is assumed that the cost of life is the main concern in the costestimates.The expected cost of life for each damage level is calculated by the product of the averagenumber of occupants (i.e. 910 people), the cost per life ($1,250,000 per life in 1980 dollars) and the deathrate (listed in the Table 5.9 and 5.10 above). The result is listed in the following table.TABLE 5.11Expected Cost of Life For Each Damage State(In 1980 Dollars)Damage CDF Existing RehabilitatedState (%) Church Church1 0 0 02 0.5 1,100 03 5 11,000 04 20 114,000 05 45 1,138,000 1,1006 80 11,375,000 11,0007 100 227,500,000 114,000The expected cost of life for the existing church could be assigned as part of the direct costs foroption 1 (Do-Nothing option) and the expected cost of life for rehabilitated church can be assigned as partof the direct costs for option 2 (Life-safety rehabilitation). The expected costs of life related to option 3and 4 are assumed to be minimal since these two retrofit options provide much more strengthening for thestructure than the life-safety requirement does and are expected to eliminated deaths.5.2.3 Indirect CostsIndirect costs refer to costs of economic and social impacts due to earthquake damages. It is hardto estimate, or assign monetary value to, impacts adversely on people or community resulting fromdamages and casualties. The impacts may not be tangible at first but will appear later and endure for a77Chapter 5 Loss Estimatelong period of time. It is hard to estimate the impacts for future events, since it is already difficult enoughto measure them after an earthquake had happened.There is a gap in the knowledge of the overall economic and social consequences of catastrophicearthquakes. Researches were mostly concentrated on geotechnical or engineering aspects. Yet,economic and social impacts are as important as direct losses. (Building Systems Development et aL,1989)Economic impacts are considered minimal here. Damage of the Church may affect touristrelated businesses on campus, such as selling of souvenir items, food courts opened in the summer, etc. Itwill also affect the normal operation of the Church, such as religious activities, weddings, etc. But it willnot affect the number of applicants to the University each year, or the administration of the University.On the other hand, social impacts would be significant if the Church were damaged. The Churchis a memorial to the founder of the University and the centerpiece of the campus. To many people,especially the faculty members, alumni / alumnae and students, it is a symbol of Stanford University.Furthermore, the Church has high values in its architecture and decorative elements. The mosaic wasmade in Venice, Italy and shipped to California. The mosaic facade was the largest in America when itwas built. The original construction cost and the reconstruction cost added up to about $20 million in1980 dollars. The effort and money put into constructing the Church were enormous.FEMA-174 (Building Systems Development et aL, 1989) suggests that gross estimates of indirectcosts should be no less than the direct costs estimated. The essence is that indirect costs are as importantas the direct costs. The direct cost, according to FEMA-227 (VSP, 1992), is calculated by the product ofthe replacement cost and the CDF. It is increasing with the damage factors. The indirect costs shouldalso increase with increasing damages.For historic buildings, like the Church in this project, the direct costs associated with repair andreplacement do not increase with increasing damages. Repair costs for partially damaged historicbuildings are always higher than replacement costs. When damages reach a certain level where repair isimpossible, replacement is needed and the cost drops. In the estimates for direct costs for repair and78Chapter 5 Loss Estimatereplacement, the cost rises from $0 for damage state 1 to $20 million for damage state 5 (CDF=50%) andthen drops from $20 million to $7 million for damage state 7 (CDF=100%).There is no doubt that indirect cost should vaiy in proportion to the damage states. Therelationship could be linear or exponential, depending on individual cases. It is assumed that the indirectcosts vaiy linearly with damage factors in this project. The maximum indirect cost will be equal to thereplacement cost of the Church, i.e. $7,000,000. This is equivalent to the assumption that the price tocompensate the social disruption and psychological trauma caused by the damage is proportional to theprice of reconstructing the structure. The indirect cost is therefore calculated by:IndirectCost = CDF x $7,000,000.The costs is calculated and listed in the following table.TABLE 5.12Indirect Costs (In 1980 Dollars)Damage CDF IndirectState (%) Costs1 0 02 0.5 35,0003 5 350,0004 20 1,400,0005 45 3,150,0006 80 5,600,0007 100 7,000,0005.2.4 Summary of Damage Cost EstimatesDifferent decision makers may have different emphasis on the damage costs. For example,University Financial Officers may have more concern in the direct costs, whereas State RegulatoryOfficials with Board of Education may also consider the indirect costs. An alumni I alumnae who wasmarried in the Church and had children attending Stanford would take the costs of life into account. Inthis study, the interest is to find the best decision considering different combination of cost scenes.79Chapter 5 Loss EstimateFour sets of costs will be used in the decision analysis. They are listed as follows:1. Direct costs (associated with repair and replacement);2. Direct costs plus indirect costs;3. Direct costs with costs of life;4. Direct costs with costs of life plus indirect costThe values in the first two sets are the same for all four retrofit options. The last two sets, i.e.when the costs of life is taken into account, have different values for different retrofit options. Note thatthe costs of life are zero for option 3 and 4 since these two options are intended to eliminated death andprovide for building integrity strengthening. The four data sets are listed in Table 5.13, 5.14 and 5.15 asfollows.TABLE 5.13Case 1: Direct Costsand Case 2: Direct Costs Plus Indirect CostsFor All Retrofit Options (All Costs in 1980 Dollars)Damage State Direct Costs Direct + Indirect Costs1 0 02 145,000 180,0003 1,448,000 1,798,0004 8,032,000 9,432,0005 20,081,000 23,231,0006 11,574,000 17,174,0007 7,000,000 14,000,000TABLE 5.14Case 3: Direct Costs with Costs of Life(All Costs in 1980 Dollars)Damage State Option 1 Option 2 Option 3 & 41 0 0 02 146,000 145,000 145,0003 1,459,000 1,448,000 1,448,0004 8,146,000 8,032,000 8,032,0005 21,219,000 20,082,000 20,081,0006 22,949,000 11,585,000 11,574,0007 234,500,000 7,114,000 7,000,00080Chapter 5 Loss EstimateTABLE 5.15Case 4: Direct Costs with Costs of LifePlus Indirect Costs(All Costs in 1980 Dollars)Damage State Option 1 Option 2 Option 3 & 41 0 0 02 181,000 180,000 180,0003 1,809,000 1,798,000 1,798,0004 9,546,000 9,432,000 9,432,0005 24,369,000 23,232,000 23,231,0006 28,549,000 17,185,000 17,174,0007 241,500,000 14,114,000 14,000,00081Chapter 6 Decision AnalysisCHAPTER 6DECISION ANALYSISThe data developed in the previous chapters will be organized to construct an expected valuedecision model for selecting an optimal retrofit option for the Memorial Church. Net Present Costs (NPC)will be used to rank the four options. The NPC of an option is defined as the sum of the initial investmentand the expected present value of the total damage cost, over the life span of the structure. In this chapter,the calculation of NPCs will be explained and the optimal option will be selected. The accumulativeexpense from 1980 to 1990 will be estimated assuming the optimal option was adopted in 1980. Theprojected expense will then be compared with the actual accumulative expense to examine the difference.6.1 DEFINITION OF VAREABLES• NPC: Net Present Cost of a retrofit option.• INV: Initial inVesment of the retrofit option in present value which is established in Chapter 3.• PTD: Present value of the Total Damage cost which is the sum of the damage cost expected to accrueeach year over the life span of the structure corresponding to each retrofit option.• AED: Annual Expected Damage cost corresponding to each retrofit option.• TCF: Time Conversion Factor which converts the damage cost accrue each year over the life span toa lump sum in present value.• EDC: Expected value of the Damage Cost corresponding to a retrofit option. This is the weightedaverage of the average damage cost associated with each earthquake intensity level.82Chapter 6 Decision Analysis• F, (I V): Probability of Occurrence of one or more earthquakes with intensity equals to or greaterthan MN’ll level V in one year, see Section 4.4.• P(11): Probability of earthquake with intensity level if an earthquake with intensity equals to orgreater than level V occurs, see Table 4.4, Section 4.4.• ADC: Average Damage Cost corresponding to each earthquake intensity level. This is the weightedaverage of the damage cost associated with each damage state given an earthquake intensity level andadjusted by the expected reduction in damage factors.• ERD: Expected Reduction in Damage Factor, assigned according to the past performance of theChurch and the effectiveness of each retrofit options. They are defined in Chapter 5.• P(D1 J): Probability of the structure suffering damage state D when an earthquake with intensityIj occurs. These probabilities are obtained from the Damage Probability Matrix in Table 5.3.• C: Damage Cost at damage state D which are defined in Chapter 5.6.2 DECISION TREEThe decision can be best visualized by organizing all the elements of concern into a form of adecision tree. The first group of branches indicate the available alternatives, namely the proposed retrofitschemes and the initial investment costs. Following the alternatives are the possible future eventscontrolled by nature, that is, the earthquake levels and the probability associated with each MMI level. Inthis study, earthquake intensities lower than MMI V are ignored since damages related to these levels areusually minimal. For each MMI level, there is a group of possible outcomes, i.e., the damage states. Theprobability and cost associated with each damage state are assigned accordingly. See Figure 6.1 for anoverview of the elements involved in the decision.83Chapter 6 Decision AnalysisFIGURE 6.1 Decision TreeClc2C3C4CsC6C7IW2NV31NV4Investmentof each OptionEarthquakeProbabilitiesDamage Pmbability Damageof each Damage State Costsat each Mlvii level84Chapter 6 Decision Analysis6.3 INITL4L INVESTMENT OF RETROFIT OPTIONS (INV)The retrofit options and the initial investment required for each option are discussed in Chapter3. A summary is listed in Table 6.1.TABLE 6.1Retrofit Options and Investment CostsOption Description 1NV (in 1 980$)1. Do Nothing Add new structural system to support the weight of the 1,961,000new organ and install the new organ.2. Life-Safety In additional to the Do Nothing option, seismic 3,502,000Strengthening strengthening the Church to meet life-safety standards.3. Building Seismic strengthening the Church to not only protect 5,577,000Integrity A occupants but also to prevent major damage tostructural and architectural elements.4. Building Same objective as option 3, with removal of URM and 11,193,000Integrity B reconstruction of the Crossing area with reinforcedconcrete.6.4 TIME CONVERSION FACTOR (TCF)If the annual expected damage (AED) costs are different for each year within the life span of thestructure, then the present value of the total damage cost (PTD) can be calculated by the followingequation:PTD= AED1 + AED2 + + AEDT (6.1)(1+1) (1+1)2 (1+)Twhere i is the discount rate and T is the planning horizon or the life span of the structure. Each year’sdamage cost is discounted to its present value and then added together to yield the present value of thetotal expected damage cost.85Chapter 6 Decision AnalysisIf the annual expected damage cost is assumed to be constant each year, then the equation abovecan be simplffied asPTD=AEDxTCF (6.2)where1 (l+._TTCF= “ (6.3)as suggested by FEMA-227 (VSP, 1992). Assuming the annual expected damage cost constant eveiy yearis equivalent to assuming that the annual probabilities of future earthquakes of various intensities areconstant and that the effectiveness of the rehabilitation in reducing casualties, damages and losses is alsoconstant.The annual probabilities of future earthquakes, in fact, vaiy depending on the preceding seismicevents. “The probability of an earthquake along a fault segment is initially low following a large segmentrupturing earthquake and increases with time as stress on the segment recovers the stress drop of the priorehquake.” (Working Group On California Earthquake Probabilities, 1990) The effect of the variation isquite obvious in the short term. However, in the long term, the effect of the variation would be averagedout. Furthermore, the probabilities adopted in this project are based on historic records and they areintended to be used for long term estimates. The assumption is therefore considered valid.The effectiveness of the retrofit and the performance of the structure can be considered asconstant throughout the life of the structure if the building is properly maintained. As time goes by, theconcrete will get stronger and the rebars will stay the same as long as they are not rusted.6.4.1 Life Span TIn general, for ordinary buildings, the life span or the length of the planning horizon is usuallytaken as 30 to 50 years (VSP, 1992). Due to the importance of this Church, a life span of 100 years isused.86Chapter 6 Decision Analysis6.4.2 Discount Rate IIn simple terms, the discount rate I is the real interest rate, that is the bank interest rate minus theinflation rate. There are many different ways and divergent opinions on deriving or choosing anappropriate discount rate for benefit-cost analysis. The selection of discount rate I is discussed in Section3.4C, p.3-19 of FEMA-227 (VSP, 1992). Three general approaches are list as follows:1. Cost of Capital Approach: The cost of capital or the government long term borrowing rate are usedas discount rate. The rate is not adjusted for inflation. The suggested discount rate in 1981 is 10%.2. Market Failure with Social Time Preference Approach: The discount rate is calculated by subtractingthe interest rate (r ) by the percent change in GNP implicit price deflator (dp, which is the annualrate of inflation). Both terms are averaged from the observed data of the past 3 years and theforecasted data of the future 17 years with respect to the year of concern. The Social Time Preferencediscount rate can be formulated as follows:rt dp= t1 — (6.4)20 20The calculated rate for 1986, by Young and Howe (1988) (as quoted in VSP, 1992), for public sectorswas 3% using the return on the municipal bonds, and for private investments was 6.5% using thereturn on corporate bonds instead.3. Market Failure with Social Opportunity Cost Approach: The discount rate is based on the banks’prime lending rate with adjustment for the rate of inflation and for the corporate income tax. Thediscount rate suggested by this approach is 3% for 1981.Assume that Stanford is borrowing funds from the bank to finance the rehabilitation project andfuture damage repairs. The cost of the funds is the bank rate. Since the funds will be paid back ininflated dollars in the future, the real discount rate of the fund is the bank rate minus the inflation rate.Therefore, approaches 2 and 3 are considered appropriate for calculating the discount rate.87Chapter 6 Decision AnalysisIn general, a discount rate of 3% or 4% is considered reasonable for public sectors and slightlyhigher rates, 4% to 6 % are reasonable for private sectors (VSP, 1992).For this study, the discount rate is assumed to be 4% in 1980. Using I = 4% and T = 100 years,TCF = 24.505. If a lower discount rate I is used, the value of TCF will be higher. The correspondingPTD becomes higher which will yield a more conservative estimates of the future damage cost.6.5 CALCULATION OF NET PRESENT COSTS (NPC)The calculation of the NPC for each option starts from the right end of the decision tree andprogress to the left side. The steps are listed in the following.The expected value of the damage cost at intensity level Ij is the sum of the products of theconditional probabilities from the DPM, P(D1 /Ij). and the damage costs C1 of the damage states. The setof probabilities is mutually exclusive and exhaustive. These are the data on the third and fourth columnon the decision tree. The sum is then adjusted by the ERI) factors to take into account the pastperformance of the Church and the expected effectiveness of the retrofit The ERD factors are different atdifferent intensity levels for each retrofit scheme. The adjusted expected damage cost is called the averagedamage cost, ADC, for intensity level as shown in Eqn. (6.5) below:(6.5)The ADC(Jj) is then brought to the end of the second column on the decision tree and multipliedby the earthquake probability, P(Jj) at the same intensity level. The set of earthquake probabilities ismutually exclusive and exhaustive. The expected value of the damage cost, EDC, corresponds to a retrofitoption is then calculated by adding the products of the ADCs and the earthquake probabilities:EDC = P(I1)xADC(11) (6.6)88Chapter 6 Decision AnalysisThe EDC is converted to annual expected damage cost, AED, by multiplying by the annualprobability of occurrence of earthquake greater than MIvil V. i.e. P, (I V)as shown in Eqn. (6.7):AED=EDCxP,(IV) (6.7)The AED is the expected damaged cost that would accrue each year over the life span of thestructure corresponding to a retrofit scheme. As discussed in Section 6.4, the present value of the totaldamage cost, PTD, can be calculated by multiplying the AED by a time conversion factor, TCF, as shownin the following equation:PTD = AED x TCF (6.8).The net present cost, NPC, of a retrofit scheme can then be calculated by:NPC=INV+PTD (6.9)where INV is the initial investment.6.6 RESULTSAs mentioned in Chapter 5, different decision makers may have different emphasis on the costscenes. In order to find the best decision considering different combination of costs, four sets of damagecosts are used:1. Direct costs (associated with repair and replacement);2. Direct costs plus indirect costs;3. Direct costs with cost of life;4. Direct costs with cost of life plus indirect costs.The results of the calculation are shown in Table 6.2. The table also indicates the initialinvestment for each option (extracted from Table 6.1).89Chapter 6 Decision AnalysisTABLE 6.2Results of Decision Analysis(All Cost in 1980 Dollars)Option 1, do nothing option, has the highest NPC. It indicates that by doing nothing in presenttime may result in tremendous expenses on repairing earthquake damages in the future. The differencebetween the NPC of option 2, life-safety retrofit, and the NPC of option 4, building-integrity B, areconsiderably large. This suggests that the high INV of option 4 is justified in reducing the threat ofearthquake damages and the hassle of damage repair in the future if there is only option 2 and option 4available. However, when comparing to the NPC of option 3, the high 1NV of option 4 soundsuneconomical. The NPC of option 3 is about 2/3 of that of option 4. Therefore, the decision analysisrecommended option 3, the building integrity A option, as the optimal option among the four options.Note that the outcome and the ranking of the decision is not affected by the addition of the costsof life and the indirect costs. The NPCs are not increased significantly when the costs of life or indirectcosts are taken into account in the calculation. The two costs are significant in high damage states, whichare associated with high Mlvii levels. In calculating the expected values, the influence of the two costs arereduced by multiplying with the small probabilities of high Mlvii levels.Furthermore, adding the cost of life and indirect costs just further increases the gap between theNPCs of the first two options (option 1 and 2) and the last two options (option 3 and 4). This could be dueto the big differences between the expected reduction in damage of the two groups. In this decisionanalysis, the direct costs associated with repair and replacement dominate the outcome of the decision.The indirect costs and the cost life are not as important and influential as anticipated.Option 1 Option 2 Option 3 Option 41NV 1,961,000 3,502,000 5,577,000 11,193,000Case Net Present Costs (Followed by Ranicing)1 26,208,000 4 18,120,000 3 8,316,000 1 12,381,000 22 31,210,000 4 21,129,000 3 8,799,000 1 12,630,000 23 29,465,000 4 18,122,000 3 8,316,000 1 12,381,000 24 34,466,000 4 21,131,000 3 8,799,000 1 12,630,000 290Chapter 6 Decision Analysis6.7 COST COMPARISONIn this section, the accumulative expense of two scenarios will be compared. The first case is theactual case, i.e. what was really done to the Church from 1980 to 1990. The second case is the proposalby the decision analysis, i.e. doing seismic strengthening option 3 in 1980 during the organ installation.TABLE 6.3The Description of the Two CasesCase 1 Case 2Year Actual Case Decision Analysis Suggestion1980 Organ installation, structural Organ installation, structuralupgrade in foyer area. upgrade in foyer area, buildingintegrity seismic strengthening(option 3).1985 Roof repair. No repair necessary.1990 after Repair and building integrity Repair small damages associatedLoma Prieta seismic strengthening. with MIvil VIII.Earthquake(Mtvll VIII)The accumulative expense of each scenario is expressed in 1990 dollars. The conversion is doneby assuming a discrete compounding and a discount rate I of 4%. The conversion for case 1 is listed inTable 6.4.TABLE 6.4Accumulative Expense from 1980 to 1990 of Case 1: Actual CaseYear Work Cost multiplied Cost inby 1990$1980 Organ installation, structural 1,961,000 ( 1 + I )‘ 2,903,000upgrade in foyer area.1985 Roof repair. 1,750,000 ( 1 + I )5 2,129,0001990 after Repair and building integrity 8,500,000 1 8,500,000Earthquake seismic strengthening.Total Expense: 13,532,00091Chapter 6 Decision AnalysisIf retrofit option 3 were done in 1980, the repair cost for damages in the Loma Prieta earthquakewould be estimated as follows. The first step is to select the MDF from the DPM in Table 5.3. The MDFis about 20% at Ivilvil VIII. The ERD factor for option 3 in large earthquakes is 90% in Table 5.6. Theexpected damage will be:(1—0.90)x20% =2%and the associated damage cost is about-_x$14,479,000=$579,000 (in 1980 dollars).The high cost of repair for even low damage percentage, is mainly due to the delicacy of the architecturalelements, mainly refers to the mosaic. Strengthening the four mosaic angels was on the strengtheningscheme, yet the others around the interior walls and on the facade were not completely included.Therefore, there is still a chance that the mosaic would be damaged in a major earthquake. The projectedaccumulative expense of adopting retrofit option 3 in 1980 is calculated in the following table.TABLE 6.5Accumulative Expense from 1980 to 1990 of Case 2: Decision Analysis SuggestionYear Work Cost multiplied Cost inby 1990$1980 Organ installation, structural 5,577,000 ( 1 + j )10 8,255,000upgrade in foyer area, buildingintegrity seismic strengthening(option 3).1985 No roof repair necessary. 0 0 01990 after Repair small damages. 579,000 (1 + I )10 857,000EarthquakeTotal Expense: 9,112,000Compare the accumulative expenses of the two cases,$13,532,000 -$9,112,000 = $4,420,000 (in 1990 dollars).If the 2% damage in the Loma Prieta Earthquake does not require repair,$13,532,000 - $8,255,000 = $5,277,000 (in 1990 dollars).Hence, by doing the building integrity seismic strengthening during the organ installation in1980, about $4.4 million (in 1990 dollars) would have been saved by 1990. There is a very high92Chapter 6 Decision Analysislikelihood that the minor damages to the Church in the 1989 Loma Prieta Earthquake would not requirerepair if the strengthening was done in 1980. Therefore, the saving is very likely to be close to $5.3million (in 1990 dollars) which is about 40% of the accumulative expense of the actual case.The short term saving of $5.3 is mainly due to the occurrence of the Loma Prieta earthquakewithin the 10 years time frame. According to the decision model, considering a life span of 10 years from1980, the expected future damage cost of option 1 is about $11.8 million whereas the expected futuredamage cost of option 3 is only $1.3 million. The estimated difference is about $10.5 million in the shortterm. Considering a 100-year life span, the difference in the expected future damage cost will be evengreater. The expected future damage cost of option 1 is about $35.8 million whereas that of option 3 is $4million. The difference would be $31.8 million in the long run. (All costs in 1990 dollars)93Chapter 7 Sensitivity AnalysisCHAPTER 7SENSITIVITY ANALYSISThe objective of this chapter is to detect the sensitivity of the outcome of the decision to thevariation in the input data. Since the input data used in the analysis are mainly estimated and involvemany uncertainties, it is important to find out if the outcome is sensitive to the accuracy of the input. Themajor input data include:1. Seismic Data;2. ER]) (Expected Reduction in Damage) Factors;3. Damage Costs;4. Time Conversion Factor: Discount Rate and Life Span.In the sensitivity analysis, each set of data will be varied within reasonable ranges. Therelationship between the changes in data and the outcome of the decision will be examined. The outcomeof the decision refers to the optimal option selected based on the lowest net present cost (NPC). Theranking of the options is also concerned. When appropriate, the changes in the values of the NPC of eachoption will also be studied.7.1 SEISMIC DATAThe earthquake probabilities derived in Chapter 4 are based on the annual occurrence rates givenby Algermissen et aL (1980). These rates could be overestimated or underestimated for the site asdiscussed in Section 4.6. It is assumed that the accuracy is within ±25% of the data. In order to examinethe effect of the accuracy of annual occurrence rates, the annual occurrence rate of each MMT level will be94Chapter 7 Sensitivity Analysisvaried by ±25% each time. For example, the annual occurrence rate of MtvII V is reduced by 25% in thefirst set of data and increased by 25% in the second set of data as shown in Table 7.1.TABLE 7.1Example of Data Set 1 & 2Varying Annual Occurrence Rate of MMI V By ±25%Mvil Original Set 1 Set 2V 1.97 1.4775 2.4625VI 0.74 0.74 0.74VII 0.281 0.281 0.281VIII 0.106 0.106 0.106IX 0.040 0.040 0.040X 0.015 0.015 0.015XI 0.0057 0.0057 0.0057XII 0.0021 0.0021 0.0021Note that since only one rate is varied at a time, there are in total 16 sets of data tested. Thechanges in the 16 data sets are summarized in the Table 7.2.TABLE 7.2Data Sets for Variation inAnnual Occurrence Rate of Each MN4I LevelData Set MIvil level Changes Substitute Value1 V -25% 1.47752 V +25% 2.46253 VI -25% 0.5554 VI +25% 0.9255 VII -25% 0.210756 VII +25% 0.351257 VIII -25% 0.07958 VIII +25% 0. 13259 IX -25% 0.03010 IX +25% 0.05011 X -25% 0.0112512 X +25% 0.0187513 XI -25% 0.00427514 Xl +25% 0.00712515 XLI -25% 0.00157516 XII +25% 0.002625The NPCs calculated by using these 16 sets of data are obtained and listed in Table 7.3. Thepercentage change from the original NPCs is calculated to compare the influence of the accuracy of each95$1 1kz 00<%C)00CD0 CD rJ) CD I 1.000-I t.)(-b) C .zoac00000O0).0.-.JaUiUi000.‘00CUi.Ui.0000III•I-I--———-I-000000000000-0000-000s000CDI—00..00-.Ui‘.000‘.01Ui‘.0—)-..UiC’.t)00000‘.0-c..000.C’‘-o 0-c3cc0000000000000000000000000000000000i-.....—oa0Ui0o-—I-s-——II————————!a.I-•-I-’I-—III00-.‘.0.C)Ui0.1t.)(.60’,00Ui-Ui-.1CCt’.)‘.00’,00-.‘.0-t%)t’.).)Chapter 7 Sensitivity AnalysisAs observed from Table 7.3, the outcome of the decision remains unchanged, option 3 is theoptimal option with the lowest NPC in all the trials. The ranking is also unchanged, option 3 followed byoption 4, option 2 and 1. Changing the annual occurrence rates does not affect the values of the NPCs ofthe four options significantly.The percentage changes of set 1 and 2 reflect the influence of the annual occurrence rate of MMJV, the percentage changes of set 3 and 4 reflect the influence of the annual occurrence rate of Mlvii VI,and so on. The percentage changes of set 1 & 2 are the greatest among all data sets in Table 7.4. It issuggested that the accuracy of the annual occurrence rate of Mlvii V has, relative to other MMI levels, thegreatest influence on the NPCs. The percentage changes of set 5 & 6, 7 & 8 and 9 & 10 are quite obviousin comparison to other data sets. Hence, the accuracy of the annual occurrence rates of MMI VII, VIIIand IX have moderate effects on the NPCs whereas the other levels have minimal effects.In general, the percentage changes in Table 7.4 are considered small. The maximum is only14% whereas most are less than 5%. It can be concluded that the values of the NPCs are not sensitive tothe changes, within ±25%, in the annual occurrence rates. The outcome of the decision is also insensitiveto the changes in the annual occurrence rates.7.2 ER]) FACTORSThe original ERD factors assigned in this project are listed in the following table.TABLE 7.5The Original ER]) FactorsMilOption V-VI Vil-IX X-XII1 20 5 02 65 40 253 99 90 804 99 95 9097Chapter 7 Sensitivity AnalysisThe ER]) factors are assigned mainly based on engineering knowledge and judgment. Theassessment is subjective and could be quite different when assigned by different people. It is assumed thatdifferent assessments could be made ±25% around the original estimates. The ERD factors of each optionwill be varied by ±25% at a time for sensitivity analysis.Note that it is not necessary to vary the whole set together since it will just change all the NPCsproportionally, which will yield the same outcome as before. Also note that changes in the ERD factors ofoption 1 will also cause changes in the ER]) factors of option 2 since the ERI) factors of option 2 aredependent on that of option 1 (see derivation in Section The changes in the ER]) factors in eachset of data are listed in the following table.TABLE 7.6Data Sets for Variationin ER]) Factors of Each Retrofit OptionData Set Options Changes Substitute ER]) FactorsV-V1 Vil-IX X-Xll1 Optioni -25% 15 4 0(Option 2) (same amount) 60 39 252 Optioni +25% 25 6 0(Option 2) (same amount) 70 41 253 Option 2 -25% 49 30 194 Option 2 +25% 81 50 315 Option 3 -25% 74 68 606 Option 3 +25% 100 100 1007 Option 4 -25% 74 71 688 Option 4 +25% 100 100 100In Set 6 and 7, the ER]) factors of option 3 are higher than the ERD factors of option 4. This isin contradiction to the definition of the retrofit schemes: option 4 is supposed to provide more safety forthe structure than option 3. In option 4 all the unreinforced masonry walls have to be removed and rebuiltwith reinforced concrete but in option 3 the unreinforced masonry walls will be strengthened. Theexpected performance of the structure by adopting option 4 should always be better than that of option 3.Hence, these two data sets will be ignored. The resulted NPCs of each set are listed as follows.98Chapter 7 Sensitivity AnalysisTABLE 7.7Net Present Costs By Varying the ER]) Factors of Each Retrofit Option(All Costs in Thousand and in 1980 Values)______Net Present Costs (Followed by Ranking)Data Set Option 1_ Option 2_ Option 3_ Option 4_1 26,746 4 18,657 3 8,316 1 12,381 22 25,671 4 17,583 3 8,316 1 12,381 23 26,208 4 21,065 3 8,316 1 12,381 24 26,208 4 15,175 3 8,316 1 12,381 25 26,208 4 18,120 3 14,337 2 12,381 18 26,208 4 18,120 3 8,316 1 11,193 2As observed from data sets 1 to 4, changing the ER]) factors of option 1 and option 2 by ±25%does not affect the outcome and the ranking of the decision. Option 3 still has the lowest NPC, followedby option 4, option 2 and then option 1. This is mainly due to the large differences in the NPCs betweenoption 1 & 2 and option 3 & 4.In data set 5, the ER]) factors of option 3 are reduced by 25%, which leads to a change in theoutcome of the decision. The NPC of option 3 becomes higher than that of option 4. Hence, option 4becomes the optimal option.On the other hand, in data set 8, increasing the ER]) factors of option 4 to 100% for all Mlviilevels does not change the outcome. This suggests that even if there is no future earthquake damage byadopting retrofit option 4, the initial investment of option 4 is still more expensive than the sum of theinitial investment and the present value of the future damage costs of option 3.Further investigations were made on the effect on NPCs of changing the ER]) factors of option 3and option 4. The results are listed in the following table.TABLE 7.8Net Present Costs of Option 3 by Using Different ER]) Factors(All Costs in Thousand and in 1980 Values)Data Set ER]) Factors (%) NPC ($)V-v1 Vil-Ix x-xIINo Damage 100 100 100 6,004Original 99 90 80 8,316-10% 89 81 72 10,725-15% 84 77 68 11,929-20% 79 72 64 13,133-25% 74 68 60 14,33799Chapter 7 Sensitivity AnalysisTable 7.9Net Present Costs of Option 4 by Using Different ER]) Factors(All Costs in Thousand and in 1980 Values)Data Set ER]) Factors (%) NPC ($)V-VT Vil-IX X-XllNoDaxnage 100 100 100 11,193Original 99 95 90 12,381-10% 89 86 81 14,902-15% 84 81 77 16,162-20% 79 76 72 17,423-25% 74 71 68 18,683When the ER]) factors of option 3 are reduced by more than 20%, its NPC will exceed theoriginal NPC of option 4. Option 4 will become the optimal option. Option 4 will always have a chanceto become the optimal option if its ER]) factors are not reduced by more than 10% from the originalestimates. The outcome depends on the ER]) factors of both option 3 and option 4. It can be concludedthat the outcome of the decision is sensitive to the changes in the ER]) factors of option 3 and option 4,but not sensitive to the changes in the ER]) flictors of option 1 and option 2.7.3 DAMAGE COSTS7.3.1 Direct CostsDirect costs refer to the repair costs of the physical damages to the structure and its contents.The costs can usually be estimated quite accurately by professionals. There may be some deviation, but itis expected that the accuracy is within ±20%.Two sets of direct costs are used. Set 1 is the original reduced by 20% and set 2 is the originalincreased by 20%. The values are listed in Table 7.10 and the results are listed in Table 7.11.100Chapter 7 Sensitivity AnalysisTABLE 7.10Data Sets for Direct Costs(AU Costs in Thousand and in 1980 Value)Damage States Original Set 1 Set 21 0 0 02 145 116 1743 1448 1158 17384 8032 6426 96385 20081 16065 240976 11574 9259 138897 7000 5600 8400TABLE 7.11Net Present Costs By Using Different Direct Costs(All Costs in Thousand and in 1980 Values)Net Present Costs (Followed by Ranking)Data Set Option 1 Option 2 Option 3 Option 4Original 26,208 4 18,120 3 8,316 1 12,380 21 21,357 4 15,196 3 7,854 1 12,143 22 31,059 4 21,044 3 8,779 1 12,618 2The NPCs of option 3 remains the lowest, followed by option 4, option 2 and option 1. Thechanges in the direct costs have less effect on the NPCs of option 3 and 4 than on the NPCs of option 1and 2. The changes in the NPCs of option 3 and 4 are about ±6% and ±2%, respectively. The changes inthe NPCs of option 1 and 2 are about ±19% and ±16%, respectively.Each damage state represents a range of damage factors but only one damage cost is assignedbased on the central damage factor (CDF) for each damage state. For example, the CDF for damage state4 is 20% whereas the damage factors of this damage state ranged from 10% to 30%. The actual damagecost could vaiy substantially within a defined state. It is assumed that the variation is ±50% around theoriginal estimate. The damage cost of each individual damage state will be varied at a time to examinethe effect on the NPCs.The data set is listed in Table 7.12 and the results are listed in Table 7.13.101C-)0000CD D)CDgCD-00 CD•8CD—.CDOCDI0 SC-0Ic,)C)CD .(-)-CD g•0—0CD—- I—0000<tTl ciI0 So —.0 ‘0 00 CD- CD I C, 0 I0 j.)‘(.)00‘0t300‘0—a‘—a.0CJ00‘00‘000.(i00o-z-—.I-.L’-)—3I—1.000000-0UU‘0C000000‘—U‘00t300CD‘0‘000Ji0’00‘000.U000000o-—0 0000000000-00—0000000000-‘00000.—.)J0—0C..)O—‘0.0-—-———I-I--)-I--—•-—-‘C-C--1C-——C-CC-C-—t.-t•-)t-t-t-)sv i-a’..C-C..)00-C..00-t-)C..)—a‘000—00C.)00.00OC’.C..)‘00C.)‘00o———‘Jt—.)t-)t-.)t-)t’)tt’.)%C00C..)-’C,) gC,)—)—)C’.C’.CJU..C.)..))C•Cfl000000000000c U)<I-C-C.)-.—.—CJC00.-3CD00C’.00.)C-.-)0CC-00C,)CD Cl) IChapter 7 Sensitivity AnalysisTABLE 7.14The Percentage Changes From the Original NPCsDue to Changes in Damage Cost of Each Damage StateData Set Option 1 Option 2 Option 3 Option 41 -0.6 -0.4 -0.0 -0.02 0.6 0.4 0.0 0.03 -13.2 -9.6 -1.8 -0.74 13.2 9.6 1.8 0.75 -17.5 -16.0 -5.8 -2.06 17.5 16.0 5.8 2.07 -12.6 -12.0 -4.9 -1.78 12.6 11.9 4.9 1.79 -2.2 -2.3 -1.3 -0.410 2.2 2.3 1.36 0.411 -0.1 -0.1 -0.0 -0.012 0.1 0.1 0.1 0.0Comparing the percentage changes listed in Table 7.14, the data set 5 and 6 have the greatestchanges, followed by set 3 and 4 and set 7 and 8. In data set 5 and 6, the direct cost of damage state 4 arechanged by ±50%. It suggests that the direct cost of this damage state (damage factors range from 10 to30%, CDF is 20%) has a relatively great effect on the NPCs. Similarly, the direct costs of damage state 3(damage factors range from 1 to 10%, CDF is 5%) and damage state 5 (damage factors range from 30 to60%, CDF is 45%) also affect the NPCs. The effect of changing the direct costs of the other damagestates are considered minimal, especially for damage state 7. The percentage changes of data set 11 & 12almost equal to zero for all options.This study suggests that, in estimating the damage costs, more attention should be paid to theaccuracy of the direct costs of damage states 3, 4 and 5, i.e. damage factors 1-10%, 10-30% and 30-60%.Among these three states, damage state 4 is the most important one. On the other hand, the accuracy ofthe direct cost of damage state 7, i.e. the replacement cost, is the least important one.103Chapter 7 Sensitivity Analysis7.3.2 Indirect CostsIndirect costs refers to costs of economic and social impacts due to earthquake damages. There isno particular rules for assigning indirect costs. In Chapter 5, it is assumed that the indirect cost is theproduct of the central damage factor (CDF) and the replacement cost. In the sensitivity analysis, threesets of indirect costs will be used. The indirect costs in data set 1 are the original indirect costs increasedby 50%, in set 2 are the original indirect costs increased by 100% and in set 3 are equal to the originaldirect costs. The values are listed in Table 7.15 and the results are listed in Table 7.16.TABLE 7.15Data Sets of Indirect Costs(All Costs in Thousand and in 1980 Values)Damage States Original Set 1 Set 2 Set 31 0 0 0 02 35 53 70 1453 350 525 700 14484 1400 2100 2800 80325 3150 4725 6300 200816 5600 8400 11200 115747 7000 10500 1400 7000TABLE 7.16Net Present Costs By Using Different Indirect Costs(All Costs in Thousand and in 1980 Values)Net Present Costs (Followed by Ranking)Data Set Option 1 Option 2 Option 3 Option 41 33,712 4 22,634 3 9,041 1 12,754 22 36,211 4 24,138 3 9,282 1 12,879 23 50,456 4 32,738 3 10,629 1 13,569 2The outcome and the ranking of the decision remain unchanged when the indirect costs areincreased by 50%, 100% or even equal the direct costs. Option 3 still has the lowest NPC. This suggeststhat the indirect costs may not be as important and influential as expected in the decision maldng.104Chapter 7 Sensitivity Analysis7.4 TIME CONVERSION FACTORS: DISCOUNT RATE AND LIFE SPAN7.4.1 Discount RateThere are different approaches in estimating discount rates, as discussed in Chapter 6. Thepossible values of discount rate range from 3 to 10%. Four discount rates will be used: 4%, 6%, 8% and10%.TABLE 7.17Effect of Discount Rate on the Net Present Costs(All Costs in Thousand and in 1980 Values)Net Present Costs (Followed by Ranking)Discount TCF Option 1 Option 2 Option 3 Option 4Rate0.04 24.5 26,208 4 18,120 3 8,316 1 12,380 20.06 --16.6 18,404 4 13,415 3 7,572 1 11,999 20.08 12.5 14,324 4 10,955 2 7,183 1 11,799 30.10 10.0 11,855 4 9,467 2 6,948 1 11,678 3As discount rate increases, the PTD (present value of the total damage costs) decreases andhence, the NPC decreases. Option 3 has the lowest NPC in all cases. The ranking of option 2 and option4 are switched when the discount rate exceeds 8%. Note that the NPCs of option 1 and option 4 are veiyclose when the discount rate reaches 10%. This suggests that when the discount rate is high, the decisionwill shift to less expensive and less safe options because money spent in the future costs less in the presenttime. Eagerness to invest decreases, and willingness to take the risk of paying future damage costincreases. Using a lower discount rate is considered more conservative, since it amplifies the presentvalues of the future costs.The discount rates commonly recommended are around 3 to 6%. Discount rates of 8% and 10%are uncommon. If the discount rate only varied within the 3 to 6% range, the outcome and the ranking ofthe decision will remain the same.105Chapter 7 Sensitivity Analysis7.4.2 Life SyanThree different life spans will be used: 100, 50 and 30 years. For ordinaiy buildings, a 30-year or50-year life span is sufficient but for historic buildings, a life span of 100 years is usually recommended.TABLE 7.18Effect of Life Span on the Net Present Costs(All Costs in Thousand and in 1980 Values)_______Net Present Costs (Followed by Ranking)Life Span TCF Option 1 Option 2 Option 3_ Option 4100 24.5 26,208 4 18,120 3 8,316 1 12,380 250 21.5 23,217 4 16,317 3 8,031 1 12,234 230 17.3 19,071 4 13,717 3 7,636 1 12,031 2As life span shortens, the P11) decreases and hence the NPC decreases. However, the reductiondoes not affect the outcome and the ranking of the decision. Option 3 still has the lowest NPC, followedby option 4, option 2 and option 1. The present value of the total damage costs that accrued between year30 to year 100 is quite small in comparison to the present value of the total damage costs that accruedbetween year 1 to year 30. Changing the life span from 100 to 30 years will not reduce the PTDsignificantly. Hence, it can be concluded that the outcome of the decision is insensitive to the changes inthe life span.7.5 CONCLUSION OF SENSITWITY ANALYSISSeismic DataThe outcome and the ranking of the decision are insensitive to the annual occurrence ratesvarying within ±25% of the original data. Hence, an accuracy of 25% is considered sufficient for thisdecision analysis. Among different MIvil levels, the annual occurrence rate of Mlvii V has the greatest106Chapter 7 Sensitivity Analysisinfluence on the NPCs. The annual occurrence rates of Mlvii VII, VIII and IX also affect the NPCsslightly whereas those of Mlvii X and above have minimal effects. if higher accuracy in the outcome isneeded, more attention should be paid on the estimation of annual occurrence rates of Mlvii V to IX thanthose of Mlvii X and above. This suggests that the seismic data of moderate (MMI V - Vi) and large(MMI VII- IX) earthquakes are more important and influential than the seismic data of great (MMI X -XII) earthquakes.ERD FactorsThe outcome of the decision is sensitive to the changes in the ER]) factors of both option 3 andoption 4 but not sensitive to the changes in the ERD factors of option 1 and option 2. There are manypossible combinations of ER]) factors to be assigned for option 3 and option 4. Guidelines for estimatingeffectiveness of retrofits and better methods for predicting structural behavior are needed to improve theaccuracy of the assessment. It is also recommended that consensus opinion should be obtained from well-informed and experienced engineers in order to construct a fair and representative set of ERD factors.Damage CostsThe direct costs are varied by ±20% as a whole and also varied by ±50% at each individualdamage state. The outcome of the decision is insensitive to changes in both sets of cases. It is found thatchanging the direct cost of damage state 4 (damage factors 10 to 30%) induces the highest percentagechange in the NPCs, followed by damage state 3 (damage factors 1 to 10%) and damage state 5 (damagefactors 30 to 60%). This suggests that, if higher accuracy in the outcome is needed, more attention shouldbe paid on damage state 3, 4 and 5 when estimating direct costs. The change in the direct cost of damagestate 7, i.e. the replacement cost, induces almost zero changes in the NPCs. Hence, there is no need topursuit a very high accuracy in the estimates of replacement cost.Three sets of indirect costs are used: increased by 50%, 100% and equal to the direct costs. Theoutcome and the ranking of the decision remain unchanged. This suggests that the indirect costs are notas important and influential as expected in the outcome of the decision.107Chapter 7 Sensitivity AnalysisTime Conversion Factors: Discount Rate and Life SpanIf the discount rate is varied within a reasonable range, 3 - 6%, the outcome of the decision isstable and insensitive to the changes. If the discount rate exceeds 8%, the outcome remains the same, butthe ranking will change. Option 3 remains as the optimal option, but option 2 is then preferred overoption 4. In general, as the discount rate increase, the decision will shift to less expensive and less safetyoption.Three life spans are tested: 100, 50 and 30 years. The outcome and the ranking are insensitive tothe changes in the life span used. However, since historic buildings are of concern in this project, a 100-year life span is still recommended.108Chapter 8 ConclusionCHAPTER 8CONCLUSIONIn this thesis, the process for selecting and deriving the necessaiy data to construct an expectedvalue decision model for selecting seismic retrofit schemes for a historic building was demonstratedthrough a case study. Net present costs (NPC) were used to rank the retrofit options. The NPC of anoption was defined to be the sum of the initial investment cost and the present expected value of the totalfuture damage costs.Four retrofit options were assumed to be proposed to upgrade the Stanford Memorial Church in1980. Option 1 was to do nothing in tenns of seismic strengthening, at a cost of about $2 million. Option2 was to strengthen the Church to life-safety standard, at $3.5 million. Option 3 was strengthening tobuilding integrity level without removing the unreinforced masomy (URM) walls, at $5.6 million, andoption 4 was strengthening to building integrity level with removal of URM walls, at $11.2 million (all in1980 dollars).Seismic data were selected to derive a set of earthquake probabilities. A Damage ProbabilityMatrix (DPM) was developed for the Church. ERD (Expected Reduction of Damage) factors wereassigned for each retrofit option. Damage costs, including direct costs, indirect costs, and costs of life,and the corresponding expected values of damage, were estimated. A discount rate and a life span werechosen to discount the future expected damage costs to present values.Option 3 consistently had the lowest NPC and was determined to be the optimal option. Thisrecommendation is considered as a confirmation to the common sense developed by those who studied thecase closely, If retrofit option 3 had been adopted in 1980, the projected accumulative expense from1980 to 1990 would be about $5 million, in 1990 dollars, less than the actual accumulative expense. Thesaving was about 40% of the actual accumulative expense. If the earthquake had not occurred, the shortterm saving from 1980 to 1990 would be about $10.5 million, in 1990 dollars, estimated by the decision109Chapter 8 Conclusionmodel. In the long term, i.e. using a 100-year life span, the difference between the present expected valueof the future damage costs would be about $31.8 million, in 1990 dollars, between option 1 and option 3.A sensitivity analysis was carried out. The outcome and the ranking of the decision analysiswere robust to changes in seismic data and damage costs within reasonable ranges. The outcome wasinsensitive to changes in discount rates and life spans as well. On the other hand, the outcome of thedecision was affected by the assessment of ER]) factors of option 3 and 4.Observed from the outcomes of the decision analysis and the sensitivity analysis, the costs of lifeand the indirect costs were not as important and influential as anticipated. The direct costs, associatedwith costs of repair, were sufficient to represent the future damage costs. It is recommended that moreeffort should be put into estimating the expected performance of the retrofit since the ER]) factorsdominated the outcome of the decision. To further improve the accuracy of the analysis, more attentioncould be paid to estimating earthquake probabilities associated with the middle range of the intensity scale(MIvil V to IX) and damage costs associated with damage states 3 to 5 (CDF 5 to 45%). It was found thatthe probabilities and damage costs associated with moderate to large earthquakes (MIvil V to IX) weremore important in affecting the decision than those associated with great earthquakes (Ivilvil X andabove).To perform a decision analysis in the selection of seismic retrofit schemes requires a combinationof knowledge from different fields, including seismology, structural engineering, economics, and socialimpacts due to earthquake damage. In the process of collecting data, it was found that researches weremostly concentrated on geotechnical and engineering aspects. Seismic data currently available in theUnited States provide adequate information for decision analysis in this study. There are codes providinggeneral methodology for evaluating and retrofitting existing buildings. However, there are not sufficientguidelines for estimating future earthquake damages, especially for retrofitted structures. Better methodsfor predicting structural behavior are also needed. There is also a gap in the knowledge of the overalleconomic and social impacts. These impacts could be very important when historic buildings areconcerned.110Chapter 8 ConclusionBut the main concern here is not getting the perfect data, it is to make consistent decision usingthe available information. In carrying out a decision analysis, the decision maker is forced to recognizeand quantify the unknown aspects involved in making the decision. He or she can obtain more insightfrom the analysis, and thus be in a better position to make judgment. It is believed that making use of thedecision model purposed in this study is a good start.111ReferencesREFERENCES1. Algennissen, S.T., Perkins, D.M., Thenhaus, P.C., and Ziony, J.I. 1980. Probabilistic Estimates OfMaximum Seismic Horizontal Ground Motion On Rock In Coastal California And The AdjacentOuter Continental She USGS Open File Report 80-924 Preliminary. United States GeologicalSurvey, Denvor, CO.2. Algermissen, S.T., et al. 1982. Probabilistic Estimates ofMaximum Acceleration and Velocity inRock in the Contiguous United States, USGS Open File Report 82-1033. United States GeologicalSurvey, Denvor, Co.3. Allen, P.C. 1980. Stanford: From the Foothills to the Bay. Stanford Alumni Association andStanford Historical Society, Stanford, CA. 228 pp.4. Applied Technology Council. 1985. Earthquake Damage Evaluation Datafor C’ahfornia. ATC-13 /1985. Applied Technology Council, Redwood City, CA.5. Bartholomew, K. 1992a. “The Rebuilding of Memorial Church”. The Stanford Observer, July -August 1992 issue. Stanford University, CA.6. Bartholomew, K. 1992b. “Memorial Church: A Building Overview”, October 2, 1992.7. Benjamin, J.R and Cornell C.A. 1970. Probability Statistics, and Decision for Civil Engineers.McGraw-Hill Book Company, New York. 684 pp.8. Bolt, B.A. 1988. Earthquakes (Revised).W.H. Freeman and Company, New York. 282 pp.9. Bone, L. 1993. “The Fallen Angel: A Mosaic Restoration at Stanford University” in Flash Point,Vol. 6 No. 2, April - June 1993. Tile Heritage Foundation, Healdsburg, CA.10. Building Systems Development, Inc., Integrated Design Services and Claire B. Rubin, Consultant.1989. Establishing Programs And Priorities For The Seismic Rehabilitation of Buildings: AHandbook FEMA-174 I May 1989. Federal Emergency Management Agency, Washington, D.C.122 pp.11. Building Technology Inc. 1990a. Financial Incentives for Seismic Rehabilitation of HazardousBuildings - An Agendafor Action, Volume 1: Findings, Conclusions and Recommendations. FEMA198 / September 1990. Federal Emergency Management Agency, Washington, D.C.12. Building Technology Inc. 1990b. Financial Incentives for Seismic Rehabilitation of HazardousBuildings - An Agenda for Action, Volume 2: Establishing State and Local Case Studies andRecommendations. FEMA-199 / September 1990. Federal Emergency Management Agency,Washington, D.C.13. Coburn, A. and Spence, R. 1992. Earthquake Protection. John Wiley & Sons, Chichester, Britain.355 pp.14. TheDailyPaloAlto. 1903. Vol. XXII, No. 16; Sunday, January25, 1903.15. The Daily Palo Alto. 1906a. Second Special Edition, Vol. XXVIII, No. 66; Wednesday, April 18,1906.112References16. The Daily Palo Alto. 1906b. Vol. XXVIII, No. 69; Saturday, April 21, 1906.17. H.J. Degenkoib Associates. 1987. Evaluating the Seismic Resistance ofExisting Buildings (ATC14). Applied Technology Council, Redwood City, CA.18. H.J. Degenkoib Associates. 1989. Letter submitted to Pieron, 0., Project Manager of FacilitiesProject Management, Stanford University, CA; contents of the letter include damage assessment,preliminary retrofit recommendation, structural drawings, etc. of The Memorial Church; November21, 1989.19. H.J. Degenkolb Associates. 1990. Seismic Evaluation and Strengthening Proposals for The StanfordUniversity Memorial Church, Stanford, California. August 1990. Degenkolb Associates, Engineers,San Francisco, CA.20. H.J. Degenkoib Associates. 1992. Details: Balancing Historic Preservation and Seismic Safety.Degenkolb Associates, Engineers, San Francisco, CA. 14 pp.21. Dinwiddie Construction. 1990. Memorial Church Preliminary Construction Cost Estimates.Dinwiddie Construction Company, San Francisco, CA.22. Earthquake Engineering Research Institute (EER1) and National Research Council (NRC). 1990.Loma Prieta Earthquake Preliminary Reconnaissance Report. Earthquake Engineering ResearchInstitute, El Cerrito, CA.23. Englekirk and Hart Consulting Engineers, Inc. 1988a. Typical Costs for Seismic Rehabilitation ofExisting Buildings, Volume 1: Summary. FEMA-156 I February 1988. Federal EmergencyManagement Agency, Washington, D.C.24. Englekirk and Hart Consulting Engineers, Inc. 1988b. Typical Costs for Seismic Rehabilitation ofExisting Buildings, Volume 2: Supporting Documentation. FEMA-157 / February 1988. FederalEmergency Management Agency, Washington, D.C.25. Facilities Project Management of Stanford University. June 1980. Internal record of reconstructionof North wall of Memorial Church and new organ installation.26. Green Library, Archives / Special Collections. Index Card (without date). Stanford University, CA.27. Hogg, R.V., Ledolter, J. 1987. Engineering Statistics. Macmillan Publishing Company, New York,New York. 420 pp.28. Holden, R and Real, C.R. 1990. Seismic Hazard Information Needs Of The Insurance Industry,Local Government, And Property Owners In California: An Analysis (Special Publication 108).California Department of Conservation, Division of Mines and Geology, Sacramento, CA.29. Kreysler, W. 1993. “In Defiance of Gravity: The Restoration of Stanford’s Angels” in Flash Point,Vol. 6 No. 2, April- June 1993. Tile Heritage Foundation, Healdsburg, CA.30. Lawson, A.C. et a!. 1908. The California Earthquake of April 18, 1906: Report of the StateEarthquake Investigation Commission. Volume 1, Part 2. Carnegie Institution of Washington,Washington, D.C.31. Panel On Earthquake Loss Estimation Methodology, Committee On Earthquake Engineering,Commission On Engineering and Technical Systems, National Research Council. 1989. Estimating113ReferencesLosses From Future Earthquakes: Panel Report and Technical Background. FEMA-177. FederalEmergency Management Agency, Washington, D.C.32. Poland, C.D. and Reis, E.M. 1992. “The Repair and Strengthening of the historic StanfordMemorial Church”, Earthquake Engineering, Tenth World Conference, 1992, Balkema, Rotterdam.p. 5341 - 5346.33. Reis, Evan. Interview with author on April 23, 1993.34. Reiter, L. 1990. Earthquake HazardAnalysis. Columbia University Press, New York.35. Schwein I Christensen Laboratories, Inc. 1989. Report of interior stone arch distress testing(attached with Degenkolb, 1989); November 17, 1989. Schwein I Christensen Laboratories, Inc.,Lafayette, CA36. Seismic Safety Commission. 1987. Guidebook To Identfy And Mitigate Seismic Hazards InBuildings. Seismic Safety Commission, State of California, Sacramento, CA.37. Smith, G.W. and Reitherman, R 1984. Damage to Unreinforced Masonry Buildings At StanfordUniversity In The 1906 San Francisco Earthquake. Scientific Service, Inc., Redwood City, CA.38. The StanfordAlumnus, Volume 1, June, 1899.39. The StanfordAlumnus, Volume 7, 1905 - 1906.40. The Stanford University News. Jan. 21, 1953. Article “for release to PM’s of January 24 and AM’sof January 25, 1953”. Stanford University, CA.41. Stockholm, G. 1980. Stanford Memorial Church: An Appreciative Guide For the Not-so-causalVisitor. Stanford Memorial Church and Office of Public Affairs, Stanford University, CA. 86 pp.42. Taylor, J.A. 1990. “Stanford Memorial Church: An Inspiration in Italian Mosaic”. The Italian TileCenter, New York.43. Turner, P.V., Vetrocq, M.E., Weitze, K. 1976. The Founders & the Architects: The Design ofStanford University. Department of Art, Stanford University, Stanford, CA. 96 pp.44. VSP Associates, Inc. 1992a. A Benefit Cost Model For The Seismic Rehabilitation of HazardousBuildings, Volume 1: A User ManuaL FEMA-227 / April 1992. Federal Emergency ManagementAgency, Washington, D.C.45. VSP Associates, Inc. 1992b. A Benefit Cost Model For The Seismic Rehabilitation of HazardousBuildings, Volume 2: Supporting Documentation. FEMA-228 / April 1992. Federal EmergencyManagement Agency, Washington, D.C.46. Working Group On California Earthquake Probabilities. 1990. Probabilities OfLarge EarthquakesIn The San Francisco Bay Region, California. United States Geological Survey, Denvor, CO.114


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