Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_1994-0025.pdf [ 4.04MB ]
Metadata
JSON: 831-1.0050435.json
JSON-LD: 831-1.0050435-ld.json
RDF/XML (Pretty): 831-1.0050435-rdf.xml
RDF/JSON: 831-1.0050435-rdf.json
Turtle: 831-1.0050435-turtle.txt
N-Triples: 831-1.0050435-rdf-ntriples.txt
Original Record: 831-1.0050435-source.json
Full Text
831-1.0050435-fulltext.txt
Citation
831-1.0050435.ris

Full Text

APPLICATION OF DECISION ANALYSIS TO SEISMIC REHABILiTATION OF HISTORIC BUILDINGS: A CASE STUDY OF REHABILITATION OF STANFORD UNiVERSITY MEMORIAL CHURCH  by JOANNA KWAN B.A.Sc. (Hons.), The University of British Columbia, 1991  A THESIS SUBMITTED IN PARTiAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA November 1993  ©JoannaKwan, 1993  In presenting this thesis  in partial fulfilment of the  requirements for an  advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  (Signature)  Department of  L v’L.  él  The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  NcV  &  3  ABSTRACT  The construction of an expected value decision model for selecting seismic retrofit schemes for a historic building is demonstrated through a case study. Net Present Costs (NPC) are used to rank the retrofit options. NPC is defined as the sum of the initial investment cost and the present expected value of the 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 seismic strengthening the Church with increasing level of safety and costs. Seismic data are selected to derive a set of earthquake probabilities. Damage probabilities and damage costs, including direct costs, indirect costs, and costs of life, are estimated. A discount rate and a life span are chosen to discount the future damage costs to present expected values. Option 3, strengthening the Church to building integrity standard without removing the unreinforced masomy (URM) walls, has the lowest NPC and is considered as the optimal option. If it had been recommended and adopted in 1980, about 40% of the accumulative expense from 1980 to 1990 would have been saved. A sensitivity analysis is carried out in order to determine the importance of variables that are only 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 the expected 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 is recommended.  II  TABLE OF CONTENTS  ABSTRACT TABLE OF CONTENTS  iii  LIST OF TABLES  v  LIST OF FIGURES  viii  ACKNOWLEDGEMENT  ix  CHAPTER 1 iNTRODUCTION  1  CHAPTER 2 THE MEMORIAL CHURCH AT STANFORD UNIVERSITY 2.1 Brief History of The Memorial Church 2.2 The Original Structure 2.3 Reconstruction After the 1906 San Francisco Earthquake 2.4 Renovation in 1980 and 1985 2.4.1 New Organ Installation and Partial Strengthening in 1980 2.4.2 Roof Strengthening in 1985 2.5 The Loma Prieta Earthquake in 1989 2.5.1 Damage Assessment 2.5.2 Fund Raising and Planning 2.5.3 Analysis and Design 2.5.4 Building Strengthening Schemes 2.5.5 Final Design and Construction 2.5.5.1 Major Structural Strengthening 2.5.5.2 Miscellaneous Non-structural Repairs 2.5.5.3 Facilities Improvements  5 5 6 10 14 14 15 16 17 20 20 21 23 24 30 32  CHAPTER 3 RETROFIT OPTIONS AND COST ESTIMATES 3.1 Do Nothing Option 3.2 Life-Safety Option 3.3 Building Integrity A Option 3.4 Building Integrity B Option 3.5 Summary  33 34 34 37 39 40  CHAPTER 4 SEISMIC DATA 4.1 Definitions 4.2 Ground Motion Parameter: Intensity Scale 4.3 Seismic Data 4.3.1 Location of Stanford University 4.3.2 Maximum Probable Earthquake 4.3.3 Annual Occurrence Rates 4.4 Derivation of Earthquake Probabilities 4.5 Local Site Effects 4.6 Discussion  42 43 44 46 47 49 52 53 54 55  111  CHAPTERS LOSS ESTIMATE 5.1 Damage Assessment 5.1.1 Damage Probability Matrices (DPM) 5.1.2 Establishing the Basic DPM for the Memorial Church 5.1.3 Expected Reduction in Damage (ERD) 5.1.3.1 Past Performance of the Memorial Church 5.1.3.2 Effectiveness of the Retrofit Schemes 5.1.3.3 ERDFactorsfortheFourOptions 5.1.3.4 Summaxy of ERD Factors 5.2 Damage Cost Estimate 5.2.1 Direct Costs: Repair and Replacement Costs 5.2.1.1 Inventory List 5.2.1.2 Replacement Cost 5.2.1.3 Repair Cost For 50% Damages 5.2.1.4 Assigning Damage Costs to Damage States 5.2.2 Costs of Deaths and Injuries 5.2.3 Indirect Costs 5.2.4 Summaiy of Damage Cost Estimates  57 58 58 61 63 63 64 65 66 67 68 68 70 71 72 74 77 79  CHAPTER 6 DECISION ANALYSIS 6.1 Definition of Variables 6.2 Decision Tree 6.3 Initial Investment of Retrofit Options (1NV) 6.4 Time Conversion Factor (TCF) 6.4.1 Life SpanT 6.4.2 Discount Rate 1 6.5 Calculation of Net Present Costs (NPC) 6.6 Results 6.7 Cost Comparison  82 82 83 85 85 86 87 88 89 91  CHAPTER 7 SENSITIVITY ANALYSIS 7.1 Seismic Data 7.2 ERD Factors 7.3 Damage Costs 7.3.1 Direct Costs 7.3.2 Indirect Costs 7.4 Time Conversion Factors: Discount Rate and Life Span 7.4.1 Discount Rate 7.4.2Life Span 7.5 Conclusion of Sensitivity Analysis  94 94 97 100 100 104 105 105 106 106  CHAPTER 8 CONCLUSION  109  REFERENCES  112  iv  LIST OF TABLES 3.1  Cost of Life-Safety Strengthening (In 1990 Dollars)  36  3.2  Cost of Building Integrity A Retrofit (In 1990 Dollars)  38  3.3  Cost of Building Integrity B Retrofit (In 1990 Dollars)  40  3.4  Summary of Investment Costs (In 1980 Dollars)  41  4.1  Modified Mercalli Intensity Scale  45  4.2  Conversion Between Intensities and Magnitudes Using Equation (4.2)  47  4.3  Annual Occurrence Rate for Zone 24  52  4.4  Probabilities of Earthquake Intensity I.  53  5.1  Definition of Damage States and Corresponding Damage Factors  59  5.2 a  Damage Probability Matrix For Type 75: Unreinforced Masonry (Bearing Wall, Low  Rise) Buildings  59  Damage Probability Matrix For Type 78: Unreinforced Masonry (Load Bearing Frame, Low Rise) Buildings  60  5.3  The Basic Damage Probability Matrix For The Memorial Church  62  5.4  Important Earthquakes Near Stanford, 1917  64  5.5  Expected Rehabilitation Effectiveness of Life Safety Retrofit  64  5.6  Expected Reduction in Damage (ER])) of Each Retrofit Option  67  5.7  Summary of Estimated Repair Costs For 50% Damage (In 1980 Dollars)  72  5.8  Direct Costs: Facilities Repair and Replacement For Each Damage State (In 1980 Dollars)  74  5.9  Expected Death and Injury Rates For Existing Vulnerable Buildings  75  5.10  Expected Death and Injury Rates For Life-Safety Rehabilitated Buildings  76  5.11  Expected Cost of Life For Each Damage State (In 1980 Dollars)  77  5.12  Indirect Costs (In 1980 Dollars)  79  5.13  Case 1: Direct Costs and Case 2: Direct Costs Plus Indirect Costs, For All Retrofit Options (All Costs in 1980 Dollars)  80  Case 3: Direct Costs with Costs of Life (All Costs in 1980 Dollars)  80  5.2 b  5.14  -  v  1980  5.15  Case 4: Direct Costs with Costs of Life Plus Indirect Costs (All Costs in 1980  81  Dollars) 6.1  Retrofit Options and Investment Costs  85  6.2  Results of Decision Analysis (All Costs in 1980 Dollars)  90  6.3  The Description of the Two Cases  91  6.4  Accumulative Expense from 1980 to 1990 of Case 1: Actual Case  91  6.5  Accumulative Expense from 1980 to 1990 of Case 2: Decision Analysis Suggestion  92  7.1  Example of Data Set 1 & 2, Varying Annual Occurrence Rate of MMI VBy ±25%  95  7.2  Data Sets for Variation in Annual Occurrence Rate of Each MN’ll Level  95  7.3  Net Present Costs By Vaiying Annual Occurrence Rate of Each MMI Level (All Costs in Thousand and in 1980 Values)  96  The Percentage Change from the Original NPCs Due to Changes in Annual Occurrence Rates  96  7.5  The Original ER]) Factors  97  7.6  Data Sets for Variation in ER]) Factors of Each Retrofit Option  98  7.7  Net Present Costs By Varying the ER]) Factors of Each Retrofit Option (All Costs in Thousand and in 1980 Values)  99  Net Present Costs of Option 3 by Using Different ERD Factors (All Costs in Thousand and in 1980 Values)  99  Net Present Costs of Option 4 by Using Different ER]) Factors (All Costs in Thousand and in 1980 Values)  100  7.10  Data Sets for Direct Costs (All Costs in Thousand and in 1980 Values)  101  7.11  Net Present Costs By Using Different Direct Costs (All Costs in Thousand and in 1980 Values)  101  Data Sets for Variation in Damage Cost of Each Damage State Thousand and in 1980 Values)  102  7.4  7.8  7.9  7.12  7.13  7.14  7.15  (All Costs in  Net Present Costs By Changing Damage Cost of Each Damage State (All Costs in Thousand and in 1980 Values)  102  The Percentage Changes From the Original NPCs Due to Changes in Damage Cost of Each Damage State  103  Data Sets of Indirect Costs (All Costs in Thousand and in 1980 Values)  104  vi  7.16  7.17  7.18  Net Present Costs By Using Different Indirect Costs (AU Costs in Thousand and in 1980 Values)  104  Effect of Discount Rate on the Net Present Costs (AU Costs in Thousand and in 1980 Values)  105  Effect of Life Span on the Net Present Costs (AU Costs in Thousand and in 1980 Values)  106  vu  LIST OF FIGURES 2.1  Map of Stanford University Showing Location of the Memorial Church  5  2.2  The Original Memorial Church in 1904  7  2.3  Floor Plan of the Memorial Church  7  2.4  The Original Facade in 1904  8  2.5  One of the Arch Mosaic Angels  9  2.6 a  Front View of the Memorial Church after 1906 Earthquake  11  2.6 b  Side View of the Memorial Church after 1906 Earthquake  11  2.6 c  Interior Damage of the Memorial Church after 1906 Earthquake  12  2.7  The Memorial Church after 1913 Reconstruction  13  2.8  Map of Affected Regions and Epicenter of Loma Prieta Earthquake in 1989  16  2.9 a  Damage to Mosaic Angel Uriel  17  2.9 b  Damage to Stone Veneer at Apex of Crossing Arches  18  2.9 c  Damage to Plaster Frieze at Crossing Drum  18  2.9 d  Damage to the Organ Loft Balcony Railing  19  2.9 e  Cracking in the Stone Cross above North Wall  19  2.10  Strengthening of Arches, New Crossing Diaphragm System and Addition of Collectors  25  2.11 a  Roof Diaphragm Strengthening: Key Plan  26  2.11 b  Roof Diaphragm Strengthening: Connection of Roof Trusses to Walls  27  2.12  Addition of Roof Diaphragm in Nave Arcades  28  2.13  Addition of Roof Diaphragm in Gallery Stair Towers  29  2.14  Repair of Non-Structural Elements  31  4.1  Location of Major Faults in San Francisco Bay Region  48  4.2  Seismogenic Zones in Coastal and Offshore California  50  4.3  Estimated Maximum Magnitude for Each Seismogenic Zone  51  6.1  Decision Tree  84  viii  ACKNOWLEDGEMENT  I would like to thank my supervisors Prof. R.G. Sexsmith and Prof. R.O. Foschi for their time and effort in helping me to develop a thesis out of my own interest. This thesis would not be made possible without their support and advice. I would also like to thank Mr. F. Bendimerad, Manager of Seismic Engineering, Facilities Project Management of Stanford University for granting me permission to obtain information on the rehabilitation project of Stanford Memorial Church and Mr. C. Poland, President of H.J. Degenkoib Associates 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 the documents I needed and sending them to me. Special thanks to those who have assisted me in gathering information or given me valuable advice: Ms. P. Ehret of Facilities Project Management at Stanford; Prof. C. Thiel of Civil Engineering at Stanford; Prof. A. Kiremidjian of Earthquake Engineering at Stanford; Mr. 3. McDonald of Green Library at 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 in UBC. Last but not least, I would like to express my gratitude towards Kenny Lam who has always been there for me.  ix  Chapter 1 Introduction  C11APTER 1 INTRODUCTION  In recent decades, there has been an increased awareness of seismic hazards throughout the  world. This has raised concerns regarding seismic retrofit of existing buildings located in seismically active areas. The conununities in the west coast of the United State of America, located in high seismic zones, are exposed to the possibility of a major earthquake at any moment. The US government has charged a variety of agencies for preparation of guidelines for seismic rehabilitation and investigating methodology for testing and retrofitting existing buildings for seismic safety. The primaiy goal of seismic retrofitting for existing buildings is to ensure life safety and preserve conununity functions. For public institutions, such as govenunent buildings, emergency facilities, and schools, an operational level is required to be maintained after an earthquake. If a building has special historic or architectural value, preservation of the structure and its content is also a concern in the retrofitting program. Among various types of existing buildings, historic buildings are among the most vulnerable to earthquakes.  Historic buildings are generally built in unreinforced masomy, which may not have  sufficient 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 upgraded  incorrectly in the past. Even though a historic building may have survived past earthquakes, it may not be able to withstand further future earthquakes. According to the Seismic Safety Commission of California (1987), it is recommended that hazard mitigation of historic buildings should follow the State Historical Building Code which contains Sections 18950 through 18961 of the Health and Safety Code, and Part 8 of Title 24 of the California Administrative Code.  The basic requirement in these codes is to provide for building integrity and  continued operation of a facility after a major earthquake. However, there is no specific rule as to what  1  Chapter 1 Introduction  extent the strengthening is really required. In general, it is up to the engineer to suggest and the owner to decide. 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) to compare the benefit and cost of rehabilitation projects. The documents of the program are referred as FEMA-227 (VSP Associates, 1992a) and FEMA-228 (VSP Associates, 1992b).  There are other  documents which address the issues of typical costs or financial incentives for seismic rehabilitation of existing buildings, such as: FEMA-156 (Englekirk and Hart Consulting Engineers, 1988a) and FEMA 157 (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. et al., 1989). The aim of the FEMA Benefit Cost Model computer program is to calculate the benefit-cost ratio of a life-safety seismic rehabilitation program applied to groups of ordinary residential or commercial buildings.  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 different retrofit schemes. The other documents mentioned above are intended for ordinary buildings as well and thus, cannot be applied to seismic rehabilitation of historic buildings directly. Decision analysis is a useful approach for selection of a seismic retrofit scheme for individual historic buildings. It offers an effective way of comparing different seismic retrofit options. The objective is to select the retrofit option which has the lowest total cost, i.e. the sum of the initial retrofit cost and the  expected value of the future damage cost. The cost of retrofit will usually be more expensive if higher level 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 estimated in a probabilistic manner. The Bayesian statistical decision theory provides a mathematical model for making decisions in the face of uncertainty (Benjamin and Cornell, 1970). The theory suggests the use of expected values to  rank the available alternatives. The decision maker has to identify the possible events, assign probabilities and estimate the consequences related to these events. The expected value is the sum of the products of  2  Chapter 1 Introduction  probability and consequence of each possible event. In other words, the expected value is the weighted average of the possible outcomes of an alternative. For selecting seismic retrofit scheme for historic buildings, net present costs are recommended in this thesis for ranking the alternatives. The net present cost is the sum of the initial investment of a retrofit scheme and the present expected value of the future consequence as a result of adopting that retrofit scheme. The future consequence is the total earthquake damage cost expected to accrue over the life span of the historic building. It depends on the frequencies and the sizes of future earthquakes at the site, the predicted performance of the structure, the possible damage states and the damage costs. Both earthquake probabilities and damage probabilities are taken into account in calculating the expected value of 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 Memorial Church was built in 1899. In 1980, the Church was partially upgraded to support the excessive load of a new organ. The Loma Prieta earthquake in 1989 caused substantial damage to the Church which lead to a comprehensive seismic rehabilitation program, designed by H.J. Degenkolb Associates, in 1990.  The  history 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 partial upgrade, is examined.  Three seismic retrofit schemes are developed according to the strengthening  proposal by Degenkoib (1990). The details of the retrofit schemes are described in Chapter 3. The derivation of the seismic data is explained in Chapter 4 and the future earthquake damages are estimated in Chapter 5. In Chapter 6, the data are used to carry out a decision analysis. Since the input data involve uncertainty, a sensitivity analysis is done in Chapter 7 to assess the sensitivity of the outcome of the decision to the variation in the input data. In constructing the expected value decision model, there are difficulties in the selection of seismic 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 referred  3  Chapter 1 Introduction  by other documents, such as FEMA-227 (VSP Associates, 1992a) and FEMA-174 (Building Systems Development Inc. et a!., 1989).  Furthermore, the time effect on the future costs has to be taken into  account properly. The main objective of this thesis is to point out what data are needed, and how they can be obtained and organized for decision analysis in the selection of a seismic retrofit scheme for historic buildings. Effort is put into making a reasonable choice or a fair estimate of the required data. The rationale for obtaining each set of data is discussed in each chapter accordingly. The purpose is to provide a 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 of the hypothetical case in this thesis. If a decision analysis had been carried out to recommend a seismic retrofit scheme in 1980 and the recommendation had been adopted, what would be the difference in the total expense on the Church between 1980 and 1990, after the Loma Prieta earthquake? It is believed that the 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, it should be repaired and restored to its original form as much as possible. It is hoped that this thesis will provide some hindsight on the advantage of seismic rehabilitation of historic buildings prior to damaging events.  4  Chapter 2 The Memorial Church at Stanford University  CHAPTER 2 TN1 MEMORIAL CE[URCH AT STANFORD UNiVERSITY  2.1 BRIEF HISTORY OF THE MEMORIAL CHURCH  The Memorial Church was built by Jane Stanford (1828  -  1905) as a memorial to her husband  Leland Stanford (1824 1893) who was the founder of Stanford University (Allen, 1980). It was intended -  to be one of the most beautiful and imposing structures in the United States. “The interior will be the richest that perfect taste can devise,” said Mrs. Stanford (The Stanford Alumnus, 1899).  It was not  dedicated for any one particular faith or denomination but for emphasizing the importance of seeking spiritual truth and offering a sanctuary to people of eveiy persuasion (Taylor, 1990). The Church is located 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 Church  5  Chapter 2 The Memorial Church at Stanford University  The excavation was started in May 1899 and the cornerstone was laid on January 29, 1900. The construction was completed in 1902 (The Stanford Alumnus, 1905-1906). The Church was dedicated on Sunday, Januaiy 25, 1903 (The Stanford University News, 1953).  Work on some of the decoration  continued 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 STRUCTURE  Architect Charles A. Coolidge worked on the project in the 1880’s.  In 1899, when the  construction finally began, the contract was granted to architect Clinton Day of San Francisco and the architect on the premises to supervise workmen was Charles Hodges of Palo Alto (Stockholm, 1980). The original budget was over $250,000 (The StanfordAlumnus, 1899) in 1899 dollars (i.e. about $6 million in 1980 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 long down the main aisle; center of nave is 50 ft across (Stockholm, 1980). The building area is 28,000 sq. ft approximately (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.  6  Chapter 2 The Memorial Church at Stanford University  FIGURE 2.2 The Original Memorial Church in 1904 (From Figure 32, p. 43 of Turner et at., 1976)  4-  -4 . CROSSING (Gallery Above)  rAlRS 1  STAIRS  EAST  NAVE  VEST  VESTIBULE  .  —  —  .  ARCADE  FIGURE 2.3 Floor Plan of the Memorial Church (From p.2 of Taylor, 1990)  7  Chapter 2 The Memorial Church at Stanford University  As for the Round Room, there is no floor plan available. According to inspection, the wall is unreinforced masonry covered with wood paneling or stone veneer. The roof consists of straight-sheathed boards 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 the Clock Tower. The Facade was located at the north entrance above the North Arcade (See Figure 2.4). It was a 2-foot thick brick wall, 84 feet across the base and 86 feet in height, with mosaics and stained glass windows.  The mosaic, showing Christ welcoming the righteous into the Kingdom of God (Matthew  25:34), 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 My Husband Leland Stanford.” (Taylor, 1990)  II1 FIGURE 2.4 The Original Facade in 1904 (From Figure 39, p. 50 of Turner etal., 1976)  8  Chapter 2 The Memorial Church at Stanford University  The Crossing consisted of four 73-foot tall brick arches on each side, supporting a circular painted frieze, called the Drum. There were four large mosaic angels in the corner pendentives. The mosaic angels were 16 feet tall with a 22-foot wingspan (Bartholomew, 1992a). The name of the angels are Michael, Gabriel, Raphael and Uriel. (See Figure 2.5)  N  -  FIGURE 2.5 One of the Arch Mosaic Angels (From p. 3 of Taylor, 1990)  The Clock Tower was a 80-foot tall steel frame, masonry and wood tower set atop the crossing arches (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 produced by Salviati & Co. in Venice, Italy and shipped to California to install. More than 20,000 different shades 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 also thick 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.  9  Chapter 2 The Memorial Church at Stanford University  Lamb of J.& R. Lamb, New York. •  The organ was constructed by Murray M. Harris Organ Co., LA. The total weight of the organ was 25 tons and worth $15,500 in 1903 dollars (i.e. about $318,000 in 1980 dollars). (The Daily Palo Alto, 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 1903 dollars (about $12,766,000 in 1980 dollars). About 60% of the total construction cost was spent on the interior decoration. No particular seismic design criteria was used at that time. Effort was made to take earthquake protection 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.  The  Memorial Church, unfortunately, was built in the second phase. (Smith and Reitherman, 1984)  2.3 RECONSTRUCTION AFTER THE 1906 SAN FRANCISCO EARTHQUAKE  The epicenter of the San Francisco earthquake on April 18, 1906 was near the north coast of the San Andreas Fault. The magnitude was estimated to be about 8 on the Richter Scale (Working Group On California 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 the  Church (See Figure 2.6), The roofs collapsed, the Facade and the upper portion of the Clock Tower were destroyed and portions of the brick walls was damaged. The Crossing and the Round Room suffered minimal damage.  The organ and the stained glass windows were only slightly damaged. Nearly all  buttresses and ornamental supports were demolished. (The Daily Palo Alto, 1906a & b)  10  Chapter 2 The Memorial Church at Stanford University  FIGURE 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)  11  Chapter 2 The Memorial Church at Stanford University  .IiH [1* -,  FIGURE 2.6c Interior Damage of the Memorial Church after 1906 Earthquake (From Figure 46, p. 56 of Turner et al., 1976)  12  Chapter 2 The Memorial Church at Stanford University  According to the engineers report in The Daily Palo Alto (1906b), “the damage sustained by the church was due chiefly to the crash of the falling clock-tower, which tumbled northward, carrying the roof through near the dome. The sides of the transept were broken away from the church by the force of the earthquake.  When the crash of the clock-tower came, timbers, bricks, mortar and stones weighing  hundreds 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 within  the 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 new steel frame was erected to support gravity loads from the roofs and reinforced concrete walls were cast around the frame where the unreinforced brick walls once were. The stone, wood and stained glass were reset and a new wood roof added. The Facade was rebuilt in concrete. The Clock Tower was replaced with 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)  13  Chapter 2 The Memorial Church at Stanford University  The 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 Green Library, 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). The marble apostles were not replaced. The cost would have been around $740 to $1340 in 1909 dollars for each (i.e. $12,000  -  $22,000 in 1980 dollars). The marble altar was replaced at the original cost in year  1901 plus $200. Plumbing cost about $700 in 1909 dollars ($11,300 in 1980 dollars). At that time one of the engineers suggested laying steel bars in the floor for about $4000 in 1909 dollars ($65,000 in 1980 dollars). This was almost rejected by the University officials for economic reasons, but the plan was passed 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 spent on the architectural elements and the other three quarters (about $289,000 in 1909 dollars or $4,680,000 in 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 University News, 1953). Minor repairs lasted until 1917.  2.4 RENOVATION IN 1980 AND 1985  2.4.1 New Organ Installation And Partial Strengthening In 1980  A new Baroque tracker-type organ was to be purchased and installed in the choir loft over the foyer at the north end of the Church. Due to the inadequate capacity of the existing structure, a new structural system was needed to carry the weight, over 20,000 pounds, of the organ. The project was approved by the Board of Trustees in June, 1980.  14  Chapter 2 The Memorial Church at Stanford University  A structural box” frame was designed to provide vertical and lateral support to the organ plafform and the Facade. New steel columns would be installed at the arcade level and connected with horizontal steel beams at the floor and ceiling levels of the arcade. Vertical steel trusses in the choir loft would be extended and new concrete walls would be poured around the base of the north wall in order to provide 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 were authorized in February 1980 for organ enhancements. The total budget was $1,961,000, among which about $1,095,000 was for construction and management and $866,000 was for the new organ and voice improvements. (All these costs are in 1980 dollars.) The construction started in April, 1981 and was completed in May, 1982 which was 4 months later than planned. The delay was due to serious structural problems uncovered during demolition. The problems included: insufficient anchorage of structural beams to walls, inadequate structural connections of some members and discontinuous foundations.  They were corrected accordingly during the  construction. The organ builder, C.B. Fisk, started the organ construction in July, 1982 and delivered the organ 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 1985  In 1985, the hipped roof above the Crossing was strengthened with plywood when the skylight and roofing was replaced to eliminate a leakage problem.  It is assumed that the strengthening was  seismic strengthening and the cost was about $1,750,000 in 1985 dollars. (Facilities Project Management of Stanford University, 1980)  15  Chapter 2 The Memorial Church at Stanford University  2.5 THE LOMA PRIETA EARTHQUAKE IN 1989  In October 17, 1989, the Loma Prieta Earthquake caused substantial damage to the Church. The earthquake was centered along the San Andreas Fault east of Santa Cruz (Figure 2.8) and measured. 7.1 on the Richter Scale. The MMI level was estimated to be VIII and the ground motion was 0.29g with a duration of 10-15 seconds at the Stanford Campus. (EERI and NRC, 1990)  OUNA$  ‘I  .  r  ismIcr  •Ik  T  SAN  t.ANO  •  Cl  cc  s  CTfl 11*01  \  1’  SAN  S?ATI 11*01  pr. ..o  I  —  —  -.  I  UndslideS anClBOCldaJIS  ‘S  \  €mcetr  \  ® I  ..,..‘  5’  I —  $1_lI  F?O2 .. 1 •. S4 UCl.ilClOft GfQ.21Cl P*  s So*i.  .  41.10w  FIGURE 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) 16  Chapter 2 The Memorial Church at Stanford University  Since then, funds were raised and a seismic rehabilitation program was carried out.  The  rehabilitation program not only included repairing the damaged portion of the structure, but also included improving the seismic resistance of the structure and updating the electrical and mechanical features.  2.5.1 Damage Assessment  According to the damage assessment report done by H. J. Degenkolb Associates (1989), major damage was in the masorny arches supporting the central portion of the church below the dome. Cracks and displacement of some of the sandstone elements of the arches were observed. Since the masonry wall was 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 heavy mass 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 Crossing dislodged and fell.  Portions of the railing of the organ loft balcony were dislodged as well.  The  chandelier and a portion of the ballery in the east transept were damaged by the falling stone of the easterly 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)  17  Chapter 2 The Memorial Church at Stanford University  FIGURE 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)  18  Chapter 2 The Memorial Church at Stanford University  FIGURE 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)  19  Chapter 2 The Memorial Church at Stanford University  SchweinlChristensen Laboratories, Inc. carried out a detailed investigation on the interior stone arch and made a report (SchweinlChristensen, 1989) outlining test methods, dimensions and construction method of the arches.  2.5.2 Fund Raising and Planning  The fund raising committee was established in the Spring of 1990 with Melvin B. Lane as the chair person. Together with the effort of the Dean of the Chapel Robert Gregg and other members of the committee, the committee raised 10 million dollars by the end of 1991. The donations came from major corporations, Stanford alumni, and individual undergraduate students. One unique characteristic of this rehabilitation project was that fund raising and construction proceeded simultaneously in early 1990. This was due to the support of William Hewlett of Hewlett Packard. Initially, the Stanford University officials planned to limit the rehabilitation to the extent of repairing earthquake damage and bracing the structure against future earthquake.  But Mr. Lane  developed 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, and upgrading light and sound systems. (Bartholomew, 1992a)  2.5.3 Analysis And Design  In 1990, Stanford University retained H.J. Degenkolb Associates, a San Francisco structural engineering 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 Reis was the project engineer. The evaluation carried out by the consultant was based on Evaluating the Seismic Resistance of Existing Buildings (ATC-14)  by Degenkolb Associates, Engineers (1987).  20  ATC-14 is a consensus  Chapter 2 The Memorial Church at Stanford University  document which provides a consistent procedure for the life safety seismic evaluations of existing buildings in the United States.  At the request of the Stanford Seismic Evaluation Committee, the  minimum base shear coefficient used for the evaluation was increased to 13.3%g from 8.0%g required by ATC-14. In addition the building was checked for conformance to the Santa Clara County Ordinance Number 1100.78. Further evaluation was also done based on Essential Building Provisions of Title 24 of the California Adminisfrative Code for Hospital Construction. This requirement is intended to provide for building integrity and continued operation of a facility after a major earthquake. The detaiLed seismic analysis of the Memorial Church consisted of performing calculations to determine 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-built Church dated 1909-1913, plans of the subsequent additions in 1980 and 1985 and results of exploratory tests performed on the Church. (Degenkoib, 1990)  2.5.4 Building Strengthening Schemes  According 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 which might cause death, serious injury or entrapment of building occupants. This scheme was developed based on the evaluation done according to ATC-14 (Degenkolb, 1987).  b.  Building Integnty: A higher level of strengthening which would mitigate life-safety hazards and additionally limit damage to the structural and non-structural elements of the building to a level which would require minimal repair.  This scheme was developed based on the evaluation done  according to Title-24. For each level of strengthening the following options were considered: 1.  Minimal Disruption: Strengthening schemes which would not temporarily or permanently alter  21  Chapter 2 The Memorial Church at Stanford University  architectural features of the building including the overall building plan, stone, wood and mosaic finishes and other historical elements of the Church. 2.  Without Regard: Strengthening schemes which allow for the possibility of significant, temporary or permanent alternations to the building’s architectural features. Due to the important historic value of the Church, the strengthening scheme of either life safety  or building integrity adopted the minimum disruption option. The unreinforced masonry (URM) walls in the crossing area were the biggest problem in developing the strengthening scheme since URM is not acceptable under the current building code.  Dismantling the URM and rebuilding with reinforced  concrete 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 was discovered between the brick walls above the crossing arches. The void space ran full length of the arch walls, and ranged from about 6 feet high at the arch apex to 15 feet in the corners. The discovery of the void space allowed the engineers to develop an effective strengthening system for the crossing, which served as an alternative to the dismantling scheme. The fact that the strengthening system could be hidden 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 increase lateral stability.  2.  Add steel bracing system of “strong-back” columns and girders and new roof diaphragm above the arches 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 increase lateral 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 to reduce forces on the interior walls.  22  Chapter 2 The Memorial Church at Stanford University  7.  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 to  architectural finishes. (b) Building Integrity Strengthening Scheme: In addition to the seven points of the life safety strengthening scheme listed above, other strengthening 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 to prevent cracking.  9.  Place reinforced concrete slab between the discontinuous wall of the Gallery Stair Towers and the lower parallel wall which extents to the foundation to transfer load away from the perpendicular walls.  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 transept galleries. Preliminary cost estimate was done by Dinwiddie Construction Company (1990). The cost of the life 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 Construction  According 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 the structure in an attempt to prevent a major collapse or other catastrophic damage which could lead to considerable loss of life.” “The level of strengthening used represented essential compliance with the lateral force requirements of the current Ca1fornia Administrative Code for Hospital Construction and County of Santa Clara Regulations.” ...  23  Chapter 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 California Administrative Code.”  2.5.5.1 Major Structural Strengthening  1.  Strengthening of Arches: Reinforced concrete infihled inside existing 20-inch-wide cavity between the 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 a  steel beam anchored diagonally at each corner to interconnect the four walls. Extended from the two ends of each diagonal steel beam were two W14 x 193 strongback columns anchored to the face of the bricks to further stabilize the brick walls. A 18” x 54” concrete perimeter cap beam was doweled into the 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 the crossing 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 replaced  with 3/4” structural I plywood diaphragm on straight roofs or with two sheets of flexible 3/8” plywood on curve roofs. Connection of roof trusses and plywood diaphragms to arches, the north wall and the concrete walls around the perimeter of the Church were strengthened. Spanish tiles were placed back on 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 and replaced with 3/4” structural plywood.  Connection of roof diaphragm to Round Room walls was  strengthened. 6.  Addition of New Roof Slabs at Arcades: A 6” reinforced concrete slab was added under the roof of each 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 under the roof of the gallery stair towers. (See Figure 2.13)  24  Chapter 2 The Memorial Church at Stanford University  (N) I rxz4 CONCRETE CAP BEAM DOWELED 1(10 BRICK  (N)RE4FORCED CONCRETE I’FLL. NSIDE )WAU. VITY  BETWEEN BRICK  I I  (N)CONCRETE ANO STEEL  FIGURE 2.10 Strengthening of Arches, New Crossing Diaphragm System and Addition of Collectors (From Figure 11, p. 5346 of Poland and Reis, 1992)  25  C’  CD  1W  CD  p  I1  0  -n  ii  r  -C’ U  0 E  I  I  •1  C-)  Chapter 2 The Memorial Church at Stanford University  r4 cMpPL .4AL.. L  c cr+c.  X1i9e OC WAt.-L.  JUNC.TiQIi  cr  EL-AM  A9..Ae  c CTIO  CCF IC L-.JALL  FIGURE 2.1 lb Roof Diaphragm Strengthening: Connection of Roof Trusses to Walls (From Figure lOb of Degenkoib, 1990)  27  Chapter 2 The Memorial Church at Stanford University  ()  COr4. wrfl4 rot4  V  ADI1CN C WOr IAHIAM 1r4 NAVE AR.CAE  FIGURE 2.12 Addition of Roof Diaphragm in Nave Arcades (From Figure 11 of Degenkoib, 1990)  28  Chapter 2 The Memorial Church at Stanford University  (H) &?_i’w..etfr .y4e.B” t...Na lEI-Iep Ir4T )  EMOV (ZTft.a F  (9) Pt44TZ C.IL’  (7%  A1ITICr4 C CF ‘14PHRAfr1 LLY eTAR TcWR IN  K-r PLAN  FIGURE 2.13 Addition of Roof Diaphragm in Gallery Stair Towers (From Figure 13 of Degenkoib, 1990)  29  t4WIN  Chapter 2 The Memorial Church at Stanford University  2.5.5.2 Miscellaneous Non-structural Repairs  1.  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 stone panel below. In the horizontal direction, the railing was doweled to arch columns to strengthen the connection.  3.  Crossing arch stone repair: The horizontal cracks on the faces of the outer voussoir stones were  epoxied and doweled together. The stones that had slipped, maximum about 2 inches, out of place were jacked up into position and long dowels were installed horizontally from both sides, anchoring each voussoir to the brick arch in between. The voussoir stones that needed to be replaced were replaced by the same material as the original. 4.  Chandelier anchorages were strengthened by attaching cable to roof truss above and replacing the existing 1/2” bolts by 1/2” A325 x bolts.  5.  Mosaic angels strengthening: Threaded robs were bolted through concrete and limestone beneath the mosaic to metal T-bars behind each angel. After cleaning, three layers of epoxy and fiberglass cloth were applied on the back of each angel. Dislodged mosaic tiles were glued back on to the mosaic and the 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 on the west transept windows done in 1988 were removed. The glasses were cleaned. The windows were considered structurally safe for earthquake because the stained glass could move and shift and yield to the motion induced by an earthquake. Some frame separated slightly from the sandstone settings around but did not impose any danger.  7.  Round Room parapet strengthening  8.  Reinforcement of pedestal  9.  Murray-Harris Organ Bracing  (See Figure 2.14)  30  Chapter 2 The Memorial Church at Stanford University  uj 2  0 0 Z  >..  is  +4  \ ,—2/-  of Li  1  777\  Si-N_  LU  J U’  —1  UI  -‘  .  Ic  I  I 4  ç izi  I  1  uJ i.-.:11  1 FIGURE 2.14 Repair of Non-Structural Elements (From Figure 12 b of Degenkolb, 1990)  31  I  Chapter 2 The Memorial Church at Stanford University  2.5.5.3 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 have  programmed 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 bulbs were put in the large nave chandelier.  3.  Reopening of Transept Balconies: The fake double doors on the south side of each transept were transformed into real doors for the reopening of the 2 transept balconies. The stone and brick walls were cut through in order to make connections in each transept to the existing hidden staircase. The cost was about $500,000.  4.  Fire Protection: Fire sprinklers were installed around the ceiling. In order to protect the Fisk-Nanney organ from accidental water breakout, a dry-pipe system which holds water in reserve was used and a two-step system was chosen to detect both smoke and heat before sending water into the sprinkler pipes. Furthermore, to satis1’ fire code, an emergency exit from the west balcony had to be cut through 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 2.5.5.3 is from Bartholomew, 1992) The final total rehabilitation cost was not the same as the preliminary cost estimate due to certain changes 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 and strengthening architectural elements and improving other facilities (Reis, 1993). The remaining portion of the fund, about $1.5 millions, was saved as a preservation fund and would be used for maintenance and future upgrading. Three years after the earthquake, Memorial Church was reopened on November 1, 1992. (Bartholomew, 1992)  32  Chapter 3 Retrofit Options and Cost Estimates  CHAPTER 3  RETROFIT OPTIONS AND COST ESTIMATES  In this chapter, four retrofit options are defined and the investment of each option is estimated, in terms of a decision considered in 1980, before the new organ installation and structural upgrade in the foyer 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 structural upgrade for supporting the new organ.  The seismic retrofit options are defined based on “Seismic  Evaluation 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. Construction technology may have changed quite a bit in the decade in between. However, it is assumed that a similar set of safety levels would still be defined and the essence of the retrofit schemes would also be similar. It is 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 Construction Company (1990). The costs given by that report included both damage repair costs and strengthening costs. The costs related to damage repair are taken out and certain adjustment are made to construct estimates of the investment of each retrofit option. The investment costs are then converted to 1980 dollars by assuming discrete compounding and using a discount rate i of 4%, i.e., Investment =  Total Cost Estimates— Repair Cost (1—i)  10  The choice of the discount rate I will be discussed in Chapter 6.  All the investments are  estimated based on preliminary values. Effort is put into making consistent and reasonable estimates but  33  Chapter 3 Retrofit Options and Cost Estimates  it is not guaranteed that these data could accurately represent the actual case. However, the estimates do reflect the relative extent and expense among the options.  3.1 DO NOTHING OPTION  The “Do Nothing” option refers to the addition of a new structural system required to support the weight, over 20,000 pounds, of the new Baroque tracker-type organ. The details of the new structural system are described in Section 2.4.1. Even though the new structural system may contribute to a certain degree of seismic strengthening 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 three retrofit 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 the new Baroque tracker-type organ and voice improvement and $1,095,000 for management and construction of the new structural system. (Facilities Project Management, 1980)  3.2 LIFE-SAFETY OPTION  The purpose of the life-safety scheme is to strengthen the structure to provide sufficient lateral resistance for preventing catastrophic damage or collapse which would cause death, serious injury, or entrapment of occupants in a major earthquake. This scheme is developed based on the evaluation done according to Evaluating the Seismic Resistance ofExisting Buildings (ATC-14) by Degenkoib Associates, Engineers (1987). ATC-14 provides  34  Chapter 3 Retrofit Options and Cost Estimates  procedures 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 evaluating  different type of buildings. This document is widely recognized in the engineering conununity both in the United States and Canada. It is currently being used as the basis for the development of a national standard in the United States for the seismic evaluation of existing buildings. This strengthening scheme will meet the minimum standard regarding the safety of the occupants as required by ATC-14 but will not fully confonu to the current code requirements for new buildings.  The strengthened structure may not be usable immediately after a moderate or major  earthquake. 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 the void space and doweled to the brick, thus interconnecting the arch walls and giving them significantly more bending strength perpendicular to their plane.  2.  Provide perpendicular bracing of the four arches to each other with a new steel bracing system and roof 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 with bolts.  3.  Transfer the forces generated in the Crossing arches into the stronger concrete walls by adding collectors at each corner of the Crossing.  4.  Improve the lateral resisting strength of the roofs of the Nave, Chancel and Transepts, by temporarily removing the Spanish tile roof and replacing the straight sheathed boards underneath with plywood.  35  Chapter 3 Retrofit Options and Cost Estimates  Additionally, 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 the previous point.  6.  Reduce the forces in the interior walls of the West and East Arcades by temporarily removing the roofs of the arcades and placing a six-inch reinforced concrete slab above the plaster ceiling between the interior and the exterior Arcade walls.  7.  Avoid falling hazards by repairing several non-structural elements, such as: stone cross, balcony railings, 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 3.1 Cost of Life-Safety Strengthening (In 1990 Dollars) Work Number 1,2,3 4 5 6 7 Total  Cost Estimate 2,164,000 720,000 54,480 157,000 898,000 3,993,480  Repair Cost 327,000 0 0 0 305,000 632,000  Retrofit only 1,837,000 720,000 54,480 157,000 593,000 3,361,480  The first colunm indicates the work number which corresponds to the description above. The second column is the original cost estimate, including material and labor of the repair and seismic strengthening of each work item, given by Dinwiddie Construction (1990). A 20% contingency cost for labor 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 alone does not represent the damage cost if no seismic strengthening work is required. It is the cost of material and labor spent on repairing damages, and it does not include the cost of construction facilities, such as  36  Chapter 3 Retrofit Options and Cost Estimates  temporary protection, scaffolding, hoisting, electricity, etc., which will be required if the repair is done alone. There is no repair related work stated explicitly in work item 4 to 6. Hence, the repair costs for these three items are all assumed minimal.  The fourth column is the difference between the second  column and the third column, i.e. the cost of seismic strengthening only. According to the preliininaiy cost estimate (Dinwiddie Construction, 1990), an extra 20% overall design and construction contingency fee is added to the final total cost. This 20% contingency fee is considered 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 (1+0.04)’°  =  $2,725,000.  In addition to the retrofit cost, the cost of the new structural system at the foyer area to support the new organ and the cost of the new organ should be included. Note that the cost of constructing the new structural system at the foyer area should be less than that in option 1 since construction facilities are set up for the retrofit. It is assumed that the cost of construction of the new structural system at the foyer area 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 new structural 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 OPTION  The purpose of the building integrity A scheme is to strengthen the structure not only to provide sufficient 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 the  37  Chapter 3 Retrofit Options and Cost Estimates  architectural elements to a level which would require minimal repair and to ensure continued operation of the facility after a major earthquake. The scheme is developed based on the Essential Building Provisions of Title-24 of the Calfornia Administrative Code for Hospital Construction. This code has stricter criteria on the evaluation and strengthening requirement than ATC-14 (Degenkoib, 1987). The minimal damage goal in Title-24 is suitable 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 the previous option, with increased member sizes of the “strong-back” columns and girders of the new Crossing 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 a lower parallel wall which extends to the foundation, in order to transfer loads away from the perpendicular walls.  9.  Remove the stained glass windows and retrofit the frames to provide a gap, isolating the windows from 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 3.2 Cost of Building Integrity A Retrofit (In 1990 Dollars) Work Number 1,2,3 4 5 6 7 8 9 10 Total  Cost Estimate 2,172,000 720,000 54,480 157,000 898,000 108,000 2,500,000 455,500 7,065,000  38  Repair only 327,000 0 0 0 305,000 0 0 0 632,000  Retrofit only 1,845,000 720,000 54,480 157,000 593,000 108,000 2,500,000 455,500 6,433,000  Chapter 3 Retrofit Options and Cost Estimates  The retrofit cost is then converted back to 1980 dollars by using a discount rate of 4%: Retrofit Cost=  $6 433 000 (1+0.04)  10  =$4,346,000.  Therefore, the total cost of option 3, including the new organ, the new structural system at the foyer area  and 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 and may suffer significant damages during an earthquake. The walls of the Crossing arches and the walls of the Round Room are unreinforced masomy.  The strengthening of the wails of the Round Room by  reinforced concrete is considered sufficient. But the strengthening of the walls of the Crossing arches will not be. Hence, this strengthening scheme is not considered fully compliant with the Essential Building Provisions of Title-24.  3.4 BUILDING INTEGRITY B OPTION  The Building Integrity B option is essentially the same as the Building Integrity A option, except for 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 roof  of and taking down the drum, mosaic angels and stone veneer in the Crossing, demolishing the brick arches and pouring new reinforced concrete arches in their place. All the architectural elements would then be replaced. As mentioned in the previous section, Title-24 prohibits the use of unreinforced masonry construction. By removing the unreinforced masonry in the Crossing arches and reconstructing with reinforced concrete, there will be a higher confidence in achieving the desired safety level. However, the  39  Chapter 3 Retrofit Options and Cost Estimates  cost associated with this is very high compared to the previous option. The extra cost can be seen as the investment on purchasing lower risk. The cost estimates are listed in Table 3.3.  TABLE 3.3 Cost of Building Integrity B Retrofit (In 1990 Dollars) Work Number 1 3 4 5 6 7 8 9 10 Total Cost -  Cost Estimate 10,158,000 720,000 54,480 157,000 898,000 108,000 2,500,000 455,500 15,051,000  Repair only 0 0 0 0 305,000 0 0 0 305,000  Retrofit only 10,158,000 720,000 54,480 157,000 593,000 108,000 2,500,000 455,500 14,746,000  The 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 area  and 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 SUMMARY  The cost of the new organ and the structural upgrade to support the new organ is about $2 million. The church can be upgraded to life safety standard at a cost of $3.5 million, about 75% higher  than the previous option. In order to minimize the damage to architectural elements, about $5.6 million is needed for option 3. To be in full compliance with Title-24, i.e. to remove all URM walls, the cost of the  40  Chapter 3 Retrofit Options and Cost Estimates  retrofit is estimated to be $11.2 million, which is two times the cost of option 3. A summary of the costs of the four retrofit options is listed in Table 3.4.  TABLE 3.4  Summaiy of Investment Costs (In 1980 Dollars) Option 1 2 3 4  Description Do Nothing Life-Safety Building Integrity A Building Integrity B  41  Investment 1,961,000 3,502,000 5,577,000 11,193,000  Chapter 4 Seismic Data  CHAPTER 4 SEISMIC DATA  To estimate building damages and calculate expected damage costs, the size and the frequency of future earthquakes at the site are needed. Ideally, to evaluate the seismicity of a site, the first step is to identii the location of all the potential faults around the site and collect the frequency of different magnitudes of earthquakes along each 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 be considered. 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 requires a lot of mathematical and statistical computation. Furthermore, detailed local geologic information is often 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 States Geological 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 data given by this report are more specific and refined for areas within the coastal California than the report used by FEMA-227 (VSP, 1992). Moreover, the year that this report (Algermissen et a!., 1980) was prepared, 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 earthquake probabilities to be used for calculating expected values are explained. Some of the terms used in this chapter are defined in Section 4.1.  42  Chapter 4 Seismic Data  4.1 DEFINITIONS  Seismic data refers to the expected “frequency” as a function of the “size” of future earthquakes at a “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 is the reciprocal of return period and it can be greater than 1.  •  Annual Probability of Occurrence (P ): the probability that one or more earthquakes of a particular 0 level or range of levels will occur per year. It is calculated by using a Poisson Process assumption and the 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 level given that an earthquake occurs. It is the ratio between the number of occurrences of that particular level 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 estimated from instrumental observations. One commonly used parameter is Richter Magnitude. (Coburn and Spence, 1992)  •  Intensity: the measure of severity of the shaking of the ground at a particular site. One commonly used 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 on tectonic and geologic setting. They are not equivalent to “tectonic province” nor “seismotectonic province” which refer to the siting of critical facilities. (Algermissen et a!., 1980)  43  Chapter 4 Seismic Data  4.2 GROUND MOTION PARAMETER: INTENSITY SCALE  Intensity is the most commonly used parameter to measure seismic hazard in loss estimation studies. Intensity of an earthquake is the measure of severity of the shaking of the ground at a particular location. Intensity scales are essentially site-specific and non-quantitative. There are usually 12 levels  and stated in Roman numerals to differentiate from magnitude. The assessment of level depends on the behavior of the people and animals, the response of facilities and the observation of the ground in the location considered. (Coburn and Spence, 1992) There are different kinds of Intensity Scales used in different countries. The first Intensity Scale  was developed by M.S. de Rossi of Italy and F.A. Forel of Switzerland at the end of the nineteenth century. 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 advancement of 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 Mercalli  Intensity Scale (MIV[I) became the most commonly used Intensity Scale in the United States.  A brief  summary of the Modified Mercalli Intensity Scale is listed in Table 4.1. Since level assessment involves subjective evaluation and interpretation, the data should be used in conjunction with the original damage descriptions. There is also a tendency to overestimate intensity level especially for large earthquakes (Coburn and Spence, 1992). Therefore, the use of high intensity values, such as MIvil level XI and XLI, should provide explicit explanation to avoid misunderstanding since the high intensity levels emphasize ground failure, not shaking severity which differ from the criteria of lower levels (Panel On Earthquake Loss Estimation Methodology et a!., 1989).  44  Chapter 4 Seismic Data  TABLE 4.1 Modified Mercalli Intensity Scale From Appendix B, p.66 of Holden and Real (1990) MMI Level I II III  IV  V  VI  VII  VIII  IX  X  XI  XII  Description Not felt except by a very few under especially favorable circumstances. Felt only by a few persons at rest, especially on upper floors of buildings. Delicately suspended objects may swing. Felt quite noticeably indoors, especially on upper floors of buildings, but many people do not recognize it as an earthquake. Standing motor cars may rock slightly. Vibration like passing of truck. Duration estimated. During the day felt indoors by many, outdoors by few. At night some awakened. Dishes, windows, doors disturbed; walls make cracking sound. Sensation like heavy truck striking building. Standing motor cars rocked noticeably. 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. Felt by all, many frightened and run outdoors. Some heavy furniture moved; a few instances of fallen plaster of damaged chimneys. Damage slight. Everybody runs outdoors. Damage negligible in building of good design and construction; slight to moderate in well-built ordinary structures; considerable in poorly built or badly designed structures; some chimneys broken. Noticed by persons driving motor cars. Damage slight in specially designed structures; considerable in ordinary substantial 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 mud ejected in small amounts. Changes in well water. Persons driving motor cars disturbed. Damage considerable in specially designed structures; well-designed frame structures thrown out of plumb; great in substantial buildings, with partial collapse. Buildings shifted off foundations. Ground cracked conspicuously. Underground pipes broken. Some well-built wooden structures destroyed; most masonry and frame structures destroyed with foundations; ground badly cracked. Rails bent. Landslides considerable from river banks and steep slopes. Shifted sand and mud Water splashed (slopped)_over banks. 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. Damage total. Practically all works of construction are damaged greatly of destroyed. Waves seen on ground surface. Lines of sight and level are distorted._Objects are thrown upward into the air.  45  Chapter 4 Seismic Data  4.3 SEISMIC DATA  The coastal area of California is divided into 41 seismogenic zones, which are areas of similar tectonic and geologic settings. The annual occurrence rates are calculated for “those zones that have a sufficient number of earthquakes to make possible a judgment on the period of time for which each magnitude level is complete.” (Algermissen et aL, 1980) The annual occurrence rates are estimated by annual averages over the time of completeness for each 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 earthquake source zone. N is the expected number of earthquakes per year which equals to or exceeds magnitude M at the zone.(Algermissen et a!., 1980) This equation is a variation of the Gutenberg-Richter relationship which has been verified from worldwide observations of seismicity.  This relationship quantifies the  observation that the smaller earthquakes are more frequent than larger ones and hence, makes it possible to 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 Rothman and partially listed in Hays and others (1975) (as mentioned in Algernussen et a!., 1980). The historic and instrumental seismicity contained in the catalogue are dated from 1796 to 1974 (a period of 178 years) in the coastal area of California (Algermissen et a!., 1980). catalogue are recorded in intensity level.  Many of the earthquakes in the  Intensity level attenuates as the distance from the source  increases. Magnitude represents the energy release at its source which is not related to distance. In general, the distance between the source and the site where the intensity is recorded has to be taken into account in the conversion between intensity and magnitude. However, the intensity in the catalogue is  46  Chapter 4 Seismic Data  assumed to be the epicentral intensity, i.e. the intensity at the source, hence it can be converted to magnitude without taking distance into account. The relationship M=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 to each intensity level by using the equation. For each intensity level, a range of magnitude is defined using this magnitude as the center point. The data are listed in the following table.  TABLE 4.2 Conversion Between Intensities and Magnitudes Using Equation (4.2)  Intensity, I V VI VII VIII IX X XI XII  Magnitude, M 4.3 4.9 5.5 6.1 6.7 7.3 7.9 8.5  Range of M 4.0 4.6 4.6 5.2 5.2 5.8 5.8-6.4 6.4 7.0 7.0 7.6 7.6 8.2 8.2 8.8 -  -  -  -  -  -  -  4.3.1 Location of Stanford University  Stanford University is located in Palo Alto, Santa Clara County, near the western shore of the San Francisco Bay. The San Andreas fault and the San Gregono fault lie on the west side whereas the Hayward fault and the Calaveras fault lie on the east side of this area. (See Figure 4.1)  47  Chapter 4 Seismic Data  -  SanaRosa  A  —  38  Oakland  ‘\  .7  San Francisco  \-  \  P  ‘TAc*J7  SanJose  ‘\\  J,  t.OMAPRIETA EARThQUAKE  c. 7  Santa Ctuz  37 I  I  I  I  San Juan  l4oister 123  122  FIGURE 4.1 Location of Major Faults in San Francisco Bay Region (From Figure 2, p. 9 of Working Group On California Earthquake Probabilities, 1990)  48  Chapter 4 Seismic Data  Referring to the zoning map (Figure 4.2), Stanford is located on the boundary of zone 24 and zone 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 occurred along this fault and the entire zone shows evidence of Holocene movement.  There are substantial  differences in activity rates and style of deformation along segments of the fault.  There are also  significant differences in interpretation by different experts. Despite the controversy, Algermissen and others believed that the central creeping section of the fault is capable of generating a large magnitude earthquake in the future. (Algermissen et a!., 1980)  4.3.2 Maximum Probable Earthquake  Zone 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) By using equation (4.2) to convert magnitude to intensity, the maximum probable intensity is XII, which is the maximum on the MMI scale. The maximum probable earthquake is estimated based on the historical maximum magnitude experienced in that zone. This historical largest earthquake could be less than the potential maximum and is likely to be, especially if the period of record is less than the return period of the potential maximum earthquake.(Algermissen eta!., 1980) The earthquake record of United States does not exceed 500 years and is around 150 years for parts of the western United States (VSP, 1992). The catalogue used by 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, the  assigned maximum probable intensity for zone 24 is already the highest on the intensity scale. The fact that the worst scenario is expected suggests that no adjustment for the maximum probable intensity is necessary.  49  Chapter 4 Seismic Data  SEISMOGENIC ZONES IN COASTAL AND OFFSHORE V CALIFORNIA  •  L •  •  •*4ti•i  .d ....re..aI  .e*IIt*  i.t...,  sub hi...  V)h  ,  n.e  ifl  •  \  t.•_.,  ••  •3g  •  (tenS.  ,.  I••  V  -  ..  .  \\.  F  .  V  -V  I  S  d.hd  Inst. ci hfl.,s4. fence Jn  Ii,.  fl. .,r. st*d na inSt. I  inn..,  ••  V.,  .‘  \  ,nfl, — this .5. .1e ..fl i.dt..i...i.t in. ld.,t ....C.frS..%..Ie.,...,..i...  I  -  (.  -  r  —  .:.  .\\r  \\\  \  \  .  •.•  •V  .  1___.  3e•  \\c  .  •  ...  V  -  •  V  •..  V  —  •  •  .  ... :.  :, —  —  —  .  .  .  :.  -  —  ..  —  \  .1•  •  ,  .31  •  •  I. .  V  \‘L :\\ .\ ‘-...  \  •S•i._  .  Ii•••_  •  \  • .  .  .  .  .  .  •  \\ N 1 \ -  20  .-AF’\  •  \2  •••.  .1’  V  •  V  S  •.  •  •  •  ‘..  .‘.N  Sr  &  FIGURE 4.2 Seismogenic Zones in Coastal and Offshore California (From Plate 1 of Algermissen eta!., 1980)  50  \\ ••.  V  \10  S  •  )  .30  •  V  V  V  -  25  ./•  •  •  .  V  :  Chapter 4 Seismic Data  FIGURE 4.3 Estimated Maximum Magnitude for Each Seismogenic Zone (From Figure 3, p. 40 of Algermissen et aL, 1980)  51  Chapter 4 Seismic Data  4.3.3 Annual Occurrence Rates  The annual occurrence rate for each range of magnitudes for each seismogemc zone is tabulated in Table 1, p. 30 of Algermissen eta!. (1980). The data for zone 24 is selected from this table and listed in Table 4.3. TABLE 4.3 Annual Occurrence Rate for Zone 24 Intensity, I  Magnitude, M  Range of M  V VI VII VIII IX X Xl XII  4.3 4.9 5.5 6.1 6.7 7.3 7.9 8.5  4.0 4.6 4.6 5.2 5.2 5.8 5.8-6.4 6.4 7.0 7.0 7.6 7.6 8.2 8.2 8.8 -  -  -  -  -  -  -  Annual Occurrence Rate 1.9700 0.7400 0.2810 0.1060 0.0400 0.0150 0.0057 0.0021 Z = 3.1598  As mentioned in Section 4.1, the annual occurrence rate is the number of occurrence of a particular level of earthquake per year. Note that in FEMA-227 (VSP, 1992), the annual occurrence rates are used directly to calculate the expected cost, i.e.  EC=> xc  which is, in fact, the total damage cost in a year. According to the definition in Bayesian Theory, the expected value should be calculated by EV=Fxq  where probabilities are used instead of occurrence rates. The basic requirement for P is that the events be mutually exiusive and exhaustive, i.e. the sum of all P• equals to one. The value of EV will always be less than BC since P, cannot be greater than 1.0 but r• can be greater than 1.0.  52  Chapter 4 Seismic Data  4.4 DERiVATION OF EARTHQUAKE PROBABILITIES  The conditional probability of earthquake intensity 1 is defined as the probability that the intensity level is I• given that an earthquake of intensity greater than Mlvii V occurs.  It is the ratio  between the number of events of that particular intensity level per year (the annual occurrence rate, r) and the total number of events from Mlvii level V to XII per year:  P(”IQ)—---I-  (4.3)  i=1  Note that 8  =3.16  which means, on average, there are 3.16 earthquakes with intensities ranging from Ivilvil V to XII in one year. The conditional probabilities are calculated and listed in the following table.  TABLE 4.4 Probabilities of Earthquake Intensity I 1  Intensity, I  1 2 3 4 5 6 7 8  V VI VII VIII IX X XI XII  Annual Occurrence Rate, r 1.97 0.74 0.28 1 0.106 0.040 0.015 0.0057 0.002 1 =3.1598  Probability, P( I, I Q) 0.6235 0.2342 0.08893 0.03355 0.01266 0.004747 0.001804 0.0006646 z=1.0  The 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:  53  Chapter 4 Seismic Data  (IV)=l—e 0 P  (44)  where r is the occurrence rate and (is the time span. Substituting r  =  3.16 and t  1 year into the above  equation, P,(I  V)  =  1—0.0424  =  0.9576  i.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 with  intensity 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 and exhaustive events, hence they may be used in the decision tree. Being mutually exclusive means that each event does not “intersect” with each other. The MMI levels are considered as individual events. Being collectively exhaustive implies that the union of the set of events exhausts the sample space and the sum of the probabilities of all events equals to one. The sample space is defined as earthquake with intensity level between V and XII, inclusively. The intensity levels lower than V are ignored since the damage associated 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 EFFECTS  In general, local site conditions have to be taken into account in conjunction with the intensity of ground motion to estimate earthquake losses. Unfavorable soil or topographic conditions may amplify  ground 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 local ground condition or to some standard ground conditions. If a standard ground condition is used, then  modification may be needed.  54  Chapter 4 Seismic Data  Two different adjustment procedures are described in FEMA-227 (VSP, 1992): one method is  suggested by ATC-13 and one is by FEMA-227 itself  The method introduced by ATC-13 is more  complex than that by FEMA-227. In the former one, the user identifies the soil type from the five soil  types defined in Table 8.4 in ATC-13 and adjusts the damage probability matrix for the type of building under consideration using Table 8.4 again and Equation 8.2a in ATC-13. In the later method, there are only two soil types: either poor or firm. If the site has poor soil, then the mean damage factor is adjusted upward by one IvIMI level. For example, the expected damage for an MIvil VIII earthquake at a firm soil site 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 soil  type was poor. Since the soil underlying Stanford University is not poor soil type, no adjustment is necessary.  4.6 DISCUSSION  The annual occurrence rates derived by Algermissen et at. (1980) using historic data “may not fairly represent the probability of the next large earthquake in a zone where it is possible to invoke a statistical time-dependent or geophysical predictive model.” The rates could be overestimated or underestimated for a site depending on the distance between the site and the nearby source zones of future earthquakes. If the source is far away from the site, the intensity experienced by the site will be lower and the occurrence rates could be overestimated. On the other hand, if the source is closer to the site, the intensity experienced by the site will be higher and the occurrence rates could be underestimated.(VSP, 1992) The uncertainty in the annual occurrence rates estimated for zone 24 is relatively low compared to other zones. Since the San Andreas fault is a seismic active area, more research activities have been  55  Chapter 4 Seismic Data  concentrated in this zone. The tectonics and seismicity of this zone are better understood than many other zones. 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 possible nowadays. However, effort has been made to understand and evaluate the average, long-term seismicity of seismically active zones in the United States (VSP, 1992). The average, long-term seismic data are considered sufficient for decision analysis in general. concern in making rational decisions.  In fact, “correct” infonnation is not the main  It is making decisions consistent with the best available  information that matters. Sensitivity studies can always be used to decide when it is necessary to obtain better information. And when further information is obtained, a new decision can be considered.  56  Chapter 5 Loss Estimate  CHAPTER 5 LOSS ESTIMATE  There are risk analysis computer programs available in California, as reviewed in Holden and Real (1990). The user can input the structural type, the year built, the address, and the replacement cost  of the buildings and the programs will generate annual loss or average loss over a specific time span. The two 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 for the Insurance Services Office (ISO) in California. It includes 21 building categories based on the information that is readily available to insurance companies. The method are developed based on experience with California earthquakes and expert judgment.  2.  the ATC-13 method developed by the Applied Technology Council. It includes 41 building types and other classes for structures such as bridges, pipelines, dams, tunnels, etc. The data in ATC-13 are also 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 Mercalli Intensity (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 a  set of structures can be estimated. Both the ISO and ATC methods yield similar results for similar structure types. These methods are mainly designed for analyzing groups of ordinary buildings and they are not suitable for application on an individual basis or for special structures. So they can not be applied directly in this study. However, the basic method and data in ATC-13 (ATC, 1985)will be used as the main reference.  57  Chapter 5 Loss Estimate  The process of loss estimate can be divided into two main components: damage assessment and damage cost estimate. The procedures and rationales behind the development of these two components are discussed in this chapter.  5.1 DAMAGE ASSESSMENT  Damage assessment is estimating damages of a structure depending on the severity of the ground motion and the vulnerability of the structure itself Given a certain earthquake intensity, the extent of damage that the structure may suffer and the probability of occurrence of that extent of damage are needed to be estimated. The estimates require information on the performance of similar type of buildings in past earthquakes and prediction of structural behavior of that particular building.  Knowledge in damage  assessment 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 for different types of existing building in California. The results are statistically organized and tabulated in matrix forms in ATC-13 (ATC, 1985).  The damage probability is the conditional probability that a  building will suffer a certain damage state if an earthquake with certain intensity occurs. Seven building damage states are defined, ranging from none to destroyed. For each damage state, a range of damage factors and a central damage factor (CDF) are assigned. Damage factors are defined as percentage of building replacement value which reflect the percentage of physical damage to the structure. The central damage factor is defined as the midpoint of the range. The damage states and damage factors are listed in Table 5.1.  58  Chapter 5 Loss Estimate  TABLE 5.1 Definition of Damage States and Corresponding Damage Factors From 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  1 None 2 Slight  No damage. Limited localized minor damage not requiring repair. Significant localized damage of some components generally not requiring repair. Significant localized damage of many components warranting repair. Extensive damage requiring major repairs. Major widespread damage that may result in the facility being razed, demolished, or repaired. Total destruction of the majority of the facility.  -  -  3 Light -  4 Moderate -  5 Heavy 6 Major -  -  7 Destroyed -  Damage Factor Range (%) 0 0 1  Central Damage Factor (%) 0 0.5  1  5  -  10  -  10 30  20  30 60 60 100  45 80  100  100  -  -  -  There are different DPMs for different types of structures. The general form of DPM is shown in the following tables.  They are the DPMs for unreinforced masomy (URM) low rise buildings with  bearing wall (in Table 5.2 a) and with load bearing frame (Table 5.2 b).  TABLE 5.2 a Damage Probability Matrix For Type 75: Unreinforced Masomy (Bearing Wall, Low Rise) Buildings From Table 3-5, p. T3-8 of FEMA-227 by VSP (1992) (Original from ATC-13, Table 7.10, pp. 198 217) -  CDF 0.00 0.50 5.00 20.00 45.00 80.00 100.0 MDF  VI  VII  9.1 90.5 0.4  0.6 55.5 43.4 0.5  4.7  11.7  Modified Mercalli Intensity VIII IX X  10.9 66.0 22.9 0.2  0.5 22.4 65.9 11.2  24.2  43.1  59  2.0 35.0 62.5 0.5 66.7  Xl  X[I  0.1 10.1 83.1 6.7 77.7  0.1 3.4 50.4 46.1 88.0  Chapter 5 Loss Estimate  TABLE 5.2 b Damage Probability Matrix For Type 78: Unreinforced Masomy (Load Bearing Frame, Low Rise) Buildings From Table 3-5, p. T3-9 of FEMA-227 by VSP (1992) (Original from ATC-13, Table 7.10, pp. 198 217) -  CDF 0.00 0.50 5.00 20.00 45.00 80.00 100.0 MDF  Modified Mercalli Intensit VIII IX VII X  VI 5.2 38.8 55.9 0.1  3.2 84.1 12.7  0.7 37.9 55.4 6.0  3.0  6.8  15.7  5.5 52.6 40.4 1.5  0.8 20.6 60.8 17.8  30.2  45.8  Xl  XII  0.2 6.9 40.2 51.7 1.0 61.8  0.1 2.5 17.7 62.8 16.9 75.6  At the bottom of each table, a MDF is calculated for each column.  MDF represents mean  damage factor. It is the expected value of the CDFs at a particular MIvil level. For example, at MMI VI of 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 damage information for IJRM buildings is superior to all other structural types therefore, it would be valid to assume that the accuracy is about 25%. The DPMs given in ATC-13 are developed based on California data.  For cities outside  California, adjustment has to be made to account for the difference in building practices and the probable absence of seismic provisions in codes. Local DPMs could also be developed based on consensus opinion of well-informed engineers. (VSP, 1992) Since Stanford University is located in California, the DPMs can be used as references directly without adjustment for location.  60  Chapter 5 Loss Estimate  5.1.2 Establishing The Basic DPM for the Memorial Church  Although the data in the DPMs given in ATC-13 (ATC, 1985) do not needed to be adjusted for location, they should not be applied directly to damage estimates for the Memorial Church. These DPMs are evaluated for typical building types but the structure of the Church is quite different from typical residential or commercial buildings. Among various structure types, URM structures are considered as the most hazardous type because they are brittle and would suffer significant damages in an earthquake. Most URM bearing wall  structures 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 a perimeter URM wall and interior wood load bearing partitions.  Larger URM buildings, such as  warehouses, have heavier wood floors and interior columns, and thick bearing walls which are about 24 inches 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 the Round Room were built in URM whereas the walls along the perimeter of the nave, the transepts and the chancel were built in concrete. The two major types of URM buildings are bearing wall and load bearing frame. The URM portions of the Church neither completely belongs to the URM bearing wall type nor the URM load bearing frame type. The reinforced concrete walls constructed in the early 1900’s could not be considered as having the same quality as the reinforced concrete walls built in recent years. There are also 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 low rise 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 arches at the crossing.  61  Chapter 5 Loss Estimate  The basic DPM for the Church is calculated by taking the average of the DPMs of the URM low rise 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 by 66.0÷55.4 =60.7 2 where 66.0 is selected from MMI VIII and damage state 4 in Table 5.2 a and 55.4 is selected from the  same location in Table 5.2 b. Note that MMI V is not included in the DPMs because it is suggested by ATC-13 that damages are ignorable at this Mlvfl level. In this study, it is assumed that there is a 90% chance that the Church will have no damage and 10% chance that minor damage will occur for this level of earthquakes.  TABLE 5.3 The Basic Damage Probability Matrix For The Memorial Church (Without retrofit, in 1980) Damage State 1 2 3 4 5 6 7 MDF  CDF (%) 0.00 0.05 5.00 20.00 45.00 80.00 100.0  V 90.00 10.00 0 0 0 0 0 0.5  VI 2.60 23.95 73.20 0.25 0 0 0 3.85  Modified Mercalli Intensity VIII VII IX 0 0 0 1.90 0.35 0 69.80 24.40 3.00 28.05 60.70 37.50 0.25 14.45 53.15 0.10 0 6.35 0 0 0 19.94 36.65 9.22  X  XI  XII  0 0 0.40 11.30 47.90 40.15 0.25 56.21  0 0 0.10 3.50 25.15 67.40 3.85 69.79  0 0 0.05 1.30 10.55 56.60 31.50 81.79  The damage that the Church suffered in the Loma Prieta Earthquake in 1989 was approximately 10 to 20%, around the lower end of damage state 4. The intensity of the earthquake was estimated to be MIvil Vifi at Stanford. In the DPM above, the probability of damage state 4 is about 60% and the MDF is about 20% for Mtvil VIII. The probability should have been higher for damage states 3 and 4, and lower for damage state 5 which will then reduce the predicted MDF slightly. This DPM is considered slightly over-estimating the damages of the Church without retrofit in 1980. The adjustment of the DPM for the Church is discussed in the following section.  62  Chapter 5 Loss Estimate  5.1.3 Expected Reduction inDaniage (ER]))  In FEMA-227 (VSP, 1992), a factor called Expected Rehabilitation Effectiveness (ERE) is  introduced to adjust the expected damages of unrehabilitated buildings. The effectiveness is defined as the percentage reduction in expected damages in the seismically strengthened facility compared to the expected damages in the unstrengthened facility. It varies depending on the rehabilitation techniques used, on the standard, code, or safety level to which seismic rehabilitation is carried out, and on the design, construction, and condition of the building before rehabilitation. In this project, a similar factor called Expected Reduction in Damage (ERD) is used to adjust the average damage cost for each intensity level, which in effect modifies the basic DPM for each option. The  ERD 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 Moderate Large Great  MIvil Range V VI VII -IX X XII -  -  5.1.3.1 Past Performance of the Memorial Church The original Church, built in 1899 and finished in 1903, 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, the Gable Wall and the upper portion of the Clock Tower were destroyed and portions of the brick walls was  damaged. Yet the Crossing and the Round Room suffered minimal damages.  The Church was then  demolished and reconstructed except for the Crossing and the Round Room. This suggests that the URM in the Crossing area and the Round Room might be able to withstand significant amount of earthquake shaking. It could be assumed that the URM of the Church is stronger than the URM of typical buildings by 5% in large earthquakes.  63  Chapter 5 Loss Estimate  The Church was reopened in 1913. There was neither major damage recorded nor structural upgrade done along the years until 1980, the assumed present time. There were some major earthquakes which could have affected the Stanford area in this period of time (from 1917 to 1980). They are listed in the following table. TABLE 5.4 Important Earthquakes Near Stanford, 1917 1980 Extracted from Appendix B of Bolt (1988) -  Time April 7, 1957 Aug. 6, 1979  Place San Francisco Coyote Lake  MMI Vifi VII  Jan. 24, 1980  Livermore  VII  26,  Remarks Damage in West lake and Daly City area. $500,000 property damage; 16 injuries; ground displacement along Calaveras fault. Maximum horizontal displacement was 5 to 6 mm. $11.5 million damage; 50 injured; felt over 75,000 sq. km; 1500 m of discontinuous surface rupture showing a maximum of 5 to 10 mm of right lateral displacement.  The earthquakes listed above were very close to Stanford and could have affected the Stanford area. Since earthquake intensities attenuate as the distance from the epicenter increases, Stanford could have 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 assumed that the Church, at its present (1980) unrehabilitated condition, is about 20% stronger than typical URM buildings.  5.1.3.2 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 for typical URM buildings are extracted as follows. TABLE 5.5 Expected Rehabilitation Effectiveness of Life Safety Retrofit Extracted From Table 3-6a, p. T3-14 of FEMA-227 (VSP, 1992) Building Type Unreinforced Masonry (bearing wall, low rise) Unreinforced Masonry (load bearing frame, low rise)  64  Percentage Reduction in Damage (%) 50-30 40 -25  Chapter 5 Loss Estimate  Note that the high end of the range is estimated for Mlvii VI and the low end of the range is for MIvil XII. As the Mlvii level increases, the effectiveness of the retrofits is expected to be lower. Based on these values, it can be deduced that, on average, the ERE is about 50% ÷ 40%  =  45% for moderate earthquakes;  50%÷30% + 40%+25%J÷2 30% ÷ 25%  =  35% for large earthquakes;  27% or about 25% for great earthquakes.  5.1.3.3 ERD Factors for the Four Ontions The ER]) factors will be the sum of the reduction due to the past 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 is considered as do nothing in terms of seismic strengthening.  2.  Life-Safety Option: strengthening the structure to provide sufficient lateral resistance for preventing death, 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 to limit damage to the architectural elements to a level which will require minimal repair and to ensure continued operation of the facility after a major earthquake.  4.  Building Integrity B Option: similar goal as Building Integrity A, except the URM in the Crossing area 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 assigned according to the discussion in Section 5.1.3.1, the past performance of the Church. A 20% reduction in damages in moderate earthquakes and a 5% reduction in large earthquakes are expected. earthquakes, there will be no reduction expected.  65  In great  Chapter 5 Loss Estimate  Option 2: “Life-Safety” Retrofit The ER]) is the sum of the ER]) of option 1 and the ERE discussed in Section 5.1.3.2, 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 elements should 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 instead just to be conservative. The retrofits are expected to perform well even for large earthquakes. The main  difference between the two options is that there is a greater uncertainty in the effectiveness of option 3 than the effectiveness of option 4. It is because in option 4, the URM in the Crossing arches has to be  removed and the walls will be reconstructed in reinforced concrete. The uncertainty is reflected in the lower expected effectiveness estimated for option 3 than that for option 4. For option 3, the ER]) is estimated 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 from the discussion in the strengthening proposal by H.J. Degenkoib Associates (1990).  5.1.3.4 Summary of ER]) Factors The ER]) factors will be used in Chapter 6 to modify the expected damage costs for each intensity level for different retrofit options. For example, the adjusted expected damage cost for lvll41 Viii is  (1-ERD)xZP(D I 1 VJII)xC, where P(D 1 I VIII) is the damage probability and C is the damage cost of damage state D . Details of the 1 application will be explained in Chapter 6.  The assessment of ER]) factors in this study is quite  66  Chapter 5 Loss Estimate  subjective. Better methods of predicting structural behavior will improve the accuracy of the assessment  and thus the result of the analysis. The ERD factors are summarized in Table 5.6 below.  TABLE 5.6 Expected Reduction in Damage (ERD) of Each Retrofit Option  Option  Description  1 2  DoNothing Life-Safety  3  Building Integrity A  4  Building Integrity B  Expected Reduction in Damage (%) V-V1 Vil-IX X-Xfl 20 5 0 65 40 25 99 90 80 99 95 90  5.2 DAMAGE COST ESTIMATE  Damage 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 and its contents.  They are usually estimated by joint effort of engineering firms and construction  companies. •  Deaths and injuries: The estimate depends on the social function and occupancy of the structure, and the value of life. The methodology provided by ATC-13 is generally adopted as discussed in FEMA 174 (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 tax  impact. Since the structure of concern is a church, those impacts are less relevant here. One possible economic impact could be the tourist businesses on campus.  Since the Church is the symbol of  Stanford University and has special architectural elements (namely, the mosaic and the stained glass  67  ChapterS Loss Estimate  windows), it is the major attraction of the university. If it were damaged, tourist related businesses would be affected. •  Social impacts:  For most cases, they are the loss and pain experienced by individuals and the  disruption of the community as a whole. The social impacts are usually intangible, yet substantial and long term. For historic buildings, the historic value of the architectural elements and the cultural importance represented by the buildings themselves are the main concern. Damages to them are usually 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, the  knowledge on the nature of indirect costs is scarce and assessing monetary values on economic and social impacts is veiy difficult. Yet, indirect costs are very significant, especially when historic buildings are of concern. Most researchers agree that, in general, indirect costs are at least equal to the direct costs of repair and replacement, and they are long term in their effect (Building Systems Development et a!., 1989).  5.2.1 Direct Costs: Repair and Replacement Costs  The goal is to restore the Church back to its pre-damage condition but not necessary to upgrade the structure to satis1 current building codes. The damage is referred to the physical damage to the structure and to the architectural elements. The first step is to establish an inventory list of the elements of the church. Then, a replacement cost will be estimated. Costs for repairing 50% damages will also be estimated. Finally, a direct cost related to repair or replacement will be assigned for each damage level.  5.2.1.1 Inventory List In order to estimate the repair cost, an inventory of the Church and possible expense categories related to each item are developed.  The categories are stated in general terms to  provide a basis for evaluating costs of the 50% damage. The inventory and possible expense categories are listed in the following.  68  Chapter 5 Loss Estimate  Structural Elements: 1.  2.  3.  4.  5.  6.  7.  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.  South & West Transept Galleries •  repair damaged railings  •  patch cracked or damaged balcony floor  Organ loft balcony •  repair damaged railings  •  patch cracked or damaged balcony floor  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 Towers  Nave, Channel & Transepts’ roof •  repair damaged roof elements  •  repair wood finishes around roof truss  •  basic cost  Round Room •  repair or replace damaged unreinforced masonry wall  •  repair roof parapet  •  repair damaged roof  •  basic cost  Floor  69  Chapter 5 Loss Estimate  patch cracks and damages due to falling objects Architectural Elements: 1.  Mosaic: repair I replace cracks and dislodged elements of the mosaic on the facade, the interior walls and 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.  5.2.1.2 Replacement Cost “Replacement” refers to replacing the function of a demolished building served. The replacing structure could be of different construction type as the original one (VSP, 1992). It is 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 the Church according to its original floor plan. The architectural elements could be replaced by replicas to resemble 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 the cost of mosaic is out of budget. There is no need to reproduce the decorative elements in an exact manner since 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, per square foot of floor space, which is about $62 in 1980 dollars. This cost is too low considering the special structure of the original Church.  It is assumed that the replacement cost is double of the typical  replacement cost, i.e. $124 in 1980 dollars. Therefore, for the 28,000-square-foot Memorial Church the ,  typical cost is  70  Chapter 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 architectural  elements such as the mosaic and the stained glass windows, the production cost varied. It depends on the delicacy of the work required and the available budget. One reasonable estimate is to assume the cost of producing 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 $7,000,000.  5.2.1.3 Repair Cost For 50% Damages In FEMA-227 (VSP, 1992), the repair cost is defined as the product of the central damage factor (CDF) from the Damage Probability Matrix (DPM) and the replacement value of the building. This method is not applicable for the Church. The main reason is that repairing historic buildings with special architectural elements is much more expensive than replacing them. The difficulties, the excessive time and effort required to repair the damaged wing of the mosaic angels 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 by Dinwiddie Construction (1990), about $350,000 was allocated for repairing and reinforcing the damaged mosaic angel, and $50,000 was allocated for reinforcing each undamaged mosaic angel. The two costs do not include basic cost such as scaffolding and temporary protection which are standard costs in both cases. The difference, $300,000, is the cost of repair which is 6 times of the strengthening cost.  The  replacement cost varies depending on the delicacy of the workmanship and material required but would be much less than the repair cost stated above. Although the cost of repair is always more expensive than the cost of replacement, repair is still a priority due to the special historic value of the Church itself  Especially for damaged architectural  elements, the originals are expected to be preserved and restored as much as possible. Only if the damage to a particular piece is beyond repairable, replacement could be made for resemblance of the original. The repair cost for each item is estimated based on the preliminary cost estimate by Dinwiddie Construction (1990). The costs given by the report included both damage repair costs, for 10 to 20%  71  Chapter 5 Loss Estimate  damages, and life-safety strengthening costs. The labor and material costs related to strengthening, the labor and material costs related to repairing and the basic construction costs are separated for each work category. Considerable adjustments in the labor and material costs for repairing are made to account for estimating repair costs for 50% damage in this section. The adjusted labor and material costs for repair are then added to the basic construction costs to give the overall repair costs. The estimated overall repair costs are then converted back to 1980 dollars by assuming discrete compounding and a discount rate I of 4%: Cost(1980$)  =  Cost(1990$) (1 j)10  In the cost estimate (Dinwiddie, 1990), a 20% general conditions fee and a 20% contingency  fund are added to the total of the estimates.  Adding a 20% contingency fund is considered redundant  when 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 5.7 Summary of Estimated Repair Costs For 50% Damage (In 1980 Dollars)  Estimated Repair Cost 20% G.C./Fee Total Cost per square ft  Structural 4,668,000 934,000 5,602,000 200  Architectural 12,066,000 2,413,000 14,479,000 517  Total -  -  20,081,000 717  Note that the cost of architectural repair is almost three times of the cost of structural repair due to the special architectural features, i.e. the mosaic, the stained glass windows, etc.  5.2.1.4 Assigning Damage Costs to Damage States The repair cost and replacement cost will be used as references to estimate damage costs of different damage states. It is assumed that all damages will be repaired each time after an earthquake, regardless of the size of the damages. rationale on assigning damage costs to each state. State 1: Damage Factor: 0%. The associated damage cost is $0.  72  The following is the  Chapter 5 Loss Estimate  State 2: Damage Factor 0  1%, CDF  -  =  0.5%. There will be no structural damage but some  minor architectural damages. According to the definition of this damage state, no repair is required. The damage cost associated with this state could be $0. However, it is assumed that the minor architectural damage is visible and repair is desired.  The repair cost will be linearly proportional to the 50%  architectural repair cost in Section 5.2.1.3, i.e. x $14,479,000 = $145,000. 50 State 3: Damage Factor 1  10%, CDF = 5%. Similar to state 2, there will be no structural repair  -  cost but architectural repair cost which is proportional to the 50% case, i.e. $14,479,000 =$1,448,000. 50 State 4: Damage Factor 10  30%, CDF  -  =  20%. The Church suffers moderate damage on both  structural 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 structural -  and architectural elements. The cost associated with this state is equal to the 50% damage cost discussed in section 5.2.1.3., 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 can be assumed to vary linearly with respect to the repair costs estimated for 50% structural and/or architectural damage estimated. State 6: Damage Factor 60  -  100%, CDF  =  80%. According to FEMA-227 (VSP, 1992), if a  building suffers more than 60% damage, then demolition and replacement will be considered. In this case, due to the importance and historic value of the building, this may not be applicable. Repair is still a  priority over replacement. The practical concern is whether the damage is repairable. For example, given a 80% damage, the structure may still be repairable at high cost, however, it may be impossible to put the broken pieces of the mosaic or stained glass windows together again. Therefore, it can be assumed that  73  Chapter 5 Loss Estimate  the cost is a combination of repair cost of the structural elements and the replacement cost of the architectural elements. The costs of repairing structural elements are estimated in the same manner as that for 50% damage. The repair cost is about $8,074,000. The costs of replacing the architectural elements will be $3,500,000 according to Section 5.2.1.2.  The total damage cost is therefore,  $11,574,000. State 7: Damage Factor 100%. This damage suggests totally destruction of the Church. The cost related to this level is the replacement cost, $7,000,000, discussed in Section 5.2.1.2. The 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 the change in architectural damage cost from damage state 5 to damage state 6.  In damage state 5, the  architectural damage cost is associated with repair whereas in damage state 6, the architectural damage cost is associated with replacement.  TABLE 5.8 Direct Costs: Facilities Repair and Replacement For Each Damage State (In 1980 Dollars) Damage State 1 2 3 4 5 6 7  Damage Factors 0 0 1 1 10 10 30 30 60 60 100 100 -  -  -  -  -  CDF 0 0.5 5 20 45 80 100  Structural 0 0 0 2,241,000 5,602,000 8,074,000 3,500,000  Architectural 0 145,000 1,448,000 5,791,000 14,479,000 3,500,000 3,500,000  Total 0 145,000 1,448,000 8,032,000 20,081,000 11,574,000 7,000,000  5.2.2 Costs of Deaths and Injuries  The factors involved in estimating the costs of deaths and injuries include: the occupancy rate of the building, the expected death and injury rates, and the value of human lives.  74  Chapter 5 Loss Estimate  The typical number of occupants for buildings with different social functions is listed in Table 38, p. T3-19 of FEMA-227 (VSP, 1992) (original from Table 4.12, p.126  -  127 of ATC-13). The typical  occupancy 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: 28,000 sqft 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 + 0 2  =  9lopeople.  Death and injury rates increase with increasing damage states. They also depend on the structure  type and condition of individual buildings. Consensus values of expected death and injury rates for the seven damage states are given in FEMA-227 (VSP, 1992) (original from ATC-13) and listed in Table 5.9.  TABLE5.9 Expected Death and Injury Rates For Existing Vulnerable Buildings From Table 3-9, p. T3-20 of FEMA-227 (VSP, 1992) (Original from Table 9.3, p 266 of ATC-13) Damage State 1 2 3 4 5 6 7  CDF  (%) 0 0.5 5 20 45 80 100  Injury Minor Serious 0 0 0.000030 0.000004 0.000300 0.000040 0.003000 0.000400 0.030000 0.004000 0.300000 0.040000 0.400000 0.400000  Death 0 0.00000 10 0.0000 100 0.0001000 0.00 10000 0.0100000 0.2000000  These 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 frame buildings.(VSP, 1992)  75  Chapter 5 Loss Estimate  The 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 adjusted  with engineering experience and judgment. It is assumed that “the strengthening rehabilitation lowers the death and injury rates to those that would be expected if the building damage states were three states lower.”(VSP, 1992)  Strengthening programs are expected to reduce the death and injury rates  significantly since increasing life safety is the prime objective. The expected rates are listed in Table 5.10.  TABLE 5.10 Expected Death and Injury Rates For Life-Safety Rehabilitated Buildings From Table 3-9, p T3-20 of FEMA-227 (VSP, 1992) Damage State 1 2 3 4 5 6 7  CDF  (%) 0 0.5 5 20 45 80 100  Iniury Minor 0 0 0 0 0.000030 0.000300 0.003000  Serious 0 0 0 0 0.000004 0.000040 0.000400  Death 0 0 0 0 0.0000010 0.0000100 0.0001000  The cost of life used in different studies varies from few thousand dollars to over a hundred million. FEMA-174 (Building Systems Development et al., 1989) suggests using the Nuclear Regulatory Commission’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. of Agriculture) to $8 million per life (by Enviromnental Protection Agency) in 1990 dollars (i.e. about $0.7  million 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 consensus value 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.  76  Chapter 5 Loss Estimate  So 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 of  information in estimating injury cost; it is assumed that the cost of life is the main concern in the cost estimates. The expected cost of life for each damage level is calculated by the product of the average number of occupants (i.e. 910 people), the cost per life ($1,250,000 per life in 1980 dollars) and the death rate (listed in the Table 5.9 and 5.10 above). The result is listed in the following table.  TABLE 5.11 Expected Cost of Life For Each Damage State (In 1980 Dollars) Damage State 1 2 3 4 5 6 7  CDF (%) 0 0.5 5 20 45 80 100  Existing Church 0 1,100 11,000 114,000 1,138,000 11,375,000 227,500,000  Rehabilitated Church 0 0 0 0 1,100 11,000 114,000  The expected cost of life for the existing church could be assigned as part of the direct costs for option 1 (Do-Nothing option) and the expected cost of life for rehabilitated church can be assigned as part of the direct costs for option 2 (Life-safety rehabilitation). The expected costs of life related to option 3 and 4 are assumed to be minimal since these two retrofit options provide much more strengthening for the structure than the life-safety requirement does and are expected to eliminated deaths.  5.2.3 Indirect Costs  Indirect costs refer to costs of economic and social impacts due to earthquake damages. It is hard to estimate, or assign monetary value to, impacts adversely on people or community resulting from damages and casualties. The impacts may not be tangible at first but will appear later and endure for a  77  Chapter 5 Loss Estimate  long period of time. It is hard to estimate the impacts for future events, since it is already difficult enough to measure them after an earthquake had happened. There is a gap in the knowledge of the overall economic and social consequences of catastrophic earthquakes.  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 tourist  related businesses on campus, such as selling of souvenir items, food courts opened in the summer, etc. It will also affect the normal operation of the Church, such as religious activities, weddings, etc. But it will not 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 Church is 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 was made in Venice, Italy and shipped to California. The mosaic facade was the largest in America when it was built. The original construction cost and the reconstruction cost added up to about $20 million in 1980 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 indirect costs should be no less than the direct costs estimated. The essence is that indirect costs are as important as the direct costs. The direct cost, according to FEMA-227 (VSP, 1992), is calculated by the product of the replacement cost and the CDF. It is increasing with the damage factors. The indirect costs should also increase with increasing damages. For historic buildings, like the Church in this project, the direct costs associated with repair and replacement do not increase with increasing damages.  Repair costs for partially damaged historic  buildings are always higher than replacement costs. When damages reach a certain level where repair is impossible, replacement is needed and the cost drops. In the estimates for direct costs for repair and  78  Chapter 5 Loss Estimate  replacement, the cost rises from $0 for damage state 1 to $20 million for damage state 5 (CDF=50%) and then 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.  The  relationship could be linear or exponential, depending on individual cases. It is assumed that the indirect costs vaiy linearly with damage factors in this project. The maximum indirect cost will be equal to the replacement cost of the Church, i.e. $7,000,000. This is equivalent to the assumption that the price to compensate the social disruption and psychological trauma caused by the damage is proportional to the price 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 5.12 Indirect Costs (In 1980 Dollars) Damage State 1 2 3 4 5 6 7  (%)  Indirect Costs  0 0.5 5 20 45 80 100  0 35,000 350,000 1,400,000 3,150,000 5,600,000 7,000,000  CDF  5.2.4 Summary of Damage Cost Estimates  Different 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 Regulatory Officials with Board of Education may also consider the indirect costs. An alumni I alumnae who was  married in the Church and had children attending Stanford would take the costs of life into account. In  this study, the interest is to find the best decision considering different combination of cost scenes.  79  Chapter 5 Loss Estimate  Four 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 cost The 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 that the costs of life are zero for option 3 and 4 since these two options are intended to eliminated death and provide for building integrity strengthening. The four data sets are listed in Table 5.13, 5.14 and 5.15 as follows.  TABLE 5.13 Case 1: Direct Costs and Case 2: Direct Costs Plus Indirect Costs For All Retrofit Options (All Costs in 1980 Dollars) Damage State 1 2 3 4 5 6 7  Direct + Indirect Costs  Direct Costs 0 145,000 1,448,000 8,032,000 20,081,000 11,574,000 7,000,000  0 180,000 1,798,000 9,432,000 23,231,000 17,174,000 14,000,000  TABLE 5.14 Case 3: Direct Costs with Costs of Life (All Costs in 1980 Dollars) Damage State 1 2 3 4 5 6 7  Option 1  Option 2  0 146,000 1,459,000 8,146,000 21,219,000 22,949,000 234,500,000  0 145,000 1,448,000 8,032,000 20,082,000 11,585,000 7,114,000  80  Option 3 & 4 0 145,000 1,448,000 8,032,000 20,081,000 11,574,000 7,000,000  Chapter 5 Loss Estimate  TABLE 5.15 Case 4: Direct Costs with Costs of Life Plus Indirect Costs (All Costs in 1980 Dollars) Damage State 1 2 3 4 5 6 7  Option 1  Option 2  0 181,000 1,809,000 9,546,000 24,369,000 28,549,000 241,500,000  0 180,000 1,798,000 9,432,000 23,232,000 17,185,000 14,114,000  81  Option 3 & 4 0 180,000 1,798,000 9,432,000 23,231,000 17,174,000 14,000,000  Chapter 6 Decision Analysis  CHAPTER 6 DECISION ANALYSIS  The data developed in the previous chapters will be organized to construct an expected value decision 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 investment and 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 accumulative expense from 1980 to 1990 will be estimated assuming the optimal option was adopted in 1980. The projected 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 accrue each 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 to a lump sum in present value.  •  EDC: Expected value of the Damage Cost corresponding to a retrofit option. This is the weighted average of the average damage cost associated with each earthquake intensity level.  82  Chapter 6 Decision Analysis  •  F, (I  V): Probability of Occurrence of one or more earthquakes with intensity equals to or greater  than MN’ll level V in one year, see Section 4.4. •  ): Probability of earthquake with intensity level 1 P(1  if an earthquake with intensity equals to or  greater than level V occurs, see Table 4.4, Section 4.4. •  ADC: Average Damage Cost corresponding to each earthquake intensity level. This is the weighted average of the damage cost associated with each damage state given an earthquake intensity level and adjusted by the expected reduction in damage factors.  •  ERD: Expected Reduction in Damage Factor, assigned according to the past performance of the Church and the effectiveness of each retrofit options. They are defined in Chapter 5.  •  1 J): Probability of the structure suffering damage state D when an earthquake with intensity P(D Ij 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 TREE  The decision can be best visualized by organizing all the elements of concern into a form of a decision tree. The first group of branches indicate the available alternatives, namely the proposed retrofit schemes and the initial investment costs.  Following the alternatives are the possible future events  controlled by nature, that is, the earthquake levels and the probability associated with each MMI level. In this study, earthquake intensities lower than MMI V are ignored since damages related to these levels are usually minimal. For each MMI level, there is a group of possible outcomes, i.e., the damage states. The probability and cost associated with each damage state are assigned accordingly. See Figure 6.1 for an overview of the elements involved in the decision.  83  Chapter 6 Decision Analysis  Cl c2 C3 C4 Cs C6 C7  IW2  NV3  1NV4  Investment of each Option  Earthquake  Damage Pmbability  Probabilities  of each Damage State at each Mlvii level  FIGURE 6.1 Decision Tree  84  Damage Costs  Chapter 6 Decision Analysis  6.3 INITL4L INVESTMENT OF RETROFIT OPTIONS (INV)  The retrofit options and the initial investment required for each option are discussed in Chapter 3. A summary is listed in Table 6.1. TABLE 6.1 Retrofit Options and Investment Costs Option Do Nothing  1. 2.  Description 1NV (in 1 980$) Add new structural system to support the weight of the 1,961,000 new organ and install the new organ. In additional to the Do Nothing option, seismic 3,502,000 strengthening the Church to meet life-safety standards. Seismic strengthening the Church to not only protect 5,577,000 occupants but also to prevent major damage to structural and architectural elements. Same objective as option 3, with removal of URM and 11,193,000 reconstruction of the Crossing area with reinforced concrete.  Life-Safety Strengthening Building Integrity A  3.  4.  Building Integrity B  6.4 TIME CONVERSION FACTOR (TCF)  If the annual expected damage (AED) costs are different for each year within the life span of the structure, then the present value of the total damage cost (PTD) can be calculated by the following equation: PTD=  AED + AED 1 2 + (1+1) (1+1)2  +  AEDT )T + 1 (  (6.1)  where i is the discount rate and T is the planning horizon or the life span of the structure. Each year’s damage cost is discounted to its present value and then added together to yield the present value of the total expected damage cost.  85  Chapter 6 Decision Analysis  If the annual expected damage cost is assumed to be constant each year, then the equation above  can be simplffied as PTD=AEDxTCF  (6.2)  where TCF=  1  (l+._T “  (6.3)  as suggested by FEMA-227 (VSP, 1992). Assuming the annual expected damage cost constant eveiy year is equivalent to assuming that the annual probabilities of future earthquakes of various intensities are constant and that the effectiveness of the rehabilitation in reducing casualties, damages and losses is also constant. The annual probabilities of future earthquakes, in fact, vaiy depending on the preceding seismic events. “The probability of an earthquake along a fault segment is initially low following a large segment  rupturing earthquake and increases with time as stress on the segment recovers the stress drop of the prior ehquake.” (Working Group On California Earthquake Probabilities, 1990) The effect of the variation is quite obvious in the short term. However, in the long term, the effect of the variation would be averaged out. Furthermore, the probabilities adopted in this project are based on historic records and they are intended 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 as constant throughout the life of the structure if the building is properly maintained. As time goes by, the concrete will get stronger and the rebars will stay the same as long as they are not rusted.  6.4.1 Life Span T  In general, for ordinary buildings, the life span or the length of the planning horizon is usually taken as 30 to 50 years (VSP, 1992). Due to the importance of this Church, a life span of 100 years is used.  86  Chapter 6 Decision Analysis  6.4.2 Discount Rate I  In simple terms, the discount rate I is the real interest rate, that is the bank interest rate minus the inflation rate.  There are many different ways and divergent opinions on deriving or choosing an  appropriate discount rate for benefit-cost analysis. The selection of discount rate I is discussed in Section 3.4C, 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 used as 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 subtracting the interest rate (r  ) by the percent  change in GNP implicit price deflator (dp, which is the annual  rate of inflation).  Both terms are averaged from the observed data of the past 3 years and the  forecasted data of the future 17 years with respect to the year of concern. The Social Time Preference discount rate can be formulated as follows: dp  rt =  t1  20  (6.4)  —  20  The calculated rate for 1986, by Young and Howe (1988) (as quoted in VSP, 1992), for public sectors was 3% using the return on the municipal bonds, and for private investments was 6.5% using the return 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. The discount rate suggested by this approach is 3% for 1981. Assume that Stanford is borrowing funds from the bank to finance the rehabilitation project and  future damage repairs. The cost of the funds is the bank rate.  Since the funds will be paid back in  inflated 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.  87  Chapter 6 Decision Analysis  In general, a discount rate of 3% or 4% is considered reasonable for public sectors and slightly higher 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 TCF  =  =  4% and T = 100 years,  24.505. If a lower discount rate I is used, the value of TCF will be higher. The corresponding  PTD 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 and progress 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 the conditional probabilities from the DPM, P(D 1 /Ij). and the damage costs C 1 of the damage states. The set of probabilities is mutually exclusive and exhaustive. These are the data on the third and fourth column on the decision tree.  The sum is then adjusted by the ERI) factors to take into account the past  performance of the Church and the expected effectiveness of the retrofit The ERD factors are different at different intensity levels for each retrofit scheme. The adjusted expected damage cost is called the average damage 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 multiplied by the earthquake probability, P(Jj) at the same intensity level.  The set of earthquake probabilities is  mutually exclusive and exhaustive. The expected value of the damage cost, EDC, corresponds to a retrofit option is then calculated by adding the products of the ADCs and the earthquake probabilities: )x ADC(1 1 EDC = P(I ) 1  (6.6)  88  Chapter 6 Decision Analysis  The EDC is converted to annual expected damage cost, AED, by multiplying by the annual probability of occurrence of earthquake greater than MIvil V. i.e. P, (I AED=EDCxP,(IV)  V)as shown in Eqn. (6.7): (6.7)  The AED is the expected damaged cost that would accrue each year over the life span of the structure corresponding to a retrofit scheme. As discussed in Section 6.4, the present value of the total damage cost, PTD, can be calculated by multiplying the AED by a time conversion factor, TCF, as shown in 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 RESULTS  As mentioned in Chapter 5, different decision makers may have different emphasis on the cost scenes. In order to find the best decision considering different combination of costs, four sets of damage costs 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.  investment for each option (extracted from Table 6.1).  89  The table also indicates the initial  Chapter 6 Decision Analysis  TABLE 6.2 Results of Decision Analysis (All Cost in 1980 Dollars)  1NV Case 1 2 3 4  Option 1 1,961,000 26,208,000 31,210,000 29,465,000 34,466,000  4 4 4 4  Option 2 Option 3 3,502,000 5,577,000 Net Present Costs (Followed by Ranicing) 18,120,000 3 8,316,000 1 21,129,000 3 8,799,000 1 18,122,000 3 8,316,000 1 21,131,000 3 8,799,000 1  Option 4 11,193,000 12,381,000 12,630,000 12,381,000 12,630,000  2 2 2 2  Option 1, do nothing option, has the highest NPC. It indicates that by doing nothing in present time may result in tremendous expenses on repairing earthquake damages in the future. The difference between the NPC of option 2, life-safety retrofit, and the NPC of option 4, building-integrity B, are considerably large. This suggests that the high INV of option 4 is justified in reducing the threat of earthquake damages and the hassle of damage repair in the future if there is only option 2 and option 4 available.  However, when comparing to the NPC of option 3, the high 1NV of option 4 sounds  uneconomical. The NPC of option 3 is about 2/3 of that of option 4. Therefore, the decision analysis recommended 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 costs of life and the indirect costs. The NPCs are not increased significantly when the costs of life or indirect costs are taken into account in the calculation. The two costs are significant in high damage states, which are associated with high Mlvii levels. In calculating the expected values, the influence of the two costs are reduced 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 the NPCs of the first two options (option 1 and 2) and the last two options (option 3 and 4). This could be due to the big differences between the expected reduction in damage of the two groups.  In this decision  analysis, 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.  90  Chapter 6 Decision Analysis  6.7 COST COMPARISON  In  this section, the accumulative expense of two scenarios will be compared. The first case is the 1980 to 1990. The second case is the proposal  actual case, i.e. what was really done to the Church from  by the decision analysis, i.e. doing seismic strengthening option  3 in 1980 during the organ installation.  TABLE 6.3 The Description of the Two Cases  Year  1980  Case 1 Actual Case Organ installation, structural  Decision Analysis Suggestion  upgrade in foyer area.  upgrade in foyer area, building  Case 2 Organ installation, structural  integrity seismic strengthening (option 3). 1985  Roof repair.  No repair necessary.  1990 after Loma Prieta Earthquake (Mtvll VIII)  Repair and building integrity  Repair small damages associated with MIvil VIII.  seismic strengthening.  The accumulative expense of each scenario is expressed in 1990 dollars. The conversion is done by assuming a discrete compounding  and a discount rate I of 4%. The conversion for case 1 is listed in  Table 6.4.  TABLE 6.4 1980 to 1990 of Case 1: Actual Case  Accumulative Expense from Year  1980  Work  Organ installation, structural  Cost  multiplied  Cost in  1,961,000  by ( 1 + I )‘  1990$ 2,903,000  1 + I )5  2,129,000 8,500,000  upgrade in foyer area.  1985 1990 after Earthquake  Roof repair. Repair and building integrity seismic strengthening.  1,750,000 8,500,000  ( 1  Total Expense:  91  13,532,000  Chapter 6 Decision Analysis  If retrofit option 3 were done in 1980, the repair cost for damages in the Loma Prieta earthquake would be estimated as follows. The first step is to select the MDF from the DPM in Table 5.3. The MDF is about 20% at Ivilvil VIII. The ERD factor for option 3 in large earthquakes is 90% in Table 5.6. The expected damage will be: (1—0.90)x20% =2% and the associated damage cost is about -_x$14,479,000=$579,000  (in 1980 dollars).  The high cost of repair for even low damage percentage, is mainly due to the delicacy of the architectural elements, mainly refers to the mosaic.  Strengthening the four mosaic angels was on the strengthening  scheme, yet the others around the interior walls and on the facade were not completely included. Therefore, there is still a chance that the mosaic would be damaged in a major earthquake. The projected accumulative expense of adopting retrofit option 3 in 1980 is calculated in the following table.  TABLE 6.5 Accumulative Expense from 1980 to 1990 of Case 2: Decision Analysis Suggestion Year  1980  1985 1990 after Earthquake  Work  Cost  Organ installation, structural  5,577,000  upgrade in foyer area, building integrity seismic strengthening (option 3). No roof repair necessary. Repair small damages.  0 579,000  multiplied  Cost in  by (1  8,255,000  1990$ +  j )10  0 (1 + I )10  Total Expense:  0 857,000 9,112,000  Compare 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 in 1980, about $4.4 million (in 1990 dollars) would have been saved by 1990.  92  There is a very high  Chapter 6 Decision Analysis  likelihood that the minor damages to the Church in the 1989 Loma Prieta Earthquake would not require repair if the strengthening was done in 1980. Therefore, the saving is very likely to be close to $5.3 million (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 earthquake  within the 10 years time frame. According to the decision model, considering a life span of 10 years from 1980, the expected future damage cost of option 1 is about $11.8 million whereas the expected future damage cost of option 3 is only $1.3 million. The estimated difference is about $10.5 million in the short term. Considering a 100-year life span, the difference in the expected future damage cost will be even greater. The expected future damage cost of option 1 is about $35.8 million whereas that of option 3 is $4 million. The difference would be $31.8 million in the long run. (All costs in 1990 dollars)  93  Chapter 7 Sensitivity Analysis  CHAPTER 7 SENSITIVITY ANALYSIS  The objective of this chapter is to detect the sensitivity of the outcome of the decision to the variation in the input data. Since the input data used in the analysis are mainly estimated and involve many uncertainties, it is important to find out if the outcome is sensitive to the accuracy of the input. The major 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.  The  relationship between the changes in data and the outcome of the decision will be examined. The outcome of the decision refers to the optimal option selected based on the lowest net present cost (NPC). The ranking of the options is also concerned. When appropriate, the changes in the values of the NPC of each option will also be studied.  7.1 SEISMIC DATA  The earthquake probabilities derived in Chapter 4 are based on the annual occurrence rates given  by Algermissen et aL (1980).  These rates could be overestimated or underestimated for the site as  discussed in Section 4.6. It is assumed that the accuracy is within ±25% of the data. In order to examine the effect of the accuracy of annual occurrence rates, the annual occurrence rate of each MMT level will be  94  Chapter 7 Sensitivity Analysis  varied by ±25% each time. For example, the annual occurrence rate of MtvII V is reduced by 25% in the first set of data and increased by 25% in the second set of data as shown in Table 7.1.  TABLE 7.1 Example of Data Set 1 & 2  Varying Annual Occurrence Rate of MMI V By ±25% Mvil V VI VII VIII IX X XI XII  Original 1.97 0.74 0.281 0.106 0.040 0.015 0.0057 0.0021  Set 1 1.4775 0.74 0.281 0.106 0.040 0.015 0.0057 0.0021  Set 2 2.4625 0.74 0.281 0.106 0.040 0.015 0.0057 0.0021  Note that since only one rate is varied at a time, there are in total 16 sets of data tested. The changes in the 16 data sets are summarized in the Table 7.2.  TABLE 7.2 Data Sets for Variation in Annual Occurrence Rate of Each MN4I Level Data Set 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  MIvil level V V VI VI VII VII  VIII VIII IX IX X X XI Xl XLI XII  Changes -25% +25% -25% +25% -25% +25% -25% +25% -25% +25% -25% +25% -25% +25% -25% +25%  Substitute Value 1.4775 2.4625 0.555 0.925 0.21075 0.35125 0.0795 0. 1325 0.030 0.050 0.01125 0.01875 0.004275 0.007125 0.001575 0.002625  The NPCs calculated by using these 16 sets of data are obtained and listed in Table 7.3. The  percentage change from the original NPCs is calculated to compare the influence of the accuracy of each  95  .  C  (-b)  t.)  I  000-  1k  $1 I  I  •  I-  I  -  —  —  —  -  I-  -  00 00 00 0s 0 00 ‘.0 00 1 ‘.0 -.. Ui C’ . t) 00 0 0 00 . C’ ‘-  -  ..  .  .  .  —  o  a  o 0  CD  00 Ui  I-  —  t%)  -  -.  —  ‘.0 Ui -.1  I-s-  t’.)  •-  —  .)  . C  I  C)  I-’  I  Ui 0 . C t’.) ‘.0  I-  0’, 00  1  -.  t.)  —  I  I  -  0’, 00 ‘. 0 (.6  I  —  — — — — — —  -  !a. —  0Ui0o  i-  0000000000000000000000000000000000  c3cc  00 00 00 00 00 00 I— 0 0 .. 00 -. Ui Ui ‘.0 — ) c. . 0 0 ‘.0 -  I  .  0000O0) . 0 . -.J Ui a Ui 00 0 ‘0 0 C Ui . Ui . 00 00  ac0  o  % C) 00 CD  0<  0  z  z  1.  I  CD  rJ)  CD  0  Chapter 7 Sensitivity Analysis  As observed from Table 7.3, the outcome of the decision remains unchanged, option 3 is the optimal option with the lowest NPC in all the trials. The ranking is also unchanged, option 3 followed by option 4, option 2 and 1. Changing the annual occurrence rates does not affect the values of the NPCs of the four options significantly. The percentage changes of set 1 and 2 reflect the influence of the annual occurrence rate of MMJ V, 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 is suggested that the accuracy of the annual occurrence rate of Mlvii V has, relative to other MMI levels, the greatest influence on the NPCs. The percentage changes of set 5 & 6, 7 & 8 and 9 & 10 are quite obvious in comparison to other data sets. Hence, the accuracy of the annual occurrence rates of MMI VII, VIII and 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 only 14% whereas most are less than 5%. It can be concluded that the values of the NPCs are not sensitive to the changes, within ±25%, in the annual occurrence rates. The outcome of the decision is also insensitive to the changes in the annual occurrence rates.  7.2 ER]) FACTORS  The original ERD factors assigned in this project are listed in the following table.  TABLE 7.5 The Original ER]) Factors  Option 1 2 3 4  Mil Vil-IX 5 40 90 95  V-VI 20 65 99 99  97  X-XII 0 25 80 90  Chapter 7 Sensitivity Analysis  The ER]) factors are assigned mainly based on engineering knowledge and judgment.  The  assessment is subjective and could be quite different when assigned by different people. It is assumed that different assessments could be made ±25% around the original estimates. The ERD factors of each option will 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 NPCs proportionally, which will yield the same outcome as before. Also note that changes in the ERD factors of option 1 will also cause changes in the ER]) factors of option 2 since the ERI) factors of option 2 are dependent on that of option 1 (see derivation in Section 5.1.3.3). The changes in the ER]) factors in each set of data are listed in the following table.  TABLE 7.6 Data Sets for Variation in ER]) Factors of Each Retrofit Option Data Set  Options  Changes  1  Optioni (Option 2) Optioni (Option 2) Option 2 Option 2 Option 3 Option 3 Option 4 Option 4  -25% (same amount) +25% (same amount) -25% +25% -25% +25% -25% +25%  2 3 4 5 6 7 8  Substitute ER]) Factors V-V1 Vil-IX X-Xll 4 15 0 60 39 25 25 6 0 70 41 25 49 30 19 81 50 31 74 68 60 100 100 100 74 71 68 100 100 100  In Set 6 and 7, the ER]) factors of option 3 are higher than the ERD factors of option 4. This is in contradiction to the definition of the retrofit schemes: option 4 is supposed to provide more safety for the structure than option 3. In option 4 all the unreinforced masonry walls have to be removed and rebuilt with reinforced concrete but in option 3 the unreinforced masonry walls will be strengthened.  The  expected 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.  98  Chapter 7 Sensitivity Analysis  TABLE 7.7 Net Present Costs By Varying the ER]) Factors of Each Retrofit Option (All Costs in Thousand and in 1980 Values)  Data Set 1 2 3 4 5 8  Net Present Costs (Followed by Ranking) Option 2_ Option 4_ Option 3_ 4 18,657 1 12,381 3 8,316 2 4 17,583 1 12,381 2 3 8,316 4 21,065 3 1 12,381 2 8,316 4 15,175 12,381 3 8,316 1 2 4 18,120 3 14,337 2 12,381 1 4 18,120 3 8,316 1 11,193 2  Option 1_ 26,746 25,671 26,208 26,208 26,208 26,208  As 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, followed by option 4, option 2 and then option 1. This is mainly due to the large differences in the NPCs between option 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 the outcome of the decision. The NPC of option 3 becomes higher than that of option 4. Hence, option 4 becomes the optimal option. On the other hand, in data set 8, increasing the ER]) factors of option 4 to 100% for all Mlvii levels does not change the outcome. This suggests that even if there is no future earthquake damage by adopting retrofit option 4, the initial investment of option 4 is still more expensive than the sum of the initial 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 3  and option 4. The results are listed in the following table. TABLE 7.8 Net Present Costs of Option 3 by Using Different ER]) Factors (All Costs in Thousand and in 1980 Values) Data Set No Damage Original -10% -15% -20% -25%  ER]) Factors (%) V-v1 Vil-Ix x-xII 100 100 100 99 90 80 89 81 72 84 77 68 79 72 64 74 68 60  99  NPC ($) 6,004 8,316 10,725 11,929 13,133 14,337  Chapter 7 Sensitivity Analysis  Table 7.9 Net Present Costs of Option 4 by Using Different ER]) Factors (All Costs in Thousand and in 1980 Values) Data Set NoDaxnage  Original -10%  -15% -20% -25%  ER]) Factors V-VT Vil-IX 100 100 95 99 86 89 81 84 76 79 71 74  (%)  NPC  X-Xll 100 90 81 77 72 68  ($)  11,193 12,381 14,902 16,162 17,423 18,683  When the ER]) factors of option 3 are reduced by more than 20%, its NPC will exceed the original NPC of option 4. Option 4 will become the optimal option. Option 4 will always have a chance to become the optimal option if its ER]) factors are not reduced by more than 10% from the original estimates. The outcome depends on the ER]) factors of both option 3 and option 4. It can be concluded that 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 COSTS  7.3.1 Direct Costs  Direct 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 it is 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 original increased by 20%. The values are listed in Table 7.10 and the results are listed in Table 7.11.  100  Chapter 7 Sensitivity Analysis  TABLE 7.10 Data Sets for Direct Costs (AU Costs in Thousand and in 1980 Value) Damage States 1 2 3 4 5 6 7  Original 0 145 1448 8032 20081 11574 7000  Set 1 0 116 1158 6426 16065 9259 5600  Set 2 0 174 1738 9638 24097 13889 8400  TABLE 7.11 Net Present Costs By Using Different Direct Costs (All Costs in Thousand and in 1980 Values)  Data Set  Original 1 2  Net Present Costs (Followed by Ranking) Option 1 Option 2 Option 3 Option 4 26,208 4 18,120 1 12,380 3 8,316 2 21,357 4 15,196 3 7,854 1 12,143 2 31,059 4 21,044 1 12,618 3 8,779 2  The NPCs of option 3 remains the lowest, followed by option 4, option 2 and option 1. The changes in the direct costs have less effect on the NPCs of option 3 and 4 than on the NPCs of option 1  and 2. The changes in the NPCs of option 3 and 4 are about ±6% and ±2%, respectively. The changes in the 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 assigned based on the central damage factor (CDF) for each damage state. For example, the CDF for damage state 4 is 20% whereas the damage factors of this damage state ranged from 10% to 30%. The actual damage cost could vaiy substantially within a defined state. It is assumed that the variation is ±50% around the original estimate. The damage cost of each individual damage state will be varied at a time to examine the effect on the NPCs. The data set is listed in Table 7.12 and the results are listed in Table 7.13.  101  I  —.  •  CD  CD  CD  CD  8  00  g  00  CD  —  -  C)  0  S  0  —  0  0  g  . CD  CD  c,  C-  •  (-)  )  I  OCD  CD  -  D)  CD  0  0  C-)  I  0  C,  I  CD  -  .  00 ‘0 t3 00 ‘0 CJ 00 ‘0 0 -  ‘ . 0 ‘0 00 . (i 00  -  —  CD  z  )  )-  I-  - — •-  t•-)  -  - C.. 00 . 00  C-  ——  00 C.)  t.-  CC-  ‘J t—.) t-) t-.)  . .  t- t-)  — —  00 - t-) C..) O C’. C..) ‘0 0  i-  C-  v a’ —a t-  1 C-  C-  C-  s C..)  —  -‘  —  t-) t’) t  —  t’.)  ‘000 — 00 C.) ‘0 0  C  -  -  O —‘0 . 0  —  I-  0 C..)  —  I-  —  — —  -  — .) J 0  0000000000 - 00 — 0000000000 -‘0 0000 .  0  <tTl  000  I—  -  o ci  0  ‘—  -  —a —a o o  I-. . L’-) — 3 I— 1 00 00 00 - 0 U U ‘0 C 00 00 00 U ‘0 0 t3 00 ‘ 0 ‘0 00 Ji 0’ 00 ‘0 00 . U 00 00 0 0  —  (.)  ‘  j.  0  ..)  )  .  C.)  -.  — CJC 0 0  C-  —  . -3 00C’.00.)C-.-) 0CC00  I-  000000000000  C•Cfl  —) —) C’. C’. CJ U . . C.)  %C00C..)-’  CD  <  U)  c  C,)  g  C,)  CD  00  ‘  —.  0  0  So 0  I  I  Cl)  C,) CD  Chapter 7 Sensitivity Analysis  TABLE 7.14 The Percentage Changes From the Original NPCs Due to Changes in Damage Cost of Each Damage State Data Set 1 2 3 4 5 6 7 8 9 10 11 12  Option 1 -0.6 0.6 -13.2 13.2 -17.5 17.5 -12.6 12.6 -2.2 2.2 -0.1 0.1  Option 2 -0.4 0.4 -9.6 9.6 -16.0 16.0 -12.0 11.9 -2.3 2.3 -0.1 0.1  Option 3 -0.0 0.0 -1.8 1.8 -5.8 5.8 -4.9 4.9 -1.3 1.36 -0.0 0.1  Option 4 -0.0 0.0 -0.7 0.7 -2.0 2.0 -1.7 1.7 -0.4 0.4 -0.0 0.0  Comparing the percentage changes listed in Table 7.14, the data set 5 and 6 have the greatest changes, followed by set 3 and 4 and set 7 and 8. In data set 5 and 6, the direct cost of damage state 4 are changed by ±50%. It suggests that the direct cost of this damage state (damage factors range from 10 to 30%, 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 to 60%, CDF is 45%) also affect the NPCs. The effect of changing the direct costs of the other damage states are considered minimal, especially for damage state 7. The percentage changes of data set 11 & 12 almost equal to zero for all options.  This study suggests that, in estimating the damage costs, more attention should be paid to the accuracy 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 of the direct cost of damage state 7, i.e. the replacement cost, is the least important one.  103  Chapter 7 Sensitivity Analysis  7.3.2 Indirect Costs  Indirect costs refers to costs of economic and social impacts due to earthquake damages. There is no particular rules for assigning indirect costs. In Chapter 5, it is assumed that the indirect cost is the product of the central damage factor (CDF) and the replacement cost. In the sensitivity analysis, three sets of indirect costs will be used. The indirect costs in data set 1 are the original indirect costs increased by 50%, in set 2 are the original indirect costs increased by 100% and in set 3 are equal to the original direct costs. The values are listed in Table 7.15 and the results are listed in Table 7.16.  TABLE 7.15 Data Sets of Indirect Costs (All Costs in Thousand and in 1980 Values) Damage States 1 2 3 4 5 6 7  Original 0 35 350 1400 3150 5600  7000  Set 1 0 53 525 2100 4725 8400 10500  Set 2 0 70 700 2800 6300 11200 1400  Set 3 0 145 1448 8032 20081 11574 7000  TABLE 7.16 Net Present Costs By Using Different Indirect Costs (All Costs in Thousand and in 1980 Values)  Data Set 1 2 3  Net Present Costs (Followed by Ranking) Option 1 Option 2 Option 3 Option 4 33,712 4 22,634 3 9,041 2 1 12,754 36,211 4 24,138 3 9,282 1 12,879 2 50,456 4 32,738 3 10,629 2 1 13,569  The outcome and the ranking of the decision remain unchanged when the indirect costs are increased by 50%, 100% or even equal the direct costs. Option 3 still has the lowest NPC. This suggests that the indirect costs may not be as important and influential as expected in the decision maldng.  104  Chapter 7 Sensitivity Analysis  7.4 TIME CONVERSION FACTORS: DISCOUNT RATE AND LIFE SPAN  7.4.1 Discount Rate  There are different approaches in estimating discount rates, as discussed in Chapter 6.  The  possible values of discount rate range from 3 to 10%. Four discount rates will be used: 4%, 6%, 8% and 10%. TABLE 7.17 Effect of Discount Rate on the Net Present Costs (All Costs in Thousand and in 1980 Values)  Discount Rate 0.04 0.06 0.08 0.10  TCF 24.5 --16.6 12.5 10.0  Option 1 26,208 18,404 14,324 11,855  Net Present Costs (Followed by Ranking) Option 2 Option 3 Option 4 4 4 4 4  18,120 13,415 10,955 9,467  3 3 2 2  8,316 7,572 7,183 6,948  1 1 1 1  12,380 11,999 11,799 11,678  2 2 3 3  As discount rate increases, the PTD (present value of the total damage costs) decreases and hence, the NPC decreases. Option 3 has the lowest NPC in all cases. The ranking of option 2 and option 4 are switched when the discount rate exceeds 8%. Note that the NPCs of option 1 and option 4 are veiy close when the discount rate reaches 10%. This suggests that when the discount rate is high, the decision will shift to less expensive and less safe options because money spent in the future costs less in the present time.  Eagerness to invest decreases, and willingness to take the risk of paying future damage cost  increases. Using a lower discount rate is considered more conservative, since it amplifies the present values 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 of the decision will remain the same.  105  Chapter 7 Sensitivity Analysis  7.4.2 Life Syan  Three different life spans will be used: 100, 50 and 30 years. For ordinaiy buildings, a  30-year or  50-year life span is sufficient but for historic buildings, a life span of 100 years is usually recommended. TABLE 7.18 Effect of Life Span on the Net Present Costs (All Costs in Thousand and in 1980 Values)  Life Span 100 50 30  TCF 24.5 21.5 17.3  Net Present Costs (Followed by Ranking) Option 1 Option 2 Option 3_ Option 4 26,208 4 18,120 2 3 8,316 1 12,380 23,217 4 16,317 3 2 8,031 1 12,234 19,071 4 13,717 3 7,636 1 12,031 2  As life span shortens, the P11) decreases and hence the NPC decreases. However, the reduction does not affect the outcome and the ranking of the decision. Option 3 still has the lowest NPC, followed by option 4, option 2 and option 1. The present value of the total damage costs that accrued between year 30 to year 100 is quite small in comparison to the present value of the total damage costs that accrued between year 1 to year 30.  Changing the life span from 100 to 30 years will not reduce the PTD  significantly. Hence, it can be concluded that the outcome of the decision is insensitive to the changes in the life span.  7.5 CONCLUSION OF SENSITWITY ANALYSIS  Seismic Data  The outcome and the ranking of the decision are insensitive to the annual occurrence rates varying within ±25% of the original data. Hence, an accuracy of 25% is considered sufficient for this decision analysis. Among different MIvil levels, the annual occurrence rate of Mlvii V has the greatest  106  Chapter 7 Sensitivity Analysis  influence on the NPCs. The annual occurrence rates of Mlvii VII, VIII and IX also affect the NPCs slightly whereas those of Mlvii X and above have minimal effects. if higher accuracy in the outcome is needed, more attention should be paid on the estimation of annual occurrence rates of Mlvii V to IX than those 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 Factors The outcome of the decision is sensitive to the changes in the ER]) factors of both option 3 and option 4 but not sensitive to the changes in the ERD factors of option 1 and option 2. There are many possible combinations of ER]) factors to be assigned for option 3 and option 4. Guidelines for estimating effectiveness of retrofits and better methods for predicting structural behavior are needed to improve the accuracy of the assessment. It is also recommended that consensus opinion should be obtained from wellinformed and experienced engineers in order to construct a fair and representative set of ERD factors.  Damage Costs The direct costs are varied by ±20% as a whole and also varied by ±50% at each individual damage state. The outcome of the decision is insensitive to changes in both sets of cases. It is found that changing the direct cost of damage state 4 (damage factors 10 to 30%) induces the highest percentage change in the NPCs, followed by damage state 3 (damage factors 1 to 10%) and damage state 5 (damage factors 30 to 60%). This suggests that, if higher accuracy in the outcome is needed, more attention should be paid on damage state 3, 4 and 5 when estimating direct costs. The change in the direct cost of damage state 7, i.e. the replacement cost, induces almost zero changes in the NPCs. Hence, there is no need to pursuit 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. The outcome and the ranking of the decision remain unchanged. This suggests that the indirect costs are not as important and influential as expected in the outcome of the decision.  107  Chapter 7 Sensitivity Analysis  Time Conversion Factors: Discount Rate and Life Span If the discount rate is varied within a reasonable range, 3  -  6%, the outcome of the decision is  stable and insensitive to the changes. If the discount rate exceeds 8%, the outcome remains the same, but the ranking will change. Option 3 remains as the optimal option, but option 2 is then preferred over option 4. In general, as the discount rate increase, the decision will shift to less expensive and less safety option. Three life spans are tested: 100, 50 and 30 years. The outcome and the ranking are insensitive to the changes in the life span used. However, since historic buildings are of concern in this project, a 100year life span is still recommended.  108  Chapter 8 Conclusion  CHAPTER 8 CONCLUSION  In this thesis, the process for selecting and deriving the necessaiy data to construct an expected value decision model for selecting seismic retrofit schemes for a historic building was demonstrated through a case study. Net present costs (NPC) were used to rank the retrofit options. The NPC of an option was defined to be the sum of the initial investment cost and the present expected value of the total future damage costs. Four retrofit options were assumed to be proposed to upgrade the Stanford Memorial Church in 1980. Option 1 was to do nothing in tenns of seismic strengthening, at a cost of about $2 million. Option 2 was to strengthen the Church to life-safety standard, at $3.5 million. Option 3 was strengthening to building integrity level without removing the unreinforced masomy (URM) walls, at $5.6 million, and option 4 was strengthening to building integrity level with removal of URM walls, at $11.2 million (all in 1980 dollars). Seismic data were selected to derive a set of earthquake probabilities. A Damage Probability Matrix (DPM) was developed for the Church.  ERD (Expected Reduction of Damage) factors were  assigned 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 were chosen 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. This recommendation is considered as a confirmation to the common sense developed by those who studied the case closely,  If retrofit option 3 had been adopted in 1980, the projected accumulative expense from  1980 to 1990 would be about $5 million, in 1990 dollars, less than the actual accumulative expense. The saving was about 40% of the actual accumulative expense. If the earthquake had not occurred, the short term saving from 1980 to 1990 would be about $10.5 million, in 1990 dollars, estimated by the decision  109  Chapter 8 Conclusion  model. In the long term, i.e. using a 100-year life span, the difference between the present expected value of 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 analysis were robust to changes in seismic data and damage costs within reasonable ranges. The outcome was insensitive to changes in discount rates and life spans as well. On the other hand, the outcome of the decision 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 life and the indirect costs were not as important and influential as anticipated. The direct costs, associated with costs of repair, were sufficient to represent the future damage costs. It is recommended that more effort should be put into estimating the expected performance of the retrofit since the ER]) factors dominated the outcome of the decision. To further improve the accuracy of the analysis, more attention could 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 that the probabilities and damage costs associated with moderate to large earthquakes (MIvil V to IX) were more important in affecting the decision than those associated with great earthquakes (Ivilvil X and above). To perform a decision analysis in the selection of seismic retrofit schemes requires a combination of knowledge from different fields, including seismology, structural engineering, economics, and social impacts due to earthquake damage. In the process of collecting data, it was found that researches were mostly concentrated on geotechnical and engineering aspects. Seismic data currently available in the United States provide adequate information for decision analysis in this study. There are codes providing general methodology for evaluating and retrofitting existing buildings. However, there are not sufficient guidelines for estimating future earthquake damages, especially for retrofitted structures. Better methods for predicting structural behavior are also needed. There is also a gap in the knowledge of the overall economic and social impacts.  These impacts could be very important when historic buildings are  concerned.  110  Chapter 8 Conclusion  But the main concern here is not getting the perfect data, it is to make consistent decision using the available information. In carrying out a decision analysis, the decision maker is forced to recognize and quantify the unknown aspects involved in making the decision. He or she can obtain more insight from the analysis, and thus be in a better position to make judgment. It is believed that making use of the decision model purposed in this study is a good start.  111  References  REFERENCES 1.  Algennissen, S.T., Perkins, D.M., Thenhaus, P.C., and Ziony, J.I. 1980. Probabilistic Estimates Of Maximum Seismic Horizontal Ground Motion On Rock In Coastal California And The Adjacent Outer Continental She USGS Open File Report 80-924 Preliminary. United States Geological Survey, Denvor, CO.  2.  Algermissen, S.T., et al. 1982. Probabilistic Estimates ofMaximum Acceleration and Velocity in Rock in the Contiguous United States, USGS Open File Report 82-1033. United States Geological Survey, Denvor, Co.  3.  Allen, P.C. 1980. Stanford: From the Foothills to the Bay. Stanford 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.  Stanford Alumni Association and  -  -  10. Building Systems Development, Inc., Integrated Design Services and Claire B. Rubin, Consultant. 1989. Establishing Programs And Priorities For The Seismic Rehabilitation of Buildings: A Handbook 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 Hazardous Buildings An Agenda for Action, Volume 1: Findings, Conclusions and Recommendations. FEMA 198 / September 1990. Federal Emergency Management Agency, Washington, D.C. -  12. Building Technology Inc. 1990b. Financial Incentives for Seismic Rehabilitation of Hazardous Buildings An Agenda for Action, Volume 2: Establishing State and Local Case Studies and Recommendations. 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.  112  References  16. The Daily Palo Alto. 1906b. Vol. XXVIII, No. 69; Saturday, April 21, 1906. 17. H.J. Degenkoib Associates. 1987. Evaluating the Seismic Resistance of Existing Buildings (ATC 14). Applied Technology Council, Redwood City, CA. 18. H.J. Degenkoib Associates. 1989. Letter submitted to Pieron, 0., Project Manager of Facilities Project Management, Stanford University, CA; contents of the letter include damage assessment, preliminary retrofit recommendation, structural drawings, etc. of The Memorial Church; November 21, 1989. 19. H.J. Degenkolb Associates. 1990. Seismic Evaluation and Strengthening Proposals for The Stanford University 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 Research Institute, El Cerrito, CA. 23. Englekirk and Hart Consulting Engineers, Inc. 1988a. Typical Costs for Seismic Rehabilitation of Existing Buildings, Volume 1: Summary. FEMA-156 I February 1988. Federal Emergency Management Agency, Washington, D.C. 24. Englekirk and Hart Consulting Engineers, Inc. 1988b. Typical Costs for Seismic Rehabilitation of Existing Buildings, Volume 2: Supporting Documentation. FEMA-157 / February 1988. Federal Emergency Management Agency, Washington, D.C. 25. Facilities Project Management of Stanford University. June 1980. Internal record of reconstruction of 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 State Earthquake 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. Estimating  113  References  Losses From Future Earthquakes: Panel Report and Technical Background. FEMA-177. Federal Emergency Management Agency, Washington, D.C. 32. Poland, C.D. and Reis, E.M. 1992. “The Repair and Strengthening of the historic Stanford Memorial 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, CA 36. Seismic Safety Commission. 1987. Guidebook To Identfy And Mitigate Seismic Hazards In Buildings. Seismic Safety Commission, State of California, Sacramento, CA. 37. Smith, G.W. and Reitherman, R 1984. Damage to Unreinforced Masonry Buildings At Stanford University 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’s of January 25, 1953”. Stanford University, CA. 41. Stockholm, G. 1980. Stanford Memorial Church: An Appreciative Guide For the Not-so-causal Visitor. 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 Tile Center, New York. 43. Turner, P.V., Vetrocq, M.E., Weitze, K. 1976. The Founders & the Architects: The Design of Stanford University. Department of Art, Stanford University, Stanford, CA. 96 pp. 44. VSP Associates, Inc. 1992a. A Benefit Cost Model For The Seismic Rehabilitation of Hazardous Buildings, Volume 1: A User ManuaL FEMA-227 / April 1992. Federal Emergency Management Agency, Washington, D.C. 45. VSP Associates, Inc. 1992b. A Benefit Cost Model For The Seismic Rehabilitation of Hazardous Buildings, Volume 2: Supporting Documentation. FEMA-228 / April 1992. Federal Emergency Management Agency, Washington, D.C. 46. Working Group On California Earthquake Probabilities. 1990. Probabilities Of Large Earthquakes In The San Francisco Bay Region, California. United States Geological Survey, Denvor, CO.  114  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0050435/manifest

Comment

Related Items