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Quantitative analysis of factors influencing post-earthquake decisions on concrete buildings in Christchurch,… Kim, Ji Hyun 2015

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QUANTITATIVE ANALYSIS OF FACTORS INFLUENCING POST-EARTHQUAKE DECISIONS ON CONCRETE BUILDINGS IN CHRISTCHURCH, NEW ZEALAND by Ji Hyun Kim B.A.Sc., The University of British Columbia, 2010  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) June 2015 © Ji Hyun Kim, 2015  ii   Abstract The 2010-2011 Canterbury Earthquake Sequence resulted in unprecedented losses including 185 casualties, an estimated $NZ 40 billion cost of rebuild, and the demolition of 60% of reinforced concrete buildings in the Christchurch Central Business District (CBD). Intriguingly, demolition rate is unexpectedly high compared to the reported damages. This study thus sought to explore factors influencing the post-earthquake decisions on buildings (demolition or repair).  Focusing the study on multi-storey reinforced concrete buildings in the Christchurch CBD, information on building characteristics, assessed post-earthquake damage, and post-earthquake decision (demolish or repair) for 223 buildings was collected. Data were collected in 2014 in collaboration with Christchurch City Council (CCC), Canterbury Earthquake Recovery Authority (CERA), GNS Science, and local engineers. Data were obtained on approximately 88% of the 3-storey and higher reinforced concrete buildings within the CBD, or approximately 34% of all reinforced concrete buildings in the CBD. The study of descriptive statistics and trends of the database confirms that a significant portion of repairable buildings were demolished.  Logistic regression models were developed based on the collected empirical data. From the significance testing, the assessed damage, occupancy type, heritage status, number of floors, and construction year were identified as variables influencing the building-demolition decision. Their effects on the post-earthquake decisions were approximated, and the resulting likelihood of building demolition was estimated for buildings with different attributes. From personal interviews with 9 building owners and owner’s representatives, 9 building developers and investors, 5 insurance sector representatives, and 4 local engineers and government authority personnel, it was learned that the local context, such as insurance policy and changes in local legislation, also played a significant role in the decision-making process.  iii   As the first quantitative study that explores the effects of factors on the post-earthquake building demolition decisions, the findings of this study indicates that the damage is not the only factor affecting the post-earthquake decisions on buildings. Incorporation of all influential factors in the probability-of-demolition function would provide better means of estimating expected total loss by considering decision outcome scenarios and associated costs. This would benefit the decision makers with comprehensive and valuable information concerning seismic risk management and strategy. Limitations on this study are discussed and similar studies are suggested reflecting the locality of different communities with seismic risk. iv   Preface The research for this thesis was conducted in collaboration with Dr. Ken Elwood, Dr. Stephanie Chang, and Frederic Marquis at the University of British Columbia. The primary data collection was conducted by the author in Christchurch, New Zealand, in collaboration with the research team, Christchurch City Council, Canterbury Earthquake Recovery Authority, and GNS Science. The primary analysis of the research data was conducted by the author. A synthesis of chapters 3, 4, and 5 of this thesis has been accepted for publication to 11th Canadian Conference on Earthquake Engineering (Kim, Elwood, Chang & Marquis, 2015). The data collection and analyses were conducted by the author as indicated above, and the paper was written by the author and reviewed by the research team. This research project received ethics approval for personal interviews and focus group discussion from the University of British Columbia Behavioural Research Ethics Board (Reference no. H14-01332) and from the University of Auckland (UA) Human Participants Ethics Committee (Reference no. 012911).   v   Table of Contents Abstract ................................................................................................................................ ii Preface ..................................................................................................................................iv Table of Contents .................................................................................................................. v List of Tables ......................................................................................................................... ix List of Figures ........................................................................................................................ xi List of Symbols .................................................................................................................... xiii List of Abbreviations ............................................................................................................ xiv Acknowledgements ............................................................................................................. xvi Dedication .......................................................................................................................... xvii  : Introduction ........................................................................................................ 1 1.1 Background of the Canterbury Earthquakes and Recovery Progress ............................. 1 1.2 Research Question and Objective ................................................................................... 2 1.3 Research Framework and Scope ..................................................................................... 3  : Literature Review ................................................................................................ 6 2.1 Current Performance-Based Earthquake Engineering Methodology ............................. 6 2.2 Post-Earthquake Decisions on Buildings ....................................................................... 10 2.3 Logistic Regression Principles and Application in Empirical Studies ............................ 12 vi    : Source of Data and Data Collection Methodology ............................................... 15 3.1 Source Databases .......................................................................................................... 15 3.2 Assessed Damage Information ..................................................................................... 16  Christchurch Earthquake Rapid Assessments – Level 1 and Level 2 ........................ 17  CERA Engineers Risk Assessment Form .................................................................... 18  Detailed Engineering Evaluations ............................................................................. 19 3.3 Personal Interviews ....................................................................................................... 20 3.4 Focus Group Discussion for Damage Score Model ....................................................... 20 3.5 Spatial Data Analysis ..................................................................................................... 21 3.6 Foot Survey ................................................................................................................... 22  : Description and Statistics of Database ................................................................ 23 4.1 Decision Outcome and Demolition Decision Maker ..................................................... 23 4.2 Damage Indicator .......................................................................................................... 28  Damage Ratio ............................................................................................................ 28  Placard and Usability Category ................................................................................. 29  Categorical Damage .................................................................................................. 30  Damage Score ........................................................................................................... 32 4.3 Pre- and Post-Earthquake Percentage New Building Standard (%NBS) ....................... 35 vii   4.4 Seismic Force Resisting System .................................................................................... 36 4.5 Duration in Cordon ....................................................................................................... 36 4.6 Building Construction Year ........................................................................................... 38 4.7 Heritage Status .............................................................................................................. 38 4.8 Footprint Area ............................................................................................................... 39 4.9 Number of Floors .......................................................................................................... 39 4.10 Occupancy Type ............................................................................................................ 39 4.11 Database Building Statistics .......................................................................................... 40  : Logistic Regression Model .................................................................................. 51 5.1 Objective and Scope of Logistic Regression Model Analysis ........................................ 51 5.2 Description of Logistic Regression Model ..................................................................... 52 5.3 Logistic Regression Model Building Strategy ................................................................ 54  Forward Stepwise Selection ...................................................................................... 56  Backward Stepwise Selection ................................................................................... 56 5.4 Model Outcome ............................................................................................................ 58 5.5 Model Fit Test ............................................................................................................... 61 5.6 Model Selection ............................................................................................................ 63 5.7 Probability of Demolition .............................................................................................. 67 viii   5.8 Logistic Regression Model with %NBS Variable ............................................................ 72  : Discussion of Local Context Factors .................................................................... 76 6.1 Insurance ....................................................................................................................... 76 6.2 Changes in Local Legislation ......................................................................................... 77  : Conclusion ......................................................................................................... 79 7.1 Major Findings and Contributions ................................................................................ 79 7.2 Limitations and Further Research Opportunities ......................................................... 81 Bibliography ........................................................................................................................ 84 Appendix A – Building Assessment Forms ............................................................................ 90 A.1 - Christchurch Earthquake Assessment Form – Level 1 ..................................................... 91 A.2 - Christchurch Earthquake Assessment Form – Level 2 ..................................................... 92 A.3 - CERA Engineers Risk Assessment Form ............................................................................ 95 A.4 - Detailed Engineering Evaluations – Summary Table ........................................................ 97 Appendix B – List of Participants ......................................................................................... 105 Appendix C – Additional Database Building Statistics .......................................................... 108 ix   List of Tables Table 3-1: Comparison of Different Forms of Building Damage Assessments ............................. 17 Table 4-1: Description of Database ............................................................................................... 26 Table 4-2: Christchurch Earthquake Level 2 Assessment Placard and Usability Category ........... 30 Table 4-3: Christchurch Earthquake Level 2 Assessment Damage Categories ............................. 31 Table 4-4: Damage Score Model ................................................................................................... 34 Table 5-1: Dummy Variable Coding for Placard ............................................................................ 52 Table 5-2: Comparison of Categorical and Scalar Damage Ratio Variable - Probability of Demolition .................................................................................................................................... 53 Table 5-3: Logistic Regression Model Variables ........................................................................... 55 Table 5-4: Logistic Regression Model Description ........................................................................ 58 Table 5-5: Logistic Regression Model Coefficients – Model PLF and PLB (Placard) ..................... 59 Table 5-6: Logistic Regression Model Coefficients – Model DRF and DRB (Damage Ratio) ......... 59 Table 5-7: Logistic Regression Model Coefficients – Model DSF and DSB (Damage Score) ......... 60 Table 5-8: Logistic Regression Model Outcome - Summary of Selected Variables ...................... 60 Table 5-9: Hosmer-Lemeshow Contingency Table for Model DRF ............................................... 62 Table 5-10: Hosmer-Lemeshow Goodness-of-Fit Test ................................................................. 62 Table 5-11: Logistic Regression Model AIC, Delta AIC, and Relative Likelihood........................... 64 x   Table 5-12: Final Logistic Regression Model Summary* .............................................................. 65 Table 5-13: Reference Values for Independent Variables ............................................................ 68 Table 5-14: Change in Probability of Demolition .......................................................................... 70 Table 5-15: Logistic Regression Model with %NBS Summary – Case-Wise Deletion Method ..... 73 Table 5-16: Logistic Regression Model with %NBS Summary – Model DR on Pre-EQ %NBS Subset....................................................................................................................................................... 75 xi   List of Figures Figure 1-1: Research Framework .................................................................................................... 5 Figure 2-1: Performance Assessment Framework (Moehle & Deierlein, 2004; Yang et al., 2009) 6 Figure 2-2: Total Economic Loss ..................................................................................................... 8 Figure 2-3: Probability-of-Demolition Curve – (a) Definition and (b) Effects of Variables ........... 10 Figure 4-1: Map of Christchurch CBD Showing 223 Study Buildings ............................................ 24 Figure 4-2: Map of Christchurch CBD – Anchor Projects and Precincts (CCDU, 2014) ................. 25 Figure 4-3: Damage Score vs. (a) Placard and (b) Damage Ratio ................................................. 35 Figure 4-4: Changes in Cordon Zone (showing 3 out of 33 phases) ............................................. 37 Figure 4-5: Building Decision Outcome Statistics – Decision Outcome and Demolition Decision Maker ............................................................................................................................................ 43 Figure 4-6: Damage Indicator Statistics – (a) Placard, (b) Damage Ratio, and (c) Damage Score 44 Figure 4-7: Geotechnical Damage Statistics – (a) Slope Failure, (b) Ground Movement, and (c) Soil Bulging and Liquefaction............................................................................................................... 45 Figure 4-8: Building Statistics – (a) Heritage Status, (b) Seismic Force Resisting System, and (c) Number of Floors .......................................................................................................................... 46 Figure 4-9: Building Statistics – (a) Occupancy Type, (b) Construction Year, and (c) Duration in Cordon ........................................................................................................................................... 47 Figure 4-10: Building Area Statistics – (a) Footprint Area, (b) Total Floor Area, and (c) Total Floor Area by Occupancy Type ............................................................................................................... 48 xii   Figure 4-11: Building Data Availability - All Buildings, Buildings with DEE Summary Table, Buildings with Pre-EQ %NBS Data, and Buildings with Post-EQ %NBS Data ................................................ 49 Figure 4-12: All Buildings vs Buildings with DEE Summary Table – (a) Placard and (b) Damage Ratio....................................................................................................................................................... 49 Figure 4-13: Building Seismic Capacity Statistics - (a) Pre-EQ %NBS and (b) Post-EQ %NBS ....... 50 Figure 5-1: Probability of Demolition vs. Damage Ratio............................................................... 68 Figure 5-2: Probability of Demolition vs. Damage Ratio – Varying (a) Construction Year, (b) Heritage Status, (c) Occupancy Type, and (d) Number of Floors ................................................. 71  xiii   List of Symbols argmax Argument of maximum B Regression coefficient or estimator dm Damage measure dv Decision variable edp Engineering demand parameter im Intensity measure k Number of estimated parameters or degrees of freedom L Log of maximum likelihood estimate LR Log-likelihood ratio Mw   Moment magnitude scale N Number of samples P Probability of an event occurring tl Total loss x Independent variable y Dependent variable   αE Importance level for entry αR Importance level for removal Δi Difference between the minimum AIC value and the AIC value for Model i ∏ Pi function    xiv   List of Abbreviations AIC  Akaike Information Criterion ATC  Applied Technology Council BSS  Backward Stepwise Selection CBD  Central Business District CCC  Christchurch City Council CCDU  Christchurch Central Development Unit CERA  Canterbury Earthquake Recovery Authority CI  Confidence Interval CSW  Critical Structural Weakness DBH  Department of Building and Housing DEE  Detailed Engineering Evaluation DI  Damage Indicator DR  Damage Ratio DS  Damage Score EAG  Engineering Advisory Group ESRI  Environmental Systems Research Institute EQ  Earthquake FSS  Forward Stepwise Selection GDP  Gross Domestic Product GIS  Geographic Information System xv   MF  Moment Frame MFIF  Moment Frame with Infill MLE  Maximum Likelihood Estimate NBS  New Building Standard NZSEE  New Zealand Society for Earthquake Engineering PBEE  Performance-Based Earthquake Engineering PEER  Pacific Earthquake Engineering Research SFRS  Seismic Force Resisting System SW  Shear Wall UA  University of Auckland UBC  University of British Columbia    xvi   Acknowledgements I offer my enduring gratitude to Dr. Ken Elwood, Dr. Stephanie Chang, and Frederic Marquis, who inspired and taught me through this research project. Special thanks are owed to my family, who have supported me throughout my years of education. I gratefully acknowledge the contribution of David Brunsdon and Erica Seville from Resilient Organisations. I also thank the Canterbury Earthquake Recovery Authority, the Christchurch City Council, GSN Science, the University of Canterbury, the University of Auckland, the interviewees, and the local engineers for their support and collaboration.  xvii   Dedication This thesis is dedicated to my parents, Jong Tack Kim and He Kyong Kang, for their endless support, encouragement, and love for me throughout my life. 1   : Introduction This thesis presents a quantitative study of factors influencing the post-earthquake decisions on buildings affected by the 2010-2011 Canterbury Earthquake in Christchurch, New Zealand. Chapter 1 introduces the background of the Canterbury Earthquake and the city’s recovery progress and defines the research question, objective, and scope. Chapter 2 reviews literatures on performance-based earthquake engineering principle, post-earthquake decisions, and logistic regression analysis principles. Chapter 3 describes the research data source and collection methodology.  Chapter 4 defines the research database and presents descriptive statistics of the database, followed by chapter 5 which presents development of the logistic regression model and probability-of-demolition function. Chapter 6 highlights the local contextual parameters, followed by the conclusion in chapter 7.   Background of the Canterbury Earthquakes and Recovery Progress The 2010-2011 Canterbury Earthquake Sequence caused unprecedented losses in Christchurch, New Zealand. Starting with the 4 September 2010 (Mw 7.1) earthquake, the Canterbury region was hit by thousands of earthquakes, including major events that occurred on 26 December 2010 (Mw 4.7), 22 February 2011 (Mw 6.3), 13 June 2011 (Mw 6.0), and 23 December 2011 (Mw 5.8) (Bannister & Gledhill, 2012; Bradley et al., 2014).  The high intensity and large number of ground shaking events caused extensive damage to the Central Business District (CBD) of Christchurch. The Christchurch CBD includes approximately 110 city blocks and green space enclosed by the four avenues: Bealey, Deans, Moorhouse, and Fitzgerald. The area measures approximately 6.2 km2, which is equivalent to about 60% of the Vancouver downtown peninsula. The citizens of Christchurch suffered from the traumatic experience, disruption in basic needs, and uncertainties due to ongoing aftershocks. The direct impacts of the earthquake sequence include loss of 185 lives, an estimated $NZ 40 billion cost of 2   rebuild (approximately 20% of New Zealand’s Gross Domestic Product [GDP]), demolition of approximately 60% of multi-storey reinforced concrete buildings in the CBD, loss of land due to liquefaction, closure of parts of the CBD for over 2 years, and hundreds of thousands of insurance claims (Parker & Steenkamp, 2012). Unlike other major earthquakes in the world, it is estimated that 80% of the economic loss was borne by the insurance industry (Bevere & Grollimund, 2012). From 22 February to 30 April 2011, a National State of Emergency was declared under the Civil Defence Emergency Management Act (Civil Defence Emergency Management Act, 2002). The main focus was to identify dangerous buildings and take required actions (demolition or make-safe work) for immediate public safety. The Canterbury Earthquake Recovery Authority (CERA) was established in March 2011 to lead and facilitate the recovery of the community under the Canterbury Earthquake Recovery Act 2011 (CERA, 2012). One of CERA’s roles is to oversee building damage assessments and manage building demolition works. The Christchurch Central Development Unit (CCDU) within CERA was formed to aid the recovery and renewal of the city by planning and executing anchor projects and precincts (CCDU, 2012). Four years after the earthquakes, the community recovery and reconstruction efforts are still ongoing. CERA reported that since September 2010, over 35,000 building consents (i.e. building permits) worth $NZ 9.1 billion have been issued in greater Christchurch and approximately $NZ 7.5 billion in physical rebuilding has been completed (CERA, 2014).   Research Question and Objective The consequences of the 2010-2011 Canterbury Earthquakes alerted many urban communities to seismic risk. Considering the performance of reinforced concrete buildings was acceptable and as expected (Kam et al., 2011), the high demolition rate (~60%) of reinforced concrete buildings is surprising. The similarities between New Zealand and North America in the advancement of seismic engineering and building regulations make the information learned from the Canterbury Earthquakes valuable to those who study and live in earthquake-prone cities in USA and Canada. 3   The research project focuses on the two major questions:   What factors, including but not limited to degree of building damage, influence the post-earthquake demolition decisions on buildings?   What is the quantitative relationship between the influential factors and the likelihood of building demolition? The aim is to better understand the link between building performance, building characteristics, and post-earthquake decision outcome. Improved understanding of the parameters driving building demolition would provide comprehensive probability-of-demolition functions, which would contribute to further development of the performance-based earthquake engineering methodology.   Research Framework and Scope As demonstrated in Figure 1-1, the research involves the following steps to arrive at the findings: development of research question, research scope identification, data collection, database development, descriptive statistics analysis, and logistic regression analysis. This research focuses on the study of multi-storey (3-storey and higher) reinforced concrete buildings in the Christchurch CBD. Unreinforced masonry buildings are not considered in the study, as those buildings often experienced significant damage which makes demolition decision quite evident.  The developed project database contains empirical data on 223 buildings, including building characteristics, assessed post-earthquake damage, and post-earthquake decisions. It represents approximately 88% of the 3-storey and higher reinforced concrete buildings within the CBD, or approximately 34% of all reinforced concrete buildings in the CBD. Buildings with no, or very limited, available information were excluded from the database.  4   Statistical descriptive analyses are performed based on the collected empirical database to study the general trends in the study buildings. Then, logistic regression analyses are conducted to identify influencing factors, to develop probability-of-demolition function, and to quantify the relative effects of the factors on the building demolition decision.    5    Figure 1-1: Research Framework  Research QuestionScope Identificatiom•Which and how many buildings?•What variables?Data Collection•Data source confirmation•Data availability and accessibility checkDatabase Development•Data verification•Data formattingDescriptive Statistics AnalysisLogistic Regression AnalysisFindings•Influencing variables and their effects•Probability-of-demolition curves6   : Literature Review The literature review explores three main topics. Firstly, current performance-based earthquake engineering methodology is reviewed and possible improvements are discussed in line with the research project. Secondly, literature regarding post-earthquake decisions on buildings is reviewed. Lastly, logistic regression analysis principles are presented and its applications in post-disaster empirical studies are introduced.    Current Performance-Based Earthquake Engineering Methodology The Pacific Earthquake Engineering Research (PEER)’s performance-based earthquake engineering (PBEE) assessment aims to assist stakeholders in their decision-making in regards to seismic risk management by means of quantification of structural performance (Moehle & Deierlein, 2004). The performance assessment framework consists of four main steps: seismic hazard analysis, structural response analysis, damage analysis, and loss analysis, as shown in Figure 2-1 (Moehle & Deierlein, 2004).  Figure 2-1: Performance Assessment Framework (Moehle & Deierlein, 2004; Yang et al., 2009)  The first step involves evaluation of Intensity Measure (im) through probabilistic seismic hazard analysis and characterization of appropriate ground motions. Then, Engineering Demand Parameters (edp), such as deformations and accelerations, are calculated by structural response analyses. The third step is to relate Damage Measures (dm) to edp through a damage analysis. Seismic Hazard Analysis 𝜆 𝑖𝑚  im: intensity measure Structural Response Analysis 𝐺 𝑒𝑑𝑝|𝑖𝑚  edp: engineering demand parameter Damage Analysis 𝐺 𝑑𝑚|𝑒𝑑𝑝  dm: damage measure Loss Analysis 𝐺 𝑑𝑣|𝑑𝑚  dv: decision variable 7   The final step is to calculate Decision Variables (dv), which are often expressed in direct dollar losses, downtime, and casualties. Given all the above, the mean annual rate of events with decision variable exceeding a threshold decision variable (dv) value is formulated as follows:  𝛌 𝐝𝐯 < 𝐃𝐕 =  ∫ ∫ ∫ 𝐆 𝐝𝐯|𝐝𝐦  𝐝𝐆 𝐝𝐦|𝐞𝐝𝐩  𝐝𝐆 𝐞𝐝𝐩|𝐢𝐦 |𝐝𝛌 𝐢𝐦 |𝟏𝐞𝐝𝐩𝟏𝐝𝐦𝟏𝐢𝐦 ( 2-1 ) The above equation can also be expressed as: 𝝀 𝒅𝒗 < 𝑫𝑽 = ∫ 𝑮 𝒅𝒗|𝒊𝒎 |𝒅𝝀 𝒊𝒎 |𝟏𝒊𝒎 ( 2-2 ) where,  𝑮 𝒅𝒗|𝒊𝒎 = ∫ ∫ 𝑮 𝒅𝒗|𝒅𝒎 𝒅𝑮 𝒅𝒎|𝒆𝒅𝒑𝟏𝒆𝒅𝒑𝟏𝒅𝒎  𝒅𝑮 𝒆𝒅𝒑|𝒊𝒎  ( 2-3 ) Inspired by the PEER framework, many researchers have focused on developing repair cost analyses of various structural types and components (Yang et al., 2009; Hunt & Stojadinovic 2010; Ramirez et al. 2012).  A study by ATC (2012) applies the PEER framework to obtain the probable consequences such as direct economic losses. By considering either building repair or replacement (demolish and rebuild) options, the study defines the economic losses as building repair cost or replacement cost (including demolition, debris removal, and reconstruction.) The building replacement option is considered only if building is collapsed or predicted repair cost is more than 50% of replacement cost. It is implied that the study assumes building demolition is related to assessed damage and cost of repair.  After earthquake events, there are several possible post-earthquake decision outcomes on damaged buildings: full repair, partial repair, full demolition and walk-away, full demolition and reconstruction, partial demolition, and etc. In this study, two simple cases are considered; repair or demolition. Depending on the outcome, the total economic loss can take different forms. For the case of repair, the incurred costs to building owner include the cost of repair and the cost of 8   downtime (business interruption, loss of rent, etc.). Parts or all of the incurred costs may be recovered from insurance. For the case of demolition, the incurred costs are the cost of demolition and the cost of downtime. Similar to the repair case, the costs may be recovered from insurance by means of building reinstatement or cash payout. The total loss for both scenarios can be summarized as shown in Figure 2-2.  Figure 2-2: Total Economic Loss  The fundamental difference between the two outcomes is the cost of repair compared to the cost of demolition. The demolition cost of a building does not depend on the damage level, while cost of repair, up to certain extent, increases with increasing level of damage. The cost of downtime also differs for the case of repair and demolition. These distinctions depending on the decision outcome should be recognized in the total economic loss estimation. For building owners (or their engineers) who may be end users of the PEER framework, determining total economic loss directly associated with the post-earthquake decision would be a holistic approach in making an informed decision on seismic risks.  Accounting for the two possible outcomes, the conditional probability of total loss (TL) exceeding a threshold total loss value (tl) for given dv and im can be expressed as below:  𝑮 𝒕𝒍|𝒅𝒗, 𝒊𝒎 = 𝑮 𝒕𝒍|𝒓𝒆𝒑𝒂𝒊𝒓 𝑷 𝒓𝒆𝒑𝒂𝒊𝒓|𝒅𝒗 + 𝑮 𝒕𝒍|𝒅𝒆𝒎𝒐𝒍𝒊𝒕𝒊𝒐𝒏 𝑷 𝒅𝒆𝒎𝒐𝒍𝒊𝒕𝒊𝒐𝒏|𝒅𝒗   ( 2-4 ) The terms  𝑮 𝒕𝒍|𝒓𝒆𝒑𝒂𝒊𝒓  and  𝑮 𝒕𝒍|𝒅𝒆𝒎𝒐𝒍𝒊𝒕𝒊𝒐𝒏  represent the probability of total loss exceeding threshold value given that the building is to be repaired and demolished, respectively. These OR 9   terms are multiplied by  𝑷 𝒓𝒆𝒑𝒂𝒊𝒓|𝒅𝒗  and 𝑷 𝒅𝒆𝒎𝒐𝒍𝒊𝒕𝒊𝒐𝒏|𝒅𝒗  accordingly using the total probability theorem to yield 𝑮 𝒕𝒍|𝒅𝒗, 𝒊𝒎 . The probability of total loss exceeding a threshold value for given im can be expressed as below: 𝑮 𝒕𝒍|𝒊𝒎 = ∫ 𝑮 𝒕𝒍|𝒅𝒗, 𝒊𝒎 𝒅𝑮 𝒅𝒗|𝒊𝒎 𝟏𝒅𝒗  ( 2-5 ) Then, the mean annual rate of events with total loss exceeding a threshold total loss value is: 𝝀 𝒕𝒍 < 𝑻𝑳 = ∫ 𝑮 𝒕𝒍|𝒊𝒎  |𝒅𝝀 𝒊𝒎 𝟏𝒊𝒎 ( 2-6 ) In arriving at the equations 2-4, 2-5, and 2-6, appreciation of the two newly introduced terms, 𝑷 𝒓𝒆𝒑𝒂𝒊𝒓|𝒅𝒗  and  𝑷 𝒅𝒆𝒎𝒐𝒍𝒊𝒕𝒊𝒐𝒏|𝒅𝒗 , is essential. The concept of 𝑷 𝒓𝒆𝒑𝒂𝒊𝒓|𝒅𝒗  and 𝑷 𝒅𝒆𝒎𝒐𝒍𝒊𝒕𝒊𝒐𝒏|𝒅𝒗  are demonstrated in Figure 2-3a.  𝑷 𝒅𝒆𝒎𝒐𝒍𝒊𝒕𝒊𝒐𝒏|𝒅𝒗  indicates a probability of demolition for a given decision variable. Here, decision variable may be dollar loss associated with damage. Similarly, 𝑷 𝒓𝒆𝒑𝒂𝒊𝒓|𝒅𝒗  expresses a probability of repair given a decision variable, which is equivalent to 𝟏 − 𝑷 𝒅𝒆𝒎𝒐𝒍𝒊𝒕𝒊𝒐𝒏|𝒅𝒗  when considering two possible outcomes. Figure 2-3b illustrates that the probability-of-demolition curve may be shifted and/or scaled resulting in increase or decrease in the probability of demolition, depending on the effects of variables other than the decision variable.  This research project aims to develop the probability-of-demolition function accounting for various influencing parameters and to explain how each factor would affect the probability-of-demolition curve. This study is unique in its approach to identify factors affecting the building demolition and to quantify their effects on the probability-of-demolition function. 10    Figure 2-3: Probability-of-Demolition Curve – (a) Definition and (b) Effects of Variables   Post-Earthquake Decisions on Buildings  The 1994 Northridge Earthquake (Mw 6.7) in California resulted in 57 fatalities and an estimated economic loss of US $40 billion (EQE, 1995; 1997). Among 16,315 non-residential buildings inspected, 57% were found to have no apparent hazard (green placard), 14% in dangerous condition (yellow placard), and only 5% unsafe with collapse risk (red placard) (remaining 24% were unknown). Also, EQE (1995) reported that “over 80% of buildings in the damage database  sustained 10% damage or less” in terms of replacement value (the database includes single-family houses.) As conclusive building demolition rate was not reported, the number of repaired and demolished building is inferred from the building permit information reported in EQE (1997). Among the buildings in the city of Los Angeles, 63,138 permits for repair, 19,444 permits for rebuild, and 1,460 permits for demolition were issued. Assuming the total number of permits approximately represents the number of buildings in the city of Los Angeles and that the rebuild permit indicates building demolition and reconstruction, it is inferred that 75% of the buildings in the city of Los Angeles were repaired and 25% were demolished. In addition, it was reported that approximately 75% of the severely damaged apartment buildings were repaired 3 years after the event (Comerio, 1997). Literature on building demolition decision after the Northridge earthquake was not found.   𝑑𝑣 𝑃 𝐷𝑒𝑚𝑜𝑙𝑖𝑡𝑖𝑜𝑛  1.0 𝑃 𝑑𝑒𝑚𝑜|𝑑𝑣  𝑃 𝑟𝑒𝑝𝑎𝑖𝑟|𝑑𝑣  𝑑𝑣 𝑃 𝐷𝑒𝑚𝑜𝑙𝑖𝑡𝑖𝑜𝑛  1.0  Increase in 𝑃 𝑑𝑒𝑚𝑜|𝑑𝑣  Decrease in 𝑃 𝑑𝑒𝑚𝑜|𝑑𝑣  (a) Definition (b) Effects of Variables 11   In 1995, a Mw 6.9 earthquake and aftershocks struck the city of Kobe in Japan, costing 6,434 fatalities and an estimated economic loss of US $114 billion (approximately 2.5% of Japan’s GDP). More than 256,000 buildings (including fire damage) were damaged from the earthquakes; 41% were completely destroyed, 56% were partially destroyed (destruction of 50% or less), and 3% were  burned by fire  (City of Kobe, 2010). It was reported that “a large number of affected buildings went into debris disposal even when they were only partially (destruction of 50% or less) damaged directly by the earthquake or by fire” (City of Kobe, 2010). Statistics on number of building demolition/repair were not presented nor the rationale for demolition of partially damaged buildings.   The 2009 L’Aquila Earthquake (Mw 6.3) caused damages to approximately 10,000-15,000 buildings resulting in temporary evacuation of 70,000-80,000 residents in L’Aquila, Italy (Bazzurro et al., 2009). As reported in Polese et al. (2014), depending on the assessed damage and usability rating, varying amount of grants (€/m2) were provided for repair, strengthening, and seismic retrofit works by the national government. The government’s financial support for demolition and reconstruction was allowed for those buildings assessed as unusable and proven to be economically beneficial to do so.  Polese et al. (2014) studied the effects of number of floors and building age on the cost of repair, which was observed by means of descriptive statistics on the collected building information. Among heavily damaged reinforced concrete buildings studied, average unit cost of repair generally decreases with increase in number of floors, and higher repair costs were observed for older buildings. Other variables that might also influence the cost of repair or the effects of those variables on the demolition decision outcome were not explicitly explored. Considering low insured loss (14%) (Bevere & Grollimund, 2012) and the central government’s heavy involvement in the post-earthquake recovery process, it is inferred that building demolition decision would have been quite straight forward; comparison between the cost of repair and the cost of demolition and reconstruction.  In 2010, the Chilean earthquake (Mw 8.8) and tsunami affected 12.8 million people (75% of national population) causing 571 loss of lives. An estimated economic loss is US $30 billion 12   (approximately 18% of Chile’s GDP) and 27% of the loss was insured loss (Bevere & Grollimund, 2012). As a part of the National Reconstruction Plan, the Chilean government authorized recovery grants on 220,000 damaged or destroyed houses (out of 370,000 damaged houses); 52% (115,000 houses) of the eligible houses were repaired and 48% (105,000 houses) required rebuilding (MINVU, 2011). As reported in Comerio (2015), the funding program allowed the eligible owners for several options to choose from: repairing existing houses, purchasing a new house, demolish and build a new house on the same land, build a new house on a new land, or build units in new social-housing developments. Depending on the repairability, owners could choose from the above options and receive subsidy grants. No literature was found regarding how the owners made the decision on their damaged houses. There exists many literatures discussing various aspects of decision-making on post-disaster recovery, seismic risk mitigation, and structural performance objectives (Zhang et al., 2011; Egbelakin et al., 2011; May, 2004). Very few or no studies, however, have been conducted explicitly on post-earthquake decision-making on damaged buildings with a focus on variables other than level of damage and cost of repair. This research aims to quantitatively demonstrate the role of variables on post-earthquake building demolition decisions.   Logistic Regression Principles and Application in Empirical Studies This project uses logistic regression analysis to develop the probability-of-demolition function. Logistic regression principles are briefly discussed, followed by examples of its applications in other empirical studies. Logistic regression analysis is a probabilistic statistical modeling technique for estimating relationships between a bivariate dependent (or response) variable and independent (explanatory) variables. The probability of the possible outcome is modeled as a function of the 13   independent variables by estimating empirical values of the unknown parameters (regression coefficients). The logistic regression model takes a form of a log function as below: 𝒍𝒏 (𝑷𝟏−𝑷) = 𝒚 = 𝑩𝟎 +𝑩𝟏𝒙𝟏 +𝑩𝟐𝒙𝟐 +⋯+𝑩𝒏𝒙𝒏 ( 2-7 ) 𝑷 =𝟏𝟏+𝒆− 𝑩𝟎+𝑩𝟏𝒙𝟏+𝑩𝟐𝒙𝟐+⋯+𝑩𝒏𝒙𝒏  ( 2-8 ) The equation 2-7 is called a logit function and the equation 2-8 is called a logistic function. P  is the probability of an event occurring, where y  is the bivariate dependent variable. B ’s are the regression coefficients (or estimators) and x ’s are the values of the independent variables. From the empirical data, x  and y  values are known and the regression coefficients are sought.  The process of finding the best relationships between the dependent and independent variables is called “fitting of a model.” 𝑩 = 𝒂𝒓𝒈𝒎𝒂𝒙 (∏ 𝑷𝒊𝒚𝒊 𝟏 − 𝑷𝒊 𝟏−𝒚𝒊𝑵𝒊=𝟏 ) ( 2-9 ) The maximum likelihood function (equation 2-9) finds a set of regression coefficients that maximizes the probability of obtaining the observed set of data. Hence, the resulting group of regression coefficients is a set that allows the model to agree most closely with the observed outcome.  Logistic regression analysis is widely used by researchers in various disciplines to identify factors influencing the outcome and to predict the probability of an outcome. For example, Dabbour (2012) conducted logistic regression analysis on 66,252 single-vehicle collisions that occurred in the states of Ohio and Washington in 2009. The aim was to study the effects of risk factors on the probability of the occurrence of rollover collisions, which would contribute to the informed decision-making for road safety improvement.  Logistic regression analysis has also been used in post-disaster empirical studies. Padgett et al. (2012) studied 44 highway bridges damaged by Hurricane Katrina using logistic regression 14   analysis. Evaluation of hazard intensities and bridge characteristics were conducted to identify important predictors of damage level. Empirical fragility curves for bridge damage states were proposed, and regional risk-based analysis and loss estimation of bridges were suggested.   García-Rodríguez et al. (2008) conducted a study of earthquake-triggered landslide susceptibility after the destructive 2001 El Salvador Earthquakes. Logistic regression model was developed based on 235 samples to determine the important predictors, to estimate the probability of landslide occurrence, and to produce a map of relative landslide susceptibility. A similar study was conducted by Dong et al. (2011) to predict the failure probability of the landslide dams formed after the 1999 Chi-Chi Earthquake, the 2008 Wenchuan Earthquake, and the 2009 Typhoon Morakot. The authors concluded that the proposed models could be used to evaluate the risk and aid in the decision-making for hazard mitigation work. In these studies, it was emphasized that the empirical logistic regression models are rooted in the characteristics and the locality of the database used, so their application for predictions in other regions and contexts may be limited (García-Rodríguez et al., 2008; Padgett et al., 2012).  15   : Source of Data and Data Collection Methodology Chapter 3 presents the sources of the collected data and the data collection methodology in detail. The database was developed by collecting information on building characteristics, assessed post-earthquake damage, and post-earthquake decision (demolish or repair). These data were obtained from and in collaboration with the Christchurch City Council (CCC), the Canterbury Earthquake Recovery Authority (CERA), GNS Science, and from personal interviews for the purpose of this study. These data sources were used to develop, reinforce, and verify the project database. The data collection and database development process took approximately 7 months, with 3 months spent in Christchurch, New Zealand. The following subsections further describe each source.   Source Databases The Christchurch City Council (CCC) kindly agreed to support the research project by sharing relevant information from its internal databases. This information included basic building information (address, occupancy type, and name of business), building characteristics (seismic force resisting system, number of floors, construction year, and heritage status), assessed post-earthquake damage information, and building consents (i.e. building permits). The data gathered from CCC became the basis of the project database.  The Canterbury Earthquake Recovery Authority (CERA) also granted controlled access to its internal databases under appropriate confidentiality agreements signed with the research team. Although varies for each building, information available includes basic building information, building decision outcome, current building status, engineering reports, damage assessment information, photographs, and  drawings. 16    Assessed Damage Information Post-earthquake building evaluation is a complex methodical process that can have several systems depending on the purpose, scope, and timeline of the assessment. From the day of an earthquake event, the purpose of building evaluation transforms from immediate public safety assessment to usability assessment, repairability assessment, and cost estimations. Similarly, the evaluation develops from visual and superficial inspection to detailed and quantified assessments. Both purpose and scope of the post-earthquake building assessments evolve over time.  In the case of the Canterbury Earthquakes, the following forms were used for damage assessments for buildings in the Christchurch CBD:  Christchurch Earthquake Rapid Assessment Form – Level 1  Christchurch Earthquake Rapid Assessment Form – Level 2  CERA Engineers Risk Assessment Form  Detailed Engineering Evaluation (DEE) Report   Detailed Engineering Evaluation (DEE) Summary Table Table 3-1 below compares the different forms of damage assessments for their purpose, timing, detail and accuracy, data availability for the study, and format of damage assessment data. The Level 2 Rapid Assessment form was chosen as the main damage assessment information source for the research database as it is most complete across the buildings in the study, readily available, and is suitable for quantitative analysis.    17   Increase Table 3-1: Comparison of Different Forms of Building Damage Assessments  Purpose Timing Detail & Accuracy Data Availability Data Format Level 1 Rapid Assessment ▫ To assess structural damage, hazards, and building safety ▫ To determine level of occupancy ▫ To recommend required make-safe works   Shortly after  earthquake events  Approx. on 100% of study buildings (Level 1 Rapid Assessment used on 11 study buildings*)   Quantitative CERA Risk Assessment ▫ To assess risk of building collapse 24% of study buildings Quantitative Level 2 Rapid Assessment Same as Level 1 Rapid Assessment 95% of study buildings** Quantitative DEE Summary Table ▫ To assess structural damage and losses for insurance purposes ▫ To recommend repair and/or strengthening work required Typically  longer-term 39% of study buildings Quantitative DEE Report Qualitative & Quantitative * CCC database contains most up-to-date rapid assessment information and often Level 1 Rapid Assessment results were overwritten when Level 2 Rapid Assessment was conducted (scanned copies of Level 1 Rapid Assessments are likely to exist for all buildings).  ** Of the 223 buildings in this study, Level 2 Rapid Assessments for 11 buildings were not found, and Level 1 Rapid Assessment information is used instead.   Christchurch Earthquake Rapid Assessments – Level 1 and Level 2 Shortly after the Darfield Earthquake on 4 September 2010, CCC adopted NZSEE Rapid Assessment forms (NZSEE, 2009), which are similar to ATC-20 (ATC, 1995) and created the Christchurch Earthquake Rapid Assessment forms (Level 1 and Level 2). These forms can be found in appendix A.1 and A.2. Both the Level 1 and Level 2 Rapid Assessments were conducted during the period of the national state of emergency declared under the Civil Defence Emergency Management Act (Civil Defence Emergency Management Act, 2002) and after all damaging aftershocks, to identify the level of structural damage to buildings, assess building safety and hazards, assign proper level of occupancy, and recommend required make-safe works (shoring, etc.) (NZSEE, 2009). 18   The Level 1 Rapid Assessments were conducted on all buildings in Christchurch whereas the Level 2 Rapid Assessments were performed on all critical facility buildings (such as hospitals), large buildings (typically multi-storey), and on any other buildings that further and more specific assessments were warranted from the Level 1 Rapid Assessments. The Level 1 Rapid Assessments were conducted by volunteering groups of structural and civil engineers, architects, and other personnel from the building industry. The Level 2 Rapid Assessments were conducted by volunteering groups of structural, geotechnical, and building services engineers. The assessments were conducted after all subsequent earthquakes by filling in the assessment forms, and the CCC database was updated with the most recent assessment. Both the Level 1 and Level 2 Rapid Assessments include placard posting and estimated overall building Damage Ratio (DR) as damage indicators (DI). Colored placard posting represents usability of the assessed building; green (or white) for “Inspected,” yellow for “Restricted Use,” and red for “Unsafe.” Damage Ratio is a visual estimate of building damage expressed as a ratio of repair cost to replacement cost, excluding contents. Damage Ratio is expressed in ranged categories of 0-1%, 2-10%, 11-30%, 31-60%, 61-99%, or 100%. As categorical damage indicators, overall damage is assessed by severity: minor/none, moderate, or severe. In addition to all the above, the Level 2 Rapid Assessments contain more detailed lists of structural, nonstructural, and geotechnical damage that can be addressed by indicating the severity of damage with descriptive comments. Placard and Damage Ratio from the Level 2 Rapid Assessments are chosen as damage indicators for this study. More details can be found in sections 4.2.1, 4.2.2, and 4.2.2.  CERA Engineers Risk Assessment Form In addition to the Rapid Assessments, risk assessments were conducted by CERA engineers following major damaging earthquakes (refer to appendix A.3). The risk 19   assessment is a point system based on the type of construction, risk of building collapse, occupancy type, and overall damage ratio from visual inspection. As an emergency assessment for the aftershocks, the risk assessments were conducted to identify buildings with collapse risk and prioritize the make-safe or demolition work. It is, however, unclear which buildings and how many buildings were assessed based on this form. The risk assessment information is obtained for only 24% of the buildings in this study, and the assessed risk score is not used in this study due to the limited availability.  Detailed Engineering Evaluations A Detailed Engineering Evaluation (DEE) is prepared to review the building design and construction, to assess the extent of structural damage, and to understand the potential performance in further earthquakes (EAG, 2012). Necessary repair or strengthening works to restore the functionality and the compliance with the building code are proposed. It may also be used to establish losses for insurance claiming purposes (NZSEE, 2009). DEEs are prepared by engineers contracted by building owners. As outlined in EAG (2012), the DEE is comprised of qualitative and quantitative assessments, and recommended actions. The qualitative assessment includes: determination of building status and sustained damage, assessment of likely pre- and post-earthquake structural capacity (in terms of %NBS), review of existing documentation, prediction of the likely building performance and damage patterns, and site investigation of collapse hazards and critical structural weaknesses (CSWs). The quantitative assessment is conducted for the buildings with significant damage and for buildings that suffered insignificant damage but are classified as earthquake-prone buildings (%NBS < 33%) according to (Building Act, 2004). The purpose is to assess the residual capacity of the damaged buildings and to determine effective repair and/or strengthening work. The quantitative assessment is conducted generally in accordance with NZSEE (2006) with modifications as needed. 20   The DEEs were collected in two forms: a report and a summary table. The collected DEE summary tables were compiled into one database by GNS Science (Lin et al., 2015). For this study, the compiled DEE summary database is utilized for its convenience in retrieving information on a large number of buildings. Although the submission of the DEE was required by CERA for all nonresidential and apartment buildings in the Christchurch CBD, the collection process left out numerous buildings including buildings demolished early on for public safety by Civil Defence, buildings that were heavily damaged (for which demolition decision was fairly obvious), and small buildings with very minor or no damage. The DEE collection process was stopped in late 2014 as reported in Marquis (2015). The availability of DEE summary table was limited to 39% of the buildings in the study scope.    Personal Interviews The research team conducted interviews with 9 building owners and owner’s representatives, 9 building developers and investors, 5 insurance sector representatives, and 4 local engineers and government authority personnel. A list of interviewees can be found in appendix B. The interviews were held in Christchurch, Auckland, or Wellington in New Zealand under the conditions of interviewees’ consents.  The purpose was to learn about the post-earthquake decision-making process and discover factors influencing the demolition decision that cannot be easily captured or quantified from the CCC and CERA’s databases. The outcomes from the interviews are highlighted in chapter 7 and discussed in detail in Marquis (2015) and Marquis et al. (2015).   Focus Group Discussion for Damage Score Model As reported in the literature and learned from the personal interviews, many buildings were demolished as they were deemed uneconomic to repair, not because they were dangerous or 21   beyond technical repairability (Miles et al., 2014; Muir-Wood, 2012). It can be inferred that the fate of a damaged building heavily depends on the cost of repair, which is related to the assessed damage. It was not possible to retrieve information on repair costs for a large number of buildings for this study as repair cost information is typically confidential and not included in any of the databases discussed above. Instead, an effort was made to infer repair costs based on available information. A Damage Score Model was proposed and developed, which aims to integrate the structural, nonstructural, and geotechnical damages from the Level 2 Rapid Assessment into one scoring system, reflecting the relative repair costs incurred due to each type of damage by assigning weights and scales to the damage categories and severities. The Damage Score Model does not assign actual dollar values to the damage categories but ranks them in a relative sense within the scope of the study database. This means that the resulting Damage Scores (DS) do not carry any practical meaning outside of the context of this study.  The research team held a focus group discussion session with experienced local engineers. A list of participants can be found in appendix B. Typical procedures, approaches, and assumptions made during damage assessments were discussed. Each damage category in the Level 2 Rapid Assessment was reviewed for its significance in repair costs. Then, appropriate weights and scales were assigned to each damage category based on participants’ judgements and the Damage Score Model was finalized. The outcome of the Damage Score Model is discussed in section 4.2.4.    Spatial Data Analysis Geographic Information System (GIS) was used to capture the cordon zone and its change over time relative to the buildings in the study to determine duration each building was in the cordon zone. Further discussion on the cordon can be found in section 4.5. Environmental Systems Research Institute (ESRI)’s software ArcGIS for Desktop (ESRI, 2014)  was used to build a spatial 22   database. Christchurch city base map, building footprints and addresses, and CBD cordon outline layers were obtained from publicly available New Zealand Government’s online database  (Department of Internal Affairs, 2014). Buildings in the research scope were identified and dates the cordon was lifted for each building were acquired. Also, approximate building footprint areas were calculated (section 4.8).   Foot Survey For 52 buildings for which decision outcome information was unavailable from any of the data sources described above, building sites were visited to photograph and note the current operational status as of November 2014. Out of 223 buildings, the decisions on 20 buildings could not be determined even after the foot survey. They were not demolished, not occupied, and had no observed activities on the building sites at the time of data collection. It is possible that the decision had not been made or the decision had been made but no actions had been taken yet.  23   : Description and Statistics of Database The research database was developed by collecting information on building characteristics, assessed post-earthquake damage, and post-earthquake decisions for 223 buildings satisfying the following criteria: reinforced concrete structural system, 3-storey and higher, and located in the Christchurch CBD. This represents approximately 88% of the buildings meeting the criteria, excluding buildings with no, or very limited, available information.  Figure 4-1 below presents a map of Christchurch CBD identifying the 223 buildings with decision outcomes indicated in different colors. The database was completed after an extensive data collection and verification process. The sources of the information are described in chapter 3. This chapter defines the collected information and presents descriptive statistics of the buildings in the study. The research database is comprised of information such as building identification information, decision outcome, demolition decision maker, damage indicators, building conditions (in terms of pre-EQ and post-EQ %NBS), seismic force resisting system, duration in cordon, construction year, heritage status, footprint area, number of floors, and type of occupancy. Rationale for consideration of these variables are discussed in the following subsections. Table 4-1 below summarizes the collected information with descriptions and data sources.   Decision Outcome and Demolition Decision Maker In the database, the decision outcome takes three forms: demolish, repair, or unknown. The “Demolish” decision may be made by “Civil Defence,” “CCDU Demolition,” “CERA,” “Owner,” or unknown.  24     Figure 4-1: Map of Christchurch CBD Showing 223 Study Buildings CBD Outline   Demolish   Repair   Unknown 25    Figure 4-2: Map of Christchurch CBD – Anchor Projects and Precincts (CCDU, 2014)  The decision made by “Civil Defence” refers to buildings that were demolished under the authority of the Civil Defence Emergency Management Act 2002 (Civil Defence Emergency Management Act, 2002). These buildings were identified as dangerous and demolished shortly after the earthquake. Due to early and rapid demolition, detailed damage assessments and engineering reports often do not exist for such buildings.  “CCDU Demolition” indicates buildings that were demolished to clear sites for the CCDU’s anchor projects (CCDU, 2012). Figure 4-2 illustrates the location and lead agency for the anchor projects in the Christchurch CBD (CCDU, 2014). For the purpose of this study, those buildings that demolition decision was made prior to the release of CCDU’s anchor project plan (30 July 2012) are not considered as “CCDU Demolition” even when they fall in the anchor project site. CERA - Canterbury Earthquake Recovery Authority, CCC - Christchurch City Council, LINZ -Land Information New ZealandCBD Outline CERA CCC CERA & CCC Te Rūnanga o Ngāi Tahu Private sector Other public sector  26   Table 4-1: Description of Database Variable Measure/ Description Data Source Address and Business Name Used for building identification CCC Decision Outcome ▫ Demolish ▫ Repair ▫ Unknown CERA/ Foot survey Demolition Decision  Maker ▫ Civil Defence ▫ CERA ▫ Owner ▫ CCDU Demolition ▫ Unknown CERA Damage Indicator    - Damage Ratio ▫ 0-1% ▫ 2-10% ▫ 11-30% ▫ 31-60% ▫ 61-99% ▫ 100% Level 2  - Placard  ▫ Green ▫ Yellow ▫ Red Level 2  - Categorical Structural, Nonstructural & Geotechnical Damage ▫ Minor or None ▫ Moderate ▫ Severe Level 2  - Damage Score Derived from categorical structural, non-structural, and geotechnical damage Damage Score Model Pre-EQ and Post-EQ %NBS %NBS before and after the earthquakes  DEE Seismic Force Resisting System (SFRS) ▫ Moment Frame (MF) ▫ Shear Wall (SW) ▫ MF with Infill (MFIF) ▫ Combined MF & SW CCC/DEE Duration in Cordon Number of months from 22 February 2011 to date cordon lifted GIS Analysis Construction Year ▫ Pre 1965 ▫ 1965-1975 ▫ 1976-1991 ▫ 1992-2003 ▫ Post 2003 CCC/CERA/DEE Heritage Status ▫ Heritage ▫ Nonheritage CCC/CERA Footprint Area Measured in m2 GIS Analysis/DEE Number of Floors Number of floors CCC/DEE Occupancy Type ▫ Commercial  ▫ Residential  ▫ Hotel  ▫ Post-Secondary ▫ Hospital ▫ School ▫ Public Assembly ▫ Government ▫ Industrial CCC/CERA/DEE 27   The decision made by “CERA” refers to buildings that were demolished under Section 38 or 39 of the Canterbury Earthquake Recovery Act 2011 to enable a focused, timely, and expedited recovery of the city (Canterbury Earthquake Recovery Act, 2011). Under Section 38, CERA may give a demolition notice to a building owner requiring submission of demolition work plan indicating whether or not the owner intends to carry out the works and specifying the timeline of the demolition works. If the owner fails to notify CERA within 10 days after the demolition notice is given, CERA may commission the demolition works with or without the consent of the owner or occupier, and may recover the costs of carrying out the works from the owner. To facilitate the recovery process, an exemption was given which allows buildings be demolished under Section 38 or 39 without CCC’s building consents for demolition works. Under Section 39, CERA may commission urgent demolition works without giving a building owner a notice, in case of sudden emergency (loss of life, injury to a person, damage to property, and damage to the environment) and danger to any works or neighboring property.  If not required to be demolished by the “Civil Defence,” “CCDU Demolition,” or “CERA,” the building “Owner” may decide to either demolish or repair the building. In the study database, demolition of 14 buildings were initiated by building owners while demolished under Section 38 or 39. This indicates the building owners and CERA worked together to enable timely demolition work as building consents are not required if demolished under Section 38 or 39. These cases were identified as owner’s decision in this study. An “Unknown” decision outcome indicates buildings that were not demolished, not occupied, and had no observed activities on site at the time of data collection (November 2014). It is possible that the decision had not been made or the decision had been made but no actions had been taken yet.  28    Damage Indicator In this section, four damage indicators are introduced: Damage Ratio, Placard, Categorical Damage, and Damage Score. The first three damage indicators were retrieved from the Level 2 Rapid Assessment, while Damage Score was derived from Categorical Damage assessment. They are studied as they contain various levels of detail in different formats. Placard indicates usability by color coding while Damage Ratio represents approximate damage to the building in terms of ranges of percentage. Categorical Damage expresses damage severities to structural, nonstructural, and geotechnical components. Damage Score converts the assessed Categorical Damage into a numerical rating system. The four damage indicators are further described in the following subsections. For 11 building without the Level 2 Rapid Assessment, Damage Ratio and Placard information was obtained from the Level 1 Rapid Assessment instead.    Damage Ratio Damage Ratio (DR) is an estimate of building damage obtained from the Level 2 Rapid Assessment, which is intended to represent an estimate of a ratio of repair cost to replacement cost, excluding contents. Damage Ratio is expressed in six ranged categories: 0-1%, 2-10%, 11-30%, 31-60%, 61-99%, or 100% (there is no separate option for undamaged buildings.) Damage Ratio is not a calculated value, but an approximation of the damage suffered based on the visual inspection. Despite the subjective and approximate nature of this measure, it provides simple and quantitative measure of damage, making it a convenient tool for this study. The collected data is the latest Damage Ratio information available for the study buildings. 29    Placard and Usability Category Placard posting indicates damage intensity and usability of the assessed building. A green (or inspected) placard represents that there are no restrictions on use or entry, but the structure may need further inspection or repairs. A yellow (or restricted use) placard is given to buildings with safety concerns. Parts of these buildings may be off limits and entry is only allowed for short periods of time. Buildings with red (or unsafe) placards must not be entered and further assessments and risk-mitigation actions are required before any use. Buildings were reassessed after all subsequent earthquakes and may be given different placards. The collected data is the latest placard information available for the study buildings. The placard posting is further subcategorized depending on the usability. Table 4-2 below summarizes the placard posting and usability subcategory in relation to the damage intensity. For the purpose of this study, placard posting without considering the usability subcategory is used as a Damage Indicator (usability category was not available for 30 buildings). The buildings that were given a red placard due to the risks from adjacent buildings (the usability category of R3) are identified, and the placard postings based on their own damage are assigned for the logistic regression analysis (chapter 5) to ensure the placard damage indicator is solely based on the building damage, not neighbouring building conditions. For the purpose of assessing the usability of buildings, the placard posting is an efficient and effective measure. Its emphasis on building usability assessment rather than the damage and the small number of placard categories (three) reduce its efficacy as a damage indicator in this study. It may, however, serve as a comparable damage indicator to Damage Ratio. In chapter 5, Damage Ratio and Placard are used in logistic regression analysis and their effects on the analysis results are discussed.  30   Table 4-2: Christchurch Earthquake Level 2 Assessment Placard and Usability Category Damage Intensity Posting Usability Subcategory Light Damage; Low Risk Green; Inspected G1 – Occupiable, no immediate further investigation required G2 – Short term entry Medium Damage; Medium Risk Yellow; Restricted Use Y1 – Short term entry Y2 – No entry to parts until repaired or demolished Heavy Damage; High Risk Red; Unsafe R1 – Significant damage: repairs, strengthening possible R2 – Severe damage: demolition likely R3 – At risk from adjacent premises or from ground failure   Categorical Damage The Level 2 Rapid Assessment contains the categorical assessment of damage in four groups: overall, structural, nonstructural, and geotechnical damage. Each group has subcategories for which inspectors mark for damage severity (minor/none, moderate, or severe) and add comments. Table 4-3 below lists the assessed damage categories. The advantage of the categorical damage is that it provides very detailed damage assessments, item by item. The list, however, includes items that may not be easily inspected during the rapid assessments, resulting in numerous missing data. Also, the large number of subcategories makes it difficult to use as a building damage indicator in the logistic regression analysis. For this reason, the categorical damage is not directly used as a damage indicator in the analyses, but is used to develop Damage Scores as described in section 4.2.4.    31   Table 4-3: Christchurch Earthquake Level 2 Assessment Damage Categories Damage Categories Subcategory Overall Damage Collapse, partial collapse, off foundation Building or storey leaning Wall or other structural damage Overhead falling hazard Ground movement, settlement, slips Neighbouring building hazard Electrical, gas, sewerage, water, hazmats Structural Damage Foundations Roofs, floors (vertical load) Columns, pilasters, corbels Diaphragms, horizontal bracing Precast connections Beam Nonstructural Damage Parapets, ornamentation Cladding, glazing Ceiling, light fixtures Interior walls, partitions Elevators Stairs/exits Utilities (e.g., gas, electricity, water) Other Geotechnical Damage Slope failure, debris Ground movement, fissures Soil bulging, liquefaction  32    Damage Score The assessed categorical damages described in section 4.2.2 are fed into the development of the Damage Score Model. The Damage Score Model was developed from the focus group discussion with local engineers (refer to section 3.4) to assign a Damage Score (DS) reflecting the relative repair costs incurred due to each type of damage.  Each damage category’s relative contribution to total repair cost is quantified by assigning weights. The weights range from 0 to 100, with the most expensive repair item marked as 100. The damage categories that are not proper indicators of repair cost, or were not inspected during the rapid assessment are given a zero (0), effectively excluding the item from the Damage Score Model. Similarly, numerical values are assigned to each severity category (minor/none, moderate, or severe) to approximate the relative cost of repair work.  The outcome of the focus group discussion on the Damage Score Model is presented in Table 4-4. Among structural elements, damages to the foundations were identified to be the most critical component in building repair cost and was assigned the maximum weight of 100. The participants agreed that geotechnical damages were generally reflected in the foundation assessments and therefore should not be accounted again in Damage Score calculations (zero weights). Nonstructural elements such as elevators and utilities were excluded in the Damage Score Model as they were usually not assessed during the Level 2 Rapid Assessment, often due to power outage. Parapets and ornamentations were also given zero as their repair cost is generally insignificant. Different scales for “High” damage severity were assigned to reflect relative repair cost between the structural (scale of 25) and nonstructural component groups (scale of 10); severe damage to structural components are likely to be more expensive than severe damage to nonstructural components. 33   It should be noted that the Damage Score Model developed here is based on local engineers’ experiences and judgements only. Although not conducted in this study due to lack of access to information, the Damage Score Model may be improved by incorporating approximate unit costs of repair works for each damage category. The underlying concept of the Damage Score offers an ideal damage indicator for this study, but the limitation in the repair cost data inhibits the accuracy of the Damage Score Model. Using the Damage Score Model, the damage score of a building is calculated by following the four steps: 1) For each damage category, multiply the category weight by the scale for the assessed damage severity. If damage severity is unknown, ignore the damage category. 2) Sum all values from step 1. 3) Count the number of damage categories with known severity. This is referred as “number of included categories.” 4) Divide the sum from step 2 by the number of included categories from step 3.  For n number of damage categories, the damage score is calculated as presented in the equation below.                 𝑫𝒂𝒎𝒂𝒈𝒆 𝑺𝒄𝒐𝒓𝒆 =  ∑  𝑪𝒂𝒕𝒆𝒈𝒐𝒓𝒚 𝑾𝒆𝒊𝒈𝒉𝒕𝒊 × 𝑺𝒆𝒗𝒆𝒓𝒊𝒕𝒚 𝑺𝒄𝒂𝒍𝒆𝒊 𝒏𝒊=𝟏𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒊𝒏𝒄𝒍𝒖𝒅𝒆𝒅 𝒄𝒂𝒕𝒆𝒈𝒐𝒓𝒊𝒆𝒔 ( 4-1 ) “Number of included categories” is entered into the equation to normalize the damage score.    34   Table 4-4: Damage Score Model Damage Categories Weight Severity Scale Minor/None Moderate High Structural Foundations 100 1 5 25 Roof and floor 50 Columns, pilasters, and corbels 50 Diaphragms and horizontal braces 50 Pre-cast connections  50 Beams and girders 50 Nonstructural Parapets and ornamentations 0 1 5 10 Claddings and glazing 25 Ceilings and light fixtures 25 Interior walls and partitions 25 Elevators 0 Stairs and exits 50 Utilities (gas, electricity, water) 0 Geotech. Slope failure 0 - - - Ground movement 0 Soil bulging and liquefaction 0  Based on the described calculation, Damage Score can range from 0 (for completely unknown) to a maximum value of 1000 (when severity is high for all categories). The calculated Damage Score of the buildings in the study ranges from 0 to 781. It is emphasized that Damage Score reflects the relative repair costs among the buildings in the database; there was no attempt to estimate the actual repair costs given the approximate nature of the damage information and the developed model. As Damage Score is derived based on the categorical damages from the Level 2 Rapid Assessment, Damage Score is compared with Placard and Damage Ratio to observe its 35   correlations with the other two damage indicators for all buildings in the database (Figure 4-3). The solid lines represent average values of Damage Score in each Placard and Damage Ratio category. In general, increase in damage severity corresponds with increase in Damage Score.  While average Damage Score is linearly related to Placard, it has an exponential relationship with Damage Ratio. However, significant scatter about the mean is observed, which may be due to the differences in the purpose and scope of the damage indicators.    Figure 4-3: Damage Score vs. (a) Placard and (b) Damage Ratio   Pre- and Post-Earthquake Percentage New Building Standard (%NBS) The concept of percentage of New Building Standard (NBS) was adopted to approximately measure the structural capacity. Expressed as a percentage, %NBS is the assessed structural performance of an existing building compared with requirements for a new building; a %NBS of 33 or below indicates earthquake-prone building (Building Act, 2004) and a %NBS of 67 or higher implies no significant earthquake risk (NZSEE, 2006). As a part of the Detailed Engineering Evaluation (DEE) requirements by CERA, %NBS of a building is determined either in accordance 0100200300400500600700800Damage Score(a) PlacardS…0100200300400500600700800(b) Damage RatioSeries70-1%   2-10%   11-30%  31-60%  61-99%   100% Green              Yellow                Red Mean Mean 36   with NZSEE (2006) or by a comparison with current seismic loading standard in New Zealand’s structural design standards (NZS1170.5:2004) (DBH, 2012b).  The Christchurch City Council mandated seismic strengthening work on the buildings with %NBS rating 33% or below (referred to as earthquake-prone buildings) (CCC, 2010). This means that restoration of an earthquake-prone building is likely to cost more due to the required seismic strengthening work in addition to damage repair compared to other buildings with the same level of damage. Therefore, the %NBS rating is a possible factor affecting the building demolition decision. %NBS information, however, was available for only 35% of the buildings in the database, mainly because the DEEs are not available for all buildings. Details on the city’s legislation are discussed in section 6.2.    Seismic Force Resisting System Seismic Force Resisting System (SFRS) is a structural system designed to resist lateral loads induced by ground motions. SFRS is considered in this study to observe whether a specific type of SFRS results in more building demolitions, possibly driven by varying structural performance, damage, and associated cost of repair. This study focuses on multi-storey buildings with SFRS of concrete Moment Frame (MF), concrete Shear Wall (SW), concrete Moment Frame with Infill (MFIF), and combined Moment Frame and Shear Wall. Concrete tilt-up structures are not considered in this study as such structures are often popular for one- or two-storey buildings and frequently used steel connections result in different structural behavior and damage compared to the other reinforced concrete structures.   Duration in Cordon Immediately after the 22 February 2011 earthquake, a cordon (public exclusion zone) was established, covering most of the built area in the CBD as shown in Figure 4-4. The cordoned area 37   was reduced gradually in 33 phases, and the last cordon was lifted on 27 June 2013, 28 months after the establishment. The duration over which each building was inside the cordon zone may reduce the probability of demolition because the limited public access could facilitate the necessary engineering works on buildings. On the other hand, cordoned-off buildings are more likely to suffer from business interruption, which may lead to loss of tenants especially when the cordon lasts for an extended period. To determine the duration in the cordon zone, the date that the cordon was lifted for each building was obtained from the spatial data analysis (section 3.5) and the number of months in the cordon was calculated.   Figure 4-4: Changes in Cordon Zone (showing 3 out of 33 phases)  First Cordon  February - March 2011 August - October 2011 CBD Outline June 2013 38    Building Construction Year Building construction year is considered in this study because it indicates the age of building and the building code used for the structural design, which may affect the likelihood of building demolition. Often, the exact year an old building was built is difficult to find, resulting in an incomplete database. Attempts to estimate the construction year can be challenging and may lead to inaccurate information. An estimation of the construction year in ranges, on the other hand, is relatively easier and more accurate. For this reason, the building construction year is specified in five ranges reflecting the advancement of structural design standards (IPENZ, 2011): pre-1965, 1965-1975, 1976-1991, 1992-2003, or post-2003.   Heritage Status Buildings designated as heritage in the database refer to those included in the Christchurch City Plan Heritage Groups, Banks Peninsula District Plan Heritage Significance Schedules, or the New Zealand Historic Places Trust Historic Register (CCC, 2007). Although there are various levels associated with the heritage status, buildings were simply recorded as either heritage or nonheritage in the source databases, and hence in the study database as well. The owners of heritage buildings may apply for and receive financial supports for restoration works from the Heritage Incentives Grant (CCC, 2007) and the Canterbury Earthquake Heritage Buildings Fund (CEHBF, 2012). Therefore, such effort to conserve heritage buildings may decrease the probability of building demolition.   39    Footprint Area The building footprint area is an area defined by the perimeter of the building plan independent of the number of floors above. It is estimated in square meters (m2) using spatial data analysis software as indicated in section 3.5. The footprint area together with the number of floors indicate the size of a building. These are included in the study to observe the possible influence of the building size on the building demolition.   Number of Floors Number of floors above ground is recorded, which approximately relates to building height. As reported in literatures (Polese et al., 2014; Ramirez et al., 2012), a trend of decreasing unit repair cost was observed with increasing number of floors. Decrease in repair cost may decrease the probability of building demolition and therefore, the number of floor variable is considered in this study.    Occupancy Type Type of occupancy is categorized into nine groups: commercial, residential, hotel, post-secondary institution, hospital, public assembly, school, government facility, and industrial. Commercial occupancy generally includes office spaces, retail, restaurants, and parking structures. Residential occupancy refers to multi-storey condominiums and apartments.. In New Zealand, schools, hospitals, and post-secondary and public assembly buildings with large capacity are considered as Importance Level 3 or 4, which indicates higher level of importance requiring increased structural performance (DBH, 2012a). Therefore, the occupancy type is considered in the study because it implies the importance of buildings and may affect the likelihood of building demolition. For example, functioning hospitals are crucial after damaging earthquakes, and 40   therefore there may be more in need and effort to restore them. Comparatively, it is speculated that commercial buildings may more likely to be demolished.    Database Building Statistics Descriptive statistics are studied to describe the collected database. Frequency distributions of the variables and their relationships with the decision outcome variable (bivariate statistics) are graphically presented and summarized in Figure 4-5Figure 4-12. This allows for simple, yet clear understanding of the characteristics and trends of the buildings in this study. More database building statistics can be found in appendix C. The 223 buildings in this study represent approximately 88% of the 3-storey and higher reinforced concrete buildings within the Christchurch CBD (approximate total of 254 buildings); buildings with no, or very limited, information were excluded from the database. This represents approximately 34% of all reinforced concrete buildings in the CBD (approximate total of 656 buildings). As demonstrated in Figure 4-5, 62% of the buildings of interest (138 buildings) were demolished and 29% (65 buildings) were repaired. This is equivalent to demolition of 61% (750,800 m2) and repair of 30% of total floor space of the buildings considered (1,223,500 m2), assuming equal plan area for all floors (Figure 4-10c). The outcomes for the remaining 20 buildings (equivalent to 8% of total floor space) were unknown at the time of data collection. Among the demolished buildings, the decisions made by Civil Defence for immediate public safety only account for 2% (3 buildings). Majority of demolition decisions were made by either owners (30%) or CERA (25%), and CCDU demolition accounts for 5%. Out of the 223 buildings, 35% received green, 46% received yellow, and 19% received red placards (Figure 4-6a). Among the green placarded buildings, 35% were demolished. Of the 135 buildings (61%) assessed to have a relatively low Damage Ratio of 10% or less, 47% (63 buildings) 41   were demolished (Figure 4-6b). Similarly, 117 buildings (57%) received low Damage Scores of 100 or less, and 50% of them (59 buildings) were demolished (Figure 4-6c). It can thus be inferred that a significant number of reinforced concrete buildings with relatively low damage were demolished. While 28~30% of the study buildings were not assessed for geotechnical damages, the majority of the buildings (61~69%) were assessed to have minor or no slope failure, ground movement, and soil bulging and liquefaction damages (Figure 4-7). In terms of building characteristics, heritage buildings account for 16% of the database (Figure 4-8a) and it is observed that heritage buildings have lower likelihood of demolition compared to nonheritage buildings. Moment frame (39%) and shear wall (44%) structural systems are almost equally common in the Christchurch CBD (Figure 4-8b). It is found that higher rate of moment frame buildings (75%) were demolished compared to shear wall buildings (49%). A significant number of buildings are low and mid-rise buildings (Figure 4-8c). Demolition rate increases as the number of floor increases; 57% for 3-5 storey, 68% for 6-12 storey, and 73% for 13-22 storey buildings. Commercial occupancy is dominant (69%) and residential and hotel buildings account for 10% and 9%, respectively (Figure 4-9a). High rate of demolition is observed for commercial (74%) and government buildings (75%) compared to demolition rates for residential (36%), hotel (47%), and hospital (38%) buildings. Representing only 7% of the study buildings, majority of post-secondary, public assembly, school, and industrial buildings were repaired (78~100%). Buildings constructed before 1975 account for 45% of the database and 65% of those buildings were demolished; 59% of the buildings constructed after 1975 were demolished (Figure 4-9b). Buildings that were in the cordon zone for more than 1 year account for 58% of the database, and 76% of them were demolished (Figure 4-9c). The majority of buildings (78%) have a building footprint area of less than 1,000 m2, and 65% of those buildings were demolished (Figure 4-10a). Total floor area was calculated assuming equal 42   plan area for all floors (building footprint area multiplied by number of floors.) As shown in Figure 4-10b, 32% of the buildings have total floor area of 4,000 m2 or less and 62% of those buildings were demolished. Figure 4-10c presents the total floor area categorized by occupancy types. Out of 683,000 m2 of total commercial floor area in the study, 74% (119,600 m2) was demolished. On the other hand, 67% (163,500 m2) of total institutional and industrial floor area was repaired. As shown in Figure 4-11, DEE summary table was collected for 87 buildings (39%) of the study buildings, and 87% (76 buildings) and 90% (78 buildings) of those buildings were assessed for Pre-EQ and Post-EQ %NBS ratings, respectively. Of the buildings with DEE summary table, 59% were repaired, while only 29% of the total study buildings were repaired. It is inferred that the buildings with DEE summary table are more likely to be repaired. Figure 4-12 compares the assessed damage (Placard and Damage Ratio) statistics for the two sets of data: all 223 study buildings and 87 buildings with DEE summary table available. It is apparent that greater portion of the buildings with DEE summary table were assessed for minor damage; 56% received green placards compared to 35% for the entire database, and 81% were assessed for Damage Ratio of 10% or less compared to 61% for the entire database. From Figure 4-11 and Figure 4-12, it can be concluded that the buildings with DEE summary table do not represent the overall database, statistically; those buildings had less damage and are more likely to be repaired. Considering only buildings with pre- and post-EQ %NBS ratings (Figure 4-13), the demolition rate is lowest (< 11%) among those buildings with %NBS > 66% and highest (33%) for buildings with %NBS ≤ 33%. This is most likely due to the city’s earthquake-prone building policy, which mandates seismic strengthening work on buildings with %NBS ≤ 33% and hence increases the cost of restoration (repair and strengthening). More discussion on the city’s policy is provided in section 6.2.   43     Figure 4-5: Building Decision Outcome Statistics – Decision Outcome and Demolition Decision Maker  Repair65 (29%)Unknown20 (9%)CCDU Demo12 (5%)Owner Initiated66 (30%)CERA55 (25%)Civil Defence3(1%)Unknown2 (1%)Demolish138 (62%)Decision Outcome     Demolition Decision Maker 44      Figure 4-6: Damage Indicator Statistics – (a) Placard, (b) Damage Ratio, and (c) Damage Score  277239432027 11277(35%)103(46%)43(19%)020406080100120Green Yellow Red# of Buildings(a) PlacardDemolishRepairUnknownTotal2043 4319121322480 1 03133 1 0 055(25%)80(36%)54(24%)20(9%)13(6%)1(0%)020406080100# of Buildings(b) Damage RatioDemolishRepairUnknownTotal223726 276 4162718830 0931040 0 0352(23%)65(29%)38(17%)30(13%)6(3%) 4(2%)28(13%)0102030405060701-50 51-100 101-200 201-400 401-600 601-800 Unknown# of Buildings(c) Damage ScoreDemolishRepairUnknownTotal0-1%           2-10%            11-30%          31-60%          61-99%            100% 45      Figure 4-7: Geotechnical Damage Statistics – (a) Slope Failure, (b) Ground Movement, and (c) Soil Bulging and Liquefaction  1030 0 035380 0 126130 0 07154(69%)1(0%)68(30%)020406080100120140160Minor/None Moderate High Unknown Not Assessed# of Buildings(a) Slope FailureDemolish RepairUnknown Total9310 5 030372 0 125121 0 07142(64%)13(6%)5(2%) 1(0%)62(28%)020406080100120140160Minor/None Moderate High Unknown Not Assessed# of Buildings(b) Ground MovementDemolish RepairUnknown Total86145 033374 0 123122 0 0 6135(61%)20(9%)5(2%) 1(0%)62(28%)020406080100120140160Minor/None Moderate High Unknown Not Assessed# of Buildings(c) Soil Bulging and LiquefactionDemolish RepairUnknown Total46      Figure 4-8: Building Statistics – (a) Heritage Status, (b) Seismic Force Resisting System, and (c) Number of Floors 1712112536 1435(16%)188(84%)050100150200Heritage Nonheritage# of Buildings(a) Heritage StatusDemolishRepairUnknownTotal664971618404 34104 288(39%)99(44%)15(7%)21(9%)020406080100120Moment Frame Shear Wall Moment Frame& Shear WallMoment Framewith Infill# of Buildings(b) Seismic Force Resisting System (SFRS)DemolishRepairUnknownTotal7354114616310 91129(58%)79(35%)15(7%)0204060801001201403-5 6-12 13-22# of Buildings(c) Number of FloorsDemolishRepairUnknownTotal47        Figure 4-9: Building Statistics – (a) Occupancy Type, (b) Construction Year, and (c) Duration in Cordon 1148 9 1 3 0 0 3 026 11 8 7 5 3 3 1 114 3 2 1 0 0 0 0 0154(69%)22(10%) 19(9%) 9(4%) 8(4%) 3(1%) 3(1%) 4(2%) 1(0%)020406080100120140160Commercial Residential Hotel Post-secondaryHospital PublicassemblySchool Government Industrial# of Buildings(a) Occupancy TypeDemolishRepairUnknownTotal41245315511 1120158112 4 2 163(28%)37(17%)77(35%)32(14%)14(6%)020406080100Pre 1965 1965-75 1976-91 1992-03 Post 2003# of Buildings(b) Construction YearDemolishRepairUnknownTotal23533855563908012072 1 0108(4%)81(36%)5(2%)47(21%)5(2%)77(35%)0204060801000 Up to 6 7-12 13-18 19-24 25-28# of Buildings(c) Duration in Cordon (number of months)DemolishRepairUnknownTotal48      Figure 4-10: Building Area Statistics – (a) Footprint Area, (b) Total Floor Area, and (c) Total Floor Area by Occupancy Type  758481783162613706103 110(4%)80(36%)84(38%)33(15%)16(7%)020406080100<200 200-499 500-999 1000-1999 >2000# of Buildings(a) Building Footprint Area (m2)DemolishRepairUnknownTotal1038 392113179 121812591 2112 2 220(9%)52(23%)68(30%)35(16%)20(9%)28(13%)01020304050607080<1000 1000-2000 2000-4000 4000-7000 7000-10000 > 10000# of Buildings(b) Total Floor Area (m2)DemolishRepairUnknownTotal74%42%63%29%18%45%26%67%9%14% 10% 3%683,022 (56%)60,989 (5%)237,109 (19%) 242,414 (20%)0100,000200,000300,000400,000500,000600,000700,000800,000Commercial Residential Hotel Institutional/IndustrialTotal Floor Area (m2 )(c) Total Floor Area by Occupancy TypeDemolishRepairUnknownTotal49    Figure 4-11: Building Data Availability - All Buildings, Buildings with DEE Summary Table, Buildings with Pre-EQ %NBS Data, and Buildings with Post-EQ %NBS Data    Figure 4-12: All Buildings vs Buildings with DEE Summary Table – (a) Placard and (b) Damage Ratio  13825 19 186551 46 4920 11 11 11223(100%)87(39%)76(34%) 78(35%)050100150200250All buildings Buildings withDEE SummaryBuildings withPre-EQ %NBSBuildings withPost-EQ %NBS# of BuildingsDemolishRepairUnknownTotalGreen7735%Yellow10346%Red4319%All BuildingsGreen4956%Yellow3439%Red45%Buildings with DEE Summary0-1%5525%2-10%8036%11-30%5424%31-60%209%61-99%136%100%10%All Buildings0-1%3641%2-10%3540%11-30%1315%31-60%34%61-99%00%100%00%Buildings with DEE Summary(a) Placard (b) Damage Ratio 50     Figure 4-13: Building Seismic Capacity Statistics - (a) Pre-EQ %NBS and (b) Post-EQ %NBS    6 9 41195 16 25 197 2 2918(8%) 27(12%) 37(14%)147(66%)040801201600-33% 34-66% 67-100% Unknown# of Buildings(a) Pre-EQ %NBSDemolishRepairUnknownTotal7 9 21206 23 20 1682 1921(9%)34(15%)23(10%)145(65%)040801201600-33% 34-66% 67-100% Unknown# of Buildings(b) Post-EQ %NBSDemolishRepairUnknownTotal51   : Logistic Regression Model The bivariate statistics presented in section 4.11 describe the relationships between pairs of variables; individual independent variables with the decision outcome (dependent) variable. In chapter 5, logistic regression analyses are presented to encompass simultaneous and relative effects of the independent variables on the dependent variable. Chapter 5 describes the development of logistic regression models based on the collected data described in chapter 4. Utilizing two different methods (Forward and Backward Stepwise Selection methods) and three different damage indicators (Placard, Damage Ratio, and Damage Score), total of six models were developed. Then, they were tested for goodness-of-fit and screened for quality to arrive at the best model. Probability-of-demolition function from the final logistic regression model is presented and its interpretation is discussed. Separate logistic regression models considering the %NBS variable are also examined. The basic principles of logistic regression analysis were discussed in section 2.3. The statistical analysis software used for the project is IBM® SPSS® Statistics 22   Objective and Scope of Logistic Regression Model Analysis The main objective of the logistic regression model analysis is to explicitly quantify the influence of potential explanatory variables on the probability of building demolition. The aim is to express the results in terms of probability of demolition given a set of influencing factors. Although the empirical equation developed here may be used to predict the probability of building demolition, the database scope and local context should be carefully considered before using the model for prediction in other settings. Such limitation is further discussed in section 7.2.  The scope of the logistic regression model analysis is the same as the research scope: 3-storey and higher concrete buildings in the Christchurch CBD. Logistic regression models are established 52   based on the research database with a few exceptions. The buildings with unknown decision outcome (20 buildings) are excluded, as such buildings do not provide any meaningful information for the analysis. The buildings demolished under CCDU Demolition (12 buildings) are also left out because the decision outcome on such buildings is solely based on the city’s development plan, irrespective of the variables under consideration.   Description of Logistic Regression Model The basic principles of logistic regression analysis were discussed in section 2.3. For more details on logistic regression analysis and model building procedure using SPSS, refer to Hosmer et al. (2013) and IBM Corp.(2013).  In logistic regression models, the independent variables can be both categorical and scalar. The categorical variables are coded using dummy (or design) variables. Each dummy variable is given a value of either 0 or 1, and a combination of the dummy variables defines class membership of the independent variable. If a categorical variable has n  possible values, n-1 dummy variables are introduced. For example, the Placard variable has three categories (green, yellow, and red). As these are discrete categorical values, two dummy variables are introduced and coded as shown in Table 5-1. When there are two possible groups in a categorical variable, each group is simply assigned a value of either 0 or 1.  Table 5-1: Dummy Variable Coding for Placard Placard Dummy 1 Dummy 2 Green 1 0 Yellow 0 1 Red 0 0  While the Occupancy Type variable has 9 categories, the majority of the study buildings is commercial occupancy (Figure 4-9a). A large number of categories may result in relatively small 53   or zero number of observations in each category, which is the most common reason for convergence failure of a logistic regression model (Altman et al., 2003). For numerical stability and succinctness of the model, the Occupancy Type variable is reduced to two categories: Commercial and Residential/Hotel/Institutional/Industrial. Similarly, the MFIF and Combined MF/SW categories for the SFRS variable are grouped together, resulting in three categories and two dummy variables.  For the Construction Year variable, which is in categorical ranges, the median value for each range was selected as its representative scalar value.  Due to the small number of observations in the 100% Damage Ratio category, the categorical (and ordinal) Damage Ratio variable caused model instability (Altman et al., 2003). In an effort to resolve the issue, the Damage Ratio variable was converted to a linear scalar variable (1 to 6). To investigate the validity of such conversion, two univariate regression models were developed relating the Decision Outcome (dependent variable) with the two different types of the Damage Ratio variable: first model with categorical variable and second model with scalar variable. The probability of demolition from those two models are compared in Table 5-2. It is shown that the two predictions of the probability of demolition are generally in agreement with minor differences at higher damage ratios. In addition, the Level 2 Rapid Assessment form includes Damage Ratio in the form of categories (tick box for each range) and it is more likely that the inspectors consider Damage Ratio ranges as relative linear scale than as numerical ranges. Therefore, it is confirmed that the linear scale is a reasonable approximation, and such change in the variable type does not significantly affect the model outcome. Table 5-2: Comparison of Categorical and Scalar Damage Ratio Variable - Probability of Demolition  Variable Type Damage Ratio 0-1% 2-10% 11-30% 31-60% 61-99% 100% Categorical 38% 64% 84% 100% 92% 100% Scalar 38% 64% 84% 94% 98% 99%  54   Table 5-3 summarizes the coded values for all variables.  The Pre-EQ %NBS and Post-EQ %NBS variables are not included in the logistic regression model due to lack of available data for a sufficient number of buildings. Instead, the importance of the variables are studied separately in section 5.8.   Logistic Regression Model Building Strategy Among various model-building strategies, stepwise variable selection methods are chosen. The main advantage of the stepwise selection methods is that they are useful when important variables are not known from previous studies, and their relation with the outcome variable is not well understood (Hosmer et al., 2013). This aspect gives a substantial advantage since the core objective of the logistic regression analysis is to identify the factors influencing the building decision outcome. In addition, the stepwise selection methods are effective and efficient in screening many variables and fitting various models concurrently.  The stepwise selection methods utilize significance testing rules when determining inclusion or exclusion of independent variables in models. Depending on the type of methods, such decision rules vary among probability of likelihood ratio statistics, score statistics, and Wald statistics. Studies have shown that there are no significant differences among different types of tests (Hosmer et al., 2013). The stepwise selection methods used in this analysis are described in the following subsections.   55   Table 5-3: Logistic Regression Model Variables Variable Type Variable Name Notation Values Value Label Measure Dependent Decision Outcome y 0 Demolish Categorical 1 Repair Independent Footprint Area x1 Numeric [m2] Scale Construction Year x2 1932 Pre 1965 Scale 1970 1965-1975 1984 1976-1991 1998 1992-2003 2007 Post 2003 Heritage Status x3 0 Heritage Categorical 1 Nonheritage SFRS x4, x5 x4 x5  Categorical 1 0 MF 0 0 SW 0 1 MFIF, MF&SW Occupancy Type x6 0 R/H/I Categorical 1 Commercial Number of Floors x7 Numeric Scale Duration in Cordon x8 Numeric [months] Scale Placard x9, x10 x9 x10  Categorical 1 0 Green 0 1 Yellow 0 0 Red Damage Ratio x11 1 0-1% Scale 2 2-10% 3 11-30% 4 31-60% 5 61-99% 6 100% Damage Score x12 Numeric Scale  56    Forward Stepwise Selection The Forward Stepwise Selection (FSS) method performs variable entry testing based on the significance of the score statistics and variable removal testing based on the probability of likelihood ratio statistics on the maximum partial likelihood estimates. The general steps are described below: 1) The candidate independent variables are tested for inclusion one at a time based on the significance level (p-value) of the score statistics. The variable with the smallest p-value being less than the specified importance level for entry (𝛼𝐸) is included in the model.  2) After each entry, the variables that are entered into the model are tested against removal criteria. For each included variable, the significance of change in the log-likelihood is determined. The log-likelihood ratio (LR) is expressed as  𝐿𝑅𝑗 =−2(𝐿𝑗 − 𝐿), where 𝐿 is the log of maximum likelihood estimates (MLE) of the current full model and 𝐿𝑗 is the log of MLE of the model excluding one variable at a time. The variable with the largest p-value being greater than the specified importance level for removal (𝛼𝑅) is removed from the model.  3) The model is updated and the remaining variables in the model are tested based on the most current model. After all included variables are tested for removal, all steps are repeated to evaluate the remaining candidate variables. The procedure ends when all variables are assessed based on the entry and removal criteria or when the current model is the same as the previous model.  Backward Stepwise Selection Backward Stepwise Selection (BSS) method conducts variable removal testing based on the probability of the likelihood ratio statistics on the maximum partial likelihood estimates and variable entry testing based on the significance of the score statistics. The main difference to the FSS method is that the iteration procedure starts with all 57   independent variables included in the model, and the variables are tested for removal one at a time. The general steps are described below: 1) All independent variables are entered into the model as a start. Then, the variables are tested for removal one at a time based on the significance level (p-value) of log-likelihood ratio, 𝑳𝑹𝒋 = −𝟐 𝑳𝒋 − 𝑳 . The variable with the largest p-value being greater than the specified importance level for removal (𝛼𝑅) is removed from the model. The model is updated and the remaining variables in the model are tested based on the most current model. 2) After all included variables are tested for removal, the variables not in the model are checked for inclusion one at a time based on the significance level (p-value) of the score statistics. The variable with the smallest p-value being less than the specified importance level for entry (𝛼𝐸) is included in the model.  3) If the updated model is not the same as any of the previous models, all previous steps are repeated. The procedure ends when all variables are assessed based on the entry and removal criteria or when the current model is the same as the previous model. Due to the fundamental difference in the variable selection procedure, the two methods may produce different models. Both methods are used to explore and compare different model results. If the two methods generate the same model results, it would imply that the selected variables and the resulting models are robust. For both the FSS and BSS methods, the p-values of 0.05 and 0.10 are used for entry (𝛼𝐸) and for removal (𝛼𝑅), respectively.  For each damage indicator (Placard, Damage Ratio, and Damage Score), two sets of models are developed using FSS and BSS methods. Descriptive names are given to each model. Model PLF indicates model with PLacard as a DI using Forward Stepwise Selection method. Similarly, Model DRB indicates model with Damage Ratio as a DI using Backward Stepwise Selection method. Model DSF and Model DSB refer to Damage Score models with Forward and Backward Stepwise 58   Selection methods, respectively. The variable selection methods and the considered variables for the six models are summarized in Table 5-4 below.  Table 5-4: Logistic Regression Model Description Model PLF PLB DRF DRB DSF DSB Variable Selection Method FSS BSS FSS BSS FSS BSS Considered Variables Footprint Area x1       Construction Year x2       Heritage Status x3       SFRS x4, x5       Occupancy Type x6       Number of Floors x7       Duration in Cordon x8       Placard x9, x10       Damage Ratio x11       Damage Score x12       : Variable considered for inclusion   Model Outcome Logistic regression analyses are conducted for the six models as described in Table 5-4 above. Through iteration steps as described in section 5.3, the regression coefficients and the log-likelihood ratios are determined and summarized in Table 5-5, Table 5-6, and Table 5-7. The values from the last iteration step (in red) represent the final values for each model. Table 5-8 summarizes and compares the selected independent variables among the six models.    59   Table 5-5: Logistic Regression Model Coefficients – Model PLF and PLB (Placard) Iteration Steps Null Model PLF Model PLB PLF1 PLF2 PLF3 PLF4 PLB1 PLB2 PLB3 PLB4 Intercept x0 -0.66 -2.97 -1.74 -0.36 0.31 -33.21 -34.28 -35.30 -42.19 Footprint Area x1      0.00    Construction Year x2      0.02 0.02 0.02 0.02 Heritage Status x3      -1.42 -1.47 -1.35 -1.41 SFRS x4     -1.08 -0.92 -0.91 -0.93  x5     -1.00 -0.75 -0.75 -0.79  Occupancy Type x6   -1.80 -2.24 -2.10 -1.95 -1.98 -2.09 -2.19 Number of Floors x7    -0.22 -0.25 -0.23 -0.23 -0.25 -0.23 Duration in Cordon x8      -0.01 -0.01   Placard x9  3.74 3.48 3.58 3.54 3.61 3.67 3.68 3.73 x10  1.76 1.86 2.14 2.00 2.17 2.22 2.19 2.33 -2 Log-Likelihood (-2LL) 245.0 188.5 167.7 157.5 151.0 144.4 144.5 144.9 149.2 No. of included variable 0 1 2 3 4 8 7 6 5  Table 5-6: Logistic Regression Model Coefficients – Model DRF and DRB (Damage Ratio) Iteration Steps Null Model DRF Model DRB DRF1 DRF2 DRF3 DRF4 DRF5 DRB1 DRB2 DRB3 DRB4 Intercept x0 -0.66 0.72 2.95 4.19 -35.39 -45.48 -39.93 -40.33 -41.30 -45.48 Footprint Area x1       0.00 0.00   Construction Year x2     0.02 0.03 0.02 0.02 0.02 0.03 Heritage Status x3      -1.65 -1.49 -1.47 -1.54 -1.65 SFRS x4       -0.79 -0.80 -0.80  x5       -0.38 -0.39 -0.40  Occupancy Type x6  -2.13 -1.97 -2.24 -2.19 -2.10 -1.97 -2.00 -2.04 -2.10 Number of Floors x7    -0.20 -0.23 -0.20 -0.22 -0.22 -0.22 -0.20 Duration in Cordon x8       0.00    Damage Ratio x11   -1.09 -1.04 -1.04 -1.16 -1.10 -1.10 -1.12 -1.16 -2 Log-Likelihood (-2LL) 245.0 204.8 170.8 161.1 155.1 149.3 146.0 146.0 146.2 149.3 No. of included variable 0 1 2 3 4 5 8 7 6 5 60   Table 5-7: Logistic Regression Model Coefficients – Model DSF and DSB (Damage Score) Iteration Steps Null Model DSF Model DSB DSF1 DSF2 DSB1 DSB2 DSB3 Intercept x0 -0.68 0.86 2.09 -36.21 -36.22 -29.51 Footprint Area x1    0.00 0.00 0.00 Construction Year x2    0.02 0.02 0.02 Heritage Status x3    -0.80 -0.81  SFRS x4    -1.15 -1.15 -1.17 x5    -0.75 -0.74 -0.73 Occupancy Type x6  -2.29 -2.17 -2.00 -1.99 -2.02 Number of Floors x7    -0.23 -0.23 -0.25 Duration in Cordon x8    0.00   Damage Score x12   -0.01 -0.01 -0.01 -0.01 -2 Log-Likelihood (-2LL) 212.2 174.1 151.3 129.7 129.7 131.2 No. of included variable 0 1 2 8 7 6  Table 5-8: Logistic Regression Model Outcome - Summary of Selected Variables Selected Variables  Model PLF PLB DRF DRB DSF DSB Footprint Area x1       Construction Year x2       Heritage Status x3       SFRS x4, x5       Occupancy Type x6       Number of Floors x7       Duration in Cordon x8       Placard x9, x10       Damage Ratio x11       Damage Score x12       : Variable included in model 61   From the six logistic regression model outcomes, the following observations are made:  Damage indicator variable (Placard, Damage Ratio, or Damage Score) is included in all six models. This means the assessed damage is influential in the probability of demolition, which is expected and reasonable.   Occupancy Type variable is also included in all six models, indicating that the variable is influential.  Footprint Area, Construction Year, Heritage Status, SFRS, and Number of Floors variables are included in at least one model.   The two models with Damage Ratio (Model DRF and DRB) result in the same included variables and the same regression coefficients. This means that the selected variables strongly influence the decision outcome and that the model is robust. The six models are tested and screened in section 5.5 and section 5.6 for final model selections. More discussion of the selected final model can be found in section 5.6.   Model Fit Test The six models are tested to ensure the developed models properly represent the observed data. This is done using the Hosmer-Lemeshow goodness-of-fit test, which assesses whether or not the observed outcome matches with the predicted outcome in subgroups of the model population by conducting a chi-square test on the contingency table (Hosmer et al., 2013). The contingency table is created by classifying the binary outcome with a number of subgroups. Each group contains approximately equal population and is partitioned by the percentiles of the predicted probability. Here, 10 subgroups are created for each model, resulting in 2x10 contingency tables. Table 5-9 presents the contingency table for Model DRF as an example.   62   Table 5-9: Hosmer-Lemeshow Contingency Table for Model DRF Subgroup Outcome = Demolish Outcome = Repair Total Observed Expected Observed Expected 1 19 18.8 0 0.2 19 2 18 18.4 1 0.6 19 3 18 18.0 1 1.0 19 4 16 16.0 2 2.0 18 5 18 17.9 4 4.1 22 6 17 13.9 2 5.1 19 7 6 11.4 14 8.6 20 8 9 6.8 10 12.2 19 9 5 3.6 14 15.4 19 10 0 1.2 17 15.8 17  Using the contingency table, the Hosmer-Lemeshow goodness-of-fit statistic is calculated on the models and its significance value (p-value) is obtained. Detailed mathematics of the statistics can be found in the literature (Hosmer et al., 2013).  As suggested in the literature, however, the p-value from the model goodness-of-fit test should not be used to determine the relative performance of different models. Rather, it is used to check the goodness-of-fit of each model. Generally, the p-value less than 0.05 indicates that the model has a poor fit. Table 5-10 summarizes the chi-square statistics and the p-values of the six models. Except for the Model DSB, all models have the p-value greater than 0.05, indicating a good fit. Table 5-10: Hosmer-Lemeshow Goodness-of-Fit Test  PLF PLB DRF DRB DSF DSB Chi-Square 8.94 10.42 12.09 12.09 6.917 21.53 p-value 0.35 0.24 0.15 0.15 0.55 0.01 63    Model Selection Akaike Information Criterion (AIC) is a measure of the relative quality of a statistical model for a given set of data. It provides a relative estimate of the information lost when a selected model is used to represent the process that generates the data (Akaike, 1974). The AIC value is calculated using the equation shown below: 𝑨𝑰𝑪 = 𝟐𝒌 − 𝟐 𝒍𝒏 𝑳  ( 5-1 ) L is the maximum likelihood estimate of the model and −2 ln L  is equivalent to -2 Log-Likelihood presented in Table 5-5, Table 5-6, and Table 5-7. k is the number of estimated parameters, which is equivalent to the number of degrees of freedom. Increasing the number of estimated parameters improves the goodness-of-fit of the model. At the same time, however, it complicates the statistical model and may lead to model overfitting, which describes random error instead of the true relationship. Therefore, overfitting may exaggerate the noise and exacerbate the model performance. By adding the k term, the AIC accounts for the trade-off between the goodness-of-fit and the complexity of the model. Therefore, the model with the lowest AIC value is preferred.  The difference between the minimum AIC value and the AIC value for Model i (∆𝒊= 𝑨𝑰𝑪𝒎𝒊𝒏 − 𝑨𝑰𝑪𝒊) may be used to express the likelihood of Model i being the best model. As a rule of thumb, ∆𝑖 between 0 and 2 implies substantial evidence that Model i may be the best model, ∆𝑖 between 4 and 7 suggests considerably less support, and ∆𝑖 greater than 10 indicates essentially no evidence that Model i may be the best model (Burnham & Anderson, 2002). While candidate models are ranked based on the magnitude of the AIC values, the relative strength of a model can be quantified using the relative likelihood (Burnham & Anderson, 2002).  64   𝑹𝒆𝒍𝒂𝒕𝒊𝒗𝒆 𝑳𝒊𝒌𝒆𝒍𝒊𝒉𝒐𝒐𝒅 = 𝒆 𝑨𝑰𝑪𝒎𝒊𝒏−𝑨𝑰𝑪𝒊 /𝟐 ( 5-2) For example, based on equation 5-2, relative likelihood of Model PLF compared to Model PLB (minimum AIC value between the two models) is calculated as 𝒆 𝟏𝟔𝟑−𝟏𝟔𝟓 /𝟐 = 𝟎. 𝟑𝟕. This can be interpreted as Model PLF is 0.37 times as probable as Model PLB to minimize the information loss. Table 5-11 below presents the calculated AIC values, ∆𝑖 , and relative likelihoods for the six models. ∆𝑖  and relative likelihoods are calculated by comparing two models with the same damage indicator. Table 5-11: Logistic Regression Model AIC, Delta AIC, and Relative Likelihood Selected Variables Model PLF PLB DRF DRB DSF DSB -2 Log-Likelihood (LL) 151.0 149.2 149.3 149.3 151.3 131.2 No. of estimated parameters, k 7 7 6 6 3 8 AIC 165 163 161 161 157 147 ∆𝒊 2 0 0 0 10 0 Relative Likelihood 0.368 1 1 1 0.007 1  The AIC, ∆𝑖, and relative likelihood values, together with the goodness-of-fit results in Table 5-10, are used to identify the preferred model for each damage indicator. For Placard DI, Model PLB is chosen since it has lower AIC value compared to Model PLF (although difference is marginal). Also, Model PLB includes the same variables as Model DRF and DRB. For Damage Ratio DI, coefficients for Model DRF are the same as Model DRB, as demonstrated in section 5.5. For Damage Score DI, Model DSF is chosen even with higher AIC value, because Model DSB failed the goodness-of-fit test in section 5.5. Table 5-12 below summarizes the regression coefficients and the p-values for the independent variables, -2 Log-Likelihood values, goodness-of-fit p-values, and the AIC values for the chosen 65   three models. For the rest of the discussion, the last letter “F” and “B” are dropped and the chosen models are simply referred to as Model PL, DR, and DS. A regression coefficient of zero means that the corresponding variable is found to have a significance value greater than 0.05 and therefore is not included in the final model.  Table 5-12: Final Logistic Regression Model Summary* Final Model PL DR DS B p-value B p-value B p-value Independent Variables Intercept x0 -42.19 - -45.48 - 2.09 - Footprint Area x1 0 > 0.05 0 > 0.05 0 > 0.05 Construction Year x2 0.02 0.02 0.03 0.01 0 > 0.05 Heritage Status x3 -1.41 0.04 -1.65 0.02 0 > 0.05 SFRS x4 0 > 0.05 0 > 0.05 0 > 0.05 x5 0 > 0.05 0 > 0.05 0 > 0.05 Occupancy Type x6 -2.19 0.00 -2.10 0.00 -2.17 0.00 Number of Floors x7 -0.23 0.00 -0.20 0.01 0 > 0.05 Duration in Cordon x8 0 > 0.05 0 > 0.05 0 > 0.05 Placard x9 3.73 0.00 - - - - x10 2.33 0.01 - - - - Damage Ratio x11 - - -1.16 0.00 - - Damage Score x12 - - - - -0.01 0.00 -2 Log-Likelihood (-2LL) 149.2 149.3 151.3 No. of included variable 5 5 2 Goodness-of-Fit p-value 0.24 0.15 0.55 AIC 163 161 157 * Dependent variable: decision outcome In both Model PL and Model DR, Occupancy Type, Heritage Status, Number of Floors, and Construction Year variables are identified to be statistically significant with p-value less than 0.05, in addition to the damage indicator variable. Model DS identifies Damage Score and Occupancy Type variables as being important. Damage indicator and Occupancy Type variables are 66   consistently found to be important in all three models, implying robustness of their effects on the demolition decision outcome. The signs of the regression coefficients indicate the directions of the influence, that is, whether a unit increase of a variable increases or decreases the probability of demolition. The sign depends on the coding of the dependent and independent variables during the model building steps. For example, in this study, the negative regression coefficient for the Damage Ratio variable indicates that a positive change of the variable (increase in Damage Ratio) increases the probability of demolition.  Among the final three models, Model DR seems to be the best model for the following reasons:   The AIC value of Model DR is smaller than that of Model PL, while Model PL and Model DR included the same variables and presented similar results. This indicates that Model DR is better than Model PL.  Model DS indicates that  Occupancy Type  is the only variable that is important other than Damage Score. Realistically and intuitively, there are likely to be other variables influencing the odds ratio of building demolition, in which case relevant variables should be included in the model regardless of their statistical significance (Hosmer et al., 2013). For this reason, it is unlikely that Model DS would be the best model.  Damage Ratio is more refined measure of damage and less biased by external factors compared to Placard. Also, Damage Ratio is likely to have less inherent uncertainty compared to Damage Score; Damage Ratio is one overall estimate of damage while Damage Score is a collection of multiple estimates with their own uncertainty. Thus, it is inferred that Model DR is better than Model PL and Model DS.  While two different variable selection methods are used, Model DRF and Model DRB resulted in the same variables with the same regression coefficients. This indicates that Model DR and its selected variables are more robust than Model PL and Model DS; models 67   with Placard (PLF and PLB) and Damage Score (DSF and DSB) resulted in different selected variables for different variable selection methods.  Therefore, Model DR is selected to be the best model and the following discussion focuses on Model DR.    Probability of Demolition From the logistic regression analysis results, a function representing how the probability of demolition varies with level of damage and other independent variables can be derived. The regression coefficients from the established logistic regression model (Model DR) (Table 5-12) are substituted into the equations 2-7 and 2-8 to obtain the probability-of-demolition function as below:  𝒍𝒏 (𝑷𝟏−𝑷) = 𝒚 = −𝟒𝟓. 𝟒𝟖 + 𝟎. 𝟎𝟑𝒙𝟐 − 𝟏. 𝟔𝟓𝒙𝟑 − 𝟐. 𝟏𝟎𝒙𝟔 − 𝟎. 𝟐𝒙𝟕 − 𝟏. 𝟏𝟔𝒙𝟏𝟏 ( 5-3 ) Probability of Demolition = 1 − P =11+e−45.48+0.03x2−1.65x3−2.1x6−0.2x7−1.16x11 ( 5-4 ) Note that the logistic regression model was coded so that P in the above function is the probability of repair and 1-P  is the probability of demolition (Table 5-3). For visualization focusing on the level of damage, 2-dimensional probability-of-demolition curve is plotted against Damage Ratio by assuming a reference set of independent variables (fixed values of x2, x3, x6, and x7) (Figure 5-1). This curve is referred to as reference curve in the following discussion. The reference values of the independent variables are chosen at their median values from the database, and these are presented in Table 5-13.   68   Table 5-13: Reference Values for Independent Variables Variable Name Variable Reference Value Construction Year x2 1984 Heritage Status x3 Nonheritage Occupancy Type x6 Commercial Number of Floors x7 5-storey Damage Ratio x11 2-10%   Figure 5-1: Probability of Demolition vs. Damage Ratio  The observed probability-of-demolition curve in Figure 5-1 is produced by calculating the frequency of observed demolition outcome for each level of damage (referred to as cross-tabulation). The 95% confidence intervals (CI) for the predicted probability-of-demolition are calculated as follows: 1) Fitted value (y) is calculated by substituting reference values of the independent variables and a Damage Ratio value into equation 5-3. 0%10%20%30%40%50%60%70%80%90%100%Probability of DemolitionObservedPredicted95% C.I.0-1%      2-10%             11-30%           31-60%           61-99%         100% 69   2) Standard error of the fitted value (S.E. fit) is calculated using R (The R Core Team, 2014); SPSS does not have a readily available option for this calculation. 3) Upper limit (UL) and lower limit (LL) for 95% confidence of the probability of demolition are calculated as  11+e fitted y±1.96S.E.fit .  4) The above calculations are conducted for the six values of Damage Ratio variable. The drop in the observed probability of demolition at Damage Ratio of 61-99% is exaggerated by the small number of observations in that category. Figure 5-1 shows that the logistic regression model prediction is generally in good agreement with the observed probability of demolition (within 95% CI). As expected, both the predicted and observed probability-of-demolition curves indicate that the likelihood of demolition increases with severity of building damage. It is found that the probability of demolition (for both observed and predicted) for the lowest levels of damage are already quite high ranging from 31% to 47%. It should be noted that the likelihood of an undamaged building being demolished is very low (except for the buildings demolished under CCDU demolition, which were excluded from the analysis) because insurance claim is triggered by the assessed damage. Although Damage Ratio of 0-1% is supposed to include the buildings with no damage (as there is no option for “no damage” in the assessment form), the high demolition rate for the buildings with 0-1% Damage Ratio suggests that the majority of those buildings are likely to had some degree of damage.  Since the predicted probability-of-demolition curve is based on the arbitrarily chosen, median conditions of the independent variables (reference values), the change in the probability of demolition due to the change in damage severity (slope of the curve) is more informative than the absolute values of the probability of demolition. With all other variables being equal, varying Damage Ratio from 0-1% to 11-30% and to 100%  would raise the likelihood of demolition by 43% and 52%, respectively. The changes in the probability of demolition is summarized in Table 5-14, which is read from row to column and the values are subtraction of the two probabilities. 70   Table 5-14: Change in Probability of Demolition Damage Ratio 0-1% 2-10% 11-30% 31-60% 61-99% 100% 0-1% 0% 27% 43% 49% 52% 52% 2-10% -27% 0% 16% 23% 25% 26% 11-30% -43% -16% 0% 7% 9% 9% 31-60% -49% -23% -7% 0% 2% 3% 61-99% -52% -25% -9% -2% 0% 1% 100% -52% -26% -9% -3% -1% 0%   The reference curve in Figure 5-1 may be shifted and/or scaled by varying one independent variable at a time. By observing the changes in the curve, the effects of independent variables on the demolition decision can be determined. This is demonstrated in Figure 5-2.  Generally speaking, older, taller, nonheritage, commercial buildings have higher probability of demolition for a given Damage Ratio. Such effects of the independent variables, however, diminish with increase in assessed damage. That is, when a building experiences severe damage, other influencing variables become less important in the demolition decision. The effects of unit change of the independent variables on the probability of demolition can be quantified by the magnitude of the regression coefficients as seen in Table 5-12 and discussed in section 5.6. 71      Figure 5-2: Probability of Demolition vs. Damage Ratio – Varying (a) Construction Year, (b) Heritage Status, (c) Occupancy Type, and (d) Number of Floors   0%10%20%30%40%50%60%70%80%90%100%Probability of Demolition(a) Construction Year196019701980199020000%10%20%30%40%50%60%70%80%90%100%Probability of Demolition(b) Heritage StatusHeritageNon-Heritage (Ref)0%10%20%30%40%50%60%70%80%90%100%Probability of Demolition(c) Occupancy TypeCommercial (Ref)R/H/I0%10%20%30%40%50%60%70%80%90%100%Probability of Demolition(d) Number of Floors3-Storey5-Storey (Ref)10-Storey15-Storey0-1%      2-10%    11-30%   31-60%   61-99%  100% 0-1%      2-10%    11-30%   31-60%   61-99%  100% 0-1%      2-10%    11-30%   31-60%   61-99%  100% 0-1%      2-10%    11-30%   31-60%   61-99%  100% 72    Logistic Regression Model with %NBS Variable Due to the high rate of missing values (65%), the Pre-EQ %NBS and Post-EQ %NBS variables were not included in the development of the logistic regression model. As discussed in section 4.3, the %NBS variables as an indicator of a building’s seismic capacity may affect the demolition decision due to the city’s earthquake-prone building policy. To consider their effects, several methods for handling the missing value problem are considered. The most common and simple method is the case-wise deletion method, also known as complete-case-analysis, which discards any data with missing information (Little & Rubin, 2002). This method assumes that the missing data are completely random, which means that the missing %NBS information should not be related to the decision outcome or any other independent variables. %NBS information was collected as a part of the DEE requirements by CERA, but the DEEs for numerous buildings were not collected, including for those buildings demolished early on for public safety by the Civil Defence team, those that were heavily damaged and for which the demolition decision was fairly obvious, and small buildings with very minor or no damage. The statistics of the buildings with %NBS data were observed to be different from the study database in terms of assessed damage and the likelihood of demolition; higher portion of the buildings with %NBS data experienced minor damage and were repaired. These reasons are related to the damage state and building characteristics, and therefore the “missing at random” assumption is not satisfied. Since the deleted data differ systematically from the rest of the database, the estimates may be seriously biased (Little & Rubin, 2002). Moreover, due to a significantly smaller sample size (59 buildings) after the deletion, the predictive power of the model may be lost considerably (Schafer, 1999). With these cautions in mind, the case-wise deletion method was used nonetheless to develop logistic regression models on the subset. Two models were developed using the forward stepwise variable selection approach and Damage Ratio as a damage indicator (as described in section 5.3). As summarized in Table 5-15, Occupancy Type, Number of Floors, and Pre-EQ%NBS or Post-73   EQ%NBS variables are identified as important, whereas Damage Ratio variable is not found to be influential. This is probably because 80% of the buildings with the %NBS data have Damage Ratio of 10% or less and none of them has Damage Ratio greater than 60% (refer to section 4.11). This may imply that the models based on the subset are biased and/or estimation power is lost significantly. Statistical correlations between the %NBS with the Damage Ratio were not observed (Pearson correlation coefficients of -0.05 and -0.19 for Pre-EQ%NBS or Post-EQ%NBS, respectively).  Table 5-15: Logistic Regression Model with %NBS Summary – Case-Wise Deletion Method  Pre-EQ %NBS  Post-EQ %NBS  B p-value B p-value Independent Variables Intercept x0 3.44 - 3.73 - Footprint Area x1 0 > 0.05 0 > 0.05 Construction Year x2 0 > 0.05 0 > 0.05 Heritage Status x3 0 > 0.05 0 > 0.05 SFRS x4 0 > 0.05 0 > 0.05 x5 0 > 0.05 0 > 0.05 Occupancy Type x6 -2.91 0.02 -2.43 0.05 Number of Floors x7 -0.78 0.00 -0.65 0.00 Duration in Cordon x8 0 > 0.05 0 > 0.05 Damage Ratio x11 0 > 0.05 0 > 0.05 Pre-EQ %NBS x13 8.62 0.00 - - Post-EQ %NBS x14 - - 7.01 0.01 -2 Log-Likelihood (-2LL) 32 38 Goodness-of-Fit p-value 0.94 0.96 AIC 40 46 No. of cases considered 59 61 No. of included variable 3 3   74   Another approach was taken to assess whether Pre-EQ %NBS and Post-EQ %NBS variables are of importance to the probability of demolition. The steps are as follows: 1) A logistic regression model is created by fitting the “best model” based on all buildings excluding %NBS variable (determined in section 5.6) on the subset of database whose records of %NBS are available. Here, fitted means that the selected variables from the “best model” are entered into the logistic regression analysis of the subset of database, without considering the significance of the selected variables. 2) Another logistic regression model is created by adding the %NBS variable to the “best model” and fitting on the subset of the database whose records of %NBS are available. 3) These two subset models are compared to determine whether the inclusion of %NBS variable affects and/or improves the model performance. The above procedure is conducted based on Model DR for Pre-EQ %NBS and Post-EQ %NBS variables. When Model DR is fitted on the Post-EQ %NBS subset, the resulting model becomes unstable with large standard error. This is likely due to the absence of heritage buildings that were demolished; zero observation in a categorical variable may cause nonconvergence problem (Altman et al., 2003). For this reason, the rest of the discussion focuses on Model DR, which is fitted on Pre-EQ %NBS subset. Table 5-16 summarizes the considered logistic regression model results. DR_Pre%NBS indicates the Model DR fitted on the Pre-EQ %NBS subset, and the following a and b represent whether %NBS variable is added to the model or not (Step 1 and 2, respectively). It can be seen that the p-values of the Heritage Status, Construction Year, and Damage Ratio variables are greater than 0.05, which means they now become less important when fitted on the subset. The added Pre-EQ %NBS variable is found to be important with the p-value of 0.01. Intuitively and logically, the fact that Damage Ratio is insignificant is unlikely to be true. This implies that the models based on the subset are strongly biased, possibly because 80% of the buildings with the %NBS data have Damage Ratio of 10% or less and none of them has Damage Ratio greater than 60%.  75   Nonetheless, the model goodness-of-fit is acceptable for both models, and the AIC value is smaller when the subset model includes %NBS variable. These imply that the %NBS variable is important when the model is based on the subset data, and the inclusion of %NBS variable improves the subset model performance (smaller AIC value). From this, it is inferred that %NBS may play a significant role in the probability of demolition when included in the global model. It should be noted, however, that the models based on the subset are not reliable in identifying influencing variables nor in quantifying their effects on the probability of demolition due to lack of available information. Table 5-16: Logistic Regression Model with %NBS Summary – Model DR on Pre-EQ %NBS Subset  DR_Pre%NBS_a DR_Pre%NBS_b B p-value B p-value Independent Variables Intercept x0 -96.1 - -57.0 - Construction Year x2 0.05 0.01 0.03 0.17 Heritage Status x3 -1.46 0.37 -1.73 0.52 Occupancy Type x6 -2.69 0.03 -2.64 0.06 Number of Floors x7 -0.53 0.01 -0.77 0.00 Damage Ratio x11 -0.74 0.19 -0.77 0.22 Pre-EQ %NBS x13 - - 8.44 0.01 -2 Log-Likelihood (-2LL) 37.0 27.8 Goodness-of-Fit p-value 0.93 0.88 AIC 49 42 No. of cases considered 59 59 No. of included variable 5 6  Although not explored in this study, another common method for treating missing information is multiple imputation method. This method is used to complete the dataset by generating values for missing data based on the statistical distribution of the available information. Similar to the case-wise deletion method, however, without satisfying the “missing at random” assumption, it may also be misleading, because it fails to take the missing value mechanism into account. 76   : Discussion of Local Context Factors In addition to the quantitative factors discussed previously, the local context and background should also be considered for comprehensive understanding of the post-earthquake decisions on buildings.  In-person interviews (with 9 building owners and owner’s representatives, 9 building developers and investors, 5 insurance sector representatives, and 4 local engineers and government authority personnel) revealed the complexity of the post-earthquake decision-making process, which is discussed further in  Marquis (2015) and Marquis et al. (2015). This section highlights the two most distinct local contextual factors that affected the building demolition decisions in Christchurch, New Zealand.    Insurance Approximately 80% of the economic loss from the Canterbury Earthquakes was borne by the insurance industry (Bevere & Grollimund, 2012), and therefore the insurance policy poses as an important variable in the post-earthquake decisions on buildings. The majority of commercial buildings in Christchurch were insured under a reinstatement policy including all 15 case studies buildings studied by Marquis (2015), which entitles the owner to a building in a “condition as new” while being limited to a maximum insurer’s liability (sum insured). It was learned that issues such as appropriate repair extent, methodology, and costs covered under the policy caused disagreements between the owners and the insurers, which often delayed the claiming process. Some building owners expressed their frustration during the process and its influence on their decision-making process. In addition, the interviews revealed that the sum insured amount was found to be lower than the actual rebuild or replacement cost for many buildings, possibly due to the post-earthquake inflation in construction and demolition costs and the inadequate pre-77   earthquake valuation of the buildings. As reported in Marquis et al. (2015), only 2 out of 15 case study buildings are estimated to have sufficient coverage to rebuild.  Prolonged and often complex insurance claiming process and the inadequate sum insured amount led technically viable repair (and strengthening) works to be considered uneconomical. Once a building was deemed as an “economic total loss,” both the insurer and the building owner preferred to agree on a cash settlement payout, leading to the more convenient outcome of building demolition rather than the more financially risky building repair.  Although attempted, insurance information could not be collected on large number of buildings, mainly due to confidentiality issue and limited data availability; for the 15 case study buildings in Marquis (2015), insurance information could be obtained under each building owner’s permission. If collected and analyzed, type of insurance policy and quantified insurance coverage information (e.g. sum insured amount) would have been strong candidate variables affecting the building demolition decision; these variables are likely to improve the performance of the logistic regression model. Collaborative research work with insurance industry might enable the collection of insurance data for future studies.    Changes in Local Legislation  Following the September 2010 earthquake, the Christchurch City Council revised its earthquake-prone building policy, recommending that building strengthening work shall aim to meet 67% NBS, raising the target from a prior required minimum of 34% NBS (CCC, 2010). Until the Supreme Court finally ruled in December 2014 (after a High Court decision in 2013) that property owners and insurers are only required to strengthen buildings up to 34% NBS, many building owners and insurers were uncertain as to whether the change in the earthquake-prone building policy was enforceable and, if it was, who was required to pay for the additional strengthening costs.  78   Furthermore, to account for the heightened level of seismicity in Canterbury region, an amendment to the New Zealand Building Code was published after the February 2011 Earthquake (DBH, 2011) resulting in a 36% increase in the basic seismic design load for Christchurch. This revision effectively lowered the %NBS rating of many existing buildings in the region. For example, a building constructed in 2010 to comply with the Building Code could have a capacity of just 73% NBS based on the new seismic design load. These changes in the local legislation have had a substantial influence on the cost of repair and strengthening work. Also, the tenants have become more vigilant as to building performance, seeking buildings with a higher %NBS rating. These left the buildings rated below 67 %NBS with the insecurity of their future profitability. All of these factors may have led to more building demolitions than would have happened without such changes. 79   : Conclusion The 2010-2011 Canterbury Earthquake Sequence extensively disrupted the built environment of the city of Christchurch. In order to investigate the high demolition rate relative to the assessed damage of reinforced concrete buildings in the Christchurch CBD, this research sought to determine the influence of various factors on post-earthquake building demolition decisions. The empirical database was developed by collecting information for 223 buildings, and logistic regression analyses were conducted. The variables affecting the demolition decision were identified, and their effects on the probability of building demolition were estimated. In addition, major qualitative factors affecting the post-earthquake decision were discussed.   Major Findings and Contributions This research is the first study that quantitatively explains the effects of various factors, including the level of damage, on the post-earthquake building demolition decisions. The findings of this study indicate that damage is not the only factor affecting the building demolition decision and highlights that more attention should be paid to other variables.  The descriptive statistics demonstrated that a significant number of reinforced concrete buildings with relatively low assessed damage were demolished. It was inferred that there may be other variables affecting the demolition decision, which relates back to the research question: what factors, including but not limited to degree of building damage, influence the post-earthquake demolition decisions on buildings?  The logistic regression analysis results implied that the assessed damage, construction year, heritage status, number of floors, and occupancy type influenced the likelihood of building demolition. As anticipated, increase in building damage and building age increased the probability of demolition. Heritage buildings showed lower probability of demolition, which is rationale considering the heritage conservation policy. Commercial buildings were more likely to 80   be demolished compared to residential, hotel, industrial, and  institutional buildings. Opposed to the assumption made, the increase in the number of floors increased the probability of demolition. This trend may be exaggerated by the small number of tall buildings in the study database. Also, it may partly be because of the change in the public’s perception on seismic risk after the collapse of the two large buildings, which claimed the greatest number of lives. In-person interviews with building owners revealed that some tenants have shown preference for low-rise over high-rise buildings after the earthquakes. On the contrary to the initial conjecture that duration in cordon may play a significant role, the logistic regression models did not identify it to be important. Building footprint area and seismic force resisting system were found to be insignificant in the probability of building demolition. While data limitations precluded reliable analysis of the role of pre- and post- earthquake seismic capacity (%NBS), available evidence suggests that %NBS as an indication of structural capacity may have affected the building demolition decision as well; buildings with lower %NBS rating are expected to have higher probability of demolition.  The probability-of-demolition function accounting for the effects of various factors was obtained from the logistic regression analysis (equation 5-4), and the probability-of-repair function can be easily calculated assuming there are only two possible outcomes. The two functions represent 𝑷 𝒅𝒆𝒎𝒐𝒍𝒊𝒕𝒊𝒐𝒏|𝒅𝒗  and 𝑷 𝒓𝒆𝒑𝒂𝒊𝒓|𝒅𝒗  in equation 2-4, where interpreted as the probability of demolition or repair given dv  (repair cost in the form of Damage Ratio) for a given set of conditions on Occupancy Type, Heritage Status, Construction Year, and Number of Floors (i.e. the variables identified in the logistic regression analysis.) That is, the probability-of-demolition or repair functions are conditioned upon dv, which is now a vector with 5 variables. Further study is needed to develop total loss functions for both demolition and repair decision outcomes (𝑮 𝒕𝒍|𝒅𝒆𝒎𝒐𝒍𝒊𝒕𝒊𝒐𝒏  and 𝑮 𝒕𝒍|𝒓𝒆𝒑𝒂𝒊𝒓 ), with consideration of cost of repair, demolition, and downtime, and cost recovery from insurance. Then, the 4 functions combined using the total probability theorem (equation 2-4) would yield the probability of total loss exceeding a threshold value. This modified approach to the PBEE’s loss analysis would provide means of predicting total 81   loss, which considers both decision outcome scenarios and their influencing variables. This would benefit the decision makers with more comprehensive and valuable information concerning seismic risk management and strategy.   Limitations and Further Research Opportunities The outcomes (influential variables and their effects on the likelihood of demolition) of the logistic regression model presented in this thesis are based on a case study of the city of Christchurch, and these outcomes depend on the characteristics and the locality of the utilized database. That is, the model developed on the buildings in the Christchurch CBD may or may not provide reasonable predictions when applied to other earthquake-prone communities. Trends in the building characteristics (such as common structural system, occupancy type, building height, and heritage status) may differ from one city to the other. In terms of the locality of the database, the interviewees stressed that the insurance policies and the changes in the local legislation were important during their decision-making processes. Therefore, it is crucial to recognize the inherent variations among different regions and to carefully consider the limitations when applying the logistic regression model from this study to different locations. For the communities with histories of damaging earthquakes, it is recommended to conduct similar studies as presented in this thesis for better understanding of the losses due to damaging earthquakes. Communities without historic data could also benefit from various case studies with different local context factors.  With such cautions in mind, it is speculated that the logistic regression model developed here (Model DR) may be used to predict a probability of demolition of buildings in Wellington, New Zealand. Wellington is New Zealand’s second most populated city with well-known seismic risks. Compared to Christchurch, building regulations and policies, insurance, and building characteristics may be quite similar (a survey of the insurance market is needed as insurance policy may be changing after the Canterbury Earthquakes.) Damage indicator may be predicted 82   using a separate damage prediction model developed based on Wellington’s expected seismicity. Information on construction year, heritage status, number of floors, and occupancy type are relatively easy to collect. Then, Model DR could be used to predict the likelihood of demolition of buildings, and the findings could be used in assessing the seismic risk, loss, and resilience of the community. Significant portion of time and effort for this study was spent on data collection and information verification process. While having access to the two major databases (CCC and CERA) and several other sources, a number of inconsistent information was found and verifying and correcting them were difficult and time consuming, especially when structural drawings and design reports were not found. Development of an overall database compiling the building information (such as address, owner contact details, structural type, number of floors, construction year, design building code, existence of structural strengthening, design drawings and reports, etc.) would enhance the accessibility and accuracy of the building data, which is especially important during the assessments of damaged structures. In addition, when such database can be easily linked with multiple damage assessments, it would be valuable for various post-earthquake empirical studies. During the focus group session with the local engineers, it was learned that the outcomes of the Level 1 and Level 2 Rapid Assessments were likely to be very subjective depending on the inspectors. Although the inherent subjectivity of the visual assessments are recognized, it may be reduced by further developing the assessment forms, and implementing building assessment training program. For example, lack of options such as “no damage” and “damage unknown” may lead to different markings on the assessment form; some inspectors may leave the assessment item blank while others may check the “none/minor.” When the assessment forms are well-defined and the inspectors comprehend the assessment protocols, the accuracy, efficiency, and effectiveness of the rapid damage assessments will be improved, which is paramount for public safety, rapid recovery of the city, and future research in seismic engineering.  83   Another opportunity for future research is on the assessment of the residual structural capacity. The absence of proper guidelines for residual capacity assessment and ongoing aftershocks aggravating the damage resulted in great uncertainties in repairability of buildings. This may have delayed the decision-making process and the recovery of the city, and increased the building demolition rate. 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Retrieved from http://www.tandfonline.com/doi/abs/10.1080/01446193.2011.569732   90   Appendix A – Building Assessment Forms   91   A.1 - Christchurch Earthquake Assessment Form – Level 1    (Retrieved from CCC) 92   A.2 - Christchurch Earthquake Assessment Form – Level 2   93    94    (Retrieved from CCC) 95   A.3 - CERA Engineers Risk Assessment Form  96      Retrieved from CERA Database 97   A.4 - Detailed Engineering Evaluations – Summary Table  98    99    100    101    102    103    104    Retrieved from CERA Database  105  Appendix B – List of Participants     106    Participant Position/Title Company Interview Date Personal Interview Participants Owners/ Representatives Connal Townsend Chief Executive Property Council of New Zealand 14 October 2014 Darren Moses Unit Manager Christchurch City Council 29 October 2014 David Meates Chief Executive Canterbury District Health Board 24 September 2014 Gary Jarvis Group Operations Manager Heritage Hotel Management 13 October 2014 Jeff Field University Registrar University of Canterbury 26 September 2014 Josie Ogden-Schroeder Chief Executive YMCA Christchurch 25 September 2014 Mark Youthed Senior Commercial Asset Manager Knight Frank 24 September 2014 Miles Romanes Project Manager Pace Project Management 24 September 2014 Participant 1 Structural Engineer - 23 September 2014 Building Developers / Property Investors Chris Gudgeon Chief Executive Kiwi Income Property Trust 15 October 2014 Ernest Duval Trust Manager/CEO ETP/Fortis Construction 24 September 2014 Glen Boultwood Fund Manager Eureka Funds 15 October 2014 Lisle Hood Property Investor Business Building Systems 22 October 2014 Miles Middleton Property Investor Viewmount Orchards 25 September 2014 Participant 2 General Manager - 5 November 2014 Peter Rae Chairman and Managing Director Peter Rae Industries 23 September 2014 Philip Burdon Property Investor and Developer - 5 November 2014 Shaun Stockman Managing Director KPI Rothschild Property 22 September 2014  107   Participant Position/Title Company Interview Date Insurance Jimmy Higgins Executive GM – Earthquake Programme Vero NZ 15 October 2014 John Lucas Insurance Manager Insurance Council of New Zealand 17 October 2014 Murray Spicer Engineer acting for insurers MacDonald Barnett 14 October 2014 Simon Foley Distribution Manager Zurich New Zealand 15 October 2014 Storm McVay Executive Broker Crombie Lockwood 22 September 2014 Government Authorities John O'Hagan Lead Engineer–Significant Buildings Unit CERA 22 October 2014 John Snook Structural Engineer CERA 30 September 2014 Participant 3 - CERA 26 September 2014 Steve McCarthy Regulatory Services Manager CCC 26 September 2014 Focus Group Participants Structural Engineers Sean Gardiner Business Unit Leader Spiire 12 November 2014 Paul Campbell Building Structures Leader Opus International Consultants Ltd David Whittaker Technical Director BECA Craig Lewis Managing Director Lewis Bradford Consulting Engineers Dave Brunsdon Director/Lead Researcher Kestrel Group/Resilient Organizations    108  Appendix C – Additional Database Building Statistics   109     7012 3 0 136 0 0 0 111 1 0 0 087%; 11710%; 132%; 3 0%; 0 1%; 2020406080100120140Minor/None Moderate High Unknown Not assessed# of BuildingsBuilding Leaning DamageBuildings with Minor/None Soil Bulging and Liquefaction Damagevs Building Leaning Damage DemolishRepairUnknownTotal102 2 0 03 1 0 0 02 0 0 0 075%; 1515%; 3 10%; 2 0%; 0 0%; 005101520Minor/None Moderate High Unknown Not assessed# of BuildingsBuilding Leaning DamageBuildings with Moderate Soil Bulging and Liquefaction Damage vs Building Leaning Damage DemolishRepairUnknownTotal131 0 00 0 0 0 00 0 0 0 020%; 160%; 320%; 10%; 0 0%; 001234Minor/None Moderate High Unknown Not assessed# of BuildingsBuilding Leaning DamageBuildings with High Soil Bulging and Liquefaction Damage vs Leaning Damage DemolishRepairUnknownTotal 110    584 2 0 023176 0 0 0172 1 0 038%; 2942%; 3216%; 124%; 3 0%; 0 0%; 0051015202530350-1% 2-10% 11-30% 31-60% 61-99% 100%# of BuildingsBuildings with Pre-EQ %NBS Data vs Damage RatioDemolishRepairUnknownTotal583 2 0 0251770 0 0172 1 0 040%; 31 41%; 3215%; 124%; 3 0%; 0 0%; 0051015202530350-1% 2-10% 11-30% 31-60% 61-99% 100%# of BuildingsBuildings with Post-EQ %NBS Data vs Damage RatioDemolishRepairUnknownTotal8 9 2301514 6 155%; 4239%; 305%; 4-5515253545Green Yellow Red# of BuildingsBuildings with Pre-EQ %NBS Datavs PlacardDemolishRepairUnknownTotal8 9 1311714 6 155%; 4341%; 324%; 301020304050Green Yellow Red# of BuildingsBuildings with Post-EQ %NBS Datavs PlacardDemolishRepairUnknownTotal 111   15 1622119023184 0 1 01 6 2 1 0 030%; 39 31%; 4022%; 289%; 128%; 100%; 00510152025303540450-1% 2-10% 11-30% 31-60% 61-99% 100%# of Buildings3 to 5-Storey Buildings vs Damage RatioDemolishRepairUnknownTotal4221873 084 4 0 0 02 6 1 0 0 018%; 1441%; 3229%; 239%; 74%; 3 0%; 0051015202530350-1% 2-10% 11-30% 31-60% 61-99% 100%# of Buildings6 to 12-Storey Buildings vs Damage RatioDemolishRepairUnknownTotal153101120 0 0 0010 0 0 013%; 253%; 820%; 37%; 10%; 07%; 1024681012140-1% 2-10% 11-30% 31-60% 61-99% 100%# of Buildings13 to 22-Storey Buildings vs Damage RatioDemolishRepairUnknownTotal 112   153622321223 5 239%; 5041%; 5320%; 260102030405060Green Yellow Red# of Buildings3 to 5-Storey Buildings vs PlacardDemolishRepairUnknownTotal93114106 04 5 029%; 2353%; 4218%; 14051015202530354045Green Yellow Red# of Buildings6 to 12-Storey Buildings vs PlacardDemolishRepairUnknownTotal35312001027%; 453%; 820%; 3024681012141618Green Yellow Red# of Buildings13 to 22-Storey Buildings vs PlacardDemolishRepairUnknownTotal 113    17313718110131030 0 02101 1 0 021%; 3233%; 5127%; 4112%; 197%; 110%; 001020304050600-1% 2-10% 11-30% 31-60% 61-99% 100%# of BuildingsCommercial Buildings vs Damage RatioDemolishRepairUnknownTotal1241 0 0721 0 1 01 1 1 0 0 041%; 923%; 527%; 65%; 1 5%; 1 0%; 00123456789100-1% 2-10% 11-30% 31-60% 61-99% 100%# of BuildingsResidential Buildings vs Damage RatioDemolishRepairUnknownTotal250 0 1 142 20 0 0020 0 0 032%; 647%; 911%; 20%; 05%; 1 5%; 10123456789100-1% 2-10% 11-30% 31-60% 61-99% 100%# of BuildingsHotel Buildings vs Damage RatioDemolishRepairUnknownTotal 114   *All buildings not classified as commercial, residential, or hotel   052 0 0 08102 0 0 00 0 1 0 0 029%; 854%; 1518%; 50%; 0 0%; 0 0%; 002468101214160-1% 2-10% 11-30% 31-60% 61-99% 100%# of BuildingsOther Buildings* vs Damage RatioDemolishRepairUnknownTotal196134151105 7 225%; 3951%; 7923%; 360102030405060708090Green Yellow Red# of BuildingsCommercial Buildings vs PlacardDemolishRepairUnknownTotal15282 11 2 045%; 1041%; 914%; 3024681012Green Yellow Red# of BuildingsResidential Buildings vs PlacardDemolishRepairUnknownTotal 115   *All buildings not classified as commercial, residential, or hotel  4324 401 1 047%; 942%; 811%; 2012345678910Green Yellow Red# of BuildingsHotel Buildings vs PlacardDemolishRepairUnknownTotal3 3 1163 10 1 068%; 1925%; 77%; 202468101214161820Green Yellow Red# of BuildingsOther Buildings* vs PlacardDemolishRepairUnknownTotal 116     0265404 4 40 0 002310 011%; 423%; 837%; 1317%; 611%; 40%; 0024681012140-1% 2-10% 11-30% 31-60% 61-99% 100%# of BuildingsHeritage Buildings vs Damage RatioDemolishRepairUnknownTotal2041371481282040 1 03 11 0 0 0 027%; 5138%; 7222%; 417%; 145%; 91%; 1010203040506070800-1% 2-10% 11-30% 31-60% 61-99% 100%# of BuildingsNonheritage Buildings vs Damage RatioDemolishRepairUnknownTotal071074105120%; 746%; 1634%; 12024681012141618Green Yellow Red# of BuildingsHeritage Buildings vs PlacardDemolishRepairUnknownTotal276529361617 6137%; 7046%; 8716%; 310102030405060708090100Green Yellow Red# of BuildingsNonheritage Buildings vs PlacardDemolishRepairUnknownTotal 117    9172411508 820 0 0130 0 0 020%; 1832%; 2830%; 2613%; 116%; 50%; 00510152025300-1% 2-10% 11-30% 31-60% 61-99% 100%# of BuildingsMoment Frame Buildings vs Damage RatioDemolishRepairUnknownTotal1018115 50211350 1 0180 1 0 032%; 3239%; 3916%; 166%; 6 6%; 60%; 00510152025303540450-1% 2-10% 11-30% 31-60% 61-99% 100%# of BuildingsShear Wall Buildings vs Damage RatioDemolishRepairUnknownTotal10332313502 1 128%; 2544%; 3927%; 24051015202530354045Green Yellow Red# of BuildingsMoment Frame Buildings vs PlacardDemolishRepairUnknownTotal122611251414 5141%; 4145%; 4513%; 1305101520253035404550Green Yellow Red# of BuildingsShear Wall Buildings vs PlacardDemolishRepairUnknownTotal 118  75176 604610 0 025310 021%; 1325%; 1633%; 2111%; 7 10%; 60%; 005101520250-1% 2-10% 11-30% 31-60% 61-99% 100%# of BuildingsPre 1965 Buildings vs Damage RatioDemolishRepairUnknownTotal59253 05 51 0 0 01 1 0 0 0 030%; 1141%; 158%; 314%; 58%; 3 0%; 002468101214160-1% 2-10% 11-30% 31-60% 61-99% 100%# of Buildings1965-1975 Buildings vs Damage RatioDemolishRepairUnknownTotal523165 3 1117 2 0 0 00 4 0 0 0 021%; 1644%; 3423%; 186%; 54%; 3 1%; 105101520253035400-1% 2-10% 11-30% 31-60% 61-99% 100%# of Buildings1976-1991 Buildings vs Damage RatioDemolishRepairUnknownTotal 119    2472 0 0762 0 0 00 2 0 0 0 028%; 938%; 1228%; 96%; 2 0%; 0 0%; 0024681012140-1% 2-10% 11-30% 31-60% 61-99% 100%# of Buildings1992-2003 Buildings vs Damage RatioDemolishRepairUnknownTotal121 1 0 05020 1 00 1 0 0 0 043%; 621%; 3 21%; 37%; 1 7%; 1 0%; 0012345670-1% 2-10% 11-30% 31-60% 61-99% 100%# of BuildingsPost 2003 Buildings vs Damage RatioDemolishRepairUnknownTotal 120   419 1864 14 5 222%; 1444%; 2833%; 21051015202530Green Yellow Red# of BuildingsPre 1965 Buildings vs PlacardDemolishRepairUnknownTotal711692 00 2 043%; 1641%; 1516%; 6024681012141618Green Yellow Red# of Buildings1965-1975 Buildings vs PlacardDemolishRepairUnknownTotal10358155 02 2 035%; 2755%; 4210%; 8051015202530354045Green Yellow Red# of Buildings1976-1991 Buildings vs PlacardDemolishRepairUnknownTotal 121     3579601 1 041%; 1338%; 1222%; 702468101214Green Yellow Red# of Buildings1992-2003 Buildings vs PlacardDemolishRepairUnknownTotal3204310 1 050%; 743%; 67%; 1012345678Green Yellow Red# of BuildingsPost 2003 Buildings vs PlacardDemolishRepairUnknownTotal 122   93437168 104 3962 21 282 0 19%; 1425%; 3935%; 5416%; 246%; 10 8%; 130102030405060<1000 1000-2000 2000-4000 4000-7000 7000-10000 > 10000# of BuildingsCommercial Buildings vs Total Floor AreaDemolishRepairUnknownTotal13121 03 3 320 00 030 0 018%; 427%; 632%; 718%; 45%; 1 0%; 0012345678<1000 1000-2000 2000-4000 4000-7000 7000-10000 > 10000# of BuildingsResidential Buildings vs Total Floor AreaDemolishRepairUnknownTotal0 0 0 14 4121 02 20 0 0 0 1 15%; 111%; 25%; 1 5%; 137%; 7 37%; 7012345678<1000 1000-2000 2000-4000 4000-7000 7000-10000 > 10000# of BuildingsHotel Buildings vs Total Floor AreaDemolishRepairUnknownTotal

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