Vulnerability Assessment of Christchurch Buildings in Canterbury Earthquakes

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2 Vulnerability Assessment of Christchurch Buildings in Canterbury Earthquakes S. R. Uma R. P. Dhakal M. Nayyerloo GNS Science Report 2013/20 May 2013

3 BIBLIOGRAPHIC REFERENCE Uma, S. R.; Dhakal, R. P.; Nayyerloo, M Vulnerability Assessment of Christchurch Buildings in Canterbury Earthquakes, GNS Science Report 2013/ p. S. R. Uma, GNS Science, PO Box 30368, Lower Hutt 5040, New Zealand R. P. Dhakal, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand M. Nayyerloo, GNS Science, PO Box 30368, Lower Hutt 5040, New Zealand Institute of Geological and Nuclear Sciences Limited, 2013 ISSN ISBN

4 CONTENTS ABSTRACT... IV KEYWORDS... IV 1.0 INTRODUCTION GROUND MOTIONS BUILDING INVENTORY ASSESSMENT DATABASE CODE RECOMMENDATIONS PRELIMINARY OBSERVATIONS ON THE PERFORMANCE OF CBD BUILDINGS DISPLACEMENT-BASED APPROACH FOR VULNERABILITY ASSESSMENT OF BUILDINGS IN THE CBD SIMULATION OF BUILDING CHARACTERISTICS DEFINITION OF LIMIT STATES DEMAND AT INELASTIC LIMIT STATES PROBABILITY OF FAILURE COMPARISON OF ESTIMATED DAMAGE PROBABILITIES WITH OBSERVED DAMAGE STATISTICS CONCLUSIONS ACKNOWLEDGMENTS REFERENCES GNS Science Report 2013/20 i

5 FIGURES Figure 1 Tectonic setting of New Zealand (Courtesy: Clark, K. GNS) Figure 2 Details of main-shock and aftershocks since 4th Sept 2010 in Canterbury region (Courtesy: GeoNet, Langridge, R. GNS) Figure 3 Peak ground acceleration plot at various strong motion stations from the two events; the inset shows the stations near Central Business District (CBD) area. (Courtesy: Anna Kaiser, & Jim Cousins, GNS) Figure 4 Ground displacement polar plots: (i) September (left); (ii) February (right) events (Courtesy: Jim Cousins, GNS) Figure 5 Acceleration records and Fourier amplitude spectra at CCCC station from the September (for N-S component) and February (for E-W component) events Figure 6 Spectral demands from the September event Figure 7 Spectral demands from the February event Figure 8 Acceleration-displacement response spectra for median of records from 4 stations Figure 9 Building stock classifications with respect to construction material in Christchurch Figure 10 Distribution of building stock in the CBD Figure 11 Distribution of different colour-tagged buildings in CBD (See Table 2 for the definitions of different colours) Figure 12 Estimation of initial period of buildings Figure 13 Idealised capacity curve and threshold limit states Figure 14 Idealised bilinear curve with demand curves from: (i) Actual elastic spectrum as geometric mean of 4 records from February event (black solid line); (ii) respective inelastic spectrum reduced for ductility=2 (black dashed line); (iii) MCE design spectrum (grey solid line); (iv) respective inelastic spectrum reduced for ductility =2 (grey dashed line) Figure 15 Damage probabilities for post-1976 medium-rise RC frame building under DBE, MCE and Actual scenarios Figure 16 Probability of exceedence for reinforced concrete frames: post Figure 17 Probability of being in different damage states for reinforced concrete frames: post Figure 18 Probability of exceedence for reinforced concrete frames: pre Figure 19 Probability of being in different damage states for reinforced concrete frames: pre Figure 20 Mapping of damage states (DS) to tagging colours GNS Science Report 2013/20 ii

6 TABLES Table 1 Peak ground motion parameters from the September and February events Table 2 Definition of different building colour tagging categories Table 3 Proportion of colour tags in different building stock Table 4 Statistics of colour tagging for all the buildings in the CBD as per CCC database Dec Table 5 Structural parameters for RC moment resisting frame structures (pre and post 1976) Table 6 Initial properties for building groups Table 7 Median threshold drift ratios and dispersions at the effective height of for RC frame buildings Table 8 Estimated probabilities of damage states for RC moment resisting frame buildings Table 9 Estimated proportions of low rise RC buildings and observed proportions with reference to colour tags Table 10 Estimated proportions of medium rise RC buildings and observed proportions with reference to colour tags EQUATIONS Equation Equation 2a Equation 2b Equation Equation 4a Equation 4b Equation Equation Equation Equation Equation Equation Equation Equation GNS Science Report 2013/20 iii

7 ABSTRACT On 22 nd February, 2011, Christchurch City experienced a direct hit from a destructive magnitude (Mw) 6.2 aftershock following the main event of magnitude 7.1 on the 4 th September, Ground motions from the February event far exceeded the seismic design spectrum corresponding to 500 year return period which is used to design normal structures in New Zealand. This report provides a review of ground motion intensities from the September and the February events in relation to the intensities used in building design which helps to put the observed performance of the building stock into context. The report also assesses vulnerability of building stock in the Christchurch region through a probabilistic displacement-based approach under the impact of the February event to provide probabilistic estimates of damage distribution. The numerical study shows that the damage estimates are high for the February event compared to the code-based demands and expectedly more pronounced for older reinforced concrete frames. Lessons from the aftermath of the Christchurch earthquake are highlighted in terms of reflections on design practices, impact of economics on building damage status and possibly a need for fresh look at the design philosophy in New Zealand. KEYWORDS Vulnerability, displacement-based approach, reinforced concrete buildings, regional risk assessment GNS Science Report 2013/20 iv

8 1.0 INTRODUCTION The tectonic setting of New Zealand includes the boundary of the Australian and Pacific plates as shown in Figure 1, and a major portion of the country is seismically active. The seismic hazard model for New Zealand comprises many known active faults, and unidentified faults represented in terms of distributed seismicity. On 4 th September 2010, Christchurch (the second largest city of New Zealand, located within Canterbury plains) was shaken by a magnitude (Mw) 7.1 earthquake originating from the rupture of a previously unknown fault (since identified as the Greendale Fault). The epicentre was located near Darfield, about 40 km west of the main city. Among the more than one thousand aftershocks that followed; some were significant; none more so than the ones that occurred on 22 nd February, 2011 (Mw 6.2) and 13 th June, 2011 (Mw 6.0). The locations of the epicentres and the sequence of aftershocks (as of 4 th June, 2012) are shown in Figure 2. The surface fault rupture was located near Greendale for the Darfield event, whereas the other two major aftershocks featured only sub-surface fault ruptures. The epicentre of the 22 nd February 2011 aftershock was located near Lyttelton at about 10 km to the south-east of the central city and that of the 13 th June earthquake was further to the east. The impact of the June event was small compared to the other two events. Figure 1 Tectonic setting of New Zealand (Courtesy: Clark, K. GNS). GNS Science Report 2013/20 5

9 Figure 2 Details of main-shock and aftershocks since 4th Sept 2010 in Canterbury region (Courtesy: GeoNet, Langridge, R. GNS). The September event inflicted minor to moderate levels of structural damage depending on the location, shaking intensity and building typology. A few cases of partial collapse (mainly of unreinforced masonry buildings) were also observed. Damage to non-structural components and contents was widespread in many buildings. Disruption to business in many commercial buildings was mainly attributed to non-structural damage. The impact of the February event in Christchurch on the built-environment was huge and destructive. Depending on the location and typology of the building, the extent of damage varied. The impact was more clearly pronounced within the central business district (CBD), where a variety of building typologies was subjected to severe ground shaking intensity and liquefaction. Special reports on preliminary observations and understanding of ground motion characteristics, structural and geotechnical aspects from the September and February events have been published by the NZSEE (NZSEE, 2010 and 2011) and NZJGG (Kaiser et al., 2012). As of July 2012, access to some parts of the CBD is still restricted due to the on-going detailed assessment of damaged buildings and demolition process. In this paper, brief summary of the intensity of ground motions and observed performance of buildings in Christchurch city, particularly within the CBD, in the September and February earthquakes is presented. A note on the building inventory within Christchurch and the history of development of seismic design codes is also provided to provide an indication of the building vulnerability. Furthermore, an attempt has been made, using a displacementbased building vulnerability assessment approach (Uma and Bradley, 2010), to obtain probabilistic estimates of damage distributions with typical building classes under spectral demands from the February event and also under spectral demands specified in the NZ standards for seismic actions; NZS :2004 for 500-year return period (referred as design-basis earthquake, DBE, hereafter) and 2500-year return period (referred as maximum considered earthquake, MCE, hereafter). As final remarks, lessons from the aftermath of the Canterbury earthquakes are highlighted with respect to design practices and future research needs. GNS Science Report 2013/20 6

10 2.0 GROUND MOTIONS In New Zealand, GeoNet ( was conceived to provide national coverage for hazard detection, emergency response and data collection. Several components of the GeoNet system contribute to the collection and utilisation of strong ground motion data. These include both national scale and regional scale strong motion networks, and a building response monitoring programme (Cousins and McVerry, 2009; Uma, et al., 2011), which collectively resulted in a rich set of ground motion records from within Canterbury Region. Figure 3 Peak ground acceleration plot at various strong motion stations from the two events; the inset shows the stations near Central Business District (CBD) area. (Courtesy: Anna Kaiser, & Jim Cousins, GNS). Processed records are available at ftp.geonet.org.nz/strong/processed/proc. Figure 3 shows the maximum horizontal and vertical accelerations recorded in both the September and February events in and around Christchurch. There are four strong motion stations close to the CBD (i.e. CBGS Christchurch Botanical Gardens, REHS Christchurch Resthaven, CHHC - Christchurch Hospital, and CCCC Christchurch Cathedral College). These stations are in site class D ( deep or soft soil as per NZS :2004). Note that the strong motion sensors placed on the ground are usually oriented arbitrarily (e.g. at CCCC the components are in N26W and N64E orientation). The ground motions within the central city and to the east of the city were much stronger in February event than in the September event. Interestingly, most of the streets in the CBD are aligned in North-South (N-S) and East-West (E-W) directions which mean that the principal directions of the majority of the buildings are aligned N-S and E-W. Figure 4 shows typical two-dimensional plots of ground displacements in the September and February events at the CCCC station. It is obvious that in the September event, the shaking was predominantly aligned in the N-S direction. On the other hand, in the February event the ground seemed to have moved by similar amounts in both N-S and E-W directions. In comparison to the September ground motion, the February motion was much stronger in the E-W direction but a lot weaker in the N-S direction. In this study, the projected components in E-W and N-S directions are considered to better represent the actual demands on buildings in their principal directions than in the recorded orientations. GNS Science Report 2013/20 7

11 Figure 4 Ground displacement polar plots: (i) September (left); (ii) February (right) events (Courtesy: Jim Cousins, GNS). Figure 5 shows the acceleration records from the CCCC station from the September and the February events. For each event, the predominant component of the record is plotted. It is clear that the acceleration level in the September record is significantly less than that in the February record. However, the duration of strong motion is longer in the September record than in the February record. FFT plots for the respective records are shown in Figure 5 (c) and (d). These plots can be scrutinized to generate useful information related to the characteristics and damage potential of these ground motions. In both plots, there is a peak around Hz (or sec period), which raises a possibility that this may be the natural frequency of the local site/soil; thereby causing resonance and amplifying the energy content at this frequency. It can also be noticed that the September record has greater energy (compared to that of the February record) at frequencies less than 0.5 Hz (or periods longer than 2 sec), which is in line with the fact that longer period structures were excited more than expected in September. Similarly the plots also indicate that the February record has substantially more energy content in the Hz range (this is where the peak falls), which is in line with the fact that unlike in September, even some moderate-height structures (with period in the range 1-2 sec) were severely damaged in the February event. GNS Science Report 2013/20 8

12 Acceleration, g (a) CCCC_NS_Sept Liquefaction -0.6 Time, s Acceleration, g (b) CCCC_EW_Feb Liquefaction Time, s Fourier amplitude spectra (mm/s) (c) CCCC_NS_Sept Frequency (Hz) Figure 5 Acceleration records and Fourier amplitude spectra at CCCC station from the September (for N-S component) and February (for E-W component) events. The maximum (peak) ground motion parameters recorded at the four Central City stations from both events are listed in Table 1. The September event generated lower peak ground accelerations and larger peak ground displacements. The February event generated very high accelerations. Note that in the February event, the ratio of vertical acceleration to horizontal acceleration ranges between 0.5 (at CBGS) to 1.8 (at CCCC) (d) CCCC_EW_Feb Frequency (Hz) Table 1 Peak ground motion parameters from the September and February events. Peak ground acceleration, g Peak ground velocity, m/s Peak ground displacement, m Horizontal Vertical Horizontal Vertical Horiz_Max Vertical September 4th, 2010 event (N-S component) CBGS CCCC CHHC REHS February 22nd, 2011 event (E_W component) CBGS CCCC CHHC REHS GNS Science Report 2013/20 9

13 Figure 6 (a) Acceleration response spectra Spectral demands from the September event. (b) Displacement response spectra Figure 6 shows elastic acceleration response spectra and elastic displacement spectra for the four records and their geometric means (G.M) for the September event. For comparison, elastic design spectra (for site class D) recommended by NZS :2004 for DBE (500- year return period) and MCE (2500-year return period) are also plotted. It can be seen that the geometric mean of the 4 records matches the DBE design spectrum for the acceleration spectra between 0.5s to 1.5s, falls below the design spectrum in very short periods up to about 0.5s, and exceeds the design spectrum in longer periods beyond 1.5s. Note that records from CCCC and CHHC show a peak spectral acceleration of about 0.6g closer to 2.5s and the corresponding spectral displacement is about 1m, which is considerably higher than even the MCE-induced displacements. Figure 7 plots the acceleration and displacement response spectra of the records obtained from the same four stations in the February event; the geometric mean is also shown in the plot together with the design spectra corresponding to 500 and 2500 years return periods. It is clear from the figure that the February event generated stronger acceleration demands compared to the DBE elastic spectrum for all periods. Also, the spectra exceeded MCE design spectrum at periods between 0.75s and 1.75s which is in contrast to the September spectra. February records were also found to include a local peak just beyond 3s with a peak spectral displacement of about 1m. Figure 7 (a) Acceleration response spectra Spectral demands from the February event. (b) Displacement response spectra GNS Science Report 2013/20 10

14 Next, the geometric means of the four records response spectra for the September and February events are plotted in ADRS (acceleration-displacement-response-spectra) format in Figure 8. Also the DBE design spectrum from NZS is included in the same figure for comparison. It is clear that the spectral quantities exceeded the DBE design spectrum at all periods in the February event. Large displacements of about 1 m are evident in both events; (i) in the September event it was realised for periods about 10s; and (ii) in the February event, it was observed closer to 3s period. Only a few buildings with this period range existed in Christchurch. However, at about 2.25s, the demands sharply reduced for February record; and for structures with natural period between 2 and 2.5s, the September earthquake appears to be more demanding than the February event. Figure 8 Acceleration-displacement response spectra for median of records from 4 stations. GNS Science Report 2013/20 11

15 3.0 BUILDING INVENTORY ASSESSMENT DATABASE In regional risk assessments, good knowledge of the exposed inventory (or asset database) of a region will provide better understanding of the risk involved in that region. As a part of asset model development for Riskscape (King and Bell, 2009), a building inventory database has been prepared for Christchurch (totalling 160,000 buildings). As shown in Figure 9, about 64% buildings are made of timber, 30% buildings are of reinforced concrete (RC), 3% are of masonry and the remaining 3% of steel and other materials. Based on use/occupancy, the building inventory was divided into three main categories; namely residential, commercial and industrial. Residential buildings are mostly low-rise timber buildings, accommodating single-families, and apartment (timber or reinforced concrete) buildings with multiple-families. Low-rise commercial buildings used as offices, retail shops, public services, and hospitals are generally constructed in timber, masonry and RC. High-rise commercial buildings are generally RC structures and only a few are made of steel. The structural forms of the RC buildings are typically moment resisting frame in one direction and shear wall in the other direction or with core shear walls taking lateral loads and gravity frames on the exterior. Industrial buildings featuring factories and warehouses are typically low-rise with steel moment resisting or portal frame structural forms in one direction and cross bracing in the other direction. 1% 2% 3% 30% 64% Timber Reinforced Concrete Industrial Steel Brick /Conc Masonry Figure 9 Building stock classifications with respect to construction material in Christchurch. GNS Science Report 2013/20 12

16 4.0 CODE RECOMMENDATIONS Understanding the history of seismic code development is important to appreciate buildings characteristics and their possible responses under seismic actions. After several major earthquakes in New Zealand, as a first attempt, in 193, a building draft code was published with recommendations to improve the standards of building construction in relation to earthquake resistance. Significant changes were made to the design seismic forces in 1939, 1955, 1965, 1976, 1984, 1992 and A summary of the evolution of seismic zoning, soil (site) classification, design seismic coefficient, design approach and ductility requirements follows: In the 1939 and 1955 versions of the seismic design code, a uniform level of seismicity throughout the country was adopted. The 1965 version (NZS 1900:1965) introduced a map with three zones representing high seismic intensity (Zone A), moderate seismic intensity (Zone B) and low seismic intensity (Zone C) but with no distinction on site/soil classes. This zoning map was retained in the two subsequent revisions; i.e. in 1976 (NZS 4203:1976) and 1984 (NZS 4203:1984). In the 1992 revision (NZS 4203:1992), a contour map with continuously varying seismic intensity was introduced and the regional seismicity was represented with the so-called zone factor. In the latest revision (i.e. existing version) of the NZ seismic actions standard (NZS 1170:2004), the regional seismicity is developed based on a different hazard model and a hazard factor is used to represent the seismicity. The effect of soil foundations on earthquake performance was explicitly considered only from Until 1992, only two types of soils were represented: (i) rigid and intermediate subsoils; and (ii) flexible subsoils. In the 1992 revision, three site classes were included to represent: (i) rock and stiff soil; (ii) intermediate soil; and (iii) flexible soil. In the current version of the standard, four site classes are available to represent: (i) rock and weak rock (A&B); (ii) shallow soil (C); (iii) Deep soil (D); and (iv) very soft soil (E). Looking at the level of design base shear over the years, the 1939 code suggested only 8% of the building weight as minimum base shear and it was distributed equally over the height of the building. The 1955 version calculated the lateral seismic force at each story as a product of the story weight and a triangularly distributed seismic coefficient which varies between zero at the base and 0.12 at the top story. In the 1965 version, the design seismic coefficient was expressed in terms of vibration period of the structure, and the total base shear was distributed in proportion to the product of the story mass and the height of the story from the base. The design seismic coefficient was gradually refined over time by including the details of structural form, material factor, seismic risk, return period, and a nearfault factor. In the 1976 and 1984 codes, the design seismic coefficients were very similar to the 1965 code, but ultimate strength design was recommended instead of the working stress method used in the 1965 version. The codes since 1992 are based on limit state design principles considering two levels, serviceability limit state (SLS) to address operational requirements and ultimate limit state (ULS) to address life-safety requirements. Ductility is the essential ability of a structure to deform in the inelastic range without brittle failure. The current codes use capacity design principles to ensure strength and ductility at ULS. The detailing practice suggested in the existing material codes are expected to provide sufficient ductility in the critical elements of a structure so that immediate and imminent collapse is prevented even beyond the ULS. However, buildings constructed prior to 1976 generally lack specific ductile detailing. Some buildings designed prior to the introduction of the 1976 standard did incorporate ductile detailing as the principles were becoming GNS Science Report 2013/20 13

17 established in the late 1960s and early 1970 s, but this was not the norm. The 1976 and 1984 codes included a structural form factor, S to reflect ductile performance, but the material codes (until 1992) were not equipped with detailing guidelines to achieve ductility in the structure. Hence, it can be interpreted that buildings built between 1976 and 1992 could potentially lack ductile detailing. It can be considered that the majority of structures built before 1976 can achieve only limited ductility, say a maximum displacement ductility of 2 and the post 1976 buildings, particularly with 1992 detailing recommendations, are expected to demonstrate higher ductility. GNS Science Report 2013/20 14

18 5.0 PRELIMINARY OBSERVATIONS ON THE PERFORMANCE OF CBD BUILDINGS In Christchurch, there were more old buildings which predate seismic regulations (i.e. built in early 20 th century) compared to modern buildings built in the last two decades. Observed damage to the building stock varied widely depending on the shaking intensity experienced at the building location in addition to local soil conditions (e.g. liquefaction potential) and respective building characteristics. In the CBD, a wide range of building typologies including old URM buildings, timber buildings, RC buildings, light steel frame industrial buildings, and a handful number of multi-storey steel buildings existed. The majority of building stock outside the central city consists of residential buildings with timber and masonry as construction material. In the September earthquake, as evident from Figure 6, the shaking intensity level in the CBD was close to what was until then thought to be the 500-year return period shaking level for the region (i.e. the design level shaking intensity as per the pre-earthquake NZ standard NZS :2004). Note that after the September earthquake, a 27.5% increase has been enforced in the intensity of the 500-year (DBE) return period event. It could be argued that older buildings that did not conform to the current code requirements were subjected to a significantly higher intensity of shaking than they were designed for; and hence were prone to damage. A report on preliminary observations on the performance of older and modern RC buildings within the CBD in the September earthquake has been published (Kam et al., 2010). Leaving the liquefaction-induced damage aside, generally the most severely damaged buildings were unreinforced masonry (URM) buildings, which experienced partial to total collapse of different components. Older RC buildings exhibited minor to moderate damage such as cracking, plastic hinges, and joint shear failure. Modern buildings reportedly behaved better apart from experiencing considerable damage to non-structural elements and contents. However, cracking in precast flooring systems due to beam elongation, damage to staircase elements and damage in gravity load elements due to inadequate detailing to cater for the displacement demands were also observed in some modern buildings. It is worth mentioning that there was a clear North-South directionality effect in the observed damage. Even though the February event was moderate in terms of magnitude, its effects on the building stock within the CBD were more devastating because of its proximity and shallowness. A number of failure/damage patterns noticed during the September event became more distinct after the February event. In February, an E-W directionality effect was evident in the observed damage. A high level of vertical acceleration in combination with horizontal acceleration and soil liquefaction and lateral spreading exacerbated the damage to the building stock. Given the ground motion intensities were significantly higher than what even modern buildings are designed for, most old buildings were expected to collapse and modern buildings were expected to be irreparably damaged in the February event. As expected, most old buildings (URM and RC) suffered severe irreparable damage, but the damage to the majority of modern buildings (except for those affected by soil liquefaction) was technically repairable. Modern multi-storey buildings in general did well in terms of lifesafety and collapse prevention ; with the exception of two RC buildings. Comparing how the buildings performed against what was expected from them in that level of ground motion, the overall performance of the building stock can be claimed to have exceeded the expectation. The reason that only a few buildings collapsed, even though the imposed demand greatly exceeded the design capacity for many, could possibly be attributed to the short duration of the strong shaking. The unprecedented level of vertical accelerations imparted heavy GNS Science Report 2013/20 15

19 instantaneous axial force in columns; thereby dwarfing the confinement provided by the transverse reinforcement and resulting in explosive compression failure of columns in several RC frame buildings. Christchurch City Council [CCC] undertook Building Safety Evaluation tasks to place colour tags in buildings as per NZSEE guidelines (NZSEE, 2009) following the main event in September 2010 and again after the February 2011 event. The inspection included initial Level 1 Rapid Assessments and the more detailed Level 2 Assessments. A Level 2 Assessment is required on all critical facility buildings, large (typically multi-storey) buildings, and any other buildings where Level 1 Rapid Assessment identifies the need for further and more detailed inspection. A Level 1 Rapid Assessment results in a building being tagged Green, Yellow or Red, whereas Level 2 Assessments include further classifications into the six grades. The different colour tags and their implied meanings are listed in Table 2: Table 2 Definition of different building colour tagging categories. Level 1 rapid assessment Green (G) Yellow (Y) Red (R) Inspected; Apparently OK; may need further inspection or repairs Restricted use; Safety concerns; parts may be off limits; entry only for short periods of time for Unsafe; Clearly unsafe do not enter. Further assessments or evaluation required before any use retrieving important goods Level 2 rapid assessment Green 1 (G1) Green 2 (G2) Yellow 1 (Y1) Yellow 2 (Y2) Red 1 (R1) Red 2 (R2) Occupiable no immediate further investigation required Occupiable repairs required Short term entry only No entry to parts until secured or demolished Significant damage repairs strengthening possible Severe damage demolition likely Some buildings were red tagged despite having suffered little building damage because of threat from adjacent damaged buildings (Cole et al., 2011) and ground liquefaction. These were categorised as R3. A sample of buildings evaluated within the central city was analysed to obtain the statistics of building material types and the respective proportion of colour tags. Figure 10 shows the distribution of dominant building materials used in the 2036 buildings within the CBD. The tagging information was obtained from Christchurch City Council and has been processed for this exercise. The data is valid as released in December, It is clear that the URM building typology constitutes the predominant proportion of the building stock within the CBD followed by timber and reinforced concrete. GNS Science Report 2013/20 16

20 Figure 10 Table 3 Distribution of building stock in the CBD. Proportion of colour tags in different building stock. Building class Percentage in the total stock Green (%) Yellow (%) Red (%) R3 (risk from adjacent buildings) (%) Not recorded (%) (1) (2) (3) (4) (5) (6) Timber Concrete frames (including masonry infill) Unreinforced masonry Reinforced masonry Table 3 shows the percentage of four most predominant building types (i.e. URM, Timber, Concrete frame and Reinforced masonry) as in col (1). The proportions of tags related to the damage categories assigned for each building type are listed in col (2 to 6). The values in col (2 to 6) will add up to 100. The extent of damage within the CBD was very extensive mainly because of the high proportion of URM buildings; 62% of them were red-tagged. Among other building types, between 20 and 30% were red-tagged. Many of these buildings were demolished not only because they were irreparable; but also based on financial viability of the available repair options. The proportions of different damage categories for the whole building stock (totalling 2036) are also listed in Table 4. They include outcomes of both Level 1 and Level 2 assessments. Proportions of building that fell under R3 category (shown in red circle with black core) and that were not recorded (shown in black colour) are also plotted as in Figure 11. GNS Science Report 2013/20 17

21 Figure 11 colours). Distribution of different colour-tagged buildings in CBD (See Table 2 for the definitions of different Table 4 Statistics of colour tagging for all the buildings in the CBD as per CCC database Dec All buildings in CBD by tagging colour Identified as in Figure 11 Number of buildings Percentage Red Red circle Yellow Yellow circle Green Green circle R3 (At risk from ground failure or adjacent buildings) Red circle with black core 68 3 Not recorded Black circle 31 2 Total GNS Science Report 2013/20 18

22 6.0 DISPLACEMENT-BASED APPROACH FOR VULNERABILITY ASSESSMENT OF BUILDINGS IN THE CBD In this study, an attempt has been made to carry out regional vulnerability assessments for selected building classes which are included in the building stock in the CBD area. Regional assessment methods need to consider variability associated with building characteristics to capture their respective performance levels and uncertainties in ground motion parameters. A probabilistic displacement-based framework is adopted to determine the probabilities of failure of being in various damage-states for different building classes (Uma and Bradley, 2010). This approach follows the framework developed by Crowley et al. (2004). The approach is simple and practical to deal with variability in building parameters and uncertainty in ground motion demands. It is imperative that the regional assessment tools should carefully adopt building models representing the true characteristics of the local building stock and do not rely on the models developed for any other region or country (Uma et al., 2011). The key features of the displacement-based approach adopted in this study are explained below. The methodology considers a typical building representing a building class as an equivalent single degree of freedom (SDOF) oscillator. The steps involved are: (i) establishing the properties of the SDOF model through Monte Carlo approach; (ii) specification of damage limit states in terms of building displacement (or drift ratio at equivalent height of SDOF) considering uncertainties; (iii) determination of effective period corresponding to the predetermined damage limit states; (iv) obtaining spectral displacement demand at the effective period from a given earthquake scenario; and (v) estimation of damage state probability by comparing the displacement realised by the building and the earthquake demand considering various sources of uncertainties related to building parameters and ground motion parameters. As an illustrative study, the above procedure is adopted to estimate probabilistic damage distribution of RC moment resisting frames built post and pre 1976 with different heights: (a) low-rise (LR) frames of up to 3 storeys; (b) medium-rise (MR) frames of between 4 and 7 storeys; and (c) high-rise (HR) frames of 8 storeys or higher. Note that the ductility based capacity design principles were implemented in the NZ design codes for the first time in Hence, the buildings designed before and after 1976 are expected to have significantly different seismic performance; especially in their ability to meet the collapse prevention and life safety requirements. The probability of reaching various damage states is estimated for the February event demand. For comparison, the DBE and MCE demands for CBD region are also considered. The predictions are compared with building assessment statistics in terms of colour tagged placards obtained from the Christchurch City Council database. Note that the statistics was updated on December 2011 and would represent the finalised status of tagging of buildings after the September 2010, February 2011 and June 2011 events. Nevertheless, the authors believe that only the February event would be severe enough to damage most buildings to the current level, and the building damage database should have undergone little change during the minor aftershocks after the February event. Hence, comparing the predicted damage states due to the February event only with the current damage statistics should not induce a noticeable bias. Equivalences are drawn between the damage states defined within this study and the building status represented by the colour tagging. GNS Science Report 2013/20 19

23 7.0 SIMULATION OF BUILDING CHARACTERISTICS Given a building class, a Monte-Carlo procedure is adopted to generate a large set of values for the yield displacement and the natural period of the class of building using randomly generated values of geometrical and material property variables of every possible building within that class. A typical range of values assigned for concrete moment resisting frames is given in Table 5. The values listed in the Table 5 are obtained based on some real buildings in New Zealand. Note that the variables listed in Table 5 are required parameters to represent both post and pre 1976 buildings except the ones specifically mentioned. Details for other building classes can be found elsewhere (Uma and Bradley, 2010). The effective height coefficient is the ratio of the height of the effective mass of the single degree of freedom model to the total height of the actual building. U[ ] refers to uniform distribution and N[ ] refers to normal distribution. Table 5 Structural parameters for RC moment resisting frame structures (pre and post 1976). Structural Parameters Low-rise Medium-rise High-rise Number of storeys, U [1,3] U [4,7] U [8,16] S h Storey height (m),, or column height (m), h c U [3.4, 3.8] U [3.4, 3.8] U [3.4, 3.8] l b Beam length (m), U [4.0, 6.0] U [4.0, 6.0] U [4.0, 6.0] h b N s Beam depth (m), U [0.6, 0.8] U [0.6, 0.8] U [0.6, 0.8] Column depth (m) (Pre 1976), f y d c U [0.4,0.5] U[0.45,0.55] U [0.55, 0.65] Steel strength (MPa), (Post 1976) N [350,35] N [350,35] N [350,35] f y Steel strength (MPa), (Pre 1976) N [325,35] N [325,35] N [325,35] Effective height coefficient, efh *(Ns-4) *(Ns-4) Two initial parameters such as yield displacement Dy at effective height and initial period Ty are obtained using the geometrical and material properties of the simulated building. More details are given below: i. First an estimate of the initial period (i.e. corresponding to the elastic stiffness) is computed based on the empirical equation given below which is taken from the commentary of the NZ standard NZS : 2004 and is denoted as design _T ( ) 0. design _ T =. N S 75 y s h y Equation 1 There are two sources of uncertainty in the estimation of the initial period. One is the modelling (i.e. epistemic) uncertainty related to equation (1) used to estimate design _T y and the other is the aleatory uncertainty arising from the randomness of the parameters used in the equation (i.e. N s and S h ). To obtain the combined uncertainty, a unique approach is used in this study. GNS Science Report 2013/20 20

24 Figure 12 Estimation of initial period of buildings. To get a conservative estimate of the design base shear, equation (1) has been intentionally set to underestimate the period. Assuming the modelling uncertainty to follow a normal distribution and the design period ( design _T ) to represent 95% confidence level (as shown in Figure 12), the mean period, T y exceeds the y design _T y by 1.96 times standard deviation σ, which is the product of coefficient of variation (CV) and the mean (i.e. σ= CV * mean ). Hence, the mean period T y can be expressed as: ( ) design _T = T 1. 96* CV * T y y y y y ( ) T = design _ T. CV Equation 2a Equation 2b Now random values of the initial period Ty can be generated in terms of mean period, Ty and a randomly generated coefficient of variation (CV) as given in Equation (3), where randn is a normally distributed random number generator. y y ( 1 ) T = T + randn.cv Equation 3 To obtain the median_t y and the dispersion β_t y, MonteCarlo simulation is then carried out using equations (1)-(3) and using the random values of N s, S h (as given in Table 5) and the CV as (U[0.15,0.25]). ii. The displacement capacity at yield is computed at the effective height level of the structural system using established empirical relationships. In this study, expressions proposed by (Priestley et al., 2007) are used for appropriate building groups. For example, yield displacement for post-1976 and pre-1976 RC moment resisting frame buildings is calculated using Equation (4a) and (4b), respectively. ( ) D = 05. efh.n.s ε l h y s h y b b Equation 4a ( ) D = efh.n.h ε h d y s c y c c Equation 4b The values of the variables used in Equation (4) are given in Table 5 and ε y is the yield strain of the steel. GNS Science Report 2013/20 21

25 Assuming the generated data are log-normally distributed, calculated values of the median and dispersion of D y and T y (i.e. median _ D y, median _ Ty and β _Dy, β _Ty as noted in the following sections) are listed in Table 6. Note that the Monte-Carlo generated data includes only the aleatory uncertainty in D (due to randomness in geometrical and material y properties), and as the same equation is used for all calculations, it does not capture the epistemic uncertainty (which may arguably be negligible in this case as D falls at the boundary of the elastic response range which is treated similarly by different models). y Table 6 Initial properties for building groups. Yield displacement, m Initial period, s Effective height, m Median Dispersion Median Dispersion Median Dispersion Concrete Frames (Post 1976) (ductile) Low-rise Medium-rise High-rise Concrete Frames (Pre 1976) (limited ductile) Low-rise Medium-rise High-rise GNS Science Report 2013/20 22

26 8.0 DEFINITION OF LIMIT STATES The limit states are generally related to critical structural response parameters (identified as engineering demand parameters EDPs); such as the maximum values of average roof drift ratio, inter-story drift ratio etc. The relationship between a damage state and the EDPs for a given building type requires sound engineering judgement and a large amount of information on damage sustained by structural elements at different level of responses. Also, some studies have recommended considering residual displacements in combination with maximum transient displacements in defining performance objectives for buildings (Uma et al., 2010). In this study, four limit states (LS1 to LS4) are defined in terms of maximum drift ratio at the effective height of an equivalent SDOF model. The damage limit states are marked in the idealised bilinear force-deformation curve (Park, 1997) as shown in Figure 13. LS1 denotes the significant yield point in the bilinear curve which is marked well beyond the first onset of yield. LS3 is considered at a drift limit corresponding to the ultimate limit state satisfying the life-safety criteria at the DBE. LS4 is considered to be at the drift limit corresponding to collapse prevention criteria corresponding to the MCE. LS2 is defined mid-way between LS1 and LS3. It is implicit that LS0 indicates a scenario of no-damage in the building. Figure 13 Idealised capacity curve and threshold limit states. The drift ratios in terms of median and the dispersions for RC frame buildings at the four limit states are listed in Table 7. Note that the drift ratios for LS1 are, by definition, taken as the yielding drifts given by the yield displacement and the effective height given in Table 5. Similarly, the drift ratio limits for LS3 is taken as the ultimate drift for life safety as per the NZS1170.5:2004 and the drifts for LS4 are chosen as the collapse prevention drifts recommended by FEMA 273 (FEMA, 1997). The median threshold drift values ( median _ D LSi ) at a given damage limit state (LSi) is calculated as the product of the threshold values listed in Table 7 and the median values of the effective height given in Table 6. GNS Science Report 2013/20 23

27 Table 7 Median threshold drift ratios and dispersions at the effective height of for RC frame buildings. LS1 LS2 LS3 LS4 median dispersion median dispersion median dispersion median dispersion Post % % % 0.4 4% 0.45 Pre % % % % 0.4 The dispersion for LS1 is assigned such that it represents the dispersion ranges found for the post and pre-1976 building groups in Table 6. For higher limit states, gradually increasing values of dispersion are assigned (depending on the drift levels) acknowledging the fact that the modelling uncertainty increases in predicting the inelastic response far from the elastic limit. GNS Science Report 2013/20 24

28 9.0 DEMAND AT INELASTIC LIMIT STATES In Figure 13 it is obvious that the secant stiffness at a limit state is equal to the initial stiffness divided by the ductility at the limit state. The median ductility, ( median _ µ LSi ) realised at every limit state can be obtained as the ratio of median threshold drift values to the median yield. Using this correlation, the median value of the effective period (T LSi ) at drift ( median _ D y ) various damage states (LSi) and its dispersion are expressed as in the following equations. ( ) median _T = median _ D median _ D * median _T LSi LSi y y 2 (( ) ( ) ) ( ) 2 2 LSi 05 LSi y y β _T =. β_d β _D + β_t Equation 5 Equation 6 In this illustrative study, the median spectral displacement demand at a limit state, median _ S d ( demand ) LSi is directly obtained from the spectral acceleration at the period corresponding to that limit state, median _ T LSi obtained from the elastic demand spectrum. It is recogonised that the spectral acceleration demands are dependent on the period and this dependency will have an influence in the dispersion of spectral displacement demand. A method of removing the dependency is to assume a linear variation approximation of displacement demand with period (Uma and Bradley, 2010). However, when dealing with actual recorded ground motions as done in this study, a reasonably simpler expression is used where the dispersion in the spectral displacement demand is contributed mainly by the dispersion in the period. Assuming the spectral displacement demand is lognormally distributed, its dispersion can be calculated as shown below. ( ) ( ) 2 LSi =ψeff a LSi π LSi median _ S S ( median _ T ) 2 median _ T d demand β _ S d ( demand ) LSi = 2 β _ T LSi Equation 7 Equation 8 The elastic spectral displacement demands are reduced using spectra reduction factor, ψ eff to account for the increased damping due to inelastic response at various damage limit states (except for LS1). As shown in the equations below, the spectra reduction factor ψ eff is a function of equivalent viscous damping ratio ξ eff which is obtained using the ductility level achieved at a given damage limit state and the damping reduction factor, η for a given structural system as suggested by Priestly et al., For example, the damping reduction factor for RC frame buildings is ( 0. ) ψ = eff ξ eff (( µ ) µ ) ξ = η 1 eff Equation 9 Equation 10 GNS Science Report 2013/20 25

29 10.0 PROBABILITY OF FAILURE The probability of exceedence of a limit state is determined by comparing the spectral displacement demand with spectral displacement of the structure. Using standard normal cumulative distribution function, the cumulative probability of exceedence corresponding to each limit state (LS1 to LS4) can be computed as ln ( median _ Sd ( demand ) LSi median _ DLSi ) Z = 2 β _ D + β _ S P f ( LSi) = Φ( Z ) ( ) 2 d demand LSi ( LSi ) ( ) Equation 11 Equation 12 As both demand and capacity used in Equation (11) are unique the damage state being considered, the outcomes for different limit states are independent of each other. In other words, the outcome is like the conditional probability of a limit state given that lower limit states have been exceeded. Hence, to calculate the unconditional cumulative probability of exceeding a limit state the values obtained from Equation (12) for all limit states up to the one being considered should be multiplied. For example, the cumulative probability of exceedence of LS2 is expressed as a product of the two independent probabilities of exceedence at limit states: LS1 and LS2; and the cumulative probability of exceedence of LS3 is the product of the independent probabilities of exceedence of LS1, LS2 and LS3.Then, probabilities of being within a given damage state can be obtained as the difference between cumulative probabilities of exceeding consecutive limit states. Estimation of probabilities of exceedence of various limit states is discussed with reference to Figure 14, where the capacity of medium-rise RC frame (Post 1976) is compared with demands from two earthquake scenarios. The structure is assumed to be detailed as per the 1992 version of the New Zealand concrete structures standards NZS 3101:1992 to enable a ductile response. Figure 14 shows elastic and inelastic (reduced for ductility =2) spectral demands for: (i) median of the actual ground motion records; and (ii) the code-based MCE demand. DBE spectrum is not shown in Figure 14, but the damage probabilities with respect to DBE demand are included in Figure 15. Idealised bi-linear capacity spectrum and the lines showing effective stiffness corresponding to the limit states of the structure are also plotted. GNS Science Report 2013/20 26

30 Figure 14 Idealised bilinear curve with demand curves from: (i) Actual elastic spectrum as geometric mean of 4 records from February event (black solid line); (ii) respective inelastic spectrum reduced for ductility=2 (black dashed line); (iii) MCE design spectrum (grey solid line); (iv) respective inelastic spectrum reduced for ductility =2 (grey dashed line). At a chosen limit state (LSi), the median displacement realised by the structure is equal to the ( median _ D LSi ) which is compared with the spectral displacement demand with associated uncertainties as per Equation (11). For example, at LS1 the median_sd (demand) for the actual record is much higher than the displacement that could be realised at median _ D LS1 ; thereby giving a higher probability of exceedence. At LS2, where ductility=2, the MCE demand is less than the Actual demand, hence the probability of exceedence for the latter case will be higher. However, at LS3 close to the re-entrant corner of the actual record, the actual demand is less than the MCE demand; hence the probability of exceedence for the actual record is less than that for MCE. At LS4, the expected median_dlsi could be more than the median_sd(demand)lsi for both scenarios. In such cases, the probability of exceedence estimated by Equation (11) is the contribution from the uncertainties involved in the quantities. It is recognised that the probabilistic estimates will be different if a degrading capacity curve was used instead of the adopted idealised bi-linear capacity curve. Cumulative probabilities of exceedence of different limit states and probability of being within a particular damage state (DS1, DS2, DS3, DS4 or >DS4) are compared for medium rise buildings under the three demand scenarios (DBE, MCE and the actual demand from the February 2011 event) in Figure 15 (a) and (b). Figure 15 scenarios. Damage probabilities for post-1976 medium-rise RC frame building under DBE, MCE and Actual GNS Science Report 2013/20 27

31 Damage probabilities for medium-rise buildings (ref. Figure 15 (b)) show that about 70% of the buildings could fall in DS2 (i.e. experience drift limits between LS1 and LS2) under the DBE scenario; whereas in the actual event about 65% of buildings could fall in DS3 (i.e. between LS2 and LS3). About 10% of buildings are in DS4 under MCE and actual scenarios. Adopting the above methodology, a series of results were generated to estimate damage probabilities for RC moment resisting frame buildings. In general, the actual record (the February event) inflicted higher level of damage compared to the DBE and MCE scenarios. However, the distribution varied depending on the structural systems considered. For example, higher proportion of post-1976 RC frames fell in DS2 and DS3, whereas for pre 1976 RC frames, majority of buildings fell in DS4 (ref. Figure 16 to Figure 19). Figure 16 Probability of exceedence for reinforced concrete frames: post Figure 17 Probability of being in different damage states for reinforced concrete frames: post Figure 18 Probability of exceedence for reinforced concrete frames: pre GNS Science Report 2013/20 28

32 Figure 19 Probability of being in different damage states for reinforced concrete frames: pre GNS Science Report 2013/20 29

33 11.0 COMPARISON OF ESTIMATED DAMAGE PROBABILITIES WITH OBSERVED DAMAGE STATISTICS The analytical approach adopted in this study gives estimates of probabilities of being a given damage state (DS). Four independent damage states are considered in this study, viz., DS1 to DS4. The probability of a given damage state for a building group can be interpreted as the proportion of buildings in that damage state within that building group present within the portfolio under consideration. These damage states can be mapped into the colour tagging to a reasonable degree; for example the probabilities of lower damage states can be related to the percentage of Green tagged buildings; similarly probabilities of intermediate and higher damage states can be related to the percentages of Yellow and Red tagged buildings respectively. In this study, correlation between the damage states and the building tagging colour is established based on the definition of the damage states (see Table 2) and the authors experience in tagging buildings after the September 2010 and February 2011 Canterbury earthquakes. As Green tagging includes G1 (i.e. undamaged buildings) and G2 (i.e. buildings with some non-dangerous and easily repairable damage), it is assigned the whole of DS1 and the first 75% of DS2, as shown in Figure 20. Similarly, the last 25% of DS2 combined with DS3 and DS4 are grouped into Yellow to include Y1 and Y2 (i.e. buildings which are significantly damaged but with no collapsed elements); and anything beyond LS4 (i.e. collapse limit state) is interpreted as Red. R3 category is not included in the calculations as the methodology at present does not consider damages due to liquefaction or risk from adjacent buildings. The mapping between the tagging colour and the damage states are similar to recommendations of ATC 58-2 (2003). Figure 20 Mapping of damage states (DS) to tagging colours. The probability estimates are compared with the observed damage state statistics for the post and pre-1976 medium-rise RC moment resisting frame buildings. Table 8 lists the probabilities of RC moment resisting frame buildings obtained for the actual scenario from the displacement-based approach adopted in this study. GNS Science Report 2013/20 30