Empirical building fragilities from observed damage in the 2009 South Pacific tsunami

Earth-Science Reviews 107 (2011) 156–173

Contents lists available at ScienceDirect

Earth-Science Reviews j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e a r s c i r ev

Empirical building fragilities from observed damage in the 2009 South Pacific tsunami Stefan Reese a,⁎, Brendon A. Bradley b, Jochen Bind a, Graeme Smart a, William Power c, James Sturman a a b c

National Institute of Water and Atmospheric Research Ltd, Private Bag 14901, Hataitai, Wellington 6021, New Zealand Department of Civil and Natural Resources Engineering, University of Canterbury, Private Bag 4800 Christchurch 8140, New Zealand GNS Science, P.O. Box 30–368, Lower Hutt 5040, New Zealand

a r t i c l e

i n f o

Article history: Received 18 June 2010 Accepted 25 January 2011 Available online 2 February 2011 Keywords: South Pacific tsunami American Samoa Samoa fragility functions tsunami impact risk assessment

a b s t r a c t This manuscript presents empirical building fragility functions that were developed based on data obtained from the 29th September 2009 South Pacific tsunami. A multi-disciplinary reconnaissance team involving topographic surveyors, tsunami/hydrology modellers, structural engineers, and risk analysts collected observational and quantitative data on building damage and the tsunami demand. A diverse range of collected data, which included a topographic survey, observed water depths, predominant flow directions, inundation limits, building damage, and eyewitness reports, were used to recreate the peak tsunami-induced demands on structures at each of the survey locations. Using the interpreted data, fragility functions were developed for a variety of building classes using logistic regression. It was observed that residential timber structures were more fragile (i.e. have a higher likelihood of damage for a given water depth) than masonry residential structures for severe and collapse damage states. Conversely, residential reinforced concrete structures were observed to be less fragile than residential masonry structures for severe and collapse damage states. The influence of ‘shielding’ and ‘entrained debris’ effects on fragility functions were also quantified using the empirical data. Other parameters such as velocity or impact duration were not considered due to the paucity of data. The results of this study contribute to the ongoing development of robust methods for explicitly estimating tsunami-induced risk to coastal communities. © 2011 Elsevier B.V. All rights reserved.

Contents 1. 2.

3.

4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multi-disciplinary reconnaissance survey. . . . . . . . . . . . . . . 2.1. Field investigation overview . . . . . . . . . . . . . . . . . 2.2. Topographic survey instrumentation . . . . . . . . . . . . . Analysis of field data . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Eyewitness observations . . . . . . . . . . . . . . . . . . . 3.2. Maximum inundation depths . . . . . . . . . . . . . . . . . 3.3. Land topographic effects on water propagation . . . . . . . . 3.4. Damage observations and classification . . . . . . . . . . . . 3.5. Example data interpretation: Asili, American Samoa . . . . . . Fragility function development . . . . . . . . . . . . . . . . . . . 4.1. Methodology . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1. Use of fragility functions for tsunami risk assessment . 4.1.2. Logistic regression methodology . . . . . . . . . . . 4.1.3. Fragility of a ‘typical’ Samoan building . . . . . . . . 4.2. Fragility of masonry residential buildings . . . . . . . . . . . 4.2.1. Differences in American Samoan and Samoan buildings 4.2.2. Masonry residential fragility functions . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

⁎ Corresponding author at: Private Bag 14901, Hataitai, Wellington 6021, New Zealand. Tel.: + 64 4 386 0564; fax: + 64 4 386 2153. E-mail address: [email protected] (S. Reese). 0012-8252/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.earscirev.2011.01.009

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

157 157 157 159 159 159 159 160 160 160 162 162 162 165 165 165 166 166

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

4.3.

Shielding and debris effects on fragility . . . 4.3.1. Effect of shielding. . . . . . . . . 4.3.2. Effect of debris . . . . . . . . . . 4.4. Fragility of other structures . . . . . . . . 4.4.1. Reinforced concrete (RC) residential 4.4.2. Timber residential structures . . . 5. Conclusions . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . structures . . . . . . . . . . . . . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

1. Introduction On the 29th September 2009 a pair of near-simultaneous great earthquakes, each with moment magnitude approximately Mw = 8.0, occurred about 190 km south of Apia, Samoa (15.509°S, 172.034°W, USGS, 2009) at 6:48 am local time (17:48 UTC) (see Beavan et al., 2010; Lay et al., 2010 for more details. The time and epicentre coordinates quoted here refer to the outer-rise normal fault earthquake that was the first to be identified). The earthquake-induced ground motions were felt as far away as Wallis and Futuna Islands, and the earthquake-induced tsunami caused damage and casualties over a widespread area, including Samoa (formerly Western Samoa), American Samoa and Niuatoputapu, Tonga, among others. 226 people died directly as a result of the tsunami that impacted these coastal communities (Lamarche et al., 2009; Dudley et al., 2011-this issue; Okal et al., 2011-this issue). The 2009 South Pacific tsunami is another recent reminder of the destructive potential of tsunamis to coastal communities. Despite numerous occurrences of such events over the past decade (e.g. Indian Ocean tsunami — December 2004, Java — July 2006, Solomon Island — April 2007 and January 2010, Chile — February 2010 and more recently Indonesia — October 2010), and the availability of complex physical models to model tsunami wave propagation, the tools available to explicitly assess the potential impacts of tsunamis to coastal communities are still limited (Douglas, 2007). The collection of damage data and estimations of tsunami impacts before the 2004 Indian Ocean tsunami was very limited (Hatori, 1984; Shuto, 1993; Papadopoulos and Imamura, 2001). Since the 2004 tsunami, the number of studies has increased significantly. However, most studies have focused on: (1) qualitative damage analysis (Dalrymple and Kriebe, 2005; Stansfield, 2005; Ghobarah et al., 2006); (2) categorisation of building damage (EERI, 2005; Saatcioglu et al., 2007; Rossetto et al., 2007; Kaplan et al., 2009); or (3) an indexbased approach (Dominey-Howes and Papathoma, 2007; Dall'Osso et al., 2009; Omira et al., 2010). Consequently, only a limited number of fragility or vulnerability functions have been developed to date (Peiris, 2006; Ruangrassamee et al., 2006; Reese et al., 2007; Dias et al., 2009; Koshimura et al., 2009; Leone et al., 2010). Despite the limited number of fragility or vulnerability functions, such tools are key components in a risk assessment framework (Douglas, 2007), and permit rational decision making for both immediate evacuation due to an incoming tsunami as well as for long-term hazard planning and mitigation. A first step in developing explicit models of tsunami risk involves the determination of fragility functions which describe the direct damage to buildings and other infrastructure due to tsunami-induced hazards. A reconnaissance team of New Zealand scientists visited the areas damaged in the 2009 South Pacific tsunami with the aim of acquiring observational and quantitative field data for developing and validating models used to estimate building and infrastructure damage. The reconnaissance was conducted over a twelve day period, beginning approximately two weeks after the event. This manuscript firstly discusses the multi-disciplinary reconnaissance survey approach adopted, locations surveyed, and data collected. Secondly, the obtained

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

157

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

166 167 168 169 169 169 169 172 172

field data which include eyewitness observations, topographic surveys, inundation depths, and building damage observations are analysed and interpreted. Thirdly, the interpreted data is used as the basis for developing empirical fragility functions of building damage due to tsunami impact, including the effects of construction material, sheltering, and entrained debris. Finally, the implications of this study toward the goal of explicit tsunami risk assessment are discussed. 2. Multi-disciplinary reconnaissance survey In planning the methodology to adopt during the reconnaissance survey, consideration was given to the collection of observational (preferably quantitative) data which could be used in developing and/or validating building and infrastructure fragility functions. Such fragility functions provide the backbone for rigorous estimation of impacts and risk (Douglas, 2007) from tsunami-induced hazards. The desire to collect quantitative observational data for fragility function development in a post-disaster environment required a multi-disciplinary reconnaissance team and methodology for data collection. As a result, the survey team comprised one or more personnel in the areas of: topographic surveying, tsunami/hydrological modelling, structural engineering, and natural hazards risk assessment. As subsequent sections discuss in further detail, fragility functions describe a (probabilistic) relationship between demand and damage. Therefore, in the case of structures subjected to tsunamis, the demand on structures needs to be quantified as a function of one or more predictor variables such as water depth, velocity, and entrained debris. The observed building and infrastructure damage needs to be catalogued in sufficient detail to enable the post-tsunami damage state (e.g. minor, major, complete damage) of the structure to be obtained, as well as details regarding the building/infrastructure itself, to examine the dependence of fragility on structure type. The main data collected at each survey site/village therefore was: (1) A topographic survey of the site, including the limits of inundation, locations of water depth measurements, and location of structures at which damage observations were catalogued. (2) Observations of maximum water depths on buildings and surrounding vegetation, as well as inferences of water flow direction and velocity. (3) Structural classification of buildings and infrastructure damage observations, including structure attributes, observed damage state, shielding from other obstructions and possible effects of entrained debris. (4) Eyewitness reports on all aspects of the tsunami to supplement the above data. 2.1. Field investigation overview The reconnaissance team visited American Samoa and Samoa, as both countries have structures that are similar to those in New Zealand. Although traditional houses (fale) are still common, the American government has promoted the building of concrete “hurricane” houses with corrugated metal roofs to minimise storm damage in American

158

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

Fig. 1. Reconnaissance survey sites: (a) American Samoa; and (b) Samoa.

Samoa since the 1970s.1 In Samoa, on the other hand, foreign aid and tourism have resulted in modernisation of even the most isolated rural areas. Hence, these modern structures were of particular interest. Twelve areas were surveyed by the reconnaissance team, six in American Samoa and six in Samoa (Fig. 1). As the islands in both countries are of volcanic origin with steep slopes, most villages are located in low lying coastal areas. The selection of survey sites which were examined in detail was based primarily on the extent of inundation and damage observed during a preliminary visit to all of the main inhabited areas. In the selection of areas to survey (under limited time constraints), the aim was to obtain a good representation

1 (http://www.everyculture.com/A-Bo/American-Samoa.html; http://worldinfozone.com/country.php?country=AmericanSamoa, http://photo.pds.org:5005/student/printarticle?id=ar018160&ss=h2).

of different levels of inundation and damage which is primarily dependent on the topography (near-shore bathymetry, beach slope, coastal orientation, and direction of the arriving wave are considered as secondary effects) (Ghobarah et al., 2006; Reese et al., 2007; Rossetto et al., 2007). Hence, areas with different topographic profiles were selected, ranging from wide flat areas to narrow river valleys with steep landward slopes. In the twelve villages surveyed, approximately 30 transects were completed and more than 200 buildings inspected (Table 1). The majority of the buildings were residential (78%), although commercial buildings, traditional fales, churches and buildings of other use were also inspected. The fact that in American Samoa no clean-up or repair could commence without the Federal Emergency Management Agency (FEMA) having inspected the buildings favoured our survey. These FEMA inspections had not commenced or were still in progress; hence the buildings were generally in the same state they were in

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173 Table 1 Classification of building data collected according to construction type.

Masonry residential Timber residential RC1 residential Steel Church (RCa) Lava rock Fales RCa commercial Masonry non-residential Total a

Am. Samoa

Samoa

Total

84 8 9 1 4 1 4 1 4 116

36 16 4 0 2 7 7 2 11 85

120 24 13 1 6 8 11 3 15 201

RC = reinforced concrete.

immediately post-tsunami. In Samoa, however, most buildings are, according to interviewees, not insured and owners do not have to wait for any Federal agency in order to start cleaning up. Hence, finding indications of tsunami demand (e.g. flow depth) was more difficult, and additional care was required to ensure that the obtained data were reliable and unbiased. 2.2. Topographic survey instrumentation A dual-frequency kinematic GPS system was used in both American Samoa and Samoa to measure ground profiles and inundation depths across regions of interest. The equipment consisted of two GPS receivers, one serving as a base station that remained at a fixed position throughout each of the surveys, and the other as a roving unit taken to individual measurement points. Provided sufficient satellite coverage existed, positional accuracies of ±20 mm horizontal and ±30 mm vertical were achievable. Such positional accuracies, however, are relative within a particular survey and apply to absolute positions only when linked to a reference point such as a reliable survey mark. Unfortunately, suitable survey marks were not found in American Samoa and consequently a less precise method using sea level measurements and tide tables to derive absolute vertical positions was adopted. This method allowed the measurement of elevations above mean sea level with a vertical accuracy of better than ±100 mm. In Samoa, a network of survey marks along the main road around the island provided reliable reference points. These survey marks were established using precision levelling, thus providing only vertical information without accurate horizontal positions. As a consequence, the measured horizontal positions in both countries rely on the initial autonomous position for the base station which has a positional error of less than 2 m. This accuracy was deemed sufficient for our application, since individual survey points have an accuracy of ±20 mm relative to one another. The GPS surveys were carried out as post-processed kinematic surveys (PPK GPS), where positional data from the roving GPS was processed in the office with the help of data from the stationary base GPS. Kinematic GPS requires reliable satellite coverage in order to provide accurate results. However, satellite reception in densely vegetated areas is limited and vegetation proved to be an obstacle in many of the village areas surveyed. Therefore, precise levelling with a level and scaled staff was utilised as an additional tool to survey topographic profiles, inundation extents and depths. This method was only used in Samoa. 3. Analysis of field data

159

to provide complementary information. The focus of such interviews was usually to obtain eyewitness recollections of the nature of the tsunami wave-train arrival times, direction of the on-coming waves, and damage caused by entrained debris. In both American Samoa and Samoa, eyewitnesses reported consciously feeling the earthquake-induced ground motion shaking. Such shaking was also described as of long period and having a duration of a minute or more (consistent with the expected duration of rupture for an Mw = 8.0 event, and the source-to-site distance). This shaking was considered significant enough that educated eyewitnesses immediately appreciated the threat of a subsequent tsunami. Unfortunately, only a small portion of locals were considered as educated in this regard (Dudley et al., 2011-this issue) and therefore most people only began to move to higher ground once significant recession of the water along the coastlines was observed. The fact that the tsunami struck in the morning when most people were on their way to work or school helped to reduce the number of casualties. Eyewitnesses generally stated that the water first receded and left the reef bare. A “roaring” sound accompanying the incoming tsunami was usually remembered. The majority of eyewitnesses reported the second wave as being the largest, and there were differing statements that in some cases the first wave, and in others the third wave, was the most destructive one. Such statements, which were obtained in different villages, are not inconsistent because in certain cases a smaller third wave may contain significant entrained debris and cause more damage than a larger first (or second) wave. The waves were described as arriving only a minute or two apart and often with no complete withdrawal between. Some eyewitnesses remembered that the incoming tsunami broke at the coast or amongst coastal palm trees before surging through the developed areas. As was also observed in the Indian Ocean and Java tsunamis (Gregg et al., 2006; Reese et al., 2007), a lack of information caused some people to get into their cars and drive parallel to the beach where they were caught by the tsunami. According to the media2 and eyewitnesses, a large percentage of the people who died in the tsunami were elderly and young children who were not able to escape as fast as other people. Eyewitness reports were fairly consistent regarding the arrival time of the tsunami. Most people in Samoa reported that the tsunami hit the coast approximately 10 min after the earthquake. Reports regarding the arrival time varied from 15 to 30 min in American Samoa depending on the geographical location (a tide gauge in Pago Pago harbour recorded the arrival of the tsunami at 24 min after the earthquake (NOAA, 2010)). These quantitative and qualitative observations are consistent with arrival times based on tsunami simulations (Annunziato et al., 2009). Most people reported that the sequence of tsunami waves lasted less than 10 min.

3.2. Maximum inundation depths The variation of run-up and flow depths (see IOC (2008) for definitions) at both regional and local scales required the measurement of ground profiles and inundation depths along multiple transects at each survey site. A good understanding of this fine-scale variability and the course and extent of the event is necessary to enable the establishment of a correlation between hydraulic information and the observed level of damage. The observed general trend in American Samoa was that the highest flow depths and run-ups occurred at the western side of the island, in and around Poloa; however, the southwest coast, Pago Pago, and parts of the north and east coasts also suffered significant inundation. Our observations are consistent with tsunami

3.1. Eyewitness observations In addition to direct observations obtained from post-tsunami inspection of building damage, eyewitness interviews were conducted

2 See http://www.foxnews.com/world/2009/09/30/dead-villages-wiped-samoatsunami/.

160

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

modelling results from Annunziato et al. (2009) and Donahue et al. (2009). In Samoa, maximum run-up heights and flow depths were observed in the southeast corner of Upolo around Lalomanu. Only minor run-ups and depths were reported from the northern part of the island. A summary of the maximum measured run-ups, flow depths and inundation distances is shown in Table 2. Even though only a small number of areas were surveyed, the data clearly illustrates the spatial variability in intensity and extent of the inundation. Clearly, site specific features such as the near-shore bathymetry (reef morphology), coastal topography, and the existence of rivers and offshore islands played a significant role in amplifying or reducing the tsunami impacts on the coast. As the aim of the survey was to collect representative data rather than a thorough and complete survey of every site, the data below represents only the maximum values that were observed by the team. Although care was taken during the survey, including the use of complementary information, such maxima are clearly subject to significant uncertainties. Comparing the data with results from Donahue et al. (2009) or Jaffe et al. (2010) highlights differences in the observations. While the maximum inland inundation for Asili is essentially identical, Jaffe et al. (2010) measured 120 m and 260 m for the maximum inundation in Poloa and in Matatula respectively, compared with our estimates of 95 m and 225 m. For flat beach slopes some error could be attributed to specification of the shoreline position. Apart from water level or flow depth, flow velocity is another critical parameter influencing the destructive potential of tsunamis. Kamataki et al. (2005) use the head loss or pressure loss as an indication for flow velocity. If tsunami traces at the front and the rear of building are available, the flow velocity, u, can be estimated from: u=

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2g hf −hr

ð1Þ

where g is the acceleration of gravity, and hf and hr are the front and rear inundation depths, respectively. Because of differing wave heights and directions from the successive wave advances and retreats we were able to find only four reliable sets of front/rear depths from more than 200 buildings surveyed. Hence, the wave velocity cannot be used explicitly as a parameter in the development of the fragility functions based on our observed data. The same applies to effects of backwash and inundation duration as it is usually difficult to obtain this information through post-disaster field surveys. 3.3. Land topographic effects on water propagation Examination of the various ground profiles and water level measurements provides insight as to how on-shore topography affects tsunami wave propagation. Fig. 2 illustrates a selection of surveyed maximum water levels and measured ground levels, with respect to mean sea level, in transects approximately perpendicular to the shoreline. As the tsunami moves inland, the profiles show that the rate of attenuation of wave height with inland distance is a function of the topographic profile of the area. A summary of inundation distances and run-up distances taken from selected profiles is given in Table 3. In Table 3 the water level at the shore has been estimated from extrapolation of the near-shore profile and from other measurements made close to the line of the profile. The average ground slope is calculated as run-up distance divided by inundation distance. Note that the inundation distance of a single transect may be shorter than the maximum for the entire survey area reported in Table 2. Table 3 illustrates that sites with highest valley contraction factor had the highest run-up (i.e. Asili b Amanave b Poloa). The topographic contraction may have offshore influence as the shoreline wave heights were also high at these sites. The data in Table 3 also show a strong dependence of inundation distance on ground slope. Fig. 3 indicates that the decrease of inundation distance with increasing ground slope can be

Table 2 Maximum observed inundation characteristics in survey areas in Samoa and American Samoa. Locationa

Run-up (m)

Flow depth above ground (m)

Water level above mean sea level (m)

Inundation distance (m)

Ulotogia Saleapaga Lepa Coconut Poutasi Poloa Amanave Asili Leone Pago Pago Matatula

4.6 5.5 6.1 4.3 6.6 11.4 8.3 7.5 5.6 7.4 7.1

3.7 3.2 4.4 3.5 3.0 5.0 3.9 2.5 3.6 – 3.0

5.1 7.7 7.6 5.2 6.9 10.8 9.1 8.0 6.7 – 6.4

285 125 175 130 255 95 210 260 250b 550 225

a

See Fig. 1 for further details on locations. This measurement does not account for lagoon inundation. Jaffe et al. (2010) estimated 620 m including lagoon inundation. b

described by a negative logarithmic trend. The effect of surface roughness is not taken into account as all of the areas showed similar characteristics with roads, buildings and unsealed open spaces inbetween. 3.4. Damage observations and classification During the inspection of buildings which had been exposed to the tsunami, various attributes of the observed damage as well as the building itself were documented. Examples of building damage included damage to windows, interior and exterior walls, structural walls/frame, and foundation damage/scouring, among others. The main building attributes that were recorded were the construction type and use (e.g. residential masonry, residential timber, residential and commercial reinforced concrete), although additional attributes were also recorded; these included the number of storeys, roof cladding, approximate age, foundation thickness, wave orientation, and possible debris and sheltering effects (see subsequent sections for further details). Based on the observed damage given by the aforementioned indicators, each structure was assigned a damage state (DS). Five damage states were adopted in this study, and a broad description of the indicators leading to the classification of the damage state, are given in Table 4. It can be appreciated that for each damage state, different repair actions would be required to restore the structure to its pre-tsunami condition. For example, DS1, which represents non-structural damage, is likely to require only repair of interior walls that have been saturated, and possible superficial external damage (e.g. broken windows). On the other hand, DS4, represents severe damage to the structural system itself which requires partial or complete demolition of the structure (and consequent rebuilding of a replacement). Therefore, each of these damage states can be assigned a repair cost, or repair cost ratio (denoted as loss functions). These loss functions can be combined with fragility functions (the probabilistic relationship between tsunami demand and damage state) to obtain relationships between tsunami demand and repair cost. An elaborate discussion of loss functions and their combination with fragility functions is beyond the scope of this manuscript and further details can be found in Bradley et al. (2009). 3.5. Example data interpretation: Asili, American Samoa In order to illustrate the process of data collection and interpretation, this section demonstrates the process for a single village, Asili on the southwest coast of American Samoa.

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

161

Fig. 2. Profiles of on-shore water level measured approximately perpendicular to the shoreline.

Asili is located in a narrow river valley with steep slopes on both sides and a reef that is 150–300 m wide (Fig. 4a). As Fig. 4b illustrates, there is a 2 m scarp along the beach, indicating active erosion. The Asili River runs through the middle of the village and essentially separates it into an eastern and western part (Fig. 5). The main access road runs nearly parallel to the aforementioned scarp with a moderate incline at both ends of the village. Inland from the road, the terrain exhibits a gradual incline, and the elevation reaches about 6 m above mean sea level (MSL) at a distance of about 150 m from the shore (Fig. 2). A detailed reconstruction of the topography is considered essential for the reconstruction of the spatial distribution of water levels, flow depth, wave propagation and is given in Fig. 5. According to eyewitnesses, Asili was hit by two waves, with the second one being the highest. The water did not recede completely before the second wave arrived, about 1–2 min after the first one. It was reported that the second wave merged with the receding water around

the road. The wave direction (Fig. 6) was essentially perpendicular to the shore, following roughly the bathymetry of the reef. There are approximately 60 buildings in Asili. Apart from a shop, church and two fales, residential buildings were made predominantly of brick/masonry with a few timber buildings in-between. A total of 22 of these buildings were surveyed. The remaining approximately 38 buildings were either beyond the inundation line, had been completely damaged and demolished prior to our survey (such that we could not confidently include them as unbiased data), or the building structure was not representative for this purpose. Fig. 6 illustrates the surveyed buildings, their respective damage states and the approximate inundation limit. Of the buildings surveyed the number observed to be in each damage state were: DS0 = 3; DS1 = 2; DS2 = 1; DS3 = 5; DS4 = 1; DS5 = 10. The inundation limit shown in Fig. 6 is that of Jaffe et al. (2010), which has been complemented by our own data.

Table 3 Water level profile characteristics for survey areas in Samoa and American Samoa. Survey site

Transect

Inundation distance (m)

Run up (m)

Shore water level (m)

Avg. ground slope

Contraction factor (%)

Ulutogi Ulutogia Ulutogia Amanave Amanave Asili Coconut Leone Leone Leone Lepa Matatula Matatula Matatula Saleapaga Saleapaga Saleapaga Poloa Poloa

601 602 603 214 211 405 801 102 103 107 705a 313 311/315 312 701 703 704 205 204

170 285 157 105 212 181 128 122 250 97 74 121 223 174 122 126 123 93 66

4.6 4.2 3.3 8.0 8.3 6.9 4.3 4.6 3.6 5.6 6.1 6.0 3.1 3.1 5.4 5.5 5.4 10.5 9.6

4.5 5.0 5.0 9.0 9.0 7.8 5.0 7.0 6.8 7.5 7.2 6.5 7.0 7.0 8.0 6.5 6.4 10.5 10.0

0.03 0.01 0.02 0.08 0.04 0.04 0.03 0.04 0.01 0.06 0.08 0.05 0.01 0.02 0.04 0.04 0.04 0.11 0.14

0 0 0 29 29 19 0 0 0 0 0 0 0 0 0 0 0 61 61

162

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

Fig. 3. Inundation distance and average ground slope of measured profiles. A negative logarithmic trend line is shown.

The inundation line in Fig. 6 clearly shows that the tsunami was redirected up the stream leading to an amplified impact on buildings along the river. A maximum wave run-up of 7.5 m (above MSL) and a maximum inundation distance of 260 m were measured. The measured flow depth and inferred water levels for Asili are shown in Fig. 7. Eight buildings out of the 22 surveyed had clear marks of the maximum water inundation (herein referred to as water marks). The measured flow depth above ground ranged from 0.1 to 2.5 m. Such water marks, which were complemented by eyewitness reports, provide the basis for interpolation of water levels and depths over the remainder of the village. The interpolation was undertaken to increase the number of buildings that could be used in the fragility analysis of the subsequent section. Furthermore, the uncertainties associated with the interpolation were explicitly considered by assigning the inferred water depths for each building as having an uncertainty of ±0.4 m (95% percentile bounds). In contrast, water depths which were directly measured were given an uncertainty of only ±0.2 m. Water depth and levels were interpolated based on the profiles of onshore water levels as shown in Fig. 2. As can be seen in Fig. 7 the water level was not constant throughout the village. The onshore level ranged from 7.46 m (above MSL) at the eastern side of the village to 6.85 m at the western end. Tsuji et al. (1991) described that on both sides of deep rivers or streams, the maximum water level may be amplified up to 1.5 times the initial water level. Although these characteristics do not quite apply to the small stream in Asili, it still seems to have amplified the effect of the tsunami as the maximum onshore water levels (7.6–8.0 m above MSL) have occurred along the first section of the stream. Another factor

Table 4 Damage state classification and descriptions. Damage state (DS) DS0 DS1 DS2 DS3 DS4 DS5

None Light Minor Moderate Severe Collapse

causing the increased inundation is the deep channel in the middle of the bay which would have directed the tsunami into the centre of the village. The measured and interpolated water depths in Fig. 7 (with their consequent uncertainties) and the observed building damage states in Fig. 6 then provide the necessary input data to determine fragility functions. This is the focus of the following section (using such data from various survey sites). 4. Fragility function development 4.1. Methodology 4.1.1. Use of fragility functions for tsunami risk assessment As part of a tsunami risk assessment it is necessary to quantify the vulnerability of the exposed assets to tsunami risk. The vulnerability of an asset will be dictated by: (1) the likelihood of the asset experiencing a specific level of damage for a given tsunami hazard; and (2) the (direct and indirect) consequences that eventuate as a result of a specific level of damage to the asset. Fragility functions are the colloquial name given to functions which provide (1) above. Formally, fragility functions give the probability of being in or exceeding a specific damage state (DS) as a function of the demand imparted to the structure by the hazard (herein referred to as the engineering demand parameter, EDP), i.e. Pf(DS ≥ ds|EDP = edp). Because of its simplicity and apparent applicability, the lognormal distribution is typically used to define the fragility function (Porter et al., 2007):

Pf ðdsi jedpÞ = ϕ

ln½edp−μlnEDP j DSi σlnEDP j DSi

! ð2Þ

DS description None Non-structural damage only Significant non-structural damage, minor structural damage Significant structural and non-structural damage Irreparable structural damage, will require demolition Complete structural collapse

where ϕ() is the cumulative normal distribution variate; ln is the natural logarithm; and μlnEDP|DSi and σlnEDP|DSi are the mean and standard deviation of lnEDP|DSi, i.e. the capacity of the structure to withstand the ith damage state. Note that capitalised terms are used to represent variables (e.g. DS), while lower case terms are used to represent a particular value of the variable (i.e. dsi). Thus, from the

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

Fig. 4. Asili, American Samoa: (a) View onto the reef off the coast; and (b) scarp along beach front.

Fig. 5. 3-dimensional reconstruction of the Asili topography, buildings and topographic survey points.

163

164

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

Fig. 6. Surveyed buildings and observed damage states in Asili.

above formulation it can be seen that only the mean and standard deviation of the capacity are required to define the fragility function. Buildings may have multiple damage states, characterised by the discrete levels of repair required to restore the building to its

undamaged state. In such cases, each damage state is defined using a fragility function. As building fragility functions are generally sequential (i.e. the occurrence of DS = dsi implies the occurrence of DS = dsi − 1) and as the fragility function gives the probability of being

Fig. 7. Interpolated tsunami water level and flow depth measurements.

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

equal to or larger than a specified level of damage, then the probability of being in a specific damage state is given by:  P ðdsi jedpÞ =

  Pf ðdsi jedpÞ−Pf dsi + 1 jedp 1≤ibNDS Pf ðdsi jedpÞ i = NDS

ð3Þ

where NDS is the number of damage states. Fig. 8a provides an illustration of fragility functions developed as part of this study for a ‘generic’ structure for the five different damage states defined in Table 4. In this case, water depth is used as the EDP. As one would expect, it can be seen that the median (i.e. when Pf = 0.5) water depth increases for increasing damage states (i.e. there is a 50% probability of being in or exceeding DS = 3 for a water depth of 1.2 m). Using Eq. (3) the fragility functions can be used for a given water depth to compute the probability of being in a given damage state. Fig. 8b illustrates the damage state probabilities for a water depth of 1.0 m, corresponding to the fragility functions given in Fig. 8a. 4.1.2. Logistic regression methodology The aim of this manuscript is to develop empirical fragility functions based on the observed building damage from the South Pacific tsunami. Each surveyed building was assigned two types of attributes which can be used in fragility function development. The first is the observed damage state of the building post-tsunami. The second type of attribute includes one or more metrics as to the level of demand applied to the structure (the simplest being the demand = water depth, which is dealt with initially). Porter et al. (2007) examined various types of data and methods which can be used to create fragility functions. Based on their classification, the post-tsunami observations of damage obtained in the reconnaissance field survey are Type B: Bounding EDP data. Thus, for each damage state under consideration, individual building damage data provides a binary value of whether the considered

165

damage state was exceeded or not, and the maximum water depth that the building was subjected to (either measured or inferred as previously discussed). For example, if the damage state under consideration is DS2, then all buildings with an observed damage state less than DS2 will have binary value of Pf = 0, i.e. ‘survived’, while those with a damage state of DS2 or greater will have a binary value of Pf = 1, i.e. ‘failed’. In order to obtain the (mean and standard deviation) parameters of a lognormal fragility function based on this binary observational data, logistic regression with a Probit link is used (Kutner et al., 2005). Fig. 9 illustrates the individual data points that were used to develop fragility curves for one building class in this study, and the computed lognormal fragility function. 4.1.3. Fragility of a ‘typical’ Samoan building Fig. 8a illustrates building fragility functions for a ‘generic’ Samoan building which were obtained by initially ignoring any effects of building classification. The numerical values of the median and standard deviation of the fragility functions for each of the five damage states are given in Table 6. It can be seen that the first two damage states, ‘light’ and ‘minor’ damage, have median water depths of 0.29 m and 0.48 m, and relatively small lognormal standard deviations of 0.43 and 0.49, respectively. In contrast, DS3–DS5 have larger standard deviations ranging from 0.55 to 0.62. The standard deviations of the fragility functions in Fig. 8a and Table 6 are significant, and make determination of the damage state that a structure will be in for a given maximum water depth highly uncertain. For example, Fig. 8b illustrates that for a maximum water depth of 1.0 m, a generic structure is most likely (57%) to be in DS2, i.e. minor damage, but that there is a 15% chance the structure will be severely damaged (DS4), and almost a 5% chance that the structure will completely collapse (DS5). Such large uncertainties in the fragility functions for generic Samoan buildings in Fig. 8a occur because of the complexity of the process of tsunami “impact on” – and the “response of” – buildings, compared with the highly simplistic assumptions which have been made in deriving the fragility functions. These simplistic assumptions ignored any differences between the responses of different building classes (e.g. masonry, timber, and reinforced concrete) and were based on the premise that tsunami-induced demand on structures can be represented simply by the maximum water depth. The following sections seek to examine some of these assumptions in greater detail and whether there is justification in relaxing some of them. 4.2. Fragility of masonry residential buildings As can be seen from Table 1, a significant proportion (i.e. 120 out of 201, or 60%) of the total buildings surveyed were classified as of residential masonry construction. The relatively large number of

Fig. 8. (a) Example ‘generic’ Samoan fragility functions; (b) use of fragility functions to determine damage state probabilities for a water depth of 1.0 m.

Fig. 9. Illustration of the logistic regression fitting of the data for residential masonry buildings.

166

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

Table 5 Classification of residential masonry data collected according to damage state. Damage state

Am. Samoa

Samoa

Total

DS0 DS1 DS2 DS3 DS4 DS5 Total

10 6 8 14 12 34 84

1 1 10 9 9 6 36

11 7 18 23 21 40 120

observations for this single building class therefore allows an examination of: (1) the compatibility of the American Samoa and Samoa data; and (2) the amount of uncertainty (represented by the standard deviation) in the generic fragility functions due to the combination of multiple building classes. These two points are examined further below. 4.2.1. Differences in American Samoan and Samoan buildings Table 1 illustrates that the total building damage dataset is comprised of a significant number of observations from both American Samoa and Samoa. One immediate question is therefore how compatible are observations from the two different countries? While their geographical distance is small, it is possible that their typical masonry residential structures may perform differently when subjected to tsunamis (due to possible differences in building codes, construction methods, and internal fittings, among others). Visual observations of structural engineers within the survey team did not reveal any notable differences regarding the level of reinforcing and core grouting in the masonry units. Furthermore, personal discussions with locals did not reveal any differences in construction practises. Despite this, it is insightful to see if our obtained building damage data may suggest otherwise. Table 5 illustrates the distribution of masonry residential buildings surveyed based on their observed damage state. From Table 5 it can be seen that DS3 and DS4 are the damage states in which a similar, and large enough, number of observations were made. Comparisons for these damage states therefore permit statistically reasonable conclusions to be made regarding the compatibility of the data from the two

Table 6 Median and standard deviation (water depth) values of various fragility functions derived in this manuscript. Building type

Generic Masonry residential Shielded/unshielded masonry residential

Debris/no debris masonry residential

Damage state, DSi 1

2

3

4

5

x50a σb x50a σb x50a

0.29 0.43 0.29 0.46 –c

0.48 0.49 0.46 0.40 –c

σb

–c

–c

x50a –c

–c

–c

–c

–e –e –e –e

–e –e –e –e

1.84 0.62 1.86 0.41 3.11/ 1.43 0.49/ 0.40 1.43/ 1.95 0.32/ 0.40 3.45 0.54 1.26 0.4

2.77 0.55 2.49 0.40 3.89/ 2.25 0.56/ 0.42 –d

σb

1.23 0.58 1.28 0.35 1.39/ 1.16 0.37/ 0.36 0.92/ 1.38 0.36/ 0.32 1.38 0.56 1.15 0.38

Reinforced concrete residential x50a σb Timber residential x50a σb

countries. Fig. 10 illustrates the fragility functions obtained using solely data from American Samoa or Samoa for DS3 (a similar relationship was observed for DS4). It can be seen that the mean and standard deviation of the fragility functions are quite similar. Explicit consideration of the epistemic uncertainties which are inherent in the derived fragility curves (e.g. Bradley, 2010), is beyond the scope of this manuscript, but statistical tests showed that neither mean nor standard deviations of the two fragility curves in Fig. 10 are statistically different. Comparisons between the fragility curves for other damage states were also conducted, however as noted above, the lack of data for such damage states meant statistical significant inferences were difficult. Based on the finding given in Fig. 10, and the lack of evidence from observations and eyewitness discussions to suggest otherwise, it is concluded that the datasets obtained in American Samoa and Samoa can be considered compatible. Despite being unable to formally test it because of a lack of empirical data, this compatibility assumption is adopted for both masonry residential and all other building classes. 4.2.2. Masonry residential fragility functions Using the combined American Samoa and Samoa dataset for masonry residential structures, fragility functions were developed for the five damage states in Table 4 as a function of maximum tsunami water depth. Fig. 11 compares these ‘masonry residential’ fragility functions with those in Fig. 8a derived for generic Samoan buildings (i.e. ignoring building classification). While the fragility functions for a given damage state are similar in terms of median water depths (reflecting the fact that 60% of the data used to develop the ‘generic’ fragility functions is from masonry residential buildings), it is important to note that the standard deviation of the masonry residential fragility functions is significantly smaller than for the generic fragility functions for some damage states, namely DS3–DS5. As will be seen in subsequent sections, this is due to the different structural characteristics of the different building classes, which, when neglected, lead to a large standard deviation. On the other hand, the similarity between the first two damage states of the masonry residential and generic fragility function can be attributed to the fact that these two damage states (‘light’ and ‘minor’) largely represent non-structural damage (Table 4), and therefore would not be expected to vary significantly between building classes which have a similar societal use (i.e. residential, commercial etc.). 4.3. Shielding and debris effects on fragility It was seen in the previous section that by considering only a single building class (i.e. masonry residential structures), the uncertainty in the fragility functions could be reduced. This classification of buildings reflects the fact that the capacity of different building types will be different. The aim of this section is to understand how to quantify

–d 7.3 0.94 1.62 0.28

a

x50 = exp(μlnEDP|i) is equal to the median of the lognormal fragility function. σ = σlnEDP|i is the standard deviation of the lognormal fragility function. The effect of shielding and debris is not considered for DS1 and DS2. d The number of data to assess the influence of debris for DS5 is insufficient. e As discussed in the text, DS1 and DS2 are ‘non-structural’ damage states so are independent of building type (and so are equal to that for masonry residential structures). b c

Fig. 10. Comparison between DS3 fragilities for Am. Samoan and Samoan masonry residential buildings.

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

Fig. 11. Comparison of fragility functions developed using all obtained data and those using only masonry residential data.

tsunami-induced demand more precisely than simply using the maximum water depth. More specifically, the effects of shielding and debris on masonry residential fragility functions are examined. Damage caused by tsunami-induced wave impact on buildings is a function of the depth of the water, impact velocity, inundation duration and any entrained sediment or debris (Dale and Flay, 2006; Rossetto et al., 2007; Dall'Osso et al., 2010; Leone et al., 2010; Pistrika and Jonkman, 2010). Both, water depth and velocity directly influence the hydrodynamic pressure that waves apply to structures, while entrained debris can apply additional impact forces to structures, which is a function of the debris momentum (i.e. proportional to the water velocity) (Okada et al., 2005). Post-event observations of tsunami-induced damage to buildings can, however, only attempt to approximate the relative effects of these three salient features. As previously discussed, the maximum water depth of the tsunami that the structure is subjected to can be quantitatively obtained, either by direct measurement or inference. Water velocity and entrained debris, on the other hand are very difficult to measure or quantify directly and hence, are often inferred based on post-tsunami observations. Fritz et al. (2006) for instance used an indirect method to estimate flow velocities. Survivor videos were used and cross-correlation based particle image velocimetry analysis conducted. Other approaches used the thickness and grain size distribution of tsunami deposits as these are correlated to the wave height and flow velocity (Liu, 2005). The level of foundation scouring can be used as a proxy for water velocity, but this effect is highly dependent on the type and density of the foundation soil. Similarly, post-tsunami observations of nearby debris can be used as an indicator of the likely role that entrained debris may have played, but only in a few cases (via eyewitness accounts or direct observations) can entrained debris be directly attributed to observed damage. For the analysis of the debris effect we used only samples where the influence of movable objects was evident. It is important to note that these three features of the severity of a tsunami-impact on structures are of course inter-related. Tsunamiwave velocity is related to the depth of the water (Bryant, 2008) while the amount of debris which can be entrained will be related to the uplift forces (i.e. flow depth and velocity) which can be applied. It is therefore logical that an attempt to correlate building damage to tsunami wave severity first begins by examining the correlation between building damage and tsunami flow depth (as examined in the previous sections). Based on the examination of these results further inference as to the magnitude of the secondary effects of wave velocity and debris which are not accounted for by simply using flow depth can be examined. 4.3.1. Effect of shielding The geographic position of a structure relative to other structures, or topographic obstructions and vegetation (Kaplan et al., 2009), can

167

have a pronounced effect on the severity of a tsunami wave on a building (Dall'Osso et al., 2010). Vegetation and obstructions can lead to a reduction in water level, velocity and amount of entrained debris impacting the structure under consideration (herein referred to as shielding) (Iverson and Prasad, 2007). While shielding possibly reduces the amount of entrained debris impacting the structure, the reduction in water velocity also means a reduction of impact forces that any entrained debris will impart to the structure. The reduction in flow depth is directly accounted for by using flow depth as a predictor variable in the fragility functions. The other two aforementioned effects of shielding, however, are not accounted for directly, and are examined in this section. Anecdotal evidence of shielding has been previously observed in post-tsunami surveys (Reese et al., 2007; Leone et al., 2010). However, based on limited quantity of empirical data and the methodology for comparison, Reese et al. (2007) were not able to quantify the effect of shielding on fragility functions. As a result of the inability to determine the effect of shielding using data from previous tsunamis, it was explicitly decided in the present survey to classify buildings as shielded or exposed. The methodology to identify a shielded structure was based on the existence of an obstruction (either another structure or a significant topographic feature) located directly in front (i.e. on the sea-facing side) of the structure under consideration. None of the surveyed sites had mangroves and beach forests or a greenbelt to provide a significant shielding effect as described by Hiraishi and Harada (2003), Danielsen et al. (2005) or Kaplan et al. (2009). This qualitative measure of shielding was adopted because of its simplicity. It obviously does not account for effects such as tsunami impact from a direction which is not perpendicular to the shore line, or the fact that building damage can be caused by the outgoing wave as well as the incoming wave. Although information based on eyewitness accounts was collected in this regard, the information was often contradictory and highly uncertain and consequently not taken into account. Fig. 12 illustrates the observed data for masonry residential buildings and damage states DS3–DS5. In Fig. 12, surveyed buildings that were classified as shielded are identified with a green square, and unshielded buildings with a blue circle. Those data for which debris effects were significant (further explained in the following section) have been additional marked with a red centre. Based on these groups of data (i.e. shielded and unshielded), fragility functions were developed. Fig. 12 compares these shielded and unshielded fragility functions with each other, as well as relative to the masonry residential fragility functions that were developed without the shielding parameter (i.e. Fig. 11). As logic would suggest, it can be seen for all buildings in DS3, DS4, and DS5, that the probability of exceeding a given damage state for a given water depth is less for a shielded structure than for a non-shielded structure. Furthermore, the differences between the median water depths for the shielded and unshielded fragility functions are 0.23 m, 1.68 m, and 1.64 m, which illustrates that the effect of shielding is much more pronounced for DS4 and DS5 (i.e. severe and complete damage). Another feature which can be observed from Fig. 12 is that the fragility functions for shielded structures have a larger standard deviation than those developed for unshielded structures (and those ignoring shielding). While further study is needed to clarify this observation it is perceived that this is the result of both the qualitative nature of the shielding classification, and also the lower number of shielded data points which were available in the logistic regression analysis. Fig. 12 depicts the influence of shielding for masonry residential structures only for DS3–DS5, but not DS1 and DS2. Firstly, this is because the number of samples which were available for these damage states was small and no statistically significant conclusions could be drawn. Secondly, and more importantly, it is necessary to bear in mind the physical mechanisms that we are attempting to capture using the qualitative shielding variable in comparison with the physical descriptions that these damage states represent. The

168

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

As previously mentioned, any direct observations of debris-impact (i.e. from remnants of debris still wedged in/against structures, or from eyewitness reports) were catalogued as part of the building damage data collected in the survey. Therefore, by using a binary classification to describe surveyed structures as ‘debris’ impacted, or ‘no debris’ impacted, it is possible to examine possible effects on the resulting fragility functions. Fig. 13 illustrates the DS3 and DS4 masonry residential fragility functions obtained using logistic regression on data identified as debris impacted and non-debris impacted. The effect of debris on DS5 is not shown here because the lack of data meant any statistically significant inferences were not possible. It can be seen, that as expected, both DS3 and DS4 fragility functions for debris-impacted structures have a lower median water depth than non-debris impacted structures. Fig. 13a illustrates for example that at a water depth of 1.0 m there is a 60% probability of being in or exceeding DS3 for a structure impacted by debris, and only a 15% probability for a structure which is not impacted by debris. The similarity between the fragility functions for non-debris impacted structures and those ignoring debris impact altogether, represents the fact that debrisimpacted observations represented only a small proportion of the overall building damage dataset. As with shielding, it was not possible to infer the impact of debris on DS1 and DS2 based on the empirical data alone. This is primarily due to the fact that where debris-impact is significant, it is unlikely that the structure will only have light or minor damage (i.e. DS1 or DS2). Furthermore, DS1 or DS2 essentially represent non-structural damage states, whereas non-negligible debris-impact is expected to cause some structural damage. While Fig. 13 shows that debris-impact is clearly an important consideration in the fragility of masonry residential structures, as elaborated upon later in the manuscript, the consideration of debris-

Fig. 12. Effect of ‘shielding’ on building fragilities: (a) Damage state 3, DS3; (b) Damage state 4, DS4; and (c) Damage state 5, DS5. Green squares and blue circles represent ‘shielded’ and ‘unshielded’ data points, respectively. Those data in which significant debris influence was observed are further marked with a red centre.

descriptions of DS1 and DS2 (i.e. light and minor damage) in Table 4 indicate that such damage states are generally the result of nonstructural damage, which primarily occurs due to saturation of interior walls and other internal non-structural components. Such damage can be well represented by the depth of water in the building alone. It was therefore assumed that shielding (and debris effects discussed in the subsequent section) does not affect these first two damage states.

4.3.2. Effect of debris It is recognised that damage to structures resulting from tsunamis occurs both from hydrodynamic pressures as well as impact forces from entrained debris (Francis, 2006; Saatcioglu et al., 2007; Bryant, 2008). Despite this recognition, the effects of debris on building fragility have not been quantitatively examined because of the complex site- and event-specific influence of such phenomena.

Fig. 13. Illustration of the effect of debris on the fragilities of buildings: (a) Damage state 3, DS3; and (b) Damage state 4, DS4. Red and blue points represent ‘debris’ and ‘no debris’ data, respectively.

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

impact in tsunami risk assessment is complicated. Fragility functions which do not consider the effects of debris, while imprecise, are still unbiased for residential areas such as those upon which the empirical fragility functions derived here are based. One example where debris effects are very significant is in port facilities with the presence of numerous unfastened containers and other buoyant materials. In such areas, the debris-impacted fragility functions obtained here would be more appropriate. Furthermore, as previously mentioned, it is believed that shielding counteracts, to a limited extent, some debris-impact consequences (although it is not possible to test this based on the empirical data collected for this study). 4.4. Fragility of other structures The limited number of observational building damage data collected for structures other than masonry residential buildings makes robust determination of empirical fragility functions for such structures difficult. In this section, a comparison of such empirical results with the masonry residential fragility functions is given and the results are further discussed and interpreted in terms of physical observations. For both reinforced concrete and timber residential structures, only DS3–DS5 are considered based on the aforementioned logic that DS1 and DS2 are non-structural damage states, and are therefore not influenced by building class (within the residential category). 4.4.1. Reinforced concrete (RC) residential structures A total of 13 out of the 201 surveyed buildings were RC residential structures. Figs. 14a–c illustrate the observed data, computed fragility functions and their comparison with those of masonry residential structures. It can be seen that the DS3 (moderate damage) fragility functions are similar while those for DS4 and DS5 illustrate that RC residential structures are notably less fragile than masonry residential structures. Fig. 14d illustrates a RC building in Poloa which was subjected to an estimated flow depth of 5.0 m. It can be seen that the building has complete damage apart from the RC frame. Close inspection of this structure revealed in fact that the RC frame was essentially undamaged (no cracks of a visible size were observed). While the RC frame in Fig. 14d is essentially undamaged, the structure was still classed as being in DS4 (i.e. severely damaged). Hence, it is logical that the superior performance of RC frames only influences the fragility functions when severe and complete collapse of more vulnerable structures would be expected. While Fig. 14d provides clear observational evidence for the qualitative comparison between the empirically derived fragility functions for RC and masonry residential structures observed in Fig. 14a–c, care should be taken in using the derived fragility parameters for the RC residential structures directly due to the paucity of data upon which they are based. 4.4.2. Timber residential structures A total of 24 out of the 201 surveyed buildings were residential timber structures. Figs. 15a–c illustrate the observed data, computed fragility functions and their comparison with those of masonry residential structures. Similar to the observations between RC and masonry residential structures, it can be seen that the DS3 (moderate damage) fragility functions for masonry and timber residential structures are similar. One point of note regarding the computed timber residential fragility functions is that because of a lack of data for small water depths (less than 1.0 m), the two data points which had unusual debris-impact (identified in Fig. 15a and a photograph in Fig. 15d) were not considered in the logistic regression. Examination of the fragility functions for DS4 and DS5 illustrate that timber residential structures are notably more vulnerable than masonry residential structures.

169

Foundation failure was a damage mode that was frequently observed for the timber residential structures surveyed. Fig. 16 illustrates two examples of such observed foundation failures. The reasons for such failures were either direct failure of the timber itself because of insufficient foundation dimension (Fig. 16a), or failure of the structure–foundation connection (Fig. 16b). As such vulnerable failure modes were not observed in equivalent masonry residential structures, they provide visual evidence for the empirically derived differences between the DS4 and DS5 fragility curves for the two structure classes. Again, care should be taken in using the derived fragility function parameters for timber structures in Fig. 15 because of the paucity of data used in their construction. Various other building attributes such as the use or the number of storeys, which are also relevant for the vulnerability of a building (Dall'Osso et al., 2010; Dominey-Howes and Papathoma, 2007; Middelmann-Fernandes, 2010) have been collected. However, none of these additional attributes other than the building material/ construction type could be used for the derivation of the fragility functions. The use of the building is to some degree reflected in the construction type as many of the non-residential buildings (e.g. churches) were concrete buildings opposed to the residential houses which were dominantly brick/masonry or timber. Moreover, the sample size of other use classes such as commercial or accommodation was too small to undergo a statistical analysis. The same applies to the number of storeys, only 5% of the surveyed buildings had two storeys. 5. Conclusions Empirical building fragility functions have been developed based on data obtained from the 29th September 2009 South Pacific tsunami. A diverse range of data including topographic surveys, observed water depths, predominant flow directions, inundation limits, building damage, and eyewitness reports were collected by a multi-disciplinary reconnaissance team involving topographic surveyors, tsunami/hydraulic modellers, structural engineers, and risk analysts. The collected observational and quantitative data were used to create fragility functions (probabilistic building damage–demand relationships) for a variety of building types using logistic regression. The developed fragility functions show that the severe and collapse damage states (DS4 and DS5, respectively) are clearly a function of building type, with residential timber structures the most fragile, followed by masonry residential and reinforced concrete residential structures. Based on logical reasoning, the light and minor damage states (DS1 and DS2, respectively) were considered as ‘non-structural’ damage states, and therefore independent of building type. The obtained empirical data also allowed the first quantitative examination of the effects of ‘shielding’ and ‘entrained debris’ on fragility functions. Based on residential masonry building data, it was clearly shown that shielding can reduce the fragility of structures (i.e. reduce the damage state exceedance probability for a given water depth), while entrained debris increases the fragility. The probability of an unshielded building exposed to one metre of inundation to be in damage state 4 (DS4) is for instance 16% whereas the probability of a shielded one is only 0.3%. The probability of being in DS5 is 2.7% compared to 0.8% for the shielded building. These results roughly confirm the observations made in the aftermath of the Java tsunami where exposed buildings have sustained damage levels 2 to 5 times higher than the shielded ones (Reese et al., 2007). Looking at the effect of debris for the same inundation depth, the probability of being in DS3 or DS4 is approximately three times lower without debris (11% compared to 46% and 4.8% to 13.2%). The difference is significant and can be the critical factor whether a building withstands the tsunami or not. These aspects should be considered in land-use planning. It also highlights the need to protect coastal habitats which can help reduce the impacts from tsunamis.

170

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

Fig. 14. (a)–(c) Fragility functions for DS3–DS5 reinforced concrete residential structures, as compared to masonry residential structures. Green squares and blue circles represent ‘shielded’ and ‘unshielded’ data, respectively. Those data in which significant debris influence was observed are further marked with a red centre; and (d) a reinforced concrete building in Poloa which was subjected to an estimated flow depth of 5.0 m.

As Douglas (2007) stated, fragility functions are an essential component of risk assessment. The empirical fragility functions for structures subject to tsunami-induced hazards resulting from this study contribute to the ongoing development of robust methods for explicitly estimating tsunami-induced risk to coastal communities. These fragility functions will improve assessment tools such as the New Zealand multi-hazard impact and risk assessment tool RiskScape (Reese and Smart, 2008) or the Papathoma Tsunami Vulnerability Assessment model (PTVA) (Dominey-Howes and Papathoma, 2007) and allow a more realistic damage assessment of the potential tsunami impacts in other areas.

On the other hand, fragility functions have limitations, either due to some of the simplifications described in Section 4, or the lack of sufficient high quality observational evidence, in particular inundation depth, velocity and representative damage states. If for instance the range of EDPs for the buildings that experienced damage state DSi does not overlap with the range of EDPs for the buildings that did not experience this level of damage, there can be multiple values of μlnEDP|DSi that will yield a fitted lognormal distribution that passes through all the data points. Hence, there could be a range of possible solutions for the fitted functions in this bounded area (Ramirez and Miranda, 2009).

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

171

Fig. 15. (a)–(c) Fragility functions for DS3–DS5 timber residential structures, as compared to masonry residential structures. Green squares and blue circles represent ‘shielded’ and ‘unshielded’ data, respectively. Those data in which significant debris influence was observed are further marked with a red centre; and (d) a timber building in Amanave with significant entrained debris annotated in panel (a).

This is also the reason why synthetic fragility functions are often used instead of empirical functions (Middelmann-Fernandes, 2010). There is an uncertainty associated with empirical functions because they may be site-dependent and not applicable to other areas without expert's adjustments to account for regional and structural differences. There might also be some bias because of the specific circumstances of the event the data is based on. The influence of the velocity in this case could not be quantified, because of the paucity of data. Consequently, the effect is buried in the fragility functions and contributes to the uncertainty. Empirical fragility functions often do not take into account mechanical properties of the structure. Because of the time con-

straints of field surveys, comprehensive structural inspections of buildings are often not feasible. If these differences in the structural capacity are ignored, and the functions are applied to individual structures or smaller clusters of buildings, not all buildings of the same type will suffer the same level of damage for a given event intensity and damages might be under or overestimated. Some of the fragility functions are also based on a relatively small number of field observations and are hence subject to greater uncertainty. Due to contradictory data it was also not possible to analyse the influence of the wave direction and impact from backwash. Despite these limitations, the findings presented here provide a significant contribution to our understanding of tsunami damage. In

172

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173

Fig. 16. Illustrations of foundation failure of American Samoan timber residential buildings.

some areas more research is required and the sample size needs to be extended. Acknowledgements We thank the many people who willingly gave assistance, advice and encouragement during the reconnaissance mission. In particular, we would like to thank the New Zealand Ministry for Civil Defence and Emergency Management (MCDEM), the New Zealand Defence Force, and the High Commissioner in Samoa for their support and provision of data and information. We also acknowledge funding from the New Zealand Foundation for Research Science and Technology through the RiskScape programme (RISK0801). Finally, we acknowledge the efficient and helpful support of the numerous people in American Samoa and Samoa, in particular Don Vargo (Research Coordinator at the American Samoa Community College), Gerald Freyer (NOAA), and Litea Biukoto (SOPAC). The data collected in Samoa was done so as part of the UNESCOITST effort (Dominey-Howes and Kong, this issue). We would like to thank the Australian Tsunami Research Centre and the University of

the South Pacific for facilitating this effort. Furthermore, we are grateful to Adam Jowitt, Guy Urban, Roberto Tonini, Beatriz Brizuela, Gianluca Pagnoni and Faafetai Tevaga for their direct assistance in collecting the building damage data in Samoa. References Annunziato, A., Franchello, G., Ulutas, E., De Groeve, T., 2009. 29 September 2009 Samoa tsunami. JCR Scientific and Technical Reports 2009. EUR 24068 EN. Beavan, J., Wang, X., Holden, C., Wilson, K., Power, W., Prasetya, G., et al., 2010. Nearsimultaneous great earthquakes at Tongan megathrust and outer rise in September 2009. Nature 466, 959–963. Bradley, B.A., 2010. Epistemic uncertainty in component fragility functions. Earthquake Spectra 26 (1), 41–62. Bradley, B.A., Dhakal, R.P., Cubrinovski, M., MacRae, G.A., Lee, D.S., 2009. Seismic loss estimation for efficient decision making. Bulletin of the New Zealand Society for Earthquake Engineering 42 (2), 96–110. Bryant, E., 2008. Tsunami, The Underrated Hazard, 2nd ed. Springer, Chichester. Dale, K., Flay, S., 2006. Internet. Proceedings of the Australian Earthquake Engineering Society Conference; 2006 Nov 24–26; Canberra, Australia, pp. 179–184. [cited 2010 May 7] Available from: http://www.aees.org.au/Proceedings/2006_Papers/ 179_Dale_Flay.pdf. Dall'Osso, F., Gonella, M., Gabbianelli, G., Withycombe, G., Dominey-Howes, D., 2009. A revised (PTVA) model for assessing the vulnerability of buildings to tsunami damage. Natural Hazards and Earth System Sciences 9, 1557–1565.

S. Reese et al. / Earth-Science Reviews 107 (2011) 156–173 Dall'Osso, F., Maramai, A., Graziani, L., Brizuela, B., Cavalletti, A., Gonella, M., et al., 2010. Applying and validating the PTVA-3 model at the Aeolian Islands, Italy: assessment of the vulnerability of buildings to tsunamis. Natural Hazards and Earth System Sciences 10, 1547–1562. Dalrymple, R.A., Kriebe, D.L., 2005. Lessons in engineering from the tsunami in Thailand. Bridge 35, 4–13. Danielsen, F., Sørensen, M.K., Olwig, M.F., Selvam, V., Parish, F., Burgess, N.D., et al., 2005. The Asian tsunami: a protective role for coastal vegetation. Science 28, 643. doi:10.1126/science.1118387. Dias, W.P.S., Yapa, H.D., Peiris, L.M.N., 2009. Tsunami vulnerability functions from field surveys and Monte Carlo simulation. Civil Engineering and Environmental Systems 26 (2), 181–194. doi:10.1080/10286600802435918. Dominey-Howes, D., Kong, L., this issue. A coupled human–environment system study of the 2009 South Pacific tsunami. Earth Science Reviews. Dominey-Howes, D., Papathoma, M., 2007. Validating a tsunami vulnerability assessment model (the PTVA model) using field data from the 2004 Indian Ocean tsunami. Natural Hazards 40, 113–136. Donahue, J., Olsen, M., Thio, H.K., Sommerville, P., 2009. American Samoa Tsunami Reconnaissance Report, Geotechnical Extreme Events Reconnaissance Association. 2009 Sep. GEER Association Report No. GEER-019. Douglas, J., 2007. Physical vulnerability modelling in natural hazard risk assessment. Natural Hazards and Earth System Sciences 7, 283–288. Dudley, W., Faasisila, J., Fonolua, S., Johnston, J., Jowitt, A., Chan-Kau, M., Preller, C., 2011. Learning from the Victims: new physical and social science information about tsunamis from victims of the September 29, 2009 event and other tsunamis. Earth Science Reviews 107, 200–205 (this issue). EERI (Earthquake Engineering Research Institute), 2005. The Great Sumatra earthquake and Indian Ocean tsunami of December 26, 2004. EERI Special Earthquake Report, 6, pp. 1–12. Francis, M.J., 2006. Tsunami Inundation Scour of Roadways, Bridges and Foundations: Observations and Technical Guidance from the Great Sumatra Andaman Tsunami. EERI/FEMA NEHRP 2006 Professional fellowship report. Earthquake Engineering Research Institute. Fritz, H.M., Borrero, J.C., Synolakis, C.E., Yoo, J., 2006. 2004 Indian Ocean tsunami flow velocity measurements from survivor videos. Geophysical Research Letters 33, L24605. doi:10.1029/2006GL026784. Ghobarah, A., Saatcioglu, M., Nistor, I., 2006. The impact of the 26 December 2004 earthquake and tsunami on structures and infrastructure. Engineering Structures 28, 312–326. Gregg, C.E., Houghton, B.F., Paton, D., Lachman, R., Lachman, J., Johnston, D.M., et al., 2006. Natural Warning signs of tsunamis: human sensory experience and response to the 2004 Great Sumatra earthquake and tsunami in Thailand. Earthquake Spectra 22 (S3), S671–S691. Hatori, T., 1984. On the damage to houses due to tsunamis. Bulletin of the Earthquake Research Institute 59 (3), 433–439 (in Japanese). Hiraishi, T., Harada, K., 2003. Greenbelt tsunami prevention in South-Pacific region. Report of Port and Harbour Research Institute 42 (2), 3–25. IOC (Intergovernmental Oceanographic Commission), 2008. Tsunami Glossary. : IOC Technical Series, 85. UNESCO, Paris. Iverson, L.R., Prasad, A.M., 2007. Using landscape analysis to assess and model tsunami damage in Aceh Province, Sumatra. Landscape Ecology 22 (3), 323–331. Jaffe, B.E., Gelfenbaum, G., Buckley, M.L., Watt, S., Apotsos, A., Stevens, A.W., et al., 2010. Am_Sam_tsu_inun_2009. Open-File report USGS OFR. U.S. Geological Survey, Coastal and Marine Geology Program, Western Coastal and Marine Geology, Santa Cruz, CA, p. 1018. Kamataki, T., Matsutomi, H., Murakami, Y., Nishimura, Y., Sakakiyama, T., Tanioka, Y., et al., 2005. Earthquake, Tsunami and Damage in Banda Aceh and Northern Sumatra. Chapter 2, The 2004 Indian Ocean Tsunami Disaster Survey Report. [cited 2010 June 12]. Available from: www.tsunami.civil.tohoku.ac.jp/sumatra2004/C2.pdf. Kaplan, M., Renaud, F.G., Lüchters, G., 2009. Vulnerability assessment and protective effects of coastal vegetation during the 2004 tsunami in Sri Lanka. Natural Hazards and Earth System Sciences 9, 1479–1494. Koshimura, S., Namegaya, Y., Yanagisawa, H., 2009. Tsunami fragility — a new measure to identify tsunami damage. Journal of Disaster Research 4 (6), 479–488. Kutner, M., Nachtsheim, C., Neter, J., Li, W., 2005. Applied Linear Statistical Models. McGraw-Hill/Irwin, New York. Lamarche, G., Pelletier, B., Goff, J., 2009. Historique des tsunamis sur L'archipel de Futuna: Frequence, magnitude et impact sur la communaute insulaire. Historical

173

tsunami in the Futuna Archipelago: frequency, magnitude and impact on the community. Rapport de mission 6–17 Octobre 2009. National Institute of Water and Atmospheric Research, Wellington (New Zealand). Internal Report No. 140. Lay, T., Ammon, C.J., Kanamori, H., Rivera, L., Koper, K.D., Hutko, A.R., 2010. The 2009 Samoa–Tonga great earthquake triggered doublet. Nature 466, 964–968. Leone, F., Lavigne, F., Paris, R., Denain, J.C., Vinet, F., 2010. A spatial analysis of the December 26th, 2004 tsunami-induced damages: Lessons learned for a better risk assessment integrating buildings vulnerability. Applied Geography doi:10.1016/j. apgeog.2010.07.009. Liu, P.L.F., 2005. Tsunami simulations and numerical models. Bridge 35, 14–20. Middelmann-Fernandes, M.H., 2010. Flood damage estimation beyond stage-damage functions: an Australian example. Journal of Flood Risk Management 3, 88–96. NOAA, 2010. NOAA Tide Gauges Measure September 29, 2009 Samoa Tsunami. [cited 2010 Apr 26]. Available from: http://tidesandcurrents.noaa.gov/press/September09Tsunami.shtml. Okada, T., Sugano, T., Ishikawa, T., Takai, S., Tateno, T., 2005. Tsunami Loads and Structural Design of Tsunami Refuge Buildings. The Building Centre of Japan, Tokyo (Japan). [cited 2010 May 3]. Available from: http://www.bcj.or.jp/src/c05_research/results/tsunami2006_1.pdf. Okal, E.A., Borrero, J.C., Chagué-Goff, C., 2011. Historic seismic predecessors to the 2009 Samoa event and their tsunamis. Earth Science Reviews 107, 127–139 (this issue). Omira, R., Baptista, M.A., Miranda, J.M., Toto, E., Catita, C., Catalaõ, J., 2010. Tsunami vulnerability assessment of Casablanca, Morocco using numerical modelling and GIS tools. Natural Hazards 54, 75–95. Papadopoulos, G.A., Imamura, F., 2001. A proposal for a new tsunami intensity scale. Proceedings of International Tsunami Symposium; 2001 Aug 7–10; Seattle, US. IUGG, pp. 569–577. Peiris, N., 2006. Vulnerability functions for tsunami loss estimation. First European Conference on Earthquake Engineering and Seismology; 2006 Sep 3–8; Geneva, Switzerland. Paper No. 1121. Pistrika, A.K., Jonkman, S.N., 2010. Damage to residential buildings due to flooding of New Orleans after hurricane Katrina. Natural Hazards 54, 413–434. Porter, K., Kennedy, R., Bachman, R., 2007. Creating fragility functions for performancebased earthquake engineering. Earthquake Spectra 23 (2), 471–489. Ramirez, C.M., Miranda, E., 2009. Building-specific Loss Estimation Methods & Tools for Simplified Performance-based Earthquake Engineering. The John A. Blume earthquake Engineering Center, Department of Civil and Environmental Engineering, Stanford University, Stanford (CA). Report No. 171. Reese, S., Smart, G., 2008. High resolution inundation modelling as part of a multihazard loss modelling tool. In: Samuels, P., Huntington, S., Allsop, W., Harrop, J. (Eds.), Flood Risk Management. Research and Practice. : Proceedings of the European Conference on Flood Risk Management Research into Practice (FloodRisk 2008); 2008 Sep 30–Oct 02. Francis & Taylor, Oxford, UK, London, pp. 1663–1668. Reese, S., Cousins, W.J., Power, W.L., Palmer, N.G., Tejakusuma, I.G., Nugrahadi, S., 2007. Tsunami vulnerability of buildings and people in South Java. Field observations after the July 2006 Java tsunami. Natural Hazards and Earth System Sciences 7 (5), 573–589. Rossetto, T., Peiris, N., Pomonis, A., Wilkinson, S.M., Del Re, D., Koo, R., et al., 2007. The Indian Ocean tsunami of December 26, 2004: observations in Sri Lanka and Thailand. Natural Hazards 42, 105–124. Ruangrassamee, A., Yanagisawa, H., Foytong, P., Lukkunaprasit, P., Koshimura, S., Imamura, F., 2006. Investigation of tsunami-induced damage and fragility of buildings in Thailand after the December 2004 Indian Ocean tsunami. Earthquake Spectra 22 (S3), S377–S401. Saatcioglu, M., Ghobarah, A., Nistor, I., 2007. Performance of structures affected by the 2004 Sumatra tsunami in Thailand and Indonesia. In: Murty, T.S., Aswathanarayana, U., Nirupama, N. (Eds.), The Indian Ocena Tsunami. Francis & Taylor, London, pp. 297–321. Shuto, N., 1993. Tsunami intensity and disasters. In: Tinti, S. (Ed.), Tsunamis in the World. Kluwer Academic Publisher, Dortrecht, pp. 197–216. Stansfield, K., 2005. Effects of the Asian tsunami on structures. Journal of Structural Engineering 83 (11), 20–21. Tsuji, Y., Yanuma, T., Murata, I., Fujiwara, C., 1991. Tsunami ascending in rivers as an undular bore. Natural Hazards 4 (2), 257–266. USGS (U.S. Geological Survey), 2009. Magnitude 8.1 — Samoa Islands regions [Internet]. USGS Earthquake Hazards Program, Sunrise Valley (VA). [cited 2010 Mar 20]. Available from: http://earthquake.usgs.gov/earthquakes/recenteqsww/Quakes/ us2009mdbi.php (last accessed: May 2010).