Probabilistic Earthquake Damage Curves for ... - Earthquake Spectra

Probabilistic Earthquake Damage Curves for Low-Rise Buildings Based on Field Data Bjarni Bessason,a) M.EERI, Jón Örvar Bjarnason,b) Ari Gudmundsson,b) Júlíus Sólnes,a) and Scott Steedmanc)

All buildings in Iceland are registered in an official database that contains detailed information about them, and insurance against natural disasters is obligatory. When a destructive earthquake occurs, all damage is reported, and the repair and replacement cost for every affected building is evaluated. In May 2008, a shallow earthquake of magnitude M w ¼ 6.3 struck in South Iceland. A great deal of damage occurred, but fortunately, there was no loss of life. The recorded maximum PGA was 0.88 g. Detailed and complete information of all real estate property and the damage incurred, along with recorded strong-motion data and an area-specific attenuation model, have provided an opportunity to create probabilistic damage curves for the building stock in the affected area. The damage model obtained from the 2008 earthquake was tested and verified by using it to back-calculate the damage that occurred in the two South Iceland earthquakes of June 2000 ðM w ¼ 6.5Þ. [DOI: 10.1193/1.4000082]

INTRODUCTION BACKGROUND

The seismicity in Iceland is related to the Mid-Atlantic Plate boundary that crosses the country. Within the country, the boundary shifts eastward in the south and back toward the west in North Iceland through two complex fracture zones. The southern zone, called the South Iceland Seismic Zone (SISZ), is located in the South Iceland lowland, while the other, the Tjörnes Fracture Zone (TFZ), lies mostly off the northern coast of Iceland (Einarsson 1991). The largest earthquakes in the country have occurred within these zones. In South Iceland, they are mostly associated with a strike-slip motion on N-S fractures, whereas in the north, the earthquake foci seem to be concentrated on three distinct SE-NW seismic lines. In the SISZ, earthquakes tend to occur in sequences, which, on average, occur roughly every hundred years when accumulated strain energy, caused by the tectonic plate movements, is released (Einarsson 1991). Since A.D. 1700, 16 earthquakes of magnitudes greater than 6.0 ðM s Þ have occurred in the SISZ, and 9 earthquakes in the TFZ. The maximum possible magnitude is estimated to be around 7.0 ðM w Þ for both zones; this upper bound is caused by relatively low rock strength and thin crust in the earthquake zones. In the year 2000, two earthquakes (17 and 21 June) of

a) b) c)

Faculty of Civil and Environmental Engineering, University of Iceland, Hjardarhagi 2, 107 Reykjavik, Iceland VERKIS consulting Engineers Ltd., Armula 4, 108 Reykjavik, Iceland Steedman & Associates Ltd., 42 Hillgate Place, London W8 7ST, UK 1353

Earthquake Spectra, Volume 28, No. 4, pages 1353–1378, November 2012; © 2012, Earthquake Engineering Research Institute

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magnitude 6.5 ðM w Þ occurred in South Iceland. The highest recorded PGA in these quakes was 0.84 g at the Thjórsá Bridge site (Bessason and Haflidason 2004). This high acceleration peak was caused, however, by soil amplification in a very special soil profile consisting of 8–10 m thick lava cap at the top of 18–20 m thick alluvial sediments (Bessason and Kaynia 2002). On 29 May 2008, a 6.3 ðM w Þ earthquake shook the area again. The distances between the epicenters of these three earthquakes are less than 35 km. These three events constitute an earthquake sequence, typical for the area. The last sequence before the 2000 and 2008 earthquakes occurred in 1896, when five earthquakes ðM s > 6Þ struck in the area, starting in the eastern part of the SISZ and migrating west during a two-week period, with the last major earthquake around the Selfoss farm (now a small town). The SISZ covers the South Iceland lowland (SIL), the largest agricultural region in Iceland. Several small towns or villages, schools, medical centers, industrial plants, geothermal and hydropower plants, and several major bridges are within this area. In fact, it contains the entire infrastructure that characterizes modern society. The population in the region is about 18,500 inhabitants (as of January 2008), and there are approximately 6,000 residential houses, mostly low-rise buildings. In the 2000 and 2008 earthquakes, no residential buildings collapsed, and fewer than five farm buildings collapsed. However, a considerable number of houses were damaged. The most common damage consisted of walls cracking and spalling and damage to flooring and interior fixtures. At least 40 houses were judged unrepairable after the June 2000 earthquakes, and about 30 after the May 2008 earthquake. It should be emphasized that although no residential houses collapsed in the 2000 and 2008 earthquakes, in spite of high recorded peak ground accelerations, this was not the case during the 1896 earthquake sequence, when a total of 1,309 residential buildings and 2,383 farm buildings collapsed (Sigbjörnsson et al. 1998, Thoroddsen 1899) At that time walls of houses were mainly built of turf and stone, while the roof system consisted of turf supported by timber beams and rafters. Due to both the wall and the roof system,s these houses were therefore quite heavy, and they had low inherent strength against lateral forces. The earthquake magnitudes in the 1896 sequence were similar to those of the 2000 and 2008 quakes, but the population was much smaller, and the formation of villages and small towns had not yet started. PROPERTY DATABASE AND CATASTROPHE INSURANCE

All properties in Iceland are registered with an ID number in an official database, the Icelandic Property Registry. It contains detailed information about the type of use (e.g., residential, school, hospital, farm building, and so on), the date of construction, the number of stories, the building material, and the GPS coordinates of each property. It also contains results of valuation, both for taxation and reconstruction insurance value (replacement value). Fire insurance of buildings is mandatory in Iceland. The fire insurance valuation of all buildings is also assessed by the Iceland Property Registry. The fire valuation is based on replacement cost, less the depreciation of building materials, age, and upkeep. The valuation for fire insurance also provides the basis for compulsory catastrophe insurance against earthquakes, volcanic eruptions, floods, and landslides, which is managed by a public company, Iceland Catastrophe Insurance. Therefore, in the wake of a natural disaster, all damage (if any) in every estate is recorded, in order to enable compensation for the estimated repair or replacement cost. Nevertheless, it is up to the owner of each building to report damage;

PROBABILISTIC EARTHQUAKE DAMAGE CURVES FOR LOW-RISE BUILDINGS

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otherwise, no registration takes place. In general, everybody is well aware of the obligatory catastrophe insurance, so it is realistic to believe that all damage is duly recorded. The deductible for each property is also very low (US$560), so that should not dissuade owners from reporting damage. Damage claims are filed comprehensively by two trained technicians, and classified into a number of categories, as described later in this paper. The Catastrophe Fund also covers telecommunication and power lines, the public utilities system, and all road bridges with span length over 50 m, although road damage as such is not covered. The Earthquake Engineering Research Institute of the University of Iceland operates a strong-motion network in Iceland, which has been gradually expanded since its implementation in 1985 (Sigbjörnsson et al. 2004, Halldórsson et al. 2009). The South Iceland earthquakes of June 2000 and May 2008 added valuable data to the Icelandic strong-motion database. It can be accessed through the European Strong-Motion Database (ISESD; Ambraseys et al. 2002). Most of the damage in the 2000 earthquakes was spread widely over the South Iceland lowland, whereas the damage of the 2008 earthquake was more concentrated in the two small towns Selfoss and Hveragerdi, closest to the epicenter (see Figure 1). Strong-motion data were obtained and are available from both these places.

Figure 1. A map of the South Iceland lowland showing the two active faults of the 29 May 2008 earthquake and the main centers of urbanization in the region. The star shows the macroseismic epicenter: 63.98°N and 21.13°W. The figure also shows the recorded PGA (largest horizontal component) at different stations and PGA contours based on the attenuation model given by Equation 1.

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VULNERABILITY AND LOSS STUDIES

Many research projects have been carried out in the past in order to study earthquake damage, derive seismic vulnerability functions for buildings, and to use such functions for damage and loss assessment. Four main procedures can be used for evaluation of vulnerability relationships: (1) judgement-based methods like the one used in ATC-13 (ATC 1985 and 2002); (2) analytical simulations and experiments; (3) use of data from post-earthquake surveys; and, finally, (4) hybrid methods, which in some way combine the other mentioned procedures. All these methods have their advantages and drawbacks. An overview and discussion of these procedures can be found, for instance, in papers by Rosetto and Elnashai (2003) and Rota et al. (2008). Vulnerability curves (see Colombi et al. 2008 and Rosetto and Elnashai 2003), also called fragility curves (see Rota et al. 2008 and 2010), show the probability of reaching or exceeding a specific damage stage on the vertical axis and the ground motion intensity parameter on the horizontal axis. Usually, many curves are shown in the same graph, that is, one for each damage stage. Generally, one graph is needed for each building class. A number of damage scales exist. In most cases they give a descriptive damage index or a verbal description of the damage stage. For instance, none, slight, significant, and collapse in Colombi et al. (2008), or more the detailed none, slight, light, moderate, extensive, partial collapse, and collapse in Rosetto and Elnashai (2003). Each stage can have a more detailed description; for instance, slight is associated with “fine cracks in plaster partitions/infills” in Rosetto and Elnashai (2003). Other similar scales can be found in the HAZUS program (FEMA 1999) and in the European Macroseismic Scale (Grünthal 1998). The study by Hill and Rosetto (2008) addresses what important characteristics should be included in damage scales. It also provides a review, comparison, and ranking of some of the better-known scales. For descriptive scales, a relationship must be determined to convert the damage stage to a monetary loss. These relationships can be difficult to define. Many ground-intensity parameters have been used for the horizontal axis. In the beginning, intensity scales like MSK or MMC were commonly used, but the drawback of using such scales is that they are based on descriptive damage and can therefore be misleading. For this reason, instrumentally recorded parameters like PGA and PGV are more appropriate and more common today. Also, to improve the correlation between observed damage and ground motion intensity, response spectral acceleration or displacement at ordinates for the characteristic (elastic or inelastic) vibration period of the building type in question is used in some studies (Rosetto and Elnashai 2003, Colombi et al. 2008). When instrumental data is not available, attenuation models can be used to predict site-specific earthquake impact. OBJECTIVE

The main purpose of this study is to present probability distribution functions of damage for low-rise buildings, based on observed damage after the May 2008 South Iceland earthquake and an area-specific attenuation model. The damage functions are validated by simulating the damage caused by both the May 2008 South Iceland earthquake and the June 2000 earthquake, where the computed loss could be compared with the actual paid-out loss. As mentioned above vulnerability or fragility curves show the probability of reaching or exceeding a specific damage stage versus the ground motion intensity parameter. In this


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study the available comprehensive damage data has been used to create probability distribution functions (PDF) of damage for different building classes and different intensity levels. This type of presentation is similar to the one used in ATC-13 (ATC 1985 and 2002), except that in this study the PDFs are based on field data but not expert judgement. The damage is expressed as ratio of the repair cost to the official replacement value of the building. These functions are suitable for earthquake loss estimation, and they include the uncertainty in damage ratios as reflected by the data they are based on. Furthermore, if required, it is straightforward to create the expected mean value of the damage ratio as function of ground motion intensity (PGA) for a given building type or curves with some other preferred confidence level (e.g., the mean plus one standard deviation, 90% probable loss, and so on). On the other hand the functions give no information about the actual physical damage or the damage stage. However, additional information is presented in the paper, which makes it possible to split the monetary damage into structural and nonstructural loss. SEISMIC LOAD THE ÖLFUS EARTHQUAKE OF 29 MAY 2008

On 29 May 2008, a strike-slip earthquake occurred in the South Iceland Seismic Zone. It has been called the Ölfus earthquake (after the name of the region). It consisted of movements on two separate faults, as shown in Figure 1. It was initiated on the eastern fault, which triggered the slip on the western fault about one second later. A macroseismic epicenter has been determined at 63.98°N and 21.13°W (Sigbjörnsson et al. 2009). The magnitude of the combined event has been estimated to be 6.3 ðM W Þ. Accelerograms were logged on the Icelandic strong-motion network in the small towns of Hveragerdi and Selfoss (Figure 1). The new ICEARRAY system, a small-aperture strong-motion array in Hveragerdi, also collected valuable data (Halldórsson and Sigbjörnsson 2009). Selected time histories and response spectra can be found in the ISESD database (Ambraseys et al. 2002). In Hveragerdi, the maximum PGA (largest component) was recorded 0.66 g in the strongmotion network and in Selfoss at 0.54 g (Halldórsson and Sigbjörnsson 2009). PGA values as high as 0.88 g were registered at one station in the ICEARRAY system. In Figure 2, the response spectra from one station in Hveragerdi and another in Selfoss, for both lateral components, are shown. Both these stations are on rock. To relate the recorded response spectra to the seismic design load in the area, the figure also shows the linear response spectrum for rock as given in the Eurocode 8 (European Committee for Standardization 2004) and the associated national document for Iceland. It should be noted that the response spectra from both these stations exceeded the Eurocode spectrum in certain period bands. In Hveragerdi, this is evident for both the short and long (above 0.6 s) periods. Regarding the longer periods, they are most likely affected by the near-fault ground-motion (Somerville et al. 1997), which has to be taken into consideration when designing structures with long natural periods. The 370 m base-isolated Óseyrar Bridge, located close to the south end of the western fault of the Ölfus earthquake (see Figure 1), was subjected to such action and experienced some damage (Jónsson et al. 2010). At the time of the 2008 earthquake, the reference PGA for a 475-year return period was 0.4 g for both Hveragerdi and Selfoss and elsewhere in the epicentral region (used in Figure 2). In December 2010, new national annexes and a new set of Eurocodes came in effect in Iceland, whereby the 475-year return period value was

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2.5 x−component y−component EC8 − a =0.40g − Soil A g

Acceleration − (g)

2

1.5

1

0.5

0

0

0.5

1

1.5

2

2.5

3

Natural period − (s)

(a) 2.5 x−component y−component EC8 − a =0.40g − Soil A g

Acceleration − (g)

2

1.5

1

0.5

0

0

0.5

1

1.5

2

2.5

3

Natural period − (s)

(b) Figure 2. Response spectra (5% damping ratio) for the two horizontal components at (a) Hveragerdi (retirement home) and at (b) Selfoss (City Hall). Both these locations are rock sites. For comparison, the Eurocode 8 spectrum for rock sites is also shown.

increased to 0.5 g in the South Iceland lowland. The earlier version of the EC8 seismic code came into effect in Iceland in July 2002. From that date and until the Ölfus Earthquake in May 2008, about 21% of the buildings used in the study was built. This is based on information from the official property database.


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GROUND MOTION INTENSITY PARAMETER

Many buildings in the region were damaged. The observed and registered damage could only be directly related to recorded strong-motion data where damaged structures were located close to instrumented sites. To carry out a comprehensive analysis of the damaged structures, it was therefore necessary to assess ground motion intensity parameters at other sites by area-specific attenuation models. It was deemed important that the choice of parameter should reflect the earthquake response of the type of structures being studied. As the majority of buildings in South Iceland are stiff, low-rise buildings with a short natural period, a PGA-based parameter was considered preferable. PGA parameters can be defined in many ways; for instance: the largest horizontal component, the geometrical mean of both the two horizontal components, the arithmetic mean, or as some kind of effective PGA, etc. (Douglas 1993). An attenuation model based on recorded PGA values from the Icelandic strong-motion network (using both horizontal components at each station) was published in 1999 (Ólafsson 1999). After the two South Iceland Earthquakes in June 2000, which provided a wealth of instrumental data, the model was recalibrated (Ólafsson and Sigbjörnsson 2002). It can be simplified and rewritten in a well-known form as log 10 ðPGAÞ ¼ −2.165 þ 0.5 ⋅ M w − 1.5 ⋅ log 10 ðRÞ þ 0.243 ⋅ P;

EQ-TARGET;temp:intralink-;e1;62;434

(1)

where PGA (g) is the peak ground acceleration, M w is the moment magnitude of the earthquake, and R is the distance to the hypocenter ðR < 100 kmÞ, that is, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (2) R ¼ D2 þ h2 ; EQ-TARGET;temp:intralink-;e2;62;376

in which D (km) is the distance to the epicenter, and h is the depth of the hypocenter ðh ¼ 6.5 kmÞ. The last term in Equation 1 is an error term, where P is a standard normally distributed variable, i.e., P ∈ Nð0; 1Þ. Since log 10 ðPGAÞ is normally distributed, the residuals of PGA are also lognormally distributed. The PGAs from both horizontal components are therefore evenly distributed about the median curve ðP ¼ 0Þ, and the predicted or computed PGA by this method is therefore the median value of both components. It is interesting to compare the PGA ground motion intensity defined in different ways. Since the recorded PGA can be instrument-dependent and include some spikes, it is informative to use an effective PGA in this comparison, which smears out such peaks. The effective PGA can be defined as: 1 ðT 2 − T 1 Þ PGAef f ¼

Tð2

Sa ðTÞdT T1


2.5

(3)

where Sa ðTÞ is the acceleration response spectrum with 5% damping ratio. The lower cut-off period is given as T 1 ¼ 0.1 s, and the upper bound as T 2 ¼ 0.5 s (ATC 1978). For the purpose of this analysis, an upper value of 0.3s is perhaps more appropriate due the high stiffness of almost all buildings in the region. Using the cut-off periods T 1 ¼ 0.1 s and T 2 ¼ 0.3 s, the effective PGA for Hveragerdi and Selfoss is found to be 0.47 g and 0.30 g, respectively, for

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Table 1. Different PGA values as determined/calculated for urban centers in the Ölfus region in the 2008 earthquake

Town/village

Distance to epicenter (km)

PGArec (g)

PGAgeo (g)

PGAeff (g)

PGAcomp (g)

Hveragerdi Selfoss Eyrarbakki Stokkseyri Thorlákshöfn

3.0 7.5 12 14 18

0.67 0.54 -

0.56 0.42 -

0.47 0.30 -

0.50 0.31 0.19 0.16 0.12

the more intensive horizontal component (see Figure 1). The distance from the macroseismic epicenter of the Ölfus earthquake to the urban centers of Hveragerdi and Selfoss is approximately 3.0 km and 7.5 km, respectively, and based on Equation 1, the computed PGA (with P ¼ 0) is 0.50 g and 0.31 g for these two small towns. In Table 1, recorded PGA (largest horizontal component), recorded geometrical mean of PGA for the two horizontal components, effective PGA for the more intensive component based on Equation 3, and computed PGA based on Equation 1 are compared for these two places. In Figure 3, the different PGA values are compared for all stations shown in Figure 1. At distances close to epicenter, where most of the damage occurred, the predicted median values based on the attenuation model (with P ¼ 0) is quite similar to the preferred effective PGA, 0

Peak Ground Accelaraion − (g)

10

−1

10

Attenuation model − Eq.(2) PGA − Largest component PGA − Geometrical mean PGA − Effective

−2

10

0

10

1

10

2

10

Epicentral Distance − (km)

Figure 3. Comparison of the attenuation model and different PGA values computed from the recorded time series during the 2008 event, applying different methods.


Table 2.

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Intensity levels defined by the upper and lower bound of computed PGA values

Intensity level PGA (g)

1

2

3

4

0.05–0.09

0.09–0.18

0.18–0.34

0.34–0.65

but at larger distances, the difference is more pronounced. It is not possible to draw any strong conclusions from this comparison, but it is obvious that by using the attenuation model without the error term (P ¼ 0), high-frequency PGA values are to some extent filtered out as is preferable. In a paper by Rota et al. (2008) the effect of scatter in the PGA is studied, and it is found that the scatter only affects the fragility curves to a limited degree. An area-specific attenuation model for the PGAef f was not available. It was therefore decided to use the attenuation model, given by Equation 1 with P ¼ 0, for computing the ground-motion intensity at each site ðPGAcomp Þ, that is, to work with the median PGA value at all damage sites. INTENSITY LEVELS

In order to define a damage matrix, the seismic action must be divided into several intensity intervals with an associated level. This can be carried out in several ways, but a common procedure is to increase the PGA values by approximately a factor of 2 (i.e., both lower and upper bound), when going from one interval to the next. The intensity levels used in this study are shown in Table 2 and correspond to the range of PGA values presented by Wald et al. (1999). In Rota et al. (2008), a constant interval of 0.1 g is used between the upper and lower bound at each level. BUILDING TYPES The population in the South Iceland lowland is around 18,600 inhabitants (January 2008). Of these, about 14,160 live in the area close to the two faults, mostly in the small towns and villages of Selfoss (6,310), Hveragerdi (2,308), Thorlakshöfn (1,548), Eyrabakki (594), and Stokkseyri (513). The rest live in rural areas (2,887; see Figure 1). Most of the houses are single-family, low-rise buildings of one or two stories, and no buildings are taller than four stories. Only very few properties can be classified as multifamily apartment houses. Based on the official property database, 45% of the buildings are made of concrete, 48% of wood, and 8% of pumice concrete blocks. In 1996 and 1997, a field survey was carried out in the South Iceland lowland as a part of an earthquake mitigation program called SEISMIS (see Sigbjörnsson et al. 1998). The surveying procedure was based upon standardized questionnaires and inspection of architectural and engineering drawings. CONCRETE HOUSES

The field survey showed that concrete residential houses are usually one to two story shear-wall type buildings without a moment-resisting frame. The habitable area is typically 100–150 m2 for each building, and most of them (>95%) were built after 1940. Their layout

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is more or less symmetrical, and most of the interior walls, sometimes all, are non-bearing. The foundations are typically made of concrete, with limited reinforcement and directly founded on rock or thin compacted gravel or sand foundation pad on top of rock. The exterior shear walls are typically 18–20 cm thick. Concrete roof slabs are common, usually 15 cm thick. In houses built before 1980, the concrete strength is low, with characteristic compressive cylinder strength, f ck ¼ 16 MPa (C16 concrete); after 1980, it was increased, usually to C20 concrete ð f ck ¼ 20 MPaÞ, and more recently, to C25 concrete. Today, only ribbed highgrade steel bars ð f yk ¼ 500 MPaÞ are used for reinforcement, but before 1965, non-ribbed low-grade bars ð f yk ¼ 235 MPaÞ were the only alternative. It was then common to use only one or two horizontal 12 mm steel bars above window and door openings. Between 1965 and 1980, this reinforcement was generally increased to one or two 12 mm bars around all openings. After 1980, building authorities requested that a single reinforcement grid, usually 10 mm bars at 250 mm intervals in both the horizontal and vertical direction, be placed in all structural walls. After 1990, the reinforcement was again increased, and it is now common to use double grid reinforcement, except in precast sandwich elements. This issue is still being debated by building professionals. TIMBER HOUSES

Residential timber houses, excluding vacation (summer) houses which were not considered in this analysis, are mainly one-story, single-family, shear-wall buildings of the same size as the concrete residential buildings. The bottom floor slab and the foundations are usually reinforced concrete, as in the concrete houses. The exterior and bearing walls are made of timber-work with plywood cladding sheets and exterior wooden siding. In newer houses, the timber construction is more solid, forming strong shear walls. It should be noted that prescribed wind loads are very high in Iceland, among the highest in Europe. Based on old tradition and craftsmanship, the Icelandic timber houses, especially the newer ones, are therefore strongly built and well suited to withstand earthquake forces. PUMICE HOUSES

These houses are mainly one- to two-story, one-family, shear-wall buildings. They are built of hollow pumice concrete blocks. They were quite common and popular in the middle of the last century because the blocks were cheap and had good insulation properties, considering the requirements at that time. Their durability was, however, limited, and over time, the blocks tended to absorb moisture, losing their insulation capability and resulting in a bad indoor climate. These drawbacks resulted in lessening interest in such houses, and hardly any new ones have been built using this material in the last decades. In some houses, pumice blocks have been used for non-bearing infill walls in addition to the main structural concrete walls and columns. BUILDING CLASSES

When evaluating the damage after the 2008 Ölfus earthquake, all buildings in the South Iceland lowland where classified. For the low-rise residential buildings, two classes were chosen for concrete buildings, two for timber houses, and one for pumice buildings. The age of the buildings was used as a practical means to differentiate between classes. For


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concrete buildings, the dividing year was chosen to be 1980, when changes in their basic structural design took place. For timber houses, there was no equivalent major change in the construction or design practice at any particular time. For simplicity, then, it was decided to use the same year, 1980, to distinguish between the two classes. The pumice buildings are relatively few in number compared to the concrete and timber houses. As this type of structure is becoming less and less important over time, they were all grouped under one class. The classes were labeled Concreteold, Concretenew, Timberold, Timbernew, and Pumice. Figure 4 shows the spatial distribution of these types of buildings in the Ölfus region. It also shows which buildings were damaged and which were not. Table 3 shows the main characteristic of each building class, and Table 4 shows the number of buildings in each class and the intensity level in the region. In very few cases (less than 5%), the damage of buildings was

Figure 4. Spatial distribution of damaged houses after the earthquake of May 2008 (filled star). The epicenters of the 17 June and 21 June 2000 earthquakes are shown with unfilled stars.

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Building classes

Table 3.

Building class Concreteold Concretenew Timberold Timbernew Pumice

Description

No. of stories

Reinforced concrete – shear walls – built before 1980 Reinforced concrete – shear walls – built after 1980 Timber – shear walls - built before 1980 Timber – shear walls - built after 1980 Pumice – shear walls – mainly built before 1980

1–2 1–2 1–2 1–2 1–2

Table 4. Number of buildings in each category ðNÞ, number of damage buildings ðN D Þ, and number of total damaged buildings ðN TD Þ in the Ölfus region, when sorted after the ground motion intensity level and building class (see Figure 1) Intensity level 1

Building class Concreteold Concretenew Timberold Timbernew Pumice Total

2

3

4

Total

N

ND

N TD

N

ND

N TD

N

ND

N TD

N

ND

N TD

N

106 26 45 160 39 376

3 1 4 22 3 33

0 0 0 0 0 0

362 165 250 282 102 1,161

80 17 61 42 36 236

0 0 0 0 3 3

617 327 211 876 144 2,175

487 196 149 447 110 1,389

1 0 1 0 5 7

252 260 203 245 74 1,034

200 193 114 147 48 702

3 0 3 3 4 13

1337 778 709 1563 359 4,746

related to soil failure under the foundations, mainly due to tilting caused by liquefaction or compaction due to the shaking. These cases are not included in the data sample. METHODOLOGY FOR CLASSIFICATION AND IDENTIFICATION OF DAMAGE LOSS ASSESSMENT WORK

The loss assessment work started the day after the earthquake. The estimators worked in groups of two, one being the group leader. The assessment work procedure was as follows: 1. 2. 3. 4. 5.

Property owner reports damage to his local insurance company. This information is forwarded to the Iceland Catastrophe Insurance (ICI). An ICI representative makes an assessment request to the estimators. The estimators prepare the assessment work by familiarizing themselves with drawings and other related information about the damaged property. Estimators perform a first inspection of the property; owners are encouraged to participate in the inspection. All building damage is documented and marked on drawings if available. Estimators also take photos as required.


6.

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Estimators prepare a repair assessment report if any damage due to earthquake action is found. The assessment report includes a description of the damage and a cost estimate for the repairs. The repair cost estimate forms the basis for compensation to the owner.

THE LOSS DATABASE

At the beginning of the assessment work, a special database was designed to store all of the damage data, that is, the data that was gathered and registered during the estimation work. The information recorded into the database includes, for instance, the street name and number, property registry number, usage, main building material, building year, owner, fire insurance value (replacement value), and damage repair cost. The repair cost was divided into the following subcategories: • • • • • • • • • •

Excavation, fill and earthwork Foundation and bottom slab Exterior construction Roof structure Interior construction Interior finishing work Interior fixtures, including kitchen, bathroom appliances, flooring etc. Windows, glass, exterior doors, cladding etc. Painting and surface treatment Piping

THE DAMAGE MODEL As mentioned above, the damage to every building caused by the Ölfus earthquake was classified into a number of categories. In the following, the focus, however, is on the total damage value of all categories (estimated repair cost) relative to the total replacement value of each property (the official fire insurance replacement value). The policy of the ICI has been to cover the total repair cost, including cosmetic issues, such as paintwork, tile, and nonstructural floor repairs. In many cases, crack filling and repainting of nonstructural walls, as well as the repair of floor or wall tiles, constituted the main repair cost for a given structure. On the other hand, contents damage, such as the value of household furnishings, cabinets, furniture and other unfixed content, was excluded from this study. To make the damage data usable for loss estimation, it was necessary to fit an appropriate probability density function (PDF) to it. The field survey showed that a number of houses suffered no damage, while others had small to severe damage, which in some cases was judged a total loss. In practice the epithet total damage was assigned to buildings that had more than 50 to 60% damage. It turned out that the best curve fit was obtained by splitting the data for each building class into three groups: (1) undamaged buildings, (2) damaged buildings, and (3) total loss buildings. The PDFs were then only fitted to the middle group, that is, damaged buildings.

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Table 5.

BESSASON ET AL.

Parameters in damage model (undamaged and total loss buildings are discarded). Intensity level 11 0.05 < PGA ≤ 0.09


α

P1

P0 0.972 1.000 0.911 0.863 0.923

Intensity level 2 0.09 < PGA ≤ 0.18 β

P0

0.000 0.779 0.000 0.897 0.000 0.756 0.000 −4.06 0.508 0.851 0.000 0.618

Intensity level 3 0.18 < PGA ≤ 0.34


P1

α

β

P0

P1

α

β

P0

P1

α

β

0.000 0.000 0.000 0.000 0.020

−3.43 −4.05 −3.08 −3.68 −3.05

0.865 0.968 0.916 0.681 0.787

0.209 0.401 0.289 0.490 0.201

0.002 0.000 0.005 0.000 0.035

−2.98 −3.61 −3.15 −3.60 −2.88

0.693 0.740 0.837 0.755 0.956

0.194 0.258 0.424 0.388 0.297

0.008 0.000 0.015 0.012 0.054

−3.03 −3.47 −3.17 −3.47 −2.93

0.807 0.725 0.804 0.826 0.869

1

When number of damaged buildings is less than 9, no parameters are computed.

Two PDFs were tested: the beta distribution, as used in the ATC-13; and a lognormal distribution. Both these functions fit the data reasonable well; in some cases the lognormal distribution was superior, but in other cases not. Overall, the lognormal distribution proved to be a better choice. However, it should be noted that, theoretically, it has no upper bound, whereas the beta distribution can only take values up to 1, which reflects total damage. Now define X as a random variable representing the building damage ratio, that is, the ratio of combined damage to the official house replacement cost. Three mutually exclusive events are possible during an earthquake: EQ-TARGET;temp:intralink-;e4;41;388


E1 − No damage;

X ¼ 0∶ P½X ¼ 0jE1 ij ¼ 1

E2 − Damage; 0 < X < 1∶ P½X ≤ xjE 2 ij ¼ F X;ij ðx; αij ; βij Þ


E3 − Total damage;

X ¼ 1∶

P½X ¼ 1jE3 ij ¼ 1

(4) (5) (6)

Here, the F X;ij is the lognormal cumulative probability distribution function for a given building class i and load intensity level j, and αij , and βij are the distribution parameters. The probability of each event (E 1 , E 2 , and E 3 ) can easily be found by determining the number of houses with no damage, damaged buildings, and total loss cases. These are denoted, respectively as: PðE 1 Þij ¼ P½X ¼ 0ij ¼ P0;ij

(7)

PðE 2 Þij ¼ P½0 < X < 1ij ¼ PD;ij

(8)

PðE 3 Þij ¼ P½X ¼ 1ij ¼ P1;ij

(9)




It should be noted that since E 1 , E 2 , and E 3 are the only possible events, then EQ-TARGET;temp:intralink-;e10;41;127

PðE 1 Þij þ PðE 2 Þij þ PðE 3 Þij ¼ P0;ij þ PD;ij þ P1;ij ¼ 1.0

(10)


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Now the total probability theorem can be used to compute the probability of damage ðx < 1Þ:


P½X ≤ xij ¼ P½X < xjE 1 ij ⋅ PðE 1 Þij þ P½X < xjE 2 ij ⋅ PðE 2 Þij þ P½X < xjE 3 ij ⋅ PðE 3 Þij ¼ 1 ⋅ P0;ij þ F X;ij ðx; αij ; βij Þ ⋅ PD;ij þ 0 ⋅ P1;ij ¼ P0;ij þ F X;ij ðx; αij ; βij Þ ⋅ PD;ij ð11Þ

MODEL PARAMETERS

The maximum likelihood method was used to compute the two parameters in the lognormal probability distribution function, αij and βij . From these two parameters, the mean, μ, and the variance, v, of a lognormal distributed variable can be computed as: ! β2ij (12) μij ¼ exp αij þ 2 EQ-TARGET;temp:intralink-;e12;62;520

vij ¼ exp 2αij þ β2ij ⋅ exp β2ij − 1


(13)

As before, the indices i and j refer to the building class and the load intensity levels, respectively. In Table 5 the probability distribution parameters for the damage model are shown. In Figure 5 the goodness of the fit of the damage data for concrete houses is compared to the lognormal probability function for intensity levels 2, 3, and 4 on a special “lognormal paper” (if the data fits the straight line it is lognormally distributed, etc.). In Figure 6, a similar comparison is shown for the timber houses. As seen, the fit is fairly good for all 12 data sets. An Anderson–Darling goodness-of-fit test (Anderson and Darling 1952) was carried out to see if the damage data (no damage and total damaged buildings excluded) was lognormally distributed at 5% significance level. It was found that 7 of the 16 data sets with estimated lognormal parameters (see Table 5) were lognormally distributed at this level. At 1% significance level, 10 of the 16 data sets passed the test. In Figures 7, 8, and 9, the probabilistic damage curves for Iceland are compared for all five building classes and seismic intensity levels 2, 3, and 4, respectively. For all intensity levels, the Timbernew and Concretenew houses experience significantly less damage than Timberold and Concreteold. houses. Also, the damage curves for the pumice houses are significantly lower than those for the timber and concrete buildings. In general, the difference between the Timbernew and Concretenew curves is insignificant. At the highest intensity level, more timber houses have no damage, that is, P0 is 0.39 for Timbernew, but 0.26 for Concretenew. On the other hand, the variation between the Concretenew and Concreteold is much greater than between Timbernew and Timberold at this level. This can be explained by the fact that around 1980, the amount of reinforcement was increased in concrete shear wall buildings, and it seems to have reduced the damage. No such change in the construction of timber houses occurred. It is also useful to compare the expectation and the variance of the damage of each building class for a given earthquake action intensity, as it reflects the expected loss. The expected loss can be computed as: ∞ ð E½Xij ¼ x ⋅ pX;ij ðxÞdx ¼ P0;ij ⋅ 0 þ PD;ij μij þ P1;ij ⋅ 1 (14) EQ-TARGET;temp:intralink-;e14;62;119

−∞

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BESSASON ET AL.

Concrete Old 2− N =80

Concrete New 2− N =17 D

0.95 0.9 Probability

Probability

D

0.9999 0.999 0.99 0.9 0.75 0.5 0.25 0.1 0.01 0.001 0.0001

0.75 0.5 0.25 0.1 0.05

−3

10

−2

−1

10

0

10

−3

10

10

−3

10

−2

−1

10

0

10

10

Concrete Old 4− N =200

Probability

−1

10

0

10

D

Probability −2

−1

10

−2

10

Concrete New 4− N =193

D

−3

0

10

0.9999 0.999 0.99 0.9 0.75 0.5 0.25 0.1 0.01 0.001 0.0001 −3

10

0.9999 0.999 0.99 0.9 0.75 0.5 0.25 0.1 0.01 0.001 0.0001 10

−1

10

Concrete New 3− ND=196

0.9999 0.999 0.99 0.9 0.75 0.5 0.25 0.1 0.01 0.001 0.0001

Probability

Probability

Concrete Old 3− ND=487

−2

10

0

10

10

0.9999 0.999 0.99 0.9 0.75 0.5 0.25 0.1 0.01 0.001 0.0001 −3

10

Damage ratio

−2

10

−1

10

0

10

Damage ratio

Figure 5. Goodness-of-fit of the damage data for the Concreteold and Concretenew building classes to the lognormal probability function for intensity levels 2, 3, and 4 (ND denotes number of damaged buildings in each class). ∞ ð

Var½Xij ¼

ðx − μij Þ2 ⋅ pX;ij ðxÞdx −∞

∞ ð


¼ P0;ij ⋅ ð0 − μij

Þ2

þ PD;ij ðx − μij Þ2 ⋅ f X;ij ðxÞdx þ P1;ij ð1 − μij Þ2

(15)

0

¼ P0;ij ⋅ μ2ij þ PD;ij ⋅ vij þ P1;ij ð1 − μij Þ2 where pX;ij is the probability density function for a given building class i and intensity level j (including all data points), while f X;ij is the lognormal probability density function for the damaged houses only in each case. The μij and vij parameters are computed by Equation 12 and 13 while the others parameters are given in Table 5. Finally the 90% confidence values are compared. The 90% level for the damage curves can be computed from Equation 11 by finding the x-value which corresponds to the probability PðX < xÞ ¼ 0.9. Alternatively they


Timber Old 2 − N =61

Timber New 2 − N =42 D

Probability

Probability

D

0.9999 0.999 0.99 0.9 0.75 0.5 0.25 0.1 0.01 0.001 0.0001 −3

10

−2

10

−1

10

0

0.9999 0.999 0.99 0.9 0.75 0.5 0.25 0.1 0.01 0.001 0.0001 −3

10

10

−3

−2

10

−1

10

0

−3

10

10

Probability

Probability −2

10

−1

10 Damage ratio

0

10

−2

10

−1

10

0

10

Timber New 4 − ND=147

0.9999 0.999 0.99 0.9 0.75 0.5 0.25 0.1 0.01 0.001 0.0001 −3

−1

10

0.9999 0.999 0.99 0.9 0.75 0.5 0.25 0.1 0.01 0.001 0.0001

Timber Old 4 − ND=114

10

−2

10

Timber New 3 − ND=447

Probability

Probability

Timber Old 3 − ND=149 0.9999 0.999 0.99 0.9 0.75 0.5 0.25 0.1 0.01 0.001 0.0001 10

1369

0

10

0.9999 0.999 0.99 0.9 0.75 0.5 0.25 0.1 0.01 0.001 0.0001 −3

10

−2

10

−1

10 Damage ratio

0

10

Figure 6. Goodness-of-fit of the damage data for the Timberold and Timbernew building classes to the lognormal probability function for intensity levels 2, 3, and 4 (ND denotes number of damaged buildings in each class).

can be read directly from Figures 7, 8, and 9. The results of this analysis are shown in Table 6 for all five building classes and all intensity levels 1, 2, 3, and 4. From Table 6, it is also possible to compute damage curves with the mean damage ratio on the vertical axis and the intensity level on the horizontal axis. Other preferred or required percentages of the damage ratio can also be computed from the damage model. From Table 6, it can be seen that more than 90% of new concrete and new timber buildings are expected to suffer light damage (less than 10%) for intensity level 4. It is also informative to know the ratio of the damage of the structural bearing system to the total damage. This is shown in Table 7 for all categories. It is clear from the table that the damage of the structural bearing system is only a small percentage of the total damage, in fact always less than 45%. This means that most of the damage is indeed connected with cosmetic issues. The survey showed that paintwork and repair of flooring (scars and holes in parquet,

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BESSASON ET AL.

1 0.9 0.8

Probability

0.7 0.6 0.5 0.4

Concrete

old

0.3

Concretenew

0.2

Timberold

0.1

Timbernew Pumice 0

0.05

0.1

0.15

0.2

Damage ratio

Figure 7. Comparison of probability functions for damage ratios of the building classes for intensity level 2.

1 0.9 0.8

Probability

0.7 0.6 0.5 0.4

Concreteold

0.3

Concretenew

0.2

Timberold Timber

new

0.1

Pumice 0

0.05

0.1

0.15

0.2

Damage ratio


broken tiles, etc.) were by far the most costly elements. For the Concretenew buildings, however, the ratio of the damage cost of the structural bearing system to the total damage cost was much lower, at less than or around 10% for all intensity levels, and did not appear to increase with the intensity level. For Timbernew buildings, the ratio of structural damage to total


1371

1 0.9 0.8

Probability

0.7 0.6 0.5 0.4

Concreteold

0.3

Concrete

0.2

Timberold

0.1

Timbernew

new

Pumice 0

0.05

0.1

0.15

0.2

Damage ratio


damage was also low, but increases from 11% to 19% between intensity levels 3 to 4. The highest ratio of structural damage to total damage was found in the pumice buildings. Focusing on new concrete buildings (Concretenew), the information from Table 6 and 7 can be combined to conclude that more than 90% of buildings in this class will obtain less than 1% damage of the structural bearing system when subjected to an earthquake action of intensity level 4 ð6.94% × 9.0% ¼ 0.62%Þ. In Figure 10, it is shown how the expected loss is split between structural and nonstructural damage for different building classes and intensity levels.

Table 6. Expected loss, standard deviation, and 90% confidence values for different building classes and intensity levels Intensity level 11 0.05 < PGA ≤ 0.09


Building class

Mean (%)

Std. (%)

p90% (%)

Mean (%)

Std. (%)

p90% (%)

Mean (%)

Concreteold Concretenew Timberold Timbernew Pumice

0.11 0.00 0.32 0.26 0.28

1.86 1.27 -

1.04 0.29 1.69 0.47 5.22

4.75 2.87 7.22 3.08 17.2

3.58 0.28 5.64 1.86 9.20

5.28 6.59 11.3 6.49 2.14 3.27 5.56 3.01 4.78 8.90 10.8 4.75 1.86 3.43 5.24 3.85 10.23 19.8 20.7 10.5

1

Intensity level 3 0.18 < PGA ≤ 0.34 Std. (%)

p90% (%)

Intensity level 4 0.34 < PGA ≤ 0.65 Mean (%)

When number of damaged buildings is less than 9, standard deviation and p90% are not computed.

Std. (%)

p90% (%)

12.0 12.9 3.56 6.94 12.8 9.64 11.4 7.43 22.9 19.2

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BESSASON ET AL.

Table 7.

Ratio of damage of the structural bearing system to total damage


Intensity level 1 (%)




27.3 0 1.46

20.8 2.03 42.9 7.16 41.4

14.5 11.4 29.6 11.4 38.5

26.1 9.0 25.3 19.1 33.7

Concrete

Concrete

new

7

6

6

5

5

Expected loss − (%)


old

7

4 3 2 1 0

structural damage non−structural damage

4 3 2 1

2

3

0

4

2

Intensity level Timberold

6

6

5

5

4 3 2 1 0

4

Timbernew

7



7

3 Intensity level

4 3 2 1

2

3 Intensity level

4

0

2

3

4

Intensity level

Figure 10. Expected loss split into structural and nonstructural damage for different building classes and intensity levels.


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LOSS ESTIMATION The damage curves presented in this paper are based on observed field data from the M w ¼ 6.3 earthquake of 29 May 2008. As such, they provide a useful tool to predict damage in different earthquake scenarios in Iceland and for annual earthquake risk assessment, especially if the earthquake magnitudes of future scenarios are similar. For a given earthquake, with a known epicenter and magnitude, the PGA can be computed by Equation 1 for each building site, and consequently the intensity level determined. Two approaches can then be used for the loss estimation. The first approach is to use only the mean value and the standard deviation for each building class and intensity level (see Table 6), and apply the following two equations to calculate the expected damage and its variance: N X E½damage ¼ V k ⋅ E½Dk ðBC; ILÞ (16) EQ-TARGET;temp:intralink-;e16;62;493

k¼1

Var½damage ¼

N X


V 2k ⋅ Var½Dk ðBC; ILÞ

(17)

k¼1

Here V k is the replacement cost of building k from the official building registry; E½Dk ðBC; ILÞ and Var½Dk ðBC; ILÞ are the expected value and variance of the damage ratio as a function of building class ðBCÞ and intensity level ðILÞ; and N is the number of affected buildings ðPGA > 0.05 gÞ. The second approach is to use a Monte Carlo simulation technique, where the evaluated probability density functions as given by Equation 11 (see also Figures 7, 8 and 9), and the parameters specified in Table 5, are used along with generated random numbers to simulate the damage in every building. This is theoretically a more sophisticated method as is uses all the information contained in the probability distribution functions. The simulation can be repeated a number of times in order to find a mean value and the standard deviation of the computed loss. THE SOUTH ICELAND EARTHQUAKE OF MAY 2008

As a first step to verify the damage model and the estimated parameters, it seems logical to model the observed damage in the May 2008 earthquake. The estimated loss, based on a Monte Carlo simulation, is shown (one simulation) in Table 8. The damage is classified after the building class and intensity level. In Table 9, the mean and standard deviation of the total loss, based on both the two approaches mentioned above, are shown and compared to the actual loss based on the field survey. As seen in the table, the results match very well, and they indicate that fair loss estimates can be obtained by using only the mean and the standard deviation. THE SOUTH ICELAND EARTHQUAKES OF JUNE 2000

In June 2000 two shallow earthquakes, both of magnitude M w ¼ 6.5, occurred in South Iceland, on 17 and 21 June. The epicentral distance between these two events was less than 20 km (see Figure 4). Their spatial and time difference was therefore relatively small, and the affected areas overlapped. The total loss in these two earthquakes based on the field survey

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BESSASON ET AL.

Table 8. Simulated damage of concrete, timber and pumice residential buildings in the May 2008 earthquake in South Iceland, in monetary terms, based on the damage model. The values are the result of one simulation (see Table 4 for number of buildings in each class and intensity level). Intensity level 1 0.05 < PGA ≤ 0.09 (million U.S. dollars)

Intensity level 2 0.09 < PGA ≤ 0.18 (million U.S. dollars)

Intensity level 3 0.18 < PGA 0.34 (million U.S. dollars)

Intensity level 4 0.34 < PGA ≤ 0.65 (million U.S. dollars)

Total Damage (million U.S. dollars)

Concreteold Concretenew Timberold Timbernew Pumice

0.014 0.000 0.012 0.230 0.008

0.869 0.110 0.910 0.259 0.457

6.84 1.74 1.93 4.21 2.59

2.69 1.80 1.54 2.19 1.66

10.41 3.64 4.39 6.89 4.72

SUM

0.264

2.605

17.31

9.87

30.06

Building class

Table 9. Estimated loss of concrete, timber and pumice residential buildings in the May 2008 earthquake in South Iceland based on the damage model compared to actual loss based on field survey.

Estimated loss based on mean and variance Estimated loss based on Monte Carlo simulations1 Actual loss based on field survey

Expected loss (million U.S. dollars)

Standard deviation (million U.S. dollars)

29.55 29.35 29.36

1.09 1.05 -

1

Based on 1,000 simulations.

carried out by the Icelandic Catastrophe Insurance was 47.3 million U.S. dollars. As the 2000 earthquakes affected much the same building stock as the 2008 event, it was considered that this would be a useful verification of the damage model presented in this paper The five building classes in this study cover the majority of all residential buildings in South Iceland. However, there are also other types of houses that suffered damage, and which repair cost is included in the total sum above. These included summer houses, farmhouses and garages, which were treated separately in the back-calculation. Although the probabilistic damage curves for these building types were not developed separately in this study, damage data after the 2008 earthquake for these kinds of buildings does exist. It was therefore easy to compute their expected damage ratio as well as the variance for each building class and then use Equation 16 and Equation 17 for the loss estimation The lower limit of the total loss can be computed by saying that the damage of a given building k is only affected by one of the two earthquakes, selecting the one with the higher intensity level at the site. The upper limit is obtained by treating the two earthquakes as independent events. This means that some buildings, especially those located between the epicenters, will have two sources of damage. In Table 10, the upper and lower bounds of the computed damage and the corresponding standard deviation is shown.


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Table 10. Upper and lower limits of simulated losses from the two South Iceland earthquakes of June 2000 calculated using the damage model based on the data from the May 2008 earthquake, and actual loss based on field surveys.

Lower limit (Based on the worse event only) Upper limit (Added two independent events) Actual loss based on field survey

Expected loss (million U.S. dollars)

Standard deviation (million U.S. dollars)

51.11 61.06 47.25

2.78 2.93 -

The actual loss is therefore about 1.4 standard deviations below the lower limit of the calculated loss. A possible explanation for the low actual loss compared to the back-calculation result is that most of the calculated losses in the 2000 earthquakes arose from buildings in the town of Selfoss, which is located to the west of the epicenters of the earthquakes, (see Figure 4). The faults that generated both of the June 2000 earthquakes had a north-south orientation and their actual damage zone was elliptical in shape, with its major axis in a north-south direction. The damage functions developed in this study were developed using the epicentral distance, effectively simulating a radial damage pattern. Given the location of Selfoss relative to the epicenters of the 2000 earthquakes, it is therefore to be expected that the simulation would over-estimate the total damage. Social factors may also have affected the over-prediction of losses in the 2000 earthquakes from using the 2008 data. Changing social attitudes and increase in wealth over the period 2000 to 2008 and the difficult post-financial-collapse climate of 2009 may have influenced the extent and level of reported damage and repair costs, which would also lead to the model over-predicting the 2000 losses. SUMMARY AND CONCLUSIONS New probability density functions of damage for low-rise buildings, based on real earthquake damage data from Iceland have been presented. They cover five construction classes; two categories of reinforced concrete shear-wall buildings built before and after 1980, two categories of timber buildings built before and after 1980, and finally one category of pumice buildings. This last class contains special type of buildings constructed with hollow pumice blocks, which was common practice in Iceland in the middle of last century. The earthquake damage data is quite accurate and covers 4,746 buildings located in the Ölfus region in South Iceland that was struck by a 6.3 ðM w Þ magnitude earthquake on 29 May 2008. Damage of every building was investigated and reported by trained assessors and the repair cost evaluated. About 50% of the houses (2,360) in the area suffered repairable damage, which is covered by the Icelandic Catastrophe Insurance, and 0.48% (23) were a total loss. None of the “totally damaged buildings” collapsed or caused injuries or deaths, but the damage was so severe that repair was considered impractical. Four ground motion intensity levels were used to relate observed damage to the earthquake action at each site. Since low-rise buildings are stiff with a short natural period, it is preferable to use some kind of a PGA parameter to define the intensity level. In the study

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BESSASON ET AL.

predicted PGA values based on a proposed attenuation model for Iceland were used. This model predicts the median value of both horizontal acceleration components. It turned out that the predicted median PGA by the attenuation model was in fair agreement with the effective PGA for the more intensive component for those sites or stations that had recorded acceleration in areas close to the epicenter ðD < 20 kmÞ. The effective PGA used in this study was evaluated from the response spectra for this component in the period range 0.1 s to 0.3 s. The reported damage data shows that the damage ratio of new low-rise timber houses and new low-rise reinforced shear wall concrete houses is quite similar for all earthquake intensity levels. It also shows that probabilistic damage curves for high intensity actions are quite similar for the pumice buildings and the old concrete houses. The other building classes show greater earthquake resistance. The damage curves are based on four parameter models: one parameter defining the portion of houses that suffered no damage; another parameter describing the portion of houses that were considered a total loss; and, finally, two parameters in the lognormal probability distribution function defining the damage for all the damaged buildings that were not a total loss. This model resulted in a much better fit than the two-parameter lognormal probability distribution alone. It is important to note that the Icelandic data showed that much of the monetary loss was due to nonstructural damage or cosmetic damage. For instance the damage of the structural load bearing system of new concrete and new timber houses for the highest intensity level is 9% and 19% of the total damage respectively. This may be a function of social changes, where nonstructural damage has more weight or value today than it had in earlier times, when living and housing standards were lower. The study showed that new cast-in-situ, low-rise reinforced shear wall concrete buildings as well as new timber houses (both built after 1980) have an inherent and satisfactory earthquake resistance capacity. As an example, the damage curves show that for the highest earthquake action intensity, that is, when PGA is in the range 0.34−0.65 g, it can be expected that over 90% of these buildings will have only light damage, that is, damage ratio less than 10%. If structural damage is considered only (nonstructural damage excluded), the figure is less than 1.5%. The building stock in Iceland is quite uniform, and the damage curves presented are relevant in general for all regions in the country. The curves may also be of value in considering potential losses from seismic shaking for similar buildings in other countries. However building traditions vary considerably between countries, even within Europe. For instance within the earthquake-prone areas of southern Europe, the building stock is quite dissimilar from that in Iceland. Although the methodology presented herein is intended to be of general use internationally, it is not anticipated that the Icelandic damage curves published in this paper will be directly applicable elsewhere without modification based on local information. Finally, the damage model based on the data from the May 2008 earthquake was used to predict the damage in the May 2008 earthquake, and the two South Iceland earthquakes of June 2000. The estimated loss in the May 2008 earthquake, using the damage model,


1377

was very close to the actual loss based on the field survey as it should be. For the June 2000 earthquakes the actual reported damage (47.3 million U.S. dollars) was within the statistical range of the predicted lower limit of the damage (a mean value of 51.11 and a standard deviation of 2.78 million U.S. dollars). The underprediction of the actual loss in the 2000 events is likely to be due to the location of the epicenters of the two earthquakes and general social changes that have occurred in the interim period up to the 2008 event. ACKNOWLEDGEMENTS The authors wish to offer their thanks to the Icelandic Catastrophe Insurance for encouraging this study, and for placing the earthquake damage database and other relevant information at their disposal.

REFERENCES Ambraseys, N., Smith, P., Sigbjörnsson, R., Suhadolc, P., and Margaris, B., 2002. Internet Site for European Strong-Motion Data, European Commission, Research-Directorate General, Environment and Climate Programme. Anderson, T. W., and Darling, D. A., 1952. Asymptotic theory of certain “goodness-of-fit” criteria based on stochastic processes, Annals of Mathematical Statistics 23, 193–212. Applied Technology Council (ATC), 1978. Tentative Provisions for the Development of Seismic Regulations for Buildings, ATC-3-06 (NBS SP-510), U.S. Government Printing Office, Washington, D.C. Applied Technology Council (ATC), 1985. Earthquake Damage Evaluation Data for California, Report No. ATC-13, Redwood City, CA. Applied Technology Council (ATC), 2002. Commentary on the Use of ATC-13 Earthquake Damage Evaluation Data for Probable Maximum Loss Studies of California Buildings, Report No. ATC-13-1, Redwood city, CA. Bessason, B., and Haflidason, E., 2004. Recorded and numerical strong motion response of a base-isolated bridge, Earthquake Spectra 20, 309–332. Bessason, B., and Kaynia, A. M., 2002. Site amplification in lava rock on soft sediments, Soil Dynamics Earthquake Engineering 22, 525–540. Douglas, J., 2003. Earthquake ground motion estimation using strong-motion records: a review of equations for the estimation of peak ground acceleration and response spectral ordinates, Earth-Science Reviews 61, 43–104. Colombi, M., Borzi, B., Crowley, H., Onida, M., Meroni, F., and Pinho, R., 2008. Deriving vulnerability curves using Italian earthquake damage data, Bull. Earthquake Eng. 6, 485–504. Einarsson, P., 1991. Earthquakes and present-day tectonism in Iceland, Tectonophysics 189, 261–279. European Committee for Standardization (CEN), 2004. Eurocode 8—Design of Structures for Earthquake Resistance - Part 1: General Rules, Seismic Actions and Rules for Buildings, Brussels. Federal Emergency Management Agency (FEMA), 1999. HAZUS User and Technical Manuals. FEMA Report: HAZUS 1999, Washington D.C.

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