Fragility Curves for Buildings Based on Damage Data in Uki City due the 2016 Earthquake

Kazuaki TORISAWA College of Science and Engineering, Kanto Gakuin University, . E-mail: [email protected] Kei HORIE Corporate Planning Department, MS&AD InterRisk Research & Consulting, Inc., Japan. Ken KAWABE Corporate Planning Department, MS&AD InterRisk Research & Consulting, Inc., Japan. Masashi MATSUOKA Department of Architecture and Building Engineering, Institute of Technology, Japan. Munenari INOGUCHI Faculty of Sustainable Design, University, Japan. Fumio YAMAZAKI National Research Institute for Earth Science and Disaster Resilience, Japan.

A series of earthquakes hit Kumamoto Prefecture in Kyushu Island, Japan, on April 14 and 16, 2016. A large number of buildings, mostly wooden houses, were damaged. This study developed fragility curves of buildings using the damage survey data provided by the Uki City government. The damage ratios of buildings were investigated from the viewpoints of the structural material and the construction period. As the result, the damage ratio of wooden buildings was found to be larger than those of other structural materials, and the damage ratios of major, moderate+, and moderate- got smaller as the construction period became newer. Empirical fragility curves of buildings for Uki City were constructed based on the damage survey data and the estimated peak ground velocity (PGV). Compared with the result of the previous study for Mashiki Town due the 2016 Kumamoto earthquake, the major damage ratios of wooden buildings for Uki City was shown in a lower level than those for Mashiki Town in the same PGV. The fragility curves for Uki City were obtained using the damage survey data in the smaller PGV range than that for Mashiki Town, thus the regression results reflected the damage trend in the small PGVs. The fragility curves for Uki City and Mashiki Town due the 2016 Kumamoto earthquake were compared with those for Nishinomiya City and Nada Ward due the 1995 earthquake. As the result, it was observed that the fragility curves for the Kumamoto earthquake showed lower damage ratios than those for the Kobe earthquake.

Keywords: The 2016 Kumamoto earthquake, Building damage, Construction period, Peak ground velocity, Major damage ratio, Fragility curve.

1. Introduction authors (National Institute for Land and Infrastructure Management 2016; Sugino et al. A series of earthquakes hit Kumamoto Prefecture 2016; Yamada et al. 2017; Yamazaki et al. 2019). in Kyushu Island, Japan, on April 14 and 16, Also, in other municipalities in Kumamoto 2016. A large number of buildings, mostly Prefecture many building damages occurred wooden houses, were damaged and some of them (Kumamoto Prefecture 2016). were totally collapsed. Building fragility curves (vulnerability Among various types of damage due to strong functions) have been used for damage assessment shaking, building damage is one of the most studies by the national and local governments in significant effects of earthquakes, especially for Japan to plan appropriate and efficient inland (crustal) earthquakes. Many building countermeasures against future earthquakes damages occurred especially in Mashiki Town (Yamazaki and Murao 2000; and due the 2016 Kumamoto earthquake, and some Yamazaki 2000; Midorikawa et al. 2011; Cabinet analysis results of these data have already been Office of Japan 2013a). Fragility curves have reported by a lot of engineers and researchers for been created by combining the ground motion various organizations including the present distribution and the building damage survey data

Proceedings of the 30th European Safety and Reliability Conference and the 15th Probabilistic Safety Assessment and Management Conference Edited by Piero Baraldi, Francesco Di Maio and Enrico Zio Copyright c ESREL2020-PSAM15 Organizers.Published by Research Publishing, Singapore. ISBN/DOI: 978-981-14-8593-0 Proceedings of the 30th European Safety and Reliability Conference and the 15th Probabilistic Safety Assessment and Management Conference by local governments. Most of the present damage Figure 2 compares the acceleration response assessment studies use empirical fragility curves spectra (the resultant of the two horizontal from the 1995 Kobe earthquake because there components, 5% damping ratio) of the recorded were no other earthquakes with abundant damage motions at the three seismic stations shown in Fig. data. For this reason, the reconstruction of 1 for the foreshock (April 14) and the mainshock fragility curves based on damage data in the (April 16). In the figure, the result for the recent damaging earthquakes is considered an important issue, and the large amount of data obtained in the 2016 Kumamoto earthquake should be properly analyzed for estimating and mitigating damages due to future seismic events. This study developed fragility curves of buildings using the damage survey data provided by the Uki City government. The damage ratios of buildings were investigated from the viewpoints of the structural material and the construction period. Empirical fragility curves of buildings for Uki City were constructed based on the damage survey data and the estimated peak ground velocity (PGV) distribution, and the results were compared with those of the previous studies for Mashiki Town due the 2016 Kumamoto earthquake, Nishinomiya City and Nada Ward due the 1995 Kobe earthquake.

2. Estimation of Ground Motion Distribution A Mw 6.2 earthquake hit Kumamoto Prefecture on April 14, 2016 at 21:26 (JST). The epicenter was located in the Hinagu fault with a shallow depth. On April 16, 2016 at 01:25 (JST), about 28 hours after the first event, another earthquake of Mw 7.0 occurred in the Futagawa fault, closely located with the Hinagu fault. Thus, the first event was called as the "foreshock" and the second one as the "mainshock". Figure 1 shows the location of Uki City and these causative faults of the 2016 Kumamoto earthquake. Uki City is located in the southwest direction of the causative faults. Also shown in the figure are the K-NET and KiK-net stations near Uki City.

KMM006 Futagawa fault

KMM008 Hinagu fault KMMH14 Uki City Fig. 2. Acceleration response spectra (the resultant of the two horizontal components, 5% damping ratio) of Fig. 1. Location of Uki City, K-NET and KiK-net the recorded motions at K-NET Kumamoto stations near Uki City and the causative faults of the (KMM006), K-NET Uto (KMM008) and KiK-net 2016 Kumamoto earthquake Toyono (KMMH14) Proceedings of the 30th European Safety and Reliability Conference and the 15th Probabilistic Safety Assessment and Management Conference connected time histories (April 14 and April 16 in The damage extent of each building was 2 minutes interval) is also plotted. It is seen for classified into five classes by its damage level (or each station that the April 16 event has a dominant monetary loss), as current damage (loss) class influence in the all period range. shown in Table 1. Note that this classification was We estimated the seismic ground motion carried out following the unified loss assessment distribution in the disaster area with high accuracy method of Japan (Cabinet Office of Japan 2013b). by collecting a total of 1,141 strong motion In the table, an approximate correspondence with records (K-NET and KiK-net: 698; Japan visual inspection methods (Grünthal ed. 1998; Meteorology Agency (JMA): 316; local Okada and Takai 2000) is also shown. Note that governments: 111; Saibu Gas Co.: 16) for the mainshock of the 2016 Kumamoto earthquake. The Kriging interpolation was applied to these peak ground motion values considering the attenuation relationship from the causative fault plane of the mainshock and soil amplification factors, following the method adopted by QuiQuake (Matsuoka and Yamamoto 2012). Note that the resultant PGVs of the two horizontal components were used in the calculation. Figure 3 shows the estimated PGV distribution in the 250-m grid cell units for Uki City. The estimated PGV is relatively larger in the central southern area than in the northeast area closer to the causative faults. Figure 4 shows the PGV amplification factor Fig. 3. Distribution of the estimated peak ground (National Research Institute for Earthquake velocity (PGV) in the 250-m grid cell units for Uki City Science and Disaster Resilience 2018) used in the Kriging interpolation for the study area. In the coastal area of this region, there are many reclaimed lands and deltas, and thus the distribution of the PGV amplification factor shows such tendency of the surface soil.

3. Analysis of Building Damage Soon after the 2016 Kumamoto earthquake, the municipality governments carried out building damage surveys in order to issue disaster-victim certificates. Building damage caused by the 2016 Kumamoto earthquake was serious in Mashiki Town and Minami-Aso Village, which are located close to the source region, but Uki City was also heavily damaged, next to those areas (Kumamoto Fig. 4. Distribution of the PGV amplification factor in Prefecture 2016). the 250-m grid cell units for Uki City

Table 1. Earthquake loss assessment classes of buildings by local governments in Japan and schematic images of other damage classification methods (Source: Yamazaki et al. 2019)

Proceedings of the 30th European Safety and Reliability Conference and the 15th Probabilistic Safety Assessment and Management Conference the result of loss assessment by local governments area less than 20 m2, those without ground floor is important for affected people to receive and those without location information. The financial support and property tax reduction. In remaining 28,486 data were used. Uki City, the first stage assessment, viewing from Figure 5 shows the spatial distribution of outside, was conducted for the all buildings. This damaged buildings in Uki City based on the city result was shown to the residents and in case, they government’s disaster-victim certificate data. It is did not accept it, the second stage assessment, seen that the major damage buildings are viewing the damage status of inside a building, distributed in the area where many buildings were was carried out. Note that in the areas which were considered to be little damage, surveys were conducted only for the buildings requested by residents. Finally, a total of 8,560 disaster-victim certificates were issued. However, Uki City's disaster-victim certificate data do not include undamaged buildings. Therefore, the building database was constructed by matching the 50,980 taxation building data with the disaster-victim certificate data, and a building without a disaster- victim certificate was regarded as no damage. These data also include ones that are not suitable for analyzing building damage. For this reason, we excluded the following data from the constructed building database: the data on Fig. 5. Distribution of damaged buildings in Uki City storage, warehouse, garage, etc., those with the based on the city government’s disaster-victim certificate data

Table 2. Number of buildings in Uki City with respect to the damage class and the construction period

Structural Construction Major Moderate+ Moderate- Minor No damage Total type period -1951 167 83 293 283 2,758 3,584 1952-61 39 26 103 103 673 944 1962-71 60 33 201 275 2,127 2,696 1972-81 75 78 453 902 3,824 5,332 Wooden 1982-90 33 28 312 841 2,600 3,814 1991-2000 18 23 192 1,227 2,629 4,089 2001-16 13 5 43 973 2,475 3,509 Total 405 276 1,597 4,604 17,086 23,968 -1981 0 0 2 11 91 104 1982-90 0 0 0 8 71 79 RC 1991-2000 0 0 0 4 45 49 2001-2016 0 0 0 18 61 79 Total 0 0 2 41 268 311 -1981 2 4 14 25 698 743 1982-90 1 1 8 14 500 524 S 1991-2000 0 0 4 21 480 505 2001-2016 0 0 0 19 278 297 Total 3 5 26 79 1,956 2,069 -1981 1 1 8 37 360 407 1982-90 0 0 6 51 208 265 LS 1991-2000 1 0 4 132 393 530 2001-2016 1 0 1 121 288 411 Total 3 1 19 341 1,249 1,613 SRC Total 0 0 0 0 24 24 CB Total 0 0 2 3 493 498 Others Total 0 0 0 0 3 3 All Total 411 282 1,646 5,068 21,079 28,486 Proceedings of the 30th European Safety and Reliability Conference and the 15th Probabilistic Safety Assessment and Management Conference located and the large PGV values were estimated. Steel (LS)" is about 5%, "Concrete Brick (CB) "is In the areas of peninsula (west) and inland (east), about 2%, and "Steel-reinforced Concrete (SRC)" the number of buildings was small and the PGV is very few. Major damages to buildings occurred was also relatively small, and hence few major only for wooden, S and LS types. There was no damage buildings were observed. major damage to RC, SRC and CB buildings. Table 2 shows the number of buildings in Uki Figure 6 shows the damage classification of City with respect to the damage class and the buildings by the Uki City government with construction period for each structural material respect to the structural type. The major damage (structural type). With respect to the number of ratio for the all buildings is about 1.4%, and one buildings by structural type, "Wooden" accounts for wooden buildings is about 1.7%. for about 84%, "Reinforced Concrete (RC)" is Figure 7 shows the damage ratio of wooden about 1%, "Steel (S)" is about 7%, "Light-gauge buildings in Uki City with respect to the construction period. The damage ratios of major, Major Moderate+ Moderate- Minor No moderate+, and moderate- get smaller as the 23,968 311 2,069 1,613 24 498 3 28,486 100% construction period becomes newer. The minor 90% damage ratio does not correspond much to the 80% construction period, probably because the minor 70% damage is mostly to non-structural members, such 60% 50% as roofing materials and wall finishing materials, 40% whose seismic provisions are not clearly defined.

Damage Ratio Damage 30% The Japanese building standard law was 20% significantly revised in 1981, and the seismic 10% 0% provision was tightened. Therefore, buildings W RC S LS SRC CB OTHERS ALL built after 1981 are supposed to be more resistant Structural Type to earthquakes than the pre-coded buildings. The Fig. 6. Damage classification of buildings by the Uki analysis for Mashiki Town clearly showed City government with respect to the structural type declining the major damage ratio after 1982 as the effect of the revision of seismic provision in 1981 (Yamazaki et al. 2019), but it is not easy to Major Moderate+ Moderateʷ Minor No distinguish that in the analysis for Uki City 3584 944 2696 5332 3814 4089 3509 100% because those are very small. 90% Figure 8 shows the damage ratio of non- 80% wooden buildings (RC, S and LS) in Uki City with 70% 60% respect to the construction period. Their damage 50% ratios of higher than minor look to get smaller as 40% the construction period becomes newer. Damage Ratio Damage 30% 20% 10% 4. Development of Building Fragility Curves 0% -1951 1952-61 1962-71 1972-81 1982-90 1991-2000 2001-16 We developed the fragility curves based on the Construction Period Uki City’s building damage data with respect to the structural type, wooden, S, and LS buildings. Fig. 7. Damage classification of wooden buildings by The number of buildings was not enough for RC, the Uki City government with respect to the SRC, and CB buildings to develop those one. construction period In order to analyze the relationship between the seismic ground motion and the building damage Major Moderate+ Moderate- Minor No ratio, the building data and the estimated PGV at 104 79 49 79 743 524 505 297 407 265 530 411 100% each building location were combined using 90% 80% geographic information system (GIS). Note that 70% the PGV value for the residential district (“O- 60% 50% Aza” in Japanese with alphabet notation) level 40% 30% was used because the taxation building data have Damage Ratio Damage 20% only this district-level location information and it 10% 0% was difficult to convert it to the precise location -1981 -1981 -1981 2001-16 1982-90 2001-16 1982-90 2001-16 1982-90 1991-2000 1991-2000 1991-2000 (latitude and longitude). In constructing the fragility curves, after sorting based on the PGV value of each building, RC SLS several buildings with a similar level of PGV Fig. 8. Damage classification of non-wooden buildings values were classified as one data group (block). by the Uki City government with respect to the For wooden buildings, all the data were divided construction period into 20 blocks, while for S and LS buildings into Proceedings of the 30th European Safety and Reliability Conference and the 15th Probabilistic Safety Assessment and Management Conference

5 blocks because the numbers of data were small. 100%

Note that the PGV value for each block was 90% Major (Wooden) ˜ 80% calculated as the weighted mean of the PGVs of Moderate+ (Wooden) ˕ 70% buildings in the block. Moderate- (Wooden) ˚ For a ground motion index x (PGV), a fragility 60% curve of buildings was obtained by assuming the 50% 40%

cumulative probability PR(x) of the occurrence of Damage Ratio damage equal to or higher than a rank R (such as 30% “major damage”) to be lognormal as follows: 20% 10% 0% PR(x) = Φ ((ln x - λ) / ζ) (1) 0 20 40 60 80 100 PGV (cm/s) where Φ is the standard normal distribution and λ and ζ are the mean and the standard deviation of (a) Wooden ln x. The two parameters of the distributions, λ and ζ, were determined by the least square method 100% 90% Major (Steel) on a lognormal probability paper. 80% Moderate+ (Steel)

Table 4 summarizes the results of the 70% Moderate- (Steel) ˚ regression analysis for each structural type. Note 60% that the regression coefficients for major and 50% moderate+ of S and LS buildings were not 40% Damage Ratio obtained because those damage ratios were almost 30% zero level with only small changes and the slopes 20% of those regression lines became negative on the 10% lognormal probability paper. 0% 0 20 40 60 80 100 Figure 9 shows the fragility curves of buildings PGV (cm/s) of all construction periods for each damage class. The data used to construct the fragility curves are (b) Steel (S) also shown in the figure Note that as described above, no fragility curves could be obtained for 100% major and moderate+ of S and LS buildings. 90% Major (Light-gauge Steel) 80% Moderate+ (Light-gauge Steel) 5. Discussions 70% Moderate- (Light-gauge Steel) ˚ 60% Yamazaki et al. (2019) developed the fragility 50% curves due the 2016 Kumamoto earthquake using 40% Damage Ratio the damage survey data by Mashiki Town 30% government. Figure 10 shows the comparison of 20% the fragility curves of wooden buildings for the 10% 0% major damage ratio for Uki City and Mashiki 0 20 40 60 80 100 Town. It is seen in the figure that the Uki City’s PGV (cm/s) curve shows a lower damage ratio than the Mashiki Town’s one in the same PGV. The PGV (c) Light-gauge Steel (LS) values used to construct the fragility curves for Fig. 9. Fragility curves of buildings of all construction periods for each damage class for Uki City

Table 4. Regression coefficients (λ, ζ) and correlation 100% W (Nishinomiya City; 1995KobeEQ) coefficient (r) for fragility curves of buildings with 90% W (Nada Ward; 1995KobeEQ) 80% respect to the structural type W (Mashiki Town; 70% 2016KumamotoEQ) W (Uki City; 60% Structural Damage 2016KumamotoEQ) λ ζ r type class 50% 40% Major 6.62 1.16 0.86 30% Major Damage Ratio Wooden Moderate+ 6.29 1.12 0.95 20% Moderate- 5.58 1.13 0.97 10% Major - - - 0% S Moderate+ - - - 0 20 40 60 80 100 120 140 160 180 200 220 240 PGV (cm/s) Moderate- 11.02 3.27 0.81 Major - - - Fig. 10. Comparison of fragility curves of wooden LS Moderate+ - - - buildings for the major damage ratio for Uki City, Moderate- 10.41 2.83 0.73 Mashiki Town, Nishinomiya City and Nada Ward Proceedings of the 30th European Safety and Reliability Conference and the 15th Probabilistic Safety Assessment and Management Conference

Uki City was in the range from 10 cm/s to 90 cm/s Kobe earthquake. The fragility curves for Uki as shown in Fig. 9. Thus the plot for Uki City in City and Mashiki Town due the 2016 Kumamoto the range of more than about 90 cm/s in Fig. 10 is earthquake are compared with those for a sort of extrapolation. Nishinomiya City and Nada Ward in Fig. 10. It is The fragility curves for Mashiki Town were seen in the figure that the fragility curves due the developed based on the PGV data range from Kumamoto earthquake show a lower damage ratio 65cm/s to 240 cm/s (Yamazaki et al. 2019). The than those due the Kobe earthquake in the same data used to construct the fragility curves for Uki PGV. City and Mashiki Town have only small overlap A few reasons are considered to explain the in the PGV range. In other words, the damage data difference of the fragility curves due the Kobe and of Uki City is able to complement the damage data Kumamoto earthquakes. First, the change of data of Mashiki Town. Thus we tried to use the both used to construct the fragility curves may affect two datasets to develop the common fragility the result. Figure 12 shows the breakdown of the curve to cover a wide PGV range. Figure 11 number of wooden buildings with respect to the shows the comparison of the fragility curves of construction period, which were used to construct wooden buildings for Uki City, Mashiki Town, fragility curves. As there is a 21-year time and the both municipalities. It is seen in the figure difference between the Kobe and Kumamoto that the fragility curve constructed using the both earthquakes, the composition ratio of data with datasets shows a reasonable trend; it is close to the respect to the construction period has changed Uki’s curve in the small PGV range and significantly. approaches to the Mashiki’s curve in the high The difference in the damage classification of PGV range. the surveys may be the second possible reason of Yamazaki and Murao (2000) constructed the the difference of the fragility curves. It is pointed fragility curves due the 1995 Kobe earthquake out that “Major damage” was more easily issued with respect to the structural type using the in the Kobe earthquake than in the Kumamoto damage survey data for Nada Ward, conducted by earthquake. Kobe City. Yamaguchi and Yamazaki (2000) also Another possible reason is the difference in the created the fragility curves using the damage estimation methods of PGV. The PGV in the survey data of Nishinomiya City due the 1995 Kobe earthquake was estimated by analyzing the relationship between the strong motion records

100% and the building damage data around the seismic 90% W (Uki City) ˝ recording points (Yamaguchi and Yamazaki 80% W (Mashiki Town) ˜ 2001). Actually, no effective strong motion site 70% W (Uki + Mashiki) ˝+˜ existed in Nishinomiya City and only one (Kobe 60% University on a rock site) in Nada Ward at the 50% time of the Kobe earthquake. In this sense, the 40% estimated PGV in the Kumamoto earthquake may 30%

Major Damage Ratio be more reliable. 20% 10% 6. Conclusions 0% 0 20 40 60 80 100 120 140 160 180 200 220 240 PGV (cm/s) This study investigated the characteristics of building damage in Uki City due the 2016 Fig. 11. Comparison of the fragility curves of wooden Kumamoto earthquake was analyzed using the buildings for the major damage ratio for Uki City, damage survey data provided by the Uki City Mashiki Town, and the both municipalities government. As the result, the damage ratio of wooden buildings was found to be larger than 0% 20% 40% 60% 80% 100% those of other structural materials, and the damage ratios of major, moderate+, and moderate- get Nishinomiya City 21% 14% 24% 24% 17% (1995KobeEQ) smaller as the construction period becomes Nada Ward newer. 34% 21% 20% 13% 11% (1995KobeEQ) The fragility curves of buildings for Uki City Mashiki Town 8%3%7% 22% 60% (2016KumamotoEQ) were developed based on the damage survey data Uki City and the estimated peak ground velocity (PGV). 15% 4% 11% 22% 48% (2016KumamotoEQ) Compared with the result of the previous study for Mashiki Town due the 2016 Kumamoto -1951 1952-61 1962-71 1972-81 1982- earthquake, the major damage ratios of wooden Fig. 12. Comparison of the breakdown of the number of buildings for Uki City was shown in a lower level wooden buildings with respect to the construction than those for Mashiki Town in the same PGV. period for Uki City, Mashiki Town, Nishinomiya City The fragility curves for Uki City were obtained and Nada Ward using the damage survey data in the range of Proceedings of the 30th European Safety and Reliability Conference and the 15th Probabilistic Safety Assessment and Management Conference smaller PGV than those for Mashiki Town, thus 1995 Kobe Earthquake, Journal of Japan the regression curves of Uki City were considered Association for Earthquake Engineering, to reflect the trend in the small PGV range. Thus 11(4), 34-47 (in Japanese). the Uki City data can complement the Mashiki National Institute for Land and Infrastructure Town data in the higher PGV range. The fragility Management (NILIM) (2016). Quick report of curve was constructed by integrating the both the field survey on the building damage by the datasets, and the result showed a good fitting for 2016 Kumamoto earthquake, Technical Note, a wide PGV. The fragility curves for wooden No.929, buildings with respect to the construction period http://www.nilim.go.jp/lab/bcg/siryou/tnn/tnn will be developed soon by this approach. 0929.htm (in Japanese). The fragility curves for Uki City and Mashiki National Research Institute for Earthquake Science Town, due the 2016 Kumamoto earthquake, were and Disaster Resilience (NIED) (2018). compared with those for Nishinomiya City and “Japan Seismic Hazard Information Station”, Nada Ward due the 1995 Kobe earthquake. As the http://www.j-shis.bosai.go.jp/map/. result, it was seen in the figure that the fragility Okada, S. and N. Takai (2000). Classifications of curves due the Kumamoto earthquake show a structural types and damage patterns of lower damage ratio than those due the Kobe buildings for earthquake field investigation, earthquake in the same PGV. Proc. the 12th World Conference on Earthquake Engineering, paper 0705, 7. Acknowledgements Auckland, New Zealand. Sugino, M., R. Yamamuro, S. Kobayashi, S. This research was supported by "the Tokyo Murase, S. Ohmura, and Y. Hayashi (2016). Metropolitan resilience project" of the Ministry of Analyses of building damages in Mashiki Education, Culture, Sports, Science and Town in the 2016 Kumamoto Earthquake, Technology (MEXT) of Japanese Government, Journal of Japan Association for Earthquake the National Research Institute for Earth Science Engineering, 16(10), 69-85 (in Japanese). and Disaster Resilience (NIED), and Yamada, M., J. Ohmura, and H. Goto (2017). University. 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