Available Available online online at at www.sciencedirect.com www.sciencedirect.com Procedia Engineering Procedia Engineering 00 (2011) 000–000 Procedia Engineering 14 (2011) 1887–1896 www.elsevier.com/locate/procedia The Twelfth East Asia-Pacific Conference on Structural Engineering and Construction Estimation of Fragility Curve of Sewerage Pipes due to Seismic Damaged Data S Nagataa , K Yamamotob*, H Ishidac and A Kusakad b a Kajima Technical Research Institute, Kajima Corporation, Japan Risk Management Dept., Engineering & Risk Services Corporation, Japan c Kajima Technical Research Institute, Kajima Corporation, Japan d Kajima Technical Research Institute, Kajima Corporation, Japan Abstract Sewerage system is one of the most important lifeline systems for an urban society Functional suspension of sewerage system by seismic damages influences the great impact to the citizen’s daily life, business continuity of many companies, public health and so on So, it is very important that the countermeasure against the seismic damages to decrease the effect of the functional suspension of sewerage system is made in advance And a prospect of the total amount of seismic damages is important to make the restoration plan before earthquake occurrence, too In this point of view, we estimate the fragility curve function, which is the maximum ground velocity vs the damage ratio which is proportion of the total length of damaged pipes to the total length of sewerage pipes, to prospect the amount of damages © 2011 Published by Elsevier Ltd Selection and/or peer-review under responsibility of [name organizer] Keywords: earthquake, sewerage system, seismic damage to pipelines, fragility curve, lifeline * Corresponding author: E-mail address: yamamoto@ers-co.jp 1877–7058 © 2011 Published by Elsevier Ltd doi:10.1016/j.proeng.2011.07.237 1888 S Nagata al / /Procedia Authoretname ProcediaEngineering Engineering14 00(2011) (2011)1887–1896 000–000 Introduction In reviewing seismic countermeasures for sewerage facilities, just as those for other lifeline facilities, it is important to accurately estimate the damages caused by earthquakes For sewerage facilities, it is particularly necessary to estimate the damages to sewerage pipes and manholes where the damages are concentrated, as easily and accurately as possible A number of methods have been proposed for estimating seismic damages, of which empirical estimation methods using fragility curves are widely and easily applied in seismic damage estimation studies by national and local governments The fragility curves currently used, however, are intended for estimating the approximate amounts of damage in each municipality, and are based on limited information on damages for a few earthquakes, including the 1983 Nihonkai-Chubu Earthquake and 1995 Great Hanshin Earthquake For more detailed estimation of damages and restoration periods, it is necessary to compile fragility curves based on records of recent seismic damages to sewerage facilities This paper reports on newly compiled seismic damage data for the sewerage pipes and manholes in the public sewerage systems, recorded during the 2004 Mid-Niigata Prefecture Earthquake, 2007 Noto Hanto Earthquake, 2007 Niigata-ken Chuetsu-oki Earthquake and 2008 Iwate-Miyagi Nairiku Earthquake, as well as the fragility curves obtained by reviewing these data And the numerical example is carried out with the sewerage pipes in the Japanese metropolitan area Sewerage Facilities for Analysis We collected data on the locations and damages to sewerage pipes and manholes in the public sewerage systems of six municipalities, including Ojiya City (Ojiya, hereafter), former Kawaguchi Town (Kawaguchi) and former Nagaoka City (Nagaoka) during the 2004 Mid-Niigata Prefecture Earthquake, Monzen district, Wajima City (Wajima) during the 2007 Noto Hanto Earthquake, Kashiwazaki City (Kashiwazaki) during the 2007 Niigata-ken Chuetsu-oki Earthquake, and Kurihara City (Kurihara) during the 2008 Iwate-Miyagi Nairiku Earthquake, and subsequently compiled digital map data in node-and-link format 2.1 Outline of data base Table shows a summary of the digital map data for sewerage pipes and manholes compiled in the study Regarding sewerage pipe data, we analyzed the total lengths of sewerage pipes and those of damaged pipes for every quarter mesh of a standard mesh map (“250 m mesh,” hereafter) for reviewing the damage estimation function Figure shows frequency distributions of the total lengths of sewerage pipes of sewerage facilities in the six municipalities Mode intervals in the total lengths of sewerage pipes within 250 m mesh were, to 200 m for Ojiya, Kawaguchi and Nagaoka, and 200 to 400 m for Wajima, Kashiwazaki and Kurihara The average total lengths of sewerage pipes in 250 m mesh were, approximately 400 m for Kawaguchi, Wajima and Kurihara, 600 m for Ojiya, 700 m for Nagaoka, and 800 m for Kashiwazaki 1889 S Nagata et al / Procedia Engineering 14 (2011) 1887–1896 Author name / Procedia Engineering 00 (2011) 000–000 Table 1: Summary of the sewerage pipes and manholes in the analysis site Sewerage Pipe and Manhole Earthquake City and Town 2004 Mid Nigata Prefecture Earthquake Nagaoka City Ojiya City Kawaguchi Town 873 145 40.6 52.3 26.0 8.3 26,865 5,711 1,325 Number of Damaged Manhole (spots) (no collecting) 484 316 2007 Noto Hanto Eartquake Wajima City 51.7 9.2 2,079 140 Pipe Length (km) Damaged Pipe Length (km) Number of Manhole (spots) 2007 Niigata-ken Chuetsu-oki Eartquake Kashiwazaki City 398 27.9 12,444 816 2008 Iwate-Miyagi Nairiku Earthquake Kurihara City 180 4.88 4,866 259 300 1.2 200 150 100 0.8 0.6 0.4 2400＜L≦2600 2200＜L≦2400 2000＜L≦2200 1800＜L≦2000 1600＜L≦1800 1400＜L≦1600 1200＜L≦1400 800＜L≦1000 1000＜L≦1200 0.0 600＜L≦800 400＜L≦600 0.2 200＜L≦400 50 Cumulative Frequency 1.0 Ojiya City Nagaoka City Kawaguchi Town Wajima City Kashiwazaki City Kurihara City Ojiya City Nagaoka City Kawaguchi Town Wajima City Kashiwazaki City Kurihara City 0＜L≦200 Frequency (number of mesh) 250 Pipe Length in ２５０ ｍeter Square Mesh （ｍ） Figure 1: Histogram of pipe length in mesh 2.2 Ground model and sewerage pipes in the analysis site In Figures (1) to (5), the sewerage pipes and kind of liquefaction ground modeled as 250 m square meshes of five sites for analysis are shown In these Figures, the liquefaction mesh is green and nonliquefaction mesh is yellow, and the damaged pipes are shown as red lines and the non-damaged pipes are shown as blue lines, respectively These Figures show that almost of damaged pipes are buried in the liquefaction site Figure2 (1): Ojiya city and former Kawaguchi town (2004 mid-Niigata prefecture earthquake) 1890 S Nagata et al /Author Procedia Engineering (2011) 1887–1896 name / Procedia14 Engineering 00 (2011) 000–000 Figure2 (2): Former Nagaoka city (2004 mid-Niigata prefecture earthquake) Figure2 (3): Kashiwazaki city (2007 Niigata-ken chuetsu-oki earthquake) Figure2 (4): Kurihara city (2008 Iwate-Miyagi nairiku earthquake) 1891 S Nagata et al / Procedia Engineering 14 (2011) 1887–1896 Author name / Procedia Engineering 00 (2011) 000–000 Figure2 (5): Monzen district, Wajima city (2007 Noto hanto earthquake) Figure 2: Location of damaged sewerage pipes and distribution of liquefaction site (excluding manholes) Fragility Curve Function For sewerage pipes and manholes of sewerage facilities in the six municipalities, we reviewed fragility curves regarding both physical damages We used the seismic intensity for the maximum ground velocity, and a normal distribution for the basic shape of the fragility curve, as equation (1) shows, with reference to prior research results.(Maruyama and Yamazaki (2009)) ⎡ (ln Vi − λ ) ⎤ R (Vi ) = C ⋅ Φ ⎢ ⎥ ζ ⎦ ⎣ n { ε = ∑ [Ri − R(Vi )]2 ⋅ Li i =1 ∑ (v m Vi = j =1 ij ⋅ lij ) } (1) (2) (3) m ∑l ij j m Li = ∑ lij (4) j =1 where, R (Vi) is an estimated value of the physical damage ratio at a maximum ground velocity of Vi C, λ and ζ are regression coefficients calculated by minimizing the objective function ε in equation (2) with the quasi-Newton method n in equation (2) represents the total number of intervals when maximum ground velocities estimated for each 250 mesh are classified into intervals of 10 cm/s Vi, the representative value of the maximum ground velocity for interval i, which is defined as a weighted average value of maximum ground velocities with the total length of sewerage pipes in each 250 m mesh as weight coefficients, is calculated by equation (3) using the number of samples included in interval i (m), the maximum ground velocity of each sample (vij), and the total length of sewerage pipes (lij) Ri is an actual value of damage ratio calculated by using the total length of sewerage pipes and that of S Nagata et al / Procedia Engineering 14 (2011) 1887–1896 Author name / Procedia Engineering 00 (2011) 000–000 damaged pipes within interval i of the maximum ground velocity for each 250 m mesh Li, which is the total length of sewerage pipes within interval i, aggregated for computing Ri, is calculated by equation (4) 3.1 Considering about factor of coefficient In Figures to 5, three factors, which are kind of ground, pipe diameter and buried depth of pipe, are compared with damage ratio of pipe The damage occurrence of pipe is influenced by the kind of ground, the pipe diameter or the buried depth of pipe, respectively The influence by the kind of ground is especially obvious So we estimated the fragility curve function with the pipe data in the liquefaction site and in the non-liquefaction site, respectively 1400 0.35 Damaged Pipe Length(km) Non-damaged Pipe Length(km) Damage Rate 0.30 0.25 800 0.20 600 0.15 400 0.10 200 0.05 0.00 Lequifaction site NonLequifaction site Lequifaction site NonLequifaction site Lequifaction site NonLequifaction site Lequifaction site NonLequifaction site Lequifaction site NonLequifaction site Lequifaction site NonLequifaction site Pipe Length （ｋｍ） 1000 Ojiya City Nagaoka City Kawaguchi Wajima City Town Kind of Pipe Buried Site Kashiwazaki Kurihara City City Figure 3: Kind of ground vs damage ratio of pipe Damaged Pipe Length(km) Non-damaged Pipe Length(km) Damage Rate 700 0.8 0.7 0.6 500 0.5 400 0.4 300 0.3 200 0.2 100 0.1 0.0 0≦Φ＜100 100≦Φ＜300 300≦Φ＜600 600≦Φ＜2000 2000≦Φ＜500 unknown 0≦Φ＜100 100≦Φ＜300 300≦Φ＜600 600≦Φ＜2000 0≦Φ＜100 100≦Φ＜300 300≦Φ＜600 600≦Φ＜2000 2000≦Φ＜500 unknown 0≦Φ＜100 100≦Φ＜300 300≦Φ＜600 unknown 0≦Φ＜100 100≦Φ＜300 300≦Φ＜600 600≦Φ＜2000 unknown 0≦Φ＜100 100≦Φ＜300 300≦Φ＜600 600≦Φ＜2000 unknown 600 Ojiya City Kawaguchi Town Nagaoka City Diameter Figure 4: Pipe diameter vs damage ratio of pipe Wajima City Kashiwazaki City Kurihara City Damage Rate（km／km） 800 Damage Rate （km／km） 1200 Pipe Length (km) 1892 1893 S Nagata et al / Procedia Engineering 14 (2011) 1887–1896 Author name / Procedia Engineering 00 (2011) 000–000 0.6 Damaged Pipe Length(km) Non-damaged Pipe Length(km) Damage Rate 0.5 400 0.4 300 0.3 200 0.2 100 0.1 0.0 0＜D≦1 1＜D≦2 2＜D≦3 3＜D unknown 0＜D≦1 1＜D≦2 2＜D≦3 3＜D unknown 0＜D≦1 1＜D≦2 2＜D≦3 3＜D unknown 0＜D≦1 1＜D≦2 2＜D≦3 3＜D unknown 0＜D≦1 1＜D≦2 2＜D≦3 3＜D unknown 0＜D≦1 1＜D≦2 2＜D≦3 3＜D unknown Pipe Length (km) 500 Damage Rate（km／km） 600 Ojiya City Kawaguchi Town Nagaoka City Wajima City Kashiwazaki City Kurihara City Burid Depth （ｍ） Figure 5: Buried depth of pipe vs damage ratio of pipe Fragility Curves of Sewerage Pipes Damages to sewerage pipes and their consequences can be classified broadly into physical damages We reviewed fragility curves, and classified those pipe sections (sections between manholes) where damages including pipe breakage, slack and meandering, joint breakage, attachment pipe breakage and other damages occurred, that were evaluated as seismic damages in post-earthquake appraisals, as physical damages As preparatory work, we first divided all sewerage pipes in each municipality into 250 m mesh, and conducted cross tabulation of the total length of sewerage pipes, using indices including the maximum ground velocity classified into intervals of 10 cm/s, presence or absence of damages, and classification by ground conditions of sewerage pipes (i.e based on the presence or absence of backfilling soil, embankment or sandy soil, and N values; those grounds that had liquefaction potential were classified as liquefied ground, and those that did not have liquefaction potential were classified as non-liquefied ground) Although we considered various indices in the cross tabulation, the three indices mentioned above were finally selected because of their significance for the tabulation, based on prior studies and results, in order to ensure that the total lengths in each category were more than several hundred meters As representative values of maximum ground velocities within the intervals of 10 cm/s in the cross tabulation table, weighted maximum ground velocities calculated for underground conditions of the pipes, using equation (3), were used Furthermore, physical damage ratios were calculated by dividing the total length of physical damages in each classification of underground conditions of the pipes by the total length of the pipes in the same classification Figure shows fragility curves of the sewerage pipes calculated by equation (1) through (3), as well as measured values of physical damage ratios, while Table2 shows regression coefficients of the fragility curves The fragility curves of the sewerage pipes in Figure closely match the measured values, showing that the damages started to appear at the maximum ground velocity of around 30 cm/s, and became nearly flat at velocities over 85 cm/s, where the physical damage ratio of liquefied ground was approximately 15%, and that of non-liquefied ground was approximately 4% Author name / Procedia Engineering 00 (2011) 000–000 S Nagata et al / Procedia Engineering 14 (2011) 1887–1896 1894 0.40 0.35 Fragility Curve Function (all site) Fragility Curve Function (lequifaction site) Fragility Curve Function (non-lequifaction site) Damage Ratio (all data) Damage Ratio (Liquefaction site) Damage Ratio (Non Liquefaction site) Damage Ratio (km/km) 0.30 0.25 0.20 0.15 0.10 0.05 0.00 20 40 60 80 100 120 140 Maximum Ground Velocity (cm/s) 160 180 200 Figure 3: Estimated fragility curve function and sample data used in the calculation of regression Table 2: Estimated co-efficient Kind of Data C λ ζ All Site of Cities 0.126 3.898 0.220 Lequifaction Site 0.151 3.907 0.219 Non-lequifaction Site 0.045 4.022 0.198 We carried out the numerical example with the sewerage pipes in the Japanese metropolitan area by the estimated fragility curve The total length of the sewerage pipes in the analysis site is about 70,000 km And the Tokyo-wan Hokubu Earthquake is used as a hazard for the numerical example Figure 4(1) shows the distribution of the maximum ground velocity of the hazard, which is the Tokyowan Hokubu Earthquake, in the analysis site for the numerical example Figure 4(2) shows the distribution of the liquefaction site Figure 4(2) and Figure 4(4) show the distribution of the physical damage ratio and the distribution of the physical damaged pipe length within the standard mesh, which is the km square mesh, respectively The result of the numerical example shows that the total length of the damaged sewerage pipe is about 1,370 km in the analysis site by the Tokyo-wan Hokubu Earthquake S Nagata et al / Procedia Engineering 14 (2011) 1887–1896 Author name / Procedia Engineering 00 (2011) 000–000 Figure 4: Results of numerical example in the Japanese metropolitan area Conclusions We have compiled digital cartographic data for sewerage pipes as well as seismic motion data for six municipalities, including Ojiya City, former Kawaguchi Town and former Nagaoka City during the 2004 Mid-Niigata Prefecture Earthquake, Monzen district, Wajima City during the 2007 Noto Hanto Earthquake, Kashiwazaki City during the 2007 Niigata-ken Chuetsu-oki Earthquake, and Kurihara City during the 2008 Iwate-Miyagi Nairiku Earthquake Using these digital cartographic data, and adopting the maximum ground velocity as a seismic motion index, as well as a normal distribution as the shape function, we reviewed the physical damage ratio curves and malfunction ratio curves of the sewerage pipes Regarding the physical damage ratio of the sewerage pipes, damages started to appear at the maximum ground velocity of around 30 cm/s, and curves with the damage ratios of approximately 15% for liquefied ground and approximately 4% for non-liquefied ground were obtained, at the maximum ground velocity over 85 cm/s And the numerical example was carried out with the sewerage pipes in a Japanese metropolitan area by the estimated fragility curve The result of the numerical example shows that the total length of the 1895 1896 S Nagata et al / Procedia Engineering 14 (2011) 1887–1896 Author name / Procedia Engineering 00 (2011) 000–000 10 damaged sewerage pipe is about 1,370 km in t Japanese metropolitan area by the Tokyo-wan Hokubu Earthquake Acknowledgments This study was funded by a grant for the Research and Development of Construction Technology from the Ministry of Land, Infrastructure, Transport and Tourism (MLIT) in FY2009 For the collection of seismic damage data, we received invaluable support from Professor Keiko Tamura, Crisis Management Office and Assistant Professor Munenari Inoguchi, Disaster-Relief Science Center, of Niigata University, and the sewerage facility departments of the six municipalities of Ojiya City, former Kawaguchi Town, Nagaoka City, Wajima City, Kashiwazaki City and Kurihara City Strong motion records were made available from K-NET of the National Research Institute for Earth Science and Disaster Prevention, as well as from KiK-net We sincerely thank all organizations and individuals who supported the study References [1] Maruyama Y and Yamazaki F Estimation of Damage Ratio of Water Distribution Pipe Based on Recent Earthquake Damage Data Journal of Japan Association for Earthquake Engineering Vol.30, 2009, pp, 565-574 ... (2007 Noto hanto earthquake) Figure 2: Location of damaged sewerage pipes and distribution of liquefaction site (excluding manholes) Fragility Curve Function For sewerage pipes and manholes of sewerage. .. distributions of the total lengths of sewerage pipes of sewerage facilities in the six municipalities Mode intervals in the total lengths of sewerage pipes within 250 m mesh were, to 200 m for... ground velocity of each sample (vij), and the total length of sewerage pipes (lij) Ri is an actual value of damage ratio calculated by using the total length of sewerage pipes and that of S Nagata