PROPOSAL OF THE CONDITIONAL PROBABILISTIC HAZARD MAP

Transcription

1 The 4 th World Conference on Earthquake Engneerng October -, 008, Bejng, Chna PROPOSAL OF THE CODITIOAL PROBABILISTIC HAZARD MAP T. Hayash, S. Fukushma and H. Yashro 3 Senor Consultant, CatRsk Group, Toko Marne & chdo Rsk Consultng Co., Ltd., Tokyo. Japan Senor Researcher, Tokyo Electrc Power Servces Co., Ltd., Tokyo. Japan 3 Chef Consultant, CatRsk Group, Toko Marne & chdo Rsk Consultng Co., Ltd., Tokyo. Japan Emal: takayuk.hayash@tokorsk.co.jp, fukushma@tepsco.co.jp, h.yashro@tokorsk.co.jp, ABSTRACT : We propose the probablstc sesmc hazard map for the study of earthquake rsk of spatally-spreaded facltes. Ths s ntroduced as the condtonal sesmc hazard map whch s the expectaton of the ground moton ntensty at the secondary ste on the condton that the gven ground moton ntensty at the prmary ste occurs. As applcaton, the maps of two areas of Japan are estmated and study the effectveness. KEYWORDS: PSHA, Sesmc Hazard Map, Spatal Correlaton. ITRODUCTIO Probablstc sesmc hazard technque developed by Cornell(968) have been sophstcated n step wth the advances n elemental technology such as emprcal attenuaton equatons. Recently, the probablstc hazard maps estmated by ths technque have been wdely used for the settng of earthquake loads for structures or the calculaton of earthquake nsurance rate, and so on. However, n drawng up these hazard maps, the each ponts on the maps are calculated ndependently, snce the domnant earthquake for each ponts may be dfferent. Therefore, t s not adequate for the study of facltes dstrbuted n wde area. Just as examples, the estmaton of sesmc rsk of the nfrastructure as typfed by electrcty, gas and water needs to consder the events that multple facltes are damaged smultaneously. Heretofore, we used the hazard map of scenaro earthquake for such purposes. But, the damage by undentfed faults of recent years emphaszed the need for probablstc hazard analyss for wde areas. Ths paper proposes the condtonal sesmc hazard map whch s the expectaton of the ground moton ntensty at the secondary ste on the condton that the gven ground moton ntensty at the prmary ste occurs. Ths hazard map enables us to consder probablstcally the correlaton of ground moton for multple stes. As applcaton, the two areas n Kanto and Kansa dstrcts of Japan are employed, followed by the condtonal sesmc hazard maps correspondng to some ground moton ntenstes at the prmary ste, and examne the applcaton of ths map.. ESTIMATIO THE CODITIOAL PROBABILISTIC HAZARD MAP In estmatng the condtonal probablstc hazard map, at frst, we must select the prmary ste where have most mportant facltes of the estmated area. Another pont other than prmary ste are called secondary ste n ths estmaton. Sesmc hazard at prmary ste are evaluated by normal PSHA procedure. One at secondary ste are evaluated the condtonal sesmc hazard of prmary ste sesmc hazard... SEISMIC HAZARD AT PRIMARY SITE Sesmc hazard s expressed as annual exceedance probablty P (a), and when Posson process s assumed as a process of the earthquake occurrence, P (a) s gven by: P = exp[ ν ] () where ν (a) s annual frequency whch the earthquake ground moton ntensty exceeds a.

2 The 4 th World Conference on Earthquake Engneerng October -, 008, Bejng, Chna The sesmc hazard of a prmary ste s obtaned as a sum total of the earthquake hazard due to enormous earthquake events generated by sesmc source zone model. Ths s gven by: Where, ν : p ln( A / a) ν = ν p = ν Φ () = = β Annual frequency of event (a) : Annual exceedance probablty whch the earthquake ground moton ntensty exceeds a A : β : Medan of ground moton ntensty due to earthquake event Logarthmc standard devaton of estmated resduals of emprcal attenuaton equaton Φ [ ] : Standard normal dstrbuton : Total number of events.. SEISMIC HAZARD AT SECODARY SITE The sesmc hazard of secondary ste s defned as expect value of earthquake moton caused by the same ncdence when ground moton ntensty ht the prmary ste. Event frequency λ (a) whch gven ground moton ntensty a due to event occurs at secondary ste s gven by: ln{ A /( a a)} ln{ A /( a+ a)} λ = ν Φ Φ (3) β β where, a s dsaggregaton range of ground moton ntensty and s approprately set. Earthquake ground moton ntensty a and Medum value A of earthquake ground moton ntensty s related as below: a = A exp(αβ ) (4) where, α s the coeffcent of the varaton from the medan value. The varaton of the emprcal attenuaton equaton s dsaggregated to two types of varatons. One s the varaton of source, whch s due to the destructon process of fault. Other s the varaton of earthquake moton propagaton, whch s due to the path or ste amplfcaton. When the logarthm standard devatonβ, β of the emprcal attenuaton equaton by the former and the latter are assumed ndependently, β, β are related as below: β β + = β (5) Eq.(4) are as follow by usng β, β : a = A exp( α β + α ) (6) β where, α, α are the coeffcents whch also show the varaton from the medan value. α, α are gven as follow: α = α β / β, =, ()

3 The 4 th World Conference on Earthquake Engneerng October -, 008, Bejng, Chna The varaton of source s thought to be common about a prmary ste and secondary ste. Meanwhle, the varaton of propagaton s thought to have the correlaton n accordng to the nterste dstance between the prmary ste and the secondary ste. Therefore, ground moton ntensty a ~ j when ground moton ntensty a at prmary ste by event s defned below: where, a ~ j = Aj exp( γ α β+ γ α β ) (8) A s medum value of the ground moton ntensty at secondary ste j due to earthquake event. j γ, γ are the correlaton coeffcents of estmated resduals by emprcal equaton between prmary ste and secondary ste. γ = means perfect correlaton and γ = 0 means full ndependence. When γ = 0, t s gven the medum value whereas exp( γ αβ ) equals to. In ths study, we defned γ as follows based on the proposal by Hayash et al. δ γ = exp( x ), =, (9) k where, x s nterste dstance between prmary ste and secondary ste, k, δ are the coeffcents whch express the reducton of correlaton factor. Expected value a ~ j ( a ) of ground moton due to all earthquake events are gven by follow: = j = a ~ = λ a ~ λ (0) And, annual frequency λ (a) of ground moton ntensty a are gven by follow: j λ = λ () Sesmc hazard curve at secondary ste are evaluated from gven ground moton ntensty and t s annual exceedance frequency by usng Eq.(0) and Eq.(). Above mentoned procedure s llustrated n Fgure. = Prmary Ste Secondary Ste Annual Exceedance Frequency Annual Frequency Sesmc Hazard at Prmary ste a λ(a) λ(a) λ(a) Total Sum of All Events Annual Exceedance Probablty at Secondary ste.0 a Ground Moton Intensty a ~ Ground Moton Intensty Ground Moton Intensty PDF of Ground Moton Intensty at Secondary ste st Fault th Fault Fgure Outlne of condtonal hazard evaluaton

4 The 4 th World Conference on Earthquake Engneerng October -, 008, Bejng, Chna 3. APPLICATIO 3.. Estmated Area The condtonal probablstc hazard map s evaluated for the Kanto regon and the Kansa regon that s the base of ndustry n east and west of Japan as examples. Prmary stes are Tokyo Metropoltan Cty Hall and Osaka Prefectural Head Offce respectvely. And secondary ste are allocated thoroughly wthn the range of 00km n the radus to have centered on a prmary ste. Fgure shows the arrangement of a prmary ste and secondary ste. In ths fgure, marked out crcle means prmary ste, normal crcle means secondary ste. 3.. Sesmc Source Zone Sesmc source zone model of PSHA n ths study s based on Annaka and Yashro. For sesmc source zones correspondng to the actve faults and area source where large earthquake occur perodcally, the characterstcs earthquake model s employed. On the contrary, Gutenberg-Rchter model s used for sesmc zones where medum or small earthquake occur. For estmaton of ground moton ntensty, emprcal attenuaton equaton for peak ground velocty(pgv) by Annaka et al. s employed. For standard devaton of estmated resdual by attenuaton equaton, we assumed that the varaton of source s 0.46 (n natural log) and the varaton of earthquake moton propagaton s 0.4, referrng to Hayash et al. And, for the spatal correlaton, we assumed that the correlaton about source s full ndependence and the varaton about earthquake moton propagaton has the correlaton as a functon of nterste dstance proposed by Hayash et al. Ths correlaton s shown n Fgure Sol Amplfcaton and Instrumental Sesmc Intensty For estmaton of amplfcaton characterstc n surface sol, amplfcaton factor for PGV s employed referrng to Japanese sesmc hazard map by the Headquarters for Earthquake Research Promoton that s the Japanese government agency. And, In ths hazard map, ground moton ntensty are expressed by the nstrumental sesmc ntensty (SI) defned by the Japan Meteorologcal Agency. Hence, PGV are converted nto SI by the equaton proposed by Mdorkawa et. al. as follow: I =.68+. log PGV () where, I s the nstrumental sesmc ntensty, PGV s peak ground velocty at surface Condtonal Sesmc Hazard Map Condtonal sesmc hazard map s created by the proposal procedure to evaluate SI value correspondng to gven annual exceedance probablty from the condtonal sesmc hazard at secondary stes n the estmated regon. Fgure 4 and Fgure 5 show condtonal sesmc hazard map of Kanto and Kansa regon. The value of the annual exceedance probablty correspondng to SI:5 strong(5+), 6 weak(6-), 6 strong() at prmary ste are the condton n these maps. Hence SI at prmary ste s consstent wth the condton n these maps. These fgures show condtonal SI at secondary stes bascally become progressvely smaller wth dstance from the prmary ste n consderaton of spatal correlaton of earthquake moton. The SI dstrbuton of secondary ste s dfferent dependng on the SI of a prmary ste. For nstance, When SI=5+ at prmary ste, the domnant earthquake of these map s nland crustal earthquake. So, sesmc ntensty of secondary ste gets exponentally smaller wth dstance from the prmary ste. But, When SI=6-,, the coastal bg earthquakes greatly nfluence the sesmc hazard of estmated area and the dstrbuton of sesmc ntensty s smaller wth dstance from the sesmc sources. In the comparson between Kanto and Kansa regon, when SI= at prmary ste, the map of Kanto regon shows that the secondary stes of SI>= are dstrbuted near the prmary ste, because the fault of Great Kanto Earthquake whch s the bggest earthquake n ths area s close to the prmary ste. Meanwhle, n the case of Kansa, the secondary stes of SI>= are dstrbuted n narrow area and the area of SI=6- s wdely spread. Ths means that the prmary ste s far from the bggest earthquake faults and areal hazard s nfluenced by varous earthquakes.

5 The 4 th World Conference on Earthquake Engneerng October -, 008, Bejng, Chna 3 prmary secondary 33 prmary secondary 38E 39E 40E 4E 34E 35E 36E 3E Kanto regon (ncludng TOKYO) Kansa regon (ncludng OSAKA) Fgure Estmated areas.0 γ = exp( x ) Correlaton 相関係数 Factor Interste 離間距離 Dstance Fgure 3 Correlaton factor and nterste dstance

6 th The 4 World Conference on Earthquake Engneerng October -, 008, Bejng, Chna 3 38E 0 39E E 33 34E 4E E 0 39E E E 4E Fgure 4 39E 40E E 4E E 0 0 Sesmc Intensty: at Prmary Ste Condtonal hazard map of Kanto regon 3E Sesmc Intensty:6- at Prmary Ste 3 38E 36E 00 Sesmc Intensty:6- at Prmary Ste 35E E Sesmc Intensty:5+ at Prmary Ste 3 36E 00 Sesmc Intensty:5+ at Prmary Ste 35E 36E 3E Sesmc Intensty: at Prmary Ste Fgure 5 Condtonal hazard map of Kansa regon

7 The 4 th World Conference on Earthquake Engneerng October -, 008, Bejng, Chna 4. COCLUSIOS We propose the probablstc sesmc hazard map for the study of earthquake rsk of spatally-spreaded facltes. Ths s ntroduced as the condtonal sesmc hazard map whch s the expectaton of the ground moton ntensty at the secondary ste on the condton that the gven ground moton ntensty at the prmary ste occurs. As applcaton, the maps of two areas of Japan are estmated and study the effectveness. Ground moton ntensty measures at secondary ste are strongly nfluenced by the settng of spatal correlaton and the dscretzaton range of probablty densty functon. For the mprovement of the evaluaton accuracy, the replenshment of the record of observaton records and the evaluaton of regonal are needed. REFERECES Cornell, C. A. (968). Engneerng Sesmc Rsk Analyss. Bulletn of the Sesmologcal Socety of Amerca: Vol.58, o.5, pp Unted Stated Geologcal Survey. (008), The 008 U.S. Geologcal Survey (USGS) atonal Sesmc Hazard Maps (008), atonal Research Insttute for Earth Scence and Dsaster Preventon. (005), A Study on Probablstc Sesmc Hazard Maps of Japan, Techncal ote of the IED, o.5. Hayash, T., Fukushma, S. and Yashro, H.(006), Effects of the spatal correlaton between ground moton ntenstes on the sesmc rsk of portfolo of buldngs. J. Struct. Constr. Eng., o.600, pp Annaka, T. and Yashro, H. (998). A sesmc source model wth temporal dependency of large earthquake occurrence for probablstc sesmc hazard analyss n Japan. Rsk Analyss. WIT PRESS, Annaka, T., Yamazak, F. and Katahra, H. (99). Proposal of attenuaton equaton for peak ground moton and response spectra usng observaton records of JMA 8-type strong-moton sesmograph, 4 th Proceedngs of the JSCE earthquake Engneerng Symposum, pp Hayash, T., Fukushma, S. and Yashro, H. (006), Spatal correlaton between ground moton ntenstes., Archtectural Insttute of Japan, Vol.B-, pp Mdorkawa, S., Fujmoto, K. and Muramatsu, I. (999), Relatonshp between Japanese sesmc ntensty and ground moton ntensty measures, Journal of Insttute of Socal Safety Scence, Vol.. pp.5-56.