Transactons of the 17 th Internatonal Conference on Structural Mechancs n Reactor Technology (SMRT 17) Prague, Czech Republc, August 17 22, 2003 Paper # K11-3 Development of Unform Hazar Response Spectra for a Ste A.K.Ghosh an H.S.Kushwaha Reactor Safety Dvson; Bhabha Atomc Research Centre; Mumba 400085; Ina ABSTRACT Tratonally, the sesmc esgn bass groun moton has been specfe by normalse response spectral shapes an peak groun acceleraton (PGA). The mean recurrence nterval (MRI) use to be compute for PGA only. The present work evelops unform hazar response spectra.e. spectra havng the same MRI at all frequences for Tarapur Atomc Power Staton ste. Senstvty of the results to the changes n varous parameters has also been presente. These results etermne the sesmc hazar at the gven ste an the assocate uncertantes. KEY WORDS: earthquakes, sesmc hazar, faults, lneaments, lne an pont sources, peak groun acceleraton, response spectrum, mean recurrence nterval, probablty of exceeence, sesmc rsk, magntue-frequency relatonshp, unform hazar response spectrum. INTRODUCTION The objectve of asesmc esgn of power plant components an structures s to ensure safety of the plant an the people aroun n the event of an earthquake. Safety nees to be ensure aganst a set of postulate events orgnatng at varous locatons, as ctate by the local geologcal an tectonc features an ata on past earthquakes. The esgn bass groun moton s generally specfe by normalse response spectra (also known as response spectral shapes or the ynamc amplfcatons factors, DAFs) for varous values of ampng an a PGA. The former s obtane by a statstcal analyss of a large number of recors havng earthquake parameters n the range of nterest an selectng a shape wth an acceptable value of the probablty of exceeence. The varous uncertantes an ranomness assocate wth the occurrence of earthquakes an the consequences of ther effects on the NPP components an structures call for a probablstc sesmc rsk assessment (PSRA). Sesmc hazar at the ste s one of the key elements of the PSRA [1]. The sesmc hazar at a gven ste s generally quantfe n terms of the probablty of exceeence of the esgn level PGA [2] an the probablty of exceeence of the specfe groun moton response spectral shapes [3]. In the approach whch has tratonally been aopte the probablty of exceeence of the spectral shape s wth respect to the atabase from whch t has been erve an s not relate wth the temporal or spatal strbuton of earthquakes. The probablty of exceeence of the PGA s, however, evaluate conserng the spatal an temporal strbuton of earthquakes. The new SRP [4] an Regulatory Gue [5] of USNRC recommen evelopment of unnormalse response spectra. USNRC [5] further proposes to carry out a probablstc safety hazar analyss (PSHA) base on unform hazar response spectra (UHRS). The present work ams to evelop UHRS.e. response spectra havng the same mean recurrence nterval (MRI), or equvalently, the same probablty of exceeence n a specfe span of tme at all frequences for the Tarapur Atomc Power Staton Ste. The present paper evelops these spectra conserng lnear an pont sources of earthquakes. It s further recognse that the precte sesmc hazar can vary wth varous parameters nvolve. Numercal results have been presente to show ths varablty. These results wll help to etermne the sesmc hazar at the gven ste an the assocate uncertantes. 1
THEORY Cornell [2] has presente a moel for evaluatng the MRI or the probablty of exceeence, P of a specfe value of PGA. Ghosh et al. [6] extene the metho to spectral acceleraton for lne an pont sources of earthquakes conserng a generalse form of correlaton. In ths paper, a smlar methoology s apple to etermne a unform hazar response spectrum. SEISMIC HAZARD ANALYSIS The sesmc hazar analyss presente by Cornell [2] s base on the peak groun acceleraton (a p ) whch s assume to be of the form b3 a = b exp( b M) R (1) p 1 2 where b, b 1 2 an b 3 are constants, M s the earthquake magntue an R s the hypocentral stance. It has been observe that PGA precte by relatons of the type gven by equaton (1) oes not agree very well wth observatons partcularly for smaller values of R an a stance correcton term (D) has been consere by many workers. Several correlatons are avalable for efnng the peak groun acceleraton (a) for horzontal moton - each evelope from a partcular ata set, an therefore, best sute for nterpolaton wthn a partcular range of parameters. A wely use form for PGA s: a = b 1 exp(b 2 M) (R+D) -b 3 (2) where M s the magntue, R s the stance an D s a correcton term to account for zero stance. For any applcaton, an equaton has to be chosen that s best sute to a gven source-ste combnaton an the range of parameters uner conseraton. ATTENUATION RELATION FOR SPECTRAL ACCELERATION The present regulatory ocuments [4,5] requre the groun moton to be presente as the unnormalse response spectrum tself wthout scalng t to PGA. Attenuaton relaton has been evelope for the unnormalse response spectrum [6]. The response spectral acceleraton s assume to be of the same form as gven by equaton (2).e. S = S(M, R, ζ,.t) = b 1 exp(b 2 M) (R+D) -b 3 (3) where M s the magntue an R s the hypocentral stance. D s a stance correcton factor, ζ s the value of ampng an T s the pero for whch the response spectrum s beng evaluate. The constants, b 1, b 2, b 3 epen on ζ an T. Lne Source Moel Earthquakes occur along faults whch are generally lnear features or represente as ones (lneaments). It s assume that earthquakes are equally lkely to occur anywhere along the length of a fault (lneament). 2
The number of earthquake of magntue greater than or equal to M occurrng annually s gven by Rchter s equaton lo g 10 N = a M b M (4) a an b for a gven regon are etermne from the earthquake occurrence recors of that regon. Conserng the effect of all possble values of the focal stances, the cumulatve probablty obtane. P( S S ) = r 0 = C P[ S S S β b2 G R= r] f ( r) r P [ S S ] s (5) f ( R r ) - the probablty ensty functon of fnng an earthquake at a raus r, an G for varous types of fault orentaton have been presente n [6]. C = e β M 0 b β 1 b 2 an β = b ln 10. Equaton (6) yels the probablty that the spectral acceleraton (for gven values of ampng an pero) at ste, S wll excee a certan value, S, gven that an event of nterest ( M M 0 ) occurs anywhere on the fault. If certan events are Posson arrvals wth average arrval rate ν an f each of these events s nepenently, wth probablty p, a specal event, then these specal events are Posson arrvals wth average annual arrval rate p ν. The probablty, p, that any event of nterest M M 0 wll be a specal event s gven by equaton (6). Thus the number of tmes, N, that the spectral acceleraton (for gven values of ampng an pero) at the ste wll excee S n an nterval of tme t has the probablty: p ν t n e ( p ν t ) PN ( n) = P( N= n S S ) = ; n= 0,1,2,... n! (6) Of partcular nterest s the probablty strbuton of S max, the maxmum spectral acceleraton (at gven ampng an pero) over an nterval of tme t. p S [ max S ] = p[ N = 0 S S ]] = e p ν t (7) The annual probablty of exceeence of S max > S s then 1 F a p = 1 exp( Cν G S β /b 2 ) β / b 2 = Cν G S (8) 3
The mean recurrence nterval ( T y ) of the spectral acceleraton S s then the recprocal of ( 1 - F ap ).e., T y β 1 b = 2 S (9) Cν G Then equatons (7) an (9) may be use to obtan the probablty of exceeence of S n a gven span of t years as P= 1 exp( t/ Ty) (10) The sesmc hazar at a ste s quantfe by the probablty (P/S >S ) an T y an the uncertantes n these quanttes ue to varatons n the correlatons for spectral acceleraton an uncertantes n the sesmc source an occurrence moels.e. a an b, epth of focus, h. Pont Source Moel When there are clusters of earthquakes away from the ste, each cluster coul be moelle as a pont source of earthquakes. In case of a sngle pont source there s no ranomness wth respect to the locaton of the earthquake, hence for a specfe value of spectral acceleraton the magntue s also fxe by the chosen correlaton for spectral acceleraton. The probablty of exceeence of the specfe value of spectral acceleraton s therefore ece by the temporal strbuton of earthquakes. b 2 P[ S S ) = r] = C S G (11) β where G β b 3 b 2 = ( r + D) (12) Multple Lne an Pont Sources When there are a number of lne or pont sources the probablty of non-exceeence of a specfe value of spectral acceleraton s obtane by multplyng the probablty of non-exceeence of the specfe value of spectral acceleraton from each of the sources.e., p[ S NS max S ] = p[ Smax S ] fromtheth source = 1 = exp[ NS = 1 C S β b 2 G ν ] (13) 4
PRESENT STUDY The present stuy uses 144 horzontal acceleraton recors from rock stes to evelop attenuaton relaton for response spectral acceleraton [6]. The range of magntue s generally from 4.1 to 8.1 an there are few recors of magntue lower than 4.1. The stance from the fault vare generally about from about 6 km to 125 km. The salent features of the accelerograms are gven n [6]. The gtse accelerograms were obtane on magnetc tapes from the Worl Data Center[7]. In these ata, the orgnal accelerograms have been ban-pass fltere between 0.07 Hz an 25 Hz an base lne correctons have been mae. Analyss has been carre out wth the recore accelerograms representng the free-fel contons. The geologcal contons of the recorng stes, entfe by the name an number of the recorng staton, are verfe from publshe sources. It has been observe that the response spectra of the two horzontal components recore at the same locaton are often sgnfcantly fferent. Ths may be attrbute to the orentaton of the nstrument wth respect to the fault. To ensure conservatsm, the attenuaton for spectral acceleraton (equaton (3)) at any frequency was evelope by selectng only the hgher of the two horzontal spectral values of the recors at a partcular ste. The attenuaton relatons thus evelope were use for the evelopment of unform hazar response spectra. The geologcal, tectonc an sesmc stuy for the ste was earler carre out to evelop the esgn bass Groun moton [8]. The lneament map s presente n fg. 1. Each of these lneaments shown n the 300 Km. raus crcle aroun the ste has been consere as a lne source. The length of the lneaments an ther stance from the ste has been obtane from ths map. Fg. 1 also shows some of the epcenters of earthquakes. Earthquake ata for the pero 1504-2001 AD have been obtane from varous catalogues avalable as publshe lterature (global sources). Data have also been obtane from the Gaurbanur Sesmc array (GBA) of Bhabha Atomc Research Centre pero for the pero 1977-1995 AD. Broaly the ata from both the sources can be vewe as () those belongng to Koyna an () others. The frst recore earthquake from Koyna s n the year 1965. The magnutue frquency relatonshps for the earthquake ata from global sources are presente n Fgs. 2a an 2b. The fgures nclue the observe ata an results of an earler stuy by Rav Kumar et al. [9]. A least square ft of the ata was carre out (see equaton (3)) an the constant of the equaton ( a value) was ncrease to obtan a mofe ft to envelope the observe ata whch s also nclue n the fgures. The a an b values obtane from [9] yels a rather unconservatve value of the occurrence rates of earthquakes n the Koyna regon. Base on all the ata a realstc set of values have been use for obtanng the UHRS whch s close to the least square ft an conservatve for the magntue range M > 6 whch prouces acceleraton n the range of nterest for esgn. The least square analyss showe a large varaton of a values obtane from the earthquake ata from global sources an GBA (see Table-1). The varaton of a for Koyna earthquakes was, however, not sgnfcantly large. The a an b values obtane from varous stues are presente n Table-1. The Koyna earthquakes occur n a small cluster. These earthquakes are assume to be generate from a pont source. The a an b values for all the lne sources are assume to be the same. The analyss has been carre out conserng a maxmum magntue of 6.5 for earthquakes occurrng n the regon uner stuy [9]. NUMERICAL RESULTS Usually, the value of T y for PGA s requre to be of the orer of hunre years for the operatng bass earthquake (OBE or S 1 ) an ten thousan years for the safe shutown earthquake (SSE or S 2 ). Fg. 3 shows the varaton of MRI an the probablty of exceeence n 50 years as a functon of PGA. The a an b values for varous sources are the reference values gven n Table-1. A senstvty stuy was carre out to see the varaton of MRI wth PGA for varous values of a an b (Fg.4). a an b shown n Fgs 3 an 4 refer to those of the lneaments The a value for Koyna source was kept at the base value whle b followe the value for the other lneaments. Fgures 5 an 6 present the UHRS for the base values of a an b for varous values of MRI an the probablty of exceeence. The spectral acceleraton at any frequency s hgher as the probablty of exceeence reuces. From the earler stues [6] t has been observe that for a sngle source, as the stance from the fault, ncreases the value of the spectral acceleraton for a fxe MRI reuces. Smlarly, for a fxe MRI, the spectral acceleraton reuces wth ncreasng value of l, the length of the fault. At smaller values of l, all the earthquakes are concentrate n a small zone aroun the ste. So for a gven value of MRI, the spectral acceleraton wll be more than that when earthquakes are lkely to occur over a wer range of stance. As l ncreases, the results ten to become asymptotc. Dstant earthquakes affect moton n the long pero (range 0.5s - 2s). As one moves away from the ste, the same spectral acceleraton at the ste woul be requre to be generate by an earthquake of a hgher magntue. Thus the value of MRI for the specfe spectral acceleraton wll be hgher. A hgher value of 'a' or a lower value of 'b' whle the other remans unchange woul mply a hgher value of M, leang to a hgher value of spectral acceleraton. 5
REFERENCES 1. Kenney RP an Ravnra MP. Sesmc Fragltes for Nuclear Power Plant Hazar Stues, Nuclear Engneerng an Desgn, 1984; 79, 47-68. 2. Cornell, C.A. Engneerng Sesmc Hazar Analyss, Bulletn of the Sesmologcal Socety of Amerca, 1968; 59, 5, 1583-1606. 3. Ghosh AK, Rao KS an Kushwaha HS. Development of ResponseSpectral Shapes an Attenuaton Relatons from Accelerograms Recore on Rock an Sol Stes, Report BARC/1998/016, Bhabha Atomc Research Centre, Government of Ina, 1998. 4. U.S.N.R.C. Vbratory Groun Moton, Stanar Revew Plan 2.5.2, NUREG- 800, Rev.3., 1997. 5. U.S.N.R.C. Ientfcaton an Charactersaton of Sesmc Sources an Determnaton of Safe Shutown Earthquake Groun Moton, Regulatory Gue 1.165.,1997. 6. Ghosh AK an Kushwaha HS. Development of Unform Hazar Response Spectra for Rock Stes Conserng Lne an Pont Sorces of Earthquakes, Report BARC/2001/E/031, Bhabha Atomc Research Centre, Government of Ina, 2001. 7. Worl Data Centre. Catalogue of Sesmographs an Strong Moton Recors, Report SE-6, Sol Earth Geophyscs Dvson, Envronmental Data Servce, Bouler, Colorao, U.S.A, 1985. 8. Ghosh AK an Banerjee, D.C. Earthquake Desgn Bass for Tarapur Ste, Internal Report, Bhabha Atomc Research Centre; March 1990 9. Rav Kumar, M. an Bhata, S.C. A New Sesmc Hazar Map for the Inan Plate Regon Uner the Global Sesmc Hazar Assessment Programme, Current Scence,999, 77(3), 447-453. TABLE 1 Magntue Frequency Relatonshps Data Koyna Others Remarks a b a b Global 2.63 0.505 1.10 0.505 Least Square Ft ata mofe to envelope the observe values GBA 2.794 0.505 1.785 0.505 Least Square Ft ata mofe to envelope the observe values Ref [9] 2.1016 0.5989 2.1016 0.5989 2.8 0.5989 2.1016 0.5989 Base values use n analyss (see Fg. 2) 6
FIG. 1: TECTONIC MAP 1.0 0.5 0.0 obs. ata mo. ft ref. [9] use n analyss 0.5 0.0-0.5 obs. val. mo. ft ref[9] an use n analyss log 10 N -0.5-1.0 log 10 N -1.0-1.5-1.5-2.0-2.0-2.5 2 3 4 5 6 7 Magntue Fg. 2a: Magntue-Frequency Relatonshp; Koyna Data; Global Sorces -3.0 3 4 5 6 7 Magntue Fg. 2b: Magntue Frequency Relatonshp; Other Data; Global Sources 7
Return Pero (yrs) 10 4 rertun pero 10 3 probablty of exceeence 10 2 10 1 10 0 10-1 10 0 10-1 10-2 Probablty of Exceeence Return Pero (yrs) 10 4 10 3 10 2 10 1 a=2.1016; b=0.505 a=2.1016; b=0.5989 a=1.1; b=0.505 a=1.8; b= 0.505 10-2 10-3 0.00 0.05 0.10 0.15 0.20 PGA (g) Fg.3 : Return Pero an Probablty of Exceeence for PGA; a= 2.1016 an b=0.5989 for Lne Sources 10 0 0.08 0.10 0.12 0.14 0.16 0.18 0.20 PGA (g) Fg. 4: Senstvty of the Return Pero for PGA to a an b (for lne sources) Spectral Acc. (g) 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 T y = 100 yrs T y = 1000yrs T y = 10000yrs Spectral Acc. (g) 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 P=0.5 P=0.05 P=0.005 0.10 0.05 0.00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Pero (sec) Fg. 5: 5% Dampng UHRS for Varous Values of Return Pero 0.00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Pero (sec) Fg. 6: 5% Dampng UHRS for Varous Values of P 8