DEVELOPMENT OF UNIFORM HAZARD GROUND MOTION RESPONSE SPECTRA FOR A SITE

Transcription

1 13 th Worl Conference on Earthquake Engneerng Vancouver, B.C., Canaa August 1-6, 2004 Paper No DEVELOPMENT OF UNIFORM HAZARD GROUND MOTION REPONE PECTRA FOR A ITE A.K.GHOH 1 an H..KUHWAHA 2 UMMARY 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 Trombay ste. These results etermne the sesmc hazar at the gven ste an the assocate uncertantes. 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. afety 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 together wth a groun moton tme-hstory. The PGA s evaluate by emprcal relatons nvolvng earthquake magntue an the stance between the source an the ste. 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. These ata shoul be rawn from stes havng smlar geologcal contons (rock/sol). 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 (PRA). esmc hazar at the ste s one of the key elements of the PRA [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 [3-7]. 1 Reactor afety Dvson, Bhabha Atomc Research Centre, Mumba ; Ina 2 Health, afety & Envronment Group, Bhabha Atomc Research Centre, Mumba ; Ina

2 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 RP [8] an Regulatory Gue [9] of UNRC recommen evelopment of unnormalse response spectra. UNRC [9] further proposes to carry out a probablstc safety hazar analyss (PHA) base on unform hazar response spectra (UHR). The present work ams to evelop UHR.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 Trombay 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. 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. [10] conserng aeral source strbuton extene the metho for more generalse forms for the correlaton for PGA. Ths work was extene to evelop UHR conserng a unform aeral source an lne an pont sources of earthquakes [11,12]. In ths report, a smlar methoology s apple to etermne a unform hazar response spectrum. esmc hazar analyss 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 1, b 2 an b are constants, M s the earthquake magntue an R s the hypocentral stance. 3 It has been observe [13] 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. everal 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. Two wely use forms for PGA are: a = b 1 exp(b 2 M) (R+D) -b 3 (2) a = b 1 10 b 2 M (R+D) -b 3 (3)

3 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. Attenuaton relaton for spectral acceleraton The present regulatory ocuments [8,9] 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 [11,12]. The response spectral acceleraton s assume to be of the same form as gven by equaton (2).e. = (M, R, ζ,.t) = b 1 exp(b 2 M) (R+D) -b 3 (4) 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. McGure [14] has use a form smlar to equaton (3). As has been shown by Ghosh et al. [10] equatons (2) an (3) are equvalent. 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). The number of earthquake of magntue greater than or equal to M occurrng annually s gven by Rchter s equaton [15] log 10 N a bm M = (5) 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 P[ ] s obtane. P ( = ) = C r 0 P [ b β 2 G R = r ] f ( r ) r (6) 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 [12]. C = e β M 0 b β 1 b 2 an β = b ln 10.

4 Equaton (6) yels the probablty that the spectral acceleraton (for gven values of ampng an pero) at ste, wll excee a certan value,, gven that an event of nterest ( M M 0 ) occurs anywhere on the fault. Next, we conser the ranom number of occurrences n any tme pero. It s assume that the occurrences of earthquake follow a Posson arrval process wth average occurrence rate of ν per year [2]. Then the number of events, N, of nterest occurrng n the area n a tme nterval of length t years s strbute as : ν t n e ( ν t ) P ( n) = P( N= n) = ; n = 012,,,... (7) N n! 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 n an nterval of tme t has the probablty: p ν t n e ( p ν t ) PN ( n) = P( N = n ) = ; n= 0,1,2,... (8) n! Of partcular nterest s the probablty strbuton of max, the maxmum spectral acceleraton (at gven ampng an pero) over an nterval of tme t. p[ max ] = p[ N = 0 ]] Lettng t = 1 year, = e p ν t (9) p[ max ] = F a p = e P ν = exp( ν C G β / b 2 ) (10) The annual probablty of exceeence of max > s then 1 F a p = 1 exp( Cν G β / b 2 ) 1 [1 Cν G β / b 2 ]

5 β / b 2 = Cν G (11) The mean recurrence nterval ( T y ) of the spectral acceleraton s then the recprocal of ( 1 - F ap ).e., T y β 1 b 2 = (12) Cν G Then equatons (9) an (12) may be use to obtan the probablty of exceeence of n a gven span of t years as P= exp( t/ T ) (13) 1 y The sesmc hazar at a ste s quantfe by the probablty (P/ > ) an T y 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 ource 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[ ) = r] = C G (14) β where G β b 3 b 2 = ( r + D) (15) Multple Lne an Pont ources 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[ N max ] = p[ max ] fromtheth source = 1

6 = exp[ N = 1 C β b 2 G ν ] (16) The above equaton s the most general equaton for any number of sources. Assumng C, b 2 an β are constants, the above equaton smplfes to the followng. β b N 2 p[ max ] = exp[ ( C ) G ν = 1 (17) The mplcaton of the above assumpton s that 'a' can vary wth the source thus allowng fferent earthquake potental for each source, but 'b' an the constants b 1, b 2, b 3 reman unchange for the entre regon uner conseraton. When there are N sources assocate wth the parameters (a an b) for the Rchter's equaton an the parameters are (a,b) for the regon as a whole, then n orer to have the same number of earthquakes conserng ether the ensemble of the sources or the regon as a whole, the followng equalty hols. a 10 = 10 a.e. f all the sources have the same value of a then a = a log 10 ( N) (18) PREENT TUDY The present stuy uses 144 horzontal acceleraton recors from rock stes to evelop attenuaton relaton for response spectral acceleraton [11,12]. 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 [12]. The gtse accelerograms were obtane on magnetc tapes from the Worl Data Center [16]. 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 (4)) 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.

7 TABLE-1 EARTHQUAKE AROUND TROMBAY: Data from Global ources r. No. Magntue (M) Range M 0 M < M 1 No. of Earthquakes n ths Range KOYNA OTHER r. No. EARTHQUAKE AROUND TROMBAY: DATA FROM GBA Magntue (M) Range M 0 M < M 1 No. of Earthquakes n ths Range KOYNA OTHER The geologcal, tectonc an sesmc stuy for the ste was earler carre out to evelop the esgn bass Groun moton [17]. Each of these lneaments n the 300km. raus crcles aroun the ste has been consere as a lne source. An earler stuy [10] has shown that the nfluence of earthquake sources beyon 150km has nsgnfcant effect on the sesmc hazar. Earthquake ata for the pero AD has been obtane from varous catalogues ([18], for example) avalable as publshe lterature (global sources). Data have also been obtane from the Gaurbanur esmc Array (GBA) of Bhabha Atomc Research Centre pero for the pero AD [19]. 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 A summary of these ata s presente n Table-1. A least square ft of the ata was carre out (see equaton 5) an the constant of the equaton ( a value) was ncrease to obtan a mofe ft to envelope. The a an b values obtane from [20] 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 UHR 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

8 varaton of a values obtane from the earthquake ata from global sources an GBA (see Table-2). 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-2. TABLE 2 MAGNITUDE FREQUENCY RELATIONHIP Data Koyna Others Remarks a b a b Global Least quare Ft ata mofe to envelope the observe values GBA Least quare Ft ata mofe to envelope the observe values Ref [20] Base values use n analyss (see Fg. 2) 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 [20]. NUMERICAL REULT 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 1 ) an of the orer of ten thousan years for the safe shutown earthquake (E or 2 ) [21]. Fg. 1 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-2. Fgures 2a - 2c present the UHR 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.

9 Return pero (years) Return pero Probablty of exceeence Probablty of Exceeence pectral Acc. (g) % Ty=1. % Ty=10. % Ty=100. % Ty= E-3 1E PGA (g) Fg. 1: VARIATION OF MRI AND P V. PGA Per. (sec) Fg.2a: UHR for varous values of return pero DICUION From the earler stues [11,12] 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. mlarly, 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. o 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) Ty=7.50E+3 Ty=9.84E+3 Ty=1.77E+4 Ty=2.60E+4 Ty=3.44E P=0.1 P=0.2 P=0.01 P=0.02 P= pectral Acc. (g) pectral Acc. (g) Per.(sec) Fg.2b: UHR for varous values of return pero Per.(sec) Fg.2c: UHR for varous values of probablty of exceeence

10 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. It s seen that generally the spectral acceleraton for the pont source s hgher snce the earthquakes occur at the same stance, whereas the earthquake source stance s greater than or equal to for a lne source. However, for longer peros the two spectra appear to be closer. Ths s ue to contrbuton of the stant earthquakes to the long pero regon of the response spectra. These results wll be useful n carryng out the sesmc probablstc safety assessment of the plants at these stes.

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