Research on Time-history Input Methodology of Seismic Analysis

Transcription

1 Transactons, SRT 19, Toronto, August 2007 Research on Tme-hstory Input ethoology of Sesmc Analyss Jang Nabn, ao Qng an Zhang Yxong State Key Laboratory of Reactor System Desgn Technology, Nuclear Power Insttute of hna, hengu, hna STRAT Several methos exst to nput sesmc exctaton when makng the sesmc tme-hstory analyss for esgn of nuclear power plant: 1) to nput the splacement tme-hstory at the base, whch s calle splacement metho; 2) to nput the nerta loang calculate from the tme-hstory of support moton acceleraton, whch s calle acceleraton metho; 3) large mass metho. Ths paper euce the theoretcal bass of the frst two methos, an presente a new metho base on acceleraton metho, calle mofe acceleraton metho. Through a numercal example, the sesmc responses wth three methos have been compare respectvely, whle the restrcton contons for usng the three methos were scusse. Sesmc analyss of reactor coolant system of a three-loop nuclear plant was also carre out wth above-mentone three methos, an three fferent response results were gven. INTRODUTION As a major natural hazar, earthquakes may cause extremely amagng for nustral or power-generatng facltes. To avo the potental harm of earthquakes, strct safety rules have been establshe n the esgn of nuclear power plant. These sesmc safety rules can be classfe nto two levels: the Operatonal Bass Earthquake (OBE) for mantanng unt operablty for a sesmcally probable level, on ste-specfc hstorcal an geologcal bases, an the Safe Shutown Earthquake (SSE) for returnng of the reactor to a permanent shutown conton. Durng the earthquake evaluaton, safety-relate structures, systems an components classfe as sesmc category I shoul wthstan the loas mpose by these two hypothetcal earthquakes. Tme-hstory an response spectrum methos are the two basc methos that are commonly use for the sesmc ynamc analyss. The tme-hstory metho s relatvely more tme consumng, lengthy an costly. The response spectrum metho, on the other han, s relatvely more rap, concse, an economcal. However, tme-hstory metho must be employe when geometrcal an/or materal non-lneartes are present n the structural systems. Nowaays, t s more convenent for usng tme-hstory metho than before for avancng of computer s harware an software. Several methos exst to nput sesmc exctaton when makng the sesmc tme-hstory analyss for esgn of nuclear power plant: 1) to nput the splacement tme-hstory at the base, whch s calle splacement metho; 2) to nput the nerta loang calculate from the tme-hstory of support moton acceleraton, whch s calle acceleraton metho; 3) large mass metho. Ths paper euce the theoretcal bass of the frst two methos, an presente a new metho base on acceleraton metho, calle mofe acceleraton metho. Through a numercal example, the sesmc responses wth three methos have been compare respectvely, whle the restrcton contons for usng the three methos were scusse. Sesmc analyss of reactor coolant system of a three-loop nuclear plant was also carre out wth above-mentone three methos, an three fferent response results were presente. ETHODS OF SEISI INPUT IN TIE-HISTORY ANALYSIS Dsplacement etho For a three-mensonal structural system wth sesmc exctaton at supports, couple equatons of moton can be wrtten n the parttone matrx form as:

2 Transactons, SRT 19, Toronto, August 2007 T BB X&& + Z && T BB X& K + Z & K T K K BB X 0 = Z FB where a ot over a quantty enotes fferentaton wth respect to tme an the superscrpt T enotes transpose of a matrx. X s a N 1 1 vector of unknown absolute translatonal splacements at the N 1 number of nonsupport egrees of freeom. Z s a N 2 1 vector of absolute translatonal splacements at the N 2 number of support egrees of freeom., an K enote mass matrx, ampng matrx an stffness matrx, respectvely. The submatx wth subscrpt s assocate wth X, X & or X &, an BB wth Z, Z & or Z &. The subscrpt enotes the couplng term. When we use splacement metho, the splacement tme-hstory of support moton s known as the bounary conton of Eq. (1). If the ntal conton s gven, the absolute translatonal splacements X can be obtane by solvng Eq. (1). As we care more about ynamc splacement parts than the whole absolute splacements n sesmc analyss, so the output ata of splacement response has to be reprocesse. In aton, sesmc exctaton s usually recore n the form of tme-hstory of groun moton acceleraton, therefore, splacement tme-hstory has to be obtane from acceleraton tme-hstory through two tmes of tme ntegral. Ths process wll ntrouce a bt of numercal error. (1) Acceleraton etho The frst set of equatons n Eq. (1) may be rewrtten as follows: X& + X& + K X = Z&& Z& K Z (2) Eq. (2) represents a set of N 1 equatons for the unknown absolute splacements X. The rght han se of Eq. (2) represents a N 1 1 vector of known forcng functons snce the moton (.e., Z, Z & an Z & ) s specfe at the support egrees of freeom. The splacement vector X an Z can be ecompose nto statc an ynamc parts usng the followng efnton: X = X + X s (3a) Z = Z + Z s (3b) where X s a N 1 1 vector of ynamc splacements contrbutng to X; X s s a N 1 1 vector of statc splacements contrbutng to X; Z s a N 2 1 vector of ynamc splacements contrbutng to Z (Note that ths vector s entcally equal to a null vector snce Z s specfe apror); Z s s a N 2 1 vector of statc splacements contrbutng to Z ( Note that ths vector s entcally equal to Z snce Z = 0 ). The statc splacements, X s, can be calculate from Eq. (2) by settng mass an ampng matrces equal to zero. Thus, one obtans 1 X s = K K Z (4) The above equaton efnes the tme-varyng equlbrum poston X s (t) of the system uner the mpose splacements Z (t). Substtutng Eq. (3) nto Eq. (2) an utlzng Eq. (4), the followng equaton s obtane: X&& X& 1 K X K K Z&& = ] + [ K K ] Z& (5) [ where s entcally equal to a null matrx for a lumpe mass formulaton; matrx R. Thus, Eq. (5) can be smplfe as: K 1 K can be replace by the X& + X& + K X = RZ&& + R] Z& (6) [ The secon term on the rght han se of the above equaton s small n comparson wth the frst term on the rght han

3 Transactons, SRT 19, Toronto, August 2007 n the most tme. Therefore, t can be neglecte [1], an Eq. (6) can reuces to the bass equaton of acceleraton metho: X&& + X& + K X = RZ& (7) For acceleraton metho, Eq. (7) s use for tme-hstory analyss of structural systems subject to unform exctaton at supports. omparng wth splacement metho, ths metho has no nee to o any reprocessng wth the nput an output ata. ofe Acceleraton etho If the secon term on the rght han se of Eq. (6) was taken nto account, a new metho for sesmc nput n tme-hstory analyss can be obtane. If one makes the assumpton of Raylegh ampng,.e.: = α + βk (8a) Thus, Eq. (6) may be rewrtten as follows: X&& = α + βk (8b) + X& K X RZ& + = E (9a) Z & = Z&& + αz& E (9b) For mofe acceleraton metho, the velocty, Z &, can be obtane from Z & by tme ntegral, then the equvalent acceleraton Z & E can be calculate from Eq. (9b). Other processes are same as the acceleraton metho, except replacng Z & wth Z &. Obvously, the numercal error ntrouce by preprocess exctaton ata n ths metho s E smaller than the one ntrouce n splacement metho. Lke acceleraton metho, ths metho can be use only for tme-hstory analyss of structural systems subject to unform exctaton at supports. NUERIAL EXAPLE For comparng the three methos mentone above, a sample numercal example s presente. Three mass-sprng systems are connecte to the groun (see Fg. 1). Fg.2 shows the tme-hstory of groun acceleraton, an moel parameters are specfe n Tab acceleraton /ms tme /s Fg. 1 Analytcal moel Fg. 2 Tme-hstory of groun acceleraton

4 Transactons, SRT 19, Toronto, August 2007 Table 1. oel parameters ass / kg Stffness of sprngs Raylegh ampng / kn.m -1 constants K1 K2 K3 α β Table 2. The maxmum loa n sprngs for three methos of exctaton nput Dsplacement metho Acceleraton metho ofe acceleraton metho ass-sprng Force / N system 1 Tme / s ass-sprng Force / N system 2 Tme / s ass-sprng Force / N system 3 Tme / s For three methos of exctaton nput, three sets of response results can be obtane by usng ANSYS 8.0 [2] (see Tab. 2). The fferences of results between the splacement metho an the mofe acceleraton metho are relatvely small, n that they all have consere the secon term on the rght han se of Eq. (6). The responses obtane n acceleraton metho an n mofe acceleraton metho are fferent because of the fferent exctaton nput. SEISI ANALYSIS ON REATOR OOLANT SYSTE OF A THREE-LOOP NULEAR PLANT Nonlnear analytcal moelng Wth above-mentone three methos, a sesmc analyss on reactor coolant system of a PWR plant was carre out. The system conssts of the Reactor Pressure Vessel (RPV) an three loops, each comprsng a Steam Generator (SG), a Reactor oolant Pump (RP), an the reactor coolant ppes. The pressurzer s connecte to one of the loops through surge lne. The nonlneartes n the reactor coolant system manly appear at the support poston. The RPV s supporte by sx support pas that ft nto recesses n a crcular support rng mounte on a lege nse the reactor pt. Ths confguraton allows the RPV to move freely upwars, but wll lock the ownwars movement. The support legs an snubbers of the equpment an surge lne have blnear stffness characterstcs. The SG an pressurzer are supporte laterally by the stops whch mantan 1 to 4.4mm gaps between the equpment shells, also wth the nelastc stress-stran relatonshp at the SG lower lateral stops. The prmary equpment s smulate by three-mensonal beam element. The lumpe mass ponts moelng nternals attach on the beam element. Three kns of ppe elements are use accorng to the structure form of the prmary ppng an surge lne: elastc straght ppe, elastc ppe tee an elastc curve ppe (elbow). The reactor bulng nternal structure s moele by a stck moel wth three-mensonal beam an lumpe mass, representng the cvl walls an certan floors. any kns of support are nclue n the reactor coolant system such as support skrt, support leg, support rng, stop, snubber, an ppe whp restrant. Generally, the lnear supports are moele by lnear sprng. The nonlneartes n the supports nclung mutlnear stffness, gap, an nelastc are stmulate by nonlnear sprng. Fg.3 shows the analytcal moel of the reactor coolant system. The specfc crtcal ampng ratos are 2% (OBE) an 4% (SSE) for the reactor coolant system, wth 5% (OBE) an 7% (SSE) for the reactor bulng nternal structure [3]. Raylegh ampng constants can be calculate from moal

5 Transactons, SRT 19, Toronto, August 2007 ampng ratos, ξ. If ω s the natural crcular frequency of moe, α an β satsfy the relaton: α βω ξ = + (10) 2ω 2 Fg.3 Analytcal moel of the reactor coolant system Sesmc nput An artfcal tme-hstory s generate from the esgn response spectra (US NR RG1.60) at free fel for carryng out a tme-hstory analyss. The tme hstory responses can be obtane from each of the three components of the earthquake moton, two horzontal an one vertcal rectons, an combne at each tme step algebracally. The maxmum response s then erve from the combne tme soluton. Usng ths metho, the three components of the artfcal tme-hstory shoul be statstcally nepenent. Results The sesmc analyss uner SSE has been fulflle usng fnte element coe ANSYS8.0. The maxmum responses at the typcal locaton are presente n Table 3. For the complexty nuce by nonlneartes n the system, any event concluson can not obtane by comparng the results for three methos of exctaton nput. But, as a whole, the response results for mofe acceleraton metho are closer wth those for splacement metho. DISUSSION If one makes the assumpton of Raylegh ampng, the secon term on the rght han se of Eq. (6) reuces to α RZ & whch woul vansh f = 0 A α rrespectve of the value of β. For most conton n nuclear engneerng, lghtly ampe systems are consere, so acceleraton metho can be aopte [4]. But n some specal contons, such as vbraton analyss of structural systems whch are mmerse n reactor coolant, α s not so small. In these contons,

6 Transactons, SRT 19, Toronto, August 2007 acceleraton metho may have some lmtaton, so splacement metho an mofe acceleraton metho shoul be aopte, an f support exctaton s recore n the form of acceleraton tme-hstory, mofe acceleraton metho woul be better for ecreasng numercal error ntrouce urng process the nput ata. Table 3. The response results at typcal locaton for three methos of exctaton nput Horzontal splacement at steam nozzle / mm Torsonal moment Elbow at the.m SG nlet Benng moment.m Torsonal moment Elbow at the.m SG outlet Benng moment.m Axal force Lateral force RPV Outlet nozzle Torsonal moment.m Benng moment.m Horzontal loas Support at RPV nlet Vertcal loas Horzontal loas Support at RPV outlet Vertcal loas Dsplacement ofe acceleraton Acceleraton metho metho metho nmum axmum nmum axmum nmum axmum REFERENES: [1] lough, R. W. Recent Avances n atrx ethos of Structural Analyss an Desgn, Unversty of Alabama Press, [2] ANSYS, Inc, ANSYS User s manual for Revson 8.0, [3] US NR RG1.61, Dampng Values for Sesmc Analyss for Nuclear Power plants, [4] Hong Jng-fen. Overvew of Sesmc Analyss for Nuclear Power Plant, Nuclear Power Engneerng, 17 (3), 1996, pp (n hnese)