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Nuclear Engineering and Design 203 (2001) 249257

New seismic design spectra for nuclear power plants

Robin K. McGuire a,*, Walter J. Silva b, Roger Kenneally c

a Risk Engineering, Inc., Boulder, CO 80305, USAb Pacific Engineering and Analysis, El Cerrito, CA 94530, USA

c US Nuclear Regulatory Commission, Rock6ille, MD 20852, USA

Received 2 February 2000; accepted 1 July 2000

Abstract

Under a US Nuclear Regulatory Commission-sponsored project recommendations for seismic design groundmotions for nuclear facilities are being developed. These recommendations will take several forms. Spectral shapeswill be developed empirically and augmented as necessary by analytical models. Alternative methods of scaling therecommended shapes will be included that use a procedure that integrates over fragility curves to obtain approxi-mately consistent risk at all sites. Site-specific soil effects will be taken into account by recommending site-specificanalyses that can be used to modify rock hazard curves at a site. Also, a database of strong motion records will bearchived for the project, along with recommendations on the development of artificial motions. This will aid thegeneration of motions for detailed soil- and structural-response studies. 2001 Elsevier Science B.V. All rightsreserved.

www.elsevier.com:locate:nucengdes

1. Introduction

In 1996 the Nuclear Regulatory Commission(NRC) amended its regulations to update thecriteria used in decisions regarding nuclear powerplant siting, including geologic, seismic, andearthquake engineering considerations for futureapplications; USNRC (1996). As a follow-on tothe revised siting regulations, it is necessary todevelop state-of-the-art recommendations on thedesign ground motions commensurate with seis-mological knowledge and engineering needs. The

current design spectra in Regulatory Guide 1.60(USNRC, 1993) were based on limited, princi-pally western United States earthquake strong-motion records available at that time. Since 1996the NRC has funded a project to develop up-to-date seismic design spectra for the US. The workcombines empirical and analytical approaches,supplementing data where they are sparse usingtheoretical methods to develop the recommendedspectra for a range of earthquake magnitudes anddistances. Soil conditions necessarily involve site-specific parameters, and we demonstrate and rec-ommend procedures to account for local soileffects on earthquake motions. A Review Panelconsisting of Carl Stepp (Chair), David Boore,Allin Cornell, I.M. Idriss, and Robert P. Kennedy

* Corresponding author. Present address: Risk EngineeringInc., Suite A, 4155 Darley Avenue, Boulder, CO 80303, USA.Tel.: 1-303-4993000; fax: 1-303-4994850.

E-mail address: mcguire@riskeng.com (R.K. McGuire).

0029-5493:01:$ - see front matter 2001 Elsevier Science B.V. All rights reserved.

PII: S0 029 -5493 (00 )00345 -9

R.K. McGuire et al. : Nuclear Engineering and Design 203 (2001) 249257250

review the work and offer guidance on proce-dures. The prime contractor is Risk Engineering,Inc., with Pacific Engineering and Analysis devel-oping databases, spectral shapes, site responseprocedures, and spectral matching criteria. Thispaper reviews the scope of the work, indicates thedirection that recommendations are taking, andpresents preliminary results. Final results will beavailable in the project report.

2. Spectral shapes

Databases for the western US are available inthe form of strong motion accelerograms for mo-ment magnitudes M in the range 5.07.6 andsource-to-site distances R of 1200 km. Rockconditions in California are generally soft, withnear-surface shear wave velocities of 200450 m:s(7001500 ft:s).

The databases of strong motion records andempirical attenuation relations form the basis forrecommended spectral shapes on rock for definedM and R bins, augmented as necessary by analyt-ically derived shapes. In the application of thesespectral shapes for design, the MR combinationis defined by the dominant earthquake as deter-

mined from a probabilistic seismic hazard analysis(PSHA). Examples of procedures for defining thedominant earthquake are described in McGuire(1995) and USNRC (1997).

A summary of rock and soil records from thewestern US is shown in Table 1, in terms of Mand R bins. Also shown are preliminary summarystatistics for mean peak ground acceleration(PGA), mean peak ground velocity (PGV), andmean peak ground displacement (PGD). Thissummary indicates the usual trends in strong mo-tion data, i.e. that data are abundant for moder-ate magnitudes at moderate source-to-sitedistances, but are sparse for large magnitudes andshort distances and small magnitudes at long dis-tances. The former category is more troublesomefrom a design perspective and requires modelingfor confirmation.

Central and eastern US (CEUS) strong motionrecords are sparse. Thus it is necessary to aug-ment the CEUS empirical motions with analyti-cally derived spectral shapes. This analysis uses apoint- and finite-source representation of theearthquake rupture, attenuates both body andsurface waves, accounts for near-surface attenua-tion of high frequencies, and assumes that groundmotion is a band-limited, white noise process.

Table 1Characteristics of WUS records in MR b ins (preliminary)

MSite R (km) Mean PGA (g)No. of spectra Mean PGV (cm:s) Mean PGD (cm)

Rock 0.808.140.183001055.966.9 010 32 0.44 32.7 6.227 010 6 0.93 81.7 47.4

18.60.2624 3.1101055.9Soil66.9 46.9 14.8010 77 0.387 44.5 21.3010 4 0.40

0.545.080.11180Rock 105055.966.9 8.81 1.961050 238 0.137 1050 6 0.17 8.80 2.50

0.876.630.11378Soil 105055.966.9 1050 542 0.14 10.8 2.25

0.16 22.4 10.51050 56755.9 50100 32Rock 0.05 2.22 0.2166.9 50100 102 0.06 3.87 0.797 2.645.160.061050100

0.383.110.0642Soil 5010055.966.9 50100 158 0.07 6.23 1.267 50100 14 0.10 11.2 5.42

R.K. McGuire et al. : Nuclear Engineering and Design 203 (2001) 249257 251

Fig. 1. Normalized rock spectral shapes for WUS and CEUS 1-corner and 2-corner models, M6.5 and R25 km.

Calibration of the model with available recordsconfirms the underlying assumptions and providesestimates of the model parameters. One outstand-ing issue, however, is whether the seismic energyat the source has a single-corner or double-corner spectrum; this is the focus of independentresearch, and the current project will include eachmodel as an alternative. Rock conditions in theCEUS are generally hard, with near-surface shearwave velocities generally exceeding 3000 m:s(10 000 ft:s).

Fig. 1 indicates the difference in spectral shapesbetween the single- and double-corner models, forboth the WUS and CEUS. The shapes are pre-sented as ratios of spectral acceleration dividedby PGA. CEUS shapes typically have morehigh-frequency content but lower SA at interme-diate periods, when normalized by PGA. The

double-corner model has the largest influence forCEUS spectral shapes at periods longer than 0.5s.

3. Choice of spectral level

In addition to the spectral shape, the overalllevel of the spectrum must be specified. Thischoice may be made from a PSHA by defining atarget annual frequency of exceedence for thespectrum. Alternatively the level could be definedusing an acceptable annual frequency of failure Pfat the component level and convoluting the seis-mic hazard results with component fragilitycurves to relate component performance to seis-mic hazard. The failure frequency Pf can be repre-sented as:

R.K. McGuire et al. : Nuclear Engineering and Design 203 (2001) 249257252

PF&

0

H(a)dPF:a

dada (1)

where H(a) is the hazard curve and PF:a is theprobability of failure (the fragility) givenground motion amplitude a , which capturesboth response and capacity uncertainties.

With some realistic assumptions on the shapeof the hazard curve and the fragility curve, it ispossible to derive a simple expression for PF. Firstwe assume that the hazard curve H(a) is linear onlog-log scale, i.e.

H(a)kaKH (2)

where a is spectral acceleration level, k is a con-stant, and KH is the slope of the hazard curve inloglog space. Actual hazard curves tend to getsteeper at higher amplitudes, but over the impor-tant range of amplitudes for PF calculations theycan be approximated as linear on loglog scale.

Second we assume that component fragilitiesare lognormally distributed. This means that

PF:a& a

0

1

y2pbexp

!

(ln y ln y)2

2b2"

dy (3)

where ln y ln CAP50, the median component ca-pacity, and b is the logarithmic standard deviationof capacity.

Substituting Eqs. (Eq. (2)) and (Eq. (3)) into(Eq. (1)) gives

PF&

0

kaKn1

a2pbexp

!

(ln y ln y)2

2b2"

da.

(4)

Transforming the integration variable a to vari-able x ln a gives

PFk

2pb&

exp{KHx}

exp!

(x ln y)2

2b2"

dx. (5)

The integrand above is in the form

exp{cx}Z(x) (6)

where c is a constant and Z(x) is the normaldensity function. The definite integral (Eq. (5))can be solved by expansion or by published meth-ods of integrating functions of normal probabilitydistribution (e.g. Owen, 1980), yielding

PFkCAPKH50

exp!1

2(KHb)2

". (7)

This form, designated the risk equation, wasfirst derived by G. Toro and published in Sewellet al. (1991, 1996). Expressing the hazard Hs at aground motion level a* corresponding to a safe-shutdown ground motion (SSGM), using (Eq. (2))gives:

Hsk(a)KH. (8)

Solving for k and substituting into Eq. (7) gives:

PFHs(a)KHCAPKH50 exp

!12

(KHb)2"

. (9)

We can now derive a probability ratio Rp as theprobability Hs that a* will be exceeded, dividedby the probability of failure PF:

RpHs:PF. (10)

This ratio is usually much greater than unitybecause PF is much less than the hazard at a*. Rpcan be expressed as:

RpCAP50

aKH

exp!

12

(KHb)2"

. (11)

Instead of using the median capacity CAP50 todesignate capacity, we can use the high confi-dence of low probability of failure value, orHCLPF, where for a lognormal distribution thetwo are related by

HCLPFCAP50exp {xpb} (12)

where xp is the number of standard deviates corre-sponding to the frequency of failure at theHCLPF, which is 2.326 for 1% frequency of fail-ure. Also, we can express the required HCLPF interms of a* times a factor of safety FR :

HCLPFSSGMFR. (13)

Solving these last two equations for CAP50 andSSGM, and substituting into Eq. (Eq. (11)) gives:

RpFRKH exp

!xpKHb

12

(KHb)2"

. (14)

This gives a simple means to calculate PF, giventhat the hazard associated with the SSGM isknown. The probability ratio Rp depends on thefactor of safety FR, the hazard curve slope KH,

R.K. McGuire et al. : Nuclear Engineering and Design 203 (2001) 249257 253

and b of the fragility function; for the HCLPFdefined at the 1% frequency of failure point,xp2.326 as explained above.

Eq. (14) also gives an easy way to compute theeffect of hazard curve slope and fragility b on PFfor a specified hazard corresponding to a selectedUHS. Stated another way, if we pick a UHS ateach site with the same annual probability ofexceedence, and define the HCLPF in terms ofEq. (13), Eq. (14) allows us to examine the riskconsistency across sites for different hazard curveslopes KH and fragility uncertainties b. The use ofEq. (14) in this way is demonstrated below.

A couple of points about the distributions ofH(a*) and PF are important. H(a*) is uncertainbecause of lack of knowledge in the earth sciencesabout earthquake sources, ground motions, etc.This uncertainty has been quantified by EPRI andLLNL at CEUS plant sites and by utilities atseveral WUS plant sites. If we use the mean of thisdistribution we will achieve a mean PF for any setof design rules. The mean has the advantage thatwe can compute (and control) the mean PF formultiple plants. That is, we have n plants and atotal acceptable probability of component failureat these plants, we can achieve that by specifyinga mean PF at each plant. The disadvantage is thatthe mean is sensitive to low probability, highconsequence assumptions in the seismic hazardanalysis and is not as stable (from study to study)as the median.

If we use the median H(a*) we will achieve anapproximate median PF. The median has the ad-vantage that it is more stable than the mean, buta target mean or median PF over n plants cannotreadily be translated to a required median PF ateach plant. So use of the median H(a*) leads toill-constrained limits on PF over multiple plants.For this reason the use of the mean H(a) curve isrecommended.

A final point is that Rp can be controlled bydeterministic acceptance criteria associated withdesign codes and guides, and by a scale factorthat moves the capacity up or down as a functionof the hazard curve slope KH, the desired PF, orthe desired Rp for a given H(a). This scale factoris conveniently thought of as a scaling of the UHSto specify an SSGM spectrum. The total factor of

safety FR, is then a times SF, where a is theconservatism achieved by design procedures (e.g.1.67 on the HCLPF) and SF is the scale factor.The SSGM is then the UHS scaled by SF. It isappropriate to define SF to scale the UHS toaccount for the site-specific (and natural period-specific) slope of the hazard curve. R.P. Kennedy(personal communication, 1997) has suggested thefollowing scale factor:

SFmax{0.7,0.35AR1.2} (15)

where AR [logKH]1. Thus AR increases as thehazard curves become more shallow, so SF in-creases, i.e. the design values become higher forshallow hazard curves. With this definition, theSSGM can be thought of as:

SSGMUHSSF (16)

i.e. the SSGM is the UHS corrected for theslope of the hazard curve. For AR2.40 (whichcorresponds to slope KH2.63), SF1, i.e. theSSGM equals the UHS.

Another way to look at the design is throughthe total factor of safety FR (see Eq. (13)). If theamount of conservatism in design codes andguides (sometimes referred to as the determinis-tic acceptance criterion) is 1.67, then the totalfactor of safety FR is:

FR1.67SF. (17)

The advantage of using a slope-dependent scalefactor SF as defined in Eq. (15) is demonstrated inthe next section.

4. Results for example sites

To test several methods for risk-consistent spec-tra, we examined eleven sites and three groundmotion measures at each site (shown in Table 2).

For the first 27 sets of results we used theLLNL hazard curves calculated for the USNRC(Sobel, 1994). For the California site, we calcu-lated hazard at a site located near Santa Maria,California (120.5W, 35.0N), which has high fre-quencies dominated by nearby faults and longperiods dominated by the more distant San An-dreas fault. (A repeat of the 1857 earthquake

R.K. McGuire et al. : Nuclear Engineering and Design 203 (2001) 249257254

Table 2Sites and ground motion measures used for testing procedures

Measure No. SiteSite MeasureNo.

Arkansas plant1 PGA 17 Shearon Harris SV 1 HzSV 1Hz 18Arkansas plant Shearon Harris2 SV 10 Hz

Arkansas plant3 SV 10 Hz 19 Susquehanna PGAPGA 20 Susquehanna4 SV 1 HzBrowns FerrySV 1 Hz 21Browns Ferry Susquehanna5 SV 10 HzSV 10 Hz 226 VogtleBrowns Ferry PGAPGA 23Davis Besse Vogtle7 SV 1 Hz

Davis Besse8 SV 1 Hz 24 Vogtle SV 10 HzSV 10 Hz 25Davis Besse Zion9 PGA

Maine Yankee10 PGA 26 Zion SV 1 Hz11 Maine Yankee SV 1 H...