Survey of seismic fragilities used in PRA studiesof nuclear power plants1

Y.J. Park a,*, C.H. Hofmayer a & N.C. Chokshib

aBrookhaven National Laboratory, Department of Advanced Technology, P.O. Box 5000, Upton, NY 11973-50000, USAbUS Nuclear Regulatory Commission, Mail Syop T-1-L1, Washington D.C., USA

(Received 7 October 1996; accepted 29 October 1997)

In recent years, seismic PRA studies have been performed on a large number ofnuclear power plants in the USA. This paper presents a summary of a survey onfragility databases and the range of evaluated fragility values of various equipmentcategories based on past PRAs. The survey includes the use of experience data, theinterpretations of available test data, and the quantification of uncertainties. Thesurveyed fragility databases are limited to data available in the public domain such asNUREG reports, conference proceedings and other publicly available reports. Theextent of the availability of data as well as limitations are studied and tabulated forvarious equipment categories. The survey of the fragility values in past PRA studiesincludes not only the best estimate values, but also the dominant failure modes and theestimated uncertainty levels for each equipment category. The engineering judgmentsemployed in estimating the uncertainty in the fragility values are also studied.

This paper provides a perspective on the seismic fragility evaluation procedures forequipment in order to clearly identify the engineering analysis and judgment used inpast seismic PRA studies.q 1998 Elsevier Science Ltd. All rights reserved.

Keywords:PRA, Seismic fragilities, Nuclear power plants.

1 INTRODUCTION

In recent years, seismic PRA (SPRA) studies have beenperformed on a large number of nuclear power plants inthe USA1. These studies have indicated that earthquake-initiated accidents are a significant risk contributor evenfor plants in the eastern USA. Since the initiation ofSPRAs on commercial power plants in the late 1970s, themethodologies have been gradually evolving for a better andmore complete quantification of seismic-induced radio-active release.

The evaluation methodologies for the seismic fragility ofcomponents and equipment have also been improving asmore experimental/experience data have become available.

This paper presents a summary of a survey on the seismicfragility evaluation in past SPRAs from the late 1970s up to1988, including the NRC-sponsored research work such asthe development of the seismic safety margin research pro-gram (SSMRP) methodologies7,14. In developing the gen-eric fragility tables of equipment and components, availabletest data from SAFEGUARD projects and solicited expertopinions were utilized in the early 1980s6. In the late 1980sand early 1990s, more systematic evaluations of fragilityvalues were performed as more test data had become avail-able in the nuclear industry, particularly for electrical equip-ment (see, for example, Refs.9 and15). More standardizedprocedures to quantify the uncertainties associated withfragility evaluation have also become available (see, forexample, Ref.17). This survey also covers these recent sta-tistical studies as well as some limited test results on com-ponents11. The survey on the fragility data includes thedevelopment of a fragility database, the identification ofthe types of available data sources, the evaluation of domi-nant failure modes and variability, and the use of engineer-ing judgment. However, the results of the most recent SPRA

Reliability Engineering and System Safety62 (1998) 185–195q 1998 Elsevier Science Ltd.

All rights reserved. Printed in Northern Ireland0951–8320/98/$1 - see front matterPII: S 0 9 5 1 - 8 3 2 0 ( 9 8 ) 0 00 1 9 - 2

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185

*Corresponding author. Tel.: 001 5161 344 7933; fax: 001 5116344 4255; e-mail: park@dnenet.nov,dne.bn1.gov1This work was performed under the auspices of the US NuclearRegulatory Commission. The findings and opinions expressed inthis paper are those of the authors, and do not necessarily reflectthe views of the US Nuclear Regulatory Commission orBrookhaven National Laboratory

studies, i.e. independent plant examination of externalevents (IPEEE) studies, are not included in the presentedsurvey. Once the results of these new studies become pub-licly available, the presented database will be significantly

updated and expanded. The objective of this paper is toprovide a perspective on the seismic fragility evaluationprocedures for components and equipment in order toclearly identify the engineering analysis and judgmentused in past SPRAs.

In this paper, a large number of component fragilityvalues and the associated variabilities are tabulated, whichare referenced from open publications. However, thesetabulations are not intended to encourage the use of genericfragility data in lieu of plant-specific data. In order to obtainrobust insights from an SPRA, plant-specific fragility infor-mation must be used and the anchorage of equipment mustalways be checked. As demonstrated in the various listingsof past fragility studies described in this paper, a large scat-ter is found in the evaluated fragility parameter values formost of the components and equipment due to differences in

Table 1. Reviewed data sources

Datasource Number offragility data

Number of originaldata to developfragility values

Past SPRAs 354a 354Generic databases 79b 427c

Analytical studies 16 16Experimental studies 2b 28c

aNumber of fragility values.bCombined fragility values.cThe original test data before combining.

Table 2. Summary of fragility database

Category Dominant Median fragility range (g)name failure mode

Past PRAa Othersb

Nc Range Nd Range

1 Concrete containment Shear failure 8 2.50–9.20 – –2 Steel containment Shell wall buckling 1 9.00–9.00 – –3 Reactor presure vessel Anchor bolt 13 1.04–5.70 3 3.83–3.834 Steam generator Support 9 1.70–6.80 4 2.45–2.455 Reactor coolant pump Support 8 0.90–4.60 3 2.64–2.646 Recirculation pump Bracket 6 0.90–2.20 – –7 Core assembly CRD housing 21 0.60–6.71 5 2.06–2.068 Pressurizer Lateral support 1 5.73–5.73 1 2.00–2.009 Piping Support 14 2.50–13.6 – –

10 Valves Yoke support 35 0.80–13.7 22 4.83–20.511 Heat exchanger Anchor bolt 23 0.30–13.0 4 1.00–1.1812 Flat bottom tank Shell wall buckling 17 0.20–1.00 8 0.45–2.0113 Other tanks and vessels Anchor bolt 28 1.00–46.0 13 1.07–3.9114 Batteries and racks Battery cases and plates 16 0.90–5.95 54 0.80–7.3015 Motor control center Chattering 17 0.06–4.20 70 0.30–7.6316 Switchgears Chattering 26 0.40–6.90 60 2.33–8.5017 Diesel generator Anchor bolt 14 0.70–3.89 9 0.65–1.0018 Large vertical pumps – 9 0.80–7.50 2 2.21–2.2119 HVAC Deflection of fan 14 1.10–5.58 5 2.24–6.9020 Cable tray Support 9 1.10–5.80 3 2.23–2.2321 Other pumps Anchor bolt 8 2.10–5.47 3 2.80–3.1922 Motors – – – 2 12.1–12.123 Transformers Support 4 0.30–5.80 5 2.78–8.8024 Instruments Accuracy 1 4.46–4.46 52 1.15–16.325 Electric panels Chattering 11 2.77–7.60 116 1.66–11.526 Light fixtures – – – 1 9.20–9.2027 Communication

equipment– – – 1 5.00–5.00

28 Inverters Function failure 1 3.41–3.41 5 2.00–15.629 Ciorcuit breakers Trip 6 0.37–4.20 2 7.63–7.6330 Ceramic insulators – 1 0.20–0.20 9 0.20–31 Pipe support – – – 1 1.46–1.4632 Offsite power Ceramic insulator 29 0.20–0.62 – –33 Electric cabinets Chattering 2 1.10–3.88 7 7.50–7.6334 Ducts Support 1 4.89–4.89 5 3.97–3.9735 Electrical penetration Pressure loss 1 3.69–3.69 4 12.0–12.0

aGround motion PGA.bLocal floor ZPA/ASA values.cNumber of fragility values.dNumber of original data (e.g.) test data).

186 Y. J. Parket al.

Table 3. Subcategories of components

Category Subcategory Median fragility range (g)name name

Past PRAa Othersb

Nc Range Nc Range

7 Core assembly (All data) 21 0.60–6.71 5 2.06–2.06Core support 2 1.00–1.50 – –CRD assembly 7 0.90–5.85 – –Spacer grid 1 6.71 – –Fuel rods 2 1.30–1.40 – –

9 Piping (All data) 14 2.50–13.6 – –Safety injection 1 12.8 – –Containment spray 1 2.50 – –Main steam 3 2.50–7.40 – –Service water 3 2.80–4.10 – –Recirculation 5 2.70–13.6 – –

10 Valves (All data) 35 0.80–13.7 22 4.83–20.5Large motor operated 28 0.80–4.80 10 4.83–14.4Small motor operated 1 8.55 1 9.84Large relief and check 5 1.40–13.7 3 8.90Small relief and check – – 2 12.5

13 Other tanks andvessels

(All data) 28 1.00–46.0 13 1.07–3.91

Small – – 4 1.84Large vertical – – 2 1.46Large horizontal – – 3 3.00–3.91Small vertical – – 4 1.07–1.55Safety injection 1 4.23 – –Containment spray 1 3.39 – –Component cooling water 1 3.41 – –

16 Switchgears (All data) 26 0.40–6.90 60 2.33–8.50High voltage (. 400 V) 9 0.40–6.90 39 4.00–8.50Low voltage (, 400 V) 7 0.90–6.10 16 6.60–8.50

21 Other pumps (All data) 8 2.10–5.47 3 2.80–3.19Feedwater system 1 3.85 – –Residual heat removal 2 2.10–4.15 – –Safety injection 1 5.47 – –Charging 1 5.08 – –Service water 1 4.70 – –Component cooling water 1 4.26 – –

24 Instruments (All data) 1 4.46–4.46 52 1.15–16.3For sensors – – 6 7.68Transmitters 1 4.46 24 14.5Indicators – – 6 16.3

25 Electric panels (All data) 11 2.77–7.60 116 1.66–11.5For relay 2 3.62–5.38 3 1.66–4.20Power supply 1 3.33 11 9.00Instrument and control 2 3.63–4.27 41 6.30–9.00

aGround motion PGA.bLocal floor ZPA/ASA values.cNumber of fragility values for PRA data, and the number of original data (e.g. test data) for ‘Other’ data. The number of data for eachsubcategory is for the fragility data for which the subcategory name is identified in documents.

Survey of seismic fragilities used in PRA studies 187

design and evaluation procedures. The generic fragility datacan best be used for screening studies and to guide plant-specific fragility evaluations.

2 DEVELOPMENT OF A FRAGILITY DATABASE

Four types of available fragility data were reviewed as sum-marized in Table 1. The surveyed fragility databases arelimited to data available in the public domain such asNUREG reports, conference proceedings and other pub-licly available reports. These include past SPRAs (see, forexample, Refs.2–5), generic fragility databases (see,for example, Refs.6–9), analytical fragility studies (see,for example, Ref.10), and experimental studies (see, forexample, Refs.11 and 12. A total of about 450 data havebeen collected so far for components and equipment incommercial nuclear power plants (NPPs). Table 2, whichsummarizes the surveyed fragility data, includes the names

of component categories, the dominant (most frequentlyidentified) failure modes, the size of samples of the originaldata,N, and the range of mean fragility values. It should benoted that the fragility values are given in terms of theground motion PGA values for the data from past SPRAstudies, whereas the spectral acceleration or floor accelera-tion (at mounting locations) is used for other cases. For thisreason, the fragility data from past SPRA studies are listedseparately from the other data in Table 2.

The listed 35 equipment categories were determinedbased on previous studies on the development of genericfragility tables (see, for example, Refs.6–8). For severalequipment categories, equipment can be further classifiedinto subcategories as listed in Table 3. In the SPRA studies,the subcategories frequently reflect the different safetysystems, whereas in generic fragility development, thegeometry (large/small, vertical/horizontal) and equipmentfunctions are generally accounted for as a further classifica-tion, as indicated in Table 3.

Table 4. Types of fragility data sources

Category name Type of sourcea b

A C T E O M Q G S

1 Concrete containment 8 0 0 0 0 0 0 0 82 Steel containment 1 0 0 0 0 0 0 0 13 Reactor pressure vessel 13 0 0 0 1 0 0 0 144 Steam generator 7 0 0 0 0 1 2 0 105 Reactor coolant pump 8 0 0 0 1 0 0 0 96 Recirculation pump 5 1 0 0 0 0 0 1 57 Core assembly 21 0 0 0 0 1 0 1 218 Pressurizer 2 0 0 0 0 0 0 0 29 Piping 2 12 0 0 0 0 0 11 3

10 Valves 34 1 2 0 4 3 0 8 3611 Heat exchanger 20 7 0 0 0 0 0 11 1612 Flat bottom tank 21 0 0 0 2 01 0 6 1713 Other tanks and vessels 32 3 0 0 0 2 0 8 2814 Batteries and racks 13 0 8 0 0 0 0 8 1515 Motor control center 11 0 15 0 0 0 0 18 816 Switchgears 17 0 15 0 2 2 18 1617 Diesel generators 14 0 0 0 0 0 0 6 1018 Large vertical pumps 6 3 0 0 1 0 0 4 619 HVAC 9 5 0 0 0 0 0 7 920 Cable tray 3 6 0 0 0 0 1 7 321 Other pumps 10 0 0 0 0 1 0 2 822 Motors 0 0 0 0 1 3 0 1 023 Transformers 3 0 2 1 1 0 0 5 224 Instruments 0 0 4 0 1 0 0 5 125 Electric panels 2 0 16 0 0 0 0 14 726 Light fixture 0 0 0 0 1 0 0 1 027 Communication equipment 0 0 0 0 0 0 1 1 028 Inverters 0 0 2 0 0 0 2 3 129 Circuit breakers 2 0 5 0 0 0 0 5 230 Ceramic insulators 0 0 1 3 0 0 0 4 031 Pipe support 0 0 0 0 0 0 1 1 032 Offsite power 0 0 0 29 0 0 0 28 133 Electric cabinets 2 0 2 0 0 0 0 2 234 Ducts 0 2 0 0 0 0 0 1 135 Electrical penetration 0 0 2 0 0 0 0 2 0

aKey: A, analysis; C, code-based analysis; T, tests; E, experience data; O, expert opinion; M, mixed source; Q, source not clearly identified;G, generic data; S, plant-specific data.bThe tabulated numbers represent the number of fragility values.

188 Y. J. Parket al.

Various types of data sources are utilized to determinethe fragility values of components, which can be classifiedas

• structural analysis;• code-based structural analysis;• test data;• experience from past earthquake events;• expert opinions;• mixture of different data sources (e.g. tests and

expert opinions).

The same data sources can also be classified as genericdata and plant-specific data as shown in Table 4. Based onthe examination of the data sources in Table 4, the followingobservations have been made.

2.1 Structural analysis

Site-specific structural analyses are more suitable for thefollowing components based on the available design infor-mation such as a plant’s FSAR.

• Civil structures - shear walls, non-bearing partitionwalls, floor/slabs, ceiling.

• Large-sized critical components - containment,RPV, RCP, core assembly, flat-bottom tanks.

• Structural failure of equipment - anchorage andsupport failures.

Past review studies (see, for example, Ref.2) have indi-cated that the fragility estimates or consequences of failureof large-sized critical components, such as concrete contain-ments and steam generators, are usually conservativelybiased. For example, a postulated building collapse is fre-quently assumed to cause a total failure of all the equipmentand components that are housed inside the building.

2.2 Code-based analyses

For components present in large quantity in a plant, a"representative" fragility value is estimated based on thedesign code allowable stresses and the associated safetyfactors. Such components include piping, heat exchangers,cable trays and ducts (see Table 4). To account for thedifferent design stress levels, a larger uncertainty value,bu, is normally assumed, although the determination ofsuch an additional variability is highly judgmental.

2.3 Test data

The fragility values for the following failure modes can bedetermined only from available test data.

• Functional failure:

relay chatter;breaker trip;accuracy of instrument;battery damage.

• Local structural failure:

screw distortion;weld crack in cabinet.

In performing an SPRA, the above fragility values areobtained either from the qualification test data (generic orplant-specific) or available generic fragility databases (see,for example, Refs.6, 8 and 9). According to this survey, arelatively large number of fragility test data are found to beavailable for the following equipment:

• batteries;• motor control centers;• switch gears;• instruments;• electric panels/cabinets;

2.4 Experience data

The fragility value for off-site power loss has beendetermined exclusively using experience data. In olderSPRAs, a median fragility value of 0.2g was commonlyused. As more data became available from recent earth-quakes in the western USA, a higher value of 0.3-0.35g ismore frequently used. It should be noted that this fragilityestimate is based on the observed seismic damage to switch-yard equipment mostly in California and Japan.

2.5 Expert opinions

In developing a generic fragility database in Ref.6, expertopinions were solicited for various equipment items. Thistype of data should be used in conjunction with other typesof data, such as available test data.

3 FAILURE MODE

Table 5 lists the dominant failure modes and the number ofdata for components which have multiple failure modes.The results of the survey on some of the component cate-gories are described below.

3.1 Concrete containment

The dominant failure mode is always the tangential shearfailure of the bottom part of the shell. All the fragility valueslisted in Table 2 were obtained based on linear dynamicanalyses and empirical shear wall equations. The high capa-city values are due to the fact that the containment structuresare conservatively designed against a combination of SSEand LOCA loads. Available Japanese test data (see, forexample, Ref.13) indicate an additional margin in termsof energy absorbing capacity under severe seismic loadings.Therefore, the listed fragility values may still be conserva-tively biased.

Survey of seismic fragilities used in PRA studies 189

3.2 Reactor pressure vessel

The reported failure modes are the steamline failure asso-ciated with support failure or outlet nozzle fracture, whichmay result in a large LOCA. Although it has not been iden-tified as a potential failure mode in the reviewed SPRAs, theembrittlement of the shell wall and internal cracking in aBWR pressure vessel shell wall could be an issue for olderreactors. The wide range of median fragility values mayreflect differences in design and analysis conditions (e.g.different earthquake inputs).

3.3 Steam generator

Horizontal support failure and the buckling of supportcolumns are dominant failure modes. Multiple tube rupturehas not been rigorously addressed in the reviewed SPRAstudies.

3.4 Reactor coolant pump

Most of the past SPRAs identified a support failure as thecritical failure mode, which may cause a large LOCA.

Table 5. List of dominant failure modes

Failure mode N Failure mode N Failure mode N

3 Reactor pressure vessel 12 Flat bottom tank 20 Cable trayAnchor bolt 3 Shell wall buckling 17 Support 4Upper support 3 Anchor bolt 3 Brace buckling 1Support 3 Weld failure 1Nozzle fracture 2 21 Other pumps

13 Other tanks and vessels Anchor bolt 64 Steam generator Anchor bolt 8 Shaft deflection 1

Support 3 Shell wall rupture 5Support column 2 Base plate 4 23 TransformersUpper support 2 Shell wall buckling 2 Support 1Skirt 1 Support column 1 Lower support 1Lower support 1 Weld failure 1 Structural 1

Nozzle fracture 15 Reactor coolant pump Lateral support 1 24 Instruments

Support 3 Support 1 Accuracy 41Support column 1 Structural 1Anchor bolt 1 14 Batteries and racksStructural 1 Battery case and

plates46 25 Electric panels

Function failure 4 Chattering 486 Recirculation pump Lateral support 1 Electrical 28

Bracket 5 Structural 1 Structural 18Support 1 Trip 16

15 Motor control center Accuracy 117 Core assembly Chattering 39 Function failure 1

CRD housing 5 Non-recoverable 22Core support 4 Structural 19 28 InvertersShroud support 3 Trip 5 Function failure 3Bending of cores 2 Cabinet structure 1 Structural 1CRD guide tubes 2Lower support 1 16 Switchgears 29 Circuit breakers

Trip 25 Trip 310 Valves Structural 23 Chattering 2

Yoke bending 16 Chattering 13 Cabinet structure 1Yoke support 13 Electrical 13Function failure 9 Non-recoverable 5 32 Offsite powerBonnet closure 6 Support 2 Ceramic insulator 27Pipe connection 2 Support 1Mounting bolts 2 17 Diesel generatorBracket 1 Anchor bolt 4 33 Electric cabinets

Pipe connection 2 Chattering 711 Heat exchanger Function failure 1 Structural 1

Anchor bolt 9Support 6 19 HVAC 35 Electrical penetrationVertical support 1 Deflection of fan 7 Pressure loss 4Saddle support 1 Support 4 Structural 1Shell wall buckling 1 Anchor bolt 2Pipe connection 1 Base plates 1Upper support 1

190 Y. J. Parket al.

According to a detailed analysis in Ref.4, seal damage wasidentified as the critical failure mode, which may cause asmall LOCA.

3.5 Core assembly

In past SPRA studies, the fragility level for the postulatedscram failure was determined based on the manufacturer’sdetailed design analyses. As indicated in Table 3, there areno significant differences in the estimated fragility valuesfor core internals (core supports and fuel rods). However, arelatively large scatter is observed in the estimated seismicstrength of the CRD mechanism (CRD housing, CRD guidetube) mainly due to differences in design.

3.6 Piping

Piping systems were not fully considered in most SPRAstudies due to their high seismic capacities, except in sec-ondary failure scenarios, such as the support failure of alarge vessel causing connected pipe ruptures. More carefulpiping analyses were performed in the SSMRP studies (see,for example, Ref.14), and in the SPRA of Diablo CanyonNPP4, in which pipe supports were identified as a weak linkfor many pipe lines. Walkdowns should focus more onpiping systems to single out a few piping lines that mayneed more careful analyses, including possible seismicinteractions, in an SPRA.

3.7 Valves

As indicated in Table 3, relatively lower seismic capacitiesare found only on large motor operated valves. Other typesof valves are considered to be seismically robust. The domi-nant failure modes for large motor operated valves are yokebending and yoke support failure (see Table 5). Existingexperience data of industrial facilities, however, indicateno damage on such valves due to inertial loads up to a1.2g spectral acceleration level.

3.8 Flat bottom tank

Flat bottom tanks are one of the major weak links in manySPRAs due to low seismic capacities. Site-specific analyseswere performed in most of the reviewed SPRAs. The

dominant failure modes are shell wall buckling and anchorbolt pullout, although they may not immediately lead to adrainage of the contents of the tank.

3.9 Batteries and racks

The age-related degradation of batteries and the lack ofbracing in racks are major concerns identified in past testprograms (see, for example, Ref.11) and past SPRAs. Theseproblems could be corrected during walkdowns or regularmaintenance procedures. Batteries and racks were notconsidered to be a major risk contributor in past SPRAs aslong as the problems are identified during walkdowns andcorrected.

3.10 Motor control centers (MCC)

Table 6 lists available generic fragility values for motorcontrol centers. The values from Ref.8 have been developedbased on a large number of existing fragility test results, andcould be used in a trial system analysis to determine domi-nant accident scenarios. However, use of such generic datamay require a further assessment in the final risk quantifica-tion because the chattering phenomenon is very complex,and an MCC’s seismic capacity may vary widely dependingon the type of devices, state of devices (normally closed(NC)/normally open (NO), energized (E)/de-energized(DE) etc.), and frequency content. An example of fragilitytest results for an MCC is summarized in Table 715.According to Ref.15, failure modes in a typical test can belisted in the following order based on increasing test levels.

• Motor starter auxiliary contact chatter (NC, mostlyDE).

• Motor starter auxiliary contact chatter (NO, mostlyDE).

• Relay chatter.• Motor starter main contact chatter.• Motor starter change of state (auxiliary contact).• Loosening of screws and mounting bolts.• Snapping out of self-tapping screws.• Motor starter change of state (main contact).• Structural damage.

As discussed earlier, in addition to reviewing high qualitygeneric fragilities for functional failure, the anchorage for

Table 6. Generic fragility values for motor control center

Source Failure mode Median ZPA b r bu

Ref. 6, 1985 Chatter 1.66 0.57 1.40Structural 7.63 0.48 0.66

Ref. 7, 1990 Chatter 4.00 0.48 0.75Stuctural 7.63 0.48 0.66

Ref. 9, 1989 Chatter 2.3 0.09 0.18Ref. 8, 1991 Chatter 1.3 0.10 0.20

Change state 1.7 0.15 0.17Structural 2.5 0.06 0.20

Survey of seismic fragilities used in PRA studies 191

equipment must always be checked. This also applies toother equipment items such as switchgears and electricpanels.

3.11 Diesel generator

The generator itself is seismically robust, as demonstrated ina full-scale shaking test in Japan16. Lower fragility valuescome from peripheral components, e.g. anchorage failure ofthe oil tank, horizontal day tank and oil cooler, relay chatter/trip of the control panel, and oil pipe connection failure.Non-seismic random failure of a diesel generator is fre-quently considered a major risk contributor in past SPRAs.

3.12 Transformers

Dry transformers in NPPs are usually mounted directly onthe ground or floor, and the fragility values are determinedfrom anchorage strength. The transformer itself is consid-ered to be seismically robust (3.0g according to Ref.8 and4.2g according to Ref.9). However, the supports for inter-nal coils should be inspected for a potential structural failureduring walkdowns.

3.13 Electric panels

This category includes electric panels for sensors, nuclear

Table 7. Typical example of MCC fragility test result (from Ref. 15)

Electrical functions ZPA Electrical state Test resultsmonitored (g)

Change of state 0.9 Energized (E) No malfunctioncontact chatter 0.9 E (voltage set at 85% Starter chatter and. 0.5 ms then reduced to 60%) relay chatter

1.1 E Starter chatter100 ms

1.3 De-energized (DE) No malfunction2.3 DE Starter chatter;

assembly bolts broke

Table 8. Variabilities in past SPRAs

Category name Range Mean values

b r bu b r bu b t

1 Concrete containment 0.26–0.49 0.27–0.48 0.36 0.35 0.502 Steel containment 0.29–0.29 0.36–0.36 0.29 0.36 0.463 Reactor preesure vessel 0.25–0.33 0.33–0.56 0.19 0.29 0.354 Steam generator 0.31–0.48 0.30–0.54 0.24 0.32 0.405 Reactor coolant pump 0.26–0.43 0.30–0.51 0.32 0.41 0.516 Recirculation pump 0.26–0.36 0.28–0.59 0.33 0.44 0.547 Core assembly 0.15–0.41 0.23-0.46 0.28 0.35 0.458 Pressurizer 0.31–0.31 0.44–0.44 0.31 0.44 0.549 Piping 0.23–0.40 0.39–0.66 0.29 0.54 0.61

10 Valves 0.17–0.45 0.21–0.60 0.29 0.40 0.4911 Heat exchanger 0.14–0.58 0.14–0.60 0.29 0.41 0.5012 Flat bottom tank 0.21–0.40 0.28–0.47 0.28 0.33 0.4313 Other tanks and vessels 0.10–0.57 0.18–0.65 0.27 0.37 0.4514 Batteries and racks 0.26–0.45 0.18–0.93 0.34 0.47 0.5815 Motor control center 0.24–0.45 0.46-0.91 0.36 0.59 0.6916 Switchgears 0.25–0.55 0.25–0.81 0.36 0.50 0.6217 Diesel generator 0.12–0.36 0.20–0.53 0.27 0.37 0.4618 Large vertical pumps 0.15–0.56 0.17–0.68 0.29 0.44 0.5319 HVAC 0.20–0.40 0.24–0.62 0.30 0.44 0.5320 Cable tray 0.22–0.45 0.32–0.70 0.37 0.52 0.6321 Other pumps 0.29–0.46 0.18–0.59 0.33 0.30 0.4523 Transformers 0.25–0.45 0.20–0.62 0.32 0.46 0.5624 Instruments 0.27–0.27 0.20–0.20 0.27 0.20 0.3425 Electric panels 0.25–0.55 0.13–0.63 0.35 0.32 0.4828 Inverters 0.31–0.31 0.24–0.24 0.31 0.24 0.3929 Circuit breakers 0.28–0.45 0.22–0.93 0.36 0.57 0.6830 Ceramic insulators 0.20–0.20 0.25–0.25 0.20 0.25 0.3232 Offsite power 0.15–0.26 0.20–0.54 0.21 0.32 0.3933 Electric cabinets 0.31–0.43 0.27–0.82 0.37 0.55 0.6634 Ducts 0.35–0.35 0.48–0.48 0.35 0.48 0.5935 Electrical penetration 0.31–0.31 0.27–0.27 0.31 0.27 0.41

192 Y. J. Parket al.

steam supply system (NSSS) instrument and control (I andC), balanced-of-plant (BOP) I and C, and d.c. power supply.The dominant failure modes are electrical (chatter andbreaker trip), accuracy of instrument and structural (hold-down bolts, interface of racks).

4 EVALUATION OF VARIABILITIES

The variability in the fragility estimates is usually expressedin terms of two standard deviations of log-normal distribu-tion,b r andbu, representing the intrinsic randomness, whichcannot be reduced by more information, and the uncertainty,which can be reduced if more information becomes avail-able. Table 8 lists the range ofb-values and the mean valuesfrom past SPRA studies. A large scatter in theb-values formany of the component categories may reflect the highlyjudgmental nature of variability estimates, rather than thedifference in design.

Table 9 further compares theseb-values according to thetype of data sources, i.e. test, analysis, code-based genericanalysis and experience data. Theb-values tabulated inTable 9 have been obtained by averaging those of thefragility databases for each type of data source. The com-parison for the three types of data sources, i.e. test, analysisand code-based analysis, indicates that, while the random-ness (b r) is fairly constant between the three categories, alarger difference exists in the evaluated uncertainty (bu),reflecting the level of confidence of analysts on each typeof data source.

In the past SPRAs, two different methods, i.e. the factorof safety (FS) method (frequently called the Zion method)and the SSMRP method, have been used. In the FS method,available response analysis results are utilized to determinethe seismic response of components. Both the "response"part and "capacity" part are combined as a product of severalrandom variables to express the fragility value in terms of aground motion parameter, e.g. ZPA or average spectralacceleration (ASA). In the SSMRP method, on the otherhand, comprehensive new response analyses are performedusing ensembles of acceleration time histories to evaluatethe "response" part of the fragility as a separate randomvariable for each component. The "capacity" part of the

fragility is evaluated based on generic fragility databasesand/or plant- specific information. By assuming a log-normal distribution for both the "response" and "capacity"parts, the probability of failure,pF, can be obtained withouta numerical integration as

PF ¼ 1¹ Fln (MR=MC)����������������

b2R þb2

C

p" #(1)

whereF (–) is the cumulative normal distribution function,MR andMC are the medians for the response and capacity,andbR andbC are the log-normal standard deviations forthe response and capacity.

Table 10 and Table 11 list typicalb-values for some basicparameters used in past SPRAs. Largerb-values areassumed in the SSMRP method compared to those in theFS method.

Also, it is observed that there is a tendency for a largervariability to be estimated in newer studies compared toolder SPRAs. As pointed out before, the estimation of vari-abilities involves analysts’ judgments, which sometimesresult in significantly differentb-values for an identicalcomponent. Recently, efforts have been made to formulatea more standardized procedure in this area (see, forexample, Ref.17).

5 ENGINEERING JUDGMENT

A total of 200-300 components needs to be considered in atypical SPRA of a commercial plant. However, based on ascreening process, the number of components can be greatly

Table 9. Comparison of average variabilities from past SPRAsfor each data source

Data source b r bu b t

Testa 0.33 0.30 0.45(0.38) (0.48) (0.62)

Analysis 0.30 0.39 0.50Code-basedanalysis

0.30 0.51 0.59

Experienceb 0.21 0.33 0.40aValues within parentheses include values from older studies (e.g.Ref. 3).bMost of the experience data included in this paper are for offsitepower loss.

Table 10. Typical basic variability values used in FS method

Item b-valuea

ResponseSpectral shape (peak and valley) 0.2–0.3b

Earthquake direction 0.1–0.15Soil–structure interaction 0.05–0.25Frequency of structures 0.2–0.3Mode shape 0.1–0.15Structural analysis error 0.05–0.15Damping 0.3

CapacityConcrete strength 0.1–0.15Rebar strength 0.05–0.1Shear wall equation 0.15–0.20Ductility factor, m 0.3–0.45Inelastic energy absorption,Fm 0.1–0.3

EquipmentStrength capacity 0.2–0.3Building response factor 0.3–0.4Frequency 0.1–0.2Damping 0.3Ductility factor, m 0.1–0.2aCombined values ofb r andbu.bFor a higher frequency range, lower values down to about 0.1have been used.

Survey of seismic fragilities used in PRA studies 193

reduced. Useful test data may not be available for manyof the components, and analysts must fill the gap based ontheir engineering judgment. The areas where engineeringjudgments are heavily involved are reviewed from thepast SPRAs.

5.1 Identification of failure

It is observed that more failure modes are identified andevaluated in newer SPRAs than in older ones. In a simplifiedanalysis, a fragility value is estimated by extrapolating thedesign stresses up to the postulated ultimate stress. When acertain amount of ductility is expected, the inelastic energyabsorption factor,Fm, is esimated based on a ductility factor,m, at the postulated failure point. The following problemsmay be pointed out for this approach.

• A conservative design analysis may not provide a"best estimate" stress condition, and, as a result, apotential failure mode may be overlooked.

• Stress redistribution due to non-linearity is notconsidered.

• The determination of them-value is highlyjudgemental.

• The estimate of the variability in them-value is evenmore judgemental.

Whether or not a more detailed analysis would produce aless conservative fragility estimate was not clearly con-cluded from this review study.

5.2 Quantification of variability

In past SPRAs, the variabilities of fragility estimates weredetermined using the following procedures:

• statistical analysis using available databases;• by assigning a fraction of the exceedance

probability to an estimated lower/upper bound ofthe fragility values;

• judgements based on past SPRAs.

The first aproach, which is mainly used for the functionalfailure of electrical equipment, offsite power loss, and thestrength estimate of structural components (e.g. shear walls)is considered to be the most reliable. The second approach isfrequently used for estimating the ductility factor,m, ofvarious components. A small probability value (1-5%) isassigned to the lower bound of the ductility factor (m < 1)to evaluate theb-value associated with the estimatedmedianm-value.

5.3 Randomness or uncertainty?

The separation of variabilities into randomness (b r) anduncertainty (bu) is considered to be highly judgemental.For example, the material variability (e.g. the concretestrength) is considered as an uncertainty, or both a random-ness and an uncertainty, or a randomness (e.g. in mostSSMRP studies).

How to split the uncertainties intob r and bu, however,does not significantly alter the final risk quantifications asthe seismic hazard curves (particularly the slopes of thecurves) dominate the analysis. This separation of variabil-ities is considered to be more consistent in the SSMRPstudies, in which structural analyses can be performed byaccounting forb r only, and then another series of analysesby including bothb r andbu.

6 CONCLUSIONS

This paper has presented a summary of a survey on theseismic fragility evaluation in past SPRAs. A fragility data-base has been developed based on past SPRAs, genericfragility databases (see, for example, Refs.6, 8 and 9) andother analytical and experimental studies. It is observed thatthe fragility evaluation methodologies have been improvingover two decades as more experimental/experience datahave become available. However, there exist areas wherefurther efforts are needed to improve the relability and con-sistency in fragility estimates, particularly those areas whereengineering judgements are frequently utilized.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the review commentsand expert opinions provided by Dr. Robert P. Kennedy.

REFERENCES

1. Chen JT, Chokshi NC, Kenneally RM, Kelly GB, BecknerWD, McCracken C, Murphy AJ, Reiter L, Jeng D. Proceduraland submittal guidance for the individual plant examination

Table 11. Typical basic variability values used in SSMRPmethod from Refs. 7,14

Item b r bu

ResponseSoil shear modulus 0.4 0.57Soil damping 0.5 0.87Structure frequency 0.25 0.43Structure damping 0.35 0.61Subsystem frequency 0.25 0.43Subsystem damping 0.35 0.61

CapacityConcrete strength 0.15–0.17 –Rebar strength 0.07–0.10 –Shear wall equation – 0.35Storage tanks 0.28 0.30

Structure response factorPGA 0.25 –Floor response 0.35 0.2–0.25Floor spectra 0.45 0.2–0.3

194 Y. J. Parket al.

of external events (IPEEE) for severe accident vulnerabil-ities. NUREG-1407, June 1991.

2. Budnitz RJ, Amico PJ, Cornell CA, Hall WJ, Kennedy RP,Reed JW, Shinozuka M. An approach to the qualification ofseismic margins in nuclear power plants. NUREG/CR-4334,July 1985.

3. Wesley DA, Hardy GS, Campbell RD, Narver RB, Sues RH.Seismic fragilities of structures and components at the Shore-ham Nuclear Power Station. SMA 14304.01, StructuralMechanics Associates, August 1984.

4. Kipp TR, Wesley DA, Nakaki DK. Seismic fragilities of civilstructures and equipment components at the Diablo CanyonPower Plant. Attachment Q2d-1, Report Number 1643.02,PG&E, September 1988.

5. Campbell RD, Ravindra MK, Murray RC. Compilation offragility information from available probabilistic risk assess-ments. LLNL, UCID-25071, Rev. 1, September 1988.

6. Cover LE, Bohn MP, Campbell DA, Wesley DA. Handbookof nuclear power plant seismic fragilities. NUREG/CR-3558,June 1985.

7. Bohn MP, Lambright JA, Daniel SL, Johnson JJ, RavindraMK, Hashimoto PO, Mraz J, Tong WH. Analysis of coredamage frequency: Surrey Power Station, Unit 1 externalevents. NUREG/CR-4550, December 1990.

8. Bandyopadhyay KK, Hofmayer CH, Kassir MK, ShteyngartS. Seismic fragility of nuclear power plant components(phase II). NUREG/CR-4659, Vol. 4, June 1991.

9. Tsai NC, Mochizuki GL, Holman GS. Development ofseismic fragilities from high-level qualification data.

Component Fragility Research Program, Phase II. NUREG/CR-5470, June 1989.

10. Kennedy RP, Murray RC, Ravindra MK, Reed WJ, Steven-son JD. Assessment of seismic margin calculation methods.NUREG/CR-5270, March 1989.

11. Bonzon LL, Hente DB. Test series 1: seismic fragility tests ofnaturally-aged class 1E Gould NCX-2250 battery cells.NUREG/CR-3923, September 1984.

12. Holman GS, Chou CK, Shipway GD, Glozman V. Compo-nent fragility research program, phase 1 demonstration test.NUREG/CR-4900, December 1987.

13. Park YJ. Survey on the experimental studies and design prac-tice of reinforced concrete shear wall structures. Technicalreport A-3301-2/95. Brookhaven National Laboratory,February 1995.

14. Bohn MP, Shieh LC, Wells JE, Cover LC, Bernreuter DL,Chen JC, Johnson JJ, Bumpus SE, Mensing RW, O’ConnellWJ, Lappa DA. Application of the SSMRP methodology tothe seismic risk at the Zion Nuclear Power Plant. NUREG/CR-3428, LLNL, January 1984.

15. Bandyopadhyay KK, Hofmayer CH, Kassir MK and PepperSE. Seismic fragility of nuclear power plant components(phase II). NUREG.CR-4659, Vol. 2, December 1987.

16. Nuclear Power Engineering Corporation. Proving tests on theseismic reliability for nuclear power plant. Seismic provingtest of emergency diesel generator system. Japan: NUPEC,1992.

17. Reed JW, Kennedy RP. Methodology for developing seismicfragilities. EPRI TR-103959. EPRI, June 1994.

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