seismic fragility application guide 2002 tr 1002988

Seismic Fragility Application Guide

Technical Report

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AL WARNING:

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EPRI Project Manager R. Kassawara

EPRI 3412 Hillview Avenue, Palo Alto, California 94304 PO Box 10412, Palo Alto, California 94303 USA 800.313.3774 650.855.2121 [email protected] www.epri.com

Seismic Fragility Application Guide

1002988

Final Report, December 2002

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This report describes research sponsored by EPRI

The report is a corporate document that should be cited in the literature in the following manner:

Seismic Fragility Application Guide, EPRI, Palo Alto, CA: 2002. 1002988.

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REPORT SUMMARY

The Seismic Fragility Application Guide provides utilities with in-depth guidelines for performing fragility analysis as part of a seismic probabilistic risk assessment (SPRA). These cost-effective and practical procedures and the resulting SPRA can support risk-informed/performance-based (RI/PB) applications.

Background The American Nuclear Society (ANS) has developed draft standard ANS 58.21, External Event PRA Methodology Standard, for addressing the risk to nuclear power plants from earthquakes and other external events. The standard provides requirements for addressing external events ranging from simplified screening to sophisticated levels of probabilistic risk assessment. The primary focus is on seismic PRA. The standards approach for SPRA is intended to be identical to the American Society of Mechanical Engineers (ASME) standard (ASME, 2001) for internal event PRA. The standard uses a graded approach and considers the studys scope and level of detail, plant specificity, and degree of realism. Requirements for three graded SPRA levels are provided. The graded levels are labeled Capability Categories 1, 2, and 3. This document focuses on developing seismic fragilities for structures, systems, and components (SSCs) in an overall seismic PRA. Existing methodologies for developing fragilities, ranging from simplified methods to detailed analyses, were used in the individual plant examination for external events (IPEEE) program in varying degrees of detail. The U.S. Nuclear Regulatory Commission (USNRC) review of IPEEE (USNRC, 2000a) identified some shortcomings in methodology and practice that require improvements for future work. This document addresses USNRC comments, correlates existing methodologies with requirements for the three Capability Categories in the ANS standard, and provides implementation guidelines and example problems.

Objective To provide utilities with seismic fragility analysis methods to support regulatory and non-regulatory applications.

Approach The project team reviewed the ANS External Events PRA Standard requirements for the three levels of performing seismic PRA and summarized the steps necessary to satisfy the standard. Team members reviewed existing fragility methodologies (as applied to IPEEE and other commercial and research seismic PRAs) and correlated them to the standards requirements. Comments by USNRC on the IPEEE submittals were reviewed and are addressed in this report. Additionally, more recent methodological suggestions for development of fragilities (Kennedy, 1999) and supplemental test data that could enhance the database for developing fragilities (Ueki, et.al., 1999) also were reviewed and addressed.

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Supplemental methodology and procedures were developed in this study for cases where existing methodology and procedures in the technical literature were undefined. The project team developed example problems to supplement existing sample problems in the literature and to address technical methods not adequately addressed.

Results This report provides an implementation guide for deriving seismic fragilities together with representative example fragility calculations. The basic fragility methodology has been documented in selected technical papers and industry publications (for example, EPRI report TR-103959). This report updates that fragility methodology to reflect recent methodological changes in the literature and correlates the appropriate steps to the requirements of the ANS External Events Standard. Examples of fragility development that complement examples in TR-103959 are provided to enhance information available to personnel who perform fragility analysis. This document and TR-103959 provide methodology, procedures, and an array of example problems that encompass most situations that fragility analysts will encounter. The following have also been included in this report: a summary of USNRC comments on fragility methods from the IPEEE program; recommendations to address appropriate NRC comments; a review of recent experience data (test and earthquake data), which can be used for the fragility development process; a review of recent advances in the technical literature relative to seismic fragility methodology; and, a review of recent fragility requirements within the ANS External Events Standard and recommendations for meeting these requirements.

EPRI Perspective The industry and the regulators are moving toward RI/PB methods; therefore, it is important that utility engineers understand, become familiar with, and use seismic PRA methods. The basic parts of a seismic PRA are identifying the hazard, analyzing the system, and evaluating structural fragility. Of these, calculating fragilities is the closest to the structural engineering discipline. Accordingly, EPRI considers developing tools such as this report to be critical for structural engineers who use SPRA methods.

Keywords Earthquakes Seismic Risk Fragilities Probabilistic safety assessment Individual plant examination for external events

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EPRI Proprietary Licensed Material

ABSTRACT

The American Nuclear Society has developed draft standard ANS 58.21, External Event PRA Methodology Standard, for addressing the risk to Nuclear Power Plants from earthquakes and other external events. The Standard provides requirements for addressing external events from a risk-informed perspective. The requirements range from simplified screening to progressively more detailed levels of Probabilistic Risk Assessment. For seismic events the standard provides requirements for conducting Seismic Margin Assessment (SMA) and Seismic PRA. Although some examples are provided in the Standard for risk informed applications of SMA, the primary focus of the Standard is on Seismic PRA. The primary steps in conducting seismic PRA are the development of the seismic hazard, the development of a fault tree/event tree model of the plant response to earthquakes and the development of fragilities for basic events included in the plant model. The ANS Standard provides high level requirements for the seismic hazard, the plant system modeling and the development of fragilities for three progressively more detailed levels of Seismic PRA. The three levels of detail are denoted as Capability Category 1, 2 and 3. This document focuses on the development of seismic fragilities of structures, systems and components for use in Seismic PRA for any of the three catagories. The importance of the interface between the fragility analysts and the hazard and plant system modeling analysts is emphasized.

Existing methodology for development of fragilities ranges from simplified methods to detailed analysis. Existing methodology that would meet Capability Categories 1 and 2 and in many cases, Capability Category 3, is portrayed in EPRI TR-103959 and was used in the IPEEE program in varying degrees of detail. The USNRC review of IPEEE submittals (USNRC, 2000a) identified shortcomings in methodology and practice that require improvements for future work. This document addresses the USNRC comments and correlates existing methodologies with requirements for the three Capability Categories in the ANS Standard. Supplemental methodology and example problems are provided to enhance the existing methodology applied in IPEEE.

First the basic methodology for conducting Seismic PRA and development of fragilities is summarized. Then a detailed discussion of the NRC comments on IPEEE, as they relate to the ANS Standard and the existing methodology, is provided. The most important USNRC comments on methodology are related to the use of a uniform hazard spectrum, use of surrogate elements and scaling of soil-structure interaction analysis. The use of uniform hazard spectra and scaling of soil-structure interaction analysis are addressed in the ANS Standard and this document. The use of surrogate elements is not addressed in the ANS Standard. The Standard requires that screened out components have a low contribution to risk implying that they do not need to be included by representation as a surrogate element. The NRCs principal issue in IPEEE was that the screening level was too low and representation of screened out elements by

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use of a surrogate element or elements resulted in a significant contribution to risk. Screening criteria and the failure rate target for screening are addressed in this report and an example screening level fragility is presented. Other NRC comments on IPEEE are related to expertise of the analysts and reliance of non-seismically designed structures controlled by organizations outside of the plant boundary. These are not methodological issues but are nevertheless important and are discussed in this report.

A step-by-step discussion of the development of fragilities to meet the three Capability Categories in the ANS Standard is presented. Table 4-1 is a comprehensive comparison of the fragility parameters that are to be addressed, the existing methodology, lack of methodology or procedures and the requirements of the ANS Standard. Where existing methodology and examples are determined to be adequate, the methodology is referenced and is not repeated. Where existing methodology or procedures are not complete, supplemental criteria and examples are provided.

The example problems in the Appendices are primarily related to issues raised by the NRC review of IPEEE or methodology not addressed in existing Seismic PRA and fragility methodology guidelines. They address scaling of spectra, developing fragilities from earthquake experience data, developing screening levels and applying screening criteria. Other examples address the derivation of fragility from design analysis, liquefaction related fragility and the fragility of un-reinforced masonry walls.

A Capability Category 2 analysis would, in general, be required for future risk informed applications although, in some cases, Capability Category 1 should be acceptable. The minimum requirements of NUREG-1407 for Seismic IPEEE would correspond to Capability Category 1 and most IPEEE submittals did not go beyond the NUREG-1407 requirements. NUREG-1407 required that only a point estimate of CDF be calculated using a mean hazard curve and a single composite fragility curve, thus, most submittals did not contain an uncertainty analysis as required for Capability Category 2. The EPRI and LLNL hazard studies are considered to comply with Capability Category 2. In most cases, if new structural analysis was conducted, fragilities developed for IPEEE would either comply with Capability Category 2 or could easily be updated to Capability Category 2. For many cases where in-structure spectra were scaled from the design basis spectra, the fragilities would likely only be applicable to Capability Category 1 based on requirements within the ANS Standard.

The information in this document, in conjunction with EPRI TR-103959, is intended to envelop most cases for development of seismic fragilities for Capability Categories 1 through 3. Some very unique cases (such as for dams) as noted in the USNRC review of IPEEE submittals, require specialized expertise that is not documented here.

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ACRONYMS

AFRS Amplified Floor Response Spectra ANS American Nuclear Society BWR Boiling Water Reactor CDF Core Damage Frequency CDFM Conservative Deterministic Failure Margin CUS Central United States DBE Design Basis Earthquake EUS Eastern United States FOAKE First of a Kind Reactor Engineering FPS Feet per Second GERS Generic Equipment Ruggedness Spectra GIP Generic Implementation Procedure GMI Ground Motion Incoherence HCLPF High Confidence of Low Probability of Failure. HFD High Frequency Ductility IPEEE Individual Plant Examination of External Events IRS In-Structure Response Spectra LERF Large Early Release Frequency LLNL Lawrence Livermore National Laboratories NEP Non-Exceedance Probability NPP Nuclear Power Plant PGA Peak Ground Acceleration PSA Pseudo Spectral Acceleration PSHA Probabilistic Seismic Hazard Analysis PSV Pseudo Spectral Velocity PWR Pressurized Water Reactor RAI Request for Additional Information RE Reference Earthquake Spectrum from Probabilistic Hazard Study RLE Review Level Earthquake RRS Required Response Spectrum SA Spectral Acceleration SD Spectral Displacement SDOF Single Degree of Freedom SMA Seismic Margin Assessment SPRA Seismic Probabilistic Risk Assessment SPSA Seismic Probabilistic Safety Assessment SQRT Seismic Qualification Review Team SQURTS Seismic Qualification Reporting and Testing Standardization SSCs Structures, Systems and Components


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SSE Safe Shutdown Earthquake SSI Soil-Structure Interaction SSMRP Seismic Safety Margin Research Program Standard ANS 58.21 External Events PRA Methodology Standard TER Technical Evaluation Report TRS Test Response Spectrum UHS Uniform Hazard Spectra ZPA Zero Period Acceleration ZPGA Zero Period Ground Acceleration


CONTENTS

1 INTRODUCTION ....................................................................................................................1-1 1.1 Objective of Applications Guide...................................................................................1-1 1.2 Scope of the Applications Guide..................................................................................1-2

2 STATE OF THE ART AND PRACTICE OF SEISMIC PRA IN THE U.S. AND OTHER COUNTRIES..............................................................................................................................2-1

2.1 Methodology ................................................................................................................2-2 2.1.1 Key Elements of Seismic PRA ................................................................................2-3 2.1.2 Output of Seismic PRA ...........................................................................................2-6 2.1.3 Discussion of Seismic PRA Tasks ..........................................................................2-6 2.1.4 Acceptable Seismic PRA Methodology...................................................................2-9

2.1.4.1 SSMRP Method ............................................................................................2-10 2.1.4.2 Zion Method..................................................................................................2-10

2.2 Seismic Fragility Analysis Methodology.....................................................................2-10 2.2.1 Generalized Fragility Descriptions ........................................................................2-11 2.2.2 Detailed Fragility Model.........................................................................................2-13 2.2.2 Failure Modes .......................................................................................................2-16 2.2.3 Estimation of Fragility Parameters ........................................................................2-17

2.2.3.1 Fragility of Structures....................................................................................2-18 2.2.3.2 Fragility of Equipment and Other Components.............................................2-20

2.2.4 Information Sources ..............................................................................................2-23 2.2.5 Other Fragility Models ...........................................................................................2-24 2.2.6 Hybrid Method.......................................................................................................2-25

2.3 Plant Level Fragility ...................................................................................................2-26

3 FRAGILITY METHODOLOGY ISSUES AND ENHANCEMENTS .........................................3-1 3.1 Methodological Issues from USNRC Review of IPEEE Submittals .............................3-1

3.1.1 Use of Uniform Hazard Spectrum ...........................................................................3-2

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3.1.2 Use of Surrogate Elements in SPRAs.....................................................................3-3 3.1.3 The Use of New Soil Structure Interaction Analysis Versus the Use of Scaling..............................................................................................................................3-5 3.1.4 Reliance on Structures for Which the Original Design Documentation is no Longer Available...............................................................................................................3-6 3.1.5 Importance of Analysts Expertise in Component Fragility/HCLPF Assessments ....................................................................................................................3-7

3.2 Comments and Suggestions from Industry on Methodology for SPRA .......................3-8 3.3 New Test and Earthquake Experience Data..............................................................3-13

4 DEVELOPMENT OF FRAGILITIES IN ACCORDANCE WITH ANS 58.21 ...........................4-1 4.1 Understanding the Seismic Hazard .............................................................................4-2 4.2 Understanding the Development of the Risk Model and Equipment List and the Significance of Screening Thresholds ...................................................................................4-6 4.3 Determine the Seismic Response of Structures ..........................................................4-8

4.3.1 Scaling of Existing Design Analysis ........................................................................4-9 4.3.2 Conducting New Analysis .....................................................................................4-10

4.4 Plant Walkdown .........................................................................................................4-11 4.5 Structural Capacity ....................................................................................................4-12 4.6 Determine Ductility Beyond the Limit State Capacity.................................................4-13 4.7 Structural Response Factor .......................................................................................4-14

4.7.1 Spectral Shape Factor ..........................................................................................4-15 4.7.2 Damping................................................................................................................4-15 4.7.3 Modeling................................................................................................................4-16 4.7.4 Mode Combination ................................................................................................4-16 4.7.5 Earthquake Component Combination ...................................................................4-17 4.7.6 Foundation-Structure Interaction...........................................................................4-17 4.7.7 High Frequency Effect...........................................................................................4-18

4.8 Probabilistic Response: .............................................................................................4-18 4.9 Equipment Response and Capacity...........................................................................4-20

4.9.1 Initial Prescreening Using Licensing Criteria.........................................................4-21 4.9.2 Prescreening Using Earthquake Experience Data................................................4-22 4.9.3 Prescreening using the EPRI SMA Screening Tables ..........................................4-23 4.9.4 Development of Fragilities Using Plant Specific Data ...........................................4-24

5 INDEX TO EXAMPLE FRAGILITY CALCULATIONS ...........................................................5-1

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6 REFERENCES .......................................................................................................................6-1

A BENCHMARK STUDIES TO VERIFY AN APPROXIMATE METHOD FOR SPECTRA SCALING.................................................................................................................................. A-1

A.1. Background.................................................................................................................. A-1 A.2. Verification of Original Spectra to be Scaled ............................................................... A-1 A.3. Development of Scaled Spectra by Rigorous and by Simplified Means ...................... A-2 A.4. References................................................................................................................... A-4

B DEVELOPMENT OF IN-STRUCTURE RESPONSE SPECTRA FOR SEISMIC MARGIN OR SEISMIC PRA EVALUATION BY SCALING ..................................................... B-1

B.1 Introduction ................................................................................................................. B-1 B.2 Incoherence Reduced Ground Motion........................................................................ B-1 B.3 Estimation of Floor Spectra Compatible with Incoherence Reduced Ground Motion .................................................................................................................................. B-6

B.3.1 Scaling of Floor Spectra......................................................................................... B-6 B.3.2 Spectral Estimation Method ................................................................................... B-6 B.3.3 Incoherence Reduction of Selected Reference Locations ................................... B-10 B.3.4 Total Spectra Incoherence Reduction for All Locations ....................................... B-12

B.4 High Frequency Reduction of Floor Spectra Due to Ductility Effects........................ B-13 B.5 Estimation of Floor Spectra Compatible with High Frequency Ductility Reduced Pseudo Ground Motion ...................................................................................................... B-16

B.5.1 Damage Consistent Scaling of Floor Spectra ...................................................... B-16 B.5.2 Damage Consistent Reduction of Selected Reference Locations ....................... B-16

B.6 References ............................................................................................................... B-19

C ESTIMATION OF EQUIPMENT CAPACITY BASED ON EARTHQUAKE EXPERIENCE DATA................................................................................................................ C-1

References........................................................................................................................... C-5

D EXAMPLE FRAGILITY FOR INSTRUMENT CABINET DERIVED FROM EXPERIENCE DATA................................................................................................................ D-1

D.1 Demand ...................................................................................................................... D-1 D.2 Capacity...................................................................................................................... D-2 D.3 Capacity Factor........................................................................................................... D-4 D.4 Structural Response Factor ........................................................................................ D-4

D.4.1 Spectral Shape (SS) .............................................................................................. D-5 D.4.2 Damping (D)........................................................................................................... D-6

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D.4.3 Modeling (M) .......................................................................................................... D-6 D.4.4 Mode Combination (MC) ........................................................................................ D-6 D.4.5 Ground Motion Incoherence (GMI) ........................................................................ D-7 D.4.6 High Frequency Ductility Reduction (HFD) ........................................................... D-7 D.4.7 Scaling Using Random Vibration Theory (RV)....................................................... D-7 D.4.8 Structural Response Factor (FRS) ........................................................................... D-7

D.5 Fragility ....................................................................................................................... D-8 D.6 References ................................................................................................................. D-9

E DEVELOPMENT OF GENERIC FRAGILITY DESCRIPTIONS FOR PURPOSES OF SCREENING BASED UPON DESIGN CRITERIA................................................................... E-1

E.1 Establishment of Screening Level............................................................................... E-1 E.1.1 Seismic Hazard ...................................................................................................... E-1 E.1.2 Uncertainty in the Median Fragility......................................................................... E-2 E.1.3 Target Failure Rate ................................................................................................ E-2

E.2 Development of Demand on Components.................................................................. E-3 E.3 Screening Evaluation of Equipment and Distributive Systems ................................... E-3 E.4 Screening of Flexible Equipment and Distributive Systems Designed by Analysis................................................................................................................................ E-5

E.4.1 Strength Factor ...................................................................................................... E-6 E.4.2 Equipment Response Factor.................................................................................. E-6 E.4.3 Structural Response Factor ................................................................................... E-8 E.4.4 Fragility Description for Flexible Components Designed by Analysis .................... E-8

E.5 Components Qualified by Test.................................................................................... E-9 E.6 References ............................................................................................................... E-12

F EXAMPLE PROBLEM FOR SERVICE WATER PUMP ........................................................F-1 F.1 Description of Equipment.............................................................................................F-1 F.2 Strength Factor ............................................................................................................F-3 F.3 Equipment Response Factor .......................................................................................F-4

F.3.1 Qualification Method ...............................................................................................F-4 F.3.2 Damping..................................................................................................................F-5 F.3.3 Modeling..................................................................................................................F-6 F.3.4 Mode Combination ..................................................................................................F-6 F.3.5 Earthquake Component Combination .....................................................................F-6 F.3.6 Equipment Response Factor...................................................................................F-7

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F.4 Structural Response Factor .........................................................................................F-7 F.4.1 Spectral Shape........................................................................................................F-7 F.4.2 Damping..................................................................................................................F-8 F.4.3 Modeling..................................................................................................................F-8 F.4.4 Mode Combination ..................................................................................................F-9 F.4.5 Ground Motion Incoherence....................................................................................F-9 F.4.6 Structural Response Factor ....................................................................................F-9

F.5 Fragility for Service Water Pumps ...............................................................................F-9 F.6 References ................................................................................................................F-10

G GENERAL METHODOLOGY FOR LIQUEFACTION SEISMIC FRAGILITY ASSESSMENT AND EXAMPLE ANALYSIS...........................................................................G-1

G.1 Introduction .................................................................................................................G-1 G.2 Background................................................................................................................. G-1 G.3 Basis of Approach.......................................................................................................G-2 G.4 Example Case Study ..................................................................................................G-3

G.4.1 Overview of Approach............................................................................................G-3 G.4.2 Initial Liquefaction Analysis and Results ................................................................G-4 G.4.3 Detailed Liquefaction and Settlement Analysis and Results ..................................G-5

G.5 References .................................................................................................................G-9

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LIST OF FIGURES

Figure 2-1 Seismic Risk Assessment Methodology...................................................................2-4 Figure 2-2 Seismic PRA Flowchart ............................................................................................2-7 Figure 2-3 Fragility Curves.......................................................................................................2-12 Figure 2-4 Mean, Median, 5% Non-Exceedance, and 95% Non-Exceedance Fragility

Curves for a Component ..................................................................................................2-15 Figure 2-5 Discrete Family of Fragility Curves for a Component .............................................2-16 Figure 4-1 Annual Probability of Exceedance of Peak Ground Acceleration.............................4-3 Figure 4-2 Uniform Hazard Spectra for the 10-4 Annual Probability of Exceedance.

Spectra shown for three percentiles: 15th, 50th, and 85th ....................................................4-4 Figure A-1 Lumped Mass Model of Reactor Building .............................................................. A-5 Figure A-2 Reactor Building EQ Floor Spectra, Node 11 ........................................................ A-6 Figure A-3 Reactor Building NS Floor Spectra, Node 11......................................................... A-7 Figure A-4 Reactor Building Vertical Floor Spectra, Node 11.................................................. A-8 Figure A-5 RG 1.60 Spectrum Compatible Time Histories ...................................................... A-9 Figure A-6 Reactor Building E-W Floor Spectra Reconstructed Model, Node 11.................. A-10 Figure A-7 Reactor Building N-S Floor Spectra Reconstructed Model, Node 11................... A-11 Figure A-8 Reactor Building Vertical Floor Spectra Reconstructed Model, Node 11............. A-12 Figure A-9 EW Floor Response Spectrum Developed From Eigensolution of DBE

Analysis, Using RG 1.60 Time Histories ......................................................................... A-13 Figure A-10 Comparison of DBE with UHS ........................................................................... A-14 Figure A-11 RB Estimated SDOF Oscillator Response Node 11 .................................... A-15 Figure A-12 RB Estimated SDOF Oscillator Response Node 11 .................................... A-16 Figure A-13 RB UHS Scale Factors Node 11 .................................................................. A-17 Figure A-14 Scaled DBE Spectra Node 11......................................................................... A-18 Figure B-1 Reduction Function for Incoherence Across a 43.3 M (142-Foot) Foundation....... B-3 Figure B-2 Uniform Hazard Horizontal Response Spectra ...................................................... B-4 Figure B-3 Incoherence Reduced Horizontal Ground Motion for Building E............................ B-5 Figure B-4 Incoherence Reduced Vertical Ground Motion for Building E................................ B-5 Figure B-5 Response Spectra Relationships ........................................................................... B-7 Figure B-6 Incoherence Reduced Spectra for Building E Node 162610................................ B-11 Figure B-7 Incoherence Reduction Functions for Selected Nodes of Building E................... B-12 Figure B-8 Overall Incoherence Reduction Factors for Building E ........................................ B-13

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Figure B-9 Reduced Horizontal Ground Motion Spectra for Building E ................................. B-15 Figure B-10 Reduced Vertical Ground Motion Spectra for Building E ................................... B-15 Figure B-11 Overall Reduced Spectra for Building E Node 162610 ...................................... B-18 Figure D-1 Equipment Class 20 Control and Instrumentation Panels and Cabinets ............... D-3 Figure E-1 Comparison of DBE Vs Probabilistic Response Spectra Reactor Building El.

547 ................................................................................................................................... E-5 Figure E-2 Typical Overtest at High Frequency..................................................................... E-12 Figure F-1 Model of the Service Water Pump...........................................................................F-2 Figure F-2 Simplified Motor Stand Model .................................................................................F-3 Figure F-3 Demand Response Spectrum, 5% Damping...........................................................F-5 Figure G-1 Weighted Fragility Curves, Accounting for Random Variability and

Composite Variability, for End-States of: (i) Incipient Liquefaction, and (ii) Gross Liquefaction.......................................................................................................................G-7

Figure G-2 Weighted Fragility Curves, Accounting for Random Variability and Composite Variability, for End-States of Component Failure Due to Settlements Caused by Level-Ground Liquefaction, for Cases Where the Component Median Capacity Against Failure Equals (iii) 5 cm, (iv) 10 cm and (v) 20 cm................................G-8

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LIST OF TABLES

Table 4-1 Correlation Of Fragility Development Elements And Requirements Of Ans Standard For External Events ..........................................................................................4-25

able 5-1 Index To Example Fragility Calculations....................................................................5-2 T

Table B-1 Reduction Factors for 150-Foot Foundation............................................................ B-2

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1 INTRODUCTION

1.1 Objective of Applications Guide Seismic Probabilistic Risk Assessment (SPRA) studies have been conducted for many of the US Nuclear Power Plants over the last 20 years. Initially they were conducted to answer safety concerns in heavily populated areas. The most recent wide spread application of SPRA was to satisfy the USNRC request for information regarding severe accident vulnerabilities in Generic Letter 88-20, Supplement 4, (USNRC, 1991a). The USNRC is encouraging the use of PRA for making risk informed decisions and has developed a Risk-Informed Regulation Implementation Plan (USNRC, 2000b) and associated regulatory guides. The Licensees in turn are moving toward using PRA for Changes to Licensing Basis, Changes to Technical Specifications, Graded Quality Assurance, etc. Seismic issues continue to arise in operating NPPs to address the risk from installations that were not designed and constructed in accordance with current standards or in looking at potential safety issues associated with life extension. There is a desire and a need to utilize seismic PRAs to address these issues on a risk informed basis rather than applying the conventional deterministic licensing basis approach to all seismic issues.

A recent Draft ANS Standard 58.21 (ANS, 2002), External Events PRA Methodology Standard, hereafter referred to as the Standard, sets multi-level requirements for conducting SPRAs. The Standard sets requirements for three levels of PRA, Capability Category 1, 2 and 3. Most of the initial SPRAs conducted in the US in the 1980s, contained an uncertainty analysis that examined the uncertainty spread in the computed Core Damage Frequency (CDF) arising from the uncertainty in the seismic hazard and the uncertainty in the fragilities of structure, systems and components (SSCs). These studies corresponded to the fundamental requirements of Capability Category 2 in the Standard, although, the hazard studies at that time would not meet current requirements. In IPEEE, the Licensees who chose to do SPRA were only required to compute a point estimate of CDF. This would correspond to Capability Category 1, mainly because uncertainty analyses were not conducted. Capability Category 3 is more along the lines of what was done in the USNRC sponsored Seismic Safety Margins Research Program (USNRC, 1981). Capability Category 3 requires extensive effort to compute probabilistic response of structures and severely limits screening unless screened out SSCs can be shown to have very low seismic failure rate and are uncorrelated. For purposes of risk informed regulation it is intended in this Applications Guide that a Capability Category 2 SPRA will generally be the approach taken by licensees although, depending upon the issue, an application meeting Capability Category 1 may be adequate. This decision is up to the Licensees to demonstrate that full sensitivity analyses are not required to demonstrate the merits of a risk informed decision and of course requires agreement by the regulators, who must develop Safety Evaluation Reports (SERs) on the issue.

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Introduction

1.2 Scope of the Applications Guide

Significant information in the literature exists on how to generate seismic fragilities and how to conduct a SPRA. The EPRI Methodology for Developing Seismic Fragilities, (EPRI, 1994) and EPRI Methodology for Assessment of Nuclear Power Plant Seismic Margin, (EPRI, 1991b), contain most of the background and guidance needed for an analyst to develop seismic fragilities of SSCs. This Applications Guide will not repeat the guidance in those documents. Instead it will focus on the applicability of the methodology to the requirements in the Standard (including how to use the methods with respect to Capability Category 1, 2 and 3 of the Standard) and provide additions and enhancements to the existing methodology where applicable. EPRI (1994) contains methodologies for rigorous and simplified methods for developing seismic fragilities, but since the Standard was written subsequent to EPRI (1994), some direction to the analyst is appropriate on which of the methods in EPRI (1994) are applicable to the three capability categories of the Standard.

Chapter 2 presents an overall summary of the SPRA methodology and fragility methodology. This Applications Guide focuses on the detailed development of fragilities, which is one of the important technical steps in conducting a SPRA. It is important, however, for the fragility analyst to understand the background of the seismic hazard development and the systems modeling in order to assure a clear interface with the hazard and systems analysts. Chapter 3 discusses the USNRC comments on seismic IPEEE submittals and provides guidance on how to address these comments in accordance with the framework of the Standard. Chapter 3 also addresses some recent industry-suggested alternate approaches to current practice in SPRAs, and their compliance with the Standard.

Chapter 4 goes through a step by step description of the important elements of developing seismic fragilities and the correlation of each step to requirements in the Standard. Detailed fragility development procedures in EPRI (1994) are not repeated. Rather, the focus is on guiding the fragility analyst through the process of interfacing with the hazard and systems analysts and developing fragilities that are compatible with the overall SPRA process. The appendices contain a complementary set of sample problems which focus on different areas of fragility analysis than those published in EPRI (1994) in order to enhance the database of examples available to the user.

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2 STATE OF THE ART AND PRACTICE OF SEISMIC PRA IN THE U.S. AND OTHER COUNTRIES

The use of seismic probabilistic risk assessment (SPRA) methods to supplement the deterministic processes of licensing and design of nuclear power plant facilities started in the mid 1970s. Prior to this time, deterministic procedures were primarily used. In 1975 the U.S. Nuclear Regulatory Commission (USNRC) published WASH-1400, a reactor safety study of U.S. commercial nuclear power plants that employed probabilistic risk assessment procedures to assess accident risks (USNRC, 1975). In that study the annual frequency of seismically-induced core damage for an average site was reported to be 5x10-7. It was concluded that seismic events were not major contributions to risk. This study considered seismic events in only a rudimentary manner.

An SPRA was conducted in the late 1970s for the Oyster Creek Unit 1 Nuclear Generating Station. This study became the foundation for SPRA as currently practiced and characterized SPRA in terms of the integration of a site hazard curve with a plant level fragility curve to compute core damage frequency. The plant level fragility curve was formulated from individual structures, systems and components (SSCs) fragilities using fault tree/event tree logic models of the plant systems. A lognormal fragility model was used to define the fragilities. Lognormal models are still used in SPRAs conducted for nuclear plants today. A detailed fragility model was developed that addressed the randomness and uncertainty in the various underlying response and capacity variables that contribute to the success or failure of SSCs. In 1981 the Zion SPRA was submitted to the NRC (Zion, 1981). This was the first complete SPRA study of a commercial NPP. The first technical paper published that described in some detail what is referred to as the Zion method Kennedy, et.al., 1980. The method was patterned after the Oyster Creek and Zion SPRAs. About the same time, the NRC sponsored the Seismic Safety Margin Research Program (SSMRP) at the Lawrence Livermore National Laboratory (LLNL) (USNRC, 1981). The SSMRP method for performing SPRA involved detailed response analyses using the Latin hypercube simulation procedure. The Latin Hypercube procedure ensures that the full range of uncertainties of important variables are utilized but requires considerably fewer simulations than the classic Monte Carlo simulation procedure. Monte Carlo analysis usually requires thousands of simulations to assure that the full range of uncertainties of variables are incorporated. In the SSMRP method, fragilities were referenced to local accelerations rather than acceleration at the ground level. The SSMRP approach was resource intensive and is generally not used today. However, simplifications of the SSMRP approach have been used in subsequent research studies; for instance, NUREG-1150 (USRNC, 1990).

Several other studies were conducted in the early 1980s using the Zion Method methodology (Indian Point, Limerick, Susquehanna, Seabrook, Milestone 3, Oconee, Browns Ferry).

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State of the Art and Practice of Seismic PRA in the U.S. and Other Countries

In August 1985 a Severe Accident Policy statement was issued by the USNRC commissioners (USNRC, 1985). It required limited scope PRA evaluations of all commercial nuclear power plants in the United States for severe accident events. The USNRC staff was also given the responsibility for establishing the methodology and development of an alternate seismic margin approach to SPRA which used fragility and SPRA concepts in conjunction with some simplifying deterministic screening evaluation procedures. Trial guidelines for performing seismic margin reviews of nuclear power plants were developed and recommended to the USNRC (Prassinos et al., 1986). A trial review using these guidelines was performed for the Maine Yankee Atomic Power Station (Prassinos et al., 1987; Moore et al., 1987; Ravindra et al., 1987). As an alternative to the USNRC Seismic Margin Approach, EPRI developed a deterministic Seismic Margin Assessment methodology (EPRI, 1988). A trial plant applications was conducted for the Catawba PWR (EPRI, 1989b). A later trial plant application was conducted for the Hatch BWR (EPRI, 1991d).

In 1988, Pacific Gas and Electric Co. (PG&E) submitted the results of the detailed SPRA conducted for the Diablo Canyon Nuclear Power Plant to the NRC (PG&E, 1988). This was part of the PG&E Long Term Seismic Program that was a licensing condition required for plant operation. This was the most detailed SPRA performed to date. Several studies conducted during this program confirmed the validity of the methodology originally developed for the Oyster Creek and Zion studies and enhanced this methodology in some areas to reduce uncertainty.

In 1988 the USNRC issued Generic Letter 88-20 (USNRC, 1988) to nuclear power plant utilities and operators, requesting that an individual plant examination (IPE) for internally initiated events be performed. This letter was written as part of the Severe Accident Policy. In 1991 the USNRC issued Supplement 4 to Generic Letter 88-20 (USNRC, 1991a) requesting an Individual Plant Examination of External Events (IPEEE) for plant-specific external-event-initiated severe accident vulnerabilities. The USNRC also issued a procedural and submittal guidance document (USNRC, 1991b) for IPEEE programs. Probabilistic risk assessment procedures, seismic margin methodology, deterministic screening methods, and success path processes were recommended as the preferred method to resolve significant external events, primarily earthquakes.

Since 1980, seismic PRAs or seismic PSAs have been conducted for over 50 nuclear power plants worldwide. The methodology has been well established and the necessary data on the parameters of the PRA model have been generally collected. Detailed descriptions of the procedures used in SPRA are given in several published reports - PRA Procedures Guide (USNRC, 1983), PSA Procedures Guide (USRNC, 1985), (EPRI, 1994) and Budnitz, (1998).

2.1 Methodology

Seismic PRA is different from an internal event PRA in several important ways:

Earthquakes could cause initiating events different from those considered in the internal event PRA.

All possible levels of earthquakes along with their frequencies of occurrence and consequential damage to plant systems and components should be considered.

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Earthquakes could simultaneously damage multiple redundant components. This major common cause effect should be properly accounted for in the risk quantification.

The objectives of a seismic SPRA are to: Understand the most likely accident sequences induced by earthquakes (useful for accident

management), Develop an appreciation of accident behavior (i.e., consequences and role of operator), Gain an understanding of the overall likelihood of core damage induced by earthquakes, Identify the dominant seismic risk contributors, Identify the range of peak ground acceleration that contributes significantly to the plant risk

(this is helpful in making judgements on seismic margins), and Compare seismic risk with risks from other events and establish priorities for plant backfit.

2.1.1 Key Elements of Seismic PRA

The key elements of a SPRA can be identified as:

Seismic Hazard Analysis: to develop frequencies of occurrence of different levels of earthquake ground motion (e.g., peak ground acceleration) at the site.

Seismic Fragility Evaluation: to estimate the conditional probability of failure of important structures and equipment whose failure may lead to unacceptable damage to the plant (e.g., core damage). Plant walkdown is an important activity in conducting this task.

Systems/Accident Sequence Analysis: to model the combinations of structural and equipment failures that could initiate and propagate a seismic core damage sequence.

Risk Quantification: to Assemble the results of the seismic hazard, seismic fragility, and systems analyses to estimate the frequencies of core damage and plant damage states. Assessment of the impact of seismic events on the containment and consequence analyses, and integration of these results with the core damage analysis to obtain estimates of seismic risk in terms of effects on public health (e.g., early deaths and latent cancer fatalities).

Figure 2-1 shows the key elements of seismic risk assessment methodology along with the typical databases and software.

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Seismic Hazard Analysis

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Figure 2-1 Seismic Risk Assessment Methodology

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Box 1 shows the result of a seismic hazard analysis, i.e., a family of seismic hazard curves relating the frequency of exceedance to different levels of ground motion. Box 1A describes the databases needed to perform this seismic hazard analysis; note that region specific seismicity data is required for this analysis. Some of the available software for performing the seismic hazard analysis are indicated in Box 1B.

Box 2 is a pictorial representation of the systems analysis; it consists of event trees, fault trees and containment analysis. The database (shown in Box 2A) needed to perform the system analysis is the unavailabilities (i.e., random failures and operator failures) modified to reflect the severe stress induced by earthquakes. The software available for performing the systems analysis are indicated in Box 2B; they are typically used in the internal event analysis.

Box 3 shows the result of component fragility evaluation, i.e., a family of seismic fragility curves. These are developed using plant design information and realistic response analysis. There are many response analysis software programs available (Box 3B). The databases used for fragility analysis include earthquake experience data, generic equipment ruggedness spectra and fragility test results as indicated in Box 3A.

Box 4 shows the probability density functions of core damage frequency and release frequencies. These are obtained using the sequences of component failures, fragilities of components and seismic hazard curves. This is accomplished using a quantification software. Note that the quantification procedure is different from the internal event analysis in that the entire spectrum of earthquakes is considered and at each earthquake level, the component failure probabilities are different and dependencies between different component failures are to be explicitly included in the analysis. Some of the software developed for the seismic quantification are SEISIM, SEISMIC, SEIS, EQESRA, SRACOR and SECOM-2 as indicated in Box 4A. Most SPRAs conducted have been a Level 1 PRA that stops at the computation of core damage frequency (CDF). IPEEE required that the Level 1 analysis be extended to the evaluation of contaminant integrity but did not require a full Level 2 evaluation of Release Frequency.

Box 5 refers to the dispersion analysis using weather data that estimates the consequences of a core damage accident resulting in a radiological release to the atmosphere. Population distribution around the site and emergency evacuation procedures in place are considered in assessing the consequences in terms of health effects and property damage. Usually, the software and databases employed for internal events are adequate to estimate the consequences of seismic induced accidents. Sometimes, the analysts assume a reduced evacuation rate for seismic events.

Box 6 shows the risk curves. For each level of damage (e.g., number of deaths, cancer fatalities and property damage), the risk curve gives the annual frequency of exceedance of damage. The uncertainties in the risk assessment are displayed by means of a family of risk curves. Therefore, the annual frequency of exceeding a given level of damage is distributed and one could state this frequency with different levels of confidence.

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2.1.2 Output of Seismic PRA

The output from a SPRA consists of:

Seismic fragilities of components and seismic margins. Seismic fragilities of accident sequences and seismic margins. Seismic accident sequence frequencies and uncertainty distributions. Impact of nonseismic unavailabilities on seismic risk. Identification of dominant risk contributors: components, systems, sequences and procedures. Distribution on range of accelerations contributing to seismic risk. Risk reduction as a function of seismic upgrading to aid in backfit decisions.

2.1.3 Discussion of Seismic PRA Tasks

Figure 2-2 shows a flow chart of the SPRA. In the following we describe the different tasks

1. Review Plant Safety Systems and Modify Internal Event PRA Event and Fault Trees: The systems analyst will review the plant safety systems from the viewpoint of seismic safety, identify any seismic-specific initiating events and modify event and fault trees in the internal event PRA. Redundancy of multitrain safety systems is usually not credited due to correlations of response and capacity of similar or identical components.

2. Develop PRA Components List: Based on Task 1 and past seismic PRAs of similar plants, the systems analyst and fragility analyst develop a preliminary components list. The list includes the equipment and systems required to provide protection for all seismically induced initiating events, including those needed to address seismic induced fires and floods and to prevent early containment failure in an earthquake. Non safety systems are also included to take credit for non failures of normal shutdown systems.

3. Conduct Soil Failures Evaluation: The potential for soil liquefaction, slope failures and damage to buried pipelines is assessed in this task. Procedures for assessing these effects are described in EPRI (1991b). For most plants, a review based on design and construction records is considered adequate to screen these types of failures out. A detailed analysis is needed only if soil failure is deemed significant. This task is usually carried out by specialist geotechnical engineers.

4. Perform Structural Response Analysis: This task involves the derivation of the best estimate (or median-centered) seismic responses and their variability in the form of structural loads or floor response spectra that define the demand for which structures, systems and components are evaluated. These best estimates and variabilities are obtained by simulation probabilistic response analysis, by new deterministic analysis with estimated variability or by scaling of the safe shutdown earthquake (SSE) responses and assigning variability. The ground response spectrum usually used as input for this analysis is the median spectral shape for a 10,000-year return period along with variability estimates.



Develop PRAComponents List

IncludingContainment Systems

Soil Failures

Evaluation

Perform Response Analysis

Develop Floor Spectra and Structural

Response

Relay Chatter Evaluation

Perform PlantWalkdown Using

EPRI Margin Procedures

Screen OutComponents From

PRA List

Develop SeismicFragilities of

Screened-In Components

Modify Fault Trees,Develop Sequence

Equations

Seismic RiskQuantification

Seismic Hazard Curves

Develop SeismicPRA Outputs

Prepare PRAReport Peer Review

Select Peer Review Team

Input to UtilityManagement

Seismic PRACompleted

Review Plant Safety Systems and Modify

Internal Event Analysis Event and Fault Trees

Figure 2-2 Seismic PRA Flowchart

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5. Perform Peer Review: In order to assure the technical quality of the seismic PRA and to provide validation of the judgments made by the analysts, a peer review of the entire seismic PRA is often performed with the peer review team participating in the project at various critical times (e.g., review of response analysis, systems modeling, walkdown, fragility analysis and final documentation). For example, the requirements of a peer review are described in NUREG-1407 Chapter 7 (USNRC, 1991b). At this stage of the PRA, the task is to set up the peer review team and identify the scope and schedule for its participation.

6. Perform Plant Walkdown: The plant walkdown of essential components is particularly emphasized in modern seismic PRAs. In order for the walkdown to be efficiently performed, review of the design basis, preparation of procedures, collection of design/qualification data and training of the walkdown team is essential. All items on the components list must be physically examined for seismic vulnerabilities if possible using the procedures given in EPRI (1991b). The emphasis is on compliance to screening caveats, anchorage and attachment of subassemblies and parts, and seismic spatial systems interactions. The walkdown is conducted by a team of systems engineers and seismic fragility analysts.

7. Perform Screening of Components: Certain high capacity components may be screened out of the components list based on the review of seismic qualification criteria and qualification documents and walkdown screening. The decision to screen components should be based on the seismic hazard and the associated unconditional failure rate of a component with a fragility corresponding to the screening level. Deterministic screening targets are typically set based upon the lower tail of the component fragility. The reference point for screening is an acceleration level where there is 95% confidence of less than 5% probability of failure, commonly referred to as a HCLPF (high-confidence-of-low-probability-of-failure). For example, some PRA analysts screened out components with HCLPF capacities larger than 0.3 g peak ground acceleration (pga) in the IPEEE program. Based on previous seismic PRAs, the CDF contribution of components screened out at 0.3g pga HCLPF capacity was judged to be very low. However, as discussed in Chapter 3 the screening level was often too low and masked the CDF results. Screening for more seismically active regions (e.g., western US and higher seismic regions in the central and eastern US) should only be done at a higher earthquake level. Screening is primarily done by seismic fragility analysts using earthquake experience and plant specific qualifications criteria.

8. Perform Relay Chatter Evaluation: Relays whose chatter during an earthquake could result in adverse effects on plant safety must be identified and evaluated. This evaluation may be done probabilistically or by deterministic methods. The identification of relays and evaluation of the consequence of chatter on the electrical circuits are done by the systems analysts and electrical engineers; the seismic ruggedness of relays including the amplification of response through the cabinet into the relays is evaluated by the seismic fragility analysts. Often, rather than modeling the response of the systems to relay chatter, a deterministic screening is conducted to identify relays with high and low capacity and to determine if relay chatter is detrimental. Low ruggedness relays that can cause adverse effects are usually replaced. Some relays with intermediate capacities may be modeled. In this case specific or generic data on relay capacity is used to develop fragilities.

9. Develop Seismic Fragilities: Estimation of the conditional probabilities of structural or equipment failure for a given level of seismic ground motion for the screened-in components.

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Curves are developed using the fragility model whose parameters are the median acceleration capacity (Am), and logarithmic standard deviations reflecting randomness in capacity ( )R and uncertainty in the median capacity )( U . This task is performed by the seismic fragility analysts.

10. Develop Accident Sequence Equations: Perform the event tree and fault tree analyses for the seismic initiating events to obtain accident sequence Boolean equations or cutsets. This task is performed primarily by systems analysts with assistance from fragility analysts.

11. Input Seismic Hazard Curves: The seismic hazard curves developed for the site are input into the seismic quantification code.

12. Conduct Seismic Risk Quantification: This task involves assembling the results of the seismic hazard, fragility and systems analyses to estimate the frequencies of core damage and plant damage states. For some applications (e.g., Individual Plant Examination of External Events (IPEEE)), it was sufficient to obtain a mean point estimate of the core damage frequency using a single mean hazard curve and a single mean fragility curve; however, NUREG-1407 (USNRC, 1991b) encourages the analyst to make a careful study of the uncertainties. The approach followed in recent seismic PRAs is to identify the dominant sequences by point estimation and to perform uncertainty analysis of only these dominant sequences. The risk quantification is done by considering both seismic failures and non-seismic unavailabilities and operator actions.

13. Develop Seismic PRA Outputs: Since the focus of the seismic PRA is not on bottom line numbers but on the insights of the examination, a number of intermediate outputs are required as described in Section 2.1.2 above. This task is shared between the systems analysts and fragility analysts.

14. Prepare PRA Report: This task involves documenting the methodology and results of the study. Specific reporting requirements are given for example in NUREG-1407 (USNRC, 1991b).

15. Perform Final Peer Review: After the draft report is prepared, a peer review of the procedures, numerical results and insights obtained from the PRA is conducted. This is a culmination of the review process that has been implemented throughout the above tasks. The peer review is expected to produce a short report endorsing the PRA study.

16. Provide Input to Utility Management: This task involves developing a summary of the Seismic PRA, (a Tier I report) the findings, and risk informed upgrading recommendations. The objective of the task is to ensure that all responsible persons within the utility are informed of the Seismic PRA results. Each utility may have its own procedures for this task.

2.1.4 Acceptable Seismic PRA Methodology

The methodology described above has been accepted by the USNRC for the IPEEE Program and has been the most commonly used method for SPRA of nuclear power plants around the world. This is also known as the Zion Method wherein the seismic fragilities of components are

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referenced to the ground acceleration (either peak or spectral acceleration). In the early stages of development of SPRA methodology, there was a major research program at the Lawrence Livermore National Laboratory funded by the USNRC called Seismic Safety Margins Research Program (SSMRP) (USNRC, 1981). It developed a theoretical approach to estimating the seismic risk of nuclear power plants. The major differences between the SSMRP method and the Zion method are outlined in the next subsection.

2.1.4.1 SSMRP Method The structural and component fragilities are expressed in terms of local response parameters

such as stress, moment and spectral acceleration. Therefore, given an earthquake, the conditional failure probability of a structure or component is obtained by convolution of the probability distribution of the local response for the given ground acceleration and the probability distribution of the seismic resistance (capacity) of the structure or equipment.

A major emphasis of the SSMRP method lies in the computation of structural and equipment responses using a Latin Hypercube simulation technique. The joint probability distribution of the responses of different components (i.e., elements in the building, equipment and piping) characterized by mean values and a covariance matrix is developed.

The quantification of accident sequences is done cutset by cutset. Each cutset probability is obtained by integrating the joint probability distribution of the seismic response and the seismic capacity over the failure range. The cutset probabilities are added according to Hunters bound (Hunter, 1976) approach to obtain the accident sequence probability.

Because of the complexity and required resources, the SSMRP method and the softwares (i.e., SMACS and SEISIM) (USNRC, 1991) have not been used in seismic PRAs in the last 15 years. However, SMACS, which is a probabilistic response code, has been used to develop probabilistic floor response spectra for some IPEEE programs. The SSMRP method corresponds to Capability Category 3 of the Standard.

2.1.4.2 Zion Method

When the Zion method is used, some approximations are made by the analysts to account for correlations between component failures. It is also judged that the probabilistic response analysis, to capture the correlation and the quantification methodology to conduct multiple integration over the joint probability distribution, is not essential for commercial applications. Instead, some thumb rules were established to approximately account for the correlation.

The Zion method corresponds to Capability Categories 1 and 2 in the Standard.

2.2 Seismic Fragility Analysis Methodology

The seismic fragility of a structure or equipment is defined as the conditional probability of its failure at a given value of acceleration (i.e., peak ground acceleration or peak spectral acceleration at different frequencies). The methodology for evaluating seismic fragilities of structures and equipment is documented in the PRA Procedures Guide (USNRC, 1983) and is



more specifically described for application to NPPs in the EPRI Methodology for Developing Seismic Fragilities (EPRI, 1994). This general methodology has been applied in over 50 Seismic Probabilistic Risk Assessments of nuclear power plants.

The fragility methodology described herein is in accordance with the Zion Method although the capacity part of fragility development (strength of SSCs) is applicable to the SSMRP method as well.

The objective of a fragility evaluation is to estimate the capacity of a given component relative to a ground acceleration parameter such as peak ground acceleration or spectral acceleration. Typically, the seismic hazard for a plant site is defined by peak ground acceleration (pga) or spectral accelerations (Sa) at different structural frequencies; hence all fragility estimates are referenced to ground acceleration (peak ground or spectral acceleration). Although spectral acceleration is the preferred ground motion parameter, most existing hazard studies focused primarily on peak ground acceleration, and most SPRAs have been based on pga. Peak ground acceleration is used herein as an example indicator only. If the seismic hazard curves are available in terms of spectral accelerations at different frequencies they could be used as long as consistency in the hazard and fragility definitions is maintained. In spite of its shortcomings as a damage measure, peak ground acceleration is a familiar term for all analysts involved in SPRA (i.e., systems analysts, hazard analysts and fragility analysts). In the Diablo Canyon SPRA, sensitivity studies indicated only a minor change to the core damage frequency calculated using fragilities defined in terms of peak ground acceleration compared to those defined using average spectral acceleration over a specified frequency range covering the fundamental frequencies of major structures. The important conclusion is that proper interface between the analysts (i.e., hazard, fragility and systems) should take place and it does not matter so much what parameter the fragility is referenced to as long as the failure mode is properly defined and the seismic response and capacity values are consistently calculated.

2.2.1 Generalized Fragility Descriptions

The ground acceleration capacities of the components are usually estimated using information on the plant design basis and responses calculated at the design-analysis stage. The ground acceleration capacity is a random variable that can be described completely by its probability distribution. However, there is uncertainty in the estimation of the parameters of this distribution, the exact shape of this distribution, and in the appropriate failure model for the component. For any postulated failure mode and set of parameter values describing the ground acceleration capacity and shape of the probability distribution, a fragility curve depicting the conditional probability of failure as a function of peak ground acceleration can be obtained. Hence, for different models and parameter assumptions, one could obtain different fragility curves. A satisfactory way to consider these uncertainties is to represent the component fragility by means of a family of fragility curves. A subjective probability value is assigned to each curve to reflect the analysts degree of belief in the model that yielded the particular fragility curve. When represented in this fashion, the fragility curves need not appear to be smooth S-shaped curves, approximately parallel to each other. They could theoretically intersect each other and they may not even be non-decreasing functions of peak ground acceleration. The only requirement is that fragility, being a probability, should be between 0 and 1 (see Figure 2-3). Since each curve represents a different model, the fragility curves could intersect. Sometimes, a

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fragility curve for a cutset containing a failure event and a success event is plotted. This could show a decrease in the fragility (i.e., conditional probability of failure) at increased acceleration values.

Figure 2-3 Fragility Curves

At any acceleration value, the component fragility (i.e., conditional probability of failure) varies from 0 to 1; this variation is represented by a subjective probability distribution. On this distribution we can find a fragility value (say, 0.01) that corresponds to the cumulative subjective probability of 5%. We have 5% cumulative subjective probability (confidence) that the fragility is less than 0.01. Similarly, we can find a fragility value for which we have a confidence of 95%. Note that these statements can be made without reference to any probability model. Using this procedure, the median high (95%) and low (5%) confidence fragility curves can be drawn. On the high confidence curve, we can locate the fragility value of 5%; the acceleration corresponding to this fragility on the high confidence curve is the so-called high-confidence-of-low-probability-of-failure (HCLPF) capacity of the component. By characterizing the component fragility through a family of fragility curves, the analyst has expressed all his knowledge about the seismic capacity of the component along with the uncertainties. Given the same information, two analysts with similar experience and expertise would produce approximately the same fragility curves. Development of the family of fragility curves using different failure models and parameters for a large number of components in a seismic PRA is impractical if it is done as described above. Hence, a simple model for the fragility was proposed as described in the above-cited references. In the following section this fragility model is described.

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2.2.2 Detailed Fragility Model

The entire family of fragility curves for an element corresponding to a particular failure mode can be expressed in terms of the best estimate of the median ground acceleration capacity, mA , and two random variables. Thus, the ground acceleration capacity, A, is given by:

A = Am eR eU, Equation 2-1

in which eR and eU are random variables with median values of 1.0, representing, respectively, the inherent randomness about the median and the uncertainty in the median value. In this model, we assume that both eR and eU are lognormally distributed with logarithmic standard deviations, R and U, respectively. The formulation for fragility given by Eq. 2-1 and the assumption of a lognormal distribution allow easy development of the family of fragility curves that appropriately represent fragility uncertainty. For the quantification of fault trees in the plant system and accident sequence analyses, the uncertainty in fragility needs to be expressed in a range of conditional failure probabilities for a given ground acceleration. This is achieved as explained below.

With perfect knowledge of the failure mode and parameters describing the ground acceleration capacity (i.e., only accounting for the random variability, R), the conditional probability of failure, of , for a given peak ground acceleration level, a, is given by:

=R

mo

Aaln

f Equation 2-2

where [.] is the standard Gaussian cumulative distribution of the term in brackets. The relationship between of and a is the median fragility curve plotted in Figure 2-4 for a component with a median ground acceleration capacity mA = 0.87g and R = 0.25. For the median conditional probability of failure range of 5% to 95%, (- and + 1.65 log standard deviations from the mean) the ground acceleration capacity would range from mA exp (-1.65 R ) to mA exp (1.65 R ), i.e., 0.58g to 1.31g as shown in Figure 2-4.

When the modeling uncertainty U is included, the fragility becomes a random variable (uncertain). At each acceleration value, the fragility f can be represented by a subjective probability density function. The subjective probability, Q (also known as confidence) of not exceeding a fragility f is related to f by:



( )

+

=

R

1U

m

QAaIn

f Equation 2-3

where:

Q = P[f < | a]; i.e., the subjective probability (confidence) that the conditional probability of failure, f, is less than

ff for a peak ground acceleration a.

-1[.] = the inverse of the standard Gaussian cumulative distribution of the term in brackets.

For example, the conditional probability of failure f at a peak ground acceleration of 0.6g that has a 95% nonexceedance subjective probability (confidence) is obtained from Eq. 2-3 as 0.79 as shown in Figure 2-4 on the 95% confidence curve. The 5% to 95% probability (confidence) interval on the failure at 0.6g is 0 to 0.79. Computations in the seismic PRA are usually made by discretizing the random variable probability of failure f into different intervals and deriving probability qi for each interval (Figure 2-5). Note that the sum of over all the intervals is unity. The process develops a family of fragility curves, each with an associated probability q

(Figure 2-5).

iqi

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0.95

1.31

Figure 2-4 Mean, Median, 5% Non-Exceedance, and 95% Non-Exceedance Fragility Curves for a Component

A mean fragility curve is also plotted in Figure 2-4. This is obtained using Eq. 2-2 but replacing R with the composite variability C = (R2 + U2)1/2. In the IPEEE program, only a point estimate (mean value) of CDF was required, thus single mean fragility curves and the mean seismic hazard curve were convolved to calculate the unconditional probability of failure of SSCs.

The median ground acceleration capacity Am, and its variability estimates R and U are evaluated

by taking into account the safety margins inherent in capacity predictions, response analysis, and equipment qualification, as explained below.

2-15



1.0

0.8

0.6

0.4

0.2

0

0 0.4 0.8 1.2 1.6 2.0

Peak Ground Acceleration, g

q1 q2 q3 q4 q5

SSE

Figure 2-5 Discrete Family of Fragility Curves for a Component

2.2.2 Failure Modes The first step in generating fragility curves such as those in Figure 2-4 is to develop a clear definition of what constitutes failure for each of the critical elements in the plant. This definition of failure must be agreeable to both the structural analyst generating the fragility curves and the systems analyst who must judge the consequences of component failure. Several modes of failure (each with a different consequence) may have to be considered and fragility curves may have to be generated for each of these modes. For example, a motor-actuated valve may fail in any of the following ways: Failure of power or controls to the valve (typically related to the seismic capacity of such

items as cable trays, control panels, and emergency power). Since these failure modes are not related to the specific item of equipment (i.e., motor actuated valve) and are common to all active equipment, such failure modes are most easily handled as failures of separate systems linked in a series to the equipment.

Failure of the motor. Binding of the valve stem due to distortion and, thus, failure to operate. Failure of the pressure boundary due to overstress of the flange joint.

2-16



It is usually possible to identify the failure mode most likely to be caused by the seismic event by observations during the walkdown or by reviewing the equipment design. If there is clearly a dominant weak link, then only the one failure mode for the weak link is considered. If two or more failure modes have approximately equal capacity, and the failure modes are uncorrelated, then fragility curves are developed for each failure mode based on the premise that the component could fail in any one of the approximately equal capacity potential failure modes.

Identification of the credible modes of failure is largely based on the analysts experience and judgment. Review of plant design criteria, calculated stress levels in relation to the allowable limits, qualification test results, seismic fragility evaluation studies done on other plants, and reported failures (in past earthquakes, in licensee event reports and fragility tests) are useful in this task.

Structures are considered to have failed functionally when they cannot perform their designated functions. In general, structures are considered to have failed functionally when inelastic deformations under seismic load are estimated to be sufficient to potentially interfere with the operability of safety-related equipment attached to the structure, or fractured sufficiently so that equipment attachments fail. These failure modes represent a conservative lower bound of seismic capacity since a larger margin of safety against total collapse exists for nuclear structures. Also, a structural failure is generally assumed to result in a common cause failure of multiple safety systems, if these safety systems are housed in the same structure. For example, the service water pumps may be assumed to fail when the enclosure pump house roof collapses. Structures that are susceptible to sliding are considered to have failed when sufficient sliding deformation has occurred to fail buried or interconnecting piping or electrical duct banks.

For piping, failure of the support system or low cycle fatigue failure of the pressure boundary are credible failure modes. Failure modes of equipment examined may include structu

seismic fragility application guide 2002 tr 1002988

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