Seismic Fragility Application Guide
SED R I A L
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WARNING: Please read the Export Control Agreement on the back cover.
Technical Report
Seismic Fragility Application Guide 1002988
Final Report, December 2002
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 •
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CITATIONS This report was prepared by ABSG Consulting Inc. 300 Commerce Drive, Suite 200 Irvine, CA 92602 Principal Investigators R. Campbell G. Hardy K. Merz 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 riskinformed/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 standard’s 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 study’s 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 nonregulatory 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 standard’s 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 TR103959 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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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 NRC’s principal issue in IPEEE was that the screening level was too low and representation of screened out elements by vii
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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 ANS BWR CDF CDFM CUS DBE EUS FOAKE FPS GERS GIP GMI HCLPF HFD IPEEE IRS LERF LLNL NEP NPP PGA PSA PSHA PSV PWR RAI RE RLE RRS SA SD SDOF SMA SPRA SPSA SQRT SQURTS SSCs
Amplified Floor Response Spectra American Nuclear Society Boiling Water Reactor Core Damage Frequency Conservative Deterministic Failure Margin Central United States Design Basis Earthquake Eastern United States First of a Kind Reactor Engineering Feet per Second Generic Equipment Ruggedness Spectra Generic Implementation Procedure Ground Motion Incoherence High Confidence of Low Probability of Failure. High Frequency Ductility Individual Plant Examination of External Events In-Structure Response Spectra Large Early Release Frequency Lawrence Livermore National Laboratories Non-Exceedance Probability Nuclear Power Plant Peak Ground Acceleration Pseudo Spectral Acceleration Probabilistic Seismic Hazard Analysis Pseudo Spectral Velocity Pressurized Water Reactor Request for Additional Information Reference Earthquake Spectrum from Probabilistic Hazard Study Review Level Earthquake Required Response Spectrum Spectral Acceleration Spectral Displacement Single Degree of Freedom Seismic Margin Assessment Seismic Probabilistic Risk Assessment Seismic Probabilistic Safety Assessment Seismic Qualification Review Team Seismic Qualification Reporting and Testing Standardization Structures, Systems and Components ix
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SSE SSI SSMRP Standard TER TRS UHS ZPA ZPGA
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Safe Shutdown Earthquake Soil-Structure Interaction Seismic Safety Margin Research Program ANS 58.21 External Events PRA Methodology Standard Technical Evaluation Report Test Response Spectrum Uniform Hazard Spectra Zero Period Acceleration Zero Period Ground Acceleration
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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 Analyst’s 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. th th th Spectra shown for three percentiles: 15 , 50 , and 85 ....................................................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 Table 5-1 Index To Example Fragility Calculations....................................................................5-2 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. 1-1
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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 1970’s. 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 -7 core damage for an average site was reported to be 5x10 . 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 1980’s using the “Zion Method” methodology (Indian Point, Limerick, Susquehanna, Seabrook, Milestone 3, Oconee, Browns Ferry).
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EPRI Proprietary Licensed Material 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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EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries
1A
Region Specific Seismicit y
i
• EQHAZARD • SEISRISK III • HAZARD
Seismic Motion Parameter
Plant Specific Unavailabilit y
2B
SOFTWARE Event Trees Fault Trees Containment Analysis Systems Analysis
Software • • • • • •
SMACS SAP SHAKE SASSI ANSYS ETC.
Conditional Probability of Failure
3B
P
Figure 2-1 Seismic Risk Assessment Methodology
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3
Atmospheric dispersion
2
Population Evacuation
P
i
Health effects
Release Frequency
3
Databases • • • •
Component-Fragility Evaluation
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6
5
Weather data
Release Category
Frequency
i
Seismic Motion Parameter
SEISIM SRACOR EQESRA SEISMIC SEIS
4 Probability Density
2
DATABASE
SETS RISKMAN® NUPRA CAFTA RISK SPECTRUM
• • • • •
1B
SOFTWARE
2A
• • • • •
Software
Frequency of Exceedance
Frequency of Exceedance
P
4A
DATABASE
1 Seismic Hazard Analysis
Earthquake Experience GERS Fragility Tests Analyses
Property damage
3A
Consequence Analysis
Damage Risk
EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries
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. 2-6
EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries Review Plant Safety Systems and Modify Internal Event Analysis Event and Fault Trees
Perform Response Analysis
Develop PRA Components List Including Containment Systems
Soil Failures Evaluation
Develop Floor Spectra and Structural Response Select Peer Review Team
Relay Chatter Evaluation
Perform Plant Walkdown Using EPRI Margin Procedures
Screen Out Components From PRA List
Develop Seismic Fragilities of Screened-In Components
Modify Fault Trees, Develop Sequence Equations
Seismic Risk Quantification
Seismic Hazard Curves
Develop Seismic PRA Outputs
Prepare PRA Report
Peer Review
Input to Utility Management
Seismic PRA Completed
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. 2-8
EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries
Curves are developed using the fragility model whose parameters are the median acceleration capacity (Am), and logarithmic standard deviations reflecting randomness in capacity (β R ) and uncertainty in the median capacity (β 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 nonseismic 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 2-9
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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 Hunter’s 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 2-10
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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 analyst’s 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 2-11
EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries
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-oflow-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, A m , 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, βR and βU, 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, βR), the conditional probability of failure, fo , for a given peak ground acceleration level, a, is given by:
a ln A fo = Φ m βR
Equation 2-2
where Φ [.] is the standard Gaussian cumulative distribution of the term in brackets. The relationship between fo and a is the median fragility curve plotted in Figure 2-4 for a component with a median ground acceleration capacity A m = 0.87g and β 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 A m exp (-1.65 β R ) to A m exp (1.65 β R ), i.e., 0.58g to 1.31g as shown in Figure 2-4. When the modeling uncertainty β 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:
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a +βU Φ −1(Q) In A f′ = Φ m βR
Equation 2-3
where: Q
= P[f < f′ | a]; i.e., the subjective probability (confidence) that the conditional probability of failure, f, is less than f′ for a peak ground acceleration a.
Φ-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 qi over all the intervals is unity. The process develops a family of fragility curves, each with an associated probability qi (Figure 2-5).
2-14
EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries
•
Am = 0.87 g ßR = 0.25 ßU = 0.35
1
•
0.8 95% Confidence
0.79
Median
0.95
Mean
0.6
•
0.5
0.4 5% Confidence 0.2 0.58g
•
0.05 0
0
0.2
HCLPF 0.32g
0.4
0.6
0.8 0.87
1
1.2
1.31 1.4
PEAK GROUND ACCELERATION (g)
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 2 2 1/2 βR with the composite variability βC = (βR + βU ) . 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 βR and βU are evaluated by taking into account the safety margins inherent in capacity predictions, response analysis, and equipment qualification, as explained below.
2-15
EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries 1.0
0.8
q1
0.6
q2
q3
q4
q5
0.4
0.2
0 0
0.4
0.8
1.2
1.6
2.0
SSE
Peak Ground Acceleration, g 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.
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EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries
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 analyst’s 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 structural failure modes (e.g., bending, buckling of supports, anchor bolt pullout, etc.), functional failures (binding of valve, excessive deflection in rotating equipment), and breaker trip or relay chatter. Consideration should also be given to the potential for soil failure modes (e.g., liquefaction, toe bearing pressure failure, base slab uplift, and slope failures). For buried equipment (i.e., piping and tanks), failure due to lateral soil pressures may be an important mode. Seismically induced failures of structures or equipment under impact of another structure or equipment may also be a consideration. Seismically induced failures of dams, if present, resulting in either flooding or loss-of-cooling-source, should also be investigated. 2.2.3 Estimation of Fragility Parameters In estimating fragility parameters, it is convenient to work in terms of an intermediate random variable called the factor of safety. The factor of safety, F, on ground acceleration capacity above a reference level earthquake specified for design; e.g., the safe shutdown earthquake level specified for design, ASSE, is defined as follows: A = FA SSE
where A is the actual ground motion acceleration capacity
2-17
EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries F=
Actual seismic capacity of element Actual response due to SSE
This relationship is typically expanded to identify the conservatism or factor of safety in both the strength and the response. F=
Design response due to SSE Actual capacity X Design response due to SSE Acctual response due to RE
F = F F C SR
Equation 2-4
where FC is the capacity factor, FSR is the structural response factor and RE is the reference earthquake spectrum derived from the probabilistic hazard study, anchored to the same pga as the SSE. Note that F can also be defined with reference to a different earthquake such as the operating basis earthquake (OBE) level. However, the fragility analyst must be sure that the realistic failure mode at high acceleration is the same as would be identified by comparing OBE response to OBE allowable stresses. The median factor of safety, Fm, can be directly related to the median ground acceleration capacity, Am, as: Fm =
Am A
Equation 2-5
SSE
The logarithmic standard deviations of F, representing inherent randomness and uncertainty, are identical to those for the ground acceleration capacity A.
2.2.3.1 Fragility of Structures For structures, the factor of safety is typically modeled as the product of three random variables: F = FS FµFSR
Equation 2-6
The strength factor, FS , represents the ratio of ultimate strength (or strength at loss-of-function) to the stress calculated for A SSE . In calculating the value of FS , the nonseismic portion of the total load acting on the structure is subtracted from the strength as follows: S - PN F = S P -P T N
Equation 2-7
where S is the strength of the structural element for the specific failure mode, PN is the normal operating load (i.e., dead load, operating temperature load, etc.) and PT is the total load on the 2-18
EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries
structure (i.e., sum of the seismic load for A SSE and the normal operating load). For higher earthquake levels, other transients (e.g., SRV discharge in BWRs) may have a high probability of occurring simultaneously with the earthquake. The definition of PN in such cases should be extended to include the loads from these transients. The inelastic energy absorption factor (ductility factor), Fµ , accounts for the fact that an earthquake represents a limited energy source and many structures or equipment items are capable of absorbing substantial amounts of energy beyond yield without loss-of-function. A suggested method to determine the deamplification effect resulting from inelastic energy dissipation involves the use of ductility modified response spectra (Newmark, 1977). The deamplification factor is primarily a function of the ductility ratio µ defined as the ratio of maximum displacement to displacement at yield. Riddell and Newmark (1979) have shown the deamplification factor to also be a function of system damping and the slope of the force deflections curve. EPRI (1994) expands the derivation of a ductility factor, considering the shape of the hysterisis loop and duration of the earthquake. Chapter 3 of EPRI (1994) provides two methods for developing inelastic energy absorption factors. One method is an effective frequency/effective damping method and the other method is a modification to the RiddellNewmark method. The effective frequency/effective damping method takes into account the shape of the force-deflection hysterisis loop and the shift in frequency of the structure as it is stressed beyond the elastic limit. The effective Riddell-Newmark method is a modification to the original formulations for the durations of the earthquake ground motion. It is recommended that the average of the two methods be used as a median estimate of the inelastic energy absorption factor. For an example, refer to Section 6 in EPRI (1994) for the derivation of a fragility for a low-rise concrete shear walls (typical of auxiliary building walls). A system ductility, µ = 4.0, corresponds to a median ductility factor Fµ, of 2.45 at 7% damping. The variabilities in the ductility factor, Fµ , are both estimated for this case as βR = 0.21 and
βU = 0.21, taking into account the uncertainty in the predicted relationship between Fµ , µ, system damping, and the sensitivity of the inelastic deformation to the actual earthquake time history. The structure response factor, FSR is based on recognition that in the design analyses, structural response was computed using specific (often conservative) deterministic response parameters for the structure. Because many of these parameters are random (often with wide variability) the actual response may differ substantially from the calculated response for a given peak ground acceleration. The structure response factor, FSR , is modeled as a product of factors influencing the response variability: FSR = FSA FGMI Fδ FM FMC FEC FSSI
Equation 2-8
where:
2-19
EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries FSA
= spectral shape factor representing the difference and variability in response due to the difference between the SSE spectrum and the RE spectrum defined by the hazard analyst.
FGMI
= ground motion incoherence factor that accounts for the fact that a traveling seismic wave does not excite a large foundation uniformly.
Fδ
= damping factor representing variability in response due to difference between actual damping and design damping.
FM
= modeling factor accounting for any bias and uncertainty in response due to modeling assumptions.
FMC = mode combination factor accounting for any bias and variability in response due to the method used in combining dynamic modes of response. FEC = earthquake component combination factor accounting for any bias and variability in response due to the method used in combining earthquake components. FSSI = factor to account for effect of soil-structure interaction including the reduction of input motion with depth below the surface. The median and logarithmic standard deviations of F are expressed as:
Fm = FSm Fµm FSAm FGMIm Fδm FMm FMCm FECm FSSIm
Equation 2-9
and
(
βF = β s + β µ + β SA + β GMI + ⋅ ⋅ ⋅ + β SSI 2
2
2
2
)
2 1/ 2
Equation 2-10
The logarithmic standard deviation βF is further divided into random variability, βR , and uncertainty, βU . To obtain the median ground acceleration capacity A m the median factor of safety, Fm , is multiplied by the safe shutdown earthquake peak ground acceleration.
2.2.3.2 Fragility of Equipment and Other Components For equipment and other components, the factor of safety is composed of a capacity factor, FC ; a structure response factor, FSR ; and an equipment response (relative to the structure) factor, FRE Thus,
FE = FCFREFRS
2-20
Equation 2-11
EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries
The capacity factor FC for the equipment is the ratio of the acceleration level at which the equipment ceases to perform its intended function to the seismic design level. This acceleration level could correspond to a breaker tripping in a switchgear, excessive deflection of the control rod drive tubes, or failure of an equipment support. The capacity factor for the equipment may be calculated as the product of FS and Fµ . The strength factor, FS , is calculated using Eq. (2-7). The strength, S, of equipment is a function of the failure mode. Equipment failures can be classified into three categories:
•
Elastic functional failures.
•
Brittle failures.
•
Ductile failures.
Elastic functional failures involve the loss of intended function while the component is stressed below the yield point of its structural elements. Examples of this type of failure include the following:
•
Elastic buckling in tank walls and component supports.
•
Excessive blade deflection in fans.
The load level at which functional failure occurs is considered the strength of the component. Brittle failure modes are those that have little or no system inelastic energy absorption capability. Examples include the following:
•
Anchor bolt failures.
•
Component support weld failures.
•
Shear pin failures.
Each of these failure modes has the ability to absorb some inelastic energy on the component level, but the plastic zone is very localized and the system ductility for an anchor bolt or a support weld is very small. The strength of the component failing in a brittle mode is therefore calculated using the ultimate strength of the material. Ductile failure modes are those in which the structural system can absorb a significant amount of energy through inelastic deformation. Examples include the following:
•
Pressure boundary failure of piping or vessel nozzles.
•
Structural failure of cable trays and ducting.
•
Failure of component support members (plastic bending, plastic buckling).
The strength of the component failing in a ductile mode is calculated using the effective yield strength of the material for tensile loading. For flexural loading, the strength is defined as the limit load or load to develop a hinge mechanism.
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EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries
The inelastic energy absorption factor, Fµ , for a piece of equipment is a function of the ductility ratio, µ. The median value of Fµ is considered to be 1.0 for brittle and functional failure modes. For ductile failure modes of equipment that respond in the amplified acceleration region of the design spectrum, the inelastic energy absorption factor may be calculated in a manner similar to structures (refer to Section 2.2.3.1 for a description of the derivations of inelastic energy absorption factors). The equipment response factor FRE , is the ratio of equipment response calculated in the design to the realistic equipment response; both responses being calculated for design floor spectra. FRE is the factor of safety inherent in the computation of equipment response. It depends upon the response characteristics of the equipment and is influenced by some of the variables listed under Eq. (2-8). These variables differ according to the seismic qualification procedure. For equipment qualified by analysis, the important variables that influence response and variability are as follows:
•
Qualification method (QM) dynamic analysis vs static coefficient used, etc.
•
Spectral shape (SA) - including the effects of peak broadening and smoothing, and artificial time history generation.
•
Modeling (affects of mode shape and frequency results) (M).
•
Damping (affects of design damping vs. median damping) (δ).
•
Combination of modal responses (for response spectrum method) (MC).
•
Combination of earthquake components (ECC).
For rigid equipment qualified by static analysis, the variables, except the qualification method, and combination of earthquake components are not significant. The equipment response factor is the ratio of the specified static coefficient divided by the zero period acceleration of the floor level where the equipment is mounted. If the equipment is flexible and was designed via the static coefficient method, the dynamic characteristics of the equipment must be considered. This requires estimating the fundamental frequency and damping, if the equipment responds predominantly in one mode. The equipment qualification method factor is the ratio of the static coefficient to the best estimate spectral acceleration at the equipment fundamental frequency. Where testing is conducted for seismic qualification, the response and capacity may be determined from specific criteria contained in Chapter 3 of EPRI (1994), pp. 3-57 to 3-71. The overall equipment response factor is the product of these factors of safety corresponding to each of the variables identified above. The median and logarithmic standard deviations for randomness and uncertainty are estimated following Eqs. (2-9) and (2-10). The structural response factor, FSR , is based on the response characteristics of the structure at the location of the component (equipment) support. The variables pertinent to the structural response analyses used to generate floor spectra for equipment design are the only variables of interest to equipment fragility. Time-history analyses using the same structural models used to
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EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries
conduct structural response analysis for structural design are typically used to generate floor spectra. The applicable variables are as follows:
•
Spectral shape.
•
Ground motion incoherence.
•
Damping.
•
Modeling.
•
Mode combination (if mode superposition time history is used).
•
Soil-structure interaction including reduction with depth of seismic input.
For equipment with a seismic capacity level that has been reached while the structure is still within the elastic range, the structural response factors should be calculated using damping values corresponding to less than yield conditions (e.g., about 5% median damping for reinforced concrete). The combination of earthquake components is not included in the structural response since the variable is to be addressed for specific equipment orientation in the treatment of equipment response. Median Fm and variability βR and βU estimates are made for each of the parameters affecting capacity and response factors of safety. These median and variability estimates are then combined using the properties of lognormal distribution in accordance with Equations (2-9) and (2-10) to obtain the overall median factor of safety Fm and variability βR and βU estimates required to define the fragility curves for the structure or equipment. For each variable affecting the factor of safety, the random ( βR ) and uncertainty ( βU ) variabilities must be separately estimated. The differentiation is somewhat judgmental, but it can be based on general guidelines. Essentially, βR represents variability due to the randomness of the earthquake characteristics for the same peak acceleration and to the structural response parameters that relate to these characteristics. The dispersion represented by βU is due to factors such as the following:
•
Our lack of understanding of structural material properties such as strength, inelastic energy absorption, and damping.
•
Errors in calculated response due to use of approximate modeling of the structure and inaccuracies in mass and stiffness representations.
•
Usage of engineering judgment in lieu of complete plant-specific design data for equipment code capacities, and responses.
2.2.4 Information Sources Fragility evaluation utilizes data from various sources – plant specific and generic. Plant specific information would be design analysis and qualification test data. Generic information consists of earthquake experience data (EPRI 1998), (SEQUAL, 2001), and test data for relays (EPRI 1991a, EPRI 1996) and for non-relays devices (EPRI, 1991c, 1999). Fragility parameter values derived for several components in the past seismic probabilistic risk assessments have been compiled in Campbell et al. (1988).
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EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries
Several sources of information are utilized in developing plant-specific and generic fragilities for equipment. These sources include the following:
•
Seismic design calculations.
•
Seismic evaluation results from the USI A-46 resolution or IPEEE program.
•
Plant safety analysis reports.
•
Plant specific seismic qualification test data.
•
Generic equipment ruggedness data (GERS), (EPRI, 1991a, 1991c, 1995, 1998).
•
Past earthquake experience (EPRI 1998, SEQUAL 2001).
In seismic margin studies such as those conducted for many US NPPs in IPEEE, an index of seismic margin is the HCLPF capacity of the component. This quantity considers both the uncertainty and randomness variabilities and is the acceleration value for which the analyst has 95% confidence that the failure probability is less than 5%. For example, Figure 2-4 shows a HCLPF of 0.32g for a fragility description of A m = 0.87g, βR = 0.25, βU = 0.35 . That is, it is an acceleration value for the component for which we are highly confident there is only a small chance of failure given this ground acceleration level: HCLPF Capacity = A m exp {- 1.65 (βR + βU )}
Equation 2-12
For some applications, a point estimate (mean value) of core damage is considered adequate. Uncertainty analysis is not performed. In developing a point estimate of CDF, a composite fragility curve is commonly used that incorporates randomness and uncertainty into a single curve. The composite fragility curve is defined by two parameters A m and β C where A m is the median capacity as previously described and β C is the composite variability. Refer to Figure 2-4 as an example. The HCLPF capacity is then approximately defined as: a 1% conditional probability of failure (-2.33 log standard deviation below the mean). HCLPF Capacity = A m exp (−2.33βC )
Equation 2-13
2.2.5 Other Fragility Models The lognormal model for fragility has been used in most seismic PSAs conducted to date. Material strength data tends to follow a lognormal distribution whereas data on the pullout capacity of expansion anchors tends to be normally distributed. The lognormal model is mathematically easy to use and can be partly justified by the Central Limit Theorem which states that the distribution of a product of several variables tends to be log-normal regardless of the distribution of the individual variables. Ellingwood (1994) and Reed and Kennedy (EPRI, 1994) have also arrived at similar conclusions. However, there have been some attempts to use other probability models to describe the fragility of components. As a sensitivity study, Ravindra et. al., (1984) explored the use of Weibull distribution for seismic fragility. Note that the Weibull 2-24
EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries
distribution has two parameters that can be derived from the mean and standard deviation of the variable. It was concluded from this study that a Weibull model gives unrealistically high fragilities in the lower tail. The basic information needed is still the mean and standard deviation (equivalently, median, and βR and βU). There is not much empirical and analytical data available to justify use of probability models requiring more than two parameters. 2.2.6 Hybrid Method The fragility methodology of estimating the median and βR and βU described in this report is universally applicable. It does however require the median factors of safety for different variables affecting the response and capacity be estimated as well as their logarithmic standard deviations. In the U.S. nuclear industry, seismic margin assessments have been done for a number of nuclear power plants. Seismic margin is defined as the HCLPF capacity of the plant safe shutdown systems relative to the design basis or safe shutdown earthquake (DBE or SSE). The HCLPF capacity of the weakest link component in the safe shutdown path is considered the plant level HCLPF capacity. The HCLPF capacities of components are calculated using a deterministic procedure called “Conservative Deterministic Failure Margin (CDFM)” method. EPRI (1991) describes the CDFM method and provides several examples. In order to simplify the seismic PRA, a hybrid method is suggested in EPRI (1994) and Kennedy (1999). The main feature of this method is the development of seismic fragility using the HCLPF capacity. First, the HCLPF capacity of the component is determined using the CDFM method. Next, the logarithmic standard deviation, β C , is estimated using judgement and the following guidance, (Kennedy, 1999). For structures and major passive mechanical components mounted on ground or at low elevations within structures, β C typically ranges from 0.3 to 0.5. For active components mounted at high elevations in structures the typical β C range is 0.4 to 0.6. When in doubt, use of β C of 0.4 is recommended as a conservative estimate (higher β C results in a larger ratio of median to HCLPF). The median capacity is calculated using Eq. 2-13 and an approximate fragility curve for the component is thereby obtained. EPRI (1994) further recommends that this approximate fragility method initially be used for each component in the systems analysis to identify the dominant contributors to the seismic risk (e.g., core damage frequency). For the few components that dominate the seismic risk, more accurate fragility parameter values should be developed and a new quantification done to obtain a more accurate mean core damage frequency and to confirm that the dominant contributors have not changed. The CDFM method, though in concept is universally applicable, has been derived following the seismic design and qualification practices of the U.S. nuclear industry. The parameters and implied safety factors in the CDFM procedures should be appropriately modified for use in other countries reflecting the differences in design practices. The same caveat would apply to the use of generic β C values. These generic values have been arrived at using the results and insights of a number of seismic PSAs involving thousands of fragility calculations. Judgment should therefore be exercised in their use for new applications in countries outside the U.S.
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EPRI Proprietary Licensed Material State of the Art and Practice of Seismic PRA in the U.S. and Other Countries
2.3
Plant Level Fragility
It is sometimes useful to develop the plant level fragility curves. They depict the conditional probability of seismic core damage (or other damage indicators such as large early release) for different levels of ground motion input. The plant level fragility curves can be generated by quantifying the accident sequences consisting of component successes and failures. By entering the plant level fragility curves corresponding to 95% confidence at 5% conditional probability of failure, the plant HCLPF capacity can be obtained. In this case the plant HCLPF capacity is determined from the detailed modeling of the plant systems responses for an earthquake. In seismic margins assessments, the plant HCLPF capacity is assumed to be the HCLPF capacity of the weakest component in the highest capacity safe shutdown path. This is a weakest link in a chain methodology rather than a logic tree evaluation of the plant systems and components response to a seismic event. If the plant safe shutdown system capacity is dominated by a single weak link, the plant HCLPF capacities will be very similar in both cases. However, if multiple component failures all contribute to failure of the safe shutdown path(s), the results of the two methods of defining plant HCLPF capacity may differ by a significant amount.
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EPRI Proprietary Licensed Material
3 FRAGILITY METHODOLOGY ISSUES AND ENHANCEMENTS
Over the last decade, a number of issues have been raised and enhancements have taken place with regard to seismic fragility methodology. These issues and enhancements eminate principally from 3 areas: 1. The NRC comments/recommendations based on their review of SPRA submittals as part of the IPEEE program. These comments and recommendations were primarily focused on methodological areas that needed to be addressed or upgraded for SPRAs beyond IPEEE where licensees will be submitting Risk Informed Performance Based (RI/PB) applications. 2. Methodological Improvements to the fragility analysis process. 3. Publication of new data that is useful to the calculation of seismic capacity level in support of the fragility analysis. Each of these 3 enhancement areas is discussed in detail in this section.
3.1
Methodological Issues from USNRC Review of IPEEE Submittals
The United States Nuclear Regulatory Commission published a comprehensive report on their review of IPEEE submittals, (USNRC, 2000). The review primarily focused on the extent to which the licensees’ IPEEE submittal had achieved the intent of Generic Letter 88-20, Supplement 4 (USNRC, 1991a), had satisfied the IPEEE objectives and had followed the guidance of NUREG-1407 (USNRC 1991b). The reviews focused on verifying that the critical elements of acceptable IPEEE analyses were performed in accordance with the guidance in NUREG-1407. The reviews were not intended to validate or verify the licensee’s IPEEE analyses or results. Rather, methods, approaches, assumptions and results were reviewed for reasonableness. If inconsistencies were found they were reported in the plant-specific Technical Evaluation Reports, TERs. During the review process there were Requests for Additional Information, RAIs, to clarify or enhance portions of the submittals. Licensees were provided the option of conducting a Seismic PRA or a Seismic Margins Assessment. There were a total of 75 licensee submittals covering 108 operating units. Seismic PRA was conducted in 28 of the submittals covering 41 units. Methodological issues cited by NRC that are addressed in this report are focused on the issues related to Seismic PRA. The NRC staff concluded that in general, the licensees had achieved the goals of IPEEE but noted that varying degrees of detail and methodology had been used and that some of these 3-1
EPRI Proprietary Licensed Material Fragility Methodology Issues and Enhancements
methodology issues appeared to have a significant influence on the results obtained. The five major issues identified in the NRC review of seismic submittals are not all specific to the development of fragilities but are interrelated so are addressed in this report as they relate to development of fragilities. 3.1.1 Use of Uniform Hazard Spectrum USNRC Comment: “The uniform hazards spectra (UHS) shapes, as employed by the licensees of some plants in the eastern U.S. (EUS), for component fragility calculations appear uncharacteristic of conventional spectrum shapes derived from observed earthquakes. These UHS appear to have substantially reduced energy content, compared to the respective design basis SSE spectra, in the frequency range that is typically considered to have the greatest impact on the SSC responses to seismic motions. As a result, the seismic analyses using the UHS as input resulted in significant reductions (50% to 70%) in seismic demand, compared to the corresponding design-basis calculations. Furthermore, since there was no consistent guidance provided for anchoring the UHS to the zero peak ground acceleration (ZPGA), the licensees applied their engineering judgment for the anchorage of the UHS.” Discussion of Comment: While the fragility analyst is provided the seismic hazard and associated spectral shape, he must be aware of the characteristics of the site hazard and may have some technical input to the hazard analyst regarding the frequencies at which spectral ordinates are desired and whether the fragilities will be referenced to spectral acceleration in a stated frequency range or be referenced to ZPGA (pga). Reference to spectral acceleration in a frequency range of the plant structures is generally preferred in order to minimize the uncertainty between pga and spectral acceleration. ANS Standards 2.29 and 2.27 (ANS, 1997 and ANS, 2000), currently in draft form, are to be the governing documents on the development of the site-specific probabilistic seismic hazard. The ANS 58.21 External Events PRA Methodology Standard provides requirements for development of UHS for Capability Categories 1, 2 and 3. For Capability Category 2, fractile and mean ZPGA and fractile and mean UHS are required. For Capability Category 3, magnitude and distance deaggregation and seismic source deaggregation are required. The deaggregation process is described in RG 1.165 (USNRC, 1997). Existing hazard studies such as the LLNL and EPRI hazard studies used in the IPEEE evaluations would correspond to Capability Category 2. When using the LLNL and/or EPRI hazard studies, or another study done to a comparable technical level, the intent of this requirement is not to repeat the entire hazard exercise or calculations, unless compelling new site specific information and interpretations have been established in the technical literature that affect the usefulness of the seismic PRA for the intended application. ANS 58.21 high level requirement HA-G1 requires that the UHS reflects or bounds the sitespecific considerations. For Capability Category 3, the response spectrum shape used in the SPRA should be based on site-specific evaluations performed for the Probabilistic Seismic Hazard Analysis (PSHA), and reflect or bound the characteristics of spectral shapes associated with the mean magnitude and distance pairs determined in the PSHA for the important ground motion levels.
3-2
EPRI Proprietary Licensed Material Fragility Methodology Issues and Enhancements
The UHS, as used in IPEEE, are a broad banded shape that is not characteristic of a single earthquake. The ZPGA hazard may be dominated by a close in short duration high frequency earthquake whereas the low frequency range, typical of design type earthquakes, may be dominated by a larger magnitude distant earthquake characterized by a lower ZPGA. Consequently, most of the analyses conducted where the structural response was dominated by low frequency input motion, should be conservative relative to the ZPGA associated with the UHS. If deaggregation is conducted using guidelines in RG 1.165, two separate spectral shapes might be developed; one that is based on sources, magnitudes and distances that produce peak amplification in the 1-2 ½ Hz range and one where peak amplification occurs in the 5-10 Hz range. These two spectral shapes defined for a specific return period will have separate ZPGAs associated with the same return period. In essence, there are two different earthquakes to consider. Capability Category 3 requires that probabilistic response be conducted, which would have to take into account the deaggregation. Further guidance is provided in Chapter 4 on probabilistic response. The NRC comment on lack of energy in the UHS low frequency range will inherently be addressed if the hazard is defined as required in ANS 58.21. For Capability Category 1 and 2, the UHS will be conservative if the fragility is anchored to the ZPGA. If the hazard is carried out to low enough frequencies for each of the points on the UHS, the fragility can be anchored to a spectral acceleration in the frequency range of the host structure. If the fragilities are anchored to spectral acceleration, the risk analysis will be much more accurate and will reflect the correct spectral shape for the dominant frequency, range, since the frequency of occurrence of that range will be dominated by earthquakes that produce spectral accelerations in that range. 3.1.2 Use of Surrogate Elements in SPRAs USNRC Comment: “The basis and approach for surrogate element modeling are discussed in EPRI TR-103959 (EPRI, 1994). The overall concept of a surrogate element is to account quantitatively (albeit approximately) for the risk contribution of components that are screened out during the walkdown and screening phase of an SPRA. Hence, the failure of a single surrogate element represents the potential failures of several components that might normally be excluded from the SPRA model. Use of the surrogate element helps to assure that the SPRA does not overlook a potentially significant portion of the seismic CDF. Use of a surrogate element represents acceptable SPRA practice when (1) screening is performed at a sufficiently high threshold, (2) the capacity of the surrogate element is appropriately assessed to be consistent with the screening threshold and (3) the surrogate element is appropriately included in the seismic plant logic model. Otherwise, the usefulness and validity of SPRA findings may be compromised.” If the surrogate element is used to represent a low screening threshold, resulting in relatively few components having lower capacity than the surrogate element, dominant risk contributors can be masked, and the ranking of dominant sequences may be misleading. If the surrogate element is applied to represent a reasonably high screening threshold, but is not used appropriately in the seismic plant logic model, then a fraction of the seismic CDF may be missed in quantification. Such undesirable cases are more related to pitfalls associated with proper application of the surrogate element, rather than flaws in the conceptual basis for the surrogate element itself.
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EPRI Proprietary Licensed Material Fragility Methodology Issues and Enhancements
Therefore, the use and implications of the findings and perspectives derived from some of the SPRA IPEEEs that have applied the surrogate element approach need to be treated carefully. To date, an adequately detailed investigation of the implications of using the surrogate elements in IPEEEs has not been undertaken. No regulatory guidelines have been developed concerning its use (particularly with respect to sensitivities in plant logic modeling). However, in most circumstances, if failure of the surrogate element is modeled as leading to core damage and if the surrogate element is found to be only a minor contributor to seismic CDF, then its use is probably reasonable.” Discussion of Comment: In IPEEE, surrogate elements have been inconsistently applied or not applied at all for screened out components. In several cases, the screening level was too low and the surrogate element or elements comprised a significant amount of the computed CDF. The Standard (ANS 2002) does not use the terminology “surrogate element.” It refers to grouping of elements into a “super element.” In internal event PRA, the analyst selects a screening level or -8 -5 cutset frequency (e.g., 10 per year). After calculating the CDF (e.g., 10 per year), he will confirm that the screening did not have any significant impact by recalculating the CDF with the -9 cutset frequency screening set at 10 per year. When he reports the CDF, he may not add a fraction to represent the unaccounted contribution from the screened cutsets. The methods available to screen components for seismic capacity generally cannot assure failure rates as low -8 as 10 or so per year, thus, the concept of using surrogate elements to account for risk from components meeting achievable screening guidelines was conceived. The goal is to screen at high enough levels such that the risk contribution from screened out elements is low. There should be an initial interface between the systems analyst and the fragility analyst to assess the potential impact of various screening levels. There are various methodologies to screen, as discussed below that arrive at different surrogate fragilities capacity levels, thus different failure rates. A single surrogate fragility should not be used unless it represents the lowest capacity of screened out components and is shown to have very low contribution to the computed CDF. Depending upon the level of documentation available, several levels of screening can be conducted and associated generic or surrogate fragilities developed. Examples are: 1. Screen based on walkdown screening levels In EPRI NP-6041 (EPRI, 1991). This is the most common screening level but the lower level of screen at 0.8g spectral acceleration is often too low of a level to result in insignificant contribution to CDF when the surrogate elements are added to the plant model. 2. Conduct generic fragility calculations based on the inherent margin in the design basis. Often, because of excess conservatism in the design criteria used to qualify components, a fairly high screening level can be developed, subject of course to a walkdown confirmation of proper installation and absence of systems intersections. This method is applicable to both qualification by analysis and qualification by test. 3. Conduct reviews of design calculations or qualification test levels to determine a minimum design margin or qualification test margin that will correspond to a screening fragility level that is selected to result in minimal contribution to CDF. Many plants have Seismic Qualification Review Team (SQRT) forms available for all safety class equipment. These 3-4
EPRI Proprietary Licensed Material Fragility Methodology Issues and Enhancements
SQRT forms summarize the seismic qualification level and it is efficient to examine these summaries and screen out many components with a predetermined margin above the minimum qualification level. For A-46 plants, the results of anchorage calculations and outlier evaluations are readily available and can be quickly reviewed to determine which components can be screened at some target threshold and assigned a surrogate fragility represented by the screening level. The above considerations for developing surrogate fragilities could result in several generic fragility levels that represent different classes of equipment or even the same class in a different building or floor elevation. A single surrogate fragility that is the lower bound of all components screened out should not be used unless it is predetermined that a fragility based on the lowest level of screening, when convolved with the seismic hazard, will result in a very low unconditional probability of failure. The modeling of screened out components into the event tree-fault tree logic models is beyond the scope of this Fragility Applications Guide but the fragility analyst and systems analyst should mutually have an understanding of how the surrogate fragilities are to be used. Use of a single surrogate element or even one in each fault tree whose top event terminates at a branch on an event tree, to represent hundreds of screened out components that would normally be modeled as basic events in each fault tree, is conceptually non-conservative unless the capacity of the surrogate element is sufficiently high to result in very low unconditional probability of failure. 3.1.3 The Use of New Soil Structure Interaction Analysis Versus the Use of Scaling NRC Comment: “Two approaches were used in the IPEEE for developing the RLE in-structure response spectra (IRS). The first approach is associated with scaling the existing design-basis SSE IRS to the RLE IRS, following procedures outlined in EPRI NP-6041. While this approach was applied mostly by the plants founded on rock, which is appropriate under the guidelines given in EPRI NP-6041, it should be noted that a few plants founded on soil also performed this scaling. The application of the scaling method for structures founded on soil was often justified by the licensees by stating that: (1) the shapes of the RLE and SSE design ground spectra are relatively similar and the SSE IRS used for the scaling are broadened spectra. Therefore, if there is any shift in frequency due to the soil effect, it should be small and its effect on the scaling should be negligible, and (2) the damping applied in the scaling is much smaller than the damping associated with the radiation damping if the soil effects were considered. Therefore scaling was felt to still produce conservative RLE IRS. The second approach used in IPEEE requires the performance of a new seismic analysis, including the soil effect, or the soil-structure interaction (SSI) effect and the detailed structural modeling. This approach was utilized by the majority of plants founded on soil for the RLE IRS development. Regardless of the methods applied, it was noted that the new seismic analyses achieved substantial, across-the-board reductions in the RLE IRS compared to the SSE IRS, when the SSI effects were introduced in the seismic analysis. It was also noted that in many cases, especially for deep soil sites, the deconvolution analysis often produced much higher reduction of the free 3-5
EPRI Proprietary Licensed Material Fragility Methodology Issues and Enhancements
field motion from the ground surface to the basemat than would be permissible in the design process. When the scaling was used, the fragility/HCLPF computations inherited the conservatisms that existed in the design-basis analyses, whereas new SSI analyses usually remove as much conservatism as allowed, sometimes going well beyond what would be permissible in design practice. It was observed that for the plants using the scaling, the scaled RLE IRS is generally higher than the corresponding SSE IRS, whereas for those plants that performed new SSI analyses, the seismic analyses often resulted in much lower RLE IRS demand than the designbasis IRS. Therefore, comparison of the component seismic fragility/HCLPF values for two plants using the two different approaches could be misleading. The different approaches to estimating building and component seismic responses (scaling vs new SSI calculations) can significantly affect the magnitude of the reported fragility (or CDF) or HCLPF values. Hence, comparisons of the seismic capacities should be made mainly among plants which were analyzed using similar methods.” Discussion of Comment: The Standard, HLR FR-C1-C6, requires realistic seismic response. For Capability Categories 1 and 2, justification of scaling is required. HLR-FR-C4 would require new analysis in most cases of soil sites or sites with UHS spectral shapes significantly different than design spectra. For Capability Category 3, scaling is not acceptable and new probabilistic response is required. The requirements of the Standard and the guidance in EPRI TR-103959 and EPRI NP-6041 appear to be adequate to address this issue. Note that if spectra for a soil site are scaled up based on a damping value less than that of the soil-structure system, the scaled spectra will be evaluated conservative. The opposite is true of course if the scaling is down such as could be the case in the low frequency region of a typical EUS UHS. If scaling is used though, it could be done in a more accurate manner by scaling on a mode by mode basis rather than on a single dominant mode basis as is suggested in EPRI NP-6041. In Chapter 4 and Appendices A and B a more accurate procedure for mode by mode scaling of spectra is demonstrated. The scaling or reanalysis to develop in-structure spectra should be as realistic as possible. Intentionally conservatism should not be introduced in a SPRA. One should be cautious in the case of major structure founded on rock but with smaller structures, such as diesel generator buildings, founded on overburden. Scaling of the rock founded structure may be justified but scaling of the surface founded structure may not be very accurate. In this case, there could be inconsistencies in the development of fragilities for components in the two different structures that could possibly lead to erroneous risk ranking of components. 3.1.4 Reliance on Structures for Which the Original Design Documentation is no Longer Available NRC Comment: “Some plants identified dams designed by other agencies (Corps of Engineers, Bureau of Reclamation, etc.) as critical SSCs for providing emergency cooling water or AC power. In one case, although the dam is not under the quality assurance program and control of the licensee, it has been reviewed by the licensee and its consultants and found to be able to
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EPRI Proprietary Licensed Material Fragility Methodology Issues and Enhancements
successfully withstand the RLE without catastrophic failure. The availability of lake water to support the plant’s service water system is thus not jeopardized. In another plant, a dam failure was identified as leading to the depletion of the water supply to the Containment Cooling Service Water, which provides cooling water to the low pressure coolant injection for decay heat removal. This limited the plant’s capability to perform an orderly safe shutdown following a seismic event. However, since the dam was designed by other agencies, in this particular case, no documentation of the original design was available for review. Therefore, the seismic capacity of the dam could not be determined. This type of weak link, resulting from an SSC outside the plant boundary and not under plant control, could not be resolved and documented without coordination and consultation with the relevant agencies involved.” Discussion of Comment: This is not a common issue but has appeared in some US plants and elsewhere, such as in SPRAs in Switzerland. There is some guidance in EPRI NP-6041 (EPRI 1991) on how to calculate the deformation and slope stability of earthen dam structures. The Standard, does not address dams specifically. The general requirements are there to develop representative fragilities for all SSCs to be modeled. If dams, dykes, canals, or similar structures can have an effect on the calculated CDF, they must be included in the model and a representative fragility must be developed, or the screening guidance in EPRI NP-6041 must be used to demonstrate the stability at a screening level that has little impact on the calculated CDF. Guidance on the development of fragilities of earthen dams is not provided in EPRI (1994) or other fragility methodology documents. However, given a deterministic analysis of a dam on experienced fragility analyst with basic soil mechanics background should be able to derive a reasonable estimate of fragility. In many cases, an outside expert may be required to develop a fragility. Due to the very specialized nature of this issue, no detailed procedures or examples are presented in this report for dams or similar structures. 3.1.5 Importance of Analyst’s Expertise in Component Fragility/HCLPF Assessments NRC Comment: “While a complete detailed examination of a licensee’s component fragility/HCLPF assessments was beyond the scope of the IPEEE review, selected fragility calculations were requested from licensees for certain components that were reported in the IPEEE submittals as having unusually higher capacity than expected from past SPRA experiences. Because the major portion of input to fragility analysis is highly subjective, its quality relies heavily on past SPRA experience and the analyst’s expertise in these areas. A limited review of selected fragility calculations suggests that the analyst’s expertise in component fragility/HCLPF assessments and his (her) experience with past SPRAs could have a large impact on the quality of the component fragility calculations. Of the calculations reviewed, some were good quality fragility/HCLPF assessments, which followed very closely past SPRA practice in the nuclear industry and the individual analyst’s expertise was also reflected in the fragility estimates. There were other calculations, however, which appeared poorly prepared (i.e., lacking material documentation) and using unrealistic estimates of uncertainties. 3-7
EPRI Proprietary Licensed Material Fragility Methodology Issues and Enhancements
Because of the correlation between the analyst’s expertise and the quality of the fragility/HCLPF assessments, guidelines or criteria may be needed so that only analysts with sufficient qualifications will perform the fragility/HCLPF assessments in future SPRAs.” Discussion of Comment: All of the NRC methodology comments and observations relate to the expertise and experience of the personnel performing the systems and fragility work. EPRI and the nuclear industry has strived to develop methodology and applications documents so that the utility engineer, with some additional specific training, as was the case in the SQUG GIP Training and the Add On IPEEE Training, can perform the bulk of the necessary calculations. The SQUG GIP and EPRI NP-6041 have requirements for the personnel performing the walkdowns and the outlier and HCLPF calculations. EPRI TR-103959 does not address personnel requirements for performing fragility calculations. Unfortunately, SPRA is practiced by only a few organizations, thus few have been exposed to the methodologies of SPRA. In NUREG CR-5270 (Kennedy, et al. 1989) it was determined that there was more variability in analysts then in the fragility and CDFM methodologies. This of course is also true in standard design calculations performed to industry codes and standards. While design analysts are generally conservative by nature, errors are made that in some cases reduce the margin implied by codes and standards. Appendix F presents an example where the analyst had what appeared as obvious errors in the model and had focused on a failure node that is not representative of actual failure. The Standard does not provide any high level requirements for personnel performing the fragility work. However, a thorough peer review is required which should uncover the deficiencies noted in the NRC comments. In general, the personnel qualifications are similar to those in (SQUG, 1991) and (EPRI, 1991b). This document and the information in (EPRI, 1991b) and (EPRI, 1994) should be sufficient for experienced engineers meeting the requirements in (SQUG, 1991) and (EPRI, 1991b) to develop fragilities in a reasonably consistent manner. The purpose of this document is to enhance the existing methodology and provide more specific applications guidance on how to develop seismic fragilities that comply with the three capability categories of the Standard.
3.2
Comments and Suggestions from Industry on Methodology for SPRA
EPRI TR-103959 (EPRI 1994) provides a good overview of the Seismic PRA process and is the most complete source of information on the development of fragilities. It focuses on the classic method of developing fragilities, defined by a double lognormal distribution, using the separation of variables approach. Deviations to the use of a double lognormal distribution are discussed as is Monte Carlo and Latin Hypercube simulation as opposed to the separation of variables approach to define the distribution on response. Budnitz (1998) describes the state of the art of current methodologies for Seismic PSA (PRA). In this report, he observes that the six sub-methodologies of Seismic PSA are not equally mature and therefore the many different types of engineering insights from PSA are not all equally reliable. However, he goes on to state that, “whereas the methodology for seismic PSA suffers from certain problems, these problems are not necessarily more severe than the problems with the internal-initiators PSA methodology.” The six sub-methodologies discussed are: 3-8
EPRI Proprietary Licensed Material Fragility Methodology Issues and Enhancements
1. Seismic Hazard 2. Seismic Local Ground Motion and Building Motion 3. Walkdown Methodology 4. Failure Mode and Fragility Methodology 5. Seismic PSA Systems Analysis Methodology 6. Seismic PSA Methodology for Analyzing Plant response, Offsite Release and Consequences. It is correctly noted and known in the industry, that the largest distribution in computed seismic CDF arises from the large uncertainty in the seismic hazard. Even though the methodology is considered to be mature, reasonable experts differ in their assessments and this difference must be taken as genuine “uncertainty.” The methodology for sub methodologies 2, 3 and 4, as described in EPRI (1994) is considered to range from mature to very mature, it is pointed out that uncertainties remain for many items of equipment. This means that different analysts will produce different capacities and fragility curves. In Kennedy (1989) this was demonstrated when four experts varied by about a factor of 1.5 for many of the identical problems they were provided for purposes of calculating a fragility and for calculating a HCLPF by deterministic methods. When the same problems were given to experienced industry designers without previous background in development of fragility and HCLPFs, the variation was even larger. This relates to the NRC comment on expertise of the analysts in their review of IPEEE submittals (USNRC, 2000). It is noted in Budnitz (1998) that the use of lognormal mathematics is known to be an erroneous approach in the tails of the lognormal distributions, even when the lognormal shape adequately represents the data in the main parts of the distribution, because the data do not fit a lognormal distribution in the tails beyond a couple of log-standard deviations. Despite these limitations, the lognormal model is commonly used principally for calculational convenience. In a study by Ravindra et al. (1984) it was shown that a Weibull distribution produced unrealistic results in the lower tail of the fragility curve. As pointed out in Kennedy (1999) common practice is to cut off the tails of the lognormal distribution at the HCLPF value (-2.33 log standard deviations if the HCLPF is defined by a single lognormal curve. The risk results are more sensitive to the HCLPF value than the median value of the governing fragilities, so it is important to focus on the accuracy of the lower portion of the fragility curve. Systems modeling is not within the scope of this guide but it is pointed out in Budnitz (1998) the importance of the interface between the systems analyst and the seismic fragility analyst to help each other to focus on the issues deemed important. These interfaces also include the hazard analyst. Of particular importance is the correlation between component failure modes. The fragility analysts must advise the systems analysts of correlation between component responses and component capacities and the systems analysts must not only incorporate these correlations into the systems model as best as they can, they must conduct sensitive studies for different modeling interpretations of the correlations. It is pointed out that in some cases, where several components must fail together to result in core damage, and the correlations among them are not well understood, the differences between assuming full correlation and zero correlation can 3-9
EPRI Proprietary Licensed Material Fragility Methodology Issues and Enhancements
amount to an order of magnitude difference in calculated CDF. This is compared to plus or minus one order of magnitude or more in calculated CDF that can result from the uncertainty in the seismic hazard. Budnitz (1998) does not suggest any specific changes to the current methodology. The purpose of his report was to describe the current methodology and review the methodology to the extent to which current methodology produces reliable and useful results and insights. The conclusion is that, “despite the numerically large uncertainties, these uncertainties should generally not invalidate the key engineering insights concerning potential earthquake related vulnerabilities.” At the OECD/NEA Workshop on Seismic Risk held August 10-12, 1999, in Tokyo, Japan, a number of papers were given on seismic PSA methods and seismic ruggedness testing. The papers that contribute most to the current issues of fragility methodology are by Kennedy (1999), Ravindra (1999), Fleming (1999) and Watanabe (1999). In Kennedy (1999), suggestions are made for simplifying the seismic fragility development method and the systems analysis methodology with the objective of obtaining a point estimate of CDF. These recommendations arise from the conjecture that the uncertainty in the seismic hazard can be about two orders of magnitude wide in the 15% to 85% NEP range and that even the most sophisticated SPRA cannot predict a point estimate of the CDF to any better accuracy than a factor of five. Many of these suggested simplifications are outlined in EPRI (1994) and were used in the IPEEE program to satisfy the objective of identifying vulnerabilities rather than an objective of computing numerical values of CDF, and conducting uncertainty analyses, for comparison to internal event CDF. The main suggestion in Kennedy (1999) is to use a hybrid method, or a simplified hybrid method, for estimating CDF. The simplified hybrid method in conjunction with simplified risk modeling would not comply with the requirements of ANS (2002) thus is not discussed further. The hybrid method would correspond to Capability Category 1 in the Standard. The hybrid method follows the normal steps of a SPRA but the fragility curves are developed in a more simplified manner. It is recommended to estimate the HCLPF capacity of the components by the CDFM method used for Seismic Margin Assessments, EPRI (1991). The next step is to approximate the composite logarithmic standard deviation βC and calculate the median capacity using the CDFM HCLPF and the estimated βC . For structures or major passive components mounted on the ground or at low elevations, βC usually ranges from 0.3 to 0.5. For active components mounted high in the structures the typical βC ranges from 0.4 to 0.6. The estimate of βC depends upon the uncertainty in the spectral shape relative to the peak ground acceleration, typical uncertainties for demand and capacity calculations and the degree of inelastic energy absorption inherent in the structure or component. When in doubt, the lower values are the more conservative and should be used. The above recommendation is based on the fact that the final CDF is more sensitive to the HCLPF than to the median capacity, thus the accuracy of β is not so important. Note, however, that in the discussion of calculating HCLPF, Kennedy (1999) states that for critical components that he calculates the HCLPF using the CDFM method and the fragility method and if there is a significant difference, he favors the fragility method. It is not mentioned in the paper that the 3-10
EPRI Proprietary Licensed Material Fragility Methodology Issues and Enhancements
CDFM HCLPF is relative to an 84th percentile demand and must be scaled to a HCLPF relative th to a 50 percentile demand. In EPRI (1994), pages 5-5 and 5-6, the authors elaborate more on the development of a median capacity from a CDFM HCLPF. The calculated CDFM HCLPF is relative to an 84th percentile demand and must first be adjusted to a HCLPF50 by dividing the CDFM HCLPF by expβrs where βrs is the combined logarithmic standard deviation for the horizontal component response spectrum shape basic variable and is the SRSS combination of the randomness βr and uncertainty βu for this variable. The random and uncertainty βs are provided in Table 3-2 of EPRI (1994) and depend on the frequency range of interest and whether the fragility is anchored to spectral acceleration or peak ground acceleration. βrs is typically taken as about 0.3 for the simplified approach to developing fragilities from CDFM calculations. In some cases, at certain frequencies, the UHS of EPRI (1989) and USNRC (1994) have a very large difference in spectral amplification between the 50th and 84th percentile UHS and βu alone is greater than 0.3. Thus, in developing fragility curves from a CDFM HCLPF, the analyst th th should examine the difference between the 50 and 84 percentile amplification of the site specific UHS and either determine the applicability of a standard βrs of 0.3 or develop a specific βrs to correspond to the site specific UHS. Note that in the IPEEE program, the plants that chose to do seismic margins assessments were required to utilize a NUREG/CR-0098 spectral shape rather than a UHS from EPRI (1989) or USNRC (1994) in developing a CDFM HCLPF. In these cases, the difference in spectral shape between the NUREG/CR-0098 and UHS ground motion response spectra must also be accounted for. In the case of soil sites, scaling from one spectral shape to another may not be reasonable and a new structural analysis may be required if HCLPFs from an IPEEE SMA are to converted to fragilities for use in a subsequent SPRA. Chapters 2, 3 and 5 in EPRI (1994) describe the procedure for converting a CDFM HCLPF to a fragility in detail and further elaboration is not necessary in this guide. The use of surrogate elements to represent components that have been screened out is discussed in Kennedy (1999), Ravindra (1999) and Chokshi (1999) as well as in the NRC review of the IPEEE submittals, USNRC (2000). It is pointed out that the unconditional failure rates, thus risk, implied by the screened out components should be small. This was not always the case for the IPEEE submittals. Typically, components were screened out on the basis of screening tables in EPRI (1991) or by use of SQUG GIP bounding or reference spectra (SQUG, 1991) and meeting associated screening caveats. The development of a surrogate fragility to represent components screened out is described in Kennedy (1999) but as is the case for development of fragilities from CDFM HCLPFs described above, the Kennedy (1999) description does not address the ground rule that the screening level is assumed to be a CDFM HCLPF84 and must be adjusted to a HCLPF50 value. This is described in detail in Chapter 5 of EPRI (1991). The screening spectral acceleration is adjusted to a HCLPF50 spectral acceleration by dividing by the factor expβrs. HCLPF50 = Screening Level/expβrs
where βrs is as discussed above for development of a fragility from CDFM HCLPF calculations.
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EPRI Proprietary Licensed Material Fragility Methodology Issues and Enhancements
In Kennedy (1999) and EPRI (1991) it is recommended that the median capacity conservatively be twice the HCLPF50 value, implying a βC of 0.3. This is a conservative assumption since the βrs used to represent the randomness and uncertainty in the seismic hazard is typically 0.3 and the assumption of a βC of 0.3 to represent all randomness and uncertainty in demand and capacity implies that there is no variability in the demand other than in the earthquake itself and that the capacity is always equal to the demand. It would seem more rational to assume a βC in the range discussed above for development of a fragility from a CDFM HCLCF. Although, as correctly pointed out in Kennedy (1999) the end risk result is not very sensitive to the assumed βC , assuming of course we are talking about a reasonable range of values, so assuming a higher βC , and calculating a higher median capacity for the surrogate should not make that much difference in the final risk results as long as the screening level was set sufficiently high to begin with. The problem is, that for sites with medium seismic hazard (0.2 – 0.25g pga), the screening tables of EPRI (1999) may not be high enough to result in a surrogate element with a failure rate low enough to effectively not have an influence on the final results. Refer to Appendix E for an example. The influence of the surrogate element or elements developed for different types of components that are screened at different levels depends also on the modeling assumptions and the assumed correlation between screened out elements. Note that in ANS (2002), High Level Requirement FR-B1, components cannot be screened out for Capability Category 3 unless their failures can be shown to be independent of the remaining components. In any case, HLR SAB-3 states to “PERFORM an analysis of seismic-caused dependencies and correlations, in a way so that any screening of SSCs appropriately ACCOUNTS FOR those dependencies and correlations.” Fleming (1999) and Watanabe (1999) discuss the importance of properly accounting for correlation and provide examples of case studies. The issue of correlation is primarily a systems modeling issue and not in the direct scope of the development of fragilities. Nevertheless, it is important for the fragility analysts and the systems analysts to interface on this issue so that the screening levels, the effect of the screening levels on CDF and the sensitivity of screening levels to correlation are well understood by both parties. The systems analysts should set a target for the unconditional failure rate of screened out components to be represented by surrogate fragilities. Kennedy (1999) suggests a simple method to establish the screening level, given the target unconditional failure rate, PFS . Given PFS, enter the seismic hazard curve (presumed to be the mean hazard curve) at an exceedance frequency HS(a) given by:
HS(a) = 2PFS And determine the corresponding ground motion level, as . Set the screening level, SL at: SL = ≥0.8 as
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EPRI Proprietary Licensed Material Fragility Methodology Issues and Enhancements
The systems analysts should establish the value of PFS based on their knowledge of the plant design and operation and their judgment on the effects of correlations between screened out components and between screened out components and components remaining in the model. The screening level may be established as a spectral acceleration value or as a peak ground acceleration value, depending upon how the systems analysts will compute the seismic failure rate from the seismic hazard definition. It is then the job of the fragility analyst to determine the appropriate screening value. For instance, if the systems analyst sets a screening target in terms of peak ground acceleration, the fragility analyst must relate this to spectral acceleration of the ground motion spectrum for comparison to screening tables in EPRI (1991) that are defined in terms of spectral acceleration. Preferably, the systems analyst will convolve the hazard curve with candidate surrogate fragilities and determine the required surrogate fragility or HCLPF50 value for the surrogate and provide this information to the fragility analyst. Given the target HCLPF50 for the surrogate, the fragility analyst can then propagate this to a HCLPF84 value for comparison to the screening tables in EPRI (1991), taking into account the amplification of peak ground acceleration to obtain spectral acceleration. If the target screening level is set too high, the fragility analyst then knows that he must use other sources of information besides EPRI (1991) screening tables for screening. Other sources of capacity information such as summaries of qualification margins, generic fragility calculations based upon required qualification procedures and practices or other sources of ruggedness data such as Generic Equipment Ruggedness Spectra (GERS) may be used to screen at different levels.
3.3
New Test and Earthquake Experience Data
There is an ongoing effort through SQUG and EPRI to enhance and develop new GERS based upon the results of qualification testing. The Seismic Qualification Reporting and Testing Standardization (SQRTS) organization is an EPRI sponsored group of utilities which has sought to achieve both qualification test standardization and economy by conducting collective (multiple item) shake table tests of replacement equipment for NPPs. The qualification and/or fragility testing results are summarized in a standard test report format and made available through a seismic qualification data library service to all SQURTS utilities. Most of the testing is at the device level such as relays, switches, molded case circuit breakers, transmitters, etc. These data are then analyzed to either enhance existing GERS as originally reported for non relays and for relays (EPRI, 1991a, c) or develop new GERS for addition to the EPRI GERS reports. New GERS and updates of GERS were developed in EPRI TR-105988-V1 (EPRI, 1996) and EPRI TR-105988-V2 (EPRI, 1999) and incorporated as addenda to the EPRI GERS reports for non relays and relays (EPRI, 1991a, c). A pilot program was initiated to gather test data from other countries to enhance GERS. Data was obtained from the United Kingdom for Control and Instrument Panels (EQE, 2001), referred to as Instrumentation and Control Panels and Cabinets (I&C) in the SQUG GIP. Candidate GERS were developed for cabinets, including devices within the cabinets, using the rules for developing GERS for low diversity class equipment. A joint SQUG/USNRC review panel has previously ruled that I&C panels and cabinets are a high diversity class, thus there are as yet no official GERS for this class. The data from the UK is very useful in a general sense though for 3-13
EPRI Proprietary Licensed Material Fragility Methodology Issues and Enhancements
demonstrating typical damping values and fundamental frequencies. There were two groups of panels. The first group was circa 1980-1985 tested in a biaxial or triaxial mode. The second group was circa 1989 to 1997, all tested triaxially. Fundamental frequencies ranged from 7.5 to 21.4 Hz front to back and 7.8 to 33.7 Hz side to side. Panels in the second group tended to be a bit stiffer but there were individual panels in the second group with frequencies near the lower level cited. Damping ratios ranged from 3% to 13%. The lower damping ratios were generally associated with very stiff cabinets. The average of the 16 cabinets tested was above the 5% damping considered as median damping in the development of fragilities (EPRI, 1994). At the OECD/NEA Workshop held in Tokyo, 1999, several Japanese papers were presented that summarized high level shake table tests of components conducted on the NUPEC Tadotsu Engineering Laboratory shake table. Many tests are for passive large scale model structures or equipment that are specific designs. One test of a diesel generator determined, through extrapolation of response measurements, that the crankshaft locating bearing housing would be the governing failure mode when it yielded. In general, these tests are for specific designs and cannot be effectively used to develop generic ruggedness levels for typical US equipment. They do, however, reinforce the ruggedness presumed in the EPRI (1991) screening tables. NUPEC tests of more typical generic electrical equipment are summarized in Ueki, et. al. (1999). From the quoted fundamental frequencies, the equipment tested is considerably stiffer than typical SQUG database equipment, thus typically more rugged. The tests were initially conducted as proving tests and then the shaking level was increased to high levels with no reported malfunction or damage. The high level tests ranged from 3.4g zpa for metal clad switchgear (minimum side to side fundamental frequency of 22 Hz) to 8.0 g zpa for an upright panel (minimum side to side fundamental frequency of 27 Hz). These frequencies correspond to the zpa so the low frequency peak of the test response spectra at about 2 Hz has no effect on response. Due to the differences in design, the very stiff construction and the differences in manufacturers of internal devices, the data are not directly applicable for enhancement of GERS developed for US equipment. The tests do, however, further reinforce the ruggedness of stiff cabinets and devices within stiff cabinets. The development of fragilities from GERS is clearly described in EPRI (1994), Chapter 3 and needs no further explanation here. There is an ongoing effort by the SEQUAL Owners Group (SEQUAL, 2001) to utilize earthquake experience for seismic qualification of equipment in non-A46 plants. In this effort, extensive study has been made of earthquake records and the associated representation of equipment classes with the records. In the SQUG GIP, a Reference Spectrum was defined as the average of 4 ground motion records that subjected 20 generic classes of equipment to high level seismic input motion. This Reference Spectrum represented the seismic ruggedness of the 20 generic classes of equipment, subject to meeting the associated demand to capacity evaluation and specific caveats for each of the classes. The SQUG SEQUAL program has enhanced the database that formed the basis for the SQUG GIP and has taken a more statistical approach to demonstrating that the seismic experience data can be used to qualify equipment. In SEQUAL (2001), applicable earthquake records representing a minimum population of equipment in each of the 20 classes have been averaged using a weighted average method and compared to the 3-14
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SQUG Reference Spectrum in the frequency range of 2.5 to 7.5 Hz. This is the broad-banded amplified acceleration portion of the SQUG Reference Spectrum. This updated compilation of representative spectra shows small differences for each class of equipment. For some classes, the SEQUAL capacity spectra exceed the Reference Spectrum and for other classes, the SEQUAL capacity spectra are a little bit lower than the Reference Spectrum but in no case are they less than 1.1g spectral acceleration in the frequency range of 2.5 to 7.5 Hz, which is 90% of the 1.2g Reference Spectrum. These individual capacity spectra and the number of components represented by each equipment class capacity spectrum are contained in Appendix D of SEQUAL, 2001 and can be used in the development of fragilities using experience data for equipment included in the SQUG 20 generic classes of equipment. A procedure for development of fragilities from experience data using survival analysis is presented in Appendix C and an example is presented in Appendix D. It is noted that the NRC approved ground motion spectra for piping contained in USNRC (1999) would result in average spectral acceleration over the 2.5 Hz to 7.5 Hz range that is less than the SQUG Reference Spectrum. It is however noted that in many cases, the spectral accelerations are high at very low frequency and these data can be used to develop displacement capacities for very low frequency systems such as rod hung piping. The SQUG GIP reference spectrum cuts off at 2 Hz. Low frequency systems are displacement and velocity sensitive and in many instances of developing fragilities for low frequency systems such as rod hung piping or for sliding or rocking of rigid bodies, experience spectra are needed at 1 Hz and below. EPRI (1994) does not address the development of fragility from seismic experience data. SEQUAL (2001) has a generic example in Appendix B. Salmon and Kennedy (Salmon, 1994) also have an example. Both examples use the SQUG Reference spectrum as a capacity spectrum for comparison to in-structure response spectra. In these cases, the assumed βC varies slightly, thus the ratio of HCLPF to median capacity is slightly different. The median capacity in each case is statistically derived based upon an assumed number of components represented in the database. There are slight differences in the methodology but the differences would not result in any significant difference in the end item fragility, given identical demand on the component. The example developed in Appendix D of this report demonstrates a procedure for development of fragility from an earthquake experience capacity spectrum as defined in SEQUAL (2001). The example is based on the survival analysis methodology in Appendix C, as used in the SEQUAL generic example (SEQUAL, 2001). Other earthquake records may be added to enhance the SEQUAL capacity spectra. A SQUG method for gathering and validating earthquake experience data (SQUG, 2001) has been approved by the regulators (USNRC, 2001). There have been several more recent severe earthquakes world wide that have been investigated to some degree (Turkey, Taiwan, Kobe, Hualien, Lotung) but specific data gathering and evaluation in accordance with current approved criteria has not been carried out for them. Therefore, the data collected cannot effectively be used in enhancing the SEQUAL capacity spectra. In general, the observations from these events have concurred with observed damage or lack of damage from SEQUAL and SQUG database facilities.
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4 DEVELOPMENT OF FRAGILITIES IN ACCORDANCE WITH ANS 58.21
The new ANS Standard 58.21 for External Events PRA, ANS (2002), sets down high level requirements for conducting a SPRA. There are three different capability categories in the Standard that require varying degrees of sophistication. The Standard is not intended to provide methodology for meeting the requirements but does reference some applicable documents. This chapter will focus on the detailed development of fragilities and the necessary interface with the hazards analysts and systems analysts in order to make the fragilities compatible with the Standard and the intended use of the fragilities. EPRI TR-103959 (EPRI, 1994) is the most complete methodology guide available on the development of fragilities. In most cases, the methodology discussed would satisfy all three capability categories of the Standard. In some cases, the approximate methods suggested would not comply with the requirements for all capability categories in the Standard. In a few cases, the guidance should be enhanced for compliance with all capability categories in the Standard. The approach taken in this chapter is to list the step by step progression of developing fragilities and provide discussion on what is necessary to meet each of the ANS Standard capability categories. If the methodology in EPRI TR-103959 is adequate, for one or all of the capability categories it will be cited and not repeated. If the methodology needs to be expanded or is not contained in EPRI TR-103959, then guidance will be provided herein. In all cases, the guidance will be with reference to the specific capability categories in the Standard for which it is applicable. EPRI TR-103959 provides excellent examples of the development of fragilities for common structures and equipment. In cases where further examples are beneficial to cover areas not addressed in detail in EPRI TR-103959, they are developed in the Appendices. Table 4-1 provides a summary of the steps in the development of seismic fragilities and the associated high level requirements in the Standard. It also includes a column to reference the appropriate coverage in EPRI TR-103959 or other documents, if applicable. If an addition to, or expansion of, EPRI TR-103959 is required, it is noted. These additions and expansions are then discussed in more detail in the following text and references are made to example calculations if they are provided in the Appendices. The following major steps are required in a Seismic PRA. 1. Develop the seismic hazard 2. Develop a systems model that represents the plant response to earthquakes. 4-1
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
3. Calculate the response of the structures housing systems and components to the earthquake input motion (demand on structures, systems and components). 4. Review the design basis and conduct prescreening. 5. Conduct a Walkdown of the plant to identify potential seismic vulnerabilities and to screen out rugged components. 6. Develop seismic fragilities for structures, systems and components that are not screened out. a) Determine the response of the systems and components b) Determine the capacity of the structures, systems and components to withstand the seismic input motion. 7. Calculate the response of the plant due to the seismic input motion and the progressive failures of structures, systems and components. Some of these tasks may be conducted concurrently but each requires an understanding of the compatible tasks and continuous interface with the different parties conducting the tasks. The focus of this document is on steps 3, 4, 5 and 6. The interface with steps 1 and 2 is important in the implementation of steps 3, 4, 5 and 6 and this interface is also elaborated.
4.1
Understanding the Seismic Hazard
The Standard cites ANS (1997) and ANS (2000) for the development of the hazard and provides some high level requirements for three Capability Categories. The seismic hazard is typically defined as the annual probability of exceedance of a ground motion parameter or parameters, such as peak ground acceleration (pga) or spectral acceleration, Sa, occurring at the site. As was typically done in EPRI (1989) and USNRC (1994), a peak ground acceleration was developed for a range of 1E-1 to 1E-7 or lower annual probability of exceedance. Uniform Hazard Spectra (UHS) were developed for a few annual probability of exceedance values such as 1E-3, 1E-4 and 1E-5. Examples of a typical seismic hazard definition are shown in Figures 5-1 and 5-2 for peak ground acceleration and for a uniform hazard spectrum associated with 1E-4 annual probability of exceedance. Since there is uncertainty in the many parameters used to develop the seismic hazard curves and UHS, the distribution about the mean or median value of the pga hazard or UHS is also defined. In the calculation of seismic induced failure rates of SSCs, the fragility curves are convolved with the seismic hazard to compute the unconditional probability of failure. In order to conduct an accurate computation, the hazard must be defined out to a very low probability of annual exceedance, typically 1E-8 or 1E-9. In NUREG-1407, USNRC (1991b) It was required to extend the mean seismic hazard to 1.5g peak ground acceleration unless it could be shown that a cut off at a lower acceleration did not result in a significant difference in the results. As shown in Figure 4-1, this would have required an extrapolation of the mean seismic hazard to less than 1E-7 annual probability of exceedance. Note that in IPEEE, only a point estimate of CDF was required, thus only the mean seismic hazard curve was used. This would correspond to 4-2
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Capability Category 1 in the Standard. Capability Category 2 and 3 require uncertainty analysis and the full uncertainty in the seismic hazard must be considered. Given, the information as shown in Figures 4-1 and 4-2, regarding the seismic hazard, the fragility analysts and systems analysts are somewhat forced to reference the fragilities to the peak ground acceleration as opposed to spectral acceleration in a frequency range of interest. The Standard and EPRI (1994) both recommend that the fragilities be developed relative to spectral acceleration, as this reduces uncertainty in the response of the SSCs. For instance, if a structure is responding at 5 Hz, defining the hazard in terms of spectral acceleration at 5 Hz will result in less uncertainty in the structural response than if the hazard is defined as peak ground acceleration and the uncertainty between peak ground acceleration and spectral acceleration must be considered as well.
Figure 4-1 Annual Probability of Exceedance of Peak Ground Acceleration
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Figure 4-2 Uniform Hazard Spectra for the 10-4 Annual Probability of Exceedance. Spectra shown for three percentiles: 15th, 50th, and 85th
EPRI (1994) in Chapter 3, discusses three important features of the hazard definition that the fragility analyst must consider in developing fragilities. They are; 1) the relationship between the peak ground acceleration and spectral acceleration, thus spectral shape; 2) the relationship between the two orthogonal horizontal components of earthquake and 3) the relationship between the horizontal and vertical ground motion. The hazard curves developed in EPRI (1989) and USNRC (1994) were assumed to represent the average of the two horizontal components of earthquake. A specific seismic hazard for the vertical direction was not developed and the vertical hazard was typically assumed to be 2/3 of the horizontal hazard. A vibration frequency was not associated with the peak ground acceleration which, as noted in the NRC review of IPEEE submittals, USNRC (2000), resulted in one case of a misinterpretation that resulted in an unconservative CDF computation. In IPEEE there was also some confusion and misinterpretation of the control point for the hazard. The hazard was stated to be in the free field. In developing seismic hazard the earthquake is propagated from the source to the site through underlying rock. If the site is overlain by soil, the hazard analyst must then propagate the hazard to the surface to define the hazard in the free field. For shallow soil sites, this may not always be done, therefore the fragility analyst must take into account any amplification of the soil column to the foundation of structures that are not founded on the rock control point where the earthquake hazard is defined. The fragility analyst must have a clear understanding of where the control point is located for the defined hazard. EPRI (1994) in Table 3-2, provides estimates of uncertainty to be included in the fragility computations for cases where the fragility is reference to peak ground acceleration vs spectral 4-4
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
acceleration and for cases where the vertical acceleration is assumed to be two thirds of the horizontal acceleration. These uncertainties should be taken into account if the fragilities are referenced to peak ground acceleration. The random variability is also tabulated in the table. The values provided are ranges of values from studies of earthquake records. For a specific site, the random and uncertainty variables may be more or less than the ranges shown. For instance, th th in some of the IPEEE sites, at certain frequencies, the difference between 84 and 50 percentile UHS spectral acceleration is quite large when they are both anchored to the same pga. Besides the peak to peak variation random variability given in Table 3-2 of EPRI (1994), uncertainty variability may be larger than provided in EPRI (1994) and should be considered in these cases where there is a pronounced difference in the amplification of pga. Of course, if the fragility is anchored to spectral acceleration, the uncertainty variability of the spectral acceleration amplification above the pga is captured in the hazard curves during the convolution of the hazard and fragility and only the peak to peak random variability should be included in the fragility derivation. Other information that the fragility analyst may need is the peak spectral displacement, and peak spectral velocity of the earthquake ground motion. For very low frequency systems, the failure is often governed by large displacement or for cases of rigid body rocking or sliding, peak velocity is often desired. The UHS have typically been defined down to 1 Hz. Spectral velocity, Sv, and spectral displacement, Sd, can be derived from spectral acceleration, Sa, by the relationships: Sv = Sa/ω Sd = As/ω2
where ω is the circular frequency.
The peak spectral displacement usually occurs below 1 Hz, thus the hazard analyst should provide these values also or else provide hazard parameters down to say 0.25 Hz. The existing EPRI (1989) and USNRC (1994) hazard studies are considered to be applicable to Capability Category 1 and 2 in the Standard. Capability Category 3 would require a more detailed hazard analysis. In this case, de-aggregation is required and if the high frequency range and low frequency range of the UHS are governed by two or more different sources, then in effect, two or more different earthquake hazards are present with different spectral shapes and different annual frequency of occurrence. In this case, two or more separate fragility descriptions are required for each SSC and two or more separate calculations of CDF are required in order to arrive at the final CDF. The development of the seismic hazard is to be conducted in accordance with draft ANS standards 2.29 and 2.27 under preparation, ANS (1997 and ANS 2000). These standards will specify the scope of the hazard studies and the output that conforms to each of the Standard’s Capacity Categories. The fragility analyst must understand the source and meaning of the important hazard parameters.
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
4.2 Understanding the Development of the Risk Model and Equipment List and the Significance of Screening Thresholds The systems analyst will develop an event tree/fault tree risk model that will be used to calculate the CDF due to seismic events, coupled with random failures and human error probabilities. The systems model will typically contain non-safety components as well as safety components in order to capture the success (non-failure) of normal operating systems as well as the failure of safety systems. The model will also contain the non-seismic failure rate or unavailability of systems or components. A typical example is the failure of diesel generators to start or continue running, given the loss of off site power. These random failure rates are usually contained in the internal event risk model. The fragility analyst is provided a list of equipment that is to be modeled. This list may consist of 1000 or more components plus an even larger list of relays. It is not practical to develop detailed fragility descriptions for each component even if the systems analyst models each component. Typically a screening threshold is established by the systems analyst whereby the components can be screened out and either not modeled in detail, or else surrogate elements can replace groups of elements that are screened at a high capacity level. In EPRI (1994) the terminology “surrogate element” is used to denote an element introduced into the risk model that represents several components that are screened at a stated level. In practice there may be several screening levels, representing several generic types of components. The surrogate element or elements then require a fragility description that is to be developed by the fragility analyst. However, the systems analyst should set a target for the surrogate element or elements so that they have a very small contribution to risk. In practice, this use of a surrogate element has been over simplified and in some cases, as noted in USNRC (2000), some IPEEE submittals utilized a single surrogate element to represent all screened out components. This over simplification would appear to be unconservative for cases where uncorrelated components in series (OR Gates in the risk model) have similar capacities close to the screening level. Their individual failure rates are counted only once as a single failure instead of being added. This report will not provide criteria for the modeling of screened out components but it is pointed out that there needs to be close interface between the systems analyst and fragility analyst in order to assure that screening levels are either high enough to completely screen out the components or surrogate fragilities are included in the model in a manner that captures the risk contribution from the components represented by surrogate fragilities. Note that in the Standard the focus is on setting a screening level so that the screened out components do not contribute significantly to CDF or LERF. This may not always be practical and some groups of components may necessarily be represented by a fragility that does result more than an insignificant contribution to CDF or LERF. A good place to start is for the fragility analyst to develop some preliminary fragility descriptions for screening levels that may be achieved. For instance, there are two screening levels in EPRI (1991) that may be used to screen most of the components. Fortunately, the equipment list is dominated by valves and most can be screened at the higher (1.2g spectral acceleration) screening level. In many cases, certain groups of components or subsystems like piping, HVAC and electrical raceways can be preliminarily screened at some level or levels based on their conservative design criteria. Not all components or subsystems have equal margins built into their design criteria so different levels of generic fragility can be assigned to different classes of equipment based upon their seismic qualification criteria. The systems analyst can then advise if 4-6
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
the proposed or achievable screening level will have a significant effect on final risk results. If it is determined that a certain easily achievable screening level is too low, then the fragility analyst will understand that the screening level needs to be increased by some means. More effort will be required to further subdivide a large group into smaller groups, with associated generic fragilities, that may be based on different methods of generic fragility development, or it may be determined that plant specific fragilities are required for certain groups of equipment. Appendix E shows an example where the EPRI screening tables are not sufficient for screening but, because of conservatism in the design process, flexible subsystems and components could be screened. In this case, the use of surrogate elements for the achievable screening level did result in a significant, though not dominant, contributions to CDF. Hindsight indicates that the screening level should have been higher but if so, the level of effort required to develop individual or generic subclasses of fragilities would have increased significantly. The fragility analyst should also provide some guidance to the systems analyst on the correlation of components within each group of components falling into a screening level and between groups of components for different screening levels. For instance, there may be a fairly low screening level that applies to non-safety components in the power conversion system. This screening level fragility, along with a fragility for loss of off site power based on switchyard failures, may determine the failure or success of normal shutdown systems, given an earthquake. In this case, the failure of mechanical components in the power conversion system would be independent of the loss of off site power. Likewise, the failure of flexible piping in the power conversion system would be uncorrelated to the failure of rigid equipment. At the first screening level in EPRI (1991) several dissimilar types of components may have the same screening level. In this case, the fragility analyst would group the components that are considered to have correlated failure modes. The different groups of components screened at this level could then be assumed to be independent (uncorrelated). Other screening levels based on different methods for preliminary screening would be treated in a similar manner. If this information is provided to the systems analyst early in the study, the systems analyst will then have a head start on how to model screened out groups of components, accounting for expected correlation between groups. They can also feed back some guidance to the fragility analyst as to what screening levels could be tolerated without requiring plant specific fragilities. It is convenient for the fragility analyst to screen components using the screening guidelines in EPRI (1991). However, in several IPEEE submittals, it was evident that the screening level was too low and the surrogate fragility ended up to be a significant contributor to CDF, if not the most significant contributor. As discussed in Chapter 3, the selection of a screening threshold, thus the associated surrogate fragility, requires some careful thought by the systems analyst as to the correlation of components represented by the surrogate element or elements. For Capability Category 3 in the Standard, high capacity components can be screened only if they can be considered as fully independent of the remaining components. In the case of Capability Category 3, the treatment of correlation is also much more complicated. All components are to some extent partially correlated since they experience the same earthquake. This raises the issue of partial correlation. Fleming (1999) suggests that for partial correlation that fragilities be developed, where instead of the traditional βC being broken down into βR and βU , he suggests decomposing the randomness and uncertainty into βIND and βDEP . The systems analyst and fragility analyst would have to caucus on how to handle partial correlation. This 4-7
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report does not provide guidance on modeling of partial correlations. It does, however, emphasize the importance of a close interface with the systems analysts on the issue.
4.3
Determine the Seismic Response of Structures
Seismic response of structures to the earthquake hazard specified for the site is an initial part of the development of fragilities and screening levels of SSCs. The structural response is calculated to develop loads on structural members and to develop amplified floor response spectra (AFRS) to define the demand on systems and components in the structures. The Standard requires that realistic seismic response be preformed. In general, if the ground motion spectra are significantly different or if the structures are founded on soil, a new analysis is required. Reference is made to ASCE (1998) for guidance on soil-structure interaction analysis and to EPRI (1994) for determining median response and variability. Scaling of existing design response must be justified based on demonstrating adequacy of the existing models, foundation characteristics and similarity of input response spectra. Reference is made to EPRI (1991) for scaling methodology. For Capability Category 3, scaling is not permitted and probabilistic response analysis is required. Probabilistic response analysis may also be conducted for Capability Categories 1 and 2 but is not a requirement. If probabilistic response analysis is conducted, the Standard requires that that the number of simulations done using Latin Hypercube or Monte Carlo techniques is large enough to obtain stable median and 85% non-exceedance responses. The minimum requirements for Capability Category 1 and 2 are to scale existing design response analysis if justified, or to conduct a new deterministic analysis for the median ground motion spectrum to be used in the PRA. For purposes of this report, UHS will be used to represent the median ground motion spectrum determined appropriate for the PRA. For Capability Category 3, a probabilistic analysis is always required and if there are two or more dominant seismic sources as determined by the deaggregation of the probabilistically developed UHS, the probabilistic response analysis may be required for two or more ground motion spectral shapes. A situation such as this arose in a PRA of a plant in Eastern Europe where a probabilistic UHS was developed for large magnitude earthquakes and used in a probabilistic response analysis in the base PRA analysis. Another high frequency spectral shape from an actual close in lower magnitude earthquake was then used in a subsequent analysis for comparison of responses. In this case the second earthquake response was only used in a deterministic comparison of response since a complete hazard study for local sources was not carried out. The close in earthquake that had actually occurred resulted in higher structural response than the SSE in a few locations but for most locations, the SSE response was greater as was the response to the 1E-4 median UHS. Most often in past seismic PRAs, either a new deterministic analysis has been conducted or existing design analyses have been scaled. In most cases of scaling in earlier PRAs, the assumed median spectral shape was similar in broad band frequency content to design spectra and scaling was approximately conducted on a mode by mode basis. All plants in the US were designed before the regulatory requirements for soil structure interaction in USNRC (1989) were changed to be more realistic. Some of the newer plants on soil sites used soil-structure interaction computer codes in the response analysis but the previous restrictions on control point for the input motion and limits on radiation damping resulted in very conservative response. Earlier 4-8
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
NPPs used simple soil-spring models that were not capable of capturing the complex behavior of structural response on layered soil sites. For older NPPs on soil sites it is especially important that the structural response be recomputed. Usually the existing structural model can be used but the soil-structure interaction method and modeling must be updated to more modern methods. EPRI (1991) and ASCE (1998) provide detailed discussions and up to date methodology for deterministic soil-structure interaction analysis that meets all requirements of the Standard for Capability Category 1 and 2 and no further guidance is necessary here. 4.3.1 Scaling of Existing Design Analysis Scaling of existing analysis to develop realistic loads for a different ground motion input is much easier than scaling existing in-structure spectra. The scaling of loads is discussed first. EPRI (1991) provides equation 4-1 for mode by mode scaling of loads. If the mode by mode structural member loads are available the scaled load for a new UHS ground motion spectrum can be derived from:
Pi, j UHS = Pi, j SSE [Sa j UHS / Sa j SSE ]
Equation 4-1
Where Pi, j is the seismic load in element i for mode j, Sa j UHS is the spectral acceleration from the UHS for mode j at UHS modal damping and Sa j SSE is the spectral acceleration for the SSE for mode j at mode j modal damping. The element load PUHS is then the SRSS of PijUHS . For simple structures with dominant response in a single mode, the scaling of total load in a structural member can be approximately done using the applicable spectral accelerations and damping for the dominant mode. For simple lumped mass models if member loads are not provided on a mode by mode basis but the nodal masses, mode shapes and participation factors are provided, the seismic force from each node for each mode and be computed as:
Fi j = Mi Γj Φ j Saj Where FI, j = force at node i for mode j Mi = mass of node i
Γj = participation factor for mode j Φ j = mode shape for mode j Sa j = Spectral acceleration of mode j at frequency fj
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
The base shear, V, can be calculated as: 2 V = Σ(Γj Φ j Mi Sa j )
1/ 2
Scaling of spectra is more difficult. The only justification for scaling of spectra using a single mode is if the spectral shape of the UHS is similar to that of the SSE, which is rarely the case. If the complete eigensolution parameters are available, existing spectra can be scaled on a mode by mode basis with reasonable accuracy. However, for soil sites, especially sites with older, more simplified SSI analyses, scaling has little merit and new analysis is recommended. Also, in some cases it has been found that, sample models of steel frame structures that respond at very low frequencies do not have a design basis analysis that can be used for mode by mode scaling. In these cases, 3D models may have been used but the design basis response analysis was only carried out to 40 or so modes and the eigensolution was cut off at fairly low frequencies like 6-8 Hz. Thus scaling of spectra using existing eigensolution parameters could not propagate the high frequency portion of a typical EUS UHS. Appendix A shows an example of scaling of DBE spectra developed from a simple lumped mass reactor building model subjected to a RG 1.60 spectral shape anchored to 0.05g to develop spectra for a high frequency UHS anchored to 0.1g. In this case, the original model was recreated and the original spectra were verified before the scaling procedure was attempted. Scaling was done by using original eigensolution results and random vibration theory as described in Appendix B and by simplified methods using only the participation factors and scaling at only a few frequencies. The simplified method might be applicable to Capability Category 1 of the Standard. The more rigorous method using random vibration theory and the original eigensolution is considered to be applicable to Capability Category 2 of the Standard. The example conducted was done on Excel spread sheets. Since the model was simple, it was not tedious to set up the spread sheets. For complex models it would only be practical to do this if the eigensolution could be obtained in electronic form. Otherwise, the model should be rerun using a time history that matches the UHS or alternatively using a direct generation code and a new eigensolution from the existing model. The random vibration theory method in Appendix B could, though, be applied to a reduced number of modes without sacrifice of much accuracy. In Appendix B, a scaling example is presented for a more complex structure that accounts for reduction in the ground motion spectra due to the ground motion incoherence associated with the large structure. The high frequency portion of the ground motion UHS is also reduced in accordance with EPRI (1997) to account for limited ductility of components in the structure. This second reduction is applicable for mechanical components but wouldn’t be applicable for evaluation of relays. 4.3.2 Conducting New Analysis It is often beneficial, and in many instances mandatory, to conduct new response analysis. Existing results for rock sites may be scaled with reasonable accuracy as described in Section 4.3.1. In most cases, new analysis should be conducted for soil sites. Many of the design response analyses for soil sites were conducted using very conservative criteria specified by the regulators at the time. Often soil spring models were used with limits on damping. The control 4-10
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point input motion was defined as the motion at the surface and deconvolution was not allowed. In such cases, any form of scaling, especially if the UHS and DBE/SSE spectral shapes were significantly different is very inaccurate. The new analysis may be deterministic using best estimate properties for soil and damping and taking credit for deconvolutions of the free field input motion with depth of embedment. Guidance for new deterministic analysis, including variations in soil properties, is provided in ANS (2002), EPRI (1991b) and ASCE (1998). Probabilistic spectra for several seismic PRAs performed for IPEEE and for NPPs in other countries with high seismic hazard have been developed using Latin Hypercube probabilistic methods as described in USNRC (1981) for computing structural response. Although EPRI (1994) mentions conducting probabilistic response analysis by Latin Hypercube or Monte Carlo Methods, no specific references are provided for methodology or software for conducting such analyses. In EPRI (1991) limited criteria are provided for scaling of loads and for scaling of spectra. The emphasis in EPRI (1991) and EPRI (1994) is to conduct new deterministic analysis, especially for soil sites, and to determine the variability in results using the classic separation of variables approach. Regardless of the method used, the objective in calculating structural response is to determine the median response in terms of structural loads and amplified floor response spectra, and the distribution about the median value.
4.4
Plant Walkdown
The walkdown methodology is well documented in EPRI (1991). This methodology was referenced for IPEEE in USNRC (1991 b). The general sequence of performing a plant walkdown contains the following steps:
1. Review the equipment list prepared by the systems analysts: The walkdown team should review the list of components to understand what it to be included in the model. Often, questions will arise as to the detail of the list. The internal events systems model may have itemized items that can be grouped together by the “rule of the box” criteria. On the other hand, items may have been too coarsely grouped and some should be separated. For example, the jacket water heat exchanges and lube oil coolers for emergency diesel generators may or may not be engine mounted. If they are on the engine, or engine skid, they can be considered part of the engine assembly under the rule of the box criteria. If however, they are in a separate substructure mounted on the floor or a wall, they should be listed as separate components. Often, this decision cannot be made until some preliminary walkdown is performed by the systems engineers in combination with the fragility engineers. The interface between the systems engineers and fragility engineers is important at this stage to assure an accurate list of equipment to be considered in the model. 2. Determine applicable screening levels: As discussed in Section 3.1.2, there may be several screening levels that are applicable to different types of equipment. The most common screening criteria applied during the walkdown are the screening tables in EPRI (1991b). There are two levels of screen that apply to different types of components and structures. 4-11
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These screening criteria are subject to verification of the inclusion rules, including elevation above grade level, the adequacy of anchorage and the absence of systems interactions. Other levels of screening may be developed based upon the seismic design or qualification criteria. These levels of screen may be greater or less than the experience based screening levels in EPRI (1991b). For instance, it may be determined that the damping value for equipment qualified by analysis was very conservative, thus flexible components within given classes would have large margin due to over prediction of response. This over design based on over prediction of response would affect the seismic demand on the component itself and it’s anchorage. If this screening level based on design criteria exceeds one or both of the screening levels in EPRI (1991b) then it would be the basis for a higher capacity generic fragility description to represent those components screened. This type of prescreening in IPEEE studies has ranged from situations where practically all components were prescreened based upon design conservatism to cases where most components could only be screened during the walkdown at the lower screening level in EPRI (1991b). Whatever is done for screening, a representative fragility must be convolved with the hazard curve in order to assure that the calculated failure rate is lower than a target set by the systems analysts.
3. Prepare walkdown sequence: This step involves coordination with plant operations to lay out a schedule and route that minimize any effect on plant operations or maintenance. Occasionally, it is necessary to plan non-routine inspections that require bus outages for access. Often, more that one visit into the plant is necessary to access all equipment required to be examined. 4. Conduct the walkdown: During the walkdown, SSCs are examined to apply the EPRI screening, if applicable, verify that prescreening by other methods is valid, identify vulnerabilities such as spatial systems interactions, fire sources, potential for actuation of fire suppression systems, vulnerabilities to fire protection systems, verify anchorage, take field dimensions if necessary, etc. 5. Documentation of walkdown. The walkdown and screening process and screening criteria should be well documented. The walkdown documentation in effect is equivalent to a calculation that documents the verification of capacities of equipment based on various methods of field determination or predetermination of these capacities. EPRI (1991b) provides excellent guidelines on the content of the documentation and provides screening forms to document the screening level based on the EPRI screening criteria. The Standard refers to this document for guidance on documentation. Additional documentation of prescreening criteria and supporting calculations will also be necessary.
4.5
Structural Capacity
The Standard requires the identification of all relevant failure modes and the evaluation of fragilities for critical failure modes. Depending upon the design documentation available, the structural analyst may extrapolate an ultimate or limit state capacity from the design analysis. In other cases, the analyst may need to conduct a new linear analysis or conduct some degree of non-linear analysis. Usually, this task is achieved using results of linear analysis to determine 4-12
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the demand level at the ultimate capacity for concrete or limit state for steel structures. EPRI TR-103959 provides an example for determining ultimate capacity of a typical shear wall structure. The Standard makes reference to EPRI NP-6041 and ASCE-4 for determining ultimate capacity or limit state capacity. The key issue in determining the capacity is to focus on the global instability, rather than the local instability of a single element. In typical design calculations, the focus is on element capacity. To this extent, the design calculations must often be extended to determine the redundant load paths to the point of global instability. This is often done by using simplified non-linear models. Chapter 3 of EPRI TR-103959 provides a simplified non-linear analysis method based on the use of effective frequency and effective damping. Appendix G of EPRI NP-6041 provides guidance on the use and limits of equivalent viscous damping in non-linear dynamic analysis. On rare occasion, a more detailed non-linear dynamic analysis may be necessary to determine the redundant load paths and inelastic deformation in a critical structure. The guidance afforded in EPRI TR-103959 and EPRI NP-6041 is considered adequate for almost all non-linear analyses that may be required to develop the capacity of structures.
4.6
Determine Ductility Beyond the Limit State Capacity
The requirements in the Standard are general on this topic. The capability of a structure to cyclically deform beyond its limit state without failure depends upon the ductility of the construction. Ductility refers to the amount of total deformation relative to the elastic deformation. In fragility analysis, a ductility factor is derived such that the elastically calculated demand from a dynamic analysis is divided by the ductility factor to determine an equivalent spectral acceleration loading for purposes of determining stability. However, in developing fragilities for structures, inelastic deformation less than that of the stability point is considered a failure threshold due to the fact that equipment may be damaged before the structure totally collapses. EPRI NP-6041 provides conservative guidance on the ductility that can be considered when determining a HCLPF. The elastically calculated demand is multiplied by a factor of 0.8 (equal to a ductility factor of 1.25). This is considered conservative as long as the structure is ductile. DOE Standard 1020 (DOE, 1994) provides ductility factors for common types of concrete and steel structures. The recommended ductilities are associated with performance goals and are generally considered to be a HCLPF value, about 95% non-exceedance values. The median ductility factor is more judgmental since the level of distress less than collapse, associated with affecting equipment within the structure, is not a precise value. Typically, a limit on the deformation is defined by story drift. Story drift is utilized to determine the system ductility. Recommended median story drift values and their random and uncertainty variability for structures with and without safety related equipment attached are provided in Table 3-5 of EPRI TR-103959. Median system ductility of multi-story buildings can be calculated from equation 3-23 in EPRI TR-103959. Newmark (1997) original proposed a formula for calculating the ductility factor for a simple elastic-plastic model. Riddell and Newmark, refined the relationship between system ductility and ductility factor as a function of structural damping and accounting for a bilinear stress strain 4-13
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relationship. In USNRC (1994) this relationship was further refined to account for the shape of the hysteresis loop and duration of the earthquake and utilizing an effective frequency and effective damping in a simple non-linear model. EPRI TR-103959 summarizes two procedures derived from these studies for determining a median value for the ductility factor. One procedure incorporates the simplified non-linear model using effective frequency and effective damping from USNRC (1994). The other procedure utilizes a modified Riddell-Newmark ductility method. It is recommended that the average of the two methods be used to define the median value of the ductility factor. Additional randomness and uncertainty is to be added to that stated in EPRI TR-103959 for story drift values for purposes of calculating the total βR and βU for ductility. As a sanity check, the ductility factor HCLPF values calculated from the lognormal fragility model can be compared to recommended ductility values in EPRI NP-6041 and DOE Standard 1020.
4.7
Structural Response Factor
For Capability Categories 1 and 2, the Standard states “Estimate Seismic Response on a realistic basis using site specific earthquake response spectra.” Probabilistic Response is required for Capability Category 3. The separation of variables procedure described in EPRI TR-103959 for development of structural response factors is generally applied for Capability Category 1 and 2 applications although a probabilistic response analysis may be done. In the separation of variables approach a Structural Response Factor, FSR, is developed that defines the conservatism or unconservatism present in the derivation of seismic demand on structures or in the development of floor response spectra. The Structural Response Factor is applicable to both the structural fragility and the equipment fragility. EPRI TR-103959 provides a detailed description of the development of the Structural Response Factor. This factor may be different for the structures and for the equipment in the structure due to the different analytical methods used to develop structural loads and floor response spectra. For rock sites it is common practice to develop structural loads for design by the response spectrum method whereas the floor response spectra are usually developed from a mode superposition time history analysis. In some cases, floor response spectra are developed by the direct generation method that is based on random vibration theory. In all cases, the models should be the same. The differences result primarily from the spectral shape factor and damping. For soil sites, the derivation of a structural response factor from existing analysis involves scaling of response as previously discussed. In general a new median centered analysis should be conducted for soil sites, especially if the existing analysis was not based on state of the art soil structure interaction (SSI) methodology. Typically the floor response spectra are developed from a soil-structure interaction code such as SASSI or CLASSI. Often times, the structural loads are developed from a more simplified soil structure interaction model. In these cases, soil impedance functions are developed from an SSI code such as SASSI and are used to develop equivalent soil spring and damper values. This approach may be a best estimate case considered to be median centered but introduces additional uncertainty. 4-14
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A brief discussion is provided for each of the important variables considered in the separation of variables approach to developing a structural response factor. More detail on the numerical values associated with each variable are provided in EPRI TR-103959, Chapter 3. 4.7.1 Spectral Shape Factor The spectral shape factor is derived from the ground motion variables discussed in EPRI TR103959. They include the earthquake response spectrum shape used in design vs the UHS shape, the relationship of the horizontal direction peak response to the average response and the relationship of the vertical response to the horizontal response. If existing analysis is scaled, the median values of the three variables are compared to the design values to obtain an overall factor of conservatism or unconservatism. If new analysis is conducted, it should be median centered using the median values of the three variables. In this case, the spectral shape factor should be unity. EPRI TR-103959 discusses time history simulation in Chapter 3. If time history analysis is conducted, any difference between the average response spectrum resulting from the time history and the target ground motion spectrum is usually incorporated into the spectral shape factor. There is also uncertainty associated with the spectrum resulting from the time history vs the target spectrum. Note that if the seismic hazard can be defined in terms of spectral acceleration instead of the traditional peak ground acceleration, the uncertainty in the spectral shape can be significantly reduced. Refer to the discussion in Section 4.1 and in EPRI TR-103959, Chapter 3, for detail on the uncertainty associated with defining the hazard as pga as opposed to spectral acceleration. This uncertainty in spectral shape is incorporated into the overall variability of the spectral shape factor. In developing the spectral shape factor for equipment that is analyzed using the floor response spectra as the demand, additional variability exists due to the use of broadened and smoothed spectra. If raw spectra are not available and the strength factor for equipment is evaluated using the broadened and smoothed floor response spectra, then additional conservatism should be accounted for in the spectral shape factor applicable to equipment. Note that for soil sites, the floor response spectra are usually a broadened and smoothed envelope of the response of the structure for three soil stiffness cases. Thus, the fragility analyst should not double count the uncertainty associated with the soil stiffness variation in developing the spectral shape factor and the factor for Soil Structure Interaction. 4.7.2 Damping The damping factor is the ratio of response of the structure for design damping vs the response for median damping. If a new analysis is conducted, median damping should be utilized, in which case the factor should be unity. Note that the median value of damping for development of floor response spectra for equipment may be different than for defining structural failure. Modern reinforced concrete structures are quite robust and if their capacity is greater than the capacity of some critical equipment that ultimately governs the seismic risk, the median damping 4-15
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value associated with large inelastic deformation of the structure may be too high to represent median elastic response of the structure if some critical equipment failures occur while the structure is elastic. The fragility analyst needs to make final adjustments to the damping factor to reflect the appropriate value associated with the failure level of the equipment under consideration. In theory, damping appropriate for median structural response would vary with the capacity of the equipment. In practice, a damping value associated with the yield level of the structure is usually chosen as a constant value. In some plants where the concrete structures are much stronger than the equipment, a damping value associated with about ½ of yield is more appropriate. 4.7.3 Modeling Structural modeling is usually considered to be a best estimate. But in some earlier analyses, the models were very simple and torsional coupling effects were not adequately modeled. The fragility analyst must make a judgment as to the adequacy of the model. If the model is in question, it should be redone or modified to an extent that the fragility analyst considers it to be a best estimate representation. The current trend is to make very detailed finite element models as opposed to the more simplified stick models used in earlier design analyses. With modern computers, the more detailed models can be utilized, however, using an overly complex model does not necessarily guarantee better results. The UHS provided in EPRI (1989) and USNRC (1994) for IPEEE for central and eastern US sites were characterized by ground motion spectra with their peaks at high frequency. Some of the earlier models of US NPP structures were simplified stick models and in cases of lower frequency steel structures, the models would not properly capture the response at high frequencies. In these cases, the models may be acceptable for developing structural loads, governed by the low frequency portion of the UHS, but would not be appropriate for developing floor response spectra to define demand for higher frequency equipment with sensitive devices such a relays. The fragility analyst always has to deal with making best estimate judgments and the uncertainty in these judgments. However, if a Capability Category 2 analysis is to be conducted, it is likely to require some improvements in structural models of older NPPs. Uncertainty in the response of structures due to modeling results from uncertainty in frequency, uncertainty in mode shapes and for some models, torsional coupling. EPRI TR-103959 provides guidance on the uncertainty resulting from these three variables that constitute the variability resulting from modeling. 4.7.4 Mode Combination This variable is applicable to all response spectra and mode superposition time history analyses. Typically, modal responses have been combined by the SRSS rule with modifications for closely spaced modes. This is considered to be median centered. If the results of an existing analysis are being used and modes were combined by other methods, then the fragility analyst needs to make an assessment of any conservatism that may result from such a combination. EPRI TR103959 provides guidance on the range of variability associated with simple two mode models to multi-mode models. 4-16
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4.7.5 Earthquake Component Combination Current design criteria in RG 1.92 (USNRC, 1978) require that the responses to three orthogonal directions of input be combined by the SRSS rule. This is interpreted to be the combination of the end item of interest by SRSS such as stress, bolt force, etc. Often in design analyses, the analyst has combined three orthogonal forces or accelerations by SRSS to result in a vector, which implies that the three components are in phase. This is conservative and is not consistent with the intent of RG 1.92. SRSS combination of the end item of interest is considered to be median centered. Alternatively, Newmark (USNRC, 1977) recommends a simpler 100%, 40%, 40% rule as being median centered. In this combination, 100% of the dominant direction load or stress is combined arithmetically with 40% of the load or response in the other two orthogonal directions. The two criteria result in close to the same answer. The advantage of the 100-40-40 rule is that accelerations, loads or resulting stresses can be combined using the rule without altering the final end item of interest. Many fragility analysts use the 100-40-40 rule in rederiving median centered responses. Earlier NPPs often combined the worst direction horizontal response by absolute sum with the vertical response. Depending upon the shape of the structure, this could be conservative or nonconservative relative to SRSS or the 100-40-40 rule. In these cases, use of existing analysis results requires the fragility analyst to make an assessment of the degree of conservatism or nonconservatism to determine the earthquake component combination factor. Having all three components in phase is considered to be an extremely low probability event and is typically considered to be a –3 log standard deviation condition. Consequently, the random variability associated with combination of earthquake components is usually small. As noted in EPRI TR-103959, the earthquake component combination factor and variability should not be double counted when deriving fragility of equipment. It is usually examined in developing the equipment response factors and is deleted from the structural response factor as it is applied to developing equipment fragility. 4.7.6 Foundation-Structure Interaction This general variable, like the modeling variable, consists of several parts; soil structure interaction (SSI) modeling, vertical spatial variation of ground motion (deconvolution with depth) and ground motion incoherence (GMI). GMI reflects the fact that high frequency seismic waves cancel each other across the foundation/soil interface, thus do not excite the foundation uniformly along its entire surface. GMI only effects the high frequency response of structures, thus is only applicable to stiff structures on rock foundations. The vertical spatial variation of ground motion applicable for soil sites is a measure of the reduction of the effective input motion defined at the surface to a structure foundation below the ground surface. The variability of response due to foundation-structure interaction is really part of the overall structural modeling but is typically evaluated separately in SPRA fragility development. Using the separation of variables approach is perfectly valid, however, the fragility analyst must be sure that the uncertainties associated with frequency and mode shape in the modeling factor are not dominated by SSI effects and then counted again in developing uncertainty in SSI. The 4-17
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Standard, EPRI TR-103959 and EPRI NP-6041 all strongly recommend that a new SSI analysis be conducted if the UHS is significantly different in shape than the design spectrum or if the SSI modeling is not state of the art. The details of deconvolution of surface motion to the structure foundation and the modeling of the soil and foundation interface is adequately covered on ASCE 4 and EPRI NP-6041. In the Section 3.1.3 discussion of the NRC comments on IPEEE results, it was noted by the NRC that the deconvolution analysis often produced higher reduction in free field motion from the ground surface to the base mat than would be permissible in the design process. The details of this comment are unknown or whether it applied to SPRA analysis or SMA analysis. Design analyses prior to 1989, which is the case for all US NPPs, were severely restricted on deconvolution. The Standard Review Plan (USNRC, 1989) now allows a more realistic deconvolution, and restricts the reduction of input motion at the foundation to 60% of the free surface motion. EPRI TR-103959 suggests that if the deconvolution analysis predicts a larger reduction, it should not be restricted when evaluating median response for an SPRA. The guidance in ASCE-4 and EPRI NP-6041 should be followed for determining the degree of reduction of free surface motion at the foundation. Restrictions on the degree of reduction should not be applied for SPRA median response analysis. 4.7.7 High Frequency Effect In EPRI TR 102470 (EPRI, 1993), It is shown that even the smallest amount of ductility in equipment will effectively reduce the response to high frequency input motion. Rather than develop ductility factors for equipment that are variable with frequency, it was determined that the high frequency portion of the ground motion spectrum can be reduced before generating floor response spectra to account for this frequency dependent ductility factor. This is applicable to most equipment but not necessarily for relays, consequently, it was not a common practice for IPEEE. An example of a variation of this method has been conducted for a stiff structure founded on rock. Appendix B shows how existing floor spectra were scaled downward in the high frequency regime using the eigensolution of the structure and random vibration theory. In this example, the existing floor response spectra were first scaled to reflect a reduction in the high frequency portion of ground motion input due to Ground Motion Incoherence. In the next step, the GMI reduced floor response spectra were again scaled to account for reduction in response due to a minimum amount of ductility in equipment. In this case, the relay evaluations were based on the first scaling for GMI and other equipment was evaluated based upon the double scaling. If the eigensolution is available for the structural model used to develop floor response spectra, this process can be carried out efficiently in a spread sheet format. Otherwise new analyses using existing models may be an easier solution.
4.8
Probabilistic Response
Probabilistic response is required for Capability Category 3 SPRA. It may also be conducted for Capability Categories 1 and 2 and was conducted for several IPEEE studies. When probabilistic response analysis is conducted for the development of response spectra or structural loads, all important variables that affect the structural response are included. Typically, probabilistic analysis has been conducted using the SMACS computer code (USNRC, 1981). SMACS is 4-18
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based on a Latin Hypercube stratified sampling simulation process that requires significantly fewer simulations (about 30) than a Monte Carlo process. In this approach, the variables that affect response are assumed to be lognormally distributed and the probability distribution of the variables is broken up into equal parts, equal to the number of simulations. Combinations of each variable are randomly selected for inclusion in an analysis. Once a value of a variable is selected, it is not used again. In this manner it is assured that the 30 or so simulations include the total distribution defined for each variable. The time history results for each simulation are used to develop response spectra. Statistics are then applied to the resulting response spectra in order th to define median and 84 percentile response spectra. The variation in spectral shape is simulated by utilizing 30 scaled natural and synthetic time histories with median and 84th percentile response spectra ordinates that match the median and 84th percentile UHS ground motion spectra. In developing the time histories, the UHS may be first modified to incorporate GMI effects and high frequency spectral reduction to account for limited ductility of components. However, if relays are to be included in the evaluation, this second reduction is best done for non relay evaluation on the final probabilistic floor response spectra using methods in Appendix B. Otherwise, the 30 simulation analyses would have to be conducted for two cases, relays and non-relays. Other variables included in the probabilistic analysis are structural stiffness, structural damping, soil stiffness and soil damping. USNRC (1981) provides the background for the SMACS computer program and the typical ranges of the variables affecting structural response. The original studies in the SSMRP program (USNRC, 1981) comparing probabilistic response analysis using SMACS to design analysis conducted in accordance with regulatory requirements, demonstrated very large margins in typical design analyses, particularly for soil sites. With subsequent changes made to the Standard Review Plan (USNRC, 1989), much of the conservatism was removed from the structural response analysis requirements. In FOAKE (1993) the degree of conservatism remaining in the current USNRC design analysis practice was examined. In that study, three typical NPP models were evaluated for varying foundation-soil conditions. The models used in the study were a PWR Reactor Building, a BWR Reactor Building and a PWR Auxiliary Building. The three models were evaluated for an assumed fixed base rock site, a medium soil site (Vs = 1000 fps) and a soft soil site (Vs = 500 fps). The structures were embedded for the soil cases plus a surface founded case was included for the PWR Reactor Building. Spectra developed for design analysis in accordance with current regulatory criteria were compared to spectra developed probabilistically. In this study, the 30 time histories used for the simulations had a distribution on the free field response spectra such th that the 84 percentile spectrum matched the RG 1.60 spectrum. Resulting 84th percentile response spectra were compared to the design response spectra. The following conclusions regarding the conservatism in design requirements were made. 1. The response spectra produced from design analysis were always conservative relative to 84th percentile probabilistic spectra. 2. The minimum degree of conservatism was for the cases of structures founded on rock. The factor of conservatism was 1.1 or greater. The greatest degree of conservatism was for the soft soil cases with factors as high as 2.0. 4-19
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3. The taller reactor building structures resulted in more conservatism than the shorter, more squat, auxiliary building model. 4. The degree of conservatism increased with building elevation. The conclusion from this study is that there may be a lot of conservatism in response of structures founded on soft soil that is not captured in SPRA when so called median centered deterministic analysis is conducted. In EPRI TR-103959 it is recognized that probabilistic results typically produce lower response than so called median centered deterministic results. A Demand Reduction Factor, DR, is suggested to have a median value of 0.92. This would correspond closely to the conclusions from the study described above for rock sites but is likely very conservative for soil sites. In Reed et. al. (1994) a simplified approach to developing probabilistic spectra is proposed that required only two independent structural response analyses with two different damping levels instead of multiple simulations. Resulting mean in-structure spectra from the simplified approach are shown to be very close to results from a Latin Hypercube simulation. The model used in the study was a simplified six mass fixed base model and most of the response is in a single fundamental frequency mode. The simplified probabilistic approach results in a significant reduction of the peak of the in-structure spectra as compare to a single deterministic median centered analysis. This approach appears to develop more realistic in-structure spectra for SPRA than a deterministic best estimate approach. It is not clear how the results would compare for a soil site since the reduction in response is more complex than in a fixed base model with increased damping. As noted In the FOAKE study above, for soft soil sites, the difference between probabilistic spectra and spectra from a so-called median centered deterministic analysis is quite large and can be as much as a factor of 2 at high elevations in tall structures. The conclusion at this point is that conducting probabilistic response for soil sites can result in a significant reduction in response. If there is a mix of structures, the reductions can vary significantly. Consequently, if components that are significant contributors to the seismic risk are located in these different structures, the difference in demand between probabilistic spectra and deterministic spectra could alter the conclusions as to the more significant contributors to risk. The computed CDF would also be quite different. Rock sites would not be nearly as sensitive and the standard method of scaling design results or conducting a simplified probabilistic response as described in Reed et al. (1994) should not pose the question of whether structural response analytical methods can alter the ranking of dominant contributors.
4.9
Equipment Response and Capacity
For Capability Category 1, the standard allows generic data to be used if it is demonstrated to be conservative. Capability Category 2 required that fragilities be based upon plant specific data and allows generic data to be used for screening if conservative. Capability Category 3 requires that fragilities be developed from plant specific data and to “ASSURE that they are realistic.” It also required that fragilities be developed as a function of local response and to “DERIVE the joint probability distribution of the seismic capacities of different components.”
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
EPRI (1994) provides the methodology for developing the capacity and response of equipment designed by analysis or qualified by test. Methodology is also provided for deriving fragilities from Generic Equipment Ruggedness Spectra (GERS). The methodology provided complies with the requirements of the Standard for Capability Categories 1 and 2 and is generally applicable to Capability Category 3 as long as the seismic hazard is defined at the equipment/structure interface rather than at the ground. Development of equipment and subsystem fragilities from different sources of information can take on many forms. It is not practical to develop specific fragilities for all components to be addressed in the risk model. Therefore, a sequence of screening out high ruggedness components, derivation of generic fragilities for different classes or types of components and use of plant specific design documents will optimize the process and assure that screening and generic fragilities will have minimal impact on the risk results. As discussed in Section 3.1.2 and 3.2, the systems analyst should set targets for fragilities of elements that can be screened out or that will be represented by surrogate elements. This is an important initial step so that the fragility analyst does not assume that screening at some moderate level defined by the plant design requirements, EPRI screening tables (EPRI, 1991) or the SQUG Reference Spectrum (SQUG, 1991) will be acceptable in the final risk assessment. Often these levels of screening are adequate. However, before the fragility analyst begins the sequential process of screening and development of plant specific fragilities, some targets should be set by the systems analyst. 4.9.1 Initial Prescreening Using Licensing Criteria The general approach to meeting the requirements for all three levels is to make use of the design and qualification information as much a possible. For non A-46 plants, an initial screening can be done based upon the licensing criteria used for qualification of equipment and subsystems. The industry standards and regulatory requirements for seismic qualification have variable safety margin (Campbell, 1993). Generic fragilities can often be developed for different equipment and subsystem types based upon the licensing basis design and qualification criteria. These generic fragilities may demonstrate capacity above a predetermined screening target. If this initial generic approach using design and qualification criteria does not produce fragilities that are above a predetermined screening target, then the fragility analyst knows that some individual fragilities for governing cases are required. The fragility analyst should first determine what margin between design demand and design capacity is necessary to result in a fragility that meets predetermined screening levels. Then a quick review of qualification information can target the components that fall below the margin target and focus on these components for detailed fragility development. Typical components and subsystems that fit into this category are valves, cable raceways, piping, HVAC ducting and many rigid components such as horizontal pumps and chillers. Though these fragilities are termed generic, they are based on plant specific design data and are considered to meet the intent of the Standard for development of fragilities from plant specific data. Components that meet the screening target can be represented by super elements or surrogate elements in the risk model. This initial screening/generic fragility approach is also applicable to Capability Category 3 as long as the screening level is based upon local response 4-21
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
parameters, the components failure modes are considered to be independent and the screening level is at a high enough level that the risk contribution from a generic fragility representing the screened class is very small. 4.9.2 Prescreening Using Earthquake Experience Data For A-46 plants, the documented capacity is usually for anchorage and the capacity of the equipment itself can only be represented by seismic experience data. In these cases, there are two possible capacities. One capacity is based on the anchorage capacity if it is less than the capacity of the component as determined by the SQUG GIP Reference Spectrum. The other capacity is based upon the comparison of in-structure spectra to the SQUG GIP Reference Spectrum or the more updated SEQUAL spectra (SEQUAL, 2001) for individual equipment classes. Because of the limited amount of high acceleration seismic experience data, the experience spectra such as the SQUG GIP Reference Spectrum or SEQUAL spectra are limited. Consequently, the screening threshold, thus the generic fragility that represents the screening threshold, is limited. This limit, if represented by surrogate elements in a SPRA, may be too low and the resulting risk contribution too high. One of the initial steps in a SPRA is to determine if various screening thresholds, such as the SQUG GIP Reference Spectrum will result in a low enough failure rate that this form of screening is acceptable. For most central and eastern US NPPs, the SQUG GIP screening should be sufficient to assure that seismic experience based fragilities, when included in the risk model, will not dominate seismic risk. EPRI TR-103959 does not address the development of fragility from seismic experience data. In previous SPRAs, the SQUG Reference Spectrum has been assumed to represent a HCLPF capacity, considered to be a 95% confidence level of capacity. Salmon and Kennedy (1994) postulated a probabilistic methodology based on the SQUG Reference Spectrum representing a minimum resistance level analogous to a testing level. The underlying assumptions in the derivation are: 1. There are 50 independent samples in the database for each equipment class. 2. There are no incidences of failure in the database for components that meet the caveats of SQUG (1991). 3. The database equipment was subjected to a wide range of ground motions centered about the SQUG Reference Spectrum. The demand distribution about the Reference Spectrum is assumed to be lognormal with a βD of 0.3. 4. A total βC of 0.45 is a reasonable value of the total demand and capacity uncertainty. 5. The target confidence level of the median equipment capacity was assumed to be 95%. A Latin Hypercube simulation was conducted using 50 simulations and a capacity factor of 2.35 was derived. Thus, the median capacity of a component that meets the SQUG GIP caveats was estimated to be about 2.35 times the SQUG Reference Spectrum.
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
In SEQAL (2001) a similar approach is taken for deriving a fragility from seismic experience data. In this approach, the SQUG Reference Spectrum is considered to be a median demand spectrum with a lognormal distribution. Using survival statistics, where a sample size, n, has no failures and a sample size of n+1 has one failure, the 95% confidence capacity and median capacity are derived as a function of the number of independent samples in the database. A capacity factor of 2.2 is shown for a sample size of n = 30 as opposed to 2.35 derived by Salmon and Kennedy (1994) by simulation for a sample size of n = 50. For comparison, the SEQUAL survival statistics derivation method would yield a capacity factor of 2.42 for 50 samples. Both methods are based on assumptions regarding the distribution of the demand about the Reference Spectrum and the distribution of capacity about the median value. There are some slight differences in the assumptions regarding the logarithmic standard deviation of the capacity (0.45 for the simulation and 0.4 for the survival statistics analysis) which accounts for some of the small difference in results for the two methods. Appendix C contains the survival statistics derivation of the capacity factor to define the median capacity above the SQUG Reference Spectrum and knockdown factor for determining a HCLPF (95% confidence) capacity for several sample sizes ranging from n equal 15 to n equal 60. It is show that in order to consider that the SQUG Reference Spectrum is a 95% confidence capacity (HCLPF capacity), at least 30 samples are necessary. Knockdown factors are tabulated as a function of sample size. In Appendix D, an example problem is presented where an equipment class Reference Spectrum in SEQUAL for an Instrument Cabinet is used in derivation of a fragility in an eastern US plant subjected to the EPRI UHS (EPRI, 1989). In this example problem, the sample size used in determining the weighted Reference Spectrum is 46 components, resulting in a HCLPF capacity greater than the Equipment Class Reference Spectrum. SEQUAL recommends that the SQUG Reference Spectrum be used for all equipment classes which has been a typical assumption in prior SPRAs. However, in the example problem, the actual weighted spectrum and actual number of samples are used in conjunction with Appendix C survival statistics to demonstrate the process of developing a fragility from seismic experience data. SPRAs include many non-safety components that are not qualified for seismic events. The experience based screening can also be applied to non qualified components, subject to performing the walkdown and verifying that the non-safety components meet the GIP caveats and the anchorage capacity envelops the seismic experience based capacity. 4.9.3 Prescreening using the EPRI SMA Screening Tables In EPRI (1991b), screening criteria for establishing HCLPF are provided. There are two levels of screening based on ground motion spectral acceleration, 0.8g and 1.2g. A specific ground motion response spectrum is not provided but it is implied to be a NUREG/CR-0098 median spectral shape. It is also generally assumed that since the screening level spectral acceleration is more damaging at lower frequencies, that it is applicable to higher frequency range as well. Typical central and eastern US UHS in EPRI (1991) and USNRC (1994) peak at about 25 Hz and may exhibit higher spectral acceleration at 25 Hz than the NUREG/CR-0098 median spectrum or the SQUG Bounding Spectrum anchored to 0.8g spectral acceleration. The SQUG bounding spectrum is the SQUG Reference Spectrum reduced by a factor of 1.5 to be used in comparing ground motion spectra rather than in-structure spectra. In general the interpretation 4-23
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
that the screening spectral acceleration is applicable to equipment mounted in structures regardless of the frequency of the structure is reasonable as long as the screening is not applied to cabinets and panels containing devices that are mounted in very stiff structures. EPRI (1994) provides a simple example of the derivation of a fragility for equipment screened using the EPRI screening tables. In this example, it is assumed that the equipment median capacity is twice the screening level. This is generally more conservative than the above example of screening using the SQUG Reference Spectrum where it is shown that as few as 30 samples results in a median capacity of 2.2 times the Reference Spectrum. However, since the EPRI screening criteria are generally more liberal than the SQUG GIP, the assumption of a median capacity factor of 2.0 as opposed to a higher factor that could be derived, as in Appendix C from the actual number of samples, is a reasonable comprise. Fragilities derived from the EPRI screening tables would be applicable to Capability Category 1 of the Standard and could be used in Capability Category 2 studies provided that it is shown that the resulting unconditional failure rate of the screened component is above some target set to assure very small contribution to the overall risk results. The Screening Tables would not be applicable to Capability Category 3. 4.9.4 Development of Fragilities Using Plant Specific Data The overall methodology and examples in EPRI (1994) are considered to be applicable to Capability Categories 1 and 2 of the Standard and if plant specific data is used in conjunction with probabilistic spectra, the methodology is applicable to Capability Category 3. There are always, of course, unique cases not specifically addressed. One such case is the development of fragility for components that fail in a functional mode where the qualification is by analysis. Review of design reports for equipment such as fans has shown that often, the designer does not consider a minimum safety factor for deflection of the fan relative to the housing. Thus, calculating that there is still some minimal amount of clearance during the SSE does not provide the same safety margin as say a component support that is designed not to yield. This same situation has been observed in design reports where it is shown that a systems interaction due to impact will not occur but there is no consideration of a safety factor on the impact. In general, if impact is considered to be failure, analogous to reaching the ultimate strength in a component support, then there should be an analogous margin built into the design process, such as a factor of 1.4 or 1.5. This is not always the case. In these situations, the fragility analyst must first determine the consequences of impact or the real margin beyond impact. This will determine the capacity factor relative to the demand. The rest of the fragility calculation would follow the general guidance in EPRI TR-103959. The real capacity is, in most cases, a very subjective judgments but must be addressed. If the impact is considered to be failure and there is very little margin between the capacity and demand, the resulting fragility may show up as a dominant contributor to seismic risk.
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21 Table 4-1 Correlation Of Fragility Development Elements And Requirements Of Ans Standard For External Events
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Understand the development of the seismic hazard
Defines frequency of occurrence of hazard parameter, location of hazard (bed rock/rock outcrop/surface), ground motion spectral shape and uncertainties.
Methodology is well defined in RG 1.165 and draft ANS Standard , SSHAC report. Uniform hazard spectra should be defined below 1 Hz to determine maximum amplified ground motion displacement. Very flexible systems require evaluation for displacement. Hazard provided for IPEEE was cut off below 1 Hz. Guidance is needed on what frequency to assign to pga. This affects the shape of the UHS beyond 25 Hz. Relationship between horizontal and vertical spectra needed. Clarification on whether hazard is average of two horizontal components or maximum of two horizontal components is needed.
ANS standard correlates 4 SSHAC report categories to 3 capability categories in standard. ANS standards 2.27 and 2.29 under development for seismic hazard.
ANS standard correlates 4 SSHAC report categories to 3 capability categories in standard. ANS standards 2.27 and 2.29 under development for seismic hazard.
ANS standard correlates 4 SSHAC report categories to 3 capability categories in standard. ANS standards 2.27 and 2.29 under development for seismic hazard.
Determine hazard parameter to reference fragility to (peak ground acceleration, spectral acceleration)
Spectral acceleration is preferred but requires extra work for hazard analyst. Usually pga is provided which results in greater uncertainty in the development of the structural response portion of the structure or component fragility.
Methodology is well defined in NUREG 1.165, draft ANS standards and SSHAC report for developing hazard in terms of spectral acceleration or pga. Discussion on interface with hazard analyst is provided.
Capability Categories 1, 2 and 3 recommend the use of spectral acceleration but states that the use of pga is acceptable.
Capability Categories 1, 2 and 3 recommend the use of spectral acceleration but states that the use of pga is acceptable.
Capability Categories 1, 2 and 3 recommend the use of spectral acceleration but states that the use of pga is acceptable.
Determine Seismic Response of Structures
Estimating structural response is necessary to determine loads in structural members and to develop floor response spectra as input to equipment.
HLR-FR-C1-C6 requires realistic seismic response
HLR-FR-C1-C6 requires realistic seismic response
HLR-FR-C1-C6 requires realistic seismic response
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element Develop Structural Loads
Loads for PRA hazard need to be developed for evaluation of structures.
Scale Existing Loads
Loads may be approximately scaled by comparison of design basis spectra and UHS spectra.
Single Mode Scaling
Multiple Mode Scaling
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
HLR-FR-C1-C6 requires realistic seismic response
HLR-FR-C1-C6 requires realistic seismic response
HLR-FR-C1-C6 requires realistic seismic response
Some guidance is provided in EPRI NP-6041 for single mode scaling. Additional discussion on applicability of scaling for loads and for scaling of spectra would be useful. More detail on scaling methods is provided in Appendices A and B.
HLR-FR-C3 requires JUSTIFICATION of scaling. HLR-FR-C4 would require new analysis in most cases of soil sites or sites with UHS spectral shape significantly different than design spectra.
HLR-FR-C3 requires JUSTIFICATION of scaling. HLR-FR-C4 would require new analysis in most cases of soil sites or sites with UHS spectral shape significantly different than design spectra.
Scaling is not acceptable. HLR-FR-C2 requires probabilistic analysis for Capacity Category 3.
Scaling is done at a single dominant frequency of the structure. Only applicable for similarly shaped spectra and for rock sites.
Guidance exists in EPRI NP 6041 for single mode scaling and restrictions on single mode scaling. Guidance and restrictions are adequate for single mode scaling
HLR-FR-C3 requires JUSTIFICATION of scaling. HLR-FR-C4 would require new analysis in most cases of soil sites or sites with UHS spectral shape significantly different than design spectra.
HLR-FR-C3 requires JUSTIFICATION of scaling. HLR-FR-C4 would require new analysis in most cases of soil sites or sites with UHS spectral shape significantly different than design spectra.
Scaling is not acceptable. HLR-FR-C2 requires probabilistic analysis for Capacity Category 3.
A more accurate method of scaling by utilizing mode shapes and participation factors from design analysis and scaling on a mode by mode basis. May not be practical for complex models, depending on availability of eigen solution parameters. Not addressed in EPRI NP6041 but commonly done in prior PRAs.
No guidance provided. Guidance is provided in Appendices A and B.
HLR-FR-C3 requires JUSTIFICATION of scaling. HLR-FR-C4 would require new analysis in most cases of soil sites or sites with UHS spectral shape significantly different than design spectra.
HLR-FR-C3 requires JUSTIFICATION of scaling. HLR-FR-C4 would require new analysis in most cases of soil sites or sites with UHS spectral shape significantly different than design spectra.
Scaling is not acceptable. HLR-FR-C2 requires probabilistic analysis for Capacity Category 3.
General guidance provided in EPRI NP-6041, EPRI TR103959 and reference to ASCE 4. General guidance considered adequate. Limit on deconvolution are in SRP.
HLR-FR-C1-C6 requires realistic seismic response. General requirements are outlined in HLR-FR-C1 to C6.
HLR-FR-C1-C6 requires realistic seismic response. General requirements are outlined in HLR-FR-C1 to C6.
Deterministic analysis is not allowed for Capability Category III. HLR- FR-C2 has requirements for probabilistic analysis
New Deterministic Analysis for Recommended in EPRI NPUHS 6041 for soil sites and for cases where spectra are not similar in shape.
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Applicable Methodology
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology Monte Carlo and Latin hypercube methods discussed in Chapter 4 of EPRI TR103959 but no specific reference to SMACS developed in SSMRP program. Additional guidance is provided. References to LLNL SSMRP methods using SMACS and Reed/Kennedy et. al. paper on Approximate Probabilistic response methods are discussed.
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
HLR- FR-C2 has requirements for probabilistic analysis. Applications Guide needs to provide more detail than what is in EPRI TR 103959.
HLR- FR-C2 has requirements for probabilistic analysis. Applications Guide needs to provide more detail than what is in EPRI TR 103959.
HLR- FR-C2 has requirements for probabilistic analysis. Applications Guide needs to provide more detail than what is in EPRI TR 103959.
HLR-FR-C1-C6 requires realistic seismic response. General requirements are outlined in HLR-FR-C1 to C6.
HLR-FR-C1-C6 requires realistic seismic response. General requirements are outlined in HLR-FR-C1 to C6.
Deterministic analysis is not allowed for Capability Category III. HLR- FR-C2 has requirements for probabilistic analysis
New Probabilistic Analysis for UHS
Not commonly done but results in much better definition of median response and uncertainty in structural response.
Develop Floor Response Spectra
Required for development of fragilities for equipment.
Scale Existing Spectra
Difficult if design and UHS spectral shapes are not similar. For soils sites, scaling is usually inaccurate and in all cases has more uncertainty.
Some guidance is provided in EPRI NP-6041 for single mode scaling. Additional discussion on applicability of scaling for loads and for scaling of spectra is provided in Appendices A and B.
HLR-FR-C3 requires JUSTIFICATION of scaling. HLR-FR-C4 would require new analysis in most cases of soil sites or sites with UHS spectral shape significantly different than design spectra.
HLR-FR-C3 requires JUSTIFICATION of scaling. HLR-FR-C4 would require new analysis in most cases of soil sites or sites with UHS spectral shape significantly different than design spectra.
Scaling not acceptable. HLRFR-C2 requires probabilistic analysis for Capacity Category 3.
Single mode scaling
Only reasonable if structure responds primarily in a single mode.
Guidance in EPRI Np-6041. Limited application. Current guidance and application limits are considered adequate.
HLR-FR-C3 requires JUSTIFICATION of scaling. HLR-FR-C4 would require new analysis in most cases of soil sites or sites with UHS spectral shape significantly different than design spectra.
HLR-FR-C3 requires JUSTIFICATION of scaling. HLR-FR-C4 would require new analysis in most cases of soil sites or sites with UHS spectral shape significantly different than design spectra.
Scaling not acceptable. ANS requirement FR-C2 requires probabilistic analysis for Capacity Category 3.
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Correlation of ANS Standard Capability Category 3
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Guidance is provided in Appendices A and B.
HLR-FR-C3 requires JUSTIFICATION of scaling. HLR-FR-C4 would require new analysis in most cases of soil sites or sites with UHS spectral shape significantly different than design spectra.
HLR-FR-C3 requires JUSTIFICATION of scaling. HLR-FR-C4 would require new analysis in most cases of soil sites or sites with UHS spectral shape significantly different than design spectra.
Scaling not acceptable. ANS requirement FR-C2 requires probabilistic analysis for Capacity Category 3.
New Deterministic Analysis for Recommended in EPRI NPUHS 6041 for soil sites and for cases where spectra are not similar in shape.
General guidance provided in EPRI NP-6041, EPRI TR103959 and reference to ASCE 4. General guidance considered adequate. Limits on deconvolution are in SRP.
HLR-FR-C1-C6 requires realistic seismic response. General requirements are outlined in HLR-FR-C1 to C6.
HLR-FR-C1-C6 requires realistic seismic response. General requirements are outlined in HLR-FR-C1 to C6.
Deterministic analysis is not acceptable. HLR- FR-C2 requires probabilistic analysis for Capacity Category 3.
New Probabilistic Analysis for UHS
Monte Carlo and Latin HLR-FR-C2 has requirements hypercube methods discussed for probabilistic analysis. in Chapter 4 of EPRI TR103959 but no specific reference to SMACS developed in SSMRP program. Additional guidance is provided. References to LLNL SSMRP methods using SMACS and Reed/Kennedy et. al. paper on Approximate Probabilistic response method, methods are discussed.
HLR-FR-C2 has requirements for probabilistic analysis.
HLR-FR-C2 has requirements for probabilistic analysis.
Fragility Development Description of Fragility Elements Development Element Multiple Mode Scaling
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Can be done using mode shapes and participation factors. Difficult for complex structures and without electronic files on mode shapes and participation factors. More approximate methods at soil sites have shown poor correlation to new analyses.
Not commonly done but results in much better definition of median response and uncertainty in structural response.
Applicable Methodology
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Determine screening level to define minimum surrogate element (Convolve candidate surrogate fragilities and hazard to determine unconditional probability of failure that is an acceptable screening level)
Surrogate fragilities are substituted into the fault trees to represent basic events that are screened out on the basis of meeting some minimum capacity. A single surrogate fragility is often used to represent several basic events of equal or greater capacity. In IPEEE, the use of surrogate fragilities often resulted in a large portion of the computed seismic risk being driven by the low capacity fragility of the surrogate element. Some licensees used only one surrogate element to represent all screened out SSCs. This assumes that all failures of the screened out SSCs are correlated. This can be unconservative for cases where several components appear in series (OR Gates) and have similar capacities.
Clear guidance from the systems analyst to the fragility analyst is needed to determine the screening level required to result in a surrogate fragility that has very low contribution to seismic risk. Per EPRI TR103959, a surrogate element should be introduced in each fault tree to represent basic events in the fault tree logic that have been screened out. In some cases, more than one surrogate in a fault tree is appropriate, depending upon correlation. Additional guidance is provided in Applications Guide.
The terminology "surrogate element" is not specifically addressed. Lumping of groups of components into supercomponents is addressed in HLR-SA-A-3. In HLR-SA-E-3, it is stated that "a detailed set of criteria must be developed and used to assure that this screening does not eliminate elements of the model that should have been retained. This implicitly addresses the use of surrogates but the emphasis is on elimination of risk contributing elements rather than on using superelements that have too low of a capacity. HLR- FR-B1 states that criteria in NP-6041 and NUREG/CR-4334 may be used to screen out high capacity components but cautions to CHOOSE the screening level high enough that the contribution to CDF and LERF from the screened out components is not significant.
The terminology "surrogate element" is not specifically addressed. Lumping of groups of components into supercomponents is addressed in HLR-SA-A-3. In HLR-SA-E-3, it is stated that "a detailed set of criteria must be developed and used to assure that this screening does not eliminate elements of the model that should have been retained. This implicitly addresses the use of surrogates but the emphasis is on elimination of risk contributing elements rather than on using superelements that have too low of a capacity. HLR- FR-B1 states that criteria in NP-6041 and NUREG/CR-4334 may be used to screen out high capacity components but cautions to CHOOSE the screening level high enough that the contribution to CDF and LERF from the screened out components is not significant.
HLR-FR-B1 states "SCREEN high seismic capacity components ONLY if the components' failures can be considered as fully independent of the remaining components." Current guidance in EPRI documents would not meet this requirement.
Walkdown
Important for ruggedness screening and identifying vulnerabilities due to design and construction errors and systems interactions.
Requirements in ANS Standard are met by guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Review Equipment List
Necessary to prepare for walkdown and set up interface with systems engineers. List may be revised after review to incorporate rule of box or to breakdown to subcomponents as is appropriate for fragility development.
Adequately covered in EPRI NP-6041 which is standard referenced in EPRI TR103959 and NUREG-1407.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
Determine applicable screening levels. Determine if generic fragilities based on design requirements or EPRI NP-6041 screening is adequate to assure capacity of surrogate element
Develop preliminary fragility for screening levels and convolve with hazard to calculate unconditional failure rate.
Addressed in EPRI TR103959, Chapter 5, but 1st level screen in EPRI NP-6041 often results in a surrogate fragility that is too low. Additional guidance is provided on applicability of screening tables. Appendix E provides example where EPRI screening is not adequate and an alternate screening approach is taken.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
Prepare Plant Walkdown Sequence
Coordinate with plant Adequately covered in EPRI personnel to optimize time and NP-6041 which is standard minimize exposure. referenced in EPRI TR103959 and NUREG-1407.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
Conduct walkdown screening
Determine components that can be screened at levels equal or exceeding surrogate target. Identify vulnerabilities.
Adequately covered in EPRI NP-6041 which is standard referenced in EPRI TR103959 and NUREG-1407.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
Apply EPRI NP-6041 Screening Where Applicable
EPRI NP-6041 has two screening levels. Screening can only be done if level meets surrogate target.
Adequately covered in EPRI NP-6041 which is standard referenced in EPRI TR103959 and NUREG-1407.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
Component Vulnerabilities
Identify vulnerable components.
Adequately covered in EPRI NP-6041 which is standard referenced in EPRI TR103959 and NUREG-1407.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Anchorage
Obtain information on anchorage and screen if anchorage is generically rugged.
Adequately covered in EPRI NP-6041 which is standard referenced in EPRI TR103959 and NUREG-1407.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
Systems Interactions
Identify potential systems interactions (falling, proximity, SAM, spray, flood, systematic interactions).
Adequately covered in EPRI NP-6041 which is standard referenced in EPRI TR103959 and NUREG-1407.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
Seismic/Fire Issues
Seismic induced fire, inadvertent actuation of fire suppression systems, unavailability of fire suppression.
Adequately covered in EPRI NP-6041 which is standard referenced in EPRI TR103959 and NUREG-1407.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
Documentation of Walkdown
Identification of personnel, documentation of walkdown screening criteria and walkdown findings.
Adequately covered in EPRI NP-6041 which is standard referenced in EPRI TR103959 and NUREG-1407. Additional documentation guidance in NUREG-1407.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
General requirements in HLRFR-E1 through E-5. Reference to guidance in EPRI NP-6041.
Determine Structural Capacity (Ultimate Load Analysis)
Determine the point that the calculated loads would result in the structure being unstable. Ductile behavior may exist beyond this point.
ANS Standard HLR-FR-D1 and HLR-FR-D2 require the identification of all relevant failure modes and the evaluation of fragilities for critical failure modes.
ANS Standard HLR-FR-D1 and HLR-FR-D2 require the identification of all relevant failure modes and the evaluation of fragilities for critical failure modes.
ANS Standard HLR-FR-D1 and HLR-FR-D2 require the identification of all relevant failure modes and the evaluation of fragilities for critical failure modes.
Scale Existing Linear Analysis
Easiest for screening. May General guidance on scaling not be sufficient for detailed in EPRI NP-6041 and EPRI fragility development for failure TR-103959. state.
ANS Standard HLR-FR-D1 and HLR-FR-D2 require the identification of all relevant failure modes and the evaluation of fragilities for critical failure modes.
ANS Standard HLR-FR-D1 and HLR-FR-D2 require the identification of all relevant failure modes and the evaluation of fragilities for critical failure modes.
ANS Standard HLR-FR-D1 and HLR-FR-D2 require the identification of all relevant failure modes and the evaluation of fragilities for critical failure modes.
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
New Linear Analysis
May be hand or computer analysis to address redistribution of loads of failed members to point of instability.
Adequate guidance by reference in EPRI NP-6041, EPRI TR- 103959 and ASCE 4.
ANS Standard HLR-FR-D1 and HLR-FR-D2 require the identification of all relevant failure modes and the evaluation of fragilities for critical failure modes.
ANS Standard HLR-FR-D1 and HLR-FR-D2 require the identification of all relevant failure modes and the evaluation of fragilities for critical failure modes.
ANS Standard HLR-FR-D1 and HLR-FR-D2 require the identification of all relevant failure modes and the evaluation of fragilities for critical failure modes.
New Non-Linear Analysis
Conducted only for critical cases to more accurately determine failure point and reduce uncertainty.
Some guidance in Chapter 3 of EPRI TR- 103959 using effective frequency and effective damping in simple models. Further guidance in Appendix G of EPRI NP-6041 on use of equivalent viscous damping in non-linear analysis. Guidance considered adequate for general case.
ANS Standard HLR-FR-D1 and HLR-FR-D2 require the identification of all relevant failure modes and the evaluation of fragilities for critical failure modes.
ANS Standard HLR-FR-D1 and HLR-FR-D2 require the identification of all relevant failure modes and the evaluation of fragilities for critical failure modes.
ANS Standard HLR-FR-D1 and HLR-FR-D2 require the identification of all relevant failure modes and the evaluation of fragilities for critical failure modes.
Determine Ductility Beyond Ultimate Load Capacity
General guidance given for structures in EPRI and DOE documents. Use of factors requires judgment to preclude any brittle weak link failures. Generic ductility factors given in performance goal based DOE Standard 1020.
Guidance in Chapter 3 of EPRI TR-103959 on effective frequency and effective damping, simplified non-linear models and on Newmark ductility method. Both are recommended and average of results is recommended as median value of ductility, Additional recommendations on performance goal based structural ductilities are provided in DOE Standard 1020. The DOE material is referenced in the Applications Guide.
ANS Standard requirements are general regarding capacity and include only small reference to ductility such as drift. Current guidance is adequate to meet ANS requirements.
ANS Standard requirements are general regarding capacity and include only small reference to ductility such as drift. Current guidance is adequate to meet ANS requirements.
ANS Standard requirements are general regarding capacity and include only small reference to ductility such as drift. Current guidance is adequate to meet ANS requirements.
Final Structural Capacity, Capacity Factor and Variability
Separation of variables Separation of variables ANS standard has no specific approach is used. This is adequately addressed in EPRI requirements. Existing EPRI TR 103959 is adequate. more practical than a complete TR103959. simulation process.
ANS standard has no specific requirements. Existing EPRI TR 103959 is adequate.
ANS standard has no specific requirements. Existing EPRI TR 103959 is adequate.
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element Structural Response Factor and Variability
Defines conservatism or unconservatism in structural response analysis and confidence bounds on analysis.
Spectral Shape (UHS vs. Design)
Required if scaling of spectra and loads is conducted. Factor is unity if new median centered analysis is done.
Damping (Median vs. Design)
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
HLR-FR-C1 states to "Estimate seismic response on a realistic basis using site specific earthquake response spectra."
HLR-FR-C1 states to Probabilistic response "Estimate seismic response on required. a realistic basis using site specific earthquake response spectra."
Adequately covered in EPRI TR-103959. The use of a UHS is a given parameter to the fragility analyst. Refer to the discussion on seismic hazard that addresses the ANS Standard comment on making sure that the spectral shape is sufficiently rich in low frequency.
Note to HLR-FR-C1 states that "Any UHS SHOULD be used cautiously making sure that the spectral shape is sufficiently rich in low frequency. Refers to NOTE HA-G1 for further discussion on this topic. "
Note to HLR-FR-C1 states that "Any UHS SHOULD be used cautiously making sure that the spectral shape is sufficiently rich in low frequency. Refers to NOTE HA-G1 for further discussion on this topic. "
Note to HLR-FR-C1 states that "Any UHS SHOULD be used cautiously making sure that the spectral shape is sufficiently rich in low frequency. Refers to NOTE HA-G1 for further discussion on this topic. "
Required if scaling of design response is done. New analysis should be based on median damping. The resulting damping factor is then unity.
Adequately covered in EPRI TR-103959.
No specific requirements
No specific requirements
Probabilistic response required. Variables are included in simulation.
Modeling
Modeling uncertainty must be estimated regardless if existing design analysis is utilized or new deterministic analysis is done.
Adequately covered in EPRI TR-103959.
No specific requirements
No specific requirements
Probabilistic response required. Variables are included in simulation.
Mode Shape
Uncertainty in deformed shape Adequately covered in EPRI of modes. TR-103959.
No specific requirements
No specific requirements
Probabilistic response required. Variables are included in simulation.
Frequency
Uncertainty in stiffness results Adequately covered in EPRI in uncertainty in frequency and TR-103959. response.
No specific requirements
No specific requirements
Probabilistic response required. Variables are included in simulation.
Method of Analysis
Uncertainty associated with Usually incorporated into analytical methods, particularly spectral shape factor. in treatment of soil-structure interaction.
No specific requirements. No specific requirements. No specific requirements. Refers to ASCE 4 for guidance Refers to ASCE 4 for guidance Refers to ASCE 4 for guidance
4-33
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Response Spectrum (capacity only)
Response spectrum analysis commonly used for structural loads. Results are conservative since maximum components of force are reported instead of coincidental forces. SSI is simplified.
Analysis methods adequately described in ASCE 4. EPRI TR-103959 adequately addresses uncertainties in methods.
No specific requirements. No specific requirements. Probabilistic response Refers to ASCE 4 for guidance Refers to ASCE 4 for guidance required. Variables are included in simulation.
Time History (development of response spectra or loads for capacity)
Used primarily for development of in-structure spectra. Can be beneficial in reducing uncertainty and conservatism in calculation of structural loads.
Analysis methods adequately described in ASCE 4. EPRI TR-103959 adequately addresses uncertainties in methods.
No specific requirements. No specific requirements. Probabilistic response Refers to ASCE 4 for guidance Refers to ASCE 4 for guidance required. Variables are included in simulation.
Mode Combination
Applies to response spectrum analysis and mode superposition time history analysis.
Adequately addressed in EPRI No specific requirements. TR-103959.
No specific requirements.
Probabilistic response required. Variables are included in simulation.
Earthquake Component Combination
Industry standard of SRSS is considered median centered. Random variability depends on structural geometry (rectangular vs. circular) and sensitivity to vertical acceleration.
Adequately addressed in EPRI No specific requirements. TR-103959.
No specific requirements.
Probabilistic response required. Variables are included in simulation.
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Foundation Structure Interaction
Includes soil-structure interaction vertical spatial variation of ground motion and ground motion incoherence. Soil-structure interaction parameters must be addressed as part of modeling (soil stiffness, soil damping, deconvolution. New deterministic analysis should vary soil properties. Requirements are in ANS standard and described in EPRI NP-6041 and in EPRI TR-103959. New probabilistic analysis should have realistic ranges of variables.
Detailed deterministic guidance provided in EPRI NP-6041 and methods to estimate uncertainty in deterministic analyses are provided in EPRI TR-103959. Soil-structure interaction is typically treated as a separate variable but is really a part of modeling. Emphasis in EPRI documents is on new analyses using modern methods. Most existing NPPs have outdated SSI models and scaling of results is not recommended. Ground motion incoherence is usually only applicable to rock foundations. It is considered separately in this document with an example spectra reduction in Appendix B.
HLR-FR-C6 requires variations in soil stiffness and provides guidance on using median soil properties defined at strain levels corresponding to input seismic motions that dominate core damage. Refers to ASCE 4 for guidance
HLR-FR-C6 requires Probabilistic response variations in soil stiffness and required. Variables are included in simulation. provides guidance on using median soil properties defined at strain levels corresponding to input seismic motions that dominate core damage. Refers to ASCE 4 for guidance
Ground Motion incoherence
Can result in reduction of effective input motion on large stiff structures.
Addressed in EPRI TR103959.
No specific requirements.
No specific requirements.
Probabilistic response required. Variables are included in simulation.
Adequately addressed in EPRI No specific requirements. TR-102470. Can be useful for some sites with stiff structures and high frequency input motion. Example spectra reduction given in Appendix B.
No specific requirements.
Probabilistic response is required. Reduction in ground motion spectrum iat high frequency should be incorporated into probabilistic response analysis.
High Frequency Effects (Effect Can result in reduction in high on Response Spectra) frequency portion of instructure response spectra for high frequency input motion.
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element Determine Capacity of Components
Develop the ultimate capacity of component for function or structural failure.
Develop Surrogate fragilities based on screening levels.
Surrogate fragilities are based on highest screening level from walkdown or review of equipment qualification.
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Applicable Methodology
Guidance in Chapter 5 of EPRI TR-103959 on development of surrogate element from screening. Generally more than one level of surrogate element should be developed depending on what levels the components can be screened, considering component type, walkdown screening and reviews of equipment qualification documentation screening is discussed in Applications Guide and examples are given in Appendices D and E for development of generic fragilities from seismic experience data and from design criteria.
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
HLR-FR-F1 and F2 require fragilities to be based on plant specific data supplemented as appropriate by earthquake experience data, fragility test data and generic qualification test data. For all SSCs that appear in the dominant accident cutsets, ASSURE that they have site-specific fragility parameters which are derived based on plantspecific information. Exception: JUSTIFY the use of generic fragility for any SSC as being appropriate for the plant.
HLR-FR-F1 and F2 require fragilities to be based on plant specific data supplemented as appropriate by earthquake experience data, fragility test data and generic qualification test data. For all SSCs that appear in the dominant accident cutsets, ASSURE that they have site-specific fragility parameters which are derived based on plantspecific information. Exception: JUSTIFY the use of generic fragility for any SSC as being appropriate for the plant.
HLR-FR-F1 and F2 require fragilities to be based on plant specific data supplemented as appropriate by earthquake experience data, fragility test data and generic qualification test data. For all SSCs that appear in the dominant accident cutsets, ASSURE that they have site-specific fragility parameters which are derived based on plantspecific information. Exception: JUSTIFY the use of generic fragility for any SSC as being appropriate for the plant.
HLR SA-A3 refers to grouping of elements into a super element. Surrogate fragility can be a superelement. HLRSA-E3 cautions on elimination of SSCs from the model on the basis of screening. This implies representation by a surrogate fragility. HLR-FRB1 cautions against screening at too low of a level that would result in a significant contribution to CDF or LERF from the screened out components.
HLR SA-A3 refers to grouping of elements into a super element. Surrogate fragility can be a superelement. HLRSA-E3 cautions on elimination of SSCs from the model on the basis of screening. This implies representation by a surrogate fragility. HLR-FRB1 cautions against screening at too low of a level that would result in a significant contribution to CDF or LERF from the screened out components.
HLR-FR-B1 states to "SCREEN high-seismiccapacity components ONLY if the components' failures can be considered as fully independent of the remaining components.
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Walkdown Screening
Two screening levels in EPRI NP-6041 can define surrogate fragilities.
Guidance in Chapter 5 of EPRI TR-103959 on development of surrogate element from screening. Generally more than one level of surrogate element should be developed depending on what levels the components can be screened, considering component type, walkdown screening and reviews of equipment qualification documentation screening is discussed in Applications Guide and examples are given in Appendices D and E for development of generic fragilities from seismic experience data and from design criteria
HLR SA-A3 refers to grouping of elements into a super element. Surrogate fragility can be a superelement. HLRSA-E3 cautions on elimination of SSCs from the model on the basis of screening. This implies representation by a surrogate fragility. HLR-FRB1 cautions against screening at too low of a level that would result in a significant contribution to CDF or LERF from the screened out components.
HLR SA-A3 refers to grouping of elements into a super element. Surrogate fragility can be a superelement. HLRSA-E3 cautions on elimination of SSCs from the model on the basis of screening. This implies representation by a surrogate fragility. HLR-FRB1 cautions against screening at too low of a level that would result in a significant contribution to CDF or LERF from the screened out components.
HLR-FR-B1 states to "SCREEN high-seismiccapacity components ONLY if the components' failures can be considered as fully independent of the remaining components.
Screening from Review of Qualification Reports
Review of equipment qualification can result in screening at levels above or below the target surrogate fragility.
Guidance in Chapter 5 of EPRI TR-103959 on development of surrogate element from screening. Generally more than one level of surrogate element should be developed depending on what levels the components can be screened, considering component type, walkdown screening and reviews of equipment qualification documentation screening is discussed in Applications Guide and examples are given in Appendices D and E for development of generic fragilities from seismic experience data and from design criteria
HLR SA-A3 refers to grouping of elements into a super element. Surrogate fragility can be a superelement. HLRSA-E3 cautions on elimination of SSCs from the model on the basis of screening. This implies representation by a surrogate fragility. HLR-FRB1 cautions against screening at too low of a level that would result in a significant contribution to CDF or LERF from the screened out component.
HLR SA-A3 refers to grouping of elements into a super element. Surrogate fragility can be a superelement. HLRSA-E3 cautions on elimination of SSCs from the model on the basis of screening. This implies representation by a surrogate fragility. HLR-FRB1 cautions against screening at too low of a level that would result in a significant contribution to CDF or LERF from the screened out component.
HLR-FR-B1 states to "SCREEN high-seismiccapacity components ONLY if the components' failures can be considered as fully independent of the remaining components.
4-37
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Develop Limit State Capacities Capacity is based on the by Analysis lowest capacity failure mode.
General guidance in EPRI TR103959 for common modes of failure such as anchor bolts and welds. Further guidance would be useful but due to the many failure modes and different types of equipment, it is not practical. General guidance in EPRI TR-103959 is considered adequate for most fragilities.
HLR-FR-A2 allows generic data for development of fragilities but must be demonstrated to be conservative.
HLR-FA-A2 requires that fragilities be based on plant specific data. Generic data may be used for screening if conservative.
HLR -FA-A2 requires that fragilities be developed from plant specific data and to "ASSURE that they are realistic." HLR-FR-F1 also requires that fragilities be developed as a function of local response and to "DERIVE the joint probability distribution of the seismic capacities of different components"
Scale from Qualification Analysis
Most common for plants with well documented seismic qualification. A-46 plants generally only addressed anchorage and the equipment capacity is defined by the SQUG screening criteria (SQUG Bounding spectrum or 1.5 times the SQUG bounding spectrum).
General guidance in EPRI TR103959 for common modes of failure such as anchor bolts and welds. Further guidance would be useful but due to the many failure modes and different types of equipment, it is not practical. General guidance in EPRI TR-103959 is considered adequate for most fragilities.
HLR-FR-A2 allows generic data for development of fragilities but must be demonstrated to be conservative.
HLR-FA-A2 requires that fragilities be based on plant specific data. Generic data may be used for screening if conservative.
HLR -FA-A2 requires that fragilities be developed from plant specific data and to "ASSURE that they are realistic." HLR-FR-F1 also requires that fragilities be developed as a function of local response and to "DERIVE the joint probability distribution of the seismic capacities of different components"
Conduct New Analysis
Sometimes required for equipment with incomplete or no analysis. The amount of analysis depends upon the relationship of the target surrogate fragility and the screening levels achieved.
General guidance in EPRI TR103959 for common modes of failure such as anchor bolts and welds. Further guidance would be useful but due to the many failure modes and different types of equipment, it is not practical. General guidance in EPRI TR-103959 is considered adequate for most fragilities.
HLR-FR-A2 allows generic data for development of fragilities but must be demonstrated to be conservative.
HLR-FA-A2 requires that fragilities be based on plant specific data. Generic data may be used for screening if conservative.
HLR -FA-A2 requires that fragilities be developed from plant specific data and to "ASSURE that they are realistic." HLR-FR-F1 also requires that fragilities be developed as a function of local response and to "DERIVE the joint probability distribution of the seismic capacities of different components"
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Develop Ductility if Applicable
Generally applicable to flexible equipment with structural failure as the governing failure mode.
Limited guidance provided in EPRI TR-103959. EPRI NP6041 provides limited guidance on ductility associated with a HCLPF. Guidance on effective frequency and effective damping for non-linear response in EPRI TR-103959 and NUREG/CR-3805. Further guidance beyond general guidance given is difficult due to the numerous configurations of equipment.
No requirement on equipment ductility.
No requirement on equipment ductility.
No requirement on equipment ductility.
Develop Fragilities from Test Data
Qualification is commonly done by shake table testing to required response spectra.
Guidance provided in EPRI TR-103959. Guidance is result of subjective opinion of testing community. Guidance considered adequate.
No specific requirements on developing fragility from test data.
No specific requirements on developing fragility from test data.
No specific requirements on developing fragility from test data.
Specific Qualification Tests
Single test usually has limited intended safety margin, and one test is statistically insignificant, therefore HCLPF is estimated to be less than test level.
Guidance provided in EPRI TR-103959. Guidance is result of subjective opinion of testing community. Guidance considered adequate.
No specific requirements on developing fragility from test data.
No specific requirements on developing fragility from test data.
No specific requirements on developing fragility from test data.
Generic Equipment GERS are available for vendor Guidance provided in EPRI Ruggedness Spectra (GERS) and model specific equipment. TR-103959. Guidance is Limited application for fragility. result of subjective opinion of testing community. Guidance considered adequate.
No specific requirements on developing fragility from GERS.
No specific requirements on developing fragility from GERS.
No specific requirements on developing fragility from GERS.
Guidance is not provided in HlR-FA-A2 allows fragilities EPRI documents. Example from earthquake experience provided in Appendices C & D. for Capability Category I
HLR-FA-A2 restricts seismic experience to screening.
Fragility must be based on plant specific data.
Develop Fragilities From Earthquake Experience
Similar argument to qualification testing. Earthquake experience is equivalent to multiple tests of generic equipment.
4-39
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
No specific requirements on development of fragilities from similarity.
No specific requirements on development of fragilities from similarity. Plant specific data is required.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
Correlation to ANS Standard Capability Category 1
Develop Fragilities From Similarity to Other Components
This is a generic derivation commonly used for groups of similar components and modeled as supercomponents or surrogate elements in the fault trees.
Develop Equipment Response Factors for Fragilities Developed by Analysis
Defines the conservatism or unconservatism in the response used to develop equipment capacity factors.
Qualification Method (Static Analysis, Response Spectrum Analysis)
Qualification analysis methods often incorporate conservative approximations of equipment response that must be quantified.
Effect of inelastic response of structure on in-structure spectra.
Generally not addressed due Addressed in chapter 3 of to fact that weakest equipment EPRI TR-103959 by capacity is less than yield level references to literature. in structure. Important in some cases to address.
No requirements in standard.
No requirements in standard.
No requirements in standard.
Spectral Shape (Design Spectra Vs UHS Spectra and Peak Broadening and Smoothing)
Difference in calculated response between design spectra and UHS spectra must be quantified.
Guidance is provided in EPRI TR-103959. Further guidance in EPRI NP-6041. Existing guidance is adequate.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
Damping (Median Damping Vs Difference in response Design Damping) between design damping and median damping must be quantified.
Guidance is provided in EPRI TR-103959. Further guidance in EPRI NP-6041. Existing guidance is adequate.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
Modeling
Guidance is provided in EPRI TR-103959. Further guidance in EPRI NP-6041. Existing guidance is adequate.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
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Modeling is usually considered to be median centered but uncertainty results from calculated mode shapes and frequencies.
Not discussed in specific detail No specific requirements on but implied in EPRI development of fragilities from documents. This is commonly similarity. done by SPRA practitioners.
Guidance is provided in EPRI TR-103959. Further guidance in EPRI NP-6041. Existing guidance is adequate.
EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Mode Shape
Uncertainty results from model Guidance is provided in EPRI simplifications and boundary TR-103959. Further guidance condition approximations. in EPRI NP-6041. Existing guidance is adequate.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
Frequency
Uncertainty results from model and boundary condition approximations and weight estimations.
Guidance is provided in EPRI TR-103959. Further guidance in EPRI NP-6041. Existing guidance is adequate.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
Mode Combination
Usually by SRSS. Statistical Guidance is provided in EPRI uncertainty must be quantified. TR-103959. Further guidance in EPRI NP-6041. Existing guidance is adequate.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
Earthquake Component Combination
Usually by SRSS. SRSS considered to be median. Statistical uncertainty must be quantified. If ECC combination is not by SRSS, difference between combination method and median response must be quantified.
Guidance is provided in EPRI TR-103959. Further guidance in EPRI NP-6041. Existing guidance is adequate.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
Equipment Response Factor Developed from individual factors for each response and Variability variable and randomness and uncertainty for variables. Separation of variables approach commonly used.
Guidance is provided in EPRI TR-103959. Further guidance in EPRI NP-6041. Existing guidance is adequate.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
General requirements in HlRFA-C1 through C-6 apply primarily to structural response. Equipment response could be implied.
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element Develop Structural Response Factor for Equipment
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Must be derived from parameters determined for structural response in development of in-structure response spectra. (Spectral shape, damping, modeling including SSI modeling, mode combination, ground motion incoherence, high frequency effects). Defines conservatism or unconservatism in development of response spectra used to develop equipment capacity and response factors. Separation of variables approach is usually used to develop final factor from individual factors for each important variable. Probabilistic response should have factor of unity and variability is defined by statics of response (spectral acceleration vs frequency).
Guidance is provided in EPRI TR-103959. Further guidance in EPRI NP-6041. Existing guidance is adequate.
No specific requirements in Standard
No specific requirements in Standard
No specific requirements in Standard
Current practice is to treat dual train components as correlated and components within a train or in other systems as uncorrelated. All components are partially correlated due to the fact that they experience the same earthquake. Many also have correlated failure modes such as pull out of expansion anchors.
No guidance in EPRI documents. Guidance is added to the extent that it affects the fragility analyst. This is primarily a systems modeling issue.
ANS Guide requirement SAB3 says to PERFORM an analysis of seismic-caused dependencies and correlation in a way so that any screening of SSCs appropriately ACCOUNTS FOR those dependencies and correlations. This requires guidance to the fragility analyst to define correlation parameter or coefficients in the fragility description.
ANS Guide requirement SAB3 says to PERFORM an analysis of seismic-caused dependencies and correlation in a way so that any screening of SSCs appropriately ACCOUNTS FOR those dependencies and correlations. This requires guidance to the fragility analyst to define correlation parameter or coefficients in the fragility description.
ANS Guide requirement SAB3 says to PERFORM an analysis of seismic-caused dependencies and correlation in a way so that any screening of SSCs appropriately ACCOUNTS FOR those dependencies and correlations. USE plantspecific dependencies and correlation values throughout. This requires guidance to the fragility analyst to define correlation parameter or coefficients in the fragility description.
Special Topics Correlation of Basic Events
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Develop Fragility for Buried Tanks
Generally screened out for low seismicity sites. Tank design must be examined and analyst must confirm that screening level meets target surrogate fragility.
Develop Fragility for Buried Pipe Lines
Generally screened out for low Criteria for computing strains seismicity sites. Piping design in buried pipe is provided in must be examined and analyst Appendix C of EPRI NP-6041 must confirm that screening level meets target surrogate fragility.
Develop Fragilities for Items Affected by Soil Settlement Due to Ground Shaking or Liquefaction
Not commonly done. Ground settlement can occur without liquefaction. Ground settlement can affect buried pipes for service water and diesel fuel.
No guidance in EPRI documents. Special case requiring case specific criteria and analysis.
Develop Fragilities for Retaining Walls
Correlation to ANS Standard Capability Category 1
Criteria for pressure on walls No specific requirements in is developed in Appendix C of Standard EPRI NP-6041. Can be used to define approximate external pressure load on buried tanks.
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
No specific requirements in Standard
No specific requirements in Standard
No specific requirements in Standard
No specific requirements in Standard
No specific requirements in Standard
No specific requirements in Standard
No specific requirements in Standard
No specific requirements in Standard
Not a common issue but must be addressed if failure of wall can result in failure of essential equipment.
Criteria in Appendix C of EPRI No specific requirements in Standard NP-6041 for pressure on retaining walls.
No specific requirements in Standard
No specific requirements in Standard
Develop Fragilities for Dams
Not a common issue but must be addressed if failure of upstream or down stream can result in flooding or loss of ultimate heat sink.
No guidance in EPRI documents. Some guidance in Appendix C of EPRI NP6041 on slope stability. Usually requires expert in dams to evaluate.
No specific requirements in Standard
No specific requirements in Standard
No specific requirements in Standard
Develop Fragilities for HVAC
Usually not much attention paid to HVAC ducting in seismic PRA. Focus is on supports.
No guidance in EPRI TR103969. Same guidance in EPRI NP-6041. Failure mode is structural and general guidance in EPRI documents is applicable.
No specific requirements in Standard
No specific requirements in Standard
No specific requirements in Standard
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Peer Review
Independent review of methodology, modeling and results is required to assure assumptions and correct application of methods.
Requirements in NUREG1407. NUREG 1407 is referenced.
Section 5 of Standard refers to applicable Peer Review Requirements in ASME PRA Standard plus adds additional requirements for Seismic PRA, Seismic Margins and PRA of Other External Events.
Section 5 of Standard refers to applicable Peer Review Requirements in ASME PRA Standard plus adds additional requirements for Seismic PRA, Seismic Margins and PRA of Other External Events.
Section 5 of Standard refers to applicable Peer Review Requirements in ASME PRA Standard plus adds additional requirements for Seismic PRA, Seismic Margins and PRA of Other External Events.
Reporting
Proper documentation is necessary for reviews and retention of records for future risk informed applications.
Subject is addressed in TR 103959. Reporting is not addressed. Guidance on reporting is contained in NUREG- 1407 and EPRI NP6041. Guidance is adequate.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Parameter that fragility is indexed to.
Clear explanation is required of the parameter that the fragility is indexed to. Index can be pga or Sa over a frequency range of interest defined at bedrock, soil surface or rock outcrop. Fragility must reflect the definition of hazard to be use in quantification of unconditional probability of failure including whether the hazard is the average of two horizontal components the peak horizontal component.
Subject is addressed in TR 103959. Reporting is not addressed. Guidance on reporting is contained in NUREG- 1407 and EPRI NP6041. Guidance is adequate.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Failure Mode (Functional, Recoverable or Unrecoverable, Pressure Boundary Failure, Leak, Break, etc.
Clear guidance must be provided to the systems engineers as to the failure mode. Different failure modes may have different consequences in the risk model.
Subject is addressed in TR 103959. Reporting is not addressed. Guidance on reporting is contained in NUREG- 1407 and EPRI NP6041. Guidance is adequate.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Methodologies used for development of fragilities
Different methods within generally accepted practice may be used and must be clearly documented.
Subject is addressed in TR 103959. Reporting is not addressed. Guidance on reporting is contained in NUREG- 1407 and EPRI NP6041. Guidance is adequate.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Walkdown team, walkdown process and results
The walkdown team, process, screening criteria and screening results must be documented.
Subject is addressed in TR 103959. Reporting is not addressed. Guidance on reporting is contained in NUREG- 1407 and EPRI NP6041. Guidance is adequate.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
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EPRI Proprietary Licensed Material Development of Fragilities in Accordance with ANS 58.21
Fragility Development Description of Fragility Elements Development Element
Applicable Methodology
Correlation to ANS Standard Capability Category 1
Correlation of ANS Standard Capability Category 2
Correlation of ANS Standard Capability Category 3
Surrogate elements
The description of the criteria for establishing surrogate element fragility targets and the development of surrogate fragilities from walkdown screening and qualification report review must be clearly documented.
Subject is addressed in TR 103959. Reporting is not addressed. Guidance on reporting is contained in NUREG- 1407 and EPRI NP6041. Guidance is adequate.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Consequence of Interactions (falling, impact, spray, flooding, fire, explosion, etc.).
The affect of interactions with essential equipment must be identified and quantified.
Subject is addressed in TR 103959. Reporting is not addressed. Guidance on reporting is contained in NUREG- 1407 and EPRI NP6041. Guidance is adequate.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
Section 7 provides general and a few specific requirements for documentation. More specific guidance is provided in NUREG-1407 but for a specific end item of developing risk insights. The ANS standard focuses on analytical models and sufficient documentation for a living methodology for risk informed applications.
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EPRI Proprietary Licensed Material
5 INDEX TO EXAMPLE FRAGILITY CALCULATIONS
The methodology presented herein, in EPRI TR-103959, “Methodology for Developing Seismic Fragilities,” (EPRI, 1994) and in other references, describes the general procedures for developing seismic fragilities. The focus is on classic cases for brittle and ductile structural failures. However, the methodology is unfamiliar to most design engineers who work primarily with deterministic design codes and standards and, as for any technological application, having specific examples is essential to assure that the generalized methodology is understood and applied correctly. EPRI TR-103959 presents several excellent examples that address common situations that the fragility analyst will confront. The appendices to this document provide additional examples to supplement the database of examples in EPRI TR-103959. In addition, NUREG/CR-5270 (Kennedy et.al, 1989) provides a comparison of fragility calculations performed by different individuals that demonstrates some of the different considerations that a fragility analyst may make regarding the median capacity of a SSC vs the code type capacity. Table 5-1 provides an index of sample fragility calculations existing in the public literature.
5-1
EPRI Proprietary Licensed Material Index to Example Fragility Calculations Table 5-1 Index To Example Fragility Calculations
Type of SSC
5-2
Reference to Example Fragility Calculation
Reinforced Concrete Shear Wall
EPRI TR-103959, Chapter 6
Vertical Atmospherical Storage Tank
EPRI TR-103959, Chapter 7
Vertical Atmospheric Storage Tank
NUREG/CR-5270
Horizontal Heat Exchanger
EPRI-TR-103959, Chapter 8
Horizontal Heat Exchanger
NUREG/CR-5270
Expansion Anchor
EPRI TR-103959, Chapter 9
Equipment Qualified by Testing-Motor Control Center Using GERS
NUREG/CR-5270
Vertical Air Tank With Support Skirt
NUREG/CR-5270
Cantilevered Reinforced Masonry Wall
NUREG/CR-5270
Fragility of Instrument Cabinet Derived from Earthquake Experience
Appendix D
Generic Fragility Derived from Design Criteria
Appendix E
Vertical Long Column Service Water Pump
Appendix F
Ground Settlement Due to Liquefaction
Appendix H
Simplified Scaling of Spectra
EPRI NP6041SR, Chapter 4
Simplified Scaling of Spectra
Appendix A
Detailed Scaling of Spectra
Appendix B
Derivation of Fragilities from Earthquake Experience Using Survival Analysis
Appendix C
EPRI Proprietary Licensed Material
6 REFERENCES
1. ANS (1997), “ANS 2.29, Standard for Probabilistic Analysis of Natural Phenomena Hazards for Nuclear Facilities,” Draft, December. 2. ANS (2000), “ANS 2.27, Standard Covering Guidelines for Investigations of Nuclear Materials Facilities for Seismic Hazard Assessments,” Draft, September. 3. ANS (2002), “ANS 58.21, External Events PRA Methodology Standard,” Draft, April. 4. ASCE (1998), “Seismic Analysis of Safety-Related Nuclear Structures and Commentary on Standard for Seismic Analysis of Safety Related Nuclear Structures,” ASCE Standard, American Society of Civil Engineers, 1998. 5. ASME (2001), “Standard for Probabilistic Risk Assessment for Nuclear Power Plant Application,” American Society of Mechanical Engineers, 2001. 6. Budnitz, R.J. et. al, “An Approach to the Quantification of Seismic Margins in Nuclear Power Plants,” NUREG/CR-4334, August 1985. 7. Budnitz, R.J., “State of the Art Report on the Current Status of Methodologies for Seismic PSA,” Committee on the Safety of Nuclear Installations, OECD Nuclear Energy Agency, March 1998. 8. Campbell, R.D., M.K. Ravindra and R.C. Murry (1988), “Compilation of Fragility Information from Available Probabilistic Risk Assessments,” UCID-20511 Rev. 1, Lawrence Livermore National Laboratory, 1988. 9. Campbell (1993), “Insights from Probabilistic Risk Assessments and Seismic Margin Assessments Regarding The Variance of Design Margins for Seismic Events,” ASME Technology for the 90s, American Society of Mechanical Engineers, 1993 10. Chokski, N, et. al., (1999), “Lessons Learned from IPEEE Studies – Regulatory Applications Using Risk-Insights,” Proceedings of OECD/NEA Workshop on Seismic Risk,” Aug 10-12, 1999, Tokyo, Japan. 11. Ellingwood (1994), “Validation of Seismic Probabilistic Risk Assessments of Nuclear Power Plants,” NUREG/CR-0008, Jan 1994. 12. EPRI (1988), “A Methodology for Assessment of Nuclear Power Plant Seismic Margin,” EPRI NP-6041, EPRI, Palo Alto, California, October 1988.
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EPRI Proprietary Licensed Material References
13. EPRI (1989a) “Probabilistic Hazard Evaluation at Nuclear Plant Sites in the Central and Eastern United States, Resolution of the Charleston Issue,” EPRI NP-6395-D, EPRI, Palo Alto, California, April, 1989. 14. EPRI (1989b), “Seismic Margin Assessment of the Catawba Nuclear Station,” EPRI NP6359, EPRI, Palo Alto, California, April 1989. 15. EPRI (1991a) “Seismic Ruggedness of Relays,” EPRI NP-7147, EPRI, Palo Alto, California, February 1991. 16. EPRI (1991b) “A Methodology for Assessment of Nuclear Power Plant Seismic Margin,” EPRI NP-6041SL, Revision 1, EPRI, Palo Alto, California, June 1991. 17. EPRI (1991c) “Generic Seismic Ruggedness of Power Plant Equipment in Nuclear Power Plants,” EPRI NP-5223, Revision 1, EPRI, Palo Alto, California, February, 1991. 18. EPRI (1991d), “Seismic Margin Assessment of the Edwin I Hatch Nuclear Plant – Unit 1,” EPRI NP-7217, EPRI, Palo Alto, California, March 1991. 19. EPRI (1993) “Analysis of High-Frequency Seismic Effects,” EPRI TR-102470, EPRI, Palo Alto, California, October 1993. 20. EPRI (1994) “Methodology for Developing Seismic Fragilities,” EPRI TR-103959, EPRI, Palo Alto, California, June 1994. 21. EPRI (1996), “GERS Formulated using Data from the SQURTS Program,” EPRI TR105988, Volume 1, EPRI, Palo Alto, California, April, 1996. 22. EPRI (1998), “SQUG Electronic Earthquakes Experience Database Users Guide,” EPRI TR110781, EPRI, Palo Alto, California, May 1998. 23. EPRI (1999) “GERS Formulated Using Data From the SQURTS Program,” EPRI TR105988-V2, EPRI, Palo Alto, California, April 1999. 24. EPRI (2000a) “Individual Plant Examination for External Events (IPEEE) Seismic Insights,” EPRI TR-112932, Revision, EPRI, Palo Alto, California, December 2000. 25. EPRI (2000b) “Planning for Risk-Informed Seismic Regulations,” EPRI 1000896, EPRI, Palo Alto, California, December 2000. 26. Fleming, K.N. and T.J. Mikschl, (1999) “Technical Issues in the Treatment of Dependence in Seismic Risk Analysis,” Proceedings of OECD/NEA Workshop on Seismic Risk, Aug. 10-12, 1999, Tokyo, Japan. 27. FOAKE (1993), “Technical Core Group Report on FOAKE Task E-1, ASME Piping, Appendix M, Quantification of the Margin of Conservatism in Seismic Design In-Structure Response Spectra,” January, 1993.
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EPRI Proprietary Licensed Material References
28. FOAKE (1996), “Advanced Light Water Reactor (ALWR) First-of-a-Kind Engineering Project on Equipment Seismic Qualification,” Prepared by MPR Associates and EQE International for Advanced Reactor Corporation, Feb. 1996. 29. Hunter (1976), “An Upper Bound on the Probability of a Union,” Journal of Applied Probability 13, pgs. 597-603, 1976. 30. Johnson, J.J, et. al., “SMACS –Seismic Methodology Analysis Chain with Statistics,” NUREG/CR-2015, Volume 9, 1981. 31. Kennedy, R.P., C.A. Cornelle, R.D. Campbell, S. Kaplan and H.F. Perla (1980), “Probabilistic Seismic Safety Study of an Existing Nuclear Power Plant,” Nuclear Engineering and Design, Vol. 59, No. 2, pp. 305-338, 1980. 32. Kennedy, R.P. et. al, (1989), “Assessment of Seismic Margin Calculation Methods,” NUREG/CR-5270. 1989. 33. Kennedy, R.P. (1999), “Overview of Methods for Seismic PRA and Margins Analysis Including Recent Innovations,” Proceedings of OECD/NEA Workshop on Seismic Risk, Aug. 10-12, 1999, Tokyo, Japan. 34. Moore, D.L. et al., (1987), “Seismic Margin Review of the Maine Yankee Atomic Power Station,” NUREG/CR-4826, Vol. 2, 1987. 35. Newmark, N.M. and W.J. Hall (1978), “Development of Criteria for Seismic Review of Selected Nuclear Power Plants,” NUREG/CR-0098, May 1978. 36. PG&E (1988), “Final Report of the Diablo Canyon Long Term Seismic Program,” Pacific Gas and Electric Company, Docket 50-275 and 50-323, July 1988. 37. Prassinos, P.G., M.K. Ravindra and J.D. Savy (1986), “Recommendations to the Nuclear Regulatory Commission on Trial Guidelines for Seismic Margin Reviews of Nuclear Power Plants,” Lawrence Livermore National Laboratory, NUREG/CR-4482, 1986. 38. Prassinos, P.G., R.C. Murry, G.E. Cummings (1987), “Seismic Margin Review of the Maine Yankee Atomic Power Station, Summary Report,” NUREG/CR-4826, Vol. 1, 1987. 39. Ravindra, et.al. (1984), “Sensitivity Studies of Seismic Risk Models,” EPRI NP-3562, June 1984. 40. Ravindra, M.K., G.S. Hardy, P.S. Hashimoto, J.J. Griffin (1987), “Seismic Margin Review of the Maine Yankee Atomic Power Station,” NUREG/CR-4826, Vol. 3, 1987. 41. Ravindra, M.K. (1999), “Seismic PSAs – Issues, Resolutions and Insights,” Proceedings of OECD/NEA Workshop on Seismic Risk, Aug. 10 -12, 1999, Tokyo, Japan. 42. Reed, J.R. et. al.(1994), “In-Structure Response for Calculating Equipment Capacities in SMA and SPRA Reviews,” Symposium on Current Issues Related to Nuclear Power Plant Structures, Equipment and Piping, North Carolina State University, December 1994. 6-3
EPRI Proprietary Licensed Material References
43. Riddell, R and N.M. Newmark (1979), “Statistical Analysis of the Response of Nonlinear Systems Subjected to Earthquakes,” Univ. of Illinois Civil Engineering Dept. Report UILU 79-2016, August 1979. 44. Salmon, M.W. and R.P. Kennedy, “Meeting Performance Goals by the Use of Experience Data,” Lawrence Livermore National Laboratory, UCRL-CR-120813, December 1, 1994. 45. SEQUAL (2001), “Basis for Adoption of the Experience-Based Seismic Equipment Qualification (EBSEQ) Methodology by Non-A46 Nuclear Power Plants,” Topical Report, April 2001. 46. SQUG (1991), “Generic Implementation Procedure (GIP) for Seismic Verification of Nuclear Plant Equipment,” Revision 2, Corrected, Seismic Qualification utility Group, June 1991. 47. SQUG (2001), “Procedure for Gathering and Validating Earthquake Experience Data,” Revision 3, Seismic Qualification Utility Group, May 2001. 48. Ueki, T, T. Sueki, Y. Kitada, H. Niwa and Ml Fujii, (1999), “High Acceleration Level Vibration Tests for Electric Components,” Proceedings of OECD/NEA Workshop on Seismic Risk, Aug. 10-12, Tokyo, Japan. 49. USNRC (1975), “Reactor Safety Study,” WASH 1400, NUREG-73/041, 1975. 50. USNRC (1978), “Combining Modal Responses and Spatial Components in Seismic Response Analysis,” Rev. 1, Feb. 1978. 51. USNRC (1981) “Seismic Safety Margins Research Program, Phase I Final Report, SMACS – Seismic Methodology Analysis Chain with Statistics (Project VIII),” NUREG/CR-2015, Vol. 1-9, 1981. 52. USNRC (1983), “PRA Procedures Guide, Vol. 2,” NUREG/CR-2200, 1983. 53. USNRC (1984), “Engineering Characterization of Ground Motion, Task 1: Effects of Characteristics of Free-Field Motion on Structural Response,” NUREG/CR-3805, May 1984 54. USNRC (1985), “Policy Statement on Severe Accidents,” Federal Register, Vol. 50, 32138, August 8, 1985. 55. USNRC (1985), “Probabilistic Safety Analysis Procedures Guide,” NUREG/CR-2815, 1985. 56. USNRC (1988), “Individual Plant Examination for Severe Accident Vulnerabilities – 10CFR50.54f,” USNRC Generic Letter 88-20, November 23, 1988. 57. USNRC (1989), “Standard Review Plan,” NUREG-0800, Revision 2, 1989. 58. USNRC (1990), “Severe Accident Risk, An Assessment of Five US Nuclear Power Plants,” NUREG-1150, Volumes 1 and 2, December 1990.
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EPRI Proprietary Licensed Material References
59. USNRC (1991a) “Individual Plant Examination of External Events (IPEEE) for Severe Accident Vulnerabilities – 10 CFR 50.54 (f) (Generic Letter No . 88-20, Supplement 4),” June 1991. 60. USNRC (1991b), “Procedural and Submittal Guidance for the Individual plant Examination of External Events (IPEEE) for Severe Accident Vulnerabilities,” NUREG-1407, June 1991. 61. USNRC (1994), “Revised Livermore Seismic Hazard Estimates of 69 Nuclear Plant Sites East of the Rocky Mountains,” NUREG/CR-1488, Lawrence Livermore National Laboratories, April 1994. 62. USNRC (1997) “Regulatory guide 1.165 Identification and Characterization of Seismic Sources and Determination of Safe Shutdown Earth Ground Motion,” March 1997. 63. USNRC (1999), “Safety Evaluation of GE Topical Report, NEDE-31858-P, Revision 2, BWROG Report for Increasing MSIV Leakage Limits and Elimination of Leakage Control Systems, September, 1993,” USNRC, March 3, 1999. 64. USNRC (2000a), “Perspectives Gained from the Individual Plant Examination of External Events (IPEEE) Program,” NUREG-1742, April 2000. 65. USNRC (2000b), “Risk-Informed Regulation Implementation Plan,” October 2000. 66. USNRC (2001) “Review of the Seismic Qualification Utility Group Procedure for Gathering and Validating Earthquake Experience Data, Revision 2 (TAC NO. MA9464),” April 27, 2001. 67. Watanabe, Y., T Oikawa and K. Muramatsu (1999), “Reappraisal of the Effect of Correlation of Component Failures on Core Damage Frequency in Seismic PSA Using DQFM Method,” Proceedings OECD/NEA Workshop on Seismic Risk, Aug. 10-12, 1999, Tokyo, Japan. 68. Zion (1981), “Zion Probabilistic Safety Study,” Prepared by Pickard, Lowe and Garrick, Inc. for Commonwealth Edison Company, 1981.
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EPRI Proprietary Licensed Material
A BENCHMARK STUDIES TO VERIFY AN APPROXIMATE METHOD FOR SPECTRA SCALING
A.1. Background Often in conducting a SPRA, the in-structure response spectra developed for design are desired to be scaled to represent in-structure response spectra for a different earthquake with a different ground motion spectral shape. EPRI NP-6041 [A1] for Seismic Margin Assessment (SMA) cautions against scaling spectra using a simple single mode procedure if the ground motion spectral shape for the newly defined review level earthquake (RLE) is significantly different than the ground motion spectral shape used for developing the in-structure spectra to be scaled. More sophisticated scaling procedures can be applied providing that the eigensolutions for the original models are available. These scaling procedures can utilize random vibration theory, direct generation computer programs, also based on random vibration theory, or time history solutions. In some cases, the eigensolution outputs in the analysis reports are only partially complete. In the case of the reactor building model in this example, the participation factors (Γ) and eigenvectors (Φ) were available. In some cases, participation factors are provided but mode shapes are not. In this example, spectra are scaled rigorously using random vibration theory and by more simplified procedures using only frequencies and participation factors. The reactor building in-structure spectra in this example exhibit evidence of more than one significant mode contributing to the spectral shape. It is therefore a good selection for a benchmark study whereby in-structure response spectra are developed using a more sophisticated scaling method for comparison to spectra developed using a simple scaling method that could be used on other structures that do not have complete eigensolutions available.
A.2. Verification of Original Spectra to be Scaled The first step in the study was to recreate the model of the concrete reactor building using the input data contained in the dynamic analysis report. The model was constructed on SAP 2000 [A2]. Modal frequencies from the reconstructed model agreed quite well with those in the analysis report. Figure A-1 shows the lumped mass model for the concrete reactor building. Note that the reactor building is not typical of those in US PWRs. Nodes 11 and 12 represent the top of the vault structure where the steam generators (boilers) are supported. The spectral shape of the Design Basis Earthquake (DBE) was a RG 1.60 spectrum anchored to 0.05g pga. The DBE spectra were broadened and smoothed to result in conservative in-structure A-1
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
spectra to be used by the designers to qualify piping and equipment. Spectra for node 11 at the upper steam generator support are shown as Figures A-2 through A-4. Spectra for other nodes are similar in shape. From the shape of the two horizontal spectra, we would conclude that a mode or modes with frequency beyond that of the peak of the spectra have some contribution to spectral shape. We would therefore anticipate that scaling must be done at more than one frequency. Using the recreated model and artificial time histories that envelope the RG 1.60 spectral shapes, new DBE spectra were created for the reactor building at selected nodes. Figure A-5 shows the match of the spectra resulting from the artificial time history to the RG 1.60 spectral shape. A similar comparison of the original artificial time history induced spectra for the DBE was not available in the analysis report. Typically, there was conservatism in the time histories used in older analyses. Using node 11 as a representative case for comparison we find that the original DBE spectra appear to be conservative relative to the recreated spectra at the peak of the spectra for the horizontal case. For the vertical case and for higher frequencies in the two horizontal directions, the recreated spectra are slightly higher than the DBE spectra. This is likely the result of the integration scheme employed in earlier computer codes vs. that in SAP 2000. Earlier codes used integration schemes that tended to suppress higher frequency response. Figures A-6, A-7 and A-8 show the broadened spectra for node 11 for the recreated model. Four percent damped DBE spectra are partially superimposed for comparison. Since equipment for SPRA is primarily evaluated at 5% damping, the 4% damping cases developed for designs are the most meaningful for comparison. This part of the benchmark study leads to the conclusion that the original DBE spectra are comparable to spectra that would be developed by modern computer codes using artificial time histories that produced spectra that were a very close match to the specified ground motion response spectra. The conservatism at the peak of the original DBE spectra was likely due to conservatism in the original time histories. The lower spectral ordinates observed at higher frequencies is not a significant deviation from the DBE spectra plus this higher frequency response is not nearly as damaging to equipment as low frequency response. Another check conducted on the DBE spectra was to use the eigensolution values for Γ and Φ from the analysis report and conduct a response analysis using the same artificial time histories used in the SAP 2000 model. Results are shown in Figure A-9 for 4% damping, node 11, direction X. The same observations are made in the comparison of DBE spectra to a time history solution using the eigenvalues from the DBE model. In this case, the DBE spectra appear even more conservative at the peak and are slightly unconservative at about 18 Hz where a second mode is present. This further confirms the validity of the original spectra to be scaled and demonstrates some conservative bias in the DBE spectral peaks.
A.3. Development of Scaled Spectra by Rigorous and by Simplified Means Given the participation factors and the modal displacements, an approximate but accurate method for developing in structure spectra by scaling can be derived from random vibration theory. This is the basis for so called direct generation computer codes. However, inherent in the random vibration analysis, is a scale factor that is applied to the RMS response to obtain peak response. This scale factor often results in very conservative in-structure response if the absolute value is taken. A scheme to scale in-structure spectra that has been used successfully is to A-2
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
compute in-structure spectra using random vibration theory for the original DBE ground motion spectra, and for the new UHS ground motion spectra. The ratio of these two in-structure spectra at different frequencies can then be used to scale the DBE in-structure response spectra to represent in-structure spectra for the UHS. The mathematical description of this process is contained in Appendix B. The process is most easily carried out using a direct generation computer code, but may also be done on a spread sheet using eigenvalues for modes of the most interest. For this study we used a typical UHS for eastern US sites. The UHS has a peak ground acceleration of 0.1g compared to the 0.05g DBE but the peak occurred at 20 Hz as opposed to the 2.5 to 9 Hz amplified acceleration range for the RG 1.60 DBE spectrum. Figure A-10 compares these two spectra. Above 5 Hz the UHS spectral amplitudes are higher. Thus we would expect that high frequency modes would be greatly amplified by the UHS whereas there was not significant amplification for the DBE ground motion spectrum. Figures A-11 and A-12 show the node 11 responses to the DBE and the UHS using the random vibration procedure described in Appendix B. The higher mode at about 18 Hz is highly amplified by the UHS. The ratios between these two spectra are shown in Figure A-13. These ratios, as a function of frequency, can then be used to scale the DBE in-structure response spectra. Figure A14 shows the scaled DBE spectrum to represent response to the UHS. This method can be used if the participation factors and eigenvectors are available. In some cases, only frequencies and participation factors are tabulated in design reports. However, from the shape of the in-structure spectra and the participation factors, one can deduce the modes that are contributing significantly to response and to the shape of the in-structure spectra. If scale factors are developed at these significant modes and used to scale the DBE spectra, the resulting in-structure spectra for the UHS should be a reasonable approximation of UHS in-structure response spectra. This sample scaling might be considered applicable to capability Category 1 of the Standard. The next step was then to do this simple scaling for node 11 in the X direction and compare the results to the more rigorous scaling results. If we examine the DBE spectrum for node 11, direction X, Figure A-2, we observe that the mode driving the peak of the spectrum occurs at about 6.6 Hz. This is mode 1. It then appears that there is another mode or modes less than 20 Hz that contributes to response. Examining the participation factors for the X direction we find that mode 6 at 18.5 Hz has a high participation. Only modes 1 and 6 have significant participation. We would then select these two frequencies to scale the DBE spectrum. By comparing the UHS and DBE spectra in Figure A-10 at these two frequencies the resulting scale factors are: Frequency Hz
UHS Sa (g)
DBE Sa (g)
Scale Factor
6.6
0.16
0.136
1.18
18.5
0.24
0.077
3.12
The broadened DBE spectra from 5.8 to 7.2 Hz in Figure A-2 are then scaled up by the 1.18 scale factor determined at 6.6 Hz. At frequencies significantly below the broadened peak frequency the UHS exhibits lower spectral acceleration than the DBE and the amplified peak can A-3
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
conservatively be fared into the DBE spectra. From about 12 to 20 Hz the DBE spectra in Figure A-2 are flat. This is a result of broadening the peaks and smoothing. The scale factor of 3.12 should be applied to this part of the spectra. Between the broadened peak and 12 Hz the spectra should be fared using the same general shape as the DBE. The DBE zero period acceleration at 33 Hz should be scaled up by the ratio for the 6.6 Hz fundamental mode and from 20 Hz to 33 Hz the spectra should be fared. This simple scaling is also plotted on Figure A-14 for comparison to the more rigorously scaled spectrum. As can be seen, the simple scaling results in conservative spectra through the frequency range of interest. The zpa for simple scaling is about 15% lower than for the more rigorous scaling. Since the seismic issues are primarily with flexible equipment, the slightly lower zpa is of no consequence. Note that in Figures A-6 and A-7, the spectra from the recreated model were higher at about 18 Hz than the DBE spectra. This is also shown in Figure A-9 comparing the time history results using the eigensolutions to the DBE design spectrum. However, when the simple scaling is done as shown in Figure A-14, the large scale factor at 18 Hz overcompensates for this and the resulting scaled spectra are conservative except in the rigid range. This example of simple scaling for a case where more than one mode has significant response may be extended to address other cases of a dominant single mode or multiple modes of response. The scaling process using the original eigensolutions and random vibration theory is considered to be acceptable for capability Category 1 and 2 of the Standard, when limited to fixed base models. The simplified Scaling based on identifying important modes by participation factors and spectral peaks is considered to be reasonable for capability Category 1 for fixed base models. However, the analyst must be reasonably confident that the original analysis and resulting spectra to be scaled are realistic. In this case, they were shown to be conservative at the peak and slightly unconservative at higher frequency.
A.4. References A1. EPRI NP-6041 SL, “A Methodology for Assessment of Nuclear Power Plant Seismic Margin (Revision 1),” EPRI, Palo Alto, California 1991. A2. SAP 2000, “Three Dimensional Static and Dynamic Finite Element Analysis and Design of Structures,” Version 7.4, August 2000, Computers and Structures Inc., Berkeley, CA. A3. Regulatory Guide 1.60, “Design Response Spectra for Seismic Design of Nuclear Power Plants,” US Nuclear Regulatory Commission, 1973.
A-4
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
Figure A-1 Lumped Mass Model of Reactor Building
A-5
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
Figure A-2 Reactor Building EQ Floor Spectra, Node 11
A-6
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
Figure A-3 Reactor Building NS Floor Spectra, Node 11
A-7
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
Figure A-4 Reactor Building Vertical Floor Spectra, Node 11
A-8
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
Figure A-5 RG 1.60 Spectrum Compatible Time Histories
A-9
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
Figure A-6 Reactor Building E-W Floor Spectra Reconstructed Model, Node 11
A-10
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
Figure A-7 Reactor Building N-S Floor Spectra Reconstructed Model, Node 11
A-11
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
Figure A-8 Reactor Building Vertical Floor Spectra Reconstructed Model, Node 11
A-12
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
Design 11X 11X Modal Response @7%
Figure A-9 EW Floor Response Spectrum Developed From Eigensolution of DBE Analysis, Using RG 1.60 Time Histories
A-13
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
UHS
DBE
Figure A-10 Comparison of DBE with UHS
A-14
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
Figure A-11 RB – Estimated SDOF Oscillator Response – Node 11
A-15
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
Figure A-12 RB – Estimated SDOF Oscillator Response – Node 11
A-16
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
Figure A-13 RB – UHS Scale Factors – Node 11
A-17
EPRI Proprietary Licensed Material Benchmark Studies to Verify an Approximate Method for Spectra Scaling
Rigorous Scaling Simplified Scaling
Figure A-14 Scaled DBE Spectra – Node 11
A-18
EPRI Proprietary Licensed Material
B DEVELOPMENT OF IN-STRUCTURE RESPONSE SPECTRA FOR SEISMIC MARGIN OR SEISMIC PRA EVALUATION BY SCALING
B.1
Introduction
In-structure spectra developed for design often do not take advantage of methods to reduce high frequency spectral peaks that have been developed to address this issue in the US Individual Plant Examination of External Events (IPEEE). In-structure spectra are typically obtained from floor time-histories generated from a modal time-history analysis of the structures. The analyses utilize time-history base input acceleration records who’s response spectra envelope the specified ground motion uniform hazard spectra (UHS) for SPRA or the Review Level Earthquake (RLE) spectrum for seismic margin assessment. According to the guidelines for SPRA and SMA conduct (see References B8 and B1), the estimation of seismic demand is to be median-centered except that the ground motion for SPRA is to be specified as the median UHS whereas RLE is to be established at the approximate 84% non-exceedance level. This appendix discusses the various steps that can be used to affect the removal of conservative bias in the response analysis with the goal of obtaining an estimate of median-centered response conditional on the occurrence of the SPRA UHS or an RLE. For the examples shown herein, the primary power of the UHS motion is contained in the 10-20 Hz range (by contrast, the power of the RG 1.60 Spectrum used for design is contained in the 2-9 Hz range). Therefore, significant conservatism is introduced if the effects of foundation incoherence and equipment high frequency ductility are not considered. Both of these effects result in a reduction of the high frequency content of in-structure spectra. In this Appendix, the following subjects are addressed: (1) Reduction of ground motion for incoherence, (2) scaling of design floor spectra compatible with reduced ground motion spectra, and (3) reduction of floor spectra for high frequency ductility effects.
B.2
Incoherence Reduced Ground Motion
Ground motion definition spectra, such as typical UHS spectra, represent the elastic response of an oscillator due to the motion expected at a single point on the horizontal free surface of a half-space media. Actual ground motion, however, has horizontal spatial variation due to wave scattering effects and statistical incoherence of motion in the frequency domain. Considering the motion of two points on the surface with a given horizontal separation distance, measurements have indicated that the two motions can be separated into frequency-dependent in-phase B-1
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
components, or coherent motion, and frequency-dependent components with random phasing, or incoherent motion. A large rigid foundation mat or a rigid multi-cell box-type concrete structure can only achieve coherent motion over the characteristic dimension of its base. The random, or incoherent motion has a net zero average over the characteristic dimension of the foundation. Further, observational data indicates that the incoherent portion of the surface ground motion increases in the higher frequency range resulting in reduction in input at higher frequencies for structures with large plan dimension. Based on a conservative interpretation of data for motions recorded over short separation distances, References B1 and B8 provide a procedure for spectral reduction to account for statistical incoherence of the foundation input motion. Using a characteristic foundation dimension de = 150 feet as a reference value, the following spectrum reductions are recommended: Table B-1 Reduction Factors for 150-Foot Foundation Frequency, Hz
Reduction factor R150
0.2
1.0
1
1.0
5
1.0
10
0.9
20*
0.8232
≥25
0.8
*Reduction factor determined by linear log-log interpolation
For foundations with different characteristic plan dimensions, d e , the reduction value (1- R s ) may be extrapolated proportional to the characteristic foundation plan size of 150 feet
and reduction values (1-R150 ), determined from the R150 given in Table B-1, or R s = 1− (de / 150)(1− R150 )
Equation B-1
For frequencies between the reference values given in Table B-1, the values of reduction function, Rs , may be linearly interpolated as a log R s vs. log f function. The characteristic foundation dimension for a building may be taken as the square root of the building foundation plan area. In the following, an example building, designated as Building E, is used to demonstrate the spectrum scaling methods. The portion of Building E with the foundation perimeter directly supported by rock was taken as the effective foundation plan to be used for determination of the Building E incoherence reduction:
B-2
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
E Building Foundation Plan: 46.65
40.20m
de =
A = (49 .65 X40 .20 = 43 .31m = 142 feet
Using Equation (B-1), the incoherence reduction function for Building E was obtained as shown in Figure B-1. Inco herenc e R educ tion - Bu ilding E
1
0.9
0.8
Redu ction Factor, Rs
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0 0
5
10
15
20
25
30
35
40
45
50
F requ ency, hz
Figure B-1 Reduction Function for Incoherence Across a 43.3 M (142-Foot) Foundation
Figure B-2 is a tripartite presentation (log-log) to define an example UHS. This UHS is similar to the shape of a typical EUS UHS. On such plots, only one dependent variable, usually Spectral Displacement (SD), can be selected for each frequency. The other variables, denoted as the Pseudo Spectral Velocity, PSV = 2π f SD, and the Pseudo Spectral Acceleration, 2 PSA = (2π f ) SD, are derived quantities. For the current study, the often used approximation for Spectral Acceleration, SA g ≈ PSA, was used for the UHS. Each UHS was constructed by linear segments of log SA g vs. log f between frequency break points of 0.2, 1.0, 5, 10, 20, and 50 Hz B-3
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
defined for damping ratios, ζ, with values 0.5, 1.0, 2.0, 5.0 and 10 per cent of critical damping. The common ZPA value was at ≥ 50 Hz and the common displacement was at ≤ 0.2 Hz. At the break points, the spectral values were linearly interpolated as a log SA g vs. log ζ function. For frequencies between the break point values, the spectral values were linearly interpolated as a log SA g vs. log f function.
Figure B-2 Uniform Hazard Horizontal Response Spectra
The incoherence reduced ground motion spectra for a building is then obtained as the product of the UHS spectral acceleration and building reduction function, SA INg (f, ζ) = R s x SA g (f, ζ) , for the value of modal damping used in the corresponding Building analyses. Example incoherence reduced horizontal and vertical ground motion spectra for Building E, for the damping used for the analysis of Building E, are shown in Figures B-3 and B-4.
B-4
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
Building E - Horizontal Ground Motion Spectra 0.45 4.5% Damping 0.4
0.35
SAh
UHS Input Motion
SAh * Rs
Incoherency Reduced Motion
0.3
SA 0.25 , Hz 0.2
0.15
0.1
0.05
0 0
5
10
15
20
25
30
35
40
45
50
Frequency, Hz
Figure B-3 Incoherence Reduced Horizontal Ground Motion for Building E
B uilding E - Vertic al G ro und Mo tion Sp ectra
0.4 4.5% Dam p ing
0 .35
E-5 Inp ut Motio n
SAv SAv * Rs
Incoherency Reduc ed Motion
0.3
SA, g
0 .25
0.2
0 .15
0.1
0 .05
0 0
5
10
15
20
25
30
35
40
45
50
F requ ency, Hz
Figure B-4 Incoherence Reduced Vertical Ground Motion for Building E
B-5
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
B.3 Estimation of Floor Spectra Compatible with Incoherence Reduced Ground Motion B.3.1 Scaling of Floor Spectra The most direct procedure for obtaining estimates of median-centered response from analyses that have a conservative bias is to simply scale the computed results by a reduction function which approximately filters the response to remove the bias. The first step in the scaling procedure is to determine the reduction of both horizontal and vertical ground spectra, as discussed above, which accounts for the effect of ground motion incoherence for each building foundation size. The next step is to provide estimates of the reduced floor spectra that would result from the revised (reduced) median-centered ground motion spectra. Thus, each time-history generated building floor spectrum SA ni , at node n for response in (translational) direction i, is modified in accordance with the scaling relationship: SA eIN ni SAINni = SAni x SA eEni
Equation B-2
where SA INni is the scaled spectra that accounts for foundation incoherence. In the above equation, SA eEni and SA eINni are the estimated floor spectra that would result from the elastic, or unreduced UHS ground spectrum and the incoherence reduced ground spectrum, respectively. The ratio within the brackets of Equation (B-2), may be identified as the reduction function associated with the incoherence reduction. B.3.2 Spectral Estimation Method Instead of redoing the complete structural response analysis for the incoherence reduced UHS, a simple method of estimating the modal components of floor oscillator response, given a modal representation of the structure (Γ, φ) and the ground motion spectrum, SA g {f, ζ} , for the damping value, ζ, used in the building analysis may be done. The first use of a simplified method of direct (i.e., avoiding time-history analysis) floor spectrum generation was proposed by Biggs (Reference B2). This method, based on empirical amplification factors, used only the structure mode shape factors, φnij , and the participation factors, Γjr , defined for mode j, node n, response direction i, and input direction r. Vanmarke (Reference B3) showed that Bigg’s empirical amplification factors are similar to those as obtained from random vibration theory. The amplification factors presented in these studies compared the response of an uncoupled Single-Degree-of-Freedom (SDOF) oscillator mounted on the structure to the same oscillator mounted on the ground. Subsequent work (Igusa and Der Kiureghian, Reference B4) has emphasized the random vibration formulation in the development of direct structure response generation methods, including the effect of equipment mass coupling. Traditional generation of floor spectra, using time-history methods, assume that the floor motion is uncoupled from the equipment response. This assumption also can result in response conservatism, however, the consideration of this effect is somewhat application specific (knowledge of the equipment mass B-6
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
and local floor mass is required), therefore, in this study the scaling procedure did not include mass coupling effects. It should be noted that the accuracy of the spectral values obtained using an estimation method is not that important since only the ratio of the spectral estimates is used for scaling of the original spectra. The method used in this study for the estimation of floor spectra is based on the random vibration results (Crandall and Mark, Reference B5) for a cascaded set of SDOF systems (i.e., uncoupled oscillators) with white noise base motion input. Direct generation computer codes could also be used and are the preferred choice. For purposes of illustration, the Crandal and Mack random vibrations model using existing eigensolution values are utilized. This procedure can be carried out on a spreadsheet using the modes of interest. Modes that contribute little to response can be eliminated with very little loss in accuracy. Basically, the floor response spectrum ordinate at each frequency, fk , is the sum of the contribution of each structure mode, j, at that frequency. Each mode contribution was considered as the response of two cascaded SDOF systems for which the first stage output was the structure ″ modal acceleration response component Ynj = Γjφnj SA gj for base motion input where SA gj is the ground response spectrum ordinate at fj . The output of the first stage is then used as input to the second stage which is the response spectrum oscillator (on the structure) tuned to frequency fk . The output of the second stage is the modal component of the floor response spectrum ordinate. These relationships are illustrated in Figure B-5. In the following development, it will be understood that the modal response of the oscillator is associated with input direction r. SA
fj
N
SAnk = Σj(SAnkj)
ζk
Floor Response Spectrum
Znkj’’
Zzpa’’ = |Yn’’|max
ωk = 2πfk
n
Ynj’’
1
Xnj’’
SAgj
ωj = 2πfj
Xg’’
f
fk
SA
Ground Response Spectrum ζj
fj
ZPA = |Xg’’|max f
Figure B-5 Response Spectra Relationships
The ground response spectrum is a plot of the spectral acceleration for a set of SDOF oscillators attached to the ground, with damping ζ as a function of oscillator frequency f, for a given ground ″ ″ motion characterized by an acceleration time-history, Xg . If we denote X j as the absolute B-7
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
acceleration response of an ground mounted oscillator with frequency fj and damping ζ j , then the spectral acceleration is given by: SA gj = max X j
″
Equation B-3
We assume that sufficient number of modes are included in the modal representation of the structure such that:
δ m - Σ j (Γjrφnj ) = ε
Equation B-4
where |ε| < 0.1 and where δ m = 1, if the response at node n is in input direction r, and δ m = 0, if the response direction is cross-axis to input direction r.
″ Then the absolute acceleration response for structure node n, Yn , may be obtained using modal analysis as: ″ ″ ″ Yn = Σ j Y jn ≈ Σ j Γjφnj X j
Equation B-5
The floor response spectrum is a plot of the spectral acceleration for a set of SDOF oscillators attached to the structure at node n, with damping ζ k , as a function of oscillator frequency, f, for ″ a given floor motion characterized by an acceleration time-history, Yn . If we denote the ″ absolute acceleration response of the floor mounted oscillator with frequency fk as Znk , then
the spectral acceleration is given by SAnk = max Znk
″
Equation B-6
″ ″ If the floor input motion is expressed as Yn = Σ j Γjφnj X j , then each mode component may be considered as an independent input to the floor oscillator, and the contribution of each mode component to the floor oscillator response can be considered as the response of two cascaded ..
SDOF systems. Using the notation of Crandall and Mark (Reference B5), X 1 is the absolute acceleration response of the first stage with frequency fj and damping ζ j and
..
X2
is the absolute
acceleration response of the second stage frequency fk and damping ζ k . Now, given that the base input motion for the first stage is characterized as White Noise (WN), the Root-Mean-Square (RMS) response of the first and second stage may be obtained from the WN results presented in Crandall & Mark for a two-SDOF cascade. Denoting the first stage response
B-8
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling ..
..
as X 1RM S , and the second stage response as X 2RM S , the functional relations presented by Crandall and Mark may be utilized to obtain an amplification factor which compares the uncoupled response of the floor oscillator to the structure response at the point of contact. We denote this amplification function as
.. X 2RMS fk AF = .. ,ζ ,ζ f j k j X1RMS
Equation B-7
Using the notation, ..
Z nkj = Pnk x 2 RMS
Equation B-8
″ Ynj = ΓjφnjSA gj = Pgj x 1RMS ..
Equation B-9
where Pnk and Pgj are Peak Factors introduced by Vanmarke (Reference B3). Using Equations (B-7), (B-8), and (B-9), the modal floor response component may be expressed in terms of the modal structure response as:
″ Znkj = AF Γjφnj (Pnk / Pgj ) SA gj
Equation B-10
Vanmarke showed that the peak factors, P, corresponding to a given exceedance level (such as 84%) may be considered, in general, as approximately constant for a damped oscillator over the frequency range 5-50 Hz. Vanmarke also showed that the ratio Pk / Pg was approximately 0.8. We note that the order of this approximation is not relevant to the scaling procedure, since we are considering ratios of estimated Znk for the original and reduced ground motion spectra. Thus, considering the input motion to be in direction, r, and the response at node, n, in direction, i, we use the notation
″ Znirj {fk } = AF{fk / fj , ζ j , ζ k }Γrjφnij 0.8 SA gr {fj }
Equation B-11
for the response component of the floor oscillator with frequency, fk , due to the structure mode with frequency, fj , and modal response factor, Γrjφnij . Then, the total response may be estimated using the SRSS modal summation,
B-9
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
″ ″ Znir {fk } = Σ j Znirj
1/ 2
Equation B-12
where the summation is over all of the modes used in the modal analysis of the structure, and the SRSS spatial summation gives the final spectral acceleration estimate, ″ ″ Zni {fk } = Σr Znir
1/ 2
Equation B-13
where the summation is over the three translational input directions. B.3.3 Incoherence Reduction of Selected Reference Locations For the example presented, the modal frequencies, fj , associated participation factors, Γrj , and translational mode shape values, φnij , for the nodes with spectra to be scaled are utilized. This modal information, along with the scaling procedure and modal estimation method developed above, was then used to reduce the high frequency regions of the unscaled floor spectra for the selected reference locations. The computation of the ratios of the estimated response quantities, using the modal response weighting factors and the amplification factors developed above, is the bulk of the scaling effort. The method of response estimation detailed in Section B.3.2 can be incorporated into several spreadsheets, which are linked by an application specific Visual Basic encoded procedure. This procedure utilized the reduced ground motion spectra, the set of modal response weighting factors, Γrjφnij , and the associated mode frequencies as given quantities. The spectral ordinates for each oscillator frequency, consistent with the set of frequencies for each building floor spectrum, is then computed using Equations (B-7), (B-10), and (B-12). The ratios of the estimated spectral response quantities are then computed as the appropriate set of reduction functions to be applied to the spectra obtained from the analysis for the reference building locations selected. In this example, a 1.0E-5 UHS and compatible time-histories, were originally used in development of floor response spectra. Later studies indicated that 85% of the UHS was more appropriate as the site specific RLE. Therefore an additional reduction of the spectra by the 0.85 factor, as indicated in Equation (B-13) was utilized. RLEINni = 0.85 x SAINni = 0.85 x SAni x (SAEINni / SA eEni )
Equation B-14
An example of the plotted results is shown in Figure B-6, which provides an unscaled RLE spectra, the computed incoherence reduction functions, and the resulting incoherence reduced RLE spectra for Node 162610 in the Building E model. Note that the seismic experience based SQUG Reference Spectrum peak S A screening capacity of 1.2g from Reference B6 is superimposed on the spectra for comparison. The 1.2g SA peak of the Reference Spectrum is
B-10
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
extended on the basis that higher frequency acceleration is less damaging than low frequency acceleration of the same value. Building E- Unscaled Spectra - Node 162610 3
5% Damping
0.85 x E-5 Input Motion
2.5
Comp 1 x 0.85 Comp 2 x 0.85 Comp 3 x 0.85 Ref Cap (= 1.2 g)
2 SA, g 1.5 1 0.5 0 0
10
20
30
40
50
Frequency, Hz
Building E - Foundation Reduction Incoherence Reduction 1 0.9 0.8 0.7 Reduction 0.6 Factor 0.5 0.4 0.3 0.2 0.1 0
RX RY RZ
0
10
20
30
40
50
Frequency, Hz
Building E - Reduced Spectra - Node 162610 Incoherence Reduction
142 m Foundation 2.5
5% Damping
0.85 x E-5 Input Motion
2
Comp 1 x rX x 0.85 Comp 2 x rY x 0.85 Comp 3 x rZ x 0.85 Ref Cap (= 1.2 g)
SA, g 1.5 1 0.5 0 0
10
20
30
40
50
Frequency, Hz
Figure B-6 Incoherence Reduced Spectra for Building E Node 162610
B-11
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
B.3.4 Total Spectra Incoherence Reduction for All Locations Comparison of the reduction functions computed for each subset of reference nodes in a given response direction indicates that, in general, the variation of reduction factor amplitude with frequency is similar for the selected representative sample of nodes within a building. An example of a set of incoherence reduction functions obtained for Building E in one horizontal response direction is shown in Figure B-7. In general, for all buildings, if the set of reduction functions in a given direction is viewed as a statistical sample, the maximum coefficient of variation of the sample is less than 0.1. For SMA, the sample mean plus one standard deviation level can be utilized as a generic reduction function for the directional response of the building. If all of the response spectra for a given building direction were reduced for the total effects of foundation incoherence using such a generalized set of reduction factors, the resulting set of floor response spectra would have only a 16% chance of being exceeded, which would insure that equipment demand is, at least, taken at the 84% nonexceedance level. For SPRA, the mean value of the reduction function can be used and the COV can be incorporated into the structural response factor uncertainty. An example set of mean plus one standard deviation total reduction functions, based on the representative sample selected for Building E is given in Figure B-8. Build ing E Inco herence R eduction - Component X 0.9
0.89
0.88
R s , Reduction Function
0.87
0.86
RX 113121
0.85
RX 162610 RX 202610
0.84
RX 2197 RX 233607
0.83
RX 3290 RX 4506
0.82
RX m+1s
0.81
0.8 0
5
10
15
20
25
30
35
40
45
Frequency, Hz
Figure B-7 Incoherence Reduction Functions for Selected Nodes of Building E
B-12
50
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
B uild ing E R eduction Factors In cohe rence Redu ction 1
0.9
0.8
0.7
Redu ction Factors
RX m+1s RY m+1s
0.6
RZ m+1s
0.5
0.4
0.3
0.2
0.1
0 0
5
10
15
20
25
30
35
40
45
50
Frequency, Hz
Figure B-8 Overall Incoherence Reduction Factors for Building E
B.4
High Frequency Reduction of Floor Spectra Due to Ductility Effects
High frequency equipment components, mounted within structures that have floor spectra with significant high-frequency input energy, can have response levels that are significantly less then would be predicted by conventional elastic or equivalent static analysis procedures. The presence of even limited ductile energy absorbing capacity in component attachments, such as a weld, can lead to substantial reductions in response due to non-linear behavior. As an example, consider a small fillet weld with a yield displacement on the order of 0.001 inch (0.0254 mm) and the displacement at weld failure being 0.01 inch (0.254 mm). A 0.4g response at 25 Hz will require a displacement of 0.0063 inch (0.159 mm) while a 0.4g response at 5 Hz will involve a displacement of 0.157 inch (3.99 mm). The 20 Hz response level is within the ductile range of the weld while the 5 Hz response level has failed the weld. This example illustrates the so-called brittle behavior of welded anchorage associated with low frequency response while the high frequency response of the same anchorage is achieving ductile behavior. In Reference B7 the effects of ductility on high frequency response has been explored in great detail. In order to develop a procedure for a reducing a floor spectrum for high frequency ductility effects, Reference B7 considered a squat item of equipment that is controlled by weld anchorage capacity subjected to a pure base shear as the limiting case. It was concluded in Reference B7 that it is conservative to use only a single-degree-of-freedom model to obtain response spectrum reduction factors. In terms of physical description, this conservative model corresponds to an electrical cabinet that is anchored at its base by a minimum 3/16-inch (4.8 mm) fillet weld loaded in the transverse direction. The equivalent length of the weld is taken to be 1 inch (25.4 mm) with a yield displacement of 0.001 inch (0.0254 mm) and ultimate displacement of 0.01 inch (0.254 mm) based on published test data. For this limiting example it was also conservatively B-13
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
assumed that there is no nonlinear response in the cabinet structure, in the connections mounting the electrical devices to the cabinet structure, or in the devices themselves. This case was denoted as the simplified sliding model in Reference B7 for which a seven-step iterative procedure was developed to obtain a reduced spectral ordinate at a given frequency. The procedure developed in Reference B7, reduces the ground spectrum rather than directly reduce an individual floor spectrum for ductility effects. This reduced level of input motion does not represent an actual reduced ground motion but is rather a pseudo ground motion or Damage Consistent Motion which yields the ductility reduced floor motion when the reduced input is applied to the elastic building analysis model. The amplification of the building is included in the sliding model procedure by requiring a larger input scale factor, FSM , to be applied to the pseudo ground motion input level. The reason for utilizing this computational artifice is to allow the estimation of ductility reduced floor spectra using the elastic structure analysis model and direct spectra estimation methods. As a result, the scaling procedure developed for incoherence reduction of ground motion may also be used for estimation of high frequency ductility reduced floor spectra. The sliding model procedure of Reference B7 was applied with the following basic guidance: (a) the reduction is performed for frequencies 10 Hz and above; (b) the reduced pseudo ground response spectrum should be connected to the elastic spectrum at 8 Hz; (c) a spectral ordinate should not be reduced below a value equal to the peak spectral value at 10% damping divided by 1.6 or below the response level associated with just obtaining the yield displacement; and (d) for SMA evaluations the factor of safety for equipment mounted within a building should be taken as FSM = 3.0. The focus is on a spectrum reduction associated with a HCLPF capacity level rather than a median capacity level. The initial input ground motion applied to the base of the simplified sliding model is the incoherence reduced ground motion, since effects of foundation incoherence result in a reduction in actual motion input both to the structure and the equipment mounted therein. The reduction procedure detailed in Reference B7 was incorporated into an interactive spreadsheet that implemented the iterative procedure for the building. The combined incoherence and high-frequency ductility-reduced pseudo-ground-motion was then obtained as a product of the UHS acceleration and building reduction function for the value of modal damping used in the corresponding building analysis. SAHFG (f , ξ ) = (
Rs
( ) Fµ ) × SAg f , ξ
Equation B-15
Figures B-9 and B-10 provide a comparison of the results of both the horizontal and vertical high frequency ductility pseudo ground motion or damage consistent reduction with the unreduced ground spectra and the incoherence reduced ground spectra for Building E.
B-14
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
Building E - Horizontal Ground Motion Spectra 0.4 4.5% Damping 0.35
0.3
SAh
E-5 Input Motion
SAh * Rs
Incoherency Reduced Motion
SAh*Rs/Fu
Damage Consistent Motion
SA, Hz
0.25
0.2
0.15
0.1
0.05
0 0
5
10
15
20
25
30
35
40
45
50
Frequency, Hz
Figure B-9 Reduced Horizontal Ground Motion Spectra for Building E
Building E - Vertical Ground Motion Spectra 0.35 4.5% Damping E-5 Input Motion
SAv
0.3
Incoherency Reduced Motion
SAv * Rs SAv*Rs/Fu
0.25
Damage Consistent Motion
SA, g
0.2
0.15
0.1
0.05
0 0
5
10
15
20
25
30
35
40
45
50
Frequency, Hz
Figure B-10 Reduced Vertical Ground Motion Spectra for Building E
B-15
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
B.5 Estimation of Floor Spectra Compatible with High Frequency Ductility Reduced Pseudo Ground Motion B.5.1 Damage Consistent Scaling of Floor Spectra The basic scaling procedure developed for incoherence reduction can also be used to reduce each floor spectrum SA ni , at node n in (translational) direction i, for high frequency ductility effects. The damage consistent, or high frequency ductility, scaled floor spectra is obtained in two scaling steps: SA eHFni SA HFni = SA ni x SA eIN ni
SA eINni x SA eE ni
Equation B-16
where SA HFni are the scaled floor spectra which account for both foundation Incoherence and High Frequency ductility. In the above equation, SA eEni , SA eINni , and SA eHFni are the estimated floor spectra that would result from the Elastic UHS ground spectrum, Incoherence reduced ground spectrum, and the High Frequency ductility reduced pseudo ground spectrum, respectively. It should be noted that SA HFni accounts for both effects while the spectra obtained using Equation (B-2), SAINni ,account for incoherence only. The reason for utilizing the two step approach is that the high frequency ductility reduced pseudo ground spectrum is developed from the incoherence reduced ground spectrum. The ratios within the brackets of Equation B-15 may be identified as reduction functions associated with either incoherence reduction, high frequency reduction or both reductions combined. B.5.2 Damage Consistent Reduction of Selected Reference Locations The same spectral estimation procedure outlined in Section B.3.2 can be used to obtain the estimated floor spectra, SA eHFni , associated with the pseudo ground motion spectra developed for each building to account for high frequency ductility effects. The ratios of the estimated spectral response quantities are then computed as the appropriate set of reduction functions to be applied to the spectra obtained from the analysis for the reference building locations selected in Section B.3.4. As indicated in Section B.3.4, the basic scaling procedure is to factor the floor spectrum, by the ratio of the estimated floor spectra. In this example a site specific RLE, was taken as 0.85 x UHS and is applied directly in the scaling equation SA eHFni RLEHFni = 0.85 × SAHFni = 0.85 × SA ni × SA eIN ni
SA eINni × SA eE ni
Equation B-17
The quantity, SA eINni / SA eEni , is the incoherence reduction factor which is the ratio of the estimated floor spectra that would result from the INcoherence reduced ground spectrum and the estimated floor spectra that would result from the Elastic ground spectrum. The quantity, B-16
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
SA eHFni / SA eINni , is the additional reduction factor for high frequency ductility which is the ratio of the estimated floor spectrum that would result from the High Frequency ductility reduced ground spectrum and the estimated floor spectra that would result from the INcoherence reduced ground spectrum. As noted above, SA HFni accounts for both effects and SAINni accounts for incoherence only. The spectra reduced for foundation incoherence may be computed as an intermediate step since SAINni values are used for relay evaluations. SA HFni is used for screening against the extended SQUG Reference Spectrum, Reference B6, or the SMA screening tables in Reference B8 and for equipment anchorage calculations. An example of the plotted results of this example is shown in Figure B-11, which provides an unscaled RLE spectra, the combined incoherence and high frequency ductility reduction functions, and the resulting overall reduced RLE spectra for Node 162610 in the Building E model.
B-17
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
Building E- Unscaled Spectra - Node 162610 3
5% Damping
0.85 x E-5 Input Motion
2.5
Comp 1 x 0.85 Comp 2 x 0.85 Comp 3 x 0.85 Ref Cap (= 1.2 g)
2 SA, g
1.5 1 0.5 0 0
10
20
30
40
50
Frequency, Hz
Building E - Foundation and Damage Consistent Reduction Incoherence and High Frequency Ductility R d ti
1 0.9 0.8 0.7 Reduction 0.6 Factor 0.5 0.4 0.3 0.2 0.1 0
RX RY RZ
0
10
20
30
40
50
Frequency, Hz
Building E - Reduced Spectra - Node 162610 142 m Foundation 1.6
Incoherence and High Frequency Ductility R d ti
5% Damping
1.4
0.85 x E-5 Input Motion
1.2 SA, g
Comp 1 x RX x 0.85 Comp 2 x RY x 0.85 Comp 3 x RZ x 0.85 Ref Cap (= 1.2 g)
1 0.8 0.6 0.4 0.2 0 0
10
20
30
Frequency, Hz
Figure B-11 Overall Reduced Spectra for Building E Node 162610
B-18
40
50
EPRI Proprietary Licensed Material Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
B.6
References
B1. “A Methodology for Assessment of Nuclear Power Plant Seismic Margin,” (Revision 1), EPRI NP-6041-SL, EPRI, Palo Alto, California, August 1991. B2. Biggs, J.M., “Seismic Response Spectra for Equipment Design in Nuclear Power Plants,” Proceedings 1st International Conference on Structural Mechanics in Reactor Technology, Paper K4/7, pp. 329-343, 1972. B3. Vanmarcke, E.H., “Structural Response to Earthquakes,” Chapter 8 of Seismic Risk and Engineering Decisions, C. Lomnitz and E. Rosenbleuth, Editors, Elsevier, 1976. B4. Igusa, T. and Der Kiureghian, “Dynamic Characterization of Two-Degree-of-Freedom Equipment-Structure Systems,” Journal of the Engineering Mechanics Division, ASCE, Vol. 111, no. 1, pp1-19, January 1985. B5. Crandall, S.H. and Mark, W.D., “Random Vibration in Mechanical Systems,” Academic Press, New York, New York, 1963. B6. Seismic Qualification Utility Group (SQUG), “Generic Implementation Procedure (GIP) for Seismic Verification of Nuclear Power Plant Equipment,” Revision 2A, March 1993. B7. “Analysis of High-Frequency Seismic Effects,” EPRI TR-102470, EPRI, Palo Alto, California, October 1993. B8. “Methodology for Developing Seismic Fragilities,” EPRI TR-103959, EPRI, Palo Alto, California, June 1994.
B-19
EPRI Proprietary Licensed Material
C ESTIMATION OF EQUIPMENT CAPACITY BASED ON EARTHQUAKE EXPERIENCE DATA
Earthquake experience data was used to develop the SQUG Reference Spectrum (Reference C1) which is implied to be a conservative capacity spectrum for verification of seismic adequacy. This appendix utilizes survival analysis to determine the distribution on capacity for use in development of seismic fragilities. Let the average spectral capacity of a given equipment class, defined as a 5% damped spectral acceleration value averaged over the 3- 8 Hz frequency range, be represented by the random variable C. The distribution of C is taken as log-normal with a known (assumed) log-normal standard deviation, β c , but an unknown log-normal mean, ln(C), where C represents the median capacity. Let the average spectral demand that the equipment class has been subjected to, defined as a 5% damped free-field spectral acceleration value averaged over the 2.5- 8 Hz frequency range, be represented by the random variable D. The distribution of D is taken as log-normal with a known (assumed) log-normal standard deviation, βD , but an estimated log-normal mean, ln(D), where D represents the median demand. Next we consider n independent equipment items from the equipment class, with known freefield spectral demand {D1 , --, Di , --, Dn} resulting in an average Reference Spectrum value, Dave = RS . Each of the n items has survived the respective input motion represented by Di without damage. Here, caveats (installation specifications) are used to define the equipment class which exclude items with damage due to non-engineered attributes such as lack of anchorage or inadequate restraint. For this evaluation we assume that the equipment has been directly subjected to a level of mounting point motion equivalent to the free-field ground motion without building amplification (or deamplification) effects. Since we are interested in obtaining the highest estimate of capacity, we also assume that D is representative of the strong ground motion which occurs within the epicentral region of a major earthquake. If now we consider the ratio of capacity to demand for each of the n items, Ci / Di , we conclude that all n ratios are greater than unity or, Ci / Di > 1,
since no damage has been observed in any of the n equipment items belonging to the equipment class. We also note that the ratio of spectral capacity to spectral demand , X = C/D, is a logC-1
EPRI Proprietary Licensed Material Estimation of Equipment Capacity Based on Earthquake Experience Data
normal variable with mean, ln(X) = ln(C / D) , and log-normal standard deviation, βX =
{ (β
)2 + (βC )2 }
1/ 2
D
. The probability of failure for an item of equipment is given by
PF = P(X < 1) = F(X = 1) ,
where F is the cumulative distribution function (CDF) of X. If a reduced variate is defined as
u = ln(X) / β x , u0 = ln(X) / β x , then, given z = u − u0 , we may write F(X) = Φ(z) , where Φ is the normal CDF. Thus
PF = F(X = 1) = P(u < 0) = P(z < −u0 ) = Φ(−u0 ) The probability of survival for an equipment item is then,
Ps = 1− PF Now, given n pairs of independent Di , Ci with known Di and average RS but unknown Ci , we apply the constraint, Xi = Ci / Di > 1, since no failure has been observed in the n equipment items. If the Xi are ordered such that, X1 < Xi < Xn , then the minimum probability of survival is given by P(Xi > 1) = Π i {1− F(Xi )}xi =1 = (1− PF )
n
Since C is unknown, it can only be specified by the assignment of a confidence coefficient. The lower confidence limit on PF is found by considering the probability of an assumed failure for an n+1 item of equipment. This probability of failure is taken as the confidence-level , γ , such that the observed result of n cases of no failure is the best that could have occurred. Thus,
γ = 1− (1− PF )
n+1
is the probability of failure for at least one item given the survival of n items. Now we can estimate the population mean, ln(X), which assures that, for a given level of confidence, γ , the lowest capacity demand ratio of n equipment items will be greater than unity by requiring PF = 1− (1− γ )
1/(n+1)
= Φ (− u0 ) ,
or
{
− u0 = Φ −1 1− (1− γ)1 /(n + 1)
C-2
}
EPRI Proprietary Licensed Material Estimation of Equipment Capacity Based on Earthquake Experience Data
Since u0 = ln(X) / β X , we may write
X = C / D = euoβx If the median demand, D, is estimated as D = Dave = RS , then the capacity associated with 95% confidence is given by
C95 = RS euoβx The High Confidence Low Probability of Failure (HCLPF), or 95% confidence of less than a 5% failure, value is given by the 5% capacity level, or
CHCLPF = RS euoβx −1.645βc = RS Fk where we identify the factor, FK = euoβX −1.645βC , as the reduction or knockdown factor applied to the Reference Spectrum to achieve a HCLPF capacity value. Given βD = 0.3 and βC = 0.4 as representative log-normal standard deviations for spectral demand and capacity, then β X = 0.5 , and we obtain the following tabulation of capacity/demand ratio for a confidence coefficient, γ = 0.95, or a 95% confidence-level, for equipment survival for class group sizes ranging from 60 to 15. n
PF
(-uo)
X = C/D
FK
60
0.047924
-1.66533
2.299
1.191
50
0.057048
-1.58005
2.203
1.141
40
0.070461
-1.47237
2.088
1.081
35
0.079847
-1.40611
2.020
1.046
30
0.092114
-1.32785
1.942
1.006
25
0.108830
-1.23277
1.852
0.959
20
0.132946
-1.11257
1.744
0.903
15
0.170750
-0.95121
1.609
0.833
From this table, we note that a class group size of 30 is the minimum number of items necessary to demonstrate that the Reference Spectrum level represents a HCLPF capacity level for a unity or greater knockdown factor. The development outlined above provides an estimate of the population mean, ln(C), which, for high levels of confidence, will be conservative (i.e., low) compared to the true population mean. Our problem, as a set of n observations of no damage for the demand level recorded or estimated for each observation, may be interpreted as a sample taken from a large population of equipment meeting the attribute limits or caveats of the equipment class. We wish to infer an estimate of the sample mean capacity, or ln(C), for which the conservatism is removed. This would then C-3
EPRI Proprietary Licensed Material Estimation of Equipment Capacity Based on Earthquake Experience Data
provide an estimate of the true median capacity of the equipment to be used in risk informed seismic evaluations of equipment. One method of achieving this capacity estimate is to consider the HCLPF values computed above, RS FK , as one-sided lower tolerance limits based on the sample size and sample mean value. This may be represented by
ln(Cnpθ ) = ln(C) − knpθ where Cnpθ is the lower tolerance limit , such that the probability is p that at least a proportion θ lies below Cnpθ (or a proportion 1− θ lies above Cnpθ ) and where knpθ is the tolerance factor based on p, θ, and sample size, n. In general, for the case of a known (or assumed) standard deviation (Reference C2) k npθ = Φ −1(θ) + Φ −1(p) /(n)1 / 2
If p = 0.95 and θ = 0.05, and we identify, Cnpθ = CHCLPF = RS FK , then
(C / RS)tol = FK eknpθ and the following tabulation is obtained using the prior results for FK : n 60 50 40 35 30 25 20 15
FK 1.191 1.141 1.081 1.046 1.006 0.959 0.903 0.833
eknpθ 2.102 2.119 2.142 2.158 2.177 2.202 2.237 2.288
(C/RS)tol 2.503 2.418 2.317 2.258 2.190 2.113 2.021 1.907
The (C / RS)TOT and FK values obtained are based on an assumed β c of 0.40. Changes in the assumed β c affect both the FK and (C / RS)TOT values. An increase in the assumed β c , lowers the HCLPF and increases the median capacity. Conversely, a decrease in assumed β c increases the HCLPF and decreases the median value. Thus, within a reasonable range of β c , we would not expect the unconditional failure rate of a derived fragility to vary by a significant amount.
C-4
EPRI Proprietary Licensed Material Estimation of Equipment Capacity Based on Earthquake Experience Data
For comparison of the effect of changes to the assumed value of βC the sensitivity on the results is checked for n=30: βD 0.3 0.3 0.3
n 30 30 30
βC 0.450 0.400 0.335
βC 0.450 0.400 0.335
FK 0.978 1.006 1.047
βX 0.54 0.50 0.45
(C/RS)tol 2.347 2.190 2.009
References C1.
“Generic Implementation Procedures (GIP) for Seismic Verification of Nuclear Plant Equipment,” Revision 2, Seismic Qualification Utility Group (SQUG), June 1991.
C2.
Hald, A., Statistical Theory with Engineering Applications, John Wiley & Sons, 1952.
C-5
EPRI Proprietary Licensed Material
D EXAMPLE FRAGILITY FOR INSTRUMENT CABINET DERIVED FROM EXPERIENCE DATA
In this example a fragility will be developed for an instrument cabinet located in Building E as described in Appendix B. The instrument cabinet is welded to embeds and the anchorage and base stiffness are deemed to be rugged relative to the demand. GERS are not available for instrument cabinets, therefore seismic experience data is selected for derivation of a fragility. The instrument cabinet has no electro-mechanical relays, computers, programmable recorders or strip chart recorders and meets the caveats of the GIP, Reference D1.
D.1
Demand
For this example we will use the in-structure spectrum for node 162610 shown in Figure B-11 in Appendix B. This in-structure response spectrum reflects three reductions in the original Uniform Hazard ground motion spectrum. The original ground motion UHS for the area was anchored to 0.12 g and was used to develop amplified in-structure response spectra. Subsequent site-specific studies determined that 85% of the area spectrum was more appropriate as a median ground motion input. The resulting pga was 0.102g as shown in the UHS spectrum, Figure B-3 of Appendix B. The ground motion spectrum peaks at 20 Hz and further reduction can be taken for Ground Motion Incoherence (GMI) and for High Frequency Ductility (HFD) effects. Since the instrument cabinet does not contain any electro-mechanical relays, the high frequency ductility reduction is appropriate to reflect the effective reduction in damage at high frequency acceleration due to small amounts of ductility that may be experienced in the cabinet base. The resulting spectra shown in Figure B-11 are the result of the three reductions and are considered to be median centered response spectra relative to the ground motion input. Since the site was a low seismic hazard site and the structures and equipment were expected to have HCLPF values above the 1E-5 median UHS pga, the 1E-5 UHS spectrum was considered the best estimate spectral shape to define the input motion. The UHS were only defined out to1E-5/year frequency of occurrence. Peak ground acceleration was defined beyond 1E-5/year so the fragilities are anchored to pga in lieu of spectral acceleration. In accordance with the procedure in Reference D4, the narrow banded demand spectrum can be clipped to represent a more realistic demand on the instrument cabinet for comparison to the broad banded seismic experience spectrum. Referring to Figure B-11, and the clipping procedure in Reference D4, the following parameters and clipping factor are derived. D-1
EPRI Proprietary Licensed Material Example Fragility for Instrument Cabinet Derived from Experience Data
The parameter ∆f08 is the frequency band width for the spectrum taken at 80% of the peak and is about 2 Hz. The factor fc is the 14.5 Hz central frequency of the demand spectrum.
B = ∆f0.8 / fc = 0.138 For B less than 0.2, the clipping factor, CC is:
CC = 0.3 + 0.86 B = 0.42 The peak spectral acceleration of the demand spectrum at 14.5 Hz is 1.5g. The clipped peak is then:
SaC = 0.42(1.5) = 0.63g . Uncertainty, βU is defined in Reference D4 as:
βU = 0.37 − 0.5 B = 0.30
D.2
Capacity
The instrument cabinet has not been tested nor is there any available data on similar models. Therefore the capacity is determined from earthquake experience. Reference D1 provides a Reference Spectrum that was determined to be applicable to generic classes of equipment and subsystems. In support of using seismic experience for verification of new and replacement equipment in newer non A-46 plants, the SEQUAL Owners Group has done an extensive reevaluation of the seismic experience data and has presented the results in a topical report, Reference D2. A weighting of database site spectra was conducted, accounting for the number of representative examples at each database site. The resulting average of weighted database spectra very closely matches the GIP Reference Spectrum in the 2.5 to 7.5 Hz range. The comparison of the SEQUAL experience spectrum to the SQUG Reference Spectrum is shown in Figure D-1 for instrument cabinets and panels. It closely matches the SQUG reference spectrum. For purposes of defining capacity, the SEQUAL spectrum will be used. There are 46 documented independent examples of instrument cabinets and panels in the SEQUAL database. Using the survival analysis methodology described in Appendix C, the median and 95% confidence capacity spectra can be derived. For 46 examples, the multiplier, FK, is interpolated from Appendix C to be 1.117. Thus the 95% confidence spectrum is 1.117 times the SEQUAL spectrum. The median capacity multiplier, (C / RS)TOT , is 2.378. The actual fundamental frequency of the instrument cabinet is not known. Based on the guidance in Reference D3, the side to side and front to back fundamental modes would be greater than 8 Hz for a cabinet with welded anchorage and stiff base. Internal panels could also be expected to be above 8 Hz. The demand spectrum in Figure B-11 of Appendix B peaks at 14.5 Hz, thus some portions of the instrument cabinet could be in resonance with the demand. D-2
EPRI Proprietary Licensed Material Example Fragility for Instrument Cabinet Derived from Experience Data
Figure D-1 Equipment Class 20 Control and Instrumentation Panels and Cabinets
For structural type failures we would argue that the spectral acceleration capacity for high frequency input motion is at least as great as for low frequency input motion due to the fact that the displacements associated with high frequency are very much smaller than for low frequency. However, since the instrument cabinet contains numerous devices that could be subjected to cascading response for high frequency input and could fail in a brittle mode, we will consider the spectrum, as derived by SEQUAL to be representative, throughout the frequency range, just as a test response spectrum. At the 14.5 Hz peak of the demand spectrum, the SEQUAL 5% damped spectral acceleration is about 0.82g. The median capacity is then:
Cm = (C / RS)TOT (0.82g) = 2.378(0.82g) = 1.95g The 95% confidence capacity is:
C95% = FK (0.82g) = 1.117 (0.82g) = 0.92g The uncertainty in the capacity is calculated from the ratio of the median capacity to the 95% confidence capacity.
βUC = (1/ 1.65) ln (1.95 / 0.92) = 0.46
D-3
EPRI Proprietary Licensed Material Example Fragility for Instrument Cabinet Derived from Experience Data
D.3
Capacity Factor
The median value of the capacity factor FC , is the ratio of the median capacity to the median demand.
FC = 1.95/0.63 = 3.10 The uncertainty in the capacity factor is derived from the uncertainty in the capacity and the uncertainty in the clipped demand. βUFC = (0.30 2 + 0.46 2 )12 = 0.55
D.4
Structural Response Factor
There are several variables that contribute to randomness and uncertainty in development of the in-structure response spectra that define the demand. The original development of in-structure response spectra was conducted using a state of the art three dimensional model of the reinforced concrete structure. Since the model was three dimensional, torsional coupling effects are automatically included. The original in-structure spectra were developed by mode superposition time history analysis using three simultaneous independent time histories who’s response spectra closely matched the ground motion UHS. At the 14.5 Hz fundamental frequency that results in the narrow banded peak of the in-structure spectrum, the time history spectrum was about 10% higher than the target UHS spectrum. The structure is robust relative to the demand and is stressed to less than half of the yield capacity, therefore, a best estimate of structural damping of 4 ½ % was used in the analysis. The resulting in-structure spectra were then scaled to account for ground motion incoherence, (GMI) and for high frequency ductility (HFD) effects using the random vibration methodology described in Appendix B. In most cases, the parameters used are considered to be median centered thus the response factors are unity unless otherwise noted. The variables to be addressed in deriving the structural response factor and it variability are:
•
Spectral Shape (SS)
•
Damping (D)
•
Modeling (M) Frequency Mode Shape
•
Mode Combination (MC)
D-4
EPRI Proprietary Licensed Material Example Fragility for Instrument Cabinet Derived from Experience Data
In addition, there is some uncertainty associated with the scaling of in-structure spectra to account for:
•
Ground Motion Incoherence (GMI)
•
High Frequency Ductility Effects (HFD)
•
Scaling using random vibration theory (RV)
D.4.1 Spectral Shape (SS) At the frequency of interest, the response spectrum resulting from the time history input motion was about 10% greater than the target UHS. In addition, as discussed in section 5.8, probabilistic response invariably results in a lower peak response than a so called median centered deterministic response. In Reference D4, a demand reduction factor of 0.92 is suggested to account for this. The FOAKE study described in Section 5.8 showed a demand reduction of at least 10% for the three models used on rock sites. For soil sites the demand reduction was much larger. For the rock site in this problem, the demand reduction is considered to be 0.9, resulting in a demand reduction factor of: FDR = 1/0.9 = 1.11
If no reduction is considered to be about a 1% probability case (2.33 βR case),
βRDR =
1 ln 1.11 = 0.04 2.33
From Reference D4, Table 3-2, for a 14.5 Hz frequency of concern, the random variability, βR , would be about 0.18. This represents the peak to peak variation in the actual earthquake response spectrum as opposed to the smooth UHS. For fragilities anchored to pga, the uncertainty on the spectral amplification at 14.5 Hz would be about 0.14. In addition, the input motion is defined at the average of the two orthogonal components of earthquake. One direction could have a peak greater than the other. The random variability, βR , in the ratio of horizontal components is about 0.13. The resulting spectral shape factor and variability are: FSS = 1.1(1.11) = 1.22
βRSS = (0.042 + 0.182 + 0.132)1/2 = 0.23 βUSS = 0.14
D-5
EPRI Proprietary Licensed Material Example Fragility for Instrument Cabinet Derived from Experience Data
D.4.2 Damping (D) Structural damping used in deriving the in-structure spectra was 4 ½ %. For structures at less than ½ yield, Regulatory Guide 1.60 would recommend 4% for reinforced concrete. Reference D4 recommends 5% as a median value for reinforced concrete with considerable cracking. Considerable cracking at less than ½ yield was not expected for the building E structure and a compromise median damping value of 4 ½ % was used as a best estimate. FD = 1.0
Reference D4 suggests that 3% is a –1βU value for damping. In the amplified portion of the UHS, we can estimate the uncertainty is spectral acceleration due the uncertainty in damping as the logarithm of the square root of the damping ratio.
βUD = ln (4.5/3)1/2 = 0.2 D.4.3 Modeling (M) There are two variables to consider under modeling, structural frequency and mode shape. The model is considered to be a best estimate of the structural load path from roof to foundation. Per Reference D4, when code properties are used for concrete, the calculated and actual stiffness are similar, thus we consider the calculated fundamental frequency to be median centered. For a detailed model such as the one being considered, Reference D4 suggests that the uncertainty, β f , on frequency is about 0.15. The -1β frequency is then: f−1β = e−0.15 (14.5) = 12.48 Hz
The UHS ground motion response spectrum shown in Figure B-3 is fairly flat in this region and the change in spectral acceleration is only about 3%.
βUf = ln (1.03) = 0.03 For complex structures, Reference D4 recommends that the uncertainty on mode shape, βUMS = 0.15. The resulting uncertainty in the modeling is then: βUM = (0.03 2 + 0.15 2 )1 / 2 = 0.15
D.4.4 Mode Combination (MC) Mode superposition time history analysis was conducted. The combination of modal responses by SRSS was considered to be median centered. From the response spectra in Figure B-11, the D-6
EPRI Proprietary Licensed Material Example Fragility for Instrument Cabinet Derived from Experience Data
dominant direction X spectrum appears to be dominated by a single mode. Some contribution from higher modes would be present but not very influential for this case. The mode combination randomness is small and is estimated to be:
βRMC = 0.05 D.4.5 Ground Motion Incoherence (GMI) From Appendix B, the reduction factor for ground motion spectral acceleration at 14.5 Hz is about 0.87. If we consider the no reduction case to be an upper limit on input motion of about 3β, the uncertainty for GMI is:
βUGMI = (1/3) ln (1/0.87) = 0.05 D.4.6 High Frequency Ductility Reduction (HFD) From Appendix B, the high frequency reduction factor for the ground motion spectrum at 14.5 Hz is about 0.7. With no reduction being an extreme 3β limit,
βUHFD = (1/3) ln (1/0.7) = 0.12 D.4.7 Scaling Using Random Vibration Theory (RV) The scale factors developed using random vibration theory are considered to be quite accurate since the scale factors were developed from a ratio of response between the original and reduced ground motion spectra rather than comparing a single response analysis for the reduced ground motion spectrum to the original response analysis. Some uncertainty is of course present in any analysis and this uncertainty in the method of scaling is estimated to be:
βURV = 0.10 D.4.8 Structural Response Factor (FRS) All variables for structural response were unity except for spectral shape ( FSS = 1.21).
FRS = 1.21 β = SRSS of individual β s β = SRSS (βSS , βD , βM, βMC , βGMI, βHFD , βRV )
D-7
EPRI Proprietary Licensed Material Example Fragility for Instrument Cabinet Derived from Experience Data
βRRS = (0.23 2 + 0 + 0 + 0.052 + 0 + 0 + 0)1 / 2 = 0.24 βURS = (0.14 2 + 0.20 2 + 0.152 + 0 + 0.052 + 0.12 2 + 0.10 2 )1 / 2 = 0.33
D.5
Fragility
The median capacity is the product of the capacity factor, structural response factor and the pga of the ground motion spectrum.
A m = FC FRS (zpa) A m = 3.10(1.21)(0.102g) = 0.38g
βR = (0 + 0.24 2 )1 / 2 = 0.24 βU = (0.55 2 + 0.33 2 )1 / 2 = 0.64 HCLPF = 0.38g(e)−1.65( 0.24 + 0.64) = 0.09g Note in this case that the median and HCLPF capacity derived from seismic experience data are quite low. The reasons for such a low median capacity and HCLPF are several fold. First of all, the ground motion spectrum that was the basis for the structural response analysis has unusually high amplification of spectral acceleration relative to the zero period acceleration. Examining Figure B-3, the unreduced horizontal UHS input spectrum has a peak amplification of about 4 at 4 ½ percent damping. A Regulatory Guide 1.60 spectrum has a peak spectral acceleration amplification of about 3.13 at 5% damping and a NUREG/CR-0098 median spectral shape has an amplification of 2.12 at 5% damping. Typical amplifications for central and eastern US uniform hazard spectra are less than 2.5. The derivation of the ground motion spectrum was not done in accordance with detailed logic tree modeling techniques as was done in the EPRI and LLNL studies. A review of the derivation of the hazard implies that the spectrum was about an th 80 percentile spectrum and is referred to as a “Uniform Risk Spectrum.” From the LLNL and EPRI studies we don’t see much difference in the spectral shapes between the 50th and 84th percentile UHS, so for purposes of an illustrative problem, the given shape was assumed to be a median shape even though it appears to have unreasonable spectral amplification of zero period acceleration. In reality, the spectral shape factor derived should be at least 60% higher but, without redoing the hazard study, using current methodology, there is no analytical basis to alter the given shape. Second, the structure is very stiff, is founded on rock, and has low damping, so the amplification of high frequency input is large and the peak of the in-structure response spectrum exceeds the peak of the experience based spectrum. Third, there are only 46 official examples in the database that keeps the statistical capacity lower than if there were more well documented samples. Fourth, the uncertainty is very large due to the large uncertainty in the capacity itself and the uncertainty associated with peak clipping and scaling of response. Thus the ratio between the HCLPF and median capacity is greater than 4.
D-8
EPRI Proprietary Licensed Material Example Fragility for Instrument Cabinet Derived from Experience Data
In this particular case, the seismic hazard in terms of pga is very low and if convolved with the fragility, the resulting unconditional failure rate would be reasonably low and a fragility derived in this manner would be acceptable. For rock site cases at locations high in the structure, where high in-structure spectra define the demand, experience based fragility derivations may not be useful for defining seismic fragility.
D.6
References
D1. SQUG, “Generic Implementation Procedure (GIP) For Seismic Verification of Nuclear Power Plant Equipment,” Revision 2, Corrected, Seismic Qualification Utility Group, June 28, 1991. D2. SEQUAL, “Topical Report, Basis for Adoption of the Experience-Based Seismic Equipment Qualification (EBSEQ) Methodology by Non-A46 Nuclear Power Plants,” SEQUAL Owners Group, April 2001. D3. EPRI TR-102180, “Guidelines for Estimation or Verification of Equipment Natural Frequency,” EPRI, Palo Alto, California, March 1993. D4. EPRI TR-103959, “Methodology for Developing Seismic Fragilities,” EPRI, Palo Alto, California, June 1994.
D-9
EPRI Proprietary Licensed Material
E DEVELOPMENT OF GENERIC FRAGILITY DESCRIPTIONS FOR PURPOSES OF SCREENING BASED UPON DESIGN CRITERIA
E.1
Establishment of Screening Level
It is not practical to calculate fragilities for all components that are included in the risk modeling. Most components and distributive systems are inherently rugged and can be screened out on the basis that their seismic induced failure rate is low in comparison to the items that will ultimately dominate seismic risk. It is desirable to establish a fragility target where components exceeding this target may be screened out. In developing the target, three variables must be considered; seismic hazard, uncertainty in the median fragility and frequency of failure (potential core damage) relative to that for other events. A fourth variable, consequence of failure, is important, but for purposes of establishing a fragility cut off it is assumed that all failures have equal consequence. Parametric studies were conducted using the hazard and candidate fragility curves as input variables and examining the resulting failure frequencies. The example fragility descriptions were convolved with the seismic hazard to compute mean seismic failure rates. The example cases were then studied to determine an acceptable cutoff fragility level. E.1.1 Seismic Hazard Uniform hazard spectra were defined which describe the spectral accelerations at different frequencies for different return periods. The peak ground acceleration vs frequency of occurrence was provided up to 1.0g. NUREG-1407 states that the seismic hazard must be carried out to 1.5g unless sensitivity studies can show that a lower cutoff is justified. In the study to determine a target screening level fragility described in Section 1.3, the pga hazard was extrapolated to 1.5g and cases were run for 1.0g and 1.5g cutoff. For this particular site, the hazard was reasonably high having a mean 10,000 year return period pga of close to 0.3g. For components with HCLPFs in the 0.3g range, the extension of the hazard did not make a significant difference since the range of HCLPF to median capacity was enveloped by the hazard up to 1.0g. At the fragility level that was ultimately determined to be an acceptable screening level, there was enough difference between the 1.0 and 1.5g cutoff results that the screening level decision was based on a 1.5g seismic hazard cutoff.
E-1
EPRI Proprietary Licensed Material Development of Generic Fragility Descriptions for Purposes of Screening Based Upon Design Criteria
E.1.2 Uncertainty in the Median Fragility The uncertainty range for fragilities varies with the failure mode. For ductile modes of failure, such as for structures or piping, the margin to failure relative to code allowable is much larger than for brittle or functional failure modes but the uncertainty is also larger so that a dual criteria must be implemented to establish a minimum value of the median capacity and of the HCLPF. HCLPF is defined mathematically as 95% confidence of less than 5% probability of failure. For the double logarithmic fragility curve typically used, the median capacity is denoted as Am, the randomness as βR , and uncertainty as βU , where the βs are logarithmic standard deviations. The HCLPF may be computed from HCLPF = Am exp (-1.65) (βR + βU )
For ductile failure modes of flexible systems, such as for structures piping, cable raceways, etc. the ratio of median to HCLPF is typically three or greater. For brittle failure modes of rigid equipment or functional failure modes such as relay chatter, the ratio of median to HCLPF tends to be less than three but greater than two. Thus, for the same seismic failure rate, the flexible, ductile items must have a higher median but may have a lower HCLPF than for a non-ductile failure mode. The cases conducted to determine the fragility level for screening revealed that the seismic failure rate is more sensitive to HCLPF than median. Often it is more convenient to estimate or compute a deterministic HCLPF for making decisions on screening, hence the final screening value for fragility was targeted to a HCLPF value, wherein the median value is implied, depending upon the failure mode. Establishment of a HCLPF above the screening target was the approach used exclusively for screening of structures and most flexible equipment. E.1.3 Target Failure Rate Internal event core damage frequencies typically are on the order of 1.0E-5/yr. Seismic induced core damage frequencies for higher seismic zones such as the one considered here may have similar CDF. It is not practical to set the screening level too high (very low failure rates) or else nothing can be screened. On the other hand, we would not want to screen out seismic failures that could contribute more than 10% of the expected CDF so the target for screening was set at 1.0E-6/year or less for seismic failure rate for a seismic hazard extended to 1.5g pga. The 1E-6 per year screening target is comparable to screening targets for other external events set at 1E-6 per year CDF in USNRC (1991b). Also in Regulatory Guide 1.174 addressing Risk-informed changes to the licensing basis, a change in licensing basis that increases CDF by less than 1E-6 per year would be considered. The concern in this case though is if surrogate fragilities for several screened out components appear in “and gates” in the SPRA model, the cumulative contribution to CDF from screened out components could be significantly higher than 1E-6 per year.
E-2
EPRI Proprietary Licensed Material Development of Generic Fragility Descriptions for Purposes of Screening Based Upon Design Criteria
Applying the screening target above and the results of the several analyses conducted, the following approximate fragilities were determined to be the threshold for screening out components: Characteristics of Item
Am, g
HCLPF, g
Med/HCLPF
Flexible, ductile structures or equipment
1.5
0.5
3.0
Brittle or functional modes of failure
1.22
0.57
2.14
These two cases result in seismic failure rates of approximately 1.0E-6/yr for a 1.5g hazard cutoff. These values were recommended as surrogate fragilities for inclusion in fault trees whose top event terminates at a branch in an event tree. In the actual study, the use of these values for surrogate elements resulted in a significant but not dominant contribution to CDF from the surrogates. The target for screening should theoretically have been set at a higher level. This would have resulted in significantly more effort to review each seismic qualification report. Engineering studies are always a comprise between cost and refinement in the results. In this case, the weakest links in the plant were identified, which was the objective of IPEEE, but most of the plant structures, systems and components were enveloped by the surrogate fragility elements.
E.2
Development of Demand on Components
The site under consideration was a soil site. The original design bases DBE response spectrum resembled a NUREG CR-0098 median spectrum anchored to 0.25g. The UHS developed for the site was narrower banded, peaked at about 5 Hz, had a higher pga and higher spectral amplifications at 10,000 year return period than the DBE spectrum. It was determined that a new median centered SSI analysis would be necessary and that a probabilistic analysis would provide the most realistic and favorable results. Probabilistic response spectra were developed for several levels of ground motions, changing the soil properties as the acceleration levels increased. The in-structure response spectra used for screening were developed for a 0.5g pga UHS. Comparison of the probabilistic in-structure response spectra for 0.5g pga UHS to the 0.25g DBE spectra revealed significant conservatism in the DBE spectra. Further conservatism in the design analysis process had to be quantified in order to reach the screening target.
E.3
Screening Evaluation of Equipment and Distributive Systems
Most commercial equipment and distributive systems are inherently rugged as long as they are adequately supported or anchored. When this same equipment is qualified for seismic loading in an NPP environment, the qualification requirements and conservatisms in the specification of E-3
EPRI Proprietary Licensed Material Development of Generic Fragility Descriptions for Purposes of Screening Based Upon Design Criteria
seismic demand and calculation of equipment response compound to result in very large margins. In Reference E1, screening guidelines are provided that, subject to a walkdown verification of the equipment to search for vulnerabilities, would allow most equipment and distributive systems to be screened for earthquakes up to 1.2g peak spectra acceleration. This th value is to be compared to the 84 percentile ground motion spectrum defined at 5% damping. In Section E.1 screening thresholds were developed for equipment in terms of median and HCLPF capacities. The first step in screening is to compare the 84th percentile UHS to the 1.2g th screening level of Reference E1. In this case, the 84 percentile input for a 10,000 year return period was significantly greater than 1.2g so the screening tables in Reference E1 would not imply a HCLPF of 0.5g or greater required for screening based on the risk contribution criterion described in Section E.1. Therefore, an approach was taken wherein quantification of the conservatism in the design process was used in conjunction with the walkdown in order to screen out generic classes of components and distributive systems or individual components. Comparisons of the 0.5g pga median probabilistic floor response spectra to the original design floor response spectra for the 0.25g DBE reveals that they were comparable in the reactor building. This comparison demonstrates that there is about a factor of two conservatism in the original seismic demand specified for equipment. This factor is less for rigid equipment but, since the spectral acceleration in the high frequency (rigid) regime of the floor spectra is much lower than for the amplified region, the loads for rigid equipment are also low. A typical comparisons of the 0.25g DBE and 0.5g probabilistic spectra is shown in Figure E-1. The spectra comparisons alone do not demonstrate sufficient margin to screen out the components but they do make a significant contribution to the process.
E-4
EPRI Proprietary Licensed Material Development of Generic Fragility Descriptions for Purposes of Screening Based Upon Design Criteria
Figure E-1 Comparison of DBE Vs Probabilistic Response Spectra Reactor Building El. 547’
E.4 Screening of Flexible Equipment and Distributive Systems Designed by Analysis Flexible equipment and distributive systems that are designed by analysis usually have ductile failure modes but for purposes of screening it is assumed that the failure mode is non-ductile such as for failure of anchor bolts or welds or buckling. Fillet welds are shown in Reference E1 to have as much larger margin than implied by the design codes so fillet welds should not be the basis for the screening computation. The following assumptions are made for the screening calculation:
•
Probable frequency range is 3-10 Hz (flexible equipment).
•
2% damping was used for the design whereas 5% is considered median with 2% defined as a -2 βU case.
•
The screening is only applicable to locations outside of the primary containment where the effects of hydrodynamic loads are minimal.
•
Code margins are those inherent in the ASME code where the allowable stress may be as high as 70% of the specified ultimate strength, resulting in a nominal safety factor of 1.43.
E-5
EPRI Proprietary Licensed Material Development of Generic Fragility Descriptions for Purposes of Screening Based Upon Design Criteria
The safety factors of expansion anchors and welds are greater so the ASME criteria governs for the screening calculation. The methodology used follows that described in Reference E2. E.4.1 Strength Factor The Strength Factor, Fs, is: Fs =
FU − N DBE
FU is the ultimate strength (stress/load), N is the normal load or stress and DBE is the seismic load or stress. Since the 0.5g UHS in-structure spectra are essentially equal to the 0.25g DBE instructure spectra in the 3-10 Hz frequency range, the basis for DBE stress is considered to be anchored to 0.5g pga. Conservatively, consider that the only normal load effect is from weight which usually is a low contribution to the ultimate load capacity. The median normal load is assumed to be 10% of the ultimate capacity with a + 1β value equal to 20% of the ultimate capacity. The median ultimate strength is about 1.1 times the code specified value. The code specified value is set at the 95% confidence level, which is a -1.65 βU value. It is assumed that the average demand is 70% of the code allowable with 100% assumed as a 95% probability value (+ 1.65 βU ). The code allowable can be as high as 70% of the code specified ultimate strength, therefore the median load/stress is (.7)(.7) = 0.49 of the ultimate capacity based on code specified strength. The DBE load/stress is then (0.49-0.1) = 0.39 times the ultimate capacity. The strength factor is then:
Fs =
1.1 − 0.1 = 2.56 0.39
Using the approximate second moment method from Reference E2 for calculating β, the βU is computed to be 0.30. E.4.2 Equipment Response Factor The equipment response factor consists of the product of the individual factors for the variables of Qualification Method, Damping, Modeling, Mode Combination and Earthquake Component Combination. Qualification Method It is assumed that a dynamic response spectrum analysis was conducted as opposed to a more conservative static coefficient method. There is no particular bias in the response spectrum method but considerable conservatism can accumulate from several variables. In the case of piping, often the envelope response spectra were used which is very conservative. However, if we consider a single flexible component or a subsystem supported from the same elevation, this E-6
EPRI Proprietary Licensed Material Development of Generic Fragility Descriptions for Purposes of Screening Based Upon Design Criteria
conservatism cannot be counted. The practice of peak broadening and smoothing introduces conservatism. A prior study of single degree of freedom systems revealed that the degree of conservatism for spectra soothing in the frequency range of interest is about a factor of 1.2 with a βU of 0.09.
FQM = 1.2 βU = 0.09 Damping The factor of conservatism that results from using 2% damping in design vs 5% median is quantified by:
FD =
S a2% S a5%
The design spectra were used to find an average value of 1.17 for the spectral acceleration ratios between 2% and 5% damping in the 3-10 Hz frequency range. If 2% damping is a -2 βU value, the βU for damping is 0.08. FD = 1.17
β UD = 0.08 Modeling Modeling error can arise from frequency error and mode shape difference between the model and the actual response. The model would normally be median centered so the modeling factor would be unity. The spectra peak at very low frequency, are fairly flat between 5 and 10 Hz and have a factor of 2 difference from 3-5 Hz (Figure E-1). For the steepest slope between 3 and 4 Hz, a ±1 β f frequency shift results in a 25% difference in response. Thus:
β Uf = ln(1.25) = 0.22 The response βU due to mode shape error is estimated to be about 0.15. Combining βs by SRSS, the βU for modeling is: β UM = (0.22 2 + 0.15 2 ) = 0.27
E-7
EPRI Proprietary Licensed Material Development of Generic Fragility Descriptions for Purposes of Screening Based Upon Design Criteria
Mode Combination Mode combination was by SRSS which is median centered. The response variability due to mode combination is estimated as a βR of 0.15 for multimode response of distribution systems. Earthquake Component Combination Earthquake components were combined by SRSS. Response is usually dominated by the two horizontal directions. Considering the two horizontal components to be in phase as a 3 βR case:
βR =
1 ln 2 = 0.12 3
Equipment Response Factor Results Combining the response factors as the product of the individual factors and the βs by the SRSS rule, the equipment response factor and its variability are represented by: FRE = 1.4 βR = 0.19
βU = 0.29 E.4.3 Structural Response Factor Spectra were developed by probabilistic methods using a Latin Hypercube simulation process in which all important variables associated with structural response are included. The median results were used to derive the strength and response factors so the structural response factor is unity. The difference between the 50th and 84th percentile spectral accelerations in the 3-10 Hz frequency range defines the composite variability, βC . This ratio averages about 1.25 for the reactor building so the βC is 0.22. There is approximately equal variability from random and uncertainty variables and the corresponding βR and βU are 0.22/ 2 = 0.16 each. E.4.4 Fragility Description for Flexible Components Designed by Analysis The median peak ground acceleration capacity is the product of the strength, equipment response and structural response factors times the reference 0.5g peak ground acceleration for the UHS. As previously shown the 0.5g in-structure response spectra for the UHS are equivalent to the 0.25g DBE spectra, hence 0.5g is used as the reference earthquake pga to represent the DBE demand. Am = 2.56 (1.4)(1.0)(0.5g) = 1.79g
E-8
EPRI Proprietary Licensed Material Development of Generic Fragility Descriptions for Purposes of Screening Based Upon Design Criteria
The random and uncertainty variability are the SRSS of the βRs and βUs for the three variables and are computed to be: βR = .25
βU = 0.45 The HCLPF is computed as: HCLPF = 1.79g exp(-1.65) (βR + βU ) = 0.56g
This exceeds the 0.5g HCLPF and 1.50g median target set as the screening threshold in Section E.1 and, considering the conservative assumptions used in the derivation, this class of component and distribution system can be comfortably screened out subject to a walkdown verification that there are no vulnerable looking details. This calculation was used to screen out piping, cable trays and valves as well as the passive parts of instrument racks and electrical distribution cabinets. Valves are rigid but the piping systems in which they are mounted are flexible and the piping response dictates the demand for the valves. Valve qualification data were reviewed and the valves usually had a large design margin above the specified demand so the above derivation is also considered applicable to valves with the exception of those that may be identified during the walkdowns that appeared to be outside of the seismic experience database.
E.5
Components Qualified by Test
Reference E2 provides a methodology for developing fragilities for components qualified by test. The median capacity is expressed as: Am =
TRSC ⋅ FD ⋅ FRS ⋅ PGA RRSC
where: TRSC
= Clipped test response spectrum
RRSC
= Clipped required response spectrum
FD = Device capacity factor
FRS is the structural response factor and PGA is the peak ground acceleration for development of the RRS
E-9
EPRI Proprietary Licensed Material Development of Generic Fragility Descriptions for Purposes of Screening Based Upon Design Criteria TRSC = TRS (CT )(CI )
Where: CT is set at unity for broad banded multiaxis testing CI is a capacity increase factor and is recommended to be 1.1 with a βU of 0.05 (Reference E2) RRSC = RRS (CC )(DR )
Where: RRS is the required response spectrum
CC is the clipping factor. Clipping is not applicable for this case since the spectral peaks are at very low frequency relative to the equipment fundamental frequencies. DR is a demand reduction factor if the RRS is calculated by deterministic means. Probabilistic methods were used for the development of floor response spectra so DR is unity. FD is recommended in Reference E2 to be a value of 1.4 to demonstrate function during the earthquake with βR of 0.09 and βU of 0.22. FD for function after the earthquake is recommended to be 1.9 with βR of 0.09 and βU of 0.28.
FRS is the structural response factor which is unity for probabilistic spectra. The βC is computed as the logarithm of the ratio of the 84th percentile response to the 50th percentile response at the frequency of the equipment. βR and βU are assumed to be equal and are βC / 2 . The βs vary with the location of the equipment. For purposes of the generic screening, an average ratio of 84th percentile to 50th percentile response of 1.25 was used and the βC was computed to be 0.22 with βR and βU equal to 0.16 each.
PGA is the peak ground acceleration of the earthquake record used to develop the RRS. In this case the RRS was defined as the in-structure floor response spectra for 0.5g median structural response. Using the above methodology, the fragility may be expressed as: Am = (1.4)(1.1)(0.5g)
E-10
TRS TRS = 0.77 g RRS RRS
EPRI Proprietary Licensed Material Development of Generic Fragility Descriptions for Purposes of Screening Based Upon Design Criteria
βR = 0.18
βU = 0.28 HCLPF = 0.36
TRS g RRS
For the example shown the RRSs peak at quite low frequency (2 ½ to 3 ½ Hz) whereas the tested electrical panels are greater than 6 Hz, thus the comparison of TRS and RRS must be made at the panel frequency, not at the spectral peaks. If the TRS and RRS are equal at the fundamental frequency of the equipment, the median capacity for function during the earthquake is 0.77g and the HCLPF is 0.36g. Referring to the target screening fragility for functional modes of failure, in order to screen out components with relays that must be functional during the earthquake, the TRS needs to be a factor of 1.6 greater than the RRS at the equipment fundamental frequency. This provides a HCLPF of 0.5g and a median of 1.22g, which is the screening target. This can easily be demonstrated in many cases since the tendency is to overshoot the RRS for frequencies beyond that of the peak of the RRS if the RRS peak is at low frequency. Figure E-2 shows a typical overtest condition at frequencies beyond the peak of the RRS. Using the larger FD and larger uncertainty for function after the earthquake, the ratio of the TRS to RRS was computed to be about 1.27 for screening in order to get the HCLPF up to the 0.57g target screening level.
E-11
EPRI Proprietary Licensed Material Development of Generic Fragility Descriptions for Purposes of Screening Based Upon Design Criteria
Figure E-2 Typical Overtest at High Frequency
E.6
References
E1. EPRI-NP6041SL, “A Methodology for Assessment of Nuclear Power Plant Seismic Margin,” Revision 1, EPRI, Palo Alto, California, August 1991. E2. EPRI-TR-103959, “Methodology for Developing Seismic Fragilities,” EPRI, Palo Alto, California, June 1994.
E-12
EPRI Proprietary Licensed Material
F EXAMPLE PROBLEM FOR SERVICE WATER PUMP
In Section 2.1.5, the importance of the fragility analyst’s expertise in component fragility/HCLPF assessment is discussed. It is pointed out by the USNRC IPEEE reviewers that some IPEEE calculations appeared to be poorly prepared and used unrealistic estimates of uncertainties. In the discussion of this observation it is pointed out that this is also a problem with design calculations. In this example of a service water pump, the existing analysis of the pump was used to develop a fragility. It was determined that the failure mode focused on by the design analyst was not a realistic mode of failure, whereas another area of the pump assembly was improperly modeled and the higher response that would result from a corrected model would govern the pump failure. While it is emphasized in this Application Guide to utilize design data as much as possible for screening or for scaling results to develop fragilities, it must be emphasized that the fragility analyst must assess the validity of the design analysis. This example demonstrates an approximate correction to existing design calculations in order to derive a seismic fragility.
F.1
Description of Equipment
The Service Water Pumps are long column vertical pumps that are anchored to the concrete roof of the pump structure by expansion bolts. The pump columns are supported laterally about 10 feet below the pump motor stand. Since the unsupported column length was less than 20 feet, one might screen the pump out based on criteria in the SQUG GIP (Reference F1) as having a HCLPF exceeding 0.3g pga, whereas the DBE was 0.15g pga which corresponded approximately to the 10,000 year mean pga defined by a Uniform Hazard Spectrum for the site. However, expansion bolts are not normally used to anchor rotating equipment, thus further investigation was conducted. A finite element analysis had been conducted in support of replacement of the pumps and was available for review. In the report it was concluded that the expansion bolts for the pump anchorage were the critical element. Although the expansion bolt safety factor was less than normal manufacturers recommendations, it was close to the GIP allowable margin and it was determined in the analysis that the capacity was sufficient to assure operability in the event of a safe shutdown earthquake. The pump model is shown in Figure F-1. The pump column, motor stand and motor were modeled as beams. The base plate was modeled using plate elements. The nodes representing the location of the expansion anchors were modeled as fixed in three translational directions.
F-1
EPRI Proprietary Licensed Material Example Problem for Service Water Pump
Figure F-1 Model of the Service Water Pump
A more detailed review of the analysis indicated that the critical loading on the expansion anchors resulted from a prying action in the mounting plate. With small displacement theory and the bolt locations modeled as fixed in 3 directions of translation, a small amount of bending in the base plate produces large calculated bolt tension loads. This is not a realistic failure mode for the base plate anchorage. With a small amount of slip in the expansion anchors, the tension load due to prying is relieved and only the shear load contributes to ultimate failure. Taking this into consideration, other failure modes were examined. It was observed that the second mode of vibration was about 3.9 Hz and corresponded to translation of the pump motor. This is a much lower frequency than would be expected, thus the focus shifted to the motor stand and the validity of the model. The motor stand is a cylindrical shape with two large windows cut out, resulting in two 120-degree arcs that act as guided cantilever beams in bending when lateral acceleration is applied to the motor. Refer to Figure F-2 for a simple representation of the motor stand deformation. It was noted that the analysis was based on different dimensions of the motor stand than the field dimensions taken by the IPEEE team. The analysis dimensions were smaller, resulting in a significantly more flexible motor stand. Thus, in calculating the strength factor and the equipment response factor, the dimensions taken by the IPEEE team were used to adjust the results from the computer model.
F-2
EPRI Proprietary Licensed Material Example Problem for Service Water Pump
Motor
20.75”
9342# Motor stand Base plate
Figure F-2 Simplified Motor Stand Model
F.2
Strength Factor
Using the calculated loads from the design verification analysis, the bending moment and shear calculated at the motor to stand interface were applied to the corrected dimensions and the resulting bending plus axial stress was computed to be about 7,000 psi. The material was A-53 Grade B, with 35 ksi specified yield strength. The median yield strength for low carbon steels is about 1.20 times the specified yield, resulting in a median yield strength of 42 ksi. The median factor of safety relative to yield is then 42/7 = 6.0. It was assumed that any appreciable plasticity in the motor stand would result in misalignment between the motor and pump shafts and damage the coupling between the motor and pump assembly thus, the function would be lost. The plastic hinge shape factor in this case is greater than 1.5 but a full plastic hinge in a support assembly that assure alignment of rotating members is likely beyond a median capacity. Failure was assumed to occur at a factor of 1.5 beyond yield. The onset of yielding was considered to be about a 95% confidence value. The resulting capacity factor is:
FC = 1.50(6) = 9.0 There are two sources of uncertainty in the capacity factor—the material yield strength and the capacity beyond yield. The specified yield is a 95% confidence value, so the uncertainty on yield strength is:
βUY = (1/ 1.65) ln 1.25 = 0.14 The uncertainty in the failure threshold is estimated based on the assumptions that the yield point is a 95% confidence capacity. The resulting βU is:
βUF = (1/ 1.65) ln1.5 = 0.245 F-3
EPRI Proprietary Licensed Material Example Problem for Service Water Pump
Combining βuy and βuf by SRSS results in a βuc on capacity of: βUC = (0.14 2 + 0.245 2 )1/ 2 = 0.28
F.3
Equipment Response Factor
Equipment response variables are Qualification Method, Damping, Modeling, Mode Combination and Earthquake Component Combination. F.3.1 Qualification Method The analysis was a response spectrum finite element analysis which is considered to be unbiased. However, the modal response of the motor stand was computed at 3.9 Hz. The motor stand was modeled as being more flexible than the actual geometry. The moment of inertia calculated from the field dimensions taken by the IPEEE team showed that the stiffness in the weak axis was actually 6.5 times the stiffness calculated in the model. So the actual frequency of the motor on its stand would be greater by the square root of 6.5, or about 10 Hz vs 3.9 Hz from the computer model. This frequency is at the peak of the broadened spectrum shown in Figure F-3. The spectral acceleration defined at 2% damping used in the design analysis was 0.42g. 5% damping is considered to be a median damping value. As shown in Figure F-3, if the 5% damped design spectral peak is unbroadened, and the best estimate of frequency is 10 Hz, the qualification method factor including damping is the ratio of 2% damped spectral acceleration at 3.9 Hz vs 5% damped spectral acceleration at 10 Hz.
RQM =
F-4
0.43 = 0.86 0.50
EPRI Proprietary Licensed Material Example Problem for Service Water Pump
Assumed Unbroadened Spectrum
Figure F-3 Demand Response Spectrum, 5% Damping
The uncertainty associated with the unbroadening of the design basis response spectrum can be estimated from the ratio of the broadened to unbroadened spectral acceleration at 10 Hz. Since the peak of the broadened spectrum is an upper bound (at least a 99% non-exceedance probability value, i.e., 2.33 βU value) the qualifications method uncertainty is β UQM =
1 0.55 ln = 0.04 2.33 0.50
F.3.2 Damping The calculated dominant frequency of the motor stand was about 3.9 Hz and the associated two percent damped spectral acceleration used in the analysis was 0.42 g. Five percent damping is considered to be median centered. However, when computing the damping factor and its uncertainty on response, the frequency should first be corrected to reflect the actual motor stand geometry vs. the softer geometry used in the model. For this case the damping factor was incorporated in the qualification method factor. The response at 10 Hz is near the peak of the spectrum shown in Figure F-3. In the amplified response regime, the ratio of spectral accelerations at different damping levels can be approximated as the square root of the damping rates. If 2% damping is considered a -2 βU value, the uncertainty in damping is: β UD =
1 5 ln = 0.23 2 2
F-5
EPRI Proprietary Licensed Material Example Problem for Service Water Pump
F.3.3 Modeling At the estimated 10 Hz elastic frequency of the motor stand, and considering the unbroadened spectrum in Figure F-3, the spectrum is very steep, so a small error in frequency results in a large change in spectral acceleration. Note that we have already accounted for the conservatism in broadening in the qualification method factor. For fragility calculations, it should be considered that as the response goes beyond the linear region, the effective frequency reduces and in the case for the steep slope of the demand spectrum and the corrected pump motor stand frequency, the response could significantly reduce. It is also a common to slightly over estimate stiffness by assuming idealized inflexible bounding conditions. It was judged that a reasonable estimate of the effective spectral acceleration would be about half way between the 5% damped peak of 0.55g and the valley of 0.31g, or about 0.43g. The elastic spectral acceleration used in developing the qualification method factor was 0.5g. The modeling factor can then be computed as: The modeling factor, including damping, is then: FM =
0.50 = 1.16 0.43
The range of response from the peak to the valley is considered to be plus or minus 2.33 βU and the βU for modeling is computed as: 1 β UM = ln (.55/.31) = 0.12 2(2.33)
F.3.4 Mode Combination The analysis was multimode dynamic analysis. The first mode was predominantly the pump column and second mode was the pump motor and stand. The next modes are above 13 Hz and are not particularly influential to the pump stand response. There is no bias in the mode combination method so the mode combination factor is unity:
FMC = 1.0 The randomness on mode combination when the response is predominantly in one mode is estimated to be:
βRMC = 0.05 F.3.5 Earthquake Component Combination The analysis was in accordance with the licensing criteria wherein the worst horizontal directional response was combined with the vertical response by absolute sum. Median centered response is considered to be a combination of all three directional responses by the 100, 40, 40 F-6
EPRI Proprietary Licensed Material Example Problem for Service Water Pump
rule. The critical response is all horizontal and then 100, 40, 40 horizontal vector is 1.08 times the single direction response. The earthquake component combination factor is then: FECC = 1/1.08 = 0.93
Assuming that both horizontal components being in phase is a 3σ extreme, the βR for earthquake component combination is: = 0.09 β RECC = ln 2 1.08
F.3.6 Equipment Response Factor The equipment response factor is then: FRE = FQM (FD)(FM)(FMC)(FECC) FRE = 0.86(1.0)(1.16)(1.0)(0.93) = 0.93
βs are combined by SRSS to yield: βR = (0 + 0 + 0 + 0.052 + 0.092)1/2 = 0.10 βU = (0.042 + 0.232 + 0.122 + 0 + 0)1/2 = 0.26
F.4
Structural Response Factor
The pump structure is founded on rock and has a fundamental frequency of about 10 Hz as indicated by the top of roof response spectrum in Figure F-3. Design damping was 4% as indicated by Regulatory Guide 1.61 for structures at less than half yield. The pump structure is simple and torsional effects are minimal. Spectra were developed from a fixed base 2 dimensional model. Variables considered are spectral shape, damping, modeling, mode combination and ground motion incoherence. F.4.1 Spectral Shape The UHS spectrum for the site, when anchored to the DBE pga, exceed the DBE spectrum at the 10 Hz fundamental frequency of the structure by 45%. The resulting spectral shape factor is: FSS =
1 = 0.69 1.45
From Reference F2, the randomness is about: F-7
EPRI Proprietary Licensed Material Example Problem for Service Water Pump
β RSS = 0.20 For fragilities anchored to pga, the uncertainty at 10 Hz is about:
β USS = 0.16 In addition, the earthquake ground motion is specified as the average of two horizontal components. The peak response in one direction will govern the structural response of the 2D model. From Tables 3-2 and 3-3 of Reference F2,
Fpeak =
1 = 0.92 1.09
βRpeak = 0.13
Combining factors and β s .
FSS = 0.69(0.92) = 0.63 βRSS = 0.20 βUSS = (0.16 2 + 0.13 2 )1/ 2 = 0.21
F.4.2 Damping The 4% design damping utilized in development of response spectra is considered median for the low stress level in the structure. FD = 1.0
UHS spectra are only provided at 5% damping. At 10 Hz the UHS spectra are rising as opposed to the decayed peak of the DBE spectrum. In this case, the uncertainty in response due to damping is estimated as:
β UD = 0.15 F.4.3 Modeling The model is simple, is fixed base and dominant response is primarily in a single mode as indicated by the spectrum in Figure F-3. Code properties were used for concrete thus, according to the guidance in Reference F2, the calculated frequency is considered to be median centered. FM = 1.0
F-8
EPRI Proprietary Licensed Material Example Problem for Service Water Pump
The UHS spectra slope is not very steep at 10 Hz and the uncertainty due to variability in structural frequency is estimated as:
β Uf = 0.10 The mode shape for the short stiff fixed base structure is considered to not vary significantly from variations in modeling parameters.
β UMS = 0.05 β UM = (0.12 + 0.05 2 )1/ 2 = 0.11
F.4.4 Mode Combination The response is primarily in a single mode. FMC = 1.0
βRMC = 0.05 F.4.5 Ground Motion Incoherence The structure is 58” x 124’ in plan dimension. At 10 Hz, the GMI factor was calculated to be: FGMI = 1.07
βU = 0.03
F.4.6 Structural Response Factor The resulting structural response factor is:
FRS = FSS FD FM FMC FGMI = (0.63)(1)(1)(1)(1.07) = 0.67 βR = (0.20 2 + 0 + 0 + 0.05 2 + 0)1/ 2 = 0.21 βU = (0.212 + 0.15 2 + 0.112 + 0 + 0.03 2 )1/ 2 = 0.28
F.5
Fragility for Service Water Pumps
The median peak ground acceleration capacity is the product of the capacity factor, the equipment response factor, the structural response factor and the SSE peak ground acceleration. F-9
EPRI Proprietary Licensed Material Example Problem for Service Water Pump Am = 9(0.93)(0.67)(0.15) = 0.84g
β R = (0 + 0.10 2 + 0.212 )1/2 = 0.23 βU = (0.282 + 0.262 + 0.282 )1/ 2 = 0.47 The HCLPF is computed from: HCLPF = 0.84 exp (-1.65)(0.23 + 0.47) = 0.26g
In this case, the original target for screening was 0.3g pga. Suspicions regarding the design analysis led to the more detailed evaluations and it is shown that the target was not met.
F.6
References
F1. SQUG, “Generic Implementation Procedure (GIP) for Seismic Verification of Nuclear Power Equipment,” Revision 2, Corrected – June 1991, Seismic Qualification Utility Group. F2. EPRI TR-103959, “Methodology for Developing Seismic Fragilities,” EPRI, Palo Alto, California, June 1994.
F-10
EPRI Proprietary Licensed Material
G GENERAL METHODOLOGY FOR LIQUEFACTION SEISMIC FRAGILITY ASSESSMENT AND EXAMPLE ANALYSIS
G.1
Introduction
Determinations of liquefaction seismic fragility is uncommon, and hence, the specific methods for liquefaction fragility assessment are not as well established and commonly accepted/applied as those for failures of structures and mechanical/electrical equipment. As for any fragility assessment (FA), however, the development of liquefaction seismic fragility follows the general FA framework, that requires probabilistic characterization of seismic resistance parameters and related seismic load effects. For soil liquefaction, the probabilistic characterization of resistance requires knowledge of the methods and results of in-situ tests and collection of other geotechnical data, whereas probabilistic characterization of load effects on resistance (when the seismic load is characterized by a scalar parameter, such as peak ground acceleration [PGA] or spectral acceleration [Sa]) requires knowledge of the variability in magnitude, duration, shear-stress time histories, etc., and their relationship to liquefaction failure. Below are presented a brief summary of background on methods (both deterministic and probabilistic) for seismic liquefaction assessment, and discussion of the basis and overview of approach for seismic FA of soil failure due to liquefaction. As is the case for evaluation of structural/mechanical/electrical components, a fragility analysis should be undertaken only if the possibility of failure cannot be eliminated on a conservative basis in a screening evaluation. EPRI NP-6041-SL (1991) describes a set of procedures for performing a screening evaluation of seismic liquefaction potential. These procedures are compatible with methods for seismic liquefaction FA, and hence, any liquefaction FA should first be preceded by the appropriate screening evaluation.
G.2
Background
Assessment of soil liquefaction is a complex issue that has been studied extensively since the early 1960’s. Since the 1980’s, significant advancements have been made in identifying the parameters and relationships important to predicting the occurrence and severity of liquefaction. Kramer (1996) provides a valuable overview of seismic liquefaction assessment, including background on the development of modern methods.
G-1
EPRI Proprietary Licensed Material General Methodology for Liquefaction Seismic Fragility Assessment and Example Analysis
Liquefaction failure is manifested, principally, according to one of two failure modes: (1) flow failure, where the shear strength of the soil drops below the level needed to maintain stability under static conditions, and very large movements can be produced under the effect of static gravitational forces; and (2) cyclic mobility (including lateral spreading) failure, where incremental damage/displacements are accumulated as shear-stress/load pulses momentarily exceed the shear strength/resistance of the soil during dynamic response. Either mode of failure can lead to excessive strains, and hence, displacements that could, in turn, lead to unacceptable performance of supported structures, buried piping, tanks, etc., at a nuclear power plant. Although detailed approaches for seismic liquefaction assessment can be quite theoretical and involved, suitably accurate simplified deterministic approaches, based on empirical methods, have been developed. Perhaps the most recent and widely accepted of such approaches is that published in 1997 by the U.S. National Center for Earthquake Engineering Research (Youd and Idriss, 1997), that embodies knowledge acquired from numerous studies by several experts. Various probabilistic approaches of seismic liquefaction assessment have also been developed, and these generally are implemented in accordance with one of the following basic strategies: (a) characterizing the key parameters and relationships in a simplified deterministic model as random, and developing a derived expression or formulation/procedure for determining probability of liquefaction for a given soil deposit and seismic load amplitude; or (b) direct statistical classification and regression analysis of empirical observations where key in-situ resistance parameters and load information have been obtained. Using the latter approach, Liao et al. (1998) developed the following expression for probability of liquefaction:
PL =
1 1+ e
−[ β 0 + β1 ln(CSR) + β 2 (N1 )60 ]
where β 0 , β 1, β 2 are parameters determined from regression analysis for specific soil types (e.g., clean sands, silty sands, etc.), CSR is the cyclic stress ratio (load parameter), and (N1)60 is the standardized/corrected blow count. The reference list identifies several documents that describe probabilistic approaches for seismic liquefaction assessment. An approach that would capture the uncertainty in the methodologies would be a simulation that makes use of multiple methods.
G.3
Basis of Approach
The key parameters for liquefaction assessment are relevant measures of cyclic (shear) stress ratio. Thus, the seismic demand is expressed as a loading cyclic stress ratio, CSR, and the seismic capacity is expressed as a cyclic stress resistance ratio of the soil, CRR. The factor of safety against liquefaction, FSL , is given simply as: FSL =
cyclic shear stress required to cause liquefacti on CRR = equivalent cyclic shear stress induced by earthquake CRR
To determine CSR, it is necessary to determine the shear stresses at depth in the soil caused by the earthquake. This can be accomplished using site response analysis using a simplified G-2
EPRI Proprietary Licensed Material General Methodology for Liquefaction Seismic Fragility Assessment and Example Analysis
formula, based on a one-dimensional equivalent-linear SHAKE model or using more sophisticated software such as DE SRA-2C that takes into account the degradation of the soils due to progressive pore water pressure buildup during an earthquake. At each depth location of interest, an equivalent cyclic shear stress, τ cyc , is obtained (in terms of the maximum stress) and an equivalent number of cycles at this cyclic stress level is estimated based on magnitude. The cyclic shear stress is normalized by the effective vertical stress, and corrected for field conditions, in order to obtain the equivalent cyclic stress ratio CSR. To determine CRR, existing empirical relationships are available that depend on the measured in-situ resistance [i.e., value of (N1)60, CPT cone resistance, shear wave velocity, etc.], percent fines, effective confining stress, and magnitude. For probabilistic analysis based on strategy (a) described above, it is desirable to define and estimate variabilities βR , βU associated with the parameters and relationships involved in determining CRR and the CSR (given that the ground motion parameter is known). In some instances, it is possible to determine these values from existing results (e.g., researchers have provided statistics for many of the relationships governing the empirical determination of CRR and CSR), whereas for some components of the analysis (e.g., the determination of random variability in maximum shear stress at depth) it is beneficial to estimate variabilities from results of response simulations. Because failure of nuclear plant components will generally depend, not just on the occurrence of liquefaction, but rather on the magnitude of accumulated shear deformations or soil settlement, the fragility curves should be referenced to a state (or states) of liquefaction capable of developing shear deformations, or loss of soil strength, causing distress to plant components.
G.4
Example Case Study
G.4.1 Overview of Approach Using the above general approach, a liquefaction fragility analysis was performed for a site that would not pass the screening guidelines in EPRI (1991). A family of fragility curves (accounting for both random [aleatory] and modeling [epistemic] uncertainties) was developed for each of the following five end-states of interest:
i. Incipient liquefaction ii. Gross liquefaction iii. Level-ground liquefaction-induced settlement of about 5 cm (2 inches). iv. Level-ground liquefaction-induced settlements of about 10 cm (4 inches). v. Level-ground liquefaction-induced settlements of about 20 cm (8 inches). Probabilistic fragility calculations were performed using available information on relevant site conditions, deterministic liquefaction potential, and site-specific probabilistic seismic hazard. G-3
EPRI Proprietary Licensed Material General Methodology for Liquefaction Seismic Fragility Assessment and Example Analysis
The procedure of NCEER (Youd and Idriss, 1997) was followed in conducting individual liquefaction analyses, and the procedure of Ishihara and Yoshimine was used in computing settlements associated with level-ground liquefaction. The soil profile was subdivided into uniform layers having thickness of about 30.5 cm (one foot), over a range of depths from zero to about 25 meters (98 feet). The most important basic random variables and uncertain variables were identified and characterized by means of appropriate probability distributions. The Latin-Hypercube Simulation (LHS) approach was implemented to (a) obtain several simulated “samples” of each random and uncertain variable, and (b) randomly combine these samples to obtain several simulated “realizations” of conditions that govern liquefaction-related behavior. Each simulated combination/realization defined a set of inputs for performing computational analyses of liquefaction safety factor, post-liquefaction settlements, and settlement-related failures, for a range of ground motions. In conducting each fragility analysis (for each given end-state of interest), two sets of simulations were performed. The first set accounted for only the random components of uncertainty, whereas the second set accounted for composite uncertainty associated with both random and epistemic elements. This approach enabled the total variability of the derived fragility functions to be separated into its random and epistemic contributors. G.4.2 Initial Liquefaction Analysis and Results In an initial fragility analysis pertaining to the state of gross liquefaction, two sets of 50 simulations were generated, and liquefaction calculations were completed manually, using computational spreadsheets. In performing each of these manual calculations, plots of liquefaction safety factor versus depth were examined, and the surface peak-ground acceleration (PGA) was iteratively adjusted until a state of gross liquefaction (corresponding to the somewhat imprecise condition that liquefaction safety factor was observed to be less than unity over a significant total depth) was realized. This initial analysis resulted in fragility curves that could be approximated by a conventional double-lognormal distribution having the following equivalent fragility parameters defined at the top of the soil surface. Preliminary Fragility Parameters for Gross Liquefaction: Motion keyed to:
Ground-surface PGA
Median
βR
βU
0.41
0.24
0.33
A significant observation resulting from this initial analysis was that, in most simulations, only a relatively small increment in ground-surface PGA was generally required to go from a state of incipient liquefaction (i.e., safety factor of 1.0 in a single isolated soil layer) to gross liquefaction (i.e., safety factor below 1.0 in several soil layers). This observation suggested that the fragility parameters for gross liquefaction would not change significantly if a more precise definition of gross liquefaction were implemented. In addition, the observation implied that, for a given simulation, liquefaction-induced settlement (i.e., cumulative post-liquefaction settlement at the ground surface) would increase dramatically, from a nominal value to a limiting maximum, over G-4
EPRI Proprietary Licensed Material General Methodology for Liquefaction Seismic Fragility Assessment and Example Analysis
a comparatively narrow increment in ground-surface PGA. Hence, the initial fragility results could serve as a meaningful approximation to the fragility functions describing liquefactioninduced settlement failures. G.4.3 Detailed Liquefaction and Settlement Analysis and Results Although the initial analysis was considered to be adequate in meaningfully conveying overall liquefaction fragility additional work was performed to refine the fragility assessment and to provide a confirmatory internal quality check on the validity of the initial analysis. The additional work consisted of explicitly computing liquefaction-induced settlements, and defining failure for affected components in terms of a criterion based on settlement. For this more detailed assessment, two sets of 500 simulations were generated, liquefaction and settlement analyses were performed for each simulation using a special-purpose computer code, and fragility curves were developed for surface ground motions ranging from 0.01 g to 2.00 g. Two significant and distinct observations to be made in regard to the more detailed fragility assessment are (1) that limiting values of post-liquefaction volumetric strain limit the maximum amount of cumulative settlement that can be achieved in a given simulation, and (2) a small fraction of simulations result in a soil profile that is substantially invulnerable to gross liquefaction. The first observation means that, at some point, for all simulations, the settlement associated with level-ground liquefaction ceases to increase with ground acceleration. The second observation means that gross liquefaction will never occur, regardless of ground-motion level, for some of the simulated soil profiles (although incipient liquefaction and some small settlements can be produced for these profiles). These two implications are considered to be physically realistic for the case of level-ground liquefaction, as opposed to undesirable artifacts of the simulation process. An important consequence of these two points is that fragility curves associated with both gross liquefaction and settlement-related failures can, in some cases, have a limiting maximum value that is less than unity. The more detailed fragility analysis resulted in fragility curves for incipient liquefaction and gross liquefaction that could be well approximated by the following equivalent fragility parameters of a double-lognormal distribution. Detailed-Analysis Fragility Parameters for Incipient Liquefaction: Motion keyed to:
Ground-surface PGA
Median
βR
βU
0.27
0.24
0.36
Detailed-Analysis Fragility Parameters for Gross Liquefaction: Motion keyed to:
Ground-surface PGA
Median
βR
βU
0.40
0.23
0.36
In this analysis, incipient and gross liquefaction was defined explicitly and consistently, as follows: G-5
EPRI Proprietary Licensed Material General Methodology for Liquefaction Seismic Fragility Assessment and Example Analysis
•
Incipient liquefaction corresponded to the state where the most vulnerable soil layer just reached a liquefaction safety factor of unity.
•
Gross liquefaction corresponded to the state where liquefaction safety factors less than unity occurred over a cumulative soil depth of about 3 meters (10 feet, or 10 soil layers).
In the set of simulations that accounted only for random variability, none of the simulated soil profiles was invulnerable to gross or incipient liquefaction. For the set of simulations that accounted for composite variability, 13 out of 500 (or 2.6 percent) of the simulated soil profiles were invulnerable to gross liquefaction, but none were invulnerable to incipient liquefaction. The small fraction of soil profiles that were invulnerable to gross liquefaction limited the maximum probability of gross liquefaction (at high ground motion), in the resulting weighted composite fragility curve, to 0.974. Since this value was only a small deviation from unity, and the shape of the fragility curve was otherwise significantly lognormal in character, it was decided that the double-lognormal fragility representation was reasonable. Figure G-1 show plots of the weighted fragility curves resulting from each set of simulations, for end-states of incipient liquefaction and gross liquefaction. The definition of incipient and gross liquefaction do not, however, lead to a decision as to what would fail or what could fail. Therefore, further analyses were conducted to determine the settlement of the soil as a result of liquefaction and the consquence of the settlement to buried pipes and concrete electrical ducts. For end-states associated with component failure due to excessive settlements, more dramatic constraints on maximum failure probability were realized with increases in the component’s median resistance to settlement. As indicated previously, three related cases were examined, for components having median failure settlements of 5 cm (2 inches), 10 cm (4 inches), and 20 cm (8 inches). A double-lognormal distribution was used for characterizing a component’s ability to resist settlement, and in each of the preceding cases, parameters β R =0.30 and β U =0.60 were used to describe, respectively, random variability and modeling uncertainty in settlements causing failure. The value of β R approximately accounts both for randomness in material properties affecting resistances and randomness associated with spatial non-uniformity in settlements. The high value for β U reflects the situation that specific analysis of buried piping connecting to buildings was not available to determine settlement failure thresholds. Due to the constraints on failure probabilities, settlement-related fragility curves could not, in general, be properly conveyed by equivalent parameters of a double-lognormal probability distribution. For this reason, only the fragility curves resulting from the simulations are presented. Figure G-2 show plots of the weighted fragility curve resulting from each set of simulations, for the three cases of median failure of buried piping for settlement of 5 cm, 10 cm, and 20 cm. The fragility plots are relative to the surface pga. Examination of these figures shows that, as component median capacity against settlement increases, the asymptotic (maximum) level of failure probability decreases markedly. Again, the reason for the reduced asymptote (i.e., less than unity) of the fragility curve is that postliquefaction volumetric strains in the soil reach limiting values (that depend upon the initial relative density of the soil). These limiting strains imply maximum settlements that do not G-6
EPRI Proprietary Licensed Material General Methodology for Liquefaction Seismic Fragility Assessment and Example Analysis
increase with ground motion. The asymptotic failure probability of the fragility curve is thus controlled by the limiting maximum settlements and the component’s probability distribution of settlement capacity.
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
EPRI Proprietary Licensed Material General Methodology for Liquefaction Seismic Fragility Assessment and Example Analysis
(Median Failure Settlement = 5 cm
(Median Failure Settlement = 10 cm
(Median Failure Settlement = 20 cm
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
EPRI Proprietary Licensed Material General Methodology for Liquefaction Seismic Fragility Assessment and Example Analysis
G.5
References
1.
Blake, T.F. (1998). “LIQUEFY2 Version 1.50 Update,” LIQUEFY2 User’s Manual, Thomas F. Blake Computer Services & Software, Newbury Park, CA.
2.
Chameau, J.L., and G.W. Clough (1983). “Probabilistic Pore Pressure Analysis for Seismic Loading,” Journal of Geotechnical Engineering, ASCE, Vol. 109, No. 4, pp. 507-524.
3.
Christian, J.T., and W.F. Swiger (1973). “Statistic of Liquefaction and SPT Results,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 101, No. GT-11, pp. 1135-1150.
4.
EPRI (1991). “A Methodology for Assessment of Nuclear Power Plant Seismic Margin (Revision 1),” EPRI NP-6041-SL, EPRI, Palo Alto, CA.
5.
Fardis, M.N., and D. Veneziano (1982). “Probabilistic Analysis of Deposit Liquefaction,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 108, No. GT-3, pp. 395-417.
6.
Haldar, A., and W.H. Tang (1981). “Statistical Study of Uniform Cycles in Earthquakes,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 107, No. GT-5, pp. 577-589.
7.
Haldar, A., and W.H. Tang (1979). “Probabilistic Evaluation of Liquefaction Potential,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 105, No. GT-2, pp. 145-163.
8.
Ishihara, K. and Yoshimine, M., “Evaluation of Settlements in Sand Deposits Following Liquefaction During Earthquakes,” Soils and Foundations, Vol. 32, No. 1, pp. 173-188.
9.
Kramer, S.L. (1996). “Geotechnical Earthquake Engineering,” Prehntice-Hall Inc., Upper Saddle River, New Jersey, 653 p.
10. Liao, S.S.C., D. Veneziano, and R.V. Whitman (1988). “Regression Models for Evaluating Liquefaction Probability,” Journal of Geotechnical Engineering, ASCE, Vol. 114, No. 4, pp. 389-411. 11. Veneziano, D., and S.S.C. Liao (1984). “Statistical Analysis of Liquefaction Data,” Proceedings of the 4th Specialty Conference on Probabilistic Mechanics and Structural Reliability, ASCE, pp. 206-209. 12. Whitman, R.V. (1971). “Resistance of Soil to Liquefaction and Settlement,” Soils and Foundations, Vol. 11, No. 4, pp. 59-68. 13. Yegian, M.K., and R.V. Whitman (1978). “Risk Analysis for Ground Failure by Liquefaction,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 104, No. GT-7, pp. 921-938. 14. Youd, T.L. and I.M. Idriss (1997). “Summary Report,” Proceedings of the NCEER Workshop on Evaluation of Liquefaction Resistance of Soils (T.L. Youd and I.M. Idriss, G-9
EPRI Proprietary Licensed Material General Methodology for Liquefaction Seismic Fragility Assessment and Example Analysis
editors), held at Salt Lake City, Utah (January 5-6, 1996), Technical Report No. NCEER-97-0022. 15. Youd, T.L. and S.K. Noble (1997). “Magnitude Scaling Factors,” Proceedings of the NCEER Workshop on Evaluation of Liquefaction Resistance of Soils (T.L. Youd and I.M. Idriss, editors), held at Salt Lake City, Utah (January 5-6, 1996), Technical Report No. NCEER-97-0022. 16. Youd, T.L., K.H. Stokoe, P.K. Robertson, W.D.L. Finn, and P.M. Byrne (1996). Proceedings of a Symposium on Recent Developments in Seismic Liquefaction Assessment, Vancouver, B.C., Sponsored by ConeTec, April 12.
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