ML20087G844

Seismic Fragilities of Structures & Components at Millstone 3 Nuclear Power Station

ML20087G844
Person / Time
Site:	Millstone
Issue date:	03/31/1984
From:	Campbell R, Hashimoto P, Wesley D STRUCTURAL MECHANICS ASSOCIATES
To:
Shared Package
ML20087G829	List: B11080, Forwards Seismic Fragilities of Structures & Components at Millstone 3 Nuclear Power Station, Per 840306 Meeting Commitment ML20087G844
References
SMA-20601.01-R1, SMA-20601.01-R1-0, NUDOCS 8403200152
Download: ML20087G844 (193)

Text

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SEISMIC FRAGILITIES OF STRUCTURES A?!D COMPONENTS AT THE MILLSTONE 3 NUCLEAR POWER STATION F

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prepared for NORTHEAST UTILITIES Hartford, Connecticut k

March, 1984 I

g STRUCTURAL mECHR0lCS W""MMIM RSSOCIRTES a cent c o,o.

5100 Birch Street. Newport Beach. Calif. 92660 (7141833-7552 8403200152 840313 PDR ADOCK 05000423 A PDR

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1. SMA 20601.01-R1-0 SEISMIC FRAGILITIf J, STRUCTURES AND COMPONENTS AT THE MILLSTONE 3 NUCLEAR POWER STATION I

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by D. A. Wesley R. D. Campbell I P. S. Hashimoto T. R. Kipp W. H. Tong I

prepared for NORTHEAST UTILITIES Hartford, Connecticut l March, 1984 I

g STRUCTURAL l mECHA0KS ASSOCIATES Y A CeHf Coro 5160 Bach Street, Newport Beach, Cahf. 92660 (714) 833 7552 l -

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J TABLE OF CONTENTS

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[ Section Title Page 1 INTRODUCTION . . . . . . . . . . . . . . . . . . 1-1 2 GENERAL CRITERIA FOR DEVELOPMENT OF MEDIAN SEISMIC SAFETY FACTORS . . . . . . . . . . . . . 2-1 2.1 Definition of Failure . . . . . . . . . . . 2-2 l 2.1.1 Seismic Category I Structures ... 2-2 2.1.2 Seismic Category I Equipment and '

2-3 I

Piping . . . . . . . . . . . . . . .

2.1.3 Non-Category I Structures ..... 2-3 2.1.4 Non-Seismic Category I Equipment and Piping . . . . . . . . . . . . . 2-3 2.2 Basis for Safety Factors Derived in Study . 2-4 2.2.1 Structural Response and Capacity . . 2-4 2.2.2 Seismic Category I Piping and Equipment Response and Capacity .. 2-5 2.3 Formulation Used for Fragility Curves . . . 2-6 2.4 Design and Construction Errors ...... 2-10 2.5 Correlation between Failure Modes . . . . . 2-11 3 DIFFERENCES BETWEEN CRITERIA USED FOR DESIGN OF I MILLSTONE 3 AND PARAMETERS USED IN THE EVALUA-TION OF THE SEISMIC CAPACITY . . . . . . . . . .

3.1 Strength .................

3-1 3-2 3.2 Ductility . . . . . . . . . . . . . . . . . 3-3 3.3 System Response . . . . . . . . . . . . . . 3-4 I 3.3.1 Earthquake Characteristics . . . . .

3.3.2 System Damping . . . . . . . . . . .

3-4 3-5 3.3.3 Load Combinations ......... 3-5 3.3 A Modal Combination ......... 3-6 3.3.5 Combination of Responses for Earth-quake Directional Components . . . . 3-6 3.3.6 Structure Modeling Considerations . 3-7 N

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TABLE OF CONTENTS _(Continued) l Section Title Page 4 STRUCTURES .................. 4-1 4.1 Median Safety Factors and Logarithmic Standard Deviations ........... 4-1 4.1.1 Structure Capacity ........ 4-4 4.1.1.1 Concrete Compressive Strength . . . . . . . . . 4-4 4.1.1.2 Reinforcing Steel Yield Strength . . . . . . . . . 4-6 4.1.1.3 Shear Strength of Concrete Walls . . . . . . 4-7 4.1.1.4 Example of Shear Wall i Failure in Shear . . . . . 4-10 4.1.1.5 Strength of Shear Walls

[

in Flexure under In-Plane S Fo rc e s . . . . . . . . . . 4-11 4.1.1.6 Example of Shear Wall

{ Failure in Flexure . . . . 4-12 4.1.1.7 Structure Sliding .... 4-13

[- 4.1.1.8 Example of Sliding-Induced Failure ......... 4-14 4.1.2 Structure Ductility . . . . . . . . 4-16 4.1.2.1 Example of Ductility Factor . . . . . . . . . . 4-19 4.1.3 Structure Response Used for Struc-ture Fragility Evaluations .... 4-20 4.1.4 Spectral Shape, Damping, and Modeling Factors . . . ... . . . . 4-21 4.1.4.1 Example of Spectral Shape, Damping, and Modeling Factors ......... 4-24 4.1.5 Modal Combination ........ 4-26

[ 4.1.6 Combination of Earthquake

( Components ........-.... 4-27

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E j TABLE OF C0f0TNTS (Continued)

L Section Tith Page I 4 4.1.7 Soil-Structure Interaction (Cont.) Effects ............. 4-28 4.2 Structure Fragilities . . . . . . . . . . . 4-30 4.2.1 Containment and Internal Structures. 4-30 4.2.2 Auxiliary Building . . . . . . . . . 4-33 4.2.3 Control Building . . . . . . . . . . 4-36 4.2.4 Emergency Generator Enclosure ... 4-38 4.2.5 Engineered Safety Features i Building . . . . . . . . . . . . . . 4-39 4.2.6 Pumphouse ............. 4-40 4.2.7 Demineralized Water Storage Tank . . 4-41 4.2.8 Refueling Water Storage Tank . . . . 4-42 5 EQUIPMENT FRAGILITY .............. 5-1 5.1 Equipment Fragility Methodology . . . . . . 5-2 5.1.1 Fragility Derivation . . . . . . . . 5-2 5.1.1.1 Equipment Capacity Factor . 5-3 5.1.1.1.1 Strength Factor. 5-4 I 5.1.1.1.2 Inelastic Energy Absorption Factor . . . . . 5-8 5.1.1.2 Equipment Response Factor . 5-10 5.1.1.2.1 Qualification Method Factor . . . . . .. 5-11 5.1.1.2.1.1 Static Analy-1 sis . . . . . . . . . . . . 5-12 5.1.1.2.1.2 Dynamic Anal g sis . . . . . . . . . . .y- . 5-12 r- 5.1.1.2.1.3 Testing ... 5-13 5.1.1.2.2 Equipment Spec-tral Shape Factor . . . . . 5-13 5.1.1.2.2.1 Peak Broaden-ing and Smoothing . . . . . 5-14  ;

iii

c TABLE OF CONTENTS (Continued)

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[ Section Title Page I 5 5.1.1.2.3 Modeling Factor . 5-15 (Cont.) 5.1.1.2.4 Damping Factor. . 5-16 5.1.1.2.5 Mode Combination Factor . . . . . . . . . . . 5-17 5.1.1.2.6 Earthquake Compo-nent Cc,mbination Factor .. 5-18 5.1.1.2.7 Boundary Condi-I tions Factors (Testing) .. 5-19 l

i 5.1.1.2.3 Spectral Test Method . . . . . . . . . . . 5-20 5.1.1.2.9 Multi-Di rectional Effects .......... 5-20 5.1.1.2.9.1 Biaxial Testing 5-21 5.1.1.2.9.2 Uniaxial Test-ing ............ 5-22 5.1.1.3 Structural Response Factors. 5-22 5.1.2 Information Sources . . . ...... 5-24 1 5.1.3 Equipment Categories ........ 5-E5 5.2 Equipment Fragility Examples . . . . . . . . 5-26 5.2.1 Example of a Plant Specif,c Fragility Derivation Based Upon Summary In-formation . . . . . . . . . . . . . . 5-27 5.2.1.1 RHR Heat Exchanger Capacity Factor . . . . . . . . . . . 5-27 I 5.2.1.2 RHR Heat Exchanger Response Factor . . . . . . . . . . . 5-29 5.2.1.2.1 Qualir'ication l Method Factor .......

5.2.1.2.2 Spectral Shape 5-30 Factor . . . . . . . . . . . 5-30 I 5.2.1.2.3 Modeling Factor . 5-31 5.2.1.2.4 Damping Factor. . 5-31 5.2.1.2.5 Mode Combination Facter . . . . . . . . . . . 5-32 5.2.1 2.6 Earthquake Compo-nent Combination . . . . . . 5-32 iv

TABLE OF CONTENTS (Continued) l Section Title Page I 5.2.1.2.7 Overall Equip-ment Response Factor . . . . 5-33 I

5.2.1.3 RHR Heat Exchanger Struc-tural Response Factor ... 5-33 5.2.1.4 RHR Heat Exchanger Ground Acceleration Capacity ... 5-33 5.2.2 Example of a Plant Specific Fragility Derivation Based Upon a Review of the Component Qualification Stress Report 5-34 5.2.2.1 Containment Recirculation #

1 Cooler Capacity Factor . . . 5-35 5.2.2.2 Containment Recirculation I Cooler Equipment Response Factors .......... 5-37 5.2.2.2.1 Qualification Method Factor ....... 5-37 5.2.2.2.2 Spectral Shape Factor . . . . . . . . . . . 5-38 5.2.2.2.3 Modeling Factor . 5-39 5.2.2.2.4 Damping Factor. . 5-39 5.2.2.2.5 Mode Combination Factor . . . . . . . . . . . 5- +0 5.2.2.2.6 Earthquake Compo-I nent Combination . . . . . . 5-40 5.2.2.2.7 Overall Equip-I ment Response Factor . . . .

5.2.2.3 Containment Recirculation 5-41 Cooler Structural Response Il Factor . . . . . . . . . . .

5.2.2.4 Containment Recirculation 5-41 Cooler Ground Acceleration Capacity . . . . . . . . . . 5-42 5.2.3 Example of Generic Fragility Deriva-tion Based on Design Specifications . 5-43 5.2.3.1 B0P Piping Capacity Factor . 5-43 v

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TABLE OF CONTENTS (Continued)

I Section Title Page I

I 5 5.2.3.2 Piping Equipment Response (Cont.) Factors . . . , . . . . . . 5-45 5.2.3.3 Piping Structural Response Factors . . . . . . . . . . 5-47 5.2.3.4 Piping Ground Acceleration Capacity ......... 5-47 5.2.4 Example of a Plant Specific Frag-ility Derivation Based Upon Compo-nent Test Data . . . . . . . . . . . 5-48 5.2.4.1 480 VAC Motor Control Center Capacity Factor. . . 5-48 5.2.4.2 480 VAC Motor Control Center Equipment Response Factor .......... 5-50 5.2.4.2.1 Qualification Method Factor . . . . . . . 5-50 5.2.4.2.2 Spectral Shape Factor ......... 5-51 I 5.2.4.2.3 Boundary Condi-tions Factor. ....... 5-51 5.2.4.2.4 Damping Factor . 5-51 5.2.4.2.5 Spectral Test Methods Factor ...... 5-52 I 5.2.4.2.6 Multi-Direction-al Effects Factor . . . . . 5-52 5.2.4.2.7 Overall Equip-ment Response Factor ... 5-52 5.2.4.3 480 VAC Motor Control Center Structural Response Factor .......... 5-52 5.2.4.4 480 VAC Motor Control Center Acceleration I Capacity ......... 5-53 5.2.5 Exampic of Fragility Based on Engi-I neering Judgmer.t and Earthquake Experience . . . . . . . . . . . . . 5-53 5.2.5.1 Offsite Power Ground Accel-eration Capacity ..... 5-54 5.3 Equipment Fragility Results . . . . . . . . 5-54 vi

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TABLE OF CONTENTS (Continued)

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5ection

{ Title Page REFERENCES R-1 APPENDIX Characteristics of the Lognormal Distribution A-1 1

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l. INTRODUCTION A probabilistic risk assessment (PRA) of the Millstone 3 Nuclear Power Station is being conducted by Northeast Utilities (NU). In this I evaluation, system models, event trees, and fault trees are utilized to determine the frequency of radioactive release from the site due to J random equipment failure and failures initiated by natural hazard /

l events. Earthquakes are one of the extreme natural hazards being considered in this PRA. Structural Mechanics Associates, Inc. (SMA) is I under contract to NU to provide the required information for earthquake (seismic) capacities of structures and equipment items that are included ,

in the risk models.

The frequency of seismically-induced failure as a function of effective peak ground acceleration for both safety-related structures and equipment has been developed by SMA for the Millstone 3.f acility. Also included is the expected variability in the frequency ef failure. The determination of the seismic hazard is being conducted by others. The infonnation for both the frequency of occurrence of different levels of effective peak ground acceleration and the frequency of failure of the safety-related systems and components will then be inccrporated into the risk models by NU to determine the frequency of seismic-induced radioactive release from the site.

I In order to correctly interpret the fragilities derived in this n! port, it is necessary to define the effective peak acceleration to which these fragilities are anchored. It is recognized that the damage l potential of an earthquake depends on many factors, among which are magni-tude, peak acceleration, and duration. For the Millstone site, it is estimated that the majority of seismic risk results from earthquakes that have magnitudes between 5.3 and 6.3. This is the range represented by the ground response spectra used to evaluate the fragilities. Because 1-1

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the ground response spectra used in this study are centered around this magnitude range, the fragilities given in this report are to be anchored to the mean peak acceleration. This acceleration is the average of the peak accelerations from two orthogonal horizontal components. Note that I

if the magnitude range were different, say 6.0 to 7.0, a somewhat different set of median spectra would be required.

l The Nillstone 3 Nuclear Power Station was designed in the 1970's in accordance with criteria and codes in effect at that time (Reference 1). Table 1-1 lists some of the more important codes and specifications used in design n the structures. The Millstone 3 systems and components which are essential to the prevention or mitigation of consequences of I accidents which could affect the public health and safety were designed to enable the facility to withstand the effects of natural forces including earthquakes. The design criteria included the effects of simultaneous earthquake and loss-of-coolant-accident (LOCA) conditions.

l The plant was designed to withstand both an Operating Basis Earthquake (0BE) and a Safe Shutdown Earthqune (SSE). The structural de:;ign criteria for the SSE was based on 0.179 and the OBE on 0.09g peak horizontal ground accelerations for all Seismic Category I structures.

I Vertical accelerations of two-thirds of the corresponding horizontal values were used for both the OBE and SSE.

The plant structurn and equipment were originally divided into two categories according to their function and the degree of integrity required to protect the public. These categories are Category I and non-Category I. Millstone 3 Nuclear Power Station structures, systems and components important to safety, as well as their foundations and supports, were designed to withstand the effects of an OBE and an SSE and were, thus, designated as Seismic Category I. Seismic Category I structures include:

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Containment and Internal Structure Containment Enclosure Building i Auxiliary Building Fuel Building (Partially)

Control Building Cable Tunnel Emergency Generator Enclosure and Diesel Building Fuel Oil Tank Vault Engineered Safety Features Building I Main Steam Valve Building Circulating and Service Water Pumphouse (Partially)

Hydrogen Recombiner Building Circulating Water Disthrge Tunnel and Discharge Structure Railroad Canopy Refueling Water Storage Tank (RWST)

Demineralized Water Storage Tank (DWST)

Not all of these structures house equipment which is important to prevent core melt. For instance, the Fuel Building, Hydrogen Recombiner Building, and Railroad Canopy were designed as Category I l structures but are not essential to prevent core melt. Other structures such as the Turbine Building and the Containment Enclosure Building were I evaluated only to the extent that their failure could cause damage to one of the essential structures. The structures evaluated in detail consist of:

I Reactor containment building and concrete internals structures Engineered safety features building Auxiliary building Control building Emergency generator enclorure Service water pumphouse l

The Millstone 3 site is located on the Millstone Point near Niantic Bay on the south shore of Connecticut on the Long Island Sound.

The site consists of competent rock overlain in some areas by ablation till and dense basal till. Plant grade is at approximately El. 24 ft.

The following elastic constants were developed for use in the design analysis of the structures dynamic response:

1-3

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Young's Shear

" Modulus, Modulus, Poisson's Material E (psi) G (psi) Ratio Rock 4x106 1.5x106 0.33 Basal Till 4x105 1,4xio5 o,44

[ Ablation Till 2x7x104 9.0x103 0.49 i

I Most structures important to safety are founded on bedrock with the exception of the Emergency Generator Enclosure and the Control Building. The Control Building is founded on 1 to 4 feet of structural backfill overlying 1 to 15 feet of basal till. The Emergency Generator Enclosure is founded on approximately 20 feet of structural backfill overlying a 20 foot thick layer of basal till. No evaluation of any possible soils-related failures was conducted. The Demineralized Water Storage Tank is founded on concrete fill to bedrock. The effects of the soil-structure interaction for structures founded on fill was accounted for in the design analysis using finite element methods. For structures I founded on bedrock, elastic half-space springs based on the rock properties were used.

The ground response spectra used in the design of Millstone 3 are Newmark-type spectra which are similar to those recommended in USNRC Regulatory Guide 1.60 (Reference 2). The horizontal ground response i spectra are anchored to 0.179 for the SSE and 0.09g for the OBE. The horizontal spectra used for design are shown in Figures 1-1 and 1-2.

i Both modal response spectrum and modal time-history analyses were conducted for the Millstone 3 Category I structures. In general, the response spectrum analysis results were used for evaluation of the struc-ture seismic loads and stresses while time-history results were used to generate in-structure response spectra for the design and evaluation of 1-4

piping and equipment. The synthetic time-histories were generated based J on the ground response spectra. Comparisons of the ground response L

spectra generated by these artificial time-history records compared to the SSE design spectra are shown in Figures 1-3 through 1-6 for 2, 5, 7 and 10 percent damping (Reference 1).

I Structures, equipment, and components which are important to plant operation, but are not essential for preventing an accident which would endanger the public health and safety and are not essential for the mitigation of the consequences of these accidents, are classified as non-Category I. An example of a non-Category I structure is the Turbine 1 Building. Non-Category I structures were investigated in this project only to the extent their failure could damage a safety-related structure or component. Examples of non-Category I equipment include the offsite power and the station power transformers.

For the most part, results of existing analyses and evaluations of structures and equipment for the Millstone 3 plant were utilized in this study. As part of this evaluation, some limited analysis based on original design analysis loads was conducted to determine the expected seismic capacities of the important structures. The approach adopted in thi., study was to determine the median factor of safety and its statisti-cal variability which exists for the SSE in order to estimate the expected I- response at f ailure. The median effective peak ground acceleration was used to define failure, rather than an instrumental peak acceleration which is not considered to be as accurate a descriptor of damage. It is known that earthquakes with only one or two high acceleration spikes are not as damaging to structures and equipment as longer duration earthquakes with multiple peaks at close to the maximum acceleration level. This is because the shorter duration earthquakes do not have sufficient energy content to develop rescnances. For this reason, the fragility evaluations I described in this report are keyed to an effective peak acceleration and an earthquake of the duration expected at Millstone 3. This type of I earthquake is expected to develop narrow band response spectra.

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I An evaluation of the individual important structures and some of the equipment was conducted for specific itens and failure modes.

However, much of the piping and equipment were evaluated on the basis of a number of generic categories. Although inelastic energy dissipation is included in determining the factors of safety, no nonlinear analyses have been conducted for either the structures or equipment for Millstone 3, and all evaluations were based on elastic analysis and load distributions.

I I These results can be used together with the estimated annual frequency of occurrence of various ground motion levels to determine the frequency of seismic-induced f ailure for each safety-related structure or component in the plant. In the total study, these conditional component I f ailure frequencies are used with systems models to detennine the proba-bility of core melt frequencies and radioactive release frequencies.

I These results are then combined with the results of the consequence analysis to determine the risks induced by earthquakes.

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..: . CODES AND STANDARDS USED IN THE DESIGN OF . .s; f ;,

iN CATEGORY I 5IRUCTURES (REFERENCE 1) . " ., r

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QI y Structural Component Design Codes and Specifications 3 ... y.

yf.s. -;r 5.? 1. ACI 211.1-70 Recomended Practice for Selecting Proportions k.

o T for Nonnal Weignt Concrete [A<.y

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2. ACI 214-65 Recomended Practice for Evaluation of l9 Compression Test Results of Field Concrete k._ h+

y .V."/ ns 7,g.4.4 g '. 3. ACI 301-72 Specification for Structural Concrete for Y Buildings qvd

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% . 4S[1 g r 4. ACI 304-59 Recomended Practice for Measuring, Mixing, and 'c a g.

p Placing Concrete y 9 5. ACI 305-72 Re,omended Practice for Hot Weather Concreting 7.h.$. f"

2 f.? 6. ACI 306-66 Recomended Practice for Cold Weather Concreting A *.$y W .. 7. ACI 310-71 Building Code Requirements for Reinforced Concrete i'.} endn 4.

.7. ; , 8. ACI 347-68 Recomended Practce for Concrete Formwork VE hD.[ .i7 ,k'..

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, 9. AISC Specification for the Design, Fabrication and

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Erection of Structural Steel for Buildings  :

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14 4 T.,%

jff No.1(November (December 8, 1971 1},1970),SupplementNo.2 and Supplement No. 3 (June V 12, 1974) M. . .

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10. AISC y Specification for Structural Joints Using f.STM A325 or A490 Bolts (April 18, 1972)

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11. ASTM A 36-74 Specification for Structural Steel

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12. ASTM A 193-73 Standard Specification for Alloy Steel and M;M 1.= Stainiess Steel Bolting Materials for *hJ jg{ High-Tem;trature Services

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CATEGORY I STRUCTURES (REFERENCE 1) M

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El vp Structural Component Design Codes and Specifications &

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({g 13. ASTM A 307-74 Specification for Low Carbon Steel h&

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Externally and Internally Threaded Standard ?g

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Fasteners f; ;g  %%

yt 4g 14. ASTM A 325-74 Specification for High Strength Bolts for D.

Structural Steel Joints Including Suitable W J-5 Nuts and Plain Hardened Wasbers ', Q.

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.i- 15. ASTM A 440-74 Specification for High Strength Structural W

Y Steel M

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16. ASTM A 441-74 Specification for High Strength Low-Alloy M Structural Manganese Vanadium Steel nA:-

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17. ASTM A 490-74 i:g.

Specification for Quenched and Tempered Alloy Steel Bolts for Structural Steel Joints ' )p.; k.

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c' 5 g

18. ASTM A 588-79 Specification for High-Strength Low-Alloy #p Y Structural Steel with 50,000 psi Minimum M"

,7 =. Yield Point to 4 Inches Thick  %;'

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$~ 19. ASTM A 615-68 Standard Specification for Deformed Billet iN fg Steel Bars for Concrete Reinforcement

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• including Supplement S-1 (December, 1972)

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7 20. ASTM C 31-69 Making and Curing Concrete Compressive and 4; m Flexural Strength Test Specimens in the Field d F.

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f- 21. ASTM C 33-71 Standard Specification for Concrete Aggregates (and 1978 Revision) s.c pi,-

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22. ASTM C 94-71 Specification for Ready-Mixed Concrete m M,.

.;l 3 23. ASTM C 109-1973

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.5.] y Method of Test for Compressive Strength of 0:h

f. Hydraulic Mortars (using 2-inch (50 mm) Cube  ! 25 M' Specimens) lt 4 '

U..Jj 24. ASTM C 143-71 6f Method of Test for Slump of Portland Cement MC

25. ASTM C 150-73 Specification for Portland Cement

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Q,[ l .y.y h- 26. ASTM C227-71 Test for Potential Reactivity of Cement g ~, y P

l Aggregate Combinations (Mortar Bar Method) g

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H TABLE 1-1 (Continued)

CODES AND STANDARDS USED IN THE DESIGN OF l

CATEGORY I STRUCTURES (REFERENCE 1)

Structural Component Design Codes and Specifications

27. ASTM C 233-69 Standard Method of Testing Air-entraining Admixtures for Concrete

28. ASTM C 260-69 Air-entraining Admixtures for Concrete I 29. ASTM C 289-71 Test for Potential Reactivity of Aggregates (Chemical Method)

30. ASTM C 295-1%5 I (1973)

Recommended Practice for Petrographic Examination of Aggregates for Concrete

31. ASTM C 586-69 Test for Potential Alkali Reactivity of Carbonate Rocks for Concrete Aggregates

32. AWS D1.1-72 Structural Welding Code Rev. 1-73

33. AWS D12.1-61 Recommended Practices for Welding Rein-I forcing Steel, Metal Inserts and Connections in Reinforced Concrete Construction

34. NRC Regulatory Guides as qualified in FSAR Section 1.8 (Reference I 1) on the following tcpics:

a. Cadweld Splices 1.8.1.10 I b.

c.

d.

Reinforcing Bar Testing Structural Acceptance Testing 1.8.1.15' 1.8.1.18 Placement of Concrete 1.8.1.55 I e.

f.

Design Response Spectra Seismic Damping Values 1.8.1.60 1.8.1.61

35. 30CA Basic Building Code of the Building 1 Officials and Code Administrators International, Inc.,1970

36. State of Connecticut Basic Building Code,1971 l 1-9

[ _ _ _ _ _ _ _ _ _ _ _ _ - - - - _ _ _ - -

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I FIGURE 1-5. COMPARISON OF ARTIFICIAL EARTHQUAKE TIME HISTORY 1 SPECTRUM WITH SSE DESIGN SPECTRUM (7% DAMPING) 1-14 L __

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1-15 1

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2. GENERAL CRITERIA FOR DEVELOPMENT OF MEDIAP SEISMIC SAFETY FACTORS l

l j The f actor of safety of a structure or component ir defined 1 herein as the resistence capacity divided by the response associated with the Safe Shutdown Earthquake (SSE) of 0.17g effective peak acceleration.

The development of seismic sai9ty factors associated with the SSE is based on consideration of several variables. The variability of dynamic 1 response to the specified acceleration and the strength capacity of the structure or equipment component are the two basic considerations in l determining the variability in the f actor of safety. Several variables are involved in determining both the structural response and the struc-tural capacity, and each such variable, in turn, has a median f actor of I safety and variability associated with it. The overall f actor of safety is the product of the factors of safety for each variable. The median of the overall f actor of safety is the product of the median safety factors I of all the variables. The variabilities of the individual variables also combine to determine that of the overall safety f actor.

Variables influencing the f actor of safety on structural capac-ity to withstand seismic-induced vibration include the strength of the equipment or structure compared to the design stress level and the inelastic energy absorption capacity (ductility) of a structure or its ability to carry load beyond yield. The variability in computed struc-g tural response for a given effective peak free-field ground acceleration B is made up of many f actors. The more significant f actors include vari-ability in (1) ground motion and the associated ground response spectra for a given peak free-field ground acceleration, (2) energy dissipation (damping), (3) structural modeling, (4) method of analysis, (5) combina-tion of modes, (6) combination of earthquake co,nponents, and (7) soil-structure interaction. For structures which may be susceptible to sliding, the variability in the amount of sliding is also significant, h

2-1 l _ _ _ _ _ _ _ _ _ _ _ - - _ - _ _ _ _ _ - - _ _ _ _ - _ - -

5 I

s Equipment located inside a building acts as a secondary systm and requires the previously mentioned structural response f actors together with a similar set of equipment response factors which are specific to

{ the equipment itself (see Ch3;ter 5). The ratio between the median value of each of these f actors and the value used in design of the Millstone 3 plant and the variability of each factor are quantitatively estimated in Chapters 4 and 5 for various structures and components. These estimates are based on available test data for Millstone 3 structures and equipment, limited analysis, and engineering judgment and experience in the anclysis of nuclear power plants and components.

2.1 DEFINITION OF FAILURE In order to estimate the median f acter of safety against the structure or component failure for the SSE effective peak acceleration (0.179), it is necessary to define what constitutes failure.

I 2.1.1 Seismic Category I Structures g For purposes of this study, Ca',1 gory I structures are considered R to fail functionally when inelastic defonnations of the structure under 3

seismic load are estimated to be sufficient to potentially interfere with the operability of safety-related equipment attached to the structure.

These limits on inelastic energy absorption capability (ductility limits) l chosen for Category I structures are estimated to correspond to the onset o' significant structural damage. For m:ny potential modes of failure, this is believed to represent a conservative bou:d on the level of inelastic structural deformation which might interfere with the opera-biinty of compone7ts housed within the structure. It is important to I note that considerably greater margins of safety agatast structural collapse are believed to exist for these structures than many cases reported within this study. Thus, the conditional probabilities of failure for a given f ree-field ground acceleration reported herein for Catetory I structures are considered appropriate for equipment opera-bility limits and should not necessarily be inferred as corresponding to I

1

structure collapta. Structures which are susceptible to sliding are considered to have failed when sufficient sliding deformation is incurred L to fail buried or interconnecting piping or electrical duct banks.

F l

2.1.2 Seismic Category I Equipment and Piping -

Piping, electrical, mechanical and electro-mechanical equipment l vital to safe shutdown of the plant or mitigation of an acc C " are considered to fail when they will no longer perform their designated functions. Rupture of the pressure boundary on mechanical equipment is also considered a failure. Therefore, for mechanical equipment, a dual failure definition exists: failure to function and pressure boundary rupture. Deperding upon the equipment type, one or the other definition I will govern. For active equipment, the functional failure definition usually governs as equipment pressure boundaries are generally very conservatively designed for c'1uipment such as pumps and valves. For piping, failure of the support system or plastic collapse of the pressure bour.dary are considered to represent failure. The inelastic energy absorption limits (ductility limits) associated with these failure modes have been conservatively estimated in order to define the nargins of safety.

2.1.3 Non-Category I Structures In the Millstone 3 plant, no components identified as important to safety are located within non-Category I buildings. The non-C:itegory I structurcs are separated from Category I structures. The turbine building was evaluated only for the failure modes deemed likely to damage the adjacent important structures. No other non-Category I structures were analyzed since failures in these structures were judged to have no effect on any Category I building.

2.1.4 Non-Seismic Category I Equipment and Piping Failure of non-seismic Category I piping, electrical, mechanical and electro-mechanical equipment is defined as for Category I equipment; 2-3 L . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - . _ - - - - - - - _

3 A

1.e., failure to perform its intended function or failure of the pressure boundary. No items of non-seismic Category I equipment whose failure is L likeV to cause damage to safety-related equipment were identified during the plant visit.

I 2.2 BASIS FOR SAFETY FACTORS DGIVED IN STUDY l There was a general lack of detailed information available for this study on seismic fragility of specific Millstone 3 structures and equipment. This condition exists for all plants and occurs because existing codes and standards do not require determination 'f ultimate seismic capacities, either for structures or equipment gatlified by analysis, or for equipment or components qualified by testing. There-I fore, most median safety factors, estimates of v6eiability, and condi-tional frequencies of failure estimated in this study are based on existing analyses and qualified engineering judgment and assumptions.

Limited additional analyses were conducted to evaluate the expected failure capacities cf the important structures. The additional analyses were based for the most part on the original design analyses which were available, however. Some additional analyses were conducted to develop structural leads and load distributions for several structures. $

2.2.1 Structural Response and Capacity i

The results from dynamic analyses which were used in the design I of the important structures were extensively used in this study. These were supplemented as required to provide estimates of load redistribu-tions resulting from localized failures, etc. Levels of conservatism associated with the method of analysis used in design were estimated such that safety factors reflecting this analysis could be estimated for the l building structures and for the seismic excitation of equipment mounted within the building.

I Detailed structural design calculations were not reviewed, but the design criteria used in design as defined in the FSAR (Reference 1) were reviewed. Some ultimate load capacity analyses were conducted which served as a basis for estimating the median factor of safety on struc-tural resistance to the SSE.

2-4

2.2.2 Seismic Category I Piping and Equipment Response and Capacity

[ For most of the safety-related equipment, informatior, on analysis methods was available in sumnary form in the FSAR. Seismic

{ response information for the selected sample of safety-related equipment evaluated in this study was obtained fran available vendor seismic qualification reports or design calculations for specific components. In some cases such as for piping, only the seismic analysis requirements and stress acceptance criteria were known. Safety f actors for response and structural or functional capacity were estimated from existing i nformation. No new analyses were cor. ducted.

r In-structure response spectra for all Category I structures were generated during the design process. From these typical floor response spectra cnd knowledge or estimates of equipment fundamental frequencies, an estimate is made of the peak equipment response. The peak equipment response estimate is then compared to the dynamic response or equivalent I static coefficient used in design to determine a median safety factor on response.

Capacity f actors are derived from several sources of informa-tion; plant-specific design reports, test reports, generic fragility test data from military test programs and generic analytical derivations of capacity based on governing codes and standards. Two failure modes are censidered in developing captcity f actors for piping and equipment:

structural and functional. Equipment and piping design reports delineate stress levels for the specified seismic loading plus normal operating conditions. Where the equipment fails in a structural mode (i.e.,

I pressure boundary rupture or loss of support), the median capacity f actor and its variability are derived in the sane manner as for structures considering strength and energy absorption (ductility). In cases where equipment must function, the capacity factor is derived by comparing the equipment functional failure (or fragility) level to the design level of seismic loading. Some fragility test data are available on generic classes of equipment that have been utilized in hardened military 2-5

L install ations. Such equipment was off-the-shelf without special shock-

{ resistant design but is similar to nuclear power plant equipment. These data provide estimates of the fragility levels, and thus, safety factors i

1 can be developed for the specified design earthquake. Fragility levels g are not normally determinable from equipment qualification reports, but u the achieved test levels can be utilized to update generic fragilities derived from the military data.

2.3 FORHJLATION USED FOR FRAGILITY CURVES Seismic-induced fragility data are generally unavailable for specific plant components and are certainly unavailable for the specific Millstone 3 structures. Thus, fragility curves must be developed primarily from analysis combined heavily with engineering judgment ,

supported by very limited test data. Such fragility curves will contain a great deal of uncertainty, and it is imperative that this uncertainty be recognized in all subsequent analyses. Because of this uncertainty, I great precision in attempting to define the shape of these curves is unwarranted. Thus, a procedure which requires a minimtsn amount of information, incorporates uncertainty into the fragility curves, and easily enables the use of engineering judgnent, was used in this study.

I The entire fragility curve for any mode of failure and its uncertainty can be expressed in terms of the best estimate of the median ground acceleration capacity, k, times the product of random variables.

Thus, the ground accelerhtion, A, corresponding to f ailure is given by:

A=dc R 'U (2-1) in which cR and EU are random variables with unit median representing the inherent randomness (f ailure fraction) about the median and the uncertainty (probability) in the median value, respectively. Equation l 2-1 enables the fragility curve and its uncertainty to be represented as shown in Figure 2-1; i.e., as a set of shif ted curves with attached uncertainty levels. Thus, it is assumed that all uncertainty in the fragility curves can be expressed through uncertainty in the median alone.

2-6

Next, it is assumed that both cR and cU are lognormally

[ distributed with logarithmic standard deviations of BR and 80 '

respectively. The advantages of this formulation are:

)

1. The entire fragility curve and its uncertainty can be expressed by three parameters - As cR.

l and cy. With the very limited available data on fragiiity, it is much easier to only estimate three parameters rather than the entire shape of the fragility curve and its uncertainty.

2. The formulation in Equation 2-1 and the 1ognormal distribution are very tractable mathematically.

Another advantage of the lognormal distribution is that it is easy to convert Equation 2-1 to a deterministic composite "best estimate" f fragility curve (i.e., one which does not separate out unce*tainty from underlying randomness) defined by:

A=hc c (2-2) where c C is a lognormal random variable with unity median and logarithmic standard deviation BC given by:

5 B

C" R+8U (2-3) l This composite fragility curve (shown in Figure 2-1) can be used in preliminary deterministic safety analyses if one only needs a "best estimate" on f ailure fraction and does not desire an estimate of uncer-tainty. In this study, the guidelines used to estimate the values of B

R and By for each variable affecting A were based on considering the I inherent randomness, RS , to be associated with the earthqt'ake character-istics themselves, and B to be associated with other lack cf knowledge.

U Thus, such variability as resulting from earthquake response spectra shapes and amplification, earthquake duration, numbers and phasing of n.ak

excitation cycles, etc., together with their contributions to structure a ductility and response characteristics is attributed to randomness. In _

general, it is not considered possible to significantly reduce randomness '

I by additional analysis or test based on current state-of-the-art techniques. Uncertainty, on the other hand, is considered to result primarily from analytical modeling asstanptions and other lack of I

knowledge concerning variables such as material strength, damping, etc.,

which could in many cases be reduced by additional study or test.

l E

The lognonnal distribution can be justified as a reasonable distribution since the statistical variation of many material properties (References 3 and 4) and seismic response variables may reasonably be represented by this distribution (Reference 5). In addition, the central limit theoran states that a distribution consisting of products and I quotients of distributions of several variables tends to be lognormal even if the individual distributions are not lognonnal. Use of this distribution for estimating f ailure fractions on the ordet of one percent or greater is considered to be quite reasonable. Lower fraction esti-mates which are associated with the extreme tails of the distributions must be considered less accurate.

I Use of the lognormal distribution for estimating very low f ailure fractions of components or structures associated with the tails of the distribution is considered to be conservative because the low-frequency tails of the lognormal distribution generally extend farther from the I median than actual structural resistance or response data might indicate.

Such data generally show cut-off limits beyond which there is essentially zero f ailure fraction. The degree of conservatism introduced into the probability of release is dependent not only on the conservatism in the fragility description, but also on the seismic hazard description at low l seismic levels. If the seismic hazard for low seismic input levels is large enough, it is apparent that very low level earthquakes can govern the seismic-induced release. This is considered unrealistic for engineered structures and equipment found in nuclear power plants. Structures and 2-8

equipment are subjected to low levei dynamic loads from a ntsnber of s

I sources including wind on a repetitive basis which have never been known to produce nuclear power plant structural f ailures. Similarly, for low level earthquakes, it is expected that below some threshold, there is virtually no chance of f ailure due to seismic excitation. Material strength data, for instance, normally does not f all to very low values compared to the median value but instead normally exhibits some lower bound (Reference 3 and 4). Other variables, such as damping, also indicate both lower and upper bounds which are not zero or infinite.

Extensive studies have been conducted to develop response spectra from available earthquake records and while dispersion exists about the median values, spectra with essentially zero or infinite response do not occur (Reference 5). For these as well as other variables contributing to the seismic fragility of a given structure or component, it is apparent that I sme lower and upper bound cutoffs on the tails of the dispersion exist.

Since the overall fragility curves are based on a combination of these variables, it is expected that a threshold exists below which no failures will occur. This is supported by experience. Although quantitative data are lacking, this threshold value is expected to be at approximately minus two lognormal standard deviations for the median curves using the l "best estimate" or composite fragility variability. The composite lognormal standard deviation,CB , is used for the basis of the cut-off rather than randomness or uncertainty since the composite value combines the effects of both dispersions.

I However, it is also apparent that some variability should be associated with the cut-off. Essentially no data are available to establish the distribution of this variability or its range. A lognormal distribution is, therefore, assumed consistent with the majority of the uther variables encountered in the PRA. The following approximation is reconinended for establishing the cut-offs for the various fragility curves:

t l

l 2-9 l

L The cut-off on the lower tails of the median (50 percentile) fragility curve should be:

A =A exp (-2E )

co C.

whereE co is the cut-off on the median curve, h is the median effective l

peak ground acceleration for failure, and BCis the composite lognormal standard deviation.

l should be:

The cut-off for the lower tails of the other fragility curves 1 A co " co exp (-x8C /1.65) where x is the ratio of the deviation divided by the standard deviation.

For instance, for the median curve, x = 0; for the 25 percentile curve, x = -0.67; for the 5 percentile curve and below, x = -1.65; and for the 95 percentile curve and above, x = 1.65.

It is recommended that the cut-off on the upper tails be established as +3B C for all fragility curves. Similarly, for fragility curves invclving only uncertainty, it is recomended that the cut-offs be set at -33 Ufor the lower bound and +3SU f r the upper bound, respectively.

Sone characteristics of th' lognormal distribution as applied to seismic capacities are discussed in Appendix A of this report.

2.4 DESIGN AND CONSTRUCTION ERRORS An inadequate data base exists upon which to determine explicitly the contributions of design and construction errors to most Millstone 3 structures and equipment seismic capacities. In one exception to this, the possibility of a large throughwall flaw was considered as a lower bound for generic piping. In general, for a plant as new as Millstone 3 E

2-10

d with current design and On procedures, the possibility is considered J remote that design and ct action errors may exist which can signifi-cantly affect the seismic capacity of a component. Although some d,3crepencies have been idantified and others may be in the future, these i

items have been modified as necessary or shown to have no safety h implications . Thus, these items are not expected to significantly affect

[ the seismic capacity of the equipment or structures af ter they have been identified. However, there is a possibility that unidentified design and construction errors may exist which can affect the seismic capacity.

I It should be recognized that design and construction errors do not necessarily always result in a decrease in capacity. It is possible to install higher strength bolts than specified, larger reinforcing bars or more closely-spaced bars than required, or slip a decimal point in the I conservative as well as in the unconservative direction in the analysis. l Some additional confidence exists in that structures and equipment are subjected to normal operating loads continually. In many cases, these i loads may be large; as for instance, in the case of pressure, water hamer, and thermal loads in fluid systems when compared to seismic loads. In other cases, as for instance the wind forces on structures, the loads may be less than seismic loads but occur on a much more frequent basis. Pressure tests of contairrnent vessels, while producing g' different types of response than seismic, would likely provide an R indication if significant construction errors exist in these structures.

I Thus, although data on which to quantify accurate estimates of the effects of design and construction errors are not available, these are expected to affect a minimal number cf components.

2.5 CORRELATION BETWEEN FAILURE 500ES Many of the potential failure modes discussed in the following sections are not considered to be completely independent. The most obvious examples involve failure of one item caused by failure of a separate component. For instance, if a potential mode of failure is the collapse of a structure, f ailure of the equipment and piping located in 2-11

L that structure is also expected. Similarly, failure of relatively heavy equipment may of ten be expected to fail lighter equipment in the intnediate I vicinity. Some degree of correlation exists for all items and for all modes of failure since they are all excited by the same earthquake. An l example of very high dependency of failure modes of components and struc-tures include two identical items located very close to each other in the l same structure. For two components which are identical but located in different structures or different locations in the same structure, some degree of correlation is expected but less than 100%.

For different modes of failure in a given structure, or in similar structures, some degree of correlation between modes is also expected. For instance, if the capacity of the lateral force resisting system (i.e., the shear walls) is actually higher or lower than the value used in tha analysis, the acceleration capacities of all failure modes (including different structures) governed by the shear walls would be expected to be proportionately higher or lower. The actual capacity of the force resisting system may be different from that used in the evaluation due to differences in strength or modeling assumptions. These effects are of course included in the variabilities associated with each mode of failure for a given structure or component. However, different I degrees of correlation may exist from mode-to-mode. For instance, for a given structure with given concrete and reinforcing steel strengths, the variability on strength from mode-to-mode may be stronaly correlated, while different modeling assumptions may result in little correlation for different failure modes.

There is also a certain degree of interdependency between structural and sliding modes of failure that could be considered. In Section 4, fragilities are presented for failure modes associated with structure sliding or failure of the structure itself (i.e., shear wa'l failure). These fragilities were developed assuming that the sliding and structural failure modes were coc letely independent. That is, structural failure acceleration capacities were based upon seismic loads with the 2-12

structure bonded to the supporting rock (or soil), even if sliding was expected at lesser acceleration levels. In reality, the occurrence of I L sliding will limit the structure inertial loads since accelerations in excess of those corresponding to sliding cannot be trans,mitted through f the structure / rock (or soi? ? interface. Treatment of the structure fragilities which incorporate the probability that sliding does occur would likely result in higher structure capacities.

For failure modes with little contribution to risk, consitiera-tion of correlation between modes is probably unimportant. However, consideration should be given to possible correlation between controllina seismically-induced failure modes.

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I 2-13

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3. DIFFERENCES BETWEEN CRITERIA USED FOR DESIGN l OF MILLSTONE 3 AND PARAMETERS USED IN THE EVALUATION OF THE SEISMIC CAPACITY l

The seismic design of the Millstone 3 structures and equipment was based for the most part part on currently accepted methodology and criteria in conformance with NRC licensing requirements. Some differences exist in the use of the Newmark-type gruund spectra, in the directional combination and in the damping ratios used. Also, some differences exist between the design and analysis of the Millstone 3 Nuclear Steam Supply System (NSSS) and non-NSSS Category I components.

However, these criteria and methods together with the design codes in use at the time of the design form a conservative design basis and ensure that substantial factors of safety are introduced at various stages in I the design procedure. The exact magnitude of i..any of these safety g f actors is still a matter of considerable discussion. Nevertheless, in y order to establish a realistic value of the actual seismic capacity of a structure or equipment component, the amount of conservatism along with its variability must be established as accurately as possible. In this chapter, the design basis of the most important parameters affecting seismic capacity are identified, and the general methods used in obtaining more realistic values associated with very high seismic response levels are discussed. The detailed determination of these I parameters is described in Chapters 4 and 5 for structures and equipment, s

respectively. The estimated seismic capacities c' the most probable f ailure modes are also developed in Chapters 4 and 5.

The general approach used in the evaluation of the Millstcre 3 seismic capacities is to develop the overall factor of safety associated l with each important potential failure mode. Based on the governing design parameters, a median seismic capacity is then obtained in terms of some representative seismic input such as free-field acceleration. The I ,

l 3-1 1 1 _ - _

overall f actor of safety is typically composed of several important I contributions such as strength, allowance for inelastir sergy dissipation (ductility), and differences in median structure respore compared to p design values resulting from such parameters as earthquake characteris-

, tics, damping, and directional load components.

{

l l

3.1 STRENGTH l

The design strength of a structure or an equipment component is typically determined frcm applicable codes and standards such as the ACI building codes for concrete or the ASME boiler and pressure vessel code for mechanical equipment. Inherent in these design codes is a factor of safety on material strength. Sometimes this f actor is known reasonably  ;

accurately, such et the design allowable being one-half the minimisa yield strength or some similar relationship. At other times, it is less well defined or may be a function of the geometry or other physical character-g istics of the component such as for reinforced concrete shear walls. For E metal structures and components, the safety f actor included in the codes is usually f airly accurately known as are the relationships between minimum and mean or median strengths. For concrete structures, the f actor of safety is normally less accurately known. In this case, the l strength of the element is a function of the concrete strength, the amount and strength of the reinforcing steel, and the configuration of the element including the element geometry e.nd reinforcing steel details. In establishing the strength and seismic capacity of concrete components, the results of concrete compression tests and reinforcing steel strength and elongation tests provide a valuable basis for establishing the element strength capacity. However, the increase in concrete strength with age together with the specific details of the element must also be considered. These effects are discussed in more detail in Chapter 4 for structures and Chapter 5 for the piping and equipment.

3-2

3.2 DUCTILITY I In order to establish realistic seismic capacity levels for most h

structures and components, an assessment of the inelastic energy absorp-

{ tion must usu311y be considered. Exceptions to this are scme modes involving brittle f ailure, functional f ailure or elastic buckling.

However, most f ailures due to seismic response involve at least some g degree of yielding. This is true of reinforced concrete as well as the B somewhat more ductile metal structures and components.

Consideration of structure ductility typically results in the ability of the structure to withstand greater seismic excitation than would be predicted using liner elastic techniques. In the design analysis of the Millstone 3 structures, all design analyses were based on linear elastic analyses although both cracked and uncracked properties were considered for the containment. No nonlinear analyses of the structures were conducted. Although inelastic analysis would be I desirable in order to more accurately quantify the inelastic effects, the dissipation of inelastic energy may be adequately accounted for without the time and expense of performing nonlinecr analyses. This can be accomolished by the use of the ductility-modified response spectrum approach (References 6 and 7) together with a knowledge of tae elastic model results and the expected ductility ratios of the critical eleeants of the structure or component. This approach is based on a series of nonlinear time-history analyses using single-degree-of-freedom models with various nonlinear resistance functions and levels of damping. For different levels of ductility, the reduction in seismic response for the g nonlinear system compared to the equivalent elastic system response is R calculuted. This reduction has been shown to be a function of the frequency and damping of the system as well as the ductility. However, a reasonably accurate assessment of the reduction in response of a structure er component can be made provided the results of the elastic l analysis are available and a realistic evaluation of the system ductility can be made. In the current evaluation the effective ductility was also censidered to be a function of the earthquake magnitude.

I 3-3 E __ -

J

s c

3.3 SYSTEM RESPONSE A number of parameters must be evaluated when considering the k expected system response near f ailure compared to the design conditions, g Among these are the expected compared to the design earthquake character-I istics, directional combinations, system damping, load combinations, and system modeling approaches and assunptions. In addition, the duration of the earthquake must be considered since short duration earthquakes do not possess sufficient energy to fully excite the structural systems. Sorne of these parameters may be essentially median centered and introduce little change in the expected seismic capacity while other design criteria may be quite conservative. Several or the more important parameters required in evaluating the system seismic response are discussed below.

The factors of safety associated with these parameters are developed in the following chapters for the specific failure modes identified.

3.3.1 Earthquake Characteristics The Hillstone 3 Seismic Category I structures are founded on rock or soil deposits overlying the rock. Equipment within the structures was designed for an SSE of 0.179 defined by the Newmark-type free-field ground respon;e spectra shown in Figure 1-1. These spectra were developed from a number of earthquak% that occurred on both soil and rock sites. They were developed for design purposes and are smoothed envelopes of the actual earthquake spectra from which they were developed. Site-specific spectra are not available for Millstone 3. The spectra chosen as representative broadband spectra for the site were derived from Reference 8. A comparison between these spectra and the design spectra is presented in Figure 3-1. A comparison of the oesign spectrun at 5% design damping with the site < specific spectrun at 10%

damping is shown in Figure 3-1. As noted in Section 3.3.2 and Table 3-1, 10% damping is estimated to be a median value for reinforced concrete structures approaching yield. A comparison of these spectra indicates that the design spectrun typically exceeds the site-specific spectrum except at frequencies in excess of 20 Hz.

3-4

~

l

{

3.3.2 System Damping l Damping values used for the design analysis of the Millstone 3 plant are shown in Tables 3-1 and 3-2 for the non-NSSS and NSSS SSE I

l design, respectively. For the non-NSSS design, the damping ratios were g specified in terms of stress level for the component rather than 3 explicitly for the SSE or OBE as listed in US NRC Reg. Guide 1.61 l

(Reference 9). Damping in the rock springs used for the structures founded on bedrock was assumed to be 10 percent of critical for transla-tion and 5 percent for rocking degrees of freedom. These values are considered te be conservative but since the overall rock spring stiffnessess are so high, the damping assumptions are not expected to significantly affect the response of the structures. The soil-structure interaction design values are generally considered to be essentially median centered for structures founded on a layer of till. At response levels of structures and equipment near f ailure levels, the damping ratios based on stress levels used for design are considered conserva-tive when used in conjunction with the ductility factors used in this

{

evaluation. Very little actual test data for damping ratios exist at  !

f ailure levels, particularly for structures. However, the damping values used for design, even at the higher stress levels, are generally lower compared with median centered values recomended in References 6,10 and

11. These damping values for structures and equipment at or near yield are shown in Tables 3-1 and 3-2 in comparison with tnose used for design analysis. In accordance with the recommendations in Reference 10, the g lower levels of the pairs of values shown in Tables 3-1 and 3-2 are E considered to be lower bounds while the upper levels are considered to be essentially average values. The values of damping used for this .

evaluation were taken from Tables 3-1 and 3-2 assuming the upper level to be a median value. Review of piping damping values derived from experiments support the use of 5 percent of critical (Reference 11).

3.3.3 Load Combinations The load combinations on which the design of the Millstone 3 station Category I structures were based are shown in Tables 3-3 through 3-5 (Reference 1). These load combination criteria define a large number I

3-5

of load combinations that must be considered in design. For the reactor building structure and much of the equipment contaired within the reactor y building, these load combinations include a combination of a loss of coolant accident (LOCA) and the SSE loads. Random LOCA events have an f extremely low frequency of occurrence as do seismic events such that the frequency of both events occurring simultaneously is so small that their inclusion is judged to be not important to the risk analysis results.

3.3.4 Modal Combination The Millstone 3 seismic design analysis was conducted on the I basis of loads determined by the square-root-of-the-sum-of-the-squares (SRSS) method for both the NSSS and non-NSSS stru::tures and equipment.

I Closely spaced modes were considered in accordance with USNRC Regulatory Guide 1.92 (Reference 12). SRSS methods are considered to give approxi-mately median centered results. Although some frequency shif.ts are expected as structures approach failure, these shifts in frequency are normally not large unless very high ductility ratios exist. Also, the relationship between loads developed from individual modes may be expected to chinge once nonlinear response levels are reached. In the absence of a nonlinear analysis, the changes in the. modal ratios are unknown. For the seismic evaluation of Millstone 3, it is assumed that the load response relationships between modes does not change signifi-cantly once the structures reach the yield point. For systems where most of the response results from one mode, this assumption introduces negli-gible possibility for error. For systems with a large number of modes h with significant response levels, some additional uncertainty is introduced. The resulting assumed dispersion is discussed in Chapter 4 for structures.

3.3.5 Combination of Responses for Earthquake Directional Components With the exception of the auxiliary building, the design of the essential Millstone 3 structures was bascd on loads developed from the absolute sum cf the accelerations in one direction due to the simul-taneous responses from all three directions of input. For the design of 1

3-6

[ _ .. _

the auxiliary building, the dynamic forces of the msnbers were computed by the square-root-of-the-sun-of-the-squares (SRSS) method. Structure loads were computed using response spectra methods and a comparison was made with time history loads. Where torsion was significant, the structure was analyzed by a tt ee-dimensional model which inciuded the effects of torsion.

Depending on the degree of coupling in the structures, the absolute sun of the three-directional components may be very conservative.

Current design procedures are specified in Regulatory Guide 1.92 (Reference 12). This approach requires that the effects of two hori- l zontal directional responses be combined with the vertical response by the SRSS, and, thus, does not require that the maximun response in cach I direction occur at the same instant as the maximum response in the other two directions. Other methods of combining directional components such as delineated in Newmark and Hall (Reference 10) also yield realistic res ul ts. This approach reconsnends adding 100% of one directional component to 40% of the remaining components. This method has the advantage of being easy to use and retains a consistent relationship between loads and stresses. Both the 53SS and the 100%, 40%, 40% method l yield similar results and are considered to be essentially median centered. Therefore, no increase in the factor of safety to account for earthquake directional components was included for the auxiliary building.

Generic earthquake component response f actors were developed for components of different geometries by comparing rcsalting acceleration vectors for the applicable design criteria to median response vectors as defined by either the SRSS methodology or the 100%, 40%, 40% methodology.

3.3.6 Structure Modeling Considerationt In the seismic design analysis of Millstone 3 structures, both two-dimensional and three-dimensional, lumped-mass models were developed for the Category I structures. Two-dimensional finite element models were developed for structures founded on a layer of soil above the bedrock. To reflect the rock foundation, the design models for l

3-7 l__ -

structures founded on rock have base flexibilities developed from elastic J half-space theory. For these buildings, no stiffnesses were included to represent the embehent of the structures. For rock founded structures, this will generally have very little effect on the frequencies that were I

calculated using no embetent effects. The remaining details of the models are consistent with state-of-the-art seismic analysis and do not appear to introduce significant degrees of either conservatism or unconservatism into the results.

Some aspects of the analysis procedure yield variations which can be quantifiably assessed compared to the design results. For instance, the increase in the actual concrete strength compared to the design values may be used to evaluate the change in stiffness and, hence, the change in frequencies of the concrete structures compared to the design values. The modified frequencies may, in turn, be used to reevaluate the modal responses. Another area where modified responses are considered is in the load distribution for structures where local yielding occurs in some elements before others or through diaphragms l containing relatively large cut-outs. Neglecting the cut-outs typically overestimates the stiffness of the diaphragm and may consequently over-estimate the seismic loads calculated. For a single stick model, typically no diaphragm loads are computed. However, an estimate of the g stiffness of the diaphragn with cut-outs, and, if necessary, in the 5 f ailed condition, may be used to redistribute the seismic loads if

' redundant load paths are available and, thus, provide a more realistic ultimate seismic capacity. The details of these and similar evaluations necessa*y to account for change between parameter design values and values more representative of seismic response levels near failure are discussed in the following chapters.

I I

I 3-8 l

W U L_J T- J TABLE 3-1 COMPARISON OF CRITICAL DAMPING FOR NON-NSSS STRUCTURES AND EQUIPMENT I

I Percent Critical Damping Type of Condition of Structure, Hillstone 3 Fragility Stress Level System or Component Design (Ref. 1) Evaluation * (Refs. 6, 11)

1. Low stress, well Steel, reinforced concrete; no 0.5 to 1 NA below proportional cracking and no slipping at joints, limit. Stresses piping or components below 0.25 yield point stress

}[

2. Working stress a. Welded steel, well reinforced 2 NA limited to 0.5 concrete (with only slight yield point stress cracking) j

b. Bolted steel 5 NA  !

1

3. At or just below a. Welded steel 5 5 to 7 '

yield point b. Reinforced concrete 5 7 to 10

c. Bolted steel 7 7 to 15

4. At all stress a. Rock (translation) 10 10 levels b. Rock (rotation) 5 5 1

• Lowar values are considered to be approximately lower bounds; upper values are considered to be essentially median centered.

TABLE 3-2 f

COMPARISON OF CRITICAL DAMPING FOR NSSS EQUIPMENT Percent Critical Damping 1

! Millstone 3 Fragility l Item SSE Design (Ref. 1) Evaluation * (Refs. 6,11)

I' Primary coolant loop system components 4 5 Welded steel structures 4 5 to 7 Bolted and/or riveted steel structures 7 7 to 15 Fuel assemblies 10 10 CRDM's/CRDM supports 5 7

• Lower values are considered to be approximately lower bounds; upper values are considered to be essentially median centered.

l l

l TABLE 3-3 LOADING CONDITIONS - LINER PLATE AND ACCESS OPENINGS (REF. 1)

I Design Allowables Load (per ASME III j Category Conditions Nomenclature)

Emergency #

D+PD

• D m' b Test D+1.15P P <0.95 m y P +P <1.355 m b y

+" CAT" curve con-I siderctions Normal 100 cycles of 6P NB-3222.4 (d) or (e)

I 400 cycles of 4T 100 cycles of 1/2-SSE Severe D+P . +T . 1/2-SSE Without I Operational "" *1" P <S P"+P*b m

<1.55 m

temper-ature i

l I P +P +Q<35 m b m ANCHORS I Emergency D+P + + SSE Max. shear < .425 S l Severe D+Pg+Tg + 1/2-SSE Max. tensile <0.45 5 5 Operational NOTE:

The normal and test load combinations are producing negligible effects.

F Where:

[ D = Dead load effect of reinforced concrete structure acting W on the liner plus dead load of the liner P

D

= Design pressure (pressure resulting from design basis accident and safety margin)

T = Load due to thermal expansion, resulting when the liner D

is exposed to the design temperature SSE = Stresses in the liner derived from applying the effect of the safe shutdown earthquake 3-11

H TABLE 3-3 (Continued)

LOADING CONDITIONS - LINER PLATE AND ACCESS OPENINGS (REF. 1) l l

l AP = Differential pressure between operating pressure and l atmospheric pressure (100 cycles are assumed on the basis of 2.5 hr refueling cycles per year on a 40 year span)

AT = Load due to thermal expansion, resulting when the liner is I exposed to the differential temperature between operating and seasonal refueling temperatures (400 cycles are assumed on the basis of 10 such variations per year, on a 40 year I span (100 cycles of 1/2-SSE is an assumed number of cycles for this type of earthquake.)

Pmin: Minimum pressure resulting during operation of the containment j

g Tmin= L ad due to thermal expansion resulting when the liner 3 is exposed to the minimum pressure S = Yield strength of the material y

5, =

The smaller of 1/3-ultimate strength or 2/3-yield strength S = Ultimate strength of the stud material.

y I

I I

I I

I 3-12 w .. - _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - _ - -_ _

[ TABLE 3-4 LOADING CONDITIONS, PENETRATIONS (REF. 1)

B Areas of Analysis (See Figures 3.8-5 thru I 3.8-9 and 3.8-15 thru Stress Allowables (per ASME III 3.8-22) Category Load Combinations) Nomenclature) 1 Design Mp or Tp or Jax Pm < 0.9 Sy or J sh P ,+ Pb< 0.9 S Pconcretebea[ing I < 2,400 psi Emergency Pd+T+R P, + P b+ 9 < 3 S m d o 2 Design 818 M or T por J ax

• 8r Jsh P,<0.95[9Sy*

P m + P b< 0 Design 23 Pg+Tg + Design t > e (p , , pb) + (Pm + Pd

+ Q) < 3 Sm Design 1 Pg+Tg Normal P g+T+h g e ASME III Table NC3611.1(b)

(3)-1 or Para.

NB3222.4(d) or (e)

NOTES:

• For the pipe pcrtion, refer to Section 3.7.3.1.

Where:

W Mp = Yielding moment = Required bending moment to produce I stresses equal to the yield strength of the pipe material T

P

= Yielding torque = Required torsional moment to produce stresses equal to the yield strength of the material J = Axial jet force = Load equal to the piping design ax pressure times the inside area of the pipe, acting in the axial direction of the piping J = Shear jet force = Load equal to the piping design sh pressure times the inside area of .the pipe acting transversely to the pipe 3-13

I I TABLE 3-4 (Continued)

LOADING CONDITIONS, PENETRATIONS (REF. 1)

I 1

1 P

d = Containment design pressure .

T d = centainment design temperature P

g = Piping design pressure T

g = Piping design temperature i R, = Piping reactions due to rormal operation (including SSE effects)

= Piping reactions due to normal operation (including 1/2 -

I R, SSE)

Design'1' - Applies to the sizing of the sleeve and attachment I plate Designia .

Applies to the evaluation of stresses in the area of Analysis 2 due to the given load combinations I

I I

B I

I I

3-14

u TABLE 3-5 H

I LOADS AND LOADING COMBINATIONS (REF. 1) i l 1. Concrete Structures (Containment Internal Structures and Category I Structures, other than the containment mat, shell, and dome).

Loads and loading combinations are based on ACI 318, and "AEC Enclosure 3 - Structural Design Criteria for " valuating Ef!:ects of High I

I Energy Pipe Breaks on Category I Structures outside the containment,"

Structural Engineering Branch, Directorate of Licensing.

1. U = 1.4D + 1.7L

2. U = 1.4D + 1.7L + 1.7H 2a. U = 0.9D + 1.7H

3. U = 1.4D + 1.7L + 1.4F 3a. U= .9D + 1.4F

4. U = 0.75 ( 1.4D + 1.7L + 1.7W) 4a. U = 0.90D + 1.3W

5. U = 0.75 (1.4D + 1.7L + 1.7 x 1.1 (1/2 SSE)

Sa. U = 0.90D + 1.3 x 1.1 (1/2 SSE)

I 6. U = 1.1 D + 1.1 L + 1.1 SSE 6a. U = 0.9D + 1.1 SSE

7. U = 1.1 D + 1.1 L + 1.1 Wt 7a. U = 0.9D + 1.1 Wt

8. U = D + L + Ta + Ra + 1.5Pa

9. U = D + L + Ta + Ra + 1.25Pa + 1.25 OBE + 1.0 I (Yr + Yj + Ym)

10. U = D'+ L + Ta + Ra + Pa + SSE + 1.0 (Yr + Yj + Ym)

Notes - Concrete Structures (1) U is the required section strength based on strength design methods described in ACI 318-71.

(2) In combinations 8, 9, and 10, the maximum values of Pa, Ta, Ra, Yj, Yr, and Ym, including an appropriate dynamic load factor, shall be used unless a time-history analysis is performed to justify otherwise.

(3) For load combinations 9 and 10, local section strengths and stresses may be exceeded under the concentrated loads Yr, Yj, 3-15

I TABLE 3-5(Continued)

F LOADS AND LOADING CCMBINATICNS (REF. 1) and Ym, provided there will be no loss of function of any i safety related system.

(4) For load combinations 7 and 7a, local section strengths and stresses may be exceeded under the tornado missile load I provided there will be no loss of function of any safety related system.

l

2. Steel Structures A. Elastic Working Stress Design Service Load Conditions

1. S=D+L

2. 1.33 5 = D + L + OBE

3. 1.33 S = D + L + W Factored Load Conditions

4. 1.6 S = D + L + SSE

5. 1.6 S = D + L + Wt

6. 1.6 S = D + L + Ta + Ra + Pa

7. 1.6 5 = D + L + Ta + Ra + Pa + OBE +

1.0 (Yr+Yj+Ym)

8. 1.6 S = D + L + Ta " Ra + Pa + SSE + 1.0 (Yr+Yj+Ym) .

B. Plastic Design Factored Lead Conditions B 9. 0.9Y = D + L + Ta + Ra + 1.5 Pa g 10. 0.9Y = D + L + Ta + Ra + 1.25 Pa + 1.25 OBE y 1.0 (Yr+Yj+Ym)

11. 0.9Y = D + L + Ta + Ra + Pa + SSE + 1.0 (Yr+Yj+Ym)

Notes - Steel Structures I (1) S is the required section strength based on the elastic design methods and allowable stresses defined in Part 1 of the AISC

" Specification for the Design, Fabrication, and Erection of Structural Steel for Buildings."

(2) Y is the section strength required to resist design loads based on plastic design methods described in Part 2 of the AISC 3-16

c

_ TABLE 3-5 (Continued) s LOADS AND LOADING COMBINATIONS (REF. 1)

" Specification for the Design, Fabrication, and Erection of I Structural Steel for Buildings."

(3) Both cases of L having its full value or being completely

{ absent are checked for load combinations 1, 2, 3, 4, and S.

(4) In combinations 4 to 8 and 9 to 11, thermal loads are neglected when it can be shown that they are secondary and self-limiting in nature, or where the material is ductile.

(5) In combinations 6, 7, and 8, and 9,10, and 11, the maximum values of Pa, Ta, Ra, Yr, Yj, and Ym, including an appropriate I dynamic facter, are used unless a time-history analysis is perfcrmed to justify otherwise.

(6) Combination 5 shall be satisfied without the tornado missile I load. Combinations 7, 8, 10 and 11 shall be first satisfied without Yr, Yj, and Ym. When considering these loads, however, local section strengths may be exceeded under the effect of I these concentrated loads, provided there will be no loss of function of any safety related system. Furthermore, in computing the required section strength, S, the plastic section modulus of steel shapes may be used for combinations 7 and 8.

Loads. Definition of Terms, and Nomenclature

1. Normal Loads -

Those loads encountered during normal plant operations and shutdown. They include the following:

D - Dead loads or their related internal moments and forces including any permanent equipment loads -

I L - Live loads or their related internal moments and forces, including any movable equipment loads and other loads which vary with intensity and occurrence 3 F - Lateral and vertical pressure of liquids, or their related internal moments and forces (included in D above)

H - Lateral earth pressure, or its related internal moments and forces (included in L above)

To - Thermal loads during normal operating or shutdown conditions, based on the most critical transient or steady-state condition (included in L above) l Ro - Pipe loads during operating or shutdown conditions, based on the most critical transient or steady-state condition (included in D above) 3-17

~

TABLE 3-5 (Continued)

LOADS AND LOADING COMBINATIONS (REF. 1)

2. Severe Environmental Loads -

Those loads that could l infrequently be encountered during the plant life. They include:

OBE - Loads generated by the operating basis earthquake W - Loads generated by the design wind specified for the plant site (Section 3.3.1)

3. Extreme Environmental Loads - Those loads which are credible but highly improbable. They include:

SSE - Loads generated by the safe shutdown earthquake Wt - Loads generated by the design tornado specified for I the plant site (Section 3.3.2)

4. Abnormal Loads. Those leads generated by a postulated high-energy pipe break accident within a building and/or compartment thereof. IncludeG in this category are the following:

I Pa = Maximum differential pressure load generated by a postulated break i Ta = Thermal loads under accident conditions generater' by a postulated break Ra = Pipe and equipment reactions under accident condi-tions generated by a postulated break Yr = Loads on the structure generated by the reaction on I the broken high-energy pipe during a postulated break Yj = Jet impingement load on a structure generated by a I postulated break Ym = Missile impact load on a structure generated by or during a postulated break, such as pipe whipping.

I I

3-18 )

[ . _ _ _ _ _ - . _ _ _ _ _

Pe riorf, sec, 10.0 1. 0 0.10 0.01 300. l .

?hWN\f hh4 (iy?fNh$ ,iWffRs p I'l

s. ~ vs fX<*[>f?)f;'

-/.

u,

-y

[- v'-

2 5.

,f,. .<,<

[

( gm

,.~

. y

, Nn[v 4 ,-

/g p s p . sf 7 v,; s . ' .

/jQ' g

~

f / '

'/fg -

}

f .,

yJ'ph))k A$6 L Jgg)j l

. . h I * /,# ,

bddi s

a f':W nM iy.%sj"  % ~~ '

V 9 y

e t

.8 h*4gl3;p.A:w

(:. m k^

% W

{

%prkyf)Wgi x4

,/

e 3 x #p q%p %yy f }r

/ <

3 I , \ 'e,sf ,

X '/ / s 's\ //j sj \ /j .)

/ \

Site-Specific Spectrum 8

}

" I. 0 .

l y s -

10% Damping y/ \ , j s s 5 a c Nd8 mmh!22'jid!$WlEib,.E Bji 4 m g/lNn' N $ g yet// k, 's

\em,.k

//

N / (

a i

0. l - <. 4 .. a ... ,

h. {

0. 01 0.30 1. 0 10.0 100.0 Frequency, cpe.

! FIGURE 3-1. COMPARISON OF SSE SPECTRUM TO SITE-SPECIFIC SPECTRUM

h

4. STRUCTURES In this chapter, the median f actors of safety and logarithmic standard deviations for the important structures are developed. Based on these f actors of safety, median acceleration levels associated with '

I seismic failure are presented. For most of these structures, the original design dynamic models were used when available to generate seismic response characteristics in order to determine the median factors of safety and logarithmic standard deviations for each of the variables associated with structure response. All seismic analyses were based on linear response model results, but some seismic design loads were modified to more closely approximate the expected inelastic response at the high acceleration levels expected for f ailure.

I 4.1 MEDIAN SAFETY FACTORS AND LOGARITHMIC STANDARD DEVIATIONS As discussed in Section 2.3, the seismic fragilities of struc-tures and components are described in terms of the median ground accelera-tion, E, and random and uncertainty logarithmic standard deviations, B g and SU . In estimating these fragility parameters, it is computationally attractive to work in terms of an intermediate random variable called the factor of safety, F. The factor of safety is defined as the ratio of the ground acceleration capacity, A, to the Safe Shutdown Earthquake (SSE) acceleration used in design. For equipment and structures qualified by analysis, it is easier to estinate the median factor of safety, F, and variability parameters, S R and S , based upon the original SSE stress I U analysis than it is to directly estimate the fragility parameters. Thus, E=F A SSE (4-1)

From the existing analyses of the important structures together with a knowledge of the deterministic design criteria utilized, median f actors of safety associated with the SSE ground acceleration of 0.179

s can be estimated. These are most conveniently sep? rated into those factors associated with the seismic strength capacity and inelastic energy absorption capability of the structure and those f actors associated with the expected building response.

The f actor of safety for the structure seismic capacity consists

( of the following parts:

( l. The strength factor, Fs , based on the ratio of actual member strength to the design forces.

[ 2. The inelastic energy absorption factor, Fu ,

related to the ductility of the structure and to the magnitude range that is believed to contribute to most of the seismic risk.

Associated with the median strength factor, I s, and the median

[ ductility tactor, E , yare the corresponding logarithmic standard deviations, o s and B y . The structure strength factors of safety and logarithmic standard deviations vary from structure to structure and according to the different failure modes of a given structure. Factors of safety for the most important modes of failure are sumarized in subsequent sections.

[ The f actor of safety FR , related to building response is determined from a number of variables which include:

1. The response spectra used for design compared to the median centered spectra for rock sites from multiple seismic events.

r 2. Damping used in the analysis compared with

( damping expected at failure.

3. Modal combination methods.

4. Combination of earthquake components.

5. Modeling accuracy.

(

6. Soil-structure interaction effects.

( 4-2

_ _ _ _ __ _m_-__.--__m___ _____ ___ __..._._._______.___.m_ _ _ - _ _ _ _ _ _ _ _ - _ _ _ _ _ . . _ _ _

r

^

Based on the characteristics of the lognormal distribution, r median f actors of safety and logarithmic standard deviations for the L

various contributing effects can be combined to yield the overall estimates. For instance, the capacity f actor of safety of a structure, F

cap, is obtained from the product of the strength and ductility f actors of safety which, in turn, may include effects of more than one j variable.

I F cap = F 3 xF u (4-2) i The methods of determining these safety factors are discussed in the following sections. The logarithmic standard deviation on capacity, Scap, is found by:

I Scap = 8s + B u (4-3)

As discussed in Section 2.3, the logarithmic standard deviations are composed of both an inherent randomness and uncertainty in the median value. -

I Median factor of safety, F, and variability, BR and BU' estimates are made for each of the parameters affecting capacity and I

response. These median and variability estimates are then combined using the properties of the lognormal distribution (described in Section 2) in the same manner as Equations 4-2 and 4-3 to obtain the overall median f actor of safety and variability estimates required to define the fragility curve for the structure.

For each variable affecting the f actor of safety, t5e random variability, S p, and the uncertainty, B , must be estimated separately.

U The random variability, BR, represents those sources of dispersion in the factor of safety which cannot be reduced by more detailed evaluation or 4-3

s F

1

^

by gathering more data. Thus,R S is due primarily to the variability ,

f of an earthquake time-history and, therefore, to a structure's response

{

when the earthquake is only defined in terms of the peak effective ground  !

E acceleration. The uncertainty, S U, represents those sources of dispersion which could be reduced only through better understanding or more knowledge. s is associated with such items as our lack of u

I ability to predict the exact strength of materials (concrete and steel) l and of structures (shear walls and diaphragms); errors in calculated response due to inaccuracies in mass and stiffness representations as well as load distributions; and use of engineering judgment in the absence cf plant specific data on fragility levels.

I 1

Each of the factors presented in Chapter 3 will be discussed in l

more detail in the following sections. Examples are included to assist I in the understanding of the application of the methodology.

4.1.1 Structure Capacity The primary lateral load carrying systems of the Category I structures that were analyzed are of reinforced concrete construction with the exception of the refueling water storage tank which is fabricated of steel. For lateral load carryirm systems which are composed of reinforced concrete, the structure strength is a function of material strengths associated with the concrete and the reinforcing steel. The determinations of these strengths are presented in the following two sections.

4.1.1.1 Concrete Compressive Strength The evaluation of the strength of most concrete elements, whether loaded in compression or shear, is based on the concrete compressive strength, f .c Concrete compressive strength used for design is normally 1

specified as some value at a specific time from mixing (for example, 28 or 60 days). 141s value is verified by laboratory testing of mix samples.

The strength must meet specified values allowing a finite number of 4-4

H U

failures per number of trials. As previously stated, there are two major factors which justify the selection of a median value of concrete strength above the design strength, b

I

{

1. To meet the design specifications, the contractor attempts to create a mix that has an " average" strength above the design strength.

2. As concrete ages, it increases in strength.

Results of concrete compression testing were available for the Millstone 3 structures (Reference 13). Table 4-1 summarizes these results.

I As concrete ages, its strength increases. This must also be accounted for in determinir.g the median strength compared to the design I strength. Figure 4-1 from Reference 14 shows the increase of the concrete compressive strength with time assuming the concrete poured in the field is adequately represented by the curve designated as " air cured, dry at test." At 28 days, the concrete has a relative strength of 50 percent which approaches 60 percent asymptotically. The median' factor relating the strength of aged concrete to the 28-day strength is, therefore, 1.2. Similarly, the median aging f actor for concrete tested at 60 days was estimated to be 1.11. No infonnation is available on the standard deviation egected for aging. Logarithmic standard deviations I associated with the aging f actors were estimated to be 0.10 and 0.05 for concrete tested at 28 and 60 days, respectively. Median concrete compres-I sive strengths and variabilities used in the fragility evaluations for the Millstone 3 structures are listed in Table 4-2.

Other effects which could conceivably be included in the concrete strength evaluation include some decrease in strength in the in-place condition as opposed to the test cylinder strength, and some increase in strength resulting from rate of loading at the seismic response frequencies of the structures. The variation in the strength of in-placa concrete compared with the test cylinder strength is accounted I

4-5 C ____-- _ - _ - _ _ _ - _ - - - - - - - - -

for to a large degree in the use of empirical representations of shear

- wall capacities. These empirical capacities are typically developed by

% comparing actual wall strengths to the cylinder test strengths of the wall's concrete. Although experimental data on the in-place and rate

( effects are limited, that which is available would tend to indicate these effects are relatively small and of the same order magnitude. Since the

[ two effects are opposite, they were neglected.

I 4.1.1.2 Reinforcing Steel Yield Strength Grades 40, 50, and 60 reinforcing steel were used in the construction of the Millstone 3 structures. The results of tensile testing conducted on the reinforcement were reported in Reference 13.

Median reinforcement yield strengths and logarithmic standard deviations used in the structure fragilities caiculations were based on these data and are listed in Table 4-3. Grade 60 reinforcement was substituted for Grade 40 at some locations through the structures. This was accounted for in the fragility evaluations based on information contained in Reference 13.

I Two other effects must be considered when evaluating the yield strength of reinforcing steel. These are the variations in the cross-I sectional areas of the bars and the effects of the rate of loading. A survey of information (Reference 16) determined that the ratio of actual to nominal bar area has a mean value of 0.99 and a coefficient of varia-tion of 0.024. The same reference notes that the standard test rate of loading is 34 psi /sec. Accounting for the rate of loading anticipated in seismic response of structures results in a slight decrease in yield strength of reinforcing steel in tension. This effect is neglected in concrete compression.

4-6

l 4

4.1.1.3 Shear Strength of Con:: rete Walls

{ Recent studies have shown that the shear strength of low-rise concrete shear walls with boundary elements are conservatively predicted by the ACI 318-71 code provisions (Reference 17). This is particularly j true for walls with height to length ratios in the order of 1 or less.

Barda (Reference 18) determined that the ultimate shear strength of low-rise walls tested could be represented by the following relationship:

v u"Vc+V s

= 8.3 f -3.4 f - 0.5 +pf (4-4) uy I

where:

vu =

Ultimate shear strength, psi vc =

Contribution from concrete, psi vs =

Contribution from steel reinforcement, psi fc =

Concrete compressive strength, psi hw = Wall height, in E

w = Wall length, in "u =

Vertical steel reinforcement ratio fy = Steel yield strength, psi T.ie contribution of the concrete to the ultimate shear strength i of the wall as a function of hw/t, is shown in Figure 4-2. Also shown in Figure 4-2 are the available test values (References 18 through 21) and the corresponding ACI 318-71 formulation. The tests included load I

4-7

e l

reversals and varying reinforcement ratios and h,/t w ratios. Web 7 crushing generally controlled the failure of the test specimens. Testing g was performed with no axial loads, but an increase in shear capacity of B N/4 wt h was recommended, where N is the axial load in pounds, and h is I

the wall thickness in inches.

I l The co.itribution of the steel to the ultimate shear strength

. according to ACI 318-71 is:

vs"Phy f (4-5) where o h - horizontal steel reinforcement ratio.

Furthermore, one of the conclusions reached by Oesterle I (Reference 21) is that for low-rise shear walls (specifically h /t = 1),

vertical steel has no effect, and the entire contribution to shear strength is due to the horizontal steel.

In order to estimate the effects that the horizontal and vertical steel have, the steel contribution to wall shear strength was determined from test values for the rance of 0.5 < h,/t, < 2. Test data from the above references were used. The effective steel shear strength was assumed to be in the form:

v se = Avs u + Bvs h (4-6)

I where A, B are constants and v =

su " Puy f vertical steel contribution to shear strength v

sh " Phy f =

horizontal steel contribution to shear strength 4-8

+

~

u The constants A and B were then calculated assuming the concrete

{ contribution to the ultimate strength is given as shown in Equation 4-4.

Based on the results of this evaluation, the constants A and B can be p shown to be:

A=1 B=0 hw/tw s 0.5

= -2.0 (hw /tw) + 2.0 = 2.0 (hw /tw ) - 1.0 i =0 0.5 1 w/tw h 1 1.0 j l

=1 1.0 5 w/tw h

I and the median ultimate shear strength is given by:

I v u"Vc+Vse (4-7)

= 8.3 f -3.4 f -0.5 +P sefy

+ 41 h I where pse = Apu + Bch with A and B determined as shown above. Based on I an evaluation of the same experimental data, the logarithmic standard deviation was estimated to be 0.15.

The data used to substantiate the redian shear strength equations presented above were derived from tests conducted on cantilever walls.

The height ( for these walls is known. However, the walls evaluated in this study typically span more than one story. For these walls, the ey'tivalent cantilever wall height, hwe was taken as the ratio of the in-l plane moment to the in-plane shear at the section under consideration.

I I

4-B

r The equivalent heignt h we was used to determine the median wall shear 7 strength and provides a more accurate representation of the moment-shear i nteraction.

I l

4.1.1.4 Example of Shear Wall Failure in Shear The determination of the median shear strength of the north exterior wall of the auxiliary building for the story from El. 4'-6" to El. 24'-6" is selected as an example. This wall is 2 feet thick,102 feet long, and reinforced by #11 bars spaced at 10 inches at each face and in each direction. From Table 4-2, the median concrete compressive strength corresponding to the specified 3000 psi design strenoth was taken to be 5000 psi. Grade 60 reinforcement steel was substituted for Grade 40 I steel in the constructicn of this wall. From Table 4-3, this reinforce-ment has a median yield strength of 69 ksi. The equivalent cantilever wall height was determined to be 71 feet. The median concrete shear strength was found to be:

v c = 8.3 /5000 - 3.4 / 5000 (71/102 - 0.5)

I = 540 psi

= 77.8 ksi The steel reinforcement ratios in the horizontal and vertical directions are the same:

P " P Pse " u h I 2(1.56) 10(24)

= 0.0130 4-10  ;

I

m l

The steel shear strength was found to be: I r

g v3 , = 0.0130 (69,000)

I g = 897 psi E i

= 129.2 ksf The increase in shear strength provided by axial compression is typically e snall and was neglected. For rectangular wa'11s with uniformly distributed vertical reinforcement, the effective dapth, d, from the extreme compres-sive fiber to the resultant of the tension force was taken to be 0.61, l from Reference 21. This approximation neglects the increase in the effective depth provided by transverse, intersecting walls which behave i

as flanges. The median wall shear strength was found to be:

Vu = (77.8 + 129.2)(2) F0.6 (102)

= 25,300 k The applied shear load based on an elastic load distribution was found to be 4090 k. The median strength f actor corresponding to shear f ailure of this wall was then determined to be 6.2.

4.1.1.S Strength of Shear Walls in Flexure Under In-Plane Forces Data on reinforced concrete shear walls failing in flexure under in-plane forces can be found in Reference 21. Equations found in Reference 20 may be used to calculate the moment capacity for walls without chord steel. However, chord steel can be accounted for by increasing the depth from the extreme compressive fiber to the neutral axis to account for the yield strength of the tensile chord steel. The compression chord steel is neglected since it is near the neutral axis, and its effect on the moment capacity is snall. The total moment capacity of reinforced concrete shear walls in flexure under in-plane forces is then:

4-11

u m

u Aft 8c

[ M= 3yw[I*Afp 2

) ' [I' *c)+A 1

1 I ch y [d 2 1

(4~0) i

) N where:

I i

c = Depth to neutral axis from extreme compression fiber As =

Area of distributed steel Ach = Area of chord steel E

w = Wall length fy -

Steel yield strength N = Axial load d =

Distance from the extreme compressive fiber to the centroid of tensile chord steel

=

6 Ratio of depth of equivalent rectangular I i

1 concrete stress block to depth to neutral axis (c) ,

l 4.1.1.6 Example of Shear Wall Failure in Flexure The same wall that was analyzed for shear in Section 4.1.1.4 will be analyzed for flexure. The values to be used in Equation 4-8 are as follows:

As = 2(1.56) 10 12) = 191 in2 Ach =0 1 = 102' fy = 69 ksi N =

(as with shear strength) 8 1

=

0.85 - 0.05 500 4 = 0.8 0

l

]

From balancing the tensile and compressive forces, c = 26.9'. Using the values in Equation 4-8, the median in-plane moment capacity for this wall was found to be 1,060,000 k-ft. From the elastic load distribution, the g applied in-plane moment was determined to be 289,000 k-ft. The median L strength factor corresponding to flexural failure of this wall was calcu-m 1ated to be 3.7.

l 4.1.1.7 Structue Sliding l Resistance to structure sliding is provided by static friction between the structure foundation and the rock (or soil) below, lateral earth pressures from backfill placed against exterior walls, and shear keys embedded into rock (or soil). Gross structure sliding initiates I when the base shear acting at the foundation-rock (or soil) interface equals the available resistance. Initiation of sliding does not consti-B E tute structure or equipment failure. As a structure slides as a rigid body, it accelerations and relative story drif ts cannot exceed those l values occurring at the initiation of sliding. Failure modes resulting from structure sliding are displacement-dependent. For example, pining attached at one end to the structure that is sliding and at the other end to some adjacent structure may f ail under relative end displacement.

Also, impact with adjacent structures may cause concrete spalling and sub-sequent damage to equipment or piping mounted near the locali7ed spalling g regions. However, the sliding displacements necessary to cause these E failure modes are substantial and can occur only under peak ground accel-erations well in excess of acceleration levels initiating sliding.

An approach reconmended by Newmark (Reference 15) was used to predict structure sliding displacements. This approach is simple and results in conservative estimates of the sliding displacement. Figure 4-3 summarizes the features of Newmark's approach. The ground beneath the structare experiences a single horizontal acceleration pulse Ag that lasts for a time duration ti , and results in a velocity V. The structure is represented as a rigid body that begins to slide relative to the ground when its rigid body acceleration reaches Ng, where N is a coefficient 4-13 l

?

l relating the net sliding resistance to the total structure weight. Since the ground acceleration is conservatively assumed to be a square pulse, sliding initiates instantaneously. Structure sliding ends at time t m when the structure has achieved the ground velocity V. The relative displace- '

l ment between the ground and the structure is determined by integrating the relative velocity between the ground and the structure from time t = 0 to time t = tm*

With estimates of the net sliding resistance coefficient, N, and (

the peak ground acceleration, V, as a function of the peak ground accel-eration, Equation 4-9 (see Figure 4-3) can be used to determine the ground acceleration resulting in sufficient relative sliding displacement, ug ,

I to cause the f ailure mode under consideration. Newmark's approach is g conservative since the ground acceleration is actually a reversing B function rather than a single pulse which would greatly reduce the sliding time duration and thus the relative sliding displacement.

Due to the highly uncertain nature of structure behavior past I the initiation of sliding, the logarithmic standard deviation associated with Newmark's approach was estimated to be 0.4. Because no relative displacement can occur until sliding initiates, the acceleration capacity corresponding to the initiation of sliding can be treated as a cutoff on the fragility curve for sliding-induced failure in a manner similar to I that described in Section 2.3.

B 4.1.1.8 Example of sliding-Induced Failure Determination of the ground acceleration causing sliding-induced failure of piping attached to ths auxiliary building will be presented as an example.of the application of Newmark's approach. Accounting for sliding resistances provided by c,tatic friction from the net structure weight, the she'or keys enbedded in rock, and at. rest lateral earth

. pressure, the sliding resistance scoefficient was found to be:

N = 1.118 -0.1734 A '

I L

, m

_ . _ ~

% w

,J4 4-14 g . , ,M

r The second tenn above accounts for the reduction in sliding resistance

~

associated with a vertical seismic acceleration acting upward. The peak bedrock velocity corresponding to a peak ground acceleration of Ig was estimated to be 28 in/sec t,ased on Reference 5. Typically, two ir.ches l

clearance exists around the periphery of the pipe and the penetration so that contact between the pipe and the penetration does not occur during

{ the first 2 inches of sliding, and additional motion is required before l f ailure can occur. Because piping systems are very ductile, the median relative end displacement necessary to cause piping failure was taken to be 4 inches. The acceleration capacity was found by solving for A using Equation 4-9:

u m = 4 inches V = 28 in/sec/g

= 28A u

• 1~

m gN (4-9) y2 0 = V2  !

2gN - YgX - "m

, (28A)2 (28A)2 ,4 2(386.4)(1.118-0.1734A) , 2(386.4)A '

I I A = 2.13 p, 2.13 S 0.17

t: 13 I

! 4-15

1 u

E t

4.1.2 Structure Ductility l

A much more accurate assessment of the seismic capacity of a structure can be obtained if the inelastic energy absorption of the structure is considered in addition to the strength capacity. One '

l tractable method involves the use of ductility modified response spectra to determine the deamplification effect resulting from the inelastic energy dissipation. Early studies indicated the deamplification factor was primarily a function of the ductility ratio, u, defined as the ratio of maximum displacement to displacement at yield. More recent analytic studies (Reference 7) have shown that for single-degree-of-freedom systems with resistance functions characterized by elastic-perfectly plastic, bilinear, or stiffness-degrading models, the shape of the resistance function is, on the average, not particularly important.

However, as opposed to the earlier studies, more recent analyses have shown the deamplification factor is also a function of the system damping. For systems in the amplified acceleration region of the spectrum (i.e., between 2 Hz and 8 Hz), Figure 4-4 from Reference 7 shows the deamplification factor for several damping values as a function of the ductility ratio.

One drawback to using the Riddell-Newmark formulation from  ;

Reference 7 as it currently exists is that it does not reflect the corre-lation between earthquake magnitude and system ductility. It is well known that the fewer the number of strong motion cycles that a structure has to withstand, the greater the structure ductility for a given peak ground acceleration since the structure can absorb more energy per cycle.

There is a rough correlation between magnitude and number of strong motion cycles. As the magnitude increases, the number of strong motion cycles tends to increase. Thus, at higher magnitudes, a structure will exhibit less ductility at f ailure than at lower magnitudes.

To include this relationship in the Riddell-Newmark formulation, results from Reference 22 will be employed. As part of this analysis, four different shear wall elements, with frequencies between 2.14 and

l 1

8.54 Hz and 7 percent damping, were subjected to different earthquake y acceleration records. Two different ductility levels were used to define l

failure. The lower one, u = 1.85, represented the best estimate of inelastic deformations which would occur in a shear wall designed to remain essentially elastic for the design earthquake. The higher ductility, u = 4.27, represented a conservative lower bound for the onset l of significant structural damage. The structural model yield capacities were determined from the elastic spectral acceleration of each earthquake at 7 percent damping for each frequency. The input ground motion was then scaled by a factor, F, and the maximum inelastic response was computed by time history nonlinear structural response analyses. The scale f actors from Reference 22 necessary to achieve the ductility ratios I of 1.85 and 4.27 are presented in Tables 4-4 and 4-5, respectively. For each table, the f actors are separated into two groups: those derived from earthquakes in the 6.5-7.5 Richter magnitude range and those derived from earthquakes in the 4.5-6.0 Richter magnitude range. The mean, the median, and the range are also given for each group. Note that the distribution as represented by the median and the range is not lognormal.

However, it will suffice to create an approach that approximately predicts the median F values at the low end of range.

I

~

The Riddell-Newmark method for computing the ductility f actor, l Fu , is as follows:

I F = [(q+1)u-q]#

I where: q = 3.0Y-

• in the amplified acceleration region.

I = 2.7Y

~

in the amplified velocity region.

r = 0.48y-0.08 in the amplified acceleration region.

= 0.66Y" in the amplified velocity region.

y = percent of critical damping to be used.

h l"

L Thus, for the frequency range of interest, only the q and r values for

{ the acceleration region apply. For 7 percent damping, q = 1.67 and r =

0.411. For u = 1.85, Fy = 1.63; for u = 4.27, F u= 2.55. Comparing these Fy values to the four median F values taken from Tables 4-4 and 4-5, I the Riddell-Newnark method overpredicts the median scale factor for the 6.5-7.5 Richter magnitude range and underpredicts the median scale factor for the 4.5-6.0 Richter magnitude range. Thus, to more accurately predict F, the ductility used in the Riddell-Newmark formula needs to be t.n eff ective ductility, u*. The following fonnulation was developed to l calculate the effective ductility:

u* = 1.0 + CD (u-1.0) where CD varies depending on the magnitude range. It was found that the following values for CD produced scale f actors that were in good agreement with the median f actors from Tables 4-4 and 4-5:

I

=

C D 1.40 for 4.5 < M < 6.0

=

0. 70 f or 6.5 < M < 7. 5 I

In calculating the variabilities due to uncertainty, B , Uand randomness, S

p, the actual scale f actor was said to have only a 1 percent probability of being less than 1.0. Thus, the combined variability, B , was C

determined as follows:

SC " 2.33 tn (Fv )

e C

is the result of S U and e R

being combined by the square-root-of-the-sum-of-the-squares method, e is a measure of the dispersion that is R

represented by the range in F values as shown in Tables 4-4 and 4-5. It was decided to let BR = 0. 8 BC and e V"

• C. With this value for BR '

I the ranges of + 2 B formed around F are similar to those shown in Tables R

4-4 and 4-5, especially at the low end. Values at the high end are of no 4-18

concern, since only the low end contributes significantly to the risk. A comparison of the analytic results from Reference 22 with the results derived from the amended Riddell-Nemark procedure are shown in Table 4-6.

l As stated in Chapter 1, the majority of seismic risk for I

Millstone 3 is estimated to result from earthquakes that have Richter magnitudes between 5.3 and 6.3. This range slightly exceeds that for which CD = 1.40. Therefore, for the Millstone 3 evaluation, a value of 1.30 was used for CD -

4.1.2.1 Example of Ductility Factor Typical values used for Millstone 3 strurteres were 10 percent damping and a system ductility of 4. Thus, from Section 4.1.2:

v* =

1.0 + 1.30 (4-1) = 4.9 q =

3.0 (10)-0.30 = 1.504

=

r 0.48(10)-0.08 = 0.399 These values give:

5 =

[(1.504 + 1)(4.9)-1.504] 0.399 = 2.58 B

C 2.33 En (2.58) = 0.407

=

e R 0.8(0.407) = 0.33 s = 0.6(0.407) = 0.24 u

These values are appropriate for structures having fundamental frequencies corresponding to the amplified acceleration region of the response spectrum (approximately between 2 Hz and 8 Hz). For structures having fundamental frequencies associated with the transition region of the response spectrum (approximately between 8 Hz and 20 Hz),y 5 was interpc-lated between the value above and that appropriate for the rigid response region (see Reference 7).

l 4-19

)

4.1.3 Structure Response Used for Structure Fragility Evaluations Determination of the structure response f actors and their vari-l abilities in fragility evaluations is typically perfomed using structure responses predicted by the original design dynamic analyses. The avail-l able design infomation regarding the Millstone 3 structure loads was I reviewed and determined to be described in insufficient detail to permit an accurate assessment of the median structura loads. As an alternative, j details of the original design dynamic models and eigensolutions were obtained. Eigensolutions predicted using the model infonnation supplied 5 were generated and compared to the original design eigensolutions to verify that the dynamic model infomation was correctly interpreted.

Median-centered overall structure loads were then developed using the median-centered methods described in Section 3. These structure loads were then used to determine the median strength factors in the structures fragilities evaluations.

Because median structure responses were used directly, median response f actors were taken to be unity in the structures fragility evaluations. An exception is the emergency generator enclosure. The original design response was used in the fragility evaluation since it was based on a finite element representation of the soil-structure interaction effects that could not be improved upon within the limita-tions of this study. Also, equipment fragility evaluations were typically perfomed on the basis of the original design in-structure response spectra since generation of median-centered, in-structure spectra would require greater effort than warranted.

The following discussion describes the determination of the median structure response factors based upon comparison of the median versus design responses. This convention is retained for the benefit of understanding the structure response factors used in the emergency generatory enclosure and equipment fragility evaluations.

I i 4-20

4.1.4 Spectral Shape, Damping, and Modeling Factors As previously discussed, the important Millstone 3 structures I

were designed using the ground response spectra shown in Figure 1-2. For the SSE, five percent of critical damping was used for the reinforced l

concrete structures. For the reinforced concrete comprising the lateral load carrying structures for Millstone 3, ten percent of critical damping l is considered to be the median value expected at response levels near f ailure (Reference 10). As shown in Figure 3-1, the ten percent damped median-centered response spectrtan exceeds the five percent damped SSE l I spectrum except at frequencies in excess of about 20 Hz. The frequencies predicted by the Millstone 3 original design dynamic models were avail able. The spectral shape factor for each structure was based on the I mode or modes contributing to most of the seismic response. The spectral shape f actor at the frequency under consideration is given by: '

S l F 33 =

c = 5%

(4-10)

"c = 10% l 5

where SD = 5% represents the 5 percent damped design spectral accelera-tion and'S s W eWaW wecW acceMaN M = 1=, v e associated with k6e median site-specific response spectrum for 10 percent g dampi ng. As noted in Section 4.1.3, structure loads used in the structure y fragility evaluations of all structures except the emergency generator enclosure were derived from the median-centered response spectrum. The median spectral shape f actors for these structures are therefore unity.

In computing the spectral shape factor of safety, it is convenient to combine the damping and ground response spectrtrn effects.

In the development of logarithmic standard deviations on spectral shcpe, however, it is infonnative to consider the damping effects separately.

This implies a factor of safety of unity on damping alone since it has already been included in the factor of safety on spectral shape.

4-21

The logarithmic standard deviation on spectral acceleration, SSA, may be estimated from References 8 and 10. Reference 8 provided the mean site-specific spectrun and associated variabilities for five percent damping. It also presents a procedure by which mean spectra at I

other damping values could be calculated, but does not give the variabil-ities for these other spectra. These variabilities were estimated with the aid of Reference 10.

l The deviation on spectral acceleration resulting from damping, e , can be estimated from:

C*

Sg e in 3 (4-11) c = 10%

where S ,g is the spectral acceleration from the median site-specific spectrum at seven percent damping, and % =10% i s the spectral accelera-tion fran i.he ten percent damped median s te-specific spectrum. Seven percent damping is estimated by Reference 10 to be one standard deviation below the median damping value of ten percent. The randomness and uncertainty components of e are judged to be approximately equal. Thus, (e )c u= (s )c " ['

g I

The original design dynamic models of the Millstone 3 structures were typically determined to be adequate to predict the seismic response.

In generating loads f or the structures fragility evaluations, model modi-fications were incorporated if necessary. Modeling factors of unity typically were used.

I

___ ___ _______ - ____-____ _ _ _ _ l

3 Variability in modeling predominantly influences the calculated W

mode shapes and modal frequencies. Since the concrete strength and, consequently, the stiffness of the structures is above the design values, p calculated frequencies would be expected to be somewhat less than utual values, at least for low to moderate levels of response. At response levels approaching f ailure, softening of the structures due to concrete 1 i

cracking occurs, and for structures analyzed using untracked section j I properties, some decrease in the actual frequencies compared to the calculated values is expected. Calculated frequencies were generally assumed to be median centered unless material properties used in the original analyses differed from the material properties calculated from test data enough to significantly change the calculated frequencies.

The mode shapes were assumed to stay the same regardless of whether or not frequencies changed.

Modeling uncertainties from both the mode shapes and modal I frequencies enter into the uncertainty on calculated modal response as defined by eM . Thus, I B M"

2 2 8M5 + 8 MF (4-12) where SMS and BMF are estimated logarithmic standard deviations on structural response of a given point in the structure due to uncertainties in mode shape and due to uncertainties in modal frequency, respectively.

I Based upon experieace in performing similar analyses, BMS was estimated to be typically about 0.15. The modal frequency variability shif ts the frequency at which spectral accelerations are to be determined, so that:

I l

E"

[Nf=f) g BMF " (4-13)

(S M,f) f l

1 4-23 L__

l where fM is the median frequency estimate, and f is the 84 percent g

exceedance probability frequency estimate. The logarithmic standard devi-ation on frequency was estimated to be approximately 0.30 for the structures evaluated.

4.1.4.1 Example of Spectral Shape, Damping, and Modeling Factors l

As an example, detennination of the spectral shape, damping, and modeling f actors and variabilities appropriate for f ailure modes associ-ted with E-W response of the auxiliary building bill be presented.

l Review of the modai responses indicated that nearly all of the response quantities in the E-W direction are associated with the fundamental E-W mode. This mode was found to have a median elastic frequency of 8.8 Hz compared to the original design frequency of 7.8 Hz. This frequency I shift can be attributed to the increase in structure stiffness associated with the median rather than design concrete compressive strength.

As noted in Section 4.1.3, evaluations of the structural failure modes for the auxiliary building were tyically based on median-centered structure loads. The median spectral shape # actor for these failure modes is therefore unity. For failure modes whose fragilities were derived from the original design basis, the median spectral shape factor would be based on a comparison of the original design spectral acceleration of 0.389 at the original design frequency of 7.8 Hz for five percent design damping with the median spectral acceleration of 0.301g at the medkn frequency of 8.8 Hz for ten percent median damping-I .

F SA

• 0.38 0.301

= 1.3 From information defining the median-centered spectrum for the. Millstone 3 site, the variability associated with randomness was estimated to be 0.20 at the median frequency. The uncertainty was estimated to be 2/3 of the randamness.

E B

R

= 0.20 l

I o3 g S u I l

The composite variability associated with damping was based on a l comparison of the median spectral acceleration of 0.322g for seven percent I

damping at the median frequency at 8.8 Hz with the median spectral accel-eration of 0.309 for ten percent damping.

8

• E" I l.322h 0

C 0

\.301)l l = 0.07 i 6 '

= = 0.05 (BR )c" (fU)c I

For this structure, uncertainty on frequency was estimated to be 0.30. The -lE frequency was found to be:

f,y g= 8.8 e-0.30

= 6.5 Hz The modeling uncertainty associated with frecuency was then based on the maximum spectral acceleration for the ten percent damped median response spectrum of 0.311g which falls within the + 18f range. _

Bmf

• I" / 0.311) 0.301

= 0.03 I

l 1

E This value was combined with the estimated modeling uncertainty associated with mode shape of 0.15 to give the total modeling uncertainty:

/ 2 2 i l B M + 0.15

=Y0.03 I l

= 0.15 i

4.1.5 Modal Combination The seismic design analysis of Millstone 3 structures was perfomed by response spectrtzn analysis; therefore, phasing of the individual modal responses was unknown. Most current design analyses are nonnally conducted using response spectra techniques. The current l recommended practice of the USNRC as given in Regulatory Guide 1.92 (Reference 12) is to combine modes by the square-root-of-the-sum-of-I the-squares (SRSS). This was the approach used in the Millstone 3 analyses. Many studies have been conducted to determine the degree of conservatism or unconservatism obtained by use of SRSS combination of .,

modes. Except for very low damping ratios, these studies have shown that SRSS combination of modal responses tends to be median centered. The coefficient of variation (approximate logarithmic standard deviation) tends to increase with increasing damping ratios. Figure 4-5 (taken from Reference 23) shows the actual time-history calculated peak response versus SRSS combined modal responses for structural models with four I predominant modes. Based upon these and other similar results, it is g estimated that for ten percent structural damping, the SRSS response is y medi an-centered. The median modal combination f actor of safety was therefore taken to be 1.0 for structural and equipment fragilities based on the original design information. Similarly, the SRSS method of modal combination was used to develop the median structure loads described in Section 4.1.3. The median modal combination f actor for structural i fragilities based on these loads was also taken to be 1.0. Where individual modal responses were known, the absolute strn of these 4-26

responses was used to estimate the coefficient of variation. The j absolute sun is an upper bound estimated to be three standard deviations above the median SRSS response.

1 4.1.6 Combination of Earthquake Components The design of the essential Millstone 3 structures with the I

exception of the auxiliary ';ilding was based on loads developed from the absolute sum of the accelerations in one direction due to the simultaneous responses from all three directions of input. For the design of the auxiliary building, the dynamic forces of the members were computed by the square-root-of-the-sum-of-the-squares (SRSS) method. Current l licensing requirements consist of the SRSS combination of responses from three principal directions (Reference 12). Alternatively, it is reconmended (Reference 10) that directional effects be combined by taking 100 percent of the effects due to motion in one direction and 40 percent of the effects from the two remaining principal directions of motion.

I This was considered the median condition for the current evaluation.

Depending on the geonetry of the particular structure under consideration together with the relative magnitude of the individual load f

or stress components, the expected stresses due to the 100, 40, 40 percent method of load combinations are decreased when compared with those calculated using the original design method. For shear wall structures where the shear walls in the two principal directions act I essentially independently and are the controlling elements, tho two horizontal loads do not combine to a significant degree except for the l torsional coupling. Thus, only the vertical component affects the I individual shear wall stress. A moderate amount of vertical load slightly increases the ultimate shear ioad carrying capacity of reinforced concrete walls. However, there is an equal probability that the vertical seismic component will add to or subtract from the dead-weight loads at the time of maximum horizontal loads. Thus, while the dead load is sometimes included in the analyses, the vertical seismic component is ignored. Consequently, the f actor of safety is not strongly influenced by the directional component assumptions.

I 4-27

The coefficient of variation is calculated in the same manner as

~

it was for the modal combination factor. The absolute sum of the three components is an upper bound, estimated to be three standard deviations above the median.

1 4.1.7 Soil-Structure Interaction Effects l

l Two types of soil-structure effects are considered in the analysis of nuclear power stations. The first involves the variation in frequency and response of the structure due to the flexibility of the l soil and the dissipation of energy into the soil oy radiation (geometric) damping. For structures founded on competent bedrock such as most of the Millstone 1 Category I structures, these effects are usually small and are typically neglected in current design analyses. A second effect is the amplification of the bedrock motion through the soil. Again, for I structures founded directly on the bedrock, essentially no amplification occurs, and the motion is normally specified at the foundation level as I was done in the design of the Millstone 3 struhtures. Thus, the design of the Millstone 3 structures founded on rock was conducted using current state-of-the-art assumptions and methods of analysis in regard to the l soil-structure interaction effects.

I The original design analysis of the emergency generator enclosure, which is founded on soil, was performed using a finite element representation of the structure and the supporting media. The soil material properties were treated as being linearly viscoelastic.

I Nonlinear behavior of the soil properties was accounted for by the use of the Program SHAKE. The bottom boundary of the finite element model was established at bedrock while the side boundaries were represented as being energy transmitting. Seismic input consisted of the design time-history input at bedrock.

I I

l 4-28 1

l. _

l The finite element model of the emergency generator enclosure described above directly accounts for the stiffness and radiation damping representation of the major soil-structure interaction effects normally considered in seismic analysis. Also, because the design time-history l was input at the bedrock boundary, amplification of the bedrock motion up through the soil to the structure foundation was directly accounted for l in the seismic analysis. Based upon a review of the soil-structure interaction representation of the emergency generator enclosure, the median soil-structure interaction factor was estimated to be 1.0, with logarithmic standard deviations associated with randomness and uncertainty I of 0.06 and 0.22, respectively.

The original design seismic analysis of the control building was conducted using a fixed-base representation of the soil-structure inter-action effects. It appears that the seismic analysis was later revised using a finite element soil-structure interaction model similar to the emergency generator enclosure model. A comparison of the fundamental frequencies predicted by both models indicated very little frequency shift I when soil-structure interaction effects were accounted for. This is consistent with the presence of the very shallow layer of stiff basal till separating the structure from bedrock. For control building fragilities I based on loads generated by the original design model, the median soil-structure interaction factor was estimated to be 1.0, with logarithmic standard deviations associated with randomness and uncertainty of 0.02 and 0.10, respectively.

One other possible area of concern is the slab uplif t of the structures at high input acceleration levels. For structures founded on competent rock, there is insufficient energy in the low frequency earth-quake waves to sustain overturning motion of the structure at the very long response periods required to overturn an auxiliary buildina or containment structure. At the frequencies of maximum input energy content, although a very small amount of uplift may occur, the direction of input motion is reversed before any significant rocking motion can occur. So long as significant rock or concrete crushing does not occur, 4-29

s m

relative motion sufficient to cause piping or electrical conduit failure J is not considered a possible failure mode. The bedrock at the Millstone 3 L site is considered to be of adequate strength to preclude failures resulting from base slab uplif t.

4. 2 STRUCTURE FRAGILITIES l

The significant failure modes for each of the Millstone 3 structures included in this study were evaluated. The resultina '

fragilities for each of these structures are discussed in the following sections.

4.2.1 Containment and Internal Structures The containment structure is a reinforced concrete structure consisting of a circular cylindrical wall caoped by a hemispherical dome.

The containment wall is supported by a base mat bearing on rock.

. Principal dimensions of the containment structure are:

1 Mat Radius 79'-0"

~

Thickness 10'-3" Liner plate thickness

• 1/4" I Cylinder Inside radius 70'-0" Wall thickness I Liner plate thickness 4'-6" 3/8" Height to springline 131'-3" Dome Inside radius 70'-0" l Wall thickness Liner plate thickness 2'-6" 1/2" i The controlling mode of failure for the containment structure I was found to be shear failure of the wall near the base. Concrete with a design compressive strength of 3000 psi at 28 days was used to construct the wall. Reinforcement in the meridinnal and hoop directions were I

I 4-30 l

provided with additional reinforcement included at the discontinuities to resist increased stresses imposed by LOCA loading. Diagonal reinforce-ment was also provided in the wall for additional resistance against horizontal seismic shear forces.

F Horizontal shear forces due to seismic response of the contain-ment structure introduce tangential shear stresses in the wall. The median shear strength of the wali was determined usina emoirical relation-I ships derived from testing conducted on models of prestressed and rein-forced containment structures. Resistance to horiza tal seismic shear is provided by the concrete and the four-way reinforcement pattern. This failure mode was found to have a median acceleration caoacity of approxi-mately 4.99 Median factors of safety and variabilities for this failure mode are listed in Table 4-7. This mode of failure results in loss-of-liner integrity, failure of the reactor coolant pressure boundary, and failure of most of the safety systems and components.

I The containment internal structure consists of walls and floors I supporting the equipment housed within the containment structure. The internal structure also provides biological shielding and missile protection.

Towards the base of the internal structure, the main load-carryir.g elements are the crane wall, the primary shield wall, the in-core instrumentation tunnel walls, and the steam generator columns. These elements are founded on the base mat comon with the containment structure. Dimensions at the crane w:.sil and primar.y shield wall are:

Crane wall Outer radius 57'-6" Thickness 2'-6" above El. 46'-10" Height 132'-10" Primary shield wall Inner radius 12'-6" Thickness 4*-6" Height 51'-9" 4-31

Review of the internal structure indicated that failure due to seismic response will obviously occur towards the base of the structure.

At this location, the crane wall is perforated by several large openings that create a series of wall segments typically 3'-0" by 10'-D" sparining l from the top of the base mat to El. (-)0'-9". Internal structure failure is expected towards the base mat due to the reduction in material l available to resist seismic loading. Because the walls above El. 3'-0" are essentially interconnected, it is aopropriate to treat the walls and columns below El. 3'-0" as being tied together.

I To provide a more refined evaluation of the seismic load distri-butions to the individual members, e more detailed static model of the structure below El. 3'-0" was created. The walls and columns were recre-sented by individual elements and were rigidly connected at El. 3'-0".

Applied loading was based upon overall seismic loads acting on the internal structure predicted by the median response spectrum analysis.

Capacity of the internal structure was found to be controlled by I seismic loads acting primarily in the E-W direction. Structural vielding was found to initiate in the 3'-0" by 10'-0" crane wall columns at the west side of the structure due to tension resulting from the overall I structure overturning moment. Because of redundancy, initiation of yielding at these columns does not imply structural failure of the g internal structure. After adjusting the static model for local nonlinear-ities, failure of the internal structure was found to be controlled by in-plane shear failure of the long crane wall column at the south side of the structure. Crane wall failure was determined to have a median accel-eration capacity of approximately 2.2g. Median factors of safety and variabilities for this failure mode are listed in Table 4-8. This structural failure is expected to result in failure of the reactor coolant pressure boundary. Also, the integrity of the liner cannot be quaranteed following failure of the concrete internals.

4-32 I

~

Other failure modes investigated for the containment and g internal structures included flexural failure of the containment wall and I

sliding at the foundation. Flexural failure of the containment wall due to the overturning moment generated by horizontal seismic response was I estimated to have a median acceleration capacity of approximately 6.1q.

Although structure sliding is expected to initiate at a median l acceleration of approximately 1.1g, damage to the structurc or equipment is not expected as a result. The containment base mat is embedded in bedrock with a + 6" gap provided between the vertical base mat and rock forces. This gap is filled with concrete sealer and hollow concrete block. Even if the concrete block is crushed, the maximum sliding displacement that can occur is expected to be only slightly more than one inch. This upper bound displacement is believed to be insufficient to fail piping attached to the structure. Overturning of the containment structure is not considered to be a credible mode of failure. The periods required to result in overturning are so large compared to the rigid body rotation periods of the structure that the earthquake input is reversed in direction before significant base slab uplif t can occur.

I 4.2.2 Auxiliary Building i The auxiliary building is a reinforced concrete structure housing equipment related to the chemical and volume control, component cooling water, and reactor protection systems. It is founded on a base I mat at El. 4'-6" which bears on bedrock and spans four stories up to the roof at El. 93'-6". The primary resistance to lateral loadina is provided by shear walls. These wails also serve as bearina walls alona with steel and concrete columns to support vertical loads.

I The controlling failure mode leading to gross structure f ailure of the auxiliary building is expected to be shear wall failure. Based upon an elastic load distribution of the overall median structure loads, yielding due to in-plane overturning moment is expected to initiate at the south exterior wall between El. 4'-6" and El. 24'-6". Similar to the containment internal structure as described in Section 4.2.1, the lateral 4-33

s c

load-carrying system for the auxiliary building is redundant so that yielding of one wall does not imply gross structural failure. The seismic L load distribution was modified to account for this load redistribution.

Shear wall failure was found to be controlled by failure of the north

[ exterior wall between El. 4'-6" and El. 24'-6" at a median acceleration capacity of approximately 1.4g. Median factors of safety and vari-

{ abilities for this failure mode are listed in Table 4-9. Shear wall failure is expected to lead to damage to the critical equipment located in the auxiliary building.

p Other f ailure modes leading to localized structure damage include diaphragm failure, steel and concrete colurnn failure, and structure sliding. The concrete floor slabs serve as diaphragms trans-mitting structure inertial forces to the walls and redistributing shear wall loads due to changes in wall stiffnesses from story-to-story. The slab at El. 43'-6" adjacent to the east exterior wall is perforated by a series of several openings with removable slab covers. Failure of this portion of the slab is expected at a median acceleration capacity of approximately 1.2g. Damage only to equipment or piping mounted to the slab at El. 43'-6" between Lines F.8 and F.9 is expected at this capacity.

g Although sufficient damage is expected to the floor slab in this location 5

to result in possible loss of equipment anchorage, no failure of any fluid or electrical systems passing through the openings in the slab is expected. Remaining diaphragms are expected to have acceleration capacities in excess of this value. Median factors of safety and variabilities are listed in Table 4-10.

Many of the steel and concrete columns in the auxiliary building must provide vertical support for shear walls that are not continuous to the base mat. In-plane overturning moments acting on these walls must be I resisted by axial loads on the columns. Evaluation of the columns was g conducted on the basis of desir dead, live, and SSE loads. Typically, y capacities of the columns were found to be controlled by tension due to seismic uplift rather than compression. The median acceleration capacity l

l 4-34 l _ ______________-- _ _ - -------------_--- - - - - -

of 0.299 for Steel Column N9 was differentiated from the median accelera-7 tion capacity of 0.719 for Steel Columns N5, N8 and N11 because Column N9 was anchored to the slab by high-strength bolts while the other columns were anchored by Hilti bolts. The initial damage to Column N9 is expected to occur as a result of tensile failure in the bolts at the top of the column. However, the detail of the column will prevent the bolts from l

f alling out and, together with the shear lugs in the top plate, these bolts will provide sufficient lateral support that the column will retain its compressive capacity once the earthquake load reverses. The capacity of the column in compression is significantly greater than tension, and no failure of equipment attached to or adjacent to this column is expected as a result of fracture of the upper bolts. A similar condition exists I for the columns anchored by Hilti bolts exceot that the bolts are expected to yield rather than fracture. The amount of bolt distortion is small since the overall structure displacements result in deformation-controlled loads into the columns. The bolts and shear lugs in the column end plates will assure the columns cannot displace laterally, so their compressive capacity is not lost. The median compressive capacity l 1s over 2g peak effective ground acceleration for these columns.

I The median acceleration capacity for initial damage to the concrete colurans was estimated to be approximately 0.68g. The concrete column tensile capacity was found to be limited by pullout of the dowels from the base mat. These dowels are not hooked to develop the full median yield strength. Because the columns are not part of the primary B lateral-load resisting system, gross structural failure is not expected to result from column dowel pull out. The column earthquake loads are deformation controlled by the overall structure, and the dowels will provide sufficient lateral capacity to assure the concrete columns will function in compression after load reversal. Column uplift is not exoected to result in failure of any piping or equipment attached to the columr or in the immediate vicinity. The concrete columns have signifi-cantly higher capacity in compression and even af ter compression damage occurs in the columns, although some pipe anchorage may be lost, the 4-35 l

pipes are expected to have sufficient flexibility that failure will not occur. Based on the expected damage to both the steel and concrete columns and a site investigation of the equipment attached to the columns, failure to the equipment is not expected prior to the overall structure failure which is governed by the shear walls.

l In addition to the failure modes described above, the possibility of structure sliding was evaluated. Resistance to structure sliding is provided by static friction between the base mat and the gravel layer on which it bears, shear keys embedded in bedrock, and lateral earth pressure. Although structure sliding is expected to initiate at a median acceleration capacity of approximately 0.68 9, damage to piping attached I to the auxiliary building and running to other structures is not expected until a median acceleration capacity of approximately 2.29 4.2.3 Control Building The control building is composed of reinforced concrete floor slabs and shear walls with structural steel framing provided for additional vertical load support. The structure is founded on a base mat which bears on a thin layer of backfill overlying 1 foot to 15 feet of I basal till. Equipment related to the reactor protection and electric power systems is contained within this structure. The cable spreading area and the control room are located on the floors at El. 24'-6" and I El. 47'-6", respectively.

The controlling failure mode for the control building was found to be the diaphragm at El. 64'-6" adjacent to the west exterior wall.

This region of the floor slab is perforated by openings for a stairwell and ducting, thus reducing the material available to resist seismic shear.

The applied load consists of floor inertial forces as well as load from the discontinuous east wall at the story above, which is redistributed to g the west exterior wall. The median acceleration capacity for this failure P mode was estimated to be approximately 1.0g. Median factors of safety and variabilities are listed in Table 4-11. Due to the lack of redundancy i

in the lateral load-resisting system, diaphragm failure is expected to 7 lead to gross structural failure of the control building with resulting L damage to the equipment housed within, j

Other control building failure modes investigated included structure sliding, shear wall failure, and failure of the control room I block wall. Resistance to structure sliding is provided by shear keys l embedded in the soil below and static friction imposed at the base mat-soil interf ace. Structure sliding is expected to initiate in the I west direction at a median acceleration capacity of approximately 0.43g.

As noted in Sectic. 4.1.1.7, the initiation of sliding does not neces-sarily imply damage to critical equipment. Should the control building l slide 2 inches and impact with the adjacent building, there is a possibility of concrete spalling with subsequent damage to equipment I located or, or very near the west exterior wall. This failure mode was found to have a median acceleratien capacity of approximately 1.29 .

Median f actors of safety and variabilities for this failure mode are listed in Table 4-12.

I Median acceleration capacities for shear wall and control room block wall failure were estimated to be approximately 1.5g and 2.0g, respectively. Review of the control room ceiling specification indicated that the ceiling was required to be safety-wired. Inspection of available I drawings indicated that the light fixtures above the control room ware braced. Failure of either of these systems are expected at acceleration levels in excess of the controlling failure mode.

1 I

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4,2.4 Emergency Generator Enclosure

[ The emergency generator enclosure (EGE) contains the emergency diesel generators and related equipment. The structure is composed of concrete slabs and load-bearing concrete walls. The walls surrounding I the diesel generator units are supported by strip footings bearing on soil at El. 9'-0". Soil was backfilled between these walls up to the slab on grade at El. 24'-6". The diesel generator pedestals bear on this back-filled soil, but are separated from the slab on grade by one-inch-thick compressible material. Walls enclosing the fuel oil tank vault were cast integrally and are supported by a base mat.

I Resistance to the initiation of sliding provided by static friction between the concrete strip footings and base mat and the soil below, shearing resistance of the soil entrapped by the EF" wils through the horizontal shear plane at the bottom of the strip footings, and concrete-on-soil friction introduced by lateral earth pressure. As noted I in Section 4.1.1.7, initiation of structure sliding does not necessarily imply failure. Should the EGE slide in the south direction, the one inch expansion joints separating the pedestrian walkway slab from the EGE and the control building may close. However, this impact is expected to cause damage only to the walkway slab since the EGE and control building walls are much more heavily reinforced. The only important potential failure mode resulting from sliding is failure of attached piping. For an estimated median sliding displacement capacity of four inches, the I median bedrock acceleration capacity for sliding-infuced failure was found to be approximately 1.3g. Median factors of safety and variabilities for this failure mode are listed in Table 4-13.

I Under N-S seismic response, the E-W walls are subjected to out-of-plane loading from the adjacent soil outside the structure and entrapped within the walls and froa inertial forces associated with the l slab on grade and the walls themselves. The out-of-plane wall reactions are transmitted to the strip footings. Any horizontal loading on the footings in excess of the concrete-on-soil frictional resistance must be 4-38

[ _ .___ __ ______ __ _ . _ _ _ - - - - - _ -- _ - - - - -- - - - -

c trcnsmitted by the E-W footings acting as horizontal beams to the vault 7 base mat and the strip tooting below the west exterior wall. The strip L footings are reinforced as horizontal beams with reinforcement concen-trated at the vertical f aces. Evaluation of the footings for conserva-h tively determined lateral earth pressure loading determined a median acceleration capacity of approximately 0.88 9 . Median factors of safety and variabilities are listed in Table 4-14. Failure of the wall footings is not expected to lead to gross structural failure. However, some damage in terms of loss of anchorage may be expected to equipment mcunted on the slab near the walls at El. 24'-6" and on the walls between El. 24'-6" and El. 51'-0". Other failure modes for the EGE that were evaluated included failure of the slab on grade (analyzed similar to the wall footings) and shear wall f ailure. Median acceleration capacities of approximately 1.0g and 1.99 , respectively, were determined.

4.2.5 Engineered Safety Features Building The engineered safety features (ESF) building is composed of reinforced concrete floor slabs and load-bearing walls. It is founded on two base mats bearing on bedrock located at different elevations, one at El. 4'-6" and the other at El. (-)34'-9". The structure is partially embedded down into bedrock on the north, south, and east sides and separated from the rock faces by 1/4" thick protection board and concrete fill. The west side of the structure is separated from the containment I structure by a four inch thickness of compressible material except for the base mat at El. (-)34'-9" which butts up against the containment base mat . The ESF building houses equipment related to the containment recirculating, quench spray, residual heat removal, safety injection, and the auxiliary feedwater systems.

The controlling failure mode for the ESF bui.lding is a combined base mat - shear wall f ailure. Under loading in the west direction, in-plane shears from the E-W shear walls are transmitted to the base mat at I El. 4'-6". Resistance to sliding in the west direction is provided by a thickened portion of the base mat beneath the' east exterior wall. This I

i 4-39

thickened portion performs as a shear key and transmits the base shear into bedrock. Calculations indicate that friction developed on the L inclined key face are sufficient to prevent the key from sliding up and out of the rock trench. Capacity of the key is limited by the ability of

[ the base mat to transmit the west direction shears into the key through l

{

direct tension. Once yielding of the base mat initiates, additional l

{ resistance is provided by the shear walls spanning from the base mat at El . (-)34 '-9" to El . 4'-6". Shear from these walls is transmitted from the ESF bulding base mat to the containment base mat. The median acceleration capacity for this failure mode was estimated to be approxi-mately 1.79 Median factors of safety and variabilities are listed in l

Table 4-15. I Other potential ESF building failure modes evaluated included shear wall failure and diaphragm failure. These failure modes were found to have median acceleration capacities of approximately 2.4g and 2.7g, respectively. The structure sliding displacements in the north, south, and east directions are limited to the thickness of the protection board separating the structure from concrete fill poured to the vertical bedrock faces. Displac,ements of this magnitude are insufficient to fail piping attached to the structure.

I 4.2.6 Pumphouse The pumphouse is a reinforced concrete structure housing both the service water and circulating water pump? The structure is founded l on a base mat bearing on either excavated rock or fill concrete overlying bedrock. Below the floor at El.14'-6", the structure is essentially open to Long Island Sound with transverse guide walls channeling the water flow.

I Capacity of the pumphouse is expected to be controlled by structure sliding in the west direction with subsequent damage to the I water lines. Resistance to sliding in the N-S direction is enhanced by shear keys opposing imposed shears. Sliding in the east direction is 4-40

restricted by adjacent bedrock which is separated from the structure by fill concrete. No such condition exists against shear in the west I

direction, however, and only resistance provided by the static friction -

of the base mat bearing against the excavated / fill concrete surface is available. Sliding in the west direction is expected to initiate at a median acceleration capacity of approximately 0.48g. As noted in Section 4.1.1.7, initiation of structure sliding does not necessarily imply failure. Sufficient sliding displacement to damage the attached piping l or electrical duct banks is expected to occur at a median acceleration capacity of approximately 1.39 Median factors of safety and vari-abilities are listed in Table 4-16. Other pumphouse failure modes investigated included diaphragm and shear wall failure. Median accel-I eration capacities of approximately 1.5g and 1.6g, respectively, were found for these failure modes. Median factors of safety and vari-abilities for these failure modes are listed in Tables 4-17 and 4-18.

4.3.7 Demineralized Water Storage Tank The demineralized water storage tank (DWST) is essentially a reinforced concrete structure with a steel liner. It serves as part of the auxiliary feedwater system. The concrete walls of the DWST are supported by an octagonal base mat approximately te n feet thick.

I Inspection of field reports indicated that this base mat was poured on a fill concrete leveling mat overlying bedrock.

The median acceleration corresponding to the initiation of sliding was estimated to be approximately 0.63g. The sliding resistance is controlled by the base mat-concrete fill interface. Capacity of the tank is expected to be governed by the failure of attached piping due to sliding-induced relative displacements. The median acceleration capacity for this f ailure mcde is estimated to be approximately 1.6g. Median factors of safety and variabilities are listed in Table 4-19. Other failure modes, including failure of the concrete walls and failure of the I liner, were found to be well in excess of this 1.6g capacity.

I I 4-41

4.2.8 REFUELING WATER STORAGE TANK n The refueling water storage tank (RWST) is fabricated from 4 3A 240-304 stainless steel. It has a radius of 29'-6" and stands 59'-0"

, to the top of the side wall with plate thicknesses varying from 3/16" to L 1/2". A total of fifty 2" diameter anchor bolts are provided around the tank perimeter at the base mat. The RWST serves as part of the quench spray system.

l Capacity of the RWST was found to be governed by buckling of the lowest shell course due to overall structure overturning moment. The median acceleration capacity for this tank was estimated to be approxi-mately 0.88g. Median factors of safety and variabilities are listed in Table 4-20. Buckling of the tank wall is assumed to lead to loss of contents due to the potential for cracking at a weld.

I I

I i

1 l

l -

l w

a

~ 4-42 u

) w

hm W6 M M M M M N m 1 _E( F W ~1 F TABLE 4-1 RESULTS OF CONCRETE COMPRESSIVE STRENGTH TESTING l

Test Specified Average Strength Design Age at Test Standard Strength Testing Strength Deviation Structure (psi) (days) (psi) (psi)

?

O Containment Wall 3000 28 4380 350 Containment Internal Structure 5000 60 6510 670 Auxiliary Building 3000 28 4180 460 Auxiliary Building 5000 60 6180 350 l Control Building 3000 28 3720 280 Emergency Generator Enclosure 3000 28 4590 730 l Engineered Safety Features Building 3000 28 4200 450 l

1 Pumphouse 4000 28 493C 460 I

p__

l TABLE 4-2 MEDIAN CONCRETE COMPRESSIVE STRENGTHS AND VARIABILITIES l

Specified Design Median Logarithmic l Strength Strength, i'c Standard Structure (psi) (psi) Deviation, s Containment Wall 3000 5200 0.13 p Containment Internal Structure 5000 7200 0.11 l A Auxiliary Building 3000 5000 0.15 l Auxiliary Building 5000 6800 0.08 ,

Control Building 3000 4500 0.13 Emergency Generator Enclosure 3000 5400 0.19 Engineered Safety Features Building 3000 5000 0.15 j Pumphouse 4000 5900 0.14  ;

l

m m' WE W m mm i E L_f 7 1 TABLE 4-3 MEDIAN REINFORCEMENT YIELD STRENGTH AND VARIABILITIES l

l Median Yield Logarithmic Strength Standard Structure Grade Bar Sizes (ksi) Deviation Containment and Internal Structures 40 #4 to #8 51 0.11 40 #9 to #11 49 0.11 50 #14 59 0.05 50 #18 56 0.04 60 #7 to #9, #11 71 0.05 l [

l Auxiliary Building 40 #4 to #8 53 0.10 i 40 #9 to #11 47 0.03 l 50 #14 59 0.05 60 #7 to #9, #11 69 0.05 Engineered Safety Features 40 #4 to #9, #11 51 0.07 60 #7 to #9, #11 71 0.05 Pumphouse 40 #4 to #6 54 0.05 60 #9 to #11 68 0.06 Emergency Generator Enclosure 40 #4 to #6 53 0.09 60 #7 to #9, #11 69 0.05 Control Building 40 #4 to #11 51 0.14

E TABLE 4-4 SCALE FACTORS NEEDED TO ACHIEVE u = 1.85 L

a) Due to 6.5 - 7.5 Richter maanitude earthquakes Earthquake Record (Comp) 8.54 Hz 5.34 Hz 3.20 Hz 2.14 Hz Olympia, WA., 1949 (N86E) 1.36 1.11 1.49 1.70 Taft, Kern Co., 1952 (S69E) 1.20 1.25 1.50 1.78 El Centro Array No. 12 Imperial Valley, 1979,(140) 1.34 1.56 1.29 1.48 Pacoima Dam San Fernando, 1971 (S14W) 1.25 1.38 1.26 2.19 Hollywood Storage PE Lot, San Fernando, 1971 (N90E) 1.45 1.65 1.58 1.39 El Centro Array No. 5 Imperial Valley, 1979,(140) 1.58 1.60 1.34 1.51 i Mean = 1.47 Median = 1.47 Range = 1.11 - 2.19 I b) Due to 4.5 - 6.0 Richter magnitude earthquakes Model Structure Frequency Earthquake Record (Comp) 8.54 Hz 5.34 Hz 3.20 Hz 2.14 Hz UCSB Goleta Santa Barbara, 1978 (180) 1.35 1.65 1.41 1.49 Gilroy Array No. 2, Coyote Lake, 1979,(050) 1.36 1.93 2.00 1.86 Gavilan College Hollister, 19 N (S67W) 1.61 1.55 1.62 1.93 i Melendy Ranch Barn, Bear Valley, 1972 (N29W) 1.45 1.96 2.18 1.98 g Mean = 1.71 Median = 1.64 Range = 1.35 - 2.18 3

4-46

b E

L TABLE 4-5 g SCALE FACTORS NEEDED TO ACHIEVE u = 4.27 a) Due to 6.5 - 7.5 Richter magnitude earthquakes Model Structure Frequency Earthquake Record (Comp) 8.54 Hz 5.34 Hz 3.20 Hz 2.14 Hz Olympia, WA., 1949 I (N86E) 1.56 1.54 2.61 3.75 Taft, Kern Co., 1952 1.25 1.65 2.05 3.38 I (569E)

El Centro Array No. 12 1.56 2.29 2.10 Imperial Valley, 1979,(140) 2.14 -

l Pacoima Dam 1.70 1.86 2.67 3.89 San Fernando, 1971 (S14W)

Holly ood Storage PE Lot, 1.94  ?.50 2.60 San rernando, 1971 (N90E) 2.05 El Centro Array No. 5 2.38 2.66 2.33 Imperial Valley, 1979,(140) 3.45 i Mean = 2.33 Median = 2.22 Range = 1.25 - 3.89 I b) Due to 4.5 - 6.0 Richter magnitude earthquakes Earthquake Record (Comp) 8.54 bz 5.34 Hz 3.20 Hz 2.14 Hz UCSB Goleta 1.52 Santa Barbara, 1978 (180) 2.05 2.05 1.96 Gilroy Array No. 2, Coyote Lake, 1.56 3.85 4.36 1979,(050) 3.03 Gavilan College 2.84 2.97 Hollister, 1974 (S67W) 2.71 8.49 l Melendy Ranch Barn, Bear Valley, 1972 (N29W) 1.89 5.48 5.16 3.36 Mean = 3.33 Median = 2.91 Range = 1.52 - 8.49 4-47 t__ .. _ - _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _

m I

I TABLE 4-6 COMPARIS0NOFRECENTSTUDIES(REFERENCE 22)

L WITH AMENDED RIDDELL-NEWMARK PROCEDURE E

W Reference 22 Ridde 1-N mark Magnitude Range u Median Range Median Range 6.5 < M < 7.5 4.27 2.22 1.25 - 3.89 2.24 1.28 - 3.92 4.5 < M < 6.0 4.27 2.91 1.52 - 8.49 2.89 1.41 - 5.94 6.5 < M < 7.5 1.85 1.47 1.11 - 2.19 1.49 1.14 - 1.92 4.5 < M < 6.0 1.85 1.64 1.35 - 2.18 1.84 1.21 - 2.69 I

l i

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1 4-48

m TABLE 4-7 Structure: Containment Structure Failure Mode: Shear Failure of Containment Wall Median 8 8 f

1 Factor F. S. R U B

C Strength 11 0 0.21 0.21 l Inelastic Energy Absorption 2.6 0.33 0.24 0.41 Spectral Shape 1.0 0.24 0.16 0.29 Damping 1.0 0.07 0.07 0.10 Modeling 1.0 0 0.16 0.16 Modal Combination 1.0 0.07 0 0.07 Combination of EQ. Components 1.0 0.10 0 0.10 Soil-Structure Interaction 1.0 0 0.05 0.05 l TOTAL 29 0.43 0.40 0.59 Median Acceleration Capacity = 29 (0.179 ) = 4.9g TABLE 4-8 Structure: Containment Internal Structure Failure Mode: Crane Wall Failure l Median g , g Factor F. S. R "U C Strength 6.0 0 0.21 0.21 Inelastic Energy Absorption 2.2 0.27 0.20 0.34 Spectral Shape 1.0 0.24 0.16 0.29 Damping 1.0 0.07 0.07 0.10 Modeling 1.0 0 0.16 0.16 l Modal Combination 1.0 0.07 0 0.07 Combination of EQ. Components 1.0 0.10 0 0.10 Soil-Structure Interaction 1.0 0 0.05 0.05 TOTAL 13 0.39 0.38 0.54 Median Acceleration capacity = 13 (0.179) = 2.29 I 4-49 L _ _.__ _ ----- -_ _

I TABLE 4-9 Structure: Auxiliary Building Failure Mode: Shear Wall Failure Median J Factor F. S. 8 R

8 0

8 C

Strength l 3.4 0 0.26 0.26 Inelastic Energy Absorption 2.4 0.30 0.23 0.38 3 Spectral Shape 1.0 0.20 0.13 0.24 j

' l Damping 1.0 0.05 0.05 0.07 Modeling 1.0 0 0.15 0.15 Modal Combination 1.0 0.04 0 0.04 Combination of EQ. Components 1.0 0.06 0 0.08 Soil-Structure Interaction 1.0 0 0.05 0.05 TOTAL 8.2 0.37 0.41 0.55 Median Acceleration Capacity = 8.2 (0.179) = 1.4g i

TABLE 4-10 l

l Structure: Auxiliary Building Failure Mode: Diaphragm Failure Median 8 8 Factor F. S. R U 8

C Strength 6.1 0 0.25 0.25 Inelastic Energy Absorption 1.2 0.06 0.05 0.08 Spectral Shape 1.0 0.17 0.11 0.20 Damping 1.0 0.04 0.04 0.06 Modeling 1.0 0 0.18 0.18 l Modal Combination 1.0 0.09 0 0.09 Combination of EQ. Components 1.0 0.06 0 0.06 i

Soil-Structure Interaction 1.0 0 0.05 0.05 TOTAL 7.3 0.21 i

0.34 0.40 Median Acceleration Capacity = 7.3 (0.179) = 1.29 4-50

1 3 TABLE 4-11 Structure: Control Building Failure Mode: Diaphragm Failure (

Median Far, tor 8 8 8 {

F. S. R U C Strength 4.6 0 0.22 0.22 Inelastic Energy Absorption 1.3 0.09 0.07 0.11 Spectral Shape 1.0 0.21 0.14 0.25

1. Damping 1.0 0.05 0.05 0.07 {

Modeling 1.0 0 0.15 0.15 Modal Combination 1.0 0.01 0 0.01 Combination of EQ. Compenents 1.0 0.01 0 0.01 Soil-Structure Interaction 1.0 0.03 0.10 U.10 TOTAL 6.0 0.24 0.33 0.41 I Median Acceleration Capacity = 6.0 (0.179) = 1.0g l TABLE 4-12 Structure: Control Building Failure Mode: Structure Impact Due to Sliding Median 8 8 B Factor F. S. R U C Strength 6.8 0 0.45 0.45 Inelastic Energy Absorption 1.0 0 0 0 Spectral Shape 1.0 0.19 0.12 0.22 Damping 1.0 0 0 0 Modeling 1.0 0 0 0 Modal Combination 1.0 0 0 0 Combination of EQ. Components 1.0 0.09 0 0.09 Soil-Structure Interaction 1.0 0.02 0.08 0.08 TOTAL 6.8 0.21 0.47 0.51 Median Acceleration Capacity = 6.8 (0.179) = 1.2g I 4-51

TABLE 4-13 Structure: Emergency Generator Enclosum Failure Mode: Failure of Attached Piping Due to Structure Sliding Median 8 8 8 Factor F. S. R 0 C Strength 7.4 0 0.42 0.42 Inelastic Energy Absorption 1.0 0 0 0 Spectral Shape 1.0 0.16 0.11 0.19 Damping 1.0 0 0 0 Modeling 1.0 0 0 0 Modal Combination 1.0 0 0 0 Combination of EQ. Components 1.0 0.17 0 0.17 Soil-Structure Interaction 1.0 0.04 0.15 0.16 TOTAL 7.4 0.24 0.46 0.52 Median Acceleration Capacity = 7.4 (0.179 ) = 1.3g TABLE 4-14 )

Structure: Emergency Generator Enclosure Failure Mode: Failure of Wall Footing Median

[ Factor F. S. 8 R

8 0 8 C-Strength 3.4 0 0.27 0.27

[

1 Inelastic Energy Absorption 1.1 0.03 0.02 0.04 Spectral Shape 1.4 0.18 0.12 0.22 Damping 1.0 0.01 0.01 0.02 Modeling 1.0 0 0.27 0.27 Modal Combination 1.0 0.03 0 0.03 Combination of EQ. Components 1.0 0.05 0 0.05 Soil-Structure Interaction 1.0 0.06 0.22 0.23 J TOTAL 5.2 0.20 0.46 0.50 s

Median Acceleration Capacity = 5.2 (0.179) = 0.889 s

4-52

TABLE 4-15 Structure: Engineered Safety Features Building J Failure Mode: Base Mat / Shear Wall Failure Median

' 8 8 8 Factor F. S. R 0 C Strength 7.2 0 0.25 0.25

[

Inelastic Energy Absorption 1.4 0.12 0.09 0.15 l Spectral Shape 1.0 0.19 0.13 0.23 Damping 1.0 0.02 0.02 0.03 1

Modeling 1.0 0 0.31 0.31

! Modal Combination 1.0 0.06 0 0.06 Combination of EQ. Components 1.0 0.01 0 0.01 Soil-Structure Interaction 1.0 0 0.05 0.05 TOTAL .

10 0.23 0.43 0.49 Median Acceleration Capacity = 10 (0.179 ) = 1.7g TABLE 4-16 Structure: Pumphouse Failure Mode: Failure of Attached Piping Due to Structure Sliding Median I Factor F. S. O R

8 0

8 C

Strength 7.6 0 0.45 0.45 Inelastic Energy Absorption 1.0 0 0 0 Spectral Shape 1.0 0.17 0.12 0.21 Damping 1.0 0 0 0 Modeling 1.0 0 0 0 Modal Combination 1.0 0 0 0 Combination of EQ. Components 1.0 0.17 0 0.17 Soil-Structure Interaction 1.0 0.04 0.15 0.16 TOTAL 7.6 0.24 0.49 0.55 Median Acceleration Capacity = 7.6 (0.179) = 1.3g

~

TABLE 4-17 Structure: Pumphouse Failure Mode: Diaphragm Failure Median 8 8 B

~

Factor F. S. R U C r~ Strength 7.4 0 0.21 0.21 Inelastic Energy Absorption 1.2 0.07 0.06 0.09 Spectral Shape 1.0 0.19 0.13 0.23 Damping 1.0 0.04 0.04 0.06 Modeling 1.0 0 0.16 0.16 Modal Combination 1.0 0.08 0 0.08 Combination of EQ. Components 1.0 0.01 0 0.01 Soil-Structure Interaction 1.0 0 0.05 0.05 B TOTAL 8.9 0.22 0.31 0.38 Median Acceleration Capacity = 8.9 (0.179) = 1.5g TABLE 4-18 Structure: Pumphouse Failure Mode: Shear Wall Failure Median I Factor F. S. 8 R

8 0

8 C.

Strength 4.5 0 0.19 0.19 Inelastic Energy Absorption 2.1 0.25 0.19 0.32 Spectral Shape 1.0 0.19 0.13 0.23 Damping 1.0 0.04 0.04 0.06 Modeling 1.0 0 0.16 0.16 Modal Combination 1.0 0.08 0 0.08 Combination of EQ. Components 1.0 0.01 0 0.01 Soil-Structure Interaction 1.0 0 0.05 0.05 TOTAL 9.5 0.33 0.34 0.48 Median Acceleration Capacity = 9.5 (0.179) = 1.6g 4-54

TABLE 4-19 m

Structure: Demineralized Water Storage Tank Failure Mode: Failure of Attached Piping Due to Structure Sliding 1 Median l 8 8 8 '

Factor F. S. R 0 C l

Strength 9.2 0 0.42 0.42 Inelastic Energy Absorption 1.0 0 0 0 Spectral Shape 1.0 0.17 0.11 0.20 Damping 1.0 0 0 0 Modeling 1.0 0 0 0 Modal Combination 1.0 0 0 0 Combination of EQ. Components 1.0 0.18 0 0.18 Soil-Structure Interaction 1.0 0 0 0 TOTAL 9.4 0.25 0.43 0.50 Median Acceleration Capacity = 9.2 (0.179) = 1.6g TABLE 4-20 Structure: Refueling Water Storage Tank Failure Mode: Buckling of Shell Wall Median 8 8 8 Factor F. S. R U C Strength 5.2 0 0.27 0.27 Inelastic Energy Absorption 1.0 0 0 0 Spectral Shape 1.0 0.27 0.18 0.32 Damping 1.0 0.05 0.05 0.07 Modeling 1.0 0 0.15 0.15 Modal Combination 1.0 0.01 0 0.01 Combination of EQ. Components 1.0 0.11 0 0.11 Soil-Structure Interaction 1.0 0 0.05 0.05 TOTAL 5.2 0.30 0.36 0.47 Median Acceleration Capacity = 5.2 (0.179) = 0.889 4-55

L l

l 80 l 1

l I Air cured, dry-at-test

'g 60 y ==

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20 -

I 0 .

0 1 2 3 4 5 6 7 8 9 10 11 12 Time (Months) i FIGURE 4-1. EFFECTS OF TIME AND CURING CONDITIONS ON CONCRETE STRENGTH (FROM REFERENCE 14)

I I

l

\

O

,0 T 4 L

M ,

X M 8 9 01 1 1 22 S -

F F FF 0 L -

M E E EE R R RR 3

L A

W -

R A

emXA E M

~

H S

E

, T E

A A AA R M \ C N

O N C M N F O

N , H 0

N ,

1

/,

T G

X 1 2 N M N N 7 8

h E R

T 1 S g 3 I

\

W C .

A 2 4

\ ,

4 4 \ E R

U Q

N G I

E

\ F e X .

0 5 1 ma " e a m m

• 8 eee .

4 L

2 0 8 6 0

1 1 4 2 0

)

c 'c V f (d

p$

ll

J J

Effective vertical equivalent acceleration = A g Hydrostatic uplift = cW W Net vertical contact force on WA , base = W (1-o-A )

pW W Static horizontal force = eW l Net horizontal resistance = NV = NMg

" au Coefficient of friction = u Then N = u (1-o- A, ) - a Consider a single pulse of horizontal acceleration Ag lasting for a time et, giving a velocity V I

I Acce le ra t ion Velocity

} V - - - -

q s ,y l ____ _____,N, x i i

I ' ' I Time C E

• l m 1 m et = ,

t,

=

u, = (e,- ty)f= -

~

= (4-9)

(1-i FIGURE 4-3. NEWMARK SLIDING ACPROACH (FROM REFERENCE 15)

B 4-58

J J

sc ,... . . . . a......... .......... ......... . . . . ................. .,

f 08 j  ;

Elestoplastic Systemsj g3 _

Acceleration Region i gy - A y a q+1  :

3~

h '

4 = 3.00 A-aso j C6 t

• Q48 A-ase  :

4

fwts#sm  :

n. E '

\ '

55  !

L y i ,

N i

am

\, \ ,'

. s N i 7

4 i ,

ow R. : 4.

a tin ' Q sQN l

vre- sg 3 02 -

N 4

4 4

4 OIC

- 4 4

4 4

! !! !  !  ! l ll lllk

LS 1 3 4 5 6 7 8 9O F

FIGURE 4-4. DEAMPLIFICATION FACTORS FOR ELASTIC-PERFECTLY PLASTIC SYSTEMS IN THE ACCELERATION AMPLIFIED RANGE (FROM REFEREt:CE 7) 4-59

H l

800 hi A i k

q-16 GS t > te 3 g gg + ,,

Rb OE ',

l .

E

,e as d= hip "tin so i s -

• s., MA l ,4 JW h to A-SS 40 She&samaagame) l I

I I

FIGURE 4-5. HIST 0 GRAMS OF RATIO 0F PEAK RESPONSE TO SRSS COMPUTED RESPONSE FOR FOUR-DEGREE-0F-FREEDOM DYNAMIC MODELS (FROM REFERENCE 23)

I 4-60 l

5. EQUIPMENT FRAGILITY J

s This chapter describes the fragility development for the seismically critical equipment within the Millstone 3 Nuclear Power Plant.

l The scope of the equipment evaluation effort is limited and is based upon a preliminary evaluation of Millstone 3 equipment frag 111 ties documented in Reference 34. SMA has conducted a cursory review of the approach and methodology used in the preliminary equipment evaluation and has judged the results to be generally conservative. As a result, the detailed site-specific reevaluation of equipment fragilities was conducted on only I a selected set of components. Based upon systems information, it was judged that components exhibiting a median ground acceleration capacity (N) of 1.50g or greater will have negligible impact upon risk associated with the Millstone 3 Plant operation. Therefore, the reevaluation of l equipment fragilities documented in this report was conducted on all components which, based upon the preliminary evaluation, exhibited a calculated acceleration capacity less than 1.50 9 . The resulting list of selected equipment used the seismic portion of the Millstone 3 PRA and is I presented in Table 5-1. One additional component, the steam generator U-tubes, had a predicted median capacity greater than 29 in Reference 34.

Because of the extremely severe consequence of a steam generator tube I bundle failure, a reevaluation of the U-tubes was conducted. The median ground acceleration capacity was predicted to be greater than Sg, recon-firming the observed conservatism in fragility development in Reference 34 I Section 5.1 contains a general description of the equipment fragility methodology with a more in-depth treatment than that provided in Chapter 3. Section 5.2 presents a set of representative example fragility derivations which provide the reader with further insight into the equipment fragility determination process while Section 5.3 presents the resulting equipment fragilities for the selected Millstone 3 components.

I 5-1

[ .. _ _ _ _

5.1 EQUIPMENT FRAGILITY METHODOLOGY Fragility as used in probabilistic seismic safety studies is defined as a conditional probability of failure for a given hazard

- i npu t. In this case, the fragility of a component or system is defined as the frequency of failure as a function of effective peak ground g acceleration. The development of these fragility levels combined with a discussion of the available information sources and the selection of equipment categories are the subject of this section.

5.1.1 Fragility Derivation The procedure used in deriving fragility descriptions is similar to that used for structural fragility descriptions, wherein, factors of safety and their variability are first developed for equipment capacity and equipment response. These two factors, along with the factor of safety on structural response, are then multiplied together to obtain an overall f actor of safety for the equipment item.

E"kEC ' ER ' SR (5-1) 5 EC is the capacity factor of safety for the equipment relative to the floor acceleration used for the design, 5ER is the factor of safety inherent in the computation of equipment response, and i is the SR f actor of safety in the structural response analysis that resulted in floor spectra for equipment design. Sections 5.1.1.1, 5.1.1.2, and 5.1.1.3 of this report contain a more thorough explanation of these three factors . (5 EC

' b ER, and pSR , resoectively). The overall factor of safety, F E, is then multiplied by the reference earthquake peak ground I acceleration to obtain fragility in terns of peak ground acceleration. I d=5- E A

SSE (5-2) i I

I 5-2

s where:

L d =

Median ground acceleration capacity ASSE = Peak ground acceleration of the safe shutdown earthquake l In most instances, the SSE was used as the reference earthquake; however, the OBE was used as a reference for those cases where the OBE acceptance j criteria governed the equipment design.

The logarithmic standard deviation, 8, for each of tiase factors is obtained using the logarithmic standard deviations for each of the above f actors and based upon the lognormal model (Appendix A).

2 2 2 8

E" I8 EC # 8ER + 8 SR)g (5-3)

I where SEC' 8ER, and SSR are the logarithmic standard deviations of the equipment capacity, equipment response and structural response, respecti vely. The logarithmic standard deviations are further divided into random variability, sR, and uncertainty, BU , as described in Chapter 3.

I 5.1.1.1 Equipment Capacity Factor The equipment capacity factor is defined as the failure threshold divided by seismic design level. For the purposes of this study, the ultimate failure threshold is the acceleration level at which the component ceases to perform its intended function. This failure threshold could consist of a breaker tripping on a motor control center, excessive deflection of the control rod guide tubes or a support failure of the steam generator. Where several failure modes certaining to the I same component are found to have roughly the same capacity level, all significant~ failure modes are analyzed.

5-3

[ ___ _ ___ _ _ _ - - - - - - - -_-- _ - -

The factor of safety for the equipment seismic capacity consists l of two parts:

l L

1. The strength factor, F S, based on the components static strength and i

2. The ductility factor, Fu, related to the equipment's inelastic energy absorption capability.

l I EC = F3 Fu (5-4) l The logarithmic standard deviation on the capacity can be derived '

l by taking the SRSS of the logarithmic standard deviations on the strength factor and the ductility factor. The randomness and the uncertainty por-tion of the variability can each be derived individually from Equation 5-5, by substituting the random or the uncertainty 8's for the strength f actor and the ductility f actor (i .e., 8 for B ,

3 for 83 and B y y etc.).

8

/2 8 + B 2)i3 EC

• l S I (5-5) k u/

5.1.1.1.1 Strength F_ actor - The strength factor, F S

, is derived from the equation:

I P P C N P P D D F

3= p p (5-6) i P T

D P

N D

I where CP is the median limit state load or stress, PN is the normal operating load or stress, P T is the total normal plus seismic load or I stress and PD is the code design allowable load or stress.

I I

5-4

m Alternatively, this equation can be written:

L P P c F C- N 3 (5-7)

L P SSE F

i where P SSE is the seismic load or stress corresponding to the safe shutdown earthquake. The normal and the seismic loads (PN and PSSE) are typically derived from the seismic qualification reports and the other information sources described in Section 5.1.2. The calculation of the capacity load, PC , is a function of the failure mode for the specific equipment item. Equipment failures can be classified into three categories:

I 1. Elastic functional failures

2. Brittle failures

3. Ductile Failures.

I Elastic functional failures involve the loss of intended functicn while the component is stressed below its Yield point. Examples I of this type of failure include:

1. Elastic buckling in tank walls and component supports.

2. Chatter and trip in electrical components.

3. Excessive blade deflection in fans.

4. Shaft seizure in pumps.

The limit state load for this type of a failure is defined as the load or stress level where functional failure occurs.

I I

5-5 1

Brittle failures are defined in this study as those failure F modes which have little or no system inelastic energy absorption capability. Examples of brittle type failures include:

(

I 4 I

1. Anchor bolt failures.

[ 2. Component support weld failures.

3. Shear pin failures.

Each of these failure modes have 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.

Thus, the collapse load for a brittle failure mode is defined as the median ultimate strength of the material. For example, consider a trans-former structure whose anchor bolts have been determined to be the criti-cal failure mode. Under seismic loading, the massive transformer will typically be stressed well below its yield level while the bolts are being stressed well above the bolt yield level. The amount of system inelastic energy absorption provided by the bolts' plasticity is negligible when compared to the seismically-induced kinetic energy of the transformer structure, and thus, these bolts will fail in a brittle mode once the ultimate bolt strength is reached.

I Ductile failures coincide much more closely with the structure failures which were described in Chapter 4. Ductile failure modes are those in which the structural system can absorb a significant amount of energy through inelastic deformation. Examples of ductile failure modes l include:

1. Pressure boundary failure of piping

2. Structural failure of cable trays

3. Structural failure of ductir.g

4. Polar crane failure.

I 5-6 I

1

s The collapse load for ductile failure modes consists of the median yield F strength of the material for tensile type loading conditions. For bending type failure modes, the yield point is defined as the limit load g or stress to develop a plastic hinge. The ductility factor will then I

quantify the inherent safety factor above the yield strength to the failure threshold.

l Each variable within Equations 5-6 and 5-7 has an associated lognonnal probability distribution to express its combined randomness and uncertainty. To find the overall variance on the strength factor, a technique conrnonly referred to as the "Second Moment Method" is utilized.

The mean and variance of a function comprised of lognormally distributed variables can be derived utilizing the moments (i.e., the mean and variances) of the logarithms of the distribution of each variable I (Reference 27). The resulting equation for the logarithmic standard deviation on the strength factor derived from Equation 5-6 is given below:

2 2 C 2 sg= ,g + *S T C 2 (PC- N), (PT-PN

~

(5-8)

(PC-P) T P

N 2 Y2 (PT-PN C-PN where:

BC

= Logarithmic standard deviation on the capacity or limit load (stress).

I ST

= Logarithmic standard deviation on the total load (stress).

BN

=

Logarithmic standard deviation on the nonnal I

load (stress).

5-7 I

_ - - __ - _ _ - - - - - - -- - -l

l L

E L

Similarily, the equation for the logarithmic standard deviation on the strength factor derived from Equation 5-7 is:

( 83= P2,g2,(p 9,p)2,8SSE + Pj 8 Y2 (p _p ) (5-9) where:

[ Sc and By .have[previously been defined, and i

BSSE. = f ogarithmic standard deviation on the seismic load (stress).

5.1.1.1.2 Inelast!c Energy Absorption Fact'or - The inelastic energy absorptica capability of a piece of equipment is quantified by the

( inelastic energy-absorption f actor (or ductility factor). Brittle failure modes and functional failure modes typically have a ductility

{ f actor of 1.0, while ductile 1ype f ailure modes have ductility factors r

which are a func. tion ,of a deamplif,1 cation factor. Section 4.1.2 of this report discribes ir< great detail the methodology utilized in deriving an

{ appropriate ductility factor for M.illstone 3. The ductility factor is based on the Riddell-Newnark methodoiogy presented in Reference 7, but is

[,

has been updated to reflect the correlation between earthquake magnitude and system ductiitty. The median ductility factors and their

( variabilities wre established in7Section 4.1.2 as a function of the component's natural frequency, and are suninarized below:

( ,

a; For the,2 Hz to 8-11z range,.

( J

'=

7

~F

, (q+1)2 us.q (5-10)

[ ,

e4

/ w ='-

E e'

O s . 5-8 y

t

/

m where

-0 30 7 q = 3.0xj r = 0.48xj l

[ j = percent of critical damp;ng to be used.

u* = effective ductility ratio l = 1.0 + CD (p-1.0)

I CD = factor accounting for the earthquake duration and equals 1.30 for Millstone 3.

b. For the rigid range, I Fy = u* (5-11) where u* is as previously defined.

c. For the range 8 Hz < f < rigid range.

I A linear interpolation utilizing log-log paoer is applicable for ductile equipment with natural frequencies I in this range. A point at 8 Hz should be plotted using F from Equation 5-10 and another point should be plotted at u the lowest unamplified (rigid) frequency for the floor I spectrum using Equation 5-11. A line drawn between these two points on log-log graph paper will uniquely determine the ductility factors within this frequency range.

I The variabilities for these median ductility factor derivations are evalu-ated by estimating a 1% probability (-2.338) that the actual ductility I factor is less than 1.0. Thus, the following equations determine the composite variability, randomness and uncertainty, respectively.

8 9

=

h in(F )

B = 0.8 x g y (5-12)

=

B y 0.6 x 8 I

5-9

I The ductility ratio, p, itself is based upon the recomendations given in Reference 6. This reference gives a range of ductility values L to be used for design. The upper end of this range is considered to be a median value. Engineering judgment was utilized to match the applicable I category froniReference 6 to a particular failure mode for the equipment component.

l 5.1.1.2 Equipment Response Factor The respo,1se factors are an estimate of the conservatism or i unconservatism that may have existed in the computation of seismic response during the design process. In this section, individual response f actors are described for both plant specific and generic equipment.

These factors. differ according to the seismic qualification procedure which was used in the equipment design.

There are three types of seismic qualifications which were performed for Millstone 3 plant equipment:

1. Dynamic Analysis

2. Static Analysis

3. Testing.

For equipment qualified by dynamic analysis, the important variables that affect the computed response and its dispersion are:

I 1. Qualification Method (Fgg)

2. Spectral Shape (F35)

3. Modelin (cffects mode shape and frequency

'results (FM)

4. Damping (FI D S. Combination of Modal Responses (for response '

spectr,u:n. method)_ (FMC) -

6. Combinationof5arthquakeComponents(FECC) 5-10 ^

l

__ _ _ _ _ _ - _ - _ _ _ _ _ _ _ - _ i

E L

For equipment qualified by .tatic analysis, two subdivisions must be considered. For rigid equipment, variabilities due to .;pectral

[ shape, combination of modal responses, damping, and for the most part, modeling errors are eliminated. If the equipment is flexible and tras

[ designed via the static coefficient method, the dynamic characteristic variables and their variability must be considered. This involves j estimating the range of frequency of the equipment and introduces a much larger uncertainty in quantifying the response factor.

Where testing is conducted for seismic qualification, the I response factor must take into account:

1.

Qualifiction Method (FQM)

2. Spectral Shape (F33)

I 3. Boundary Conditions in the Test vs Installation (FBC)

4. Damping (FD )

5.

I Spectral Test Method (sine beat, sine sweep, compex waveform, etc.) (FSTM) 6.

Multi-directional Effects (FMDE)-

The overall Equipment Response Factor is the product of each of these variables. The overall variabilities (uncertainty and randomness) are calculated by taking the SRSS of the individual logarithmic standard deviations for each of the variables. A brief description of each of the variables used to develop the equipment response f actor is provided below. A more detailed discussion is contained within Reference (24).

I 5.1.1.2.1 Qualification Method Factor - The Qualification Method Factor is a measure of the conservatism /unconservatism involved in the seismic qualification method used to seismically qualify the component.

Analytical qualifications can be separated into static analysis and dynamic analysis techniques. The inherent safety factor in using these 1

5-11

qualification techniques is discussed below, while the variability on r this factor is generally accounted for within the Damping, Modeling and u

Mode Combination Factors (i.e., 80% " 80M g = 0.0).

5.1.1.2.1.1 Static Analysis - The static coefficient method is intended to be a conservative upper bound method by which simple components may be qualified. Typically, the peak spectral acceleration is multiplied by a coefficient and this product is multiplied by the weight of the comoonent to determine an equivalent static load to be applied at the subsystem l

center of gravity. If the component is comprised of more than one lumped I

mass, the same procedure may be applied at each lumped mass point in the static model or may be applied as a uniformly distributed load on the static model. If the componont is rigid (i.e., its fundamental frequency l

1s above the frequency where the response spectrum returns to the zero period acceleration), the degree of conservatism in the response level used for design is the ratio of the specified static coefficient divided by the zera period acceleration of the floor level where the equipment is mounted. If the equipment is flexible and responds predominantly in one mode, the degree of conservatism is the ratio of the static coefficient to the spectral acceleration at the equipment fundamental frequency.

5.1.1.2.1.2 Dynamic ___Analys s - Response spectrum, mode superposition time-history and direct integration time-history dynamic analysis methods may be applied in subsystem response analyses. If response for a sinale degree-of-freedom model with best estimate material properties and damping are computed by the response spectrum method, the mode superposition time-history method or the direct integratinn time-history method, we would expect to obtain equal median centered results assumina that the response spectrum and time-history inputs are compatible.

I The response spectrum method, based upon a conservative ground time history, was extensively used for dynamic analysis of components and I systems within the Millstone 3 plant. If the applicable Millstone 3 I

I 5-12

~

H floor response spectra were utilized in the desion analysis, the Oualifi-cation Method Factor, FOM, is equal to unity and the variability is E zero. If conservative generic spectrum were used to seismically qualify a component, F OM is the ratio of the spectral acceleration from the L generic spectrum divided by the spectral acceleration from the Millstone 3 site-specific spectra evaluated at the components' fundamental frequency.

5.1.1.2.1.3 Testing - In vibration testing, the test response spectrum generally envelopes the required response spectrum by approximately ten

{ percent or more depending on the frequency range. If the test response spectra are available within the test report, the overtest safety factor will be accounted for in the Qualification Method Factor (Fgq) and its variability (6gg). If the component fragility is being based on I

testing where the test response spectra are not available, FOM and SQM are used to account for the overtest safety factor and variability on a generic case-by-case basis.

I 5.1.1.2.2 Equipment Spectral Shape Factor - The Millstone 3 design floor response spectra were computed by means of a time-history (T/H) seismic analysis. The overall dynamic response of each of the critical buildinos was modeled by lumping the mass of the structure and rigidly attached I components generally at each of the floor levels. The synthesized time history accelerogram for the horizontal SSE normalized to 0.174 is shown in Figure 1-4 for 5% damping. This time history was used to gentrate the response spectra for 0.5, 1.0, 2.0, 4.0, and 8.0 percent damping. As depicted in Figure 1-4, this artificial time history was developed to envelope, as closely as possible, the ground response spectra for the Millstone 3 site. The combined conservatism /unconservatism involved in developing the floor response spectra from a time history representation of the ground response spectra and in using the specified Millstone 3 I design response spectra in lieu of median Safe Shutdown Earthquake spectra is quantified in development of the Sp'ectral Shape Factor associated with the Structural Response Factor (See Section 5.1.1.3).

I I 5-13

The response spectrum method is often referred to as being conservative, however, the conservatism compared to a time-history L analysis is primarily due to the method of developing the spectrum.

Spectra used for design purposes are generally smoothed and the peaks are I widened such that the resulting design spectrum is conservative.

I 5.1.1.2.2.1 Peak Broadening and Smoothing - The effect of smoothing and l

peak broadening varies with structure, elevation, frequency and damping.

The criteria utilized in generating Millstone 3 floor response spectra was to broaden the peak resonant value by plus and minus 15'(. Beyond this resonant range, the actual amplified response spectra are utilized exactly as shown. Figure 5-1 shows a typical example of the broadened I versus unbroadened spectra comparison for the Auxiliary Building.

Factors of conservatism for peak broadening and smoothing were generated separately for specific frequency ranges within each of the Millstone 3 structures. Table 5-2 sumarizes these factors together with their variabilities f or most Millstone 3 structures. The frequency ranges were selected to reflect the portions of particular floor response spectra where the broadening was and wasn't undertaken. For any particular frequency, this peak broadening and smoothing safety factor can be computed from Equation 5-13 below.

I S F

33 ,

a (broadened and smootbed)

(5-13)

Sa (unbroadened and unsmoothed) where:

l FSS =

Spectral shape factor due to peak broadening and smoothing Sa = Spectral acceleration value I

I 5-14

4 i

For the frequency range in question, the median ratio (FSS from Equation 7 5-13) was computed with the minimum value of 1.0 considered to be a -28 extreme. Fragility parameters tere determined at ecch floor elevation g within the structures hnusing equipment to be evaluated. Table 5-2 shows I

the spectral shape factors for each of the building floors evaluated.

The values of F 33 shown in Table 5-2 are for the case where all three earthquake components contribute to response. Since the variability, 833, is due to the shift in the frequency and the variation with flont l elevation, it is considered to be all uncertainty.

I 5.1.1.2.3 Modeling Factor - In any dynamic analysis there is uncertainty t

l in resonse due to assumptions made in modeling the structure, modelina I boundary conditions and representing material behavior. Modeling of complex systems is usually conducted using nominal dimensions, weights, and material properties and is done in such a manner that further refinement of mesh size in a finite element representation will not significantly alter the calculated response. Representation of boundary conditions in a model may have a significant influence on the response.

The misrepresentation of boundary conditions in the dynamic model by assuming greater or lesser stiffness or treatina nnnlinear gap effects linearly cannot be quantified generically and each model must be treated specifically to determine a response factor for modelina. Assuming that the analyst does his best job of modeling, modeling accuracy could be I considered to be median centered (i.e., FM = 1.0) with the variability in each of the modeling parameters amounting to variability in calculated mode shapes and frequencies. The error in calculation of mode shapes and frequencies then has an effect on the computed response.

For complex equipment which have been analyzed using state-of-the-art dynamic analysis, the logarithmic standard deviation on response is about 0.20. For simple single-frequency systems with fundamental frequencies in the amplified portion of the spectra, the .ariability is I about 0.10. For single frequency systems with fundamental f requencies I

I 5-15

[ __ _ _ _ _ _ _ _ _ _ _ _ _ _ - - _ - _ _ _ _ . - _ - - _ - - - - -

out into the rigid range, the logarithmic standard deviation is 0.0.

m These variabilities are considered to be all uncertainty and are based on past experience and engineering judgment.

5.1.1.2.4 pamping Factor - The basis for the damping factor has been addressed in Section 3.4.2 of this report. Tables 3-1 and 3-2 show the l damping values used for the SSE design analysis of Mn Istone 3 equipment.

Median damping values and their variabi'ities are a function of the material, construction details, size and stress level. Reference 24 suggests that median damping for equipment at the SSE level is about five percent. Thus, for single-degree-of-freedom systems the damping factor for Millstone 3 equipment is:

I S,(qual)

F D" S,(median) (5-14) l where:

Sa (qual) =

Spectral acceleration using the qualification design analysis damping and evaluated at the equipment fundamental frequency I Sa (median) = Spectral acceleration using the expected median damping and evaluated at the equipment fundamental frequency.

I For multi-degree-of-freedom systems, Equation 5-14 can be altered to reflect the summation of the spectral accelerations at each of the fr,quencies multiplied by their associated mass participation factors.

There is variability in damping and associated resconse that must be considered. It is indicated within Reference 24 that for a median damping value of 5 percent, the minus one logarithmic standard deviation value is about 3.5 percent. The variability in damping results in a logarithmic standard rieviation in response equal to:

{

l 5-16

L r

l 8 hac=3.5%)

0b " I" 5 (5-15) k'c=5.0%/

where S s ne 5 percent damped speckal acceleradon and Sa ac = 5% c = 3.5%

is the 3.5 percent damped spectral acceleration taken at the equioment fundamental frequency using the applicable floor response spectra. The resulting logarithmic standard deviation on the damping response factor, from Equation 5-15 above, is considered to be all uncertainty. An additional randomness variability estimated at approximately 20 percent of the uncertainty variability reflects the earthquake time-histories' effect on the median damping value.

5.1.1.2.5 _ Mode Combination Factor - The modal combination technique _

utilized within the Millstone 3 seismic design analysis was described in I general in Chapter 3 of this report. A square-root-of-the-sum-of-the- i squares (SRSS) methodology was used for all Millstone 3 equipment. This l

SRSS method (allowing for absolute sum for closely spaced modes) is in

{

accordance with current Regulatory Guide 1.92 (Reference 12) recomended practice and is considered median centered.

The response factor for combination of modes is then considered to be 1.0. The variability associated with mode combination depends upon the complexity of the model. For multi-degree-of-freedom systems, '

Reference 24 recommends that the logarithmic standard deviation due to mode combination is approximately 0.15. For single-degree-of #reedom flexible systems, the variability due to mode combination is estimated within Reference 24 to be approximately 0.10. For a single-degree-of-freedom rigid system, the variability is by definition zero. The variability due to mode combination is considered to be all random due to the random phasing of modes.

I I 5-17 I

1 L _ _ _ _ _ _ _ _ _ _ - - - _ - - . _ _ _ _ _ _ - - - - _ _ - - _ - - .

5.1.1.2.6 Earthquake Component Combination Factor - The majority of the equipment within Millstone 3 were designed based the SRSS combination of the two horizontal and the vertical earthquake components. Only the balance-of-plant piping was designed differently using the SRSS l combination of the two horizontal plus the absolute sun combination of the vertical earthquake components. The square-root-of-the-sum-of-the-squares (SRSS) methodology is considered a median-centered approach and, f

thus, the factor is unity for components qualified in this manner. It should be noted a second method using a 100%, 40%, 40% combination is also considered to yield approximate median results . Reference 10 i

recomends that the response can be represented by combining the worst case horizontal response with 40 percent of the orthogonal horizontal response and 40 percent of the vertical response. The SRSS method must

, be applied to the end item of interest, while the 100%, 40%, 40% method can be applied at the input seismic load stage or at the stress intensity of interest stage with equivalent results. Both methods yield approxi-I mately the same factors of conservatism /unconservatism. In developing the Earthquake Component Combination Factors for Millstone 3 equipment, the SRSS combination was taken as the median. The magnitude of this Factor depends on the orientation, failure mode and response characteristics of the component under consideration.

A generic study was conducted to develop earthquake component combination response f actors and their variabilities for comon two- and three-dimensional equipment idealizations. The amount of conservatism /

k unconservatism and the associated variability on this factor are a function of the following:

t 5-18

' 1. The number and direction of earthquake components F

which affect the failure mode under consideration (e.g., piping failures can be influenced by all three directional responses, but a particular relay can fail due to a particular horizontal I

seismic excitation while remaining unaffected by the vertical and the other horizontal directions)

2. The amouit of coupling that exists between directional response (i.e.

excitation cause a response, in does the an x direction y and z directions) l Table 5-3 contains the earthquake component combination response f actors for those cases which were applicable to Millstone 3 equipment.

The variability involved in the phasing of the three earthquake directional components was considered to be all random, while the variability due to the degree of coupling involved between directions was considered to be all uncertainty.

I 5.1.1.2.7 Boundary Conditions Factor (Testina) - The boundary conditions utilized in equipment seismic testing can be a significant source of

}

variability that depends almost solely upon the diligence of the test laboratory and the qualification review organization. In general, a l component that is bolted to the floor in a nuclear power plant and which '

is similarly bolted to a shake table for qualification testing, will l experience little variability in response factor due to boundary conditions . Carelessness on the part of the various oroanizations

+

involved in design, fabrication, testing and installation can result in a significant variability. For instance, the lack of a specified holt torque at the mounting interface can result in a difference between the testing and installation condition which could have a pronounced impact on the response factor.

The variability of the subsystem response due to test boundary conditions would come primarily from any mode shape and frequency shift.

The variability of mode shape and frequency and resulting response due to i

I 5-19

]

l boundary conditions varies considerably for different generic types of g equipment. For a large n:3jority of tests conducted by reputable testing laboratories, the Boundary Condition Factor is 1.0. Engineering judgment must be utilized in calculating Boundary Condition Factors for those l cases where the component to test table attachment mechanism is not representative of the actual in-plant candition. The variability is all

} uncertainty and can be calculated based on spectral accelerations obtained from estimating a 90 percent confidence interval on the equipment frequency.

5.1.1.2.8 Spectral Test Method - Synthesized time-histories are current 1v i developed directly from the Required Response Spectrum at most testing laboratories. A much better approach, as recommended in Reference 27. is to synthesize a time-history that corresponds to a power spectral density ,

which closely envelopes the RRS rather than make the direct step from the RRS to the synthesized time-history. This approach tends to smooth out the input time-history, resulting in less chance for an equipment mode to coincide with a significant peak or valley. Reference 24 recommends a spectral test method factor of unity and a total variability of 0.11.

This variability is entirely uncertainly since the use of better equipment and techniques could eliminate most of the uncertainty.

5.1.1.2.9 Multi-Directional Effects - The Multi-Directional Effects Factor is a measure of the conservative /unconservatism and corresponding variability involved in testing the three different earthquake directional components. Millstone 3 equipment fragilities were developed from plant specific and generic test data and are based on two types of testing:

biaxial and uniaxial. Biaxial qualification tests are conducted by exciting the equipment in one horizontal direction at a time along with the vertical direction, using randomly phased input time-histories.

Uniaxial qualification tests, on the other hand, are conducted in each of the three directions independently. Biaxial testing was conducted for I most plant specific equipment qualified for the Millstone 3 plant. Thus, I

I 5-20

multi-directional effect factors were developed for both biaxial testing and uniaxial testing and were applied based upon the test methodology 1

l employed.

I l 5.1.1.2.9.1 Biaxial Testing - There is a slight unconservatism involved in biaxial testing in that the actual input during a seismic event is l three-dimensional. This unconservatism along with its associated variability is a function of both the phasing and the coupling between earthquake directional components. Assuming that the median acceleration vector can be defined as recomended in Reference 10 as 100 percent of the acceleration in one direction plus 40 percent of the acceleration in the other two orthogonal directions, the degree of unconservatism associated with biaxial testing can be defined as the median response vector for biaxial testing divided by the median three-axis response. I The resulting response factor based on both phasing and coucling is calculated to be 0.853. The variability due to phasing is a function of the earthquake, and thus, is all random. The phasing variability is identical to that which has been calculated for the general three-

{

I dimensional condition (Case No. 1 of Table 5-3) for the Earthquake Component Combination Factor and is equal to 0.12. The variability due g to coupling is sn all since median coupling in testing exists by W definition for the two input directional components. Using the uncoupled case and the 100 percent coupling case as +2.338 extremes on coupling, an _

l uncertainty logarithmic standard deviation of 0.04 is calculatert.

The Multi-Directional Effects Factor and its associated B's for random vibration biaxial testing is:

I FMDE = 0.853 EMDER

= 0.12 B

MDEg

= 0. M i

1 5-21

5.1.1.2.9.2 Uniaxial Testing - A uniaxial test is, in general, unconserva-y tive in that coupling and phasing between the three-directional earthquake components is not accounted for. Again, assuming the median acceleration vector can be defined a recomended in Reference 10 as 100 percent of the j acceleration in one di. '3n plus 40 percent of the acceleration in the other two orthogonal dirt. ans, the degree of unconservatism associated

with uniaxial testing can be defined as the median response vector for uniaxial testing divided by the median three-axis response. The resulting response factor based on both phasing and coupling is calculated to be 1

0.735. The phasing variability is random and is identical to that for the biaxial case, i .e., 0.12. The uncertainty variability due to coupling, based on the uncoupled case and the 100 percent coupling case being +_2.338 extremes, is calculated to be 0.08.

i Thus, the Multi-Directional Effects Factor and its associated 6's for uniaxial testing is:

I FMDE = 0.735 BMDER

= 0.12 8 = 0.08 hDEU 5.1.1.3 Structural Response Factors Structural response factors as they relate to structural capacity i for the safety-related structures within Millstone 3 are derived in Chapter 4. The variables pertinent to the structural response analyses I used to generate floor spectra for equipment design are the only variables of interest relative to equipment fragility. Time-history analyses, using the same structural models used to conduct structural response analyses for structural design, were used to generate floor spectra. The applicable variables for equipment from those analyses are:

I I

5-22 I

o

~

1. Spectral Shape g 2. Damping

3. Modeling

4. Soil-Structure Interaction.

5. Inelastic Energy Absorption of the Building The explanation of each of these vteiables is contained in Chapter 4 and will not be repeated here. Note, the combination of earthquake components is not included in structural response since that variable is addressed for specific equipment orientation in the treatment of equipment response. As discussed in Chapter 4, a totally independent .

evaluation of the capacities of the important structures was undertaken 1 in this effort. As a result, the generated median structural response f actor was 1.0 and included its associated variabilities. This inde-pendent analysis employed the median ground spectra to define seismic input. In evaluating equipment acceleration capacities which are based upon design analysis results, a spectral shape factor associated with structural response must be computed which compares the 5% damped time history spectrum used for design with the appropriately damped median spectrum. The resultant structural response factors pertaining to the equipment fragility derivation are included in Table 5-4. Note that the structural response factors for each particular structure are broken up into two segments. Equipment with caoacities less than the approximate building yield strength have Structural Response Factors in the "a" row, and equipment with capacities approximately equal to or greater than the structure yield strength have Structural Response Factnrs in the "b" row. The approximate yield level for each of the buildings was estimated by taking the ground acceleration capacity for the lowest structural failure mode (see Chapter 4) and dividing it by the inelastic energy absorption f actor.

I I

I 5-23 I

The structural response factors within Chapter 4 have been y derived on the basis of the structure being at its failure threshold I

level. It should be noted that when the building goes inelastic, the actual floor level acceleration will be decreased over that which is l predicted using the elastic structural model. At the same time, the displacement will increase over that which is predicted by the elastic l model. Thus, acceleration sensitive equipment must have their capacities scaled up to reflect the actual lowering of the floor acceleration due to building ductility, while displacement sensitive equipment must have their capacities similarily scaled down. Reference 10 recomends ten percent median damping for reinforced concrete at or above the Yield g condition and five percent median damping for reinforced concrete at the y one-half yield condition. In addition, the structures ductility does not modify the response of the equipment unless the equipment fragility is above the building'e yield level. Thus, for the condition where the equipment capacity is less than the structure's yield level, 5%

structural damping is considered median and the structure's ductility factor is effectively unity. For the case wh6re the equipment capacity is approximately equal to or greater than the structure's yield level, 10% structural damping is considered median. As a result, a slight conservatism is introduced using the 5% structural damping for a component whose capacity is less than but is approaching the yield capacity of the structure.

5.1.2 Information Sources l Several sources of information are utilized in a PRA from which to develop plant specific and generic fragilities for equipment. Sources used in this evaluation of Millstone 3 equipment include:

1. Seismic Qualification Design Reports

2. Seismic Qualification Test Reports

3. Final Safety Analysis Report (FSAR)

I 5-24

4. Specifications for the Seismic Design of Equipment

5. Seismic Qualification Report Summaries

6. Past Earthquake Experience l

Each of the information sources above are termed " plant specific" since they pertain to specific equipment within the Millstone 3 plant. Such plant specific sources are preferred since they have been I generated for the specific items in question and their uncertainty level is reduced from those of potential generic sources of information.

5.1.3 Equipment Categories Dependirig upon the uniqueness of the equipment, the failure mode, inelastic energy absorption capability and the dynamic characteristics of the equipment, a plant-specific or a generic derivation of the fraoility description may be appropriate. The factors of safety relative to the i Safe Shutdown Earthquake are widely variable.

equipment such as piping, which possesses the ability tn undergo large In general, flexible I

inelastic deformation, will have a factor of safety against failure of I many times the Safe Shutdown Earthquake even if stressed to the maximum code allowable stress. Such equipment is a prime candidate for generic derivation of fragility descriptions. The increased uncertainty inherent in a generic derivation does not have much influence on the outcome of the seismic risk analysis if large safety factors can be demonstrated.

On the other hand, if rigid equipment with relatively brittle failure modes are stressed to code allowable for the Safe Shutdown Earthquake, the factor of safety against failure may be considerably smaller and a generic treatment may result in unsatisfactory risk predictions.

Experience gained as to relative component fragility levels must also be utilized in deciding which components should be treated generically and which components should be treated specifically. As a result, those components which through experience have been shown to possess a high degree of resistance to seismic loading may often be I

5-25

l treated in more of a generic fashion while components which have been l i

shown to possess low fragility levels are more thoroughly analyzed to provide as much accuracy as possible. Table 5-5 contains a listing of the relative fragility level for general equipment categories based on the data provided in Reference 32. The information provided within Table 5-5 is utilized within the PRA study to discern which equipment can be treated generically and which equipment should be treated on a plant specific basis.

{

5.2 EQUIPMENT FRAGILITY EXAMPLES Because of the amount of equipment to be included within the g risk model, it is impractical to describe the specific fragility deriva-y tion for each piece of equipment. This section contains selected examples of fragility derivations which ee judged to be representative of the different types of analyses which had to be undertaken for Millstone 3 equipment. The equipment fragility derivation categories applicable to the Millstone reevaluation PRA are:

I 1. Equipment whose fragility descriptions are based on stress sunnaries.

g 2. Equipment whose fragility descriptions are based 3 on a review of the component qualification stress report.

3. Equipment whose fragility descriptions are based on knowledge of the design specifications and the factors of safety inherent in the governing codes and standards.

4. Equipment whose fragility descriptions are based on component test data.

5. Equipment whose fragility descriptinns are based on engineering judgment and past earthquake I experience (non-seismically qualified components).

An exampl'e of Millstone 3 equipment whose fragility derivation stems from each of the above categories is included in this section.

I l

, 5-ze u.

l 5.2.1 Example of a Plant Specific Fragility Derivation Based Upon Sununary Information The evaluation of the majority of the equipment associated with the Nuclear Steam Supply SystLm (NSSS) was based upon sucinary stress information provided by Westinghouse. The stsnmary information generally included the faulted condition stress level for the critical regions of the components, f ailure modes, yield and/or code faulted allowable stress, and some measure as to what portion of the total stress was due to seismic response. Component fundamental frequencies were also provided in some cases. The example chosen to illustrate the derivation of fragility based upon summary information is the Residual Heat Removal Heat Exchaiger.

5.2.1.1 RHR Heat Exchanger Capacity Factor Three locations were identified by Westinghouse as being the most critical for RHR Heat Exchanger in terms of seismic stress. These were:

1. Anchor Bolts

2. Heat Exchanger Shell at the Intermediate Support Lugs

3. Baseplate Based upon the supplied stress information, it was judged that the heat exchanger fragility would be governed by the shell stresses. The following information was provided.

1. Location: ESF Building at Elevation 4'-6" with horizontal restraints at Elevations 22'-0" and 46'-0".

2. Fundamental Frequency: Horizontal 21 Hz; Vertical 11 Hz.

3. Material: SA515-Gr 70: cy = 34,600 psi.

l 4. Design Seismic Accelerations: 1.5g (Horizontal); 1.0a (Vertical).

5. Faulted Condition Stress: 47,400 psi.

6. Portion Due to Seismic: 85%.

1 5-27

The failure mode consists of a local punching failure of the shell due to the horizontal restraint reactions. Failure is judged to occur at 1.5 times the median yield strength of the material and exhibit limited ductility. The factor of 1.5 is used to properly represent the actual load the shell can carry subsequent to first yield of the shell and accounts for both the section factor and strain hardening. Based upon the data presented in Reference 33, a lower bound factor of 1.25 is estimated to represent a 95% probability of exceedance value (-1.658).

Therefore, the logarithmic standard deviation for uncertainty is calculated as:

s lS u " 1.65 "" M O M " U #

In addition, Reference 38 reports that for soft steels the median yield strength is about a f actor of 1.25 above the ASME code specified minimtsn yield strength. Again, considering the Code minimum yield strength to represent a 95% probability of exceedance value, the uncertainty variability becomes:

8 1.25u " 1.65 in (1.25/1.00) = 0.14 The failure stress and its uncertainty can then be computed as:

P C = (1.25)(1.50)(34,600) = 64,875 psi B

C = (.11 + .14 ) 2= 0.18 Using information items 5 and 6 above, the Strength Factor (FS ) is l calculated in accordance with Equation 5-7.

I 7 , (1.25)().50)(34,600) - (0.15)(47,400) = 1.43 i

l i

S (0.85)(47,400)

I '

5-28

and the logarithmic standard deviation on strength uncertainty is calcu-lated from Equation 5-9 as:

I 8

3

= 64,875(.18)/(64,875-7,110) = 0.20 Computing the duration-modified Inelastic Energy Absorption l Factor (Ductility Factor, F y) as discussed in Section 5.1.1.1.2, for a

(

limited median ductility value of p = 1.2 at a frequency of 21 Hz and for

{

a damping of 5% of critical, Fu and its variabil' ties become:

F = 1.09 S

u

= 0.03 B

y

= 0.02 The overall Capacity Factor (FEC) and its variabilities are then l computed as the combination of the Strength and Ductility Factors and l their associated variabilities as follows:

I f EC

• IS*F = (1.43)(1.09) = 1.56 2

= 8 2

,g 2 = (.002 + .03 2)y2 = 0.03 sEC R (R "R/

I 2 e

EC = 8 +3 2 =

(.20 + .02@ = 0.20 V (S U P) U I

5.2.1.2 RHR Heat Exchanger Equipment Response Factor I The RHR Heat Exchanger was analyzed using a flexible static analysis approach based upon 1.5g horizontal and 1.0g verti::al seismic static accelerations. The evaluation of the shell stresses included the effects of both seismic inertial forces and nozzle piping forces but the 1 5-29

division of stresses resulting from tnese two loading sources was not

] documented. However, since the portion of the stress level due to non-seismic sources is small, it is assumed that stresses resulting from nozzle forces and rroments is small. Therefore, the derivation of response factors is based upon the vessel dynamic characteristics.

5.2.1.2.1 Qualification Method Factor - From the design SSE floor response spectra for the ESF Building at 5% damoing, it was found that a horizontal acceleration vector of 0.335g was appropriate at the inter-I mediate lugs. Therefore, the Qualification Method Factor (Fpg) is computed as a comparison of the qualification and actual design horizontal

{

acceleration levels.

F QM

= 1.5/0.335 = 4.48 The horizontal acceleration at the upper restraints was found to be l 0.419g. Since there is uncertainty as to whether the acceleration of the main support, the intermediate restraint, or the upper support contributes l

most to the seismic stress level at the intermediate lugs, the acceler-ation at the upper supsport is taken as the 95% non-exceedance probability value resulting in a logarithmic standard deviation of 0.14. This vari-ability is all considered to be due to uncertainty.

F = 4.48 QM S

qq

= 0.00 e

gg U

5.2.1.2.2 Spectral Shape Factor - Since static acceleration coefficients were used in the design of the RHR Heat Exchanger and were compared with the appropriate design spectra at a frequency of 21 Hz, I which is above the region of peak broadening, the Spectral Shape Factor (F33) is unity with logarithmic standard deviations on both randomness and uncertainty of zero.

I i 5-30

F 33

= 1.00 L B 33

= 0.00 8

33

= 0.00 l 5.2.1.2.3 Modeling Factor - Section 5.1.1.2.3 reflects a Modeling Factor (Fn ) of 1.00 with an uncertainty variability of 0.15 for medium complex systems such as the RHR Heat Exchanger.

{

I F g

= 1.00 B

g

= 0.00 l l e s, = 0.15 5.2.1.2.4 Damping Factor - In determining the Oualification Method Factor (Fgg) the qualification seismic acceleration was comoared with the horizontal acceleration vector from the design floor spectra at 5%

damping which is considered median. Therefore, the Damping Factor (FD) is unity. As described in Section 5.1.1.2.4, there is some uncertainty as to the actual level of damping associated with equipment failure.

In accordance with Equation 5-15, 3-1/2% damping is taken as a one logarithmic standard deviation variation. However, at 21 Hz, which is approaching the rigid response range, the spectral acceleration differ-ence between 3-1/2 and 5% damping is negligible and therefore the vari-abilities are taken to be zero.

I FD

= 1.00 i B D

R

= 0.00 B

D U

B I 5-31

l 5.2.1.2.5 Mode Combination Factor - Section 5.1.1.2.5 specifies a

.nedian Mode Combination Factor (FMC) of 1.00 with a logarithmic standard k deviation on randamness of 0.10.

[ F = 1.00 MC I

l e = 0.10 nc l S MC

= 0.00 U

5.2.1.2.6 Earthquake Component Combination - The qualification of the RHR Heat Exchanger was based upon a horizontal seismic acceleration of I 1.5g and a vertical acceleration of 1.0g with vertical component contribu-tion to stress at the intermediate lug judged to be negligible. In deter-  !

mining the Qualification Method Factor (FQM) the design horizontal seismic acceleration vector was computed from the desi.}n floor spectra using 100% of the highest horizontal global acceleration (North-South) combined with 40% of the lesser horizontal acceleration (East-West). The 100%/40% has been shown in Reference 10 to be approximately a median value and therefore the Earthquake Component Combination Factor (FECC) 15 I taken to be unity. There is, however, some randomness variability on the actual phasing of the components which may occur at the Millstone 3 site. Taking 100% phasing and 0% phasing acceleration vectors as representing + 35 variation at a median value for coupling, the randomness variability for the case in which the two horizontal seismic acceleration components contribute to failure is calculated to be 0.10 as shown in Table 5-3.

I 1.00 FECC =

i B ECC = 0.10 R

B ECC U

l I 5-32 I

s 5.2.1.2.7 Overall Equipment Response Factor - The combined Equipment Response Factor (FER) and the random and uncertainty variabilities then k are:

b i

= (4.48)(1.00)(1.00)(1.00)(1.00)(1.00) = 4.48 I

ER 2

l s 2 + .10 ) V2 = 0.14 ER" = (.10 I

s 2

=(.14 + .15 ) V2= 0.20 ER U

5.2.1.3 RHR Heat Exchanger Structural Response Factor The ESF Building was found in Chapter 4 to exhibit yield and failure capacities of approximately 1.3 g's and 2.4 g's, respectively.

Since the capacity of the RHR Heat Exchanger exceeds the yield strength of the ESF Building structure, the Structural Response Factor (FSR) is calculated as the ratio of the design ground time history response l spectral acceleration at the fundamental frequency of the ESF Building based upon the design analysis (11.4 Hz) and at 5% damping to the median-centered ground response spectral acceleration at the fundamental frequency of the ESF structure based upon the median analysis (12.9 Hz) and at 10% damping. Taken from Table 5-4 iSR and its variabilities are:

i = 1.46 SR e = 0.19 SR e = 0.34 3p" I

5.2.1.4 RHR Heat Exchanger Ground Acceleration Capacity The ground acceleration capacity (5) for the RHR Heat Exchanger is calculated using Equations 5-1 and 5-2.

5=(1.56)(4.48)(1.46)(.17g's)=1.73q's i

I 5-33 I

The logarithmic standard deviations on randomness and uncertainty are cal-culated as the SRSS combination of the variabilities associated with the three f actors contributing to overall capacity in accordance with Equation 5-3.

f B =(.032 + .14 2

, , y g2 )Y2

= 0.24 R

2 2 2 B

U = (.20 + .20 +.34h=0.44 The combined variability, BC , which is a measure of the overall variability contributed by earthquake randonness and uncertainty is obtained by taking the SRSS of SR and BU-l 1 y B

C

= (.242 , ,442) 2 = 0.50 1

The three factors which make up the overall fragility of the RHR Heat Exchanger together with their logarithmic standard deviations on randomness and uncertainty are tabulated in Table 5-1 along with the remainder of the equipment addressed in this Millstone 3 PRA study. The I various factors and variabilities calcul' ted a for the RHR Heat Exchanger are presented in Table 5-6.

5.2.2 Example of a Plant Specific Fragility Derivation Based Upon

_a_ Review of the Component Qualification Stress Report The seismic qualification and stress reports were obtained for a majority of the components selected for reevaluation in this PRA study.

The qualification reports generally contained the basic information necessary to determine critical failure modes and to calculate component I capacities. As a result, most equipment responses based upon qualifica-tion parameters could accurately be converted to site-specific parameters I thus reducing the associated variabilities. The example chosen to illustrate the derivation of fragility based on stress renort information is the Containment Recirculation Cooler.

I I 5-34 L

H n 5.2.2.1 _ Containment Recirculation Cooler Capacity Factor The Containment Recirculation Cooler is a vertical heat exchanger L housed within the ESF Building but mounted on the Containment Structure Shell. Four locations were evaluated to determine that controlling the I fragility of the Cooler. These were:

I l 1. Upper Restraint Shoulder Pin

2. Upper Restraint Lug l

3. Cooler Shell at the Main Support

4. Upper Tubesheet Capacity Factors were calculated for each location, and it was founr1 that the bending failure of the Upper Restraint Shoulder Pin governs. The evaluation of the fragility of the Recirculation Cooler is based upon the following information and assumptions:

I 1. Location: ESF Building, attached to the Containment Structure Shell. Main support at Elevation 28'-3" with horizontal restraints at Elevations 11'-4" and 47'-3".

2. Fundamental Frequency: 34.2 Hz

3. Design Seismic Accelerations: 0.65g horizontal

4. Pin Materia.1: SA540-CL2; yo = 140,000 psi, = 155,000 psi u

5. Pin Properties: Area = 0.785 in2, Z = 0.098 in3

6. Nozzle Loads: It is judged from previous experience that 1 assumping 65% of the piping reactions to be from normal forces and 35% to be from seismic forces represents median values.

7. Worst Case Pin Stresses:

Total = 135,325 psi (88.7% = Nozzle; 11.3% = Inertia)

Normal = 78,115 psi 1

5-35

Since high strength steels exhibit only limited strenath beyond

] yield, ultimate tensile strer.g'th is used to define failure. For high strength steels, Reference 33 reports the median ultimate to be about a r f actor of 1.1 times the ASME Code specified ultimate tensile strength l

with the Code value' representing 95% probability of exceedance (-1.658).

The Strength Factor (F3 ) is then computed from the information given above.

~

l l

p , (1.1)(155,000) - 78,115-135,325 - 70,115

= 1.62 S

The logarithmic standard deviation on the uncertainty of calcu-lating the capacity- strength as 1.1 times the Code ultimate is 0.06. In addition, there is further uncertainty in using the ultimate strength to define failure. The variability is based upon assessing the yield l strength as representing a 95% lower bound confidence level which also results in a Sg of 0.06. Finally, there is also some uncertainty pertaining to 'the assumption on the breakdown between normal loads and seismic loads from the piping which is used to calculate N. Here the case where 50% cf the piping reactions are due to seismic forces (rather I than 35%) is judged to represent 95% confidence upper bound level.

l eg .=

1,65 1

tn (.50/.35) = 0.22 Combining the capc. u variabilities by SRSS and salving for the lagar-ithmic standard deviath an the Strength Factor in accordanced with Equation 5-9, the uncertaind . lability becomes 0.20. Since failure of the upper restraint pin, which is essentially a " brittle" failure mode, has been defined in terms of ultimate strength, the Ductility Factor (FD) is unity and its variability is zero. Therefore, the overall Capacity Factor and its variabilities are equal to the' Strength Factor and its I corresponding variabilities.

I t -

n5-36

/

l

~

\ g y +

__ ___ _ _ _ _ _ _ - - - - -- *- - - - - - - - " - - - - - - - ~ ~ ~ ' ' ' - - -

b EC

=F = 1.62 3

L B EC R

S R

[ B EC U

S U

~

5.2.2.2 Containment Recirculation Cooler Equipment Response Factors i The Recirculation Cooler Support was designed using a rigid static analysis approach based upon specified nozzle forces. It was assumed that the nozzle loads were defined from a response spectrum I dynamic analysis of the attached piping using the appropriate 1% damped ESF Building floor spectra.

I 5.2.2.2.1 Qualification Method Factor - The response spectrum method-ology used to evaluate the piping is considered median in terms of the Qualification Method Factor and therefore FQM = However, 1.00. static acceleration coefficients of 0.65g in the two horizoa.tal directions were used te define the inertial load. From the Containment Structure design spectra, the horizontal components of acceleration at the Cooler main I support are 0.387 and 0.334g. As a result, the Qualification Method Factor for the inertial portion of the pin stress is:

1 2

F QM

= (.65 2 + .65 )% / .387 2 + (.4x.334)2 2

= 2.25 I

based upon using the 100%/40% earthquake component meth'odology. These l two values of F ,9 q are combined as a weighted average based upon how the contributions of the seismic nozzle loads and the inertial loads bear on the total seismic load on the pin. This weighted average value of Fqtg is calculatd as follows since the nozzle loads contribute most to the pin stresses.

I I- )

.FQM = 1.00 + 2.25 .h5 = 1.33 I

I 5-37 l

, Uncertainty exists as to whether the spectral acceleration vector at the main support (.409 g's) or the vector at the upper restraint

(.473 g's) is a more significant contributor to the stresses in the pin.

Using the upper restraint vector results in the calculation of a weighted

[ Qualification Method Factor of 1.25. The variability is then calculated to be of 0.04 assuming the lower value to represent a 95% confidence l

lower bound. In addition, there is uncertainty that the weighted average g accurately calculates.the factor. This variability is calculated u assuming that the FQM value associated with the most significant contributor to pin stress (FQM = 1.00ffor nozzle forces in this case) represents a 95% confidence lower bound value (8 = 0.17). Combining these two variabilities which are both due to uncertainty by SRSS, the overall Qualification Method Factor and its variabilities become:

F = 1.33 QM 8 = 0.00 Qltg s a = 0.17 I vg1 0 l 5.2.2.2.2 Spectral Shape Factor - This factor which accounts for peak broadening is unity for the inertial analysis since the component is rigid. However, for the piping analysis, which is assumed to have at l least one-mode occurring in the peak broadened range for the ESF Building, a Spectral Shape Factor of 1.05 was calculated with a 8 on uncertainty of 0.02. Again, the overall Spectral Shape Factor is calculated as a weighted average.

I F 33

~

= 1.05(.3105/.4235) + 1.00(.1130/.4235) = 1.04 The variability on this weighted average is also 0.02. The resulting overall Spectral Shape Facter and its logarithmic standard deviation which is all judged to, be due to uncertainty becomes:

I 3  %

- =

g 2 L -

H l

H F 33

= 1.04 r

L 8 33

= 0.00 F

L 8 33

= 0.03 l U l

[ 5.2.2.2.3 Modeling Factor - Section 5.1.1.2.3 gives a Modeling Factor i

of 1.00 with an uncertainty variability of 0.15 for medium complex systems l

{ such as the Containment Recirculation Cooler piping.

FM

= 1.00 B

g = 0.00 E

n

= 0.15 5.2.2.2.4 Damping Factor - Similar to the calculation of Fqn and F33,

{ the calculation of the Damping Factor (F D) is based upon a weighted average of the relative contribution of piping and inertia to overall i seismic stresses. FD for the inertial portion of the defined load is

{ unity with a variability of zero since the appropriate 5% damped design spectra were used as the basis for determining the inertial portion of the Qualification Method Factor. However, Reference 1 states that 1%

damped spectra were used in the dynamic analysis of Balance-of-Plant Piping for the SSE loading. Based upon a comparison of the 1% and 5%

(interpolated between 4% and 8%) damped floor spectra for the ESF Buildina in the frequency range between 5 and 20 Hz, a median Damoina Factor for the piping portion of the pin loading was calculated to be 1.49 with a variability of 0.19. The weighted average Damping Factor is then calcu-lated as:

F D= 1.49(.3105/.4235) + 1.00(.1130/.4235) = 1.36 E

[ 5-39

H F

with a resultant uncertainty variability of 0.06. The variability due to the uncertainty as to the actual damping level associated with equipment L failure is calculated in accordance with Equation 5-15. Taking 3-1/2%

damping (interpolated between 2% and 4%) evaluated at a frequency of 7 Hz

( as a one logarithmic standard deviation variation, the variability on the damping level is computed to be 0.24. The three components of uncertainty

{ variability are combined by SRSS and the variability on randomness is estimated to be equal to 20% o? the uncertainty variability. The overall Dar$ing Factor and its variabilities then become:

{

= '1 FD 1. 36 8 = 0.

• 0, e = 0.31 0,

5.2.2.2.5 Mode Combination Factor - Since the piping loads contribute

{ most to the stresses in the pin, a median Mode Combination Factor of 1.00 with a logarithmic standard deviation on randomness of 0.15 is used based on the infonnation included in Section 5.1.1.2.5.

F MC

= 1.00 S

MC '$

R e

MC g 5.2.2.2.6 Earthquake Component Combination - In determir.ing the

{ Qualification Method Factor, the median-centered 100%/40% combination method was used for the inertial portion and therefore, FECC = 1.00.

However, Reference 1 states that the SRSS of the horizontals plus the absolute sun of the vertical method of earthquake component combination was used for the balance-of-plant piping. As a result, the Earthquake Component Combination Factor for Case 1 of Table 5-3 is apolicable for

[

[ 5-40

L the piping portion of the loading. Again computing the overall Earthquake Component Combination Factor as the weighted average, F ECC becomes:

FECC = 1.12(.3105/.4235) + 1.00(.1130/.4235) = 1.09 I with a variability of 0.02. Taking the randomness variability from Table l

5-3 and combining the uncertainty variabilities by SRSS, the overall Earthquake Component Combination Factor and its variabilities are:

FECC = 1.09 O '

ECCR '

l B

ECC U

5.2.2.2.7 Overall Equipment Response Factor - The combined Equipment Response Factor (I ER ) and the randomness and uncertainty variabilities then are:

I ER = (1.33)(1.04)(1.36)(1.00)(1.00)(1.09) = 2.05

=(.06 + .15 + .12 ) /2 = 0.20 I 2

= (.202 + .032 + .312 + .152 + .13 )V2 = 0.42 I 5.2.2.3 Containment Recirculation Cooler Structural Response Factor The Containment Structure Shell was found in Chapter 4 to exhibit yield and failure espacities of approximately 1.9 q's and 4.9 9's, respectively. Therefore, the Recirculation Cooler is more fragile than I the structure to which it is mounted and will fail at an acceleration level at which the containment shell remains elastic. Therefore, the Structural Response Factor is calculated as the ratio of the design ground time history response spectral acceleration at the fundamental frequency I 5-41 l _

L of the Containment Shell based upon the design analysis (4.7 Hz) and at r

5% damping to the median-centered ground response spectral acceleration at the fundamental frequency of the Containment Shell based upon the median analysis (5.5 Hz) and at 5% damping. Table 5-4 gives the value of j F SR and its variabilities as:

B t,= 1.4e

, s E '

SR R

E 3p u

5.2.2.4 Containment Recirculation Cooler Ground Acceleration Capacity The ground acceleration capacity (A) for the Containment Recirculation Cooler is computed from Equations 5-1 and 5-2.

d = (1.62)(2.05)(1.46)(.17 g's) = 0.82 q's The logarithmic standard deviations on randomness and uncertainty I are calculated as the SRSS combination of the variabilities associated with the three factors contributing to overall capacity in accordance with Equation 5-3.

2 2 e

R =(.00 + .20 +.25*)b = 0.32 2

g s u = (.202 + .42 2 + .24 )b = 0.52 The three factors which make up the overall fragility of the I Containment Recirculation Cooler together with their logarithmic standard deviations on randomness and uncertainty are presented in Table 5-1 while the various factors and variabilities calculated for the Recirculation Cooler are shown in Table 5-7.

I I 5-42 l

H F

L 5.2.3 Example of Generic Fragility Derivation Based on Design Specifications

[ In the majority of cases in risk studies, detailed information regarding resulting stresses, deflections, bearing loads, etc., for

{ safety-related equipment is not readily available to the risk analyst.

Classes of equipment must then be treated generically and the fragility

{ descriptions derived from knowledge of design criteria, analytical methods, service experience, etc. In this section, an example of a fragility description is developed which represents those items of equio-ment whose failure modes are structural and for which design reports or sunrnaries were not reviewed. Balance-of-Plant (B0P) piping, cable trays, b and ducting are typically addressed in this manner. Seismic capccities of Class 2 and 3 piping were derived in a generic manner and are chosen

[ as the example for this section. Balance-of-Plant piping within the

(

Auxiliary and Engineered Safety Features Buildings is specifically

{ addressed.

1 5.2.3.1 B0P Piping Capacity Factor There are three failure modes which typically are used to define l the fragility level of the Balance-of-Plant (80P) piping. The first )

pertains to rupture failure of the piping itself and is generally based upon the buckling capacity of standard weight piping (high energy piping b generally f ails at the tensile flow stress). The second failure mode pertains to rupture failure of the piping due to excessive movement of

( the structures relative to the ground or relative to other structures. l This failure mode applies to buried or interconnecting piping and has

{ been addressed in Chapter 4. The third mode pertains to failure of the piping supports due to weld failure or anchor bolt tearout. This third failure mode governs the fragility description of piping contained within the structures and is chosen as the example to illustrate the derivation of fragility based upon an understanding of the design criteria and the design specification.

s 5-43

{

+

E Due to lack of specific data, the piping supports are evaluated generically. Piping supports are tyically fabricated from carbon steel (SA36, SA106-GrB, SA516-Gr70) and are at nearly room temperature. Since higher damping levels are allowed for faulted conditions, the upset b conditions including the OBE typically govern the design of supports which carry only seismic loads (i.e., snubbers, horizontal restraints).

j Based upon significant experience, it is judged that a seismic stress level equal to 70% of the allowable represents a median value.

In the evaluation of piping supports, it has been found that the I fillet welds represent the most critical construction area. For a typical fillet weld failure mode where both tensile and shear stresses are present in the throat, it can be shown from an interaction equation that the capacity of the fillet weld is equal to approximately 73% of the base material tensile capacity. For normal steels, References 33 and 35 report the median yield strength to be about a f actor of 1.25 times the ASME Code specified minimum yield strength with the code value representina a 95% confidence lower bound. From the above infonnation, the Strength Factor is computed as:

(1.25)(.73)(oy ) -0 I F 3

r

.70(.40)(oy)

= 3.26 I

based upon an AISC allowable stress of 0.4 o for the OBE event.

I The logarithmic standard deviation on the uncertainty of calcu-lating the capacity strength as 1.25 times the Code yield is 0.14 There is also uncertainty in specifying the weld capacity as being 73% of the tensile capacity since for pure shear the capacity could be as low as 60%

of the tensile capacity. Taking the case of pure shear as representing a 95% confidence lower bound value, the uncertainty variability is 0.12.

I In addition, there is some uncertainty pertaining to the assumption that the seismic stress is approximately equal to 70% of the allowable. The I

l 5-44

L I

L case where the OBE stress level is equal to the allowable stress is taken as a + 1.658 variation resulting in an uncertainty variability of 0.22.

Combining these uncertainty variabilities in accordance with Equation 5-9:

k f 8 = [( .14+.12)2 + ( .22)23 2 = 0.34 3"

I Reference 6 recomends a ductility of 1.5 to 3 for design of critical piping systems. These are design recommendations; thus, the value of 3 is considered to be about a median value. A ductility of 1.0 represents the case where the support fails while the piping system remains elastic and is taken te be a 99% confidence lower bound or a minus 2.33 logarithmic standard deviation value. Using these assumptions and applying Equation 5-10, the median factor of safety for ductility was computed to be 2.46. The logarithmic standard deviations, 8 and 8 ,

! are calculated from Equation 5-12 to be 0.31 and 0:23, respechively. U Combining all the factors and variabilities results in a median capacity f actor of safety relative to the OBE and variability expressed in terms of logarithmic standard deviations of:

d FEC = 8.01 S

ECR = 0.31 ECU = 0.41 5.2.3.2 Piping Equipment Response Factors The equipment response factors for piping are contained within Table 5-8 and are explained briefly below. The bulk of the piping was qualified by response spectrisn analysis; thus, a factor of unity and a variability of zero are applicable for the Qualification Method Factor.

The spectral shape Factor (F33) was taken from Table 5-2 to account for peak broadening. The average value of the 5-20 Hz cases for all buildings was used.

Fss = 1.06 B = 0.00 ssR 8

1 ss U = 0.03 5-45

The modeling cf the piping systems is felt to be median-centered and of medium complexity, thus, L

FM = 1.0 B

MR = 0.0 B

l Mg = 0.15 r

The damping factor was computed by comparing response for a one-half percent damped spectrum to response for an expected median damping

, value of five percent at or near failure. One-half percent damping was utilized in designing the Balance-of-Plant piping for thE OBE case.

Since most critical piping systems are at least partially contained within the Containment Structure for which the Damping Factor was found to be l

the least, the Damping Factor (F D ) for all B0P piping is taken as:

1 FD = 1.57 Bog = 0.03 809 = 0.14 The Mode Combination Factor (FMC) is unity with random vari-ability of 0.15 as suggested in Section 5.1.1.2.5 for multiple-degree-of-freedom systems.

The Earthquake Component Combination Factor (FECC) for B0P k

piping is taken from Case 1 of Table 5-3 since the design of the B0P piping was based upon the SRSS of the horizontals plus the absolute sum of the vertical component combination methodology.

FECC = 1.12 B

ECC = 0.12 B

ECC = 0.13 5-46 I

q The overall equipment response factor, IER and the variability, SR and BU for piping are computed to be:

I ER = 1.86 L egag = 0.1g B

ERU = 0.24 5.2.3.3 Piping Structural Respo_nse Factors The structural response factors for piping are a function of the piping location (building and elevation). These structural response factors are shown in Table 5-4. The structural response factor used as l an example in Table 5-8 for piping is that for the Auxiliary Building whicii exhibits the lowest yield capacity and a comparativelv high median

~

fundamental frequency of 9.6 Hz.

I SR " 1*

e '

SR I R B

SR U

5.2.3.4 Piping Ground Acceleration Capacity The ground acceleration capacity for piping was obtained by multiplying the three factors within Equation 5-1 by the OBE level of 0.09g's, since the Capacity Factor was developed based on the OBE and not the SSE as is generally the case.

E = 2.17 g's B

R = 0.42 E

j = 0.52 I The various factors and variabilities affecting the piping fragility are shown in Table 5-8.

I 5-47

l 5.2.4 Example of a Plant Specific Fragility Derivation Based Upon Component Test Data I  !

I Many components within a nuclear power plant must be shown to properly function during the course of a seismic event since failure to {

i function might hinder safe shutdown of the plant. Mechanical equipment such as active values and pumps and electrical components such as switch-gear, batteries and motor control centers fall into this classification.

Frequently, such demonstrations of functionality is not related to stress j level but to deflection or acceleration limitations. Component testing is generally employed to demonstrate satisfaction of the operability requirements. Both functional and structural failure modes must be evaluated to determine the controlling fragility level of active components. The example chosen to illustrate the derivation of fragility based upon component test information is the 480 VAC Motor Control Center.

I 5.2.4.1 480 VAC Motor Control Center Capacity Factor The Motor Control Centers are subject to two functional failure modes which are related to chatter and tripping of the circuit breakers.

The following infonnation pertains to the fragility of the Motor Control Centers:

1. Location: Various - Auxiliary Building at Elevation 43'-6" is most critical.

2. Frequency: 5.2 Hz (S/S); 5.6 Hz (F/B).

3. Damping: Test at 1% damping.

Testing of active components is conducted to acceleration levels which envelope the required response spectrum (RRS) but are seldom carried to the point of failure which could be used to define fragility. There-fore, some basis must be used to define the " failure" capacity.

1 I

L 5-48 i

l

t During the SSE test, a chatter failure occurred which was said to be due to a " loose bolt." The bolt was tightened and the test rerun )

without recurrence of the chatter failure. Therefore, the chatter f

fragility was taken to be 1.2 times the qualification level. From the test response spectrum (TRS), the spectral accelerations at the two

{

fundamental frequencies is 5.2 and 7.5 g's. Since it is unclear which {

j mode was excited causing the failure, the chatter capacity is taken as 1.2 f

times the average of the two or 7.62 q's. Comparing this value to the l

spectral acceleration between 5.2 and 5.6 Hz obtained from the 1% damped Auxiliary Building spectrum for floor Elevation 43'-6" which is 1.70 q's, the Strength Factor for chatter is calculated as:

F 3 = 1.2(6.35)/1.70 = 4.48 (chatter) 1 The maximum and minimum spectral acceleration values .t the fundamental frequencies of the Motor Control Centers are taken as + 1.658 variation ,

I resulting in a. logarithmic standard deviation on uncertainty of 0.11.

Similarly, the uncertainty in specifying 1.2 times the qualification g acceleration to be the chatter capacity is quantified by assuming that y the qualification level represents a -1.03 variation since the chatter failure was not repeated after the bolt was tightened. The resulting I logarithmic standard deviation is 0.18.

Based upon the Huntsville SAFEGUARD shock test data of generic equipment, the median acceleration defining trip f ailure is 7.7 q's at 5%

damping. The resulting Strength Factor is:

F 3

= 7.7/0.85 = 9.06 (trip)

The uncertainty associated with the 7.7 q level used to define trio failure is quantified by assuming that the chatter Strenath Factor represents a -1.658 variation resulting in a logarithmic standard I deviation of 0.43.

I I

5-49 t

Since electrical equipment failura are judged to be " brittle", '

the Ductility Factor is unity with randomness and uncertainty variabil-ities equal to zero. As a result, the functional Capacity Factors for the Motor Control Centers are equivalent to the Strength Factors.

Chatter Trip -

S EC

=F 3 = 4.48 EC

= F 3

= 9.06 B

EC p

• O S = 0 00 EC 8

b

~

R R R i

S EC g

=8 3 -

EC g O

S 0 U s

5.2.4.2 480 VAC Motor Control Center Equipment Response Factor The Equipment Response Factor for fragility parameters based upon testing methods were developed in detail for the Seismic Safety

, Margins Research Program (SSMRP) in Reference 24 and are briefly discussed in the following subsections.

5.2.4.2.1 Qualification Method Factor - The Qualification Method Factor and its variability quantifies the effects of using the superimposed multiple sine beat testing as opposed to using a spectral analyzer to generate a time history input. The median factor and b

variability have been calculated for the SSMRP Program (Reference 24) to be:

1 FQM = 1.04

> 8 gg = 0.05

'8 = 0.11 QM 5-50

5.2.4.2.7 Spectral Shape Factor - The Spectral Shape Factor and its variabi. .ty are obtained for the 5.2 to 5.6 Hz range of the Auxiliary Building which is outside the peak broadened range. The Strength Factor was based on floor spectra which were unbroadened and thus, the spectral l shape factors for this case will be:

Fss = 1.00 Ess = 0.00 Bss = 0.00 5.2.4.2.3 Boundary Conditions Factor - Difference in boundary conditions between the test lab and the actual plant installation can cause significant differences in the equipment responses. Reference 24 discusses this variability and provides estimates for different mounting conditions. The equipment under consideration is predominantly floor mounted, and is bolted or welded in both the laboratory plant instal-lations. The response factor due to boundary conditions is considered to l

be unity and the estimated uncertainty variability, expressed as a 1 logarithmic standard deviation, is 0.15.

5. 2. 4. 2.4 Damping Factor - For chatter, FD equals unity and the vari- l abilities are zero since the test represents median damping. However, for trip failure there are two separate considerations in defining the variability in response due to damping. The first deals with the effect that variation in damping has upon response when the component is sub-jected to a seismic input, defined as an in-structure response spectrum (i.e., the applicable floor spectrum for the equioment location). The I second deals with the conversion of undamped shock test spectra to damped shock spectra. The complete derivation is contained within Reference 31 with the resulting response factor of 1.0 and logarithmic standard deviation of 0.20. The variability is considered to be all uncertainty.

Therefore, I

5-51 1

1 Chatte_r Trio FD = 1.0 FD = 1.0 B B DR = 0.00 OR

= 0.00 Bog = 0.00 S Du = 0.20 5.2.4.2.5 Spectral Test Methods Factor - The Spectral Shape Factor quantified the conservatism and variability involved in using an acceleration time history to develop the applicable floor response spectra. There also exists a variability in selecting a given I

time-history to represent a required response spectrum in vibration testing. Reference 31 states that a factor of unity with random and uncertainty logarithmic standard deviations of 0.14 and 0.10, l respectively are applicable. {

l 5.2.4.2.6 Multi-Directional Effects Factor - The multi-directional effects factor for biaxial testing is specified in Section 5.1.1.2.9.2 to be 0.853 with variabilities of SR = 0.12 and BU = 0.04.

I 5.2.4.2.7 Overall Equipment Response Factor - The overall equipment response factor was calculated to be 0.89 by taking the product of the individual response factors. The randon and uncertainty B's are calculated to be 0.19 and 0.21, respectively, for chatter and 0.19 and 0.29, respectively, for trip and are determined by takina the SRSS of the individual random and uncertainty logarithmic standard deviations, l

5.2.4.3 480 VAC Motor Control Center Structural Response Factor j The applicable Structural Response Factor for the Motor Control Centers is taken from Table 5-4 for the most critical location which is within the Auxiliary Building which reaches both its yield and failure I capacities prior to failure of the Motor Control Centers. The Structural Response Factor and its variabilities are:

i 5-52

F = 1.62 SR e gg = 0.21 S

SR U

5.2.4.4 480 VAC Motor Control Center Acceleration Capacity The ground acceleration capacities for both chatter and trip failure of the Motor Control Centers is calculated as the product of the three main fragility factors in Equation 5-1 by the SSE ground accelera-I tion level of 0.17 g's. The overall randomness and uncertainty logar-g ithmic standard deviations were calculated from Equation 5-3. The a resulting acceleration capacities for the two functional failure modes is:

Chatter Trip

= 1.09 q h = 2.21 q BR = 0.28 BR = 0.28 BU = 0.36 L

80 = 0.57 The f actors and variabilities contributing to the fragility descriptions of the Motor Control Centers are presented in Table 5-9.

t 5.2.5 Example of Fragility Based on Engineering Judgment and Earthquake Experience There are several equipment items within the list of components for the Millstone PRA for which no seismic qualification was required.

These components were not designed for seismic loading; thus, they will generally have a lower capacity and a higher uncertainty than seismically qualified components. The methodology which has been utilized on the previous four examples of developing capacity factors, response factors, duration factors, etc., is generally not applicable for unqualified components. The fragility levels for these unqualified components must i

5-53 r

be derived based on earthquake experience and engineering .iudgment. The example which has been chosen in this category is the station off-site l power.

l 5.2.5.1 Offsite Power Ground Acceleration Capacity Failure of offsite power is governed primarily by failure of ceramic insulators. A review of insulator failure in six ma.ior earth-quakes, ranging from 0.119 to 0.4g peak ground acceleration, resulted in I a median capacity for ceramic insulators of:

5 = 0.20g r-f where d is the median peak ground acceleration capacity. The loaarithmic standard deviation on this value is about 0.32 of which the estimated l randomness, BR, is about 0.20 and the uncertainty, UB , is about 0.25.

5.3 EQUIPMENT FRAGILITY RESULTS Table 5-1 contains fragility descriptions for all of the equip-ment which were selected for this PRA study. Fragility derivations were l

conducted for each of these components and are reported for those items I which have a ground acceleration capacity less than 2.5 q's based on their Capacity and Equipment Response Factors only. It is ,iudged that equipment with ground acceleration capacities greater than 1.5 q's will not significantly influence the Millstone 3 risk. Table 5-1 contains i several components with ground acceleration capacities greater than 2.5 g's. These components did not have ground acceleration capacities above 2.5 g's based on their Capacity and Equipment Response Factors but their Structural Response Factors were sufficiently high so as to increase the final acceleration capacity (h) above 2.5 q's.

Table 5-10 contains a list of those components which have ground acceleration capacities less than 1.5 g's. These components will all, to some degree, enter into the overall plant risk.

i 5-54 i

L-L l

l

(

1 TABL 7

SUMMARY

OF MILLSTONE @

a a

A Equipment 5etsatC Failure Mode

(

Qualification l

} Component Location Characteristles ve tnod Flattble. Passive Cynamic Analysis Ucoer Support Plate

,e Reactor Vessel Core C$. Various Dynamic Analysts eod Travel Housing Control Rod Drives C$. Atop RPY Fleutble. Active l 5

-4 Dynamic Aaa13 sts instrumentation Tube ApV In-Core Instrumentation C1.-27* 3* F1entble. Passive PressurtZer Rettef Tank C1.- 27' 3* Rigid. Passive Static Analysts Vessel $ hell Rfgid. Active Dynamic Analysts No221e Flange RMR pus 9 E$F. 4 '-6*

a Heat EaChanger Shell RHR Nest EaChanger E$F. 4'-6* Fleaible. Passive $tattC Analysts h Reactor Trip Breaker C8. 47*-0* Fleatble. Passive Test Anchor Bolt Off-$tte Pcuser Yard Fleatble. Passive None Insulators a

Rtgid Passive Static Analysts Upper Restraint Pf n Contalet Rectrculation C1. 28'-3*

Various Fleatble. Passtwe Cynamic Analysts Supports

• ~ BOP Piping

• Quench $ prey Pump E$F. Ig' 6* Rigid. Active $tatic Analysis Pump Hold Dowr: Bolts

.i Rfgid. Active $tatic Analysis tapeller Impact Comparent Cooling Water Pues Ava. 24'-6*

' Comoonent Cooling Surge Tank Auu. 66'-6* Rigid. Passive Static Analysts Av. hor Belt Motor Ortwen Aus Feed Pwe E5F. 19'-6* Rtgid. Active Static Analysts !sseller Isoect E$F Logic Panel C3. 47' 0* Rigid. Passive Test Function C3. 4'-6* Fleathle. 6assive Test Chatrer 4160 solt settc% ear Trip a,4 Empegency Diesel Generator EGE. 24*-6* Fleatble. Passive $tatic Analysis L.0. Cooler AncW "s 4

CB. 4'-6* Rfgid. Passive Test Function

• 125 VDC Ecttertes 125 VOC Otstributton $mitchgear C8. 4'-6* Fleattle. Passive Test Trfo CS. 4*-6* Flealble. Passive Test Function 120 VAC Converter Vartous Fleafble. Passive Test Cha tter A80 VAC Motor Control Center Trip

] .

• Does not apply to ptstreg subject to but1 ding sliding

• • Factor on 00E ground acceleration w

Ih a

e L

l 4 db

%? [

E

1 4

1 IPONENT FRAGILITIES >

Pat Capacits Factor [49$pment Resme Factor 5tructurel Resoonse Facter Growad 4cceleretton Capacity 5,

8 s gg F, s sg 4 tC, t Ett 'Ib SR s $,a $8 U

C 4 0.00 0.14 1.03 0.18 0.17 1.70 0.25 0.24 0.99 0.31 0.33 0.45 9 0.00 0.15 1.05 0.17 0.25 1.70 0.25 0.24 I.00 0.30 0.38 0.48 M M V M M M M W >2.50 M M M M M M M M V M W >2.50 M M M M M M M u A M M m2.50 M M M i 0.03 0.20 4.48 0.14 0.20 1.46 0.19 0.34 1.73 0.24 0.44 0.50 L 0.00 0.28 2.88 0.20 0.38 f.47 0.22 0.23 1.04 0.30 0.53 0.60 M M M M 4 M M M 0.20 0.20 0.25 0.32 t 0.00 0.20 2.05 0.20 0.42 1.46 0.25 0.24 0.82 0.32 0.52 0.61 I" O.31 0.41 1.86 0.19 0.24 1.62 0.21 0.21 2.17 0.42 0.52 0.67 .

5 0.00 G.47 1.70 0.13 0.35 1.46 0.19 0.34 2.93 0.23 0.68 0.72 D 0.00 0.17 1.00 0.13 0.19 1.62 0.21 0.21 1.13 0.25 0.33 0.11 r 0.00 0.27 1.00 0.03 0.10 1.62 0.21 0.21 3.16 0.21 0.36 0.41 1 0.00 0.17 1.00 0.01 0.1f 1.46 0.19 0.34 3.30 0.19 0.41 0.45 --,

p 0.00 0.J8 4.62 0.00 0.29 1.47 0.22 0.23 1.39 0.22 0.38 0.44 1 0.00 0.08 2.89 0.20 0.35 1.49 0.23 0.'! 0.88 0.29 C.40 0.49

• 3-*

3.09 0.28

} 3-"

L 0.00 0.74 0.89 0.18 0.32 1.49 0.21 0.17 0.81 0.86 .1 \ \ ,

t 0.00 0.31 0.92 0.12 0.10 1.60 0.21 0.28 0.*1 0.24 0.4? 0.49 1 0.00 0.11 8.53 0.39 0.24 1.00 0.21 0.17 I.74 0.29 0.11 0.43 i 0.00 0.08 6.82 0.15 0.24 1.23 0.21 0.17 1.71 0.26 0.30 0.40 ,

I G.00 0.08 5.15 0.19 0.30 1.30 0.21 0.17 1.37 0.28 0.35 0.45 1 0.00 0.2I 0.89 0.19 0.21 1.62 0.21 0.21 1.09 0.28 C.36 0.46

, 0.00 0.22 0.89 0.19 0.29 1.62 0.21 0.21 2.21 0.28 0.57 0.63 Also Available On Aperture Card M

6 5-55 l 8403200152-o(

M M M-W D-L_.J' TABLE 5-2 EQUIPMENT SPECTRAL SHAPE FACTORS.

Building Elevation Frequency p g

• g Range SS SS SS R U (Hz)

Control Building 24'-6" 6-9 1.11 0.00 0.05 5-20 1.04 0.02 Auxiliary Building 24'-6" 6.5-10 1.15 0.00 0.07 5-20 1.05 0.02 l 43'-6" 6.5-10 1.24 0.00 0.11 5-20 1.09 0.04

=

66'-6" 6.5-10 1.27 0.00 0.12 5-20 1.10 0.05 Reactor Containment 24'-6" 4-6.5 1.18 0.00 0.08 Internal Structures 5-20 1.06 0.03 Engineered Safety 19'-6" 9.5-15.5 1.13 0.00 0.06 Features Building 5-20 1.05 0.02 -

36'-6" 9.5-15.5 1.21 0.00 0.10 5-20 1.07 0.04

• NOTE: All variability from peak broadening is due to uncertainty

TABLE 5-3 EARTHOUAKE COMPONENT COMBINATION FACTORS Design = SRSS(H,V) Design = SRSS(H)+(V)

Case Description 8 F B 8 ECC U ECC U 1 M Case - Median Coupling - All directional components contribute to failure 1.00 0.00 1.12 0.13 0.12 i

2 2D Case - Median Coupling - Both horizontal contribute to failure 1.00 0.00 1.17 0.08 0.10 l 3 20 Case - No Coupling - Both horizontals contribute

[ to failure 1.00 0.00 1.00 0.00 0.06 T 4 2D Case - Median Coupling - 1 horizontal and the

$ vertical contribute to failure 1.00 0.00 1.25 0.04 0.09 5 2D Case - No Coupling - 1 horizontal and the vertical contribute to failure 1.00 0.00 1.00 0.00 0.03 6 10 Case - Any one of the directional components alone  ;

is responsible for the failure 1.00 0.00 1.00 0.00 0.00  !

l 1

TABLE 5-4 STRUCTURAL RESPONSE FACTORS FOR EQUIPMENT I v Building Ground Acceleration F 6 B Range (g)* SR 39 SR R U i Control Building a) < 0.78 b) 2 0.78 1.26 1.47 0.22 0.23 Auxiliary Building a) < 0.58 1.38 0.21 0.21 b) 2 0.58 1.62 Containment Structure a) <l.87 1.46 0.25 0.24 b) 21.87 1.70 Containment Internal g Structure a) <1.02 1.46 0.25 0.24 g b) 2 1.02 1.70 I Engineered Safety Features Building a) < l .29 1.40 0.19 0.34 '

b) 21.29 1.46 Emergency Generator i Enclosure ** a) < 0.80 b) 2 0.80 1.23 1.47 0.21 0.28 o Acceleration value shown reflects yield capacity of structure NBased on pedestal model I

I I

k l T

l TABLE 5-5 l

NUCLEAR POWER PLANT EQUIPMENT CATEGORIES l

Relative

=

Capacity Equipment Category Level r

High 1. Piping Ducting, Cable Trays and Electrical Conduit i 2. All Valves (Except small motor operated valves)

, Medium-High 3. Small Vessels and Heat Exchangers

4. Horizontal Pumps Compressors and Turbines

5. Fans and Air Conditioning Units  !

L

6. Diesel Generator l

7. Reactor Coolant Loop Components l

i Medium 8. Small Motor Operated Valves

9. Large Vessels and Heat Exchangers

10. Batteries and Racks

} 11. Vertical Pumps 1?. Reactor Internals and Control Rod Drive Mechanism Low-Medium 13. Motor Control Centers, Switchgear, Control Panels.

Instrument Racks

14. Non-seismically Qualified Components (e.g. Offsite PowerSystem)

I I

r 5-59

I l

TABLE 5-6 FRAGILITY DERIVATION OF RHR HEAT EXCHANGER 1

1 1

Median Randomness Uncertainty Factors Safety Variabili ty Variability Factor B 8 R U Capacity Factor (FEC}

l. Strength 1.43 0.00 0.20 f

2. Ductility 1.09 0.03 0.02 Combined -F 1.56 0.03 0.20 EC )

Equipment Response Factor (FER)

1. Qualification Method 4.48 0.00 0.14

2. Spectral Shape 1.00 0.00 0.00 L

3. Modeling 1.00 0.00 0.15

4. Damping 1.00 0.00 0.00 l

5. Mode Combination 1.00 0.10 0.00

6. Earthquake Component Combination 1.00 0.10 0.00 l Combi ned :F 4.48 0.14 0.20 ER Structural Response Factor (FSR) 1.46 0.19 0.34 l

, Ground Acceleration Capacity (A) 1.73 0.24 0.44 r

l 5 >

TABLE 5-7 l FRAGILITY DERIVATION OF CONTAINMENT RECIRCULATION COOLER Median Randomness Uncertainty Factors Safety Variability Variabili ty Factor B 3 R U 1

Capacity Factor (FEC)

1. Strength 1.62 0.00 0.20 l

2. Ductility 1.00 0.00 0.00 l Combined  : F 1.62 0.00 0.20 EC l

Equipment Response Factor (FER)

1. Qualification Method 1.33 0.00 0.20

2. Spectral Shape 1.04 0.00 0.03 i

3. Modeling 1.00 0.00 0.15

4. Damping 1.36 0.06 0.31 l

5. Mode Combination 1.00 0.15 0.00

6. Earthquake Component Combination 1.09 0.12 0.13 I Combined -F ER 2.05 0.20 0.42 Structural Response Factor (FSR) 1.46 0.25 0.24 Ground Acceleration Capacity (A) 0.82 0.32 0.52 h

I I

I I

~

5-61

I l

TABLE 5-8 FRAGILITY DERIVATION OF BALANCE-0F-PLANT PIPING Median

• Randomness Uncertainty Factors Safety Variability Variability l Factor S 8 R U ]

Capacity Factor (FEC}

1. Strength 3.26 0.00 0.34

2. Ductility 2.46 0.31 0.23 1 Combined -F EC 8.01 0.31 0.41 Equipment Response Factor (FER}

1. Qualification Method 1.00 0.00 0.00

2. Spectral Shape 1.06 0.00 0.03 1 3. Modeling 1.00 0.00 0.15

4. Damping 1.57 0.03 0.14

5. Mode Combination 1.00 0.15 0.00

6. Earthquake Component Combination 1.12 0.12 0.13 Combined :F 1.86 0.19 0.24 ER Structural Response Factor'(FSR) 1.62 0.21 0.21 Ground Acceleration Capacity (A) 2.17 0.42 0.52

• Factor on OBE ground acceleration of .099's I

I 5-62

l l

TABLE 5-9 l FRAGILITY DERIVATION OF 480 VAC MOTOR CONTROL CENTERS I

Factors I Median Safety Factor Randomness Variability B

Uncertainty Variability 8

R U Capacity Factor (FEC}

1._ Chatter .

4.48 0.00 0.21

2. Trip 9.06 0.00 0.44 Equipment Response Factor (FER)

1. Qualification Method 1.04 0.05 0.11

2. Spectral Shape 1.00 0.00 0.00

3. Boundary Conditions 1.00 0.00 0.15 4-. Damping 1.00 0.00 0.00/0.20

5. Spectral Test Method 1.00 0.14 0.10

6. Multi-DirectgonalEffects 0.85 0.12 0.04 Combined F 0.89 0.19 0.21/0.29 ER Structural Response Factor (FSR) .6 0.21 0.21 Ground Acceleration Capacity (A)

1. Chatter 1.09 .

0.28 0.36

'2. Trip 2.21 0.28 0.57 i

1 I

i .

I '

~5-63 I

TABLE 5-10 l

MILLSTONE 3 EQUIPMENT EXHIBITING GROUND ACCELERATION l CAPACITY LESS THAN 1.5 g's E v B Component A (g) 8 R

8 0

Off-Site Power 0.20 0.20 0.25 Containment Recirculation Cooler 0.82 0.32 0.52 4160 Volt Switchgear (Chatter) 0.88 0.29 0.40 Emergency Diesel Generator 0.91 0.24 0.43 Reactor Vessel Core 0.99 0.31 0.33 Control Rod Drives 1.00 0.30 0.38 Reactor Trip Breakers 1.04 0.30 0.53 480 VAC Motor Control Center 1.09 0.29 0.43 (Chatter)

Component Cooling Water Pump 1.13 0.25 0.33 120 VAC Converter 1.37 0.28 0.35 I ESF Logic Panel 1.39 0.22 0.38 l

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5-64

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5-65

I REFERENCES I

l

1. Millstone Nuclear Power Station - Unit 3 Final Safety Analysis Report, Long Island Lighting Company.

2. USNRC, " Design Response Spectra for Seismic Design of Nuclear Power Plants" USNRC Regulatory Guide 1.60, Revision 1, December, 1973.

l 3. Freudenthal, A. M., J. M. Garrelts, and M. Shinozuka, "The Analysis 3 of Structural Safety", Journal of the Structural Division, ASCE, ST 1, pp. 267-325, February, 1966.

4. Kennedy, R. P., A Stat _i_stical Analysis of the Shear Strenoth of Reinforced Concrete Beams, Technical Report No. /8, Department of fivil Engineering, Stanford University, Stanfr'd, California, April,  ;

1967

5. Newmark, N. M., "A Study of Vertical and Horizontal Earthquake  !

I Spectra", WASH 1255, Nathan M. Newmark Consulting Engineering Services, prepared for USAEC, April,1973.

l m 6. Newmark, N. M., " Inelastic Design of Nuclear Reactor Structures and g its Implications on Design of Critical Equipment". SMiRT Paper K 4/1, 1977 SMiRT Conference, San Francisco, California.

7. Riddell, R., and N. M. Newmark, " Statistical Analysis of the Response of Nonlinear Systems Subjected to Earthquakes", Department of Civil Engineering, Report UILU 79-2016, Urbana, Illinois, August, 1979.

8. Bernreuter, D. L., " Seismic Hazard Analysis, Applicatinn of Methodology, Results, and Sensitivity Studies", NUREG/CR-1582, Vol. 4, Lawrence Livermore National Laboratory, October,1981.

9. USNRC, " Damping Values for Seismic Desian of Nuclear Power Plants", l USNRC Regulatorv Guide 1.61_, October, 1973.

10. Newmark, N. M., and W. J. Hall, " Development of Criteria for Seismic Review of Selected Nuclear Power Plants", _NUREG/CR-0098, May,1978.

11. Kennedy, R. P., et al., "Probabilistic Seismic Safety Study of an i Existing Nuclear Power Plant", Nuclear Engineerina and Design, Vol. 59, No. 2, pp. 315-338. ~

12. USNRC, " Combining Modal Responses and Spatial Components in Seismic

.I Response Anairt",' _USNRC Regulatory Guide 1.92, Rev.1, February, 1976.

13. Stone and Webster calculation #12179-N.iS(B)-092, Revision 0.

l R-1 1

7

?

REFERENCES (Continued) 3 s 14. Trexell, G.E., H.E. Davis and J.W. Kelly, Composition and Properties of Concrete, McGraw-Hill, 1968.

15. Letter correspondence, N. M. Newmark to A. J. Bingaman, et al.

Subject:

Factor of Safety Against Sliding, June 10, 1975.

16. Mirza, S. A., M. Hatzinikolas, and J. G. MacGregor, " Variability of Mechanical Properties of Reinforcing Bars", Journal of Structural Division, ASCE, May, 1979.

17. ACI 318-71, " Building Code Requirements for Reinforced Concrete",

American Concrete Institute, 1971.

18. Barda, F., J. M. Hanson and W. G. Corley, " Shear Strength of low-Rise Walls with Boundary Elements", ACI Symposium, " Reinforced

( Concrete Structures in Seismic Zones", ACI, Detroit, Michigan, 1976.

19. Shiga, T., A. Shibata and J. Tabahashi, " Experimental Study on

{

Dynamic Properties of Reinforced Concrete Shear Walls", 5th World Conference on Earthquake Engineering, Rome, Italy, 1973.

20. Cardenas, A. E., et al., " Design Provisions for Shear Walls", ACI Journal, Vol. 70, No. 3, March, 1973.

21. Oesterle, R. G., et al., " Earthquake Resistant Structural Walls -

Tests of Isolated Walls - Phase II", Ccnstruction Technology Laboratories (Division of PCA), Skokie, Illinois, October, 1979.

22. " Kenned P., et al, " Engineering Characterization of Ground Motio:. y, R._

If', ects of Characteristics of Free-Field Motion on Structural Response", SMA 12702.01, prepared for Woodward-Clyde Consultants, April, 1983.

23. Merchant, H. C., and T. C. Golden, " Investigations of Bounds for the Maximum Response of Earthquake Bulletin of the pp Excited Systems"I Seismological Society of America, Vol. 64, No. , . Im-uq4, August, 1974.

24. NUREG/CR-1706, UCRL-15216, Subsystem Response Review, Seismic Safety Margin Research Program", October, 1980.

25. Amplified Response Spectra for Equipment Qualification, Millstone Nuclear Power Station Unit 3, by Stone and Webster Engineerina Corporation.  !

s

[

R-2

s

~

REFERENCES (Continu2d)

26. Smith, P. D. and O. R. Maslenikov "LLNL/ DOR Seismic Conservatism

._i

' Program, Part III: Synthetic Time Histories Generated to Satisfy NRC H Regulatory Guide 1.60", UCID-17964 (draft report) Lawrence Livennore Laboratory, Livermore, California, April, 1979.

27. " Seminar on Understanding Digital Control and Analysis in Vibration h Test Systems", sponsored by Goddard Space Flight Center, Jet Propulsion Laboratory and The Shock and Vibration Information Center p held at Goddard Space Flight Center on 17-18 hne 1975 and at the

% JPL on 22-23 July 1975.

28. HNDDSP-72-156-ED-R, " Subsystem Hardness Assurance Report, Volumes I

( and II", U.S. Army Corps of Engineers, Huntsville Division, 30 June 1975.

( 29. HNDDSP-73-161-ED-R, " Subsystem Hardness Assurance Analysis, Volumes I and II", U.S. Army Corps of Engineers, Huntsville Division, 30 June 1975.

b 30. HNDDSP-72-151-ED-R, " Shock Tests Program Plan, Volume I, Management and Technical Plan", U.S. Army Corps of Engineers, Huntsville Division,1 October 1973.

31. NUREG/CR-2405, UCRL-15407, Kennedy, R. P., R. D. Campbell, G. S.

Hardy and H. Sanon, " Subsystem Fragility - Seismic . Safety Margins Research Program (Phase 1)", Structural Mechanics Associates, Inc.,

prepared for U.S. Nuclear Regulatory Comission, February,1982.

32. Hardy, G.S. and R. D. Campbell, " Development of Fragility Descriptions of Equipment for Seismic Risk Assessment of Nuclear Power Plants", paper to be presented at the ASME Pressure Vessel and Piping Conference in Portland, June, 1983.

33. NUREG/CR-2137, " Realistic Seismic Design Margins of Pumos, Valves and Piping", by E.C. Rodabaugh and K. D. Desai, June,1981.

34. Seismic Fragility Evaluation of Millstone Unit 3 Structures and Equipment, Stone and Webster Engineering Corporation, May 1983.

L 35. ASTM DS-552 "An Evaluation of the Yield, Tensile, Creep and Rupture Strengths of Wr:ught 304, 316, 321 and 347 Stainless Steels at s Elevated Temperstures", American Society of Testing Materials.

k I

R-3

REFERENCES (Continued) m

" 36. Sargent and Lundy Report, " Evaluation of the Functional Capability of ASE Section III, Class 1, 2 and 3 Piping Components, MARK I s Containment Program, Task 3.1.5.4", September 21, 1978.

' 37. Witt, F. J., W. H. Bamford and T. C. Esselman, " Integrity of the Primary Piping Systems of Westinghouse Nuclear Power Plants During N Seismic Events", WCAP No. 9283, Westinghouse Electric Corporation,

, March, 1978.

5 38. NUREG/CR0261, ORNL/SUB-2913/8, Evaluation of the Plastic Character-istics of Piping Products in Relation to ASME Code Criteria, by p E. C. Rodabaugh and S. E. More, Battelle Columbus Laboratories, July, 1978.

39. HNDDSP-72-74-ED-R, Hardness Program-Non-Emp. Test Specification and Procedure, Electric Motor Control Center Fragility Test, U.S. Army Corps of Engineers, Huntsville Division, 20 November 1972. 1

[ 40. " San Fernando Earthquake of February 9, 1971: Effects on Power System Operation and Electrical Equipment", Prepared by the Design 3

I and Construction Division of the Department of Water and Power of the City of Los Angeles, October, 1971.

L I

L I

L R-4 I

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APPENDIX L

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CHARACTERISTICS OF THE LOGNORMAL DISTRIBUTION k .

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APPENDIX s

CHARACTERISTICS OF THE LOGNORMAL DISTRIBUTION

{ Some of the characteristics of the lognormal distribution which are useful to keep in mind when generating estimates of A, B , and 8 are R 0 7 stenarized in References Al and A2. A random variable X is said to be 5

lognomally distribated if its natural logarithm Y given by:

F H Y = in (X) (A-1)

( is nomally distributed with the mean of Y equal to in X where X is the median of X, and with the standard deviation of Y equal to 8, which will be defined herein as the logarithmic standard deviation of X. Then, the coefficient of variation, COV, is given by the relationship:

L COV=Yexp(B*)-1 '

(A-2) l l

For B values less than about 0.5, this equation becomes approximately:

1 COV = 8 (A-3)

[ and COV and 8 are often used interchangeably.

j For a lognomal distribution, the median value is used as the characteristic parameter of central tendency (50 percent of the values l are above the median value and 50 percent are below the median value).

The logarithmic standard deviation, e, or the coefficient of variation, COV, is used as a measure of the dispersion of the distribution.

L A-1

1 L

E H .

The relationship between the median value, X, logarithmic standard deviation, 8, and any value x of the random variable can be L expressed as:

H L x=i exp (n*B)

(A-1)

{ where n is the standardized Gaussian random variable, (mean zero, standard deviation one). Therefore, the frequency that X is less than any value x' equals the frequency that n is less than n' where:

ni. In (x'/X)

(A-5)

Because n is a standardized Gaussian random variable, one can simply enter

( standardized Gaussian tables to find the frequency that n is less than n' which equals the probability that X is less than x . Using cumulative

{ distribution tables for the standardized Gaussian random variable, it can be shown that X e exp (+8) of a lognormal distribution corresponds to the 84 percentile value (i.e., 84 percent of the data fall below the +8 value). The i e exp (-8) value corresponds to the value for which 16 percent of the data fall below.

One implication of the usage of the lognormal distribution is that if A, B, and C are independent lognormally distributed random vari-ables, and if A"

• B5 D= 4 c

t (A-6)

[

[

[ ,

where q, r, s and t are given constants, then D is also a lognormally distributed random variable. Further, the median value of D, denoted by

, 6, and the logarithmic variance 8 , which is the square of the logarith-j mic standard deviation, 80 , of D, are given by:

s

[ 6= *b$ q t (A-7)

C F

1 and 2

g 22 22 22 y D=rBA*58B+tSC (A-8)

F L where d, 5, and C are the median values, and BA 88 , and BC are the loga-rithmic standard deviations of A, B, and C, respectively.

F L

The formulation for fragility curves given by Equation 2-1 and

[ shown in Figure 2-1 and the use of the lognormal distribution enables easy development and expression of these curves and their uncertainty.

However, expression of uncertainty as shown in Figure 2-1 in which a range of peak accelerations are presented for a given f ailure fraction is not c very usable in the systems analyses for frequency of radioactive release.

For the systems analyses, it is preferable to express uncertainty in terms of a range of failure fractions (frequencies of failure) for a given ground acceleration. Conversion from the one description of uncertainty to the other is easily accomplished as illustrated in Figure A-1 and

[ sumarized below.

With perfect knowledge (i.e., only accounting for the random variablity, BA ), the f ailure fraction, f(a), for a given acceleration a can be obtained from:

f(a) = c[tn(a/d)\ (A-9)

( (

6 R )

[

A-3

1 L

r L in which f(*) is the standard Gaussian cumulative distribution function, and S is the logarithmic standard deviation associated with the I R underlying randomness of the capacity.

For simplicity, denote f = f(a). Similarly, f' is the failure fraction associated with acceleration a', etc. Then, with perfect

{ knowledge (no uncertainty in the failure fractions), the ground acceler-ation a' corresponding to a given frequency of failure f' is given by:

a' = exp 8 #~ (f')

R (A-10)

The uncertainty in ground acceleration capacity corresponding to a given frequency of failure as a result of uncertainty of the median

( capacity can then be expressed by the following probability statement:

P A > a"lf' =1# "in(a"/A)"

g

. u .

(A-11) in which P[A > a"lf'] represents the probability that the ground accelera-tion A exceeds a" for a given failure fraction f'. This probability is shown shaded in Figure A-1. However, it is desirable to transform this probability statement into a statement on the probability that the failure fraction f is less than f' for a given ground acceleration a", or

( in symbols P[f s f'ja"]. This probability is also shown shaded in Figure A-1. It follows that:

[

P[f 5 f'la"] = P[A > a" l f '] (A-12)

Thus, from Equations A-10 and A-11:

( .

.(

in(a"/d exp 8 o -I(f') /

l P[f5f'la"] = 1- 0 (A-13)

[

g

_ u .

C A-4 1

__ _ _ _ _ _ _ _ - - - - - - - - - - - - - - - - - - - - - - - - - ' - - - ~

~

from which:

r -

(in\a"/dexpBR ' , II -1))

{ P[f > f'la"]

~

= t (A-14) 8

( u )

which is the basic statement expressing the probability that the failure fraction exceeds f' for a ground acceleration a" given the median ground 7 acceleration capacity A, and the logarithmic standard deviations BR and L

BU associated with randomness and uncertainty, respectivdly.

F As an example, if:

L A = 0 77 eR = 0.36, eu = 0 39

{ then from Equation A-14 for typical values of f and a",

P[f > 0.5 la" = 0.40g] = 0.05 which says that there is a 5 percent probability that the failure frequency exceeds 0.5 for a ground acceleration of 0.40g.

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l REFERENCES

)

A.1 Benjamin, J. R., and Cornell, C. A.,

Probability, Statistics and

, Decision 1970.

for Civil _ Engineers, McGraw Hill Book Company, New York, A.2 Kennedy, R. P., and Chelapati, C. V.,

L " Conditional Probability of a Local Flexural Wall Failure of a Reactor Building as a Result of Aircraft Impact *, Holmes and Narver, Inc.. prepared for General  !

Electric Company, San Jose, California, June,1970.

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