ML20203E594
| ML20203E594 | |
| Person / Time | |
|---|---|
| Site: | Seabrook  |
| Issue date: | 06/30/1986 |
| From: | Campbell R, Narver R, Wesley D NTS/SMA, INC. |
| To: | |
| Shared Package | |
| ML20203E591 | List: |
| References | |
| 1589.01, 1589.01-R01, 1589.01-R1, SMA-12911.01, NUDOCS 8607240183 | |
| Download: ML20203E594 (632) | |
Text
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SMA 12911.01 Rev. 1/NTS 1589.01 Technical Report No. 1589.01 I SEISMIC FRAGILITIES OF STRUCTURES AND COMPONENTS AT THE SEABROOK GENERATING STATION, UNITS 1 AND 2 I
by D. A. Wesley I R. D. Campbell R. B. Narver G.S. Hardy M. W. Salmon Prepared by NTS Engineering 6695 East Pacific Coast Highway I Long Beach, CA 90803 Prepared for PICKARD, LOWE, AND GARRICK, INC.
Irvine, CA and New Hampshire Yankee Division Public Service Company of New Hampshire Seabrook, New Hampshire June 1986 I i I
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[ TABLE OF CONTENTS
{ Section Title Page 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . 1-1
[ 2 GENERAL CRITERIA FOR DEVELOPMENT OF MEDIAN SEISMIC SAFETY FACTORS 2-1 I
2.1 Defi ni ti on of Fail ure . . . . . . . . . . . . . . . . . . 2-2 l 2.1.1 Seismic Category I Struchres .......... 2-2 2.1.2 Seismic Category I Equipment and Piping ..... 2-2 l 2.1.3 Non-Category I Structures ............ 2-3 2.1.4 Non-Seismic Category I Equipment and Piping ... 2-3 l
2.2 Basis for Safety Factors Derived in Study . . . . . . . . 2-4 2.2.1 Structural Response and Capaci ty . . . .
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2.2.2 Seismic Category I Piping and Equipment Response and Capacity
. . . . . 2-4
.............. 2-4 2.3 Formulation Used for Fragility Curves . . . . . . . . . . 2-6 l 2.4 Design and Construction Errors ............. 2-10 I 3 DIFFERENCES BETWEEN CRITERIA USED FOR DESIGN OF SEABROOK AND PARAMETERS USED IN THE EVALUATION OF THE SEISMIC CAPACITY 3-1 3.1 Strength ........................ 3-2 3.2 Ductility . . . . . . . . . . . . . . . . . . . . . . . . 3-2 I 3.3 Ea rthq uake Du rati o n . . . . . . . . . . . . . . . . . . . 3-3 3.4 System Response . . . . . . . . . . . . . . . . . . . . . 3-4 3.4 .1 Earthquake Characteristics . . . . . . . . . . . . 3-5 l
3.4.2 System Damping . . . . . . . . . . . . . . . . . . 3-5
> 3.4.3 Load Combinations ................ 3-6 3.4.4 Modal Combination ............ ... 3-8 3.4.5 Combination of Responses for Earthquake J Di rectional Components . . . . . . . . . . . . . . 3-9 3.4.6 Structure Modeling Considerations ........ 3-9 4 STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1 4.1 Median Safety Factors and Logarithmic Standard Deviations ....................... 4-1 4.1.1 Structure Capacity . . . . . . . . . . . . . . . . 4-5 4.1.1.1 Concrete Compressive Strength . . . . . . 4-5 4.1.1.2 Reinforcing Steel Yield Strength .... 4-7 4.1.1.3 Shear Strength of Concrete Walls .... 4-7 i
I TABLE OF CONTENTS (Continued)
I Section Title Page 4.1.1.4 Example of Shear Wall Failure in Shear . . . . . . . . . . . . . . . . . . 4-10 Strength of Shear Walls in Flexure I 4.1.1.5 4.1.1.6 Under In-Pl ane Forces . . . . . . . . . . 4-12 Example of Shear Wall Failure in Flexure . . . . . . . . . . . . . . . . . 4-13 4.1.2 Structure Ductility ............... 4-14 4.1.2.1 Example of Inelastic Energy Absorption Factor .................
I- 4.1.3 Earthquake Duration ...............
4-15 4-16 4.1.4 Spectral Shape, Damping, and Modeling Factors .. 4-17 4.1.4.1 Example of Spectral Shape, Damping, .
and Modeling Factors ..........
4-21 4.1.5 Modal Combination ................ 4-22 4.1.6 Combination of Earthquake Components . . . . . . . 4-23 l 4.1.7 Soil-Structure Interaction Effects . . . . . . . . 4-24 4.2 Containment Building .................. 4-25 4.2.1 Containment Failure Modes ............ 4-26 4.3 Containment Enclosure Building ............. 4-27 4.3.1 Containment Enclosure Failure Modes ....... 4-28 4.4 Primary Auxiliary Building ............... 4-29 4.4.1 Primary Auxiliary Building Failure Modes . . . . . 4-29 4.5 Service Water Pumphouse and Circulating Water Pumphouse . 4-30 4.5.1 Service Water Pumphouse Failure Modes ...... 4-30 4.6 Service Water Cooling Tower . . . . . . . . . . . . . . . 4-31 4.6.1 Cooling Tower Failure Modes ........... 4-32
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I 4.7 Condensate Storage Tank and Enclosure . . . . . . . . . . 4-32 4.7.1 Tank and Enclosure Failure Modes . . . . . . . . . 4-33 i
4.8 Control and Diesel Generator Building . . . . . . . . . . 4-34 I 4.8.1 Control and Diesel Generator Building Failure Modes ...................... 4-34 4.9 Fuel Storage Buil di ng . . . . . . . . . . . . . . . . . . 4-35 4.9.1 Fuel Storage Building Failure Modes ....... 4-35 I
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I TABLE OF CONTENTS (Continued)
Section Title Page 5 EQUIPMENT FRAGILITY ..................... 5-1 5.1 Equipment Fragility Methodology . . . . . . . . . . . . . 5-1 ,
5.1.1 Fragili ty Derivation . . . . . . . . . . . . . . . 5-1 5.1.1.1 Equipment Capacity Factor . . . . . . . . 5-3 5.1.1.1.1 Strength Factor ....... 5-4 5.1.1.1.2 Ductility Factor . . . . . . . 5-7 5.1.1.2 Equipment Response Factor . . . . . 5-8 I 5.1.1.2.1 Qualification Method Factor
. 5-10 5.1.1.2.1.1 Static Analysis . 5-10 5.1.1.2.1.2 Dynamic Analysis 5-10 5.1.1.2.1.3 Testing . . . . . 5-11 5.1.1.2.2 Equipment Spectral Shape 5-11 Factor . . . . . . . . . . . .
5.1.1.2.2.1 Peak Broadening I 5.1.1.2.2.2 and Smoothing . .
Artificial Time-5-12 History Generation 5-13 I 5.1.1.2.3 Modeling Factor ....... 5-14 5.1.1.2.4 Damping Factor . . . . . . . . 5-15 5.1.1.2.5 Mode Combination Factor ... 5-17 5.1.1.2.6 Earthquake Component Combination Factor . . . . . . 5-17 5.1.1.2.7 Boundary Conditions Factor (Testing) .......... 5-19 5.1.1.2.8 Spectral Test Method . . . . . 5-19 5.1.1.2.9 Multi-Directional Effects .. 5-20 5.1.1.2.9.1 Biaxial Testing . 5-20 5.1.1.2.9.2 Uniaxial Testing 5-21 5.1.1.3 Structural Response Factors 5-22 I 5.1.1.4 Earthquake Duration Factor
....... 5-23 5.1.2 Information Sources ............... 5-24 5.1.2.1 Seismic Qualification Analysis Reports . 5-25 5.1.2.2 Seismic Qualification Test Reports ... 5-25 I 5.1.2.3 Final Safety Analysis Report & SQRT Summaries . . . . . . . . . . . . . . . . 5-25 iii
I TABLE OF CONTENTS (Continued)
I Section Title Page 5.1.2.4 Vendor Drawings or Design Reports from which New Analyses are Conducted . . . . . . . . . . . . . . . 5-26 5.1.2.5 Past Earthquake Experience ...... 5-26 5.1.2.6 Specification for the Design of Equipment . . . . . . . . . . . . . . . 5-26 5.1.3 Equipment Categories . . . . . . . . . . . . . . 5-27 5.2 Equipment Fragility Examples .............
I 5.2.1 Example of a Plant-Specific Design Report Fragility Derivation . . . . . . . . . . . . . .
5-28 5-29 5.2.1.1 Spray Additive Tank Capacity Factor . . 5-30 5.2.1.2 Spray Additive Tank Equipment Response Factor ................ 5-33 5.2.1.3 Spray Additive Structural Response Factors ............... 5-35 I 5.2.1.4 Spray Additive Tank Earthquake Duration Factor . . . . . . . . . . . . 5-35 5.2.1.5 Spray Additive Tank Ground Acceleration Capacity ............... 5-35 5.2.2 Example of Qualification Test Report Fragility De ri va t i on . . . . . . . . . . . . . . . . . . . 5-36 5.2.2.1 Battery Charger Capacity Factors ... 5-36 5.2.2.2 Battery Charger Equipment Response Factors . . . . . . . . . . . . . . . . 5-39 5.2.2.3 Battery Charger Structural Response Factors . . . . . . . . . . . . . . . . 5-41 5.2.2.4 Battery Chargers Earthquake Duration Factor ................. 5-42 5.2.2.5 Battery Chargers Ground Acceleration I Capacity ...............
5.2.3 Example of Generic Fragility Derivation Based on 5-42 I Design Specifications .............
5.2.3.1 Failure Modes of a Piping System ...
5-43 5-43 5.2.3.1.1 Piping Failure Modes . . . . 5-44 I 5.2.3.1.2 Support Failure Modes ... 5-45 5.2.3.2 Piping Capacity Factor ........ 5-45 5.2.3.2.1 Piping Strength Factor . . . 5-46 iv I
I TABLE OF CONTENTS (Continued)
I Section Title Page 5.2.3.2.2 Piping Ductility Factor . . 5-50 5.2.3.2.3 Piping "Three-Hinge" Factor .......... 5-50 5.2.3.3 Piping Equipment Response Factors .. 5-51 5.2.3.4 Piping Structural Response Factors . .
I 5.2.3.5 Piping Earthquake Duration Factor ..
5-52 5-52 5.2.3.6 Piping Ground Acceleration Capacity . 5-53 I 5.2.3.7 Piping Supports Capacity Factor ...
5.2.3.8 Ground Acceleration Capacity of 5-53 Piping Supports ........... 5-57 5.2.4 Example of Fragility Derivation Based Upon New Analysis ................. 5-57 5.2.4.1 RWST Capacity Factor . . . . . . . . . 5-58 5.2.4.2 RWST Equipment Response Factor . . . . 5-60 5.2.4.2.1 Qualification Method ... 5-60 5.2.4.2.2 Spectral Shape Factor . . . 5-60 5.2.4.2.3 Damping Factor . ..... 5-61 5.2.4.2.4 Modeling Factor . . . . . . 5-61 5.2.4.2.5 Mode Combination Factor . . 5-61 I 5.2.4.2.6 Earthquake Component Combi-nation Factor . . . . . . . 5-62 I 5.2.4.2.7 Overall Equipment Response Factor .......... 5-62 l 5.2.4.3 RWST Structural Response Factor ... 5-62 l
5.2.4.3.1 Spectral Shape Factor . . . 5-63 t 5.2.4.3.2 Damping . . . . . . . . . . 5-63 5.2.4.3.3 Modeling Factor . . . . . . 5-64 5.2.4.3.4 Soil-Structure Interaction. 5-64 l 5.2.4.3.5 RWST Structural Response u Factor .......... 5-64 5.2.4.4 Earthquake Duration Factor . . . . . . 5-64 5.2.4.5 RWST Capacity .... .. ...... 5-65 I
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TABLE OF CONTENTS (Contents)
I Section Title Page 5.2.5 Example of Fragility Based on Engineering Judgment and Earthquake Experience . . . . . . 5-65 5.3 Equipment Fragility Results 5-66 I
5.3.1 General Results ............... 5-67 REFERENCES APPENDIX A I
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.I l REVlSIONS - June 1986 1
Updated fragility descriptions for:
l Non-vital Electric Power 4160 Volt Switchgear I Emergency Fced Pump:
I Motor Driven Turbine Driven 120 V Instrument Bus 480 V Motor Control Centers 480 V Transformers and Busses (480 V Unit Substation)
Refueling Water Storage Tank Primary Component Cooling Water Heat Exchanger Diesel Fuel Oil Day Tank RHR Pump Safety Injection Pump Charging Pump I
Added fragility descriptions for:
Solid State Protection System Deleted Figures 5-2 through 5-7, (no longer applicable)
Revised text to incorporate updates of fragility. Revisions in text are marked with a vertical bar on the right-hand margin.
Deleted Tables 5-9, 5-10 and 5-11 (no longer applicable). Old Table 5-12 becomes 5-9).
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I
- 1. INTRODUCTION I A probabilistic risk assessment (PRA) of the Seabrook Nuclear Generating Station was completed by Pickard, Lowe and Garrick, Inc., for
'I Public Service Co. of New Hampshire in December, 1983. In that evalua-tion, system models, event trees, and fault trees were utilized to deter-mine the frequency of radioactive release from the site due to random
, equipment failure and failures initiated by natural hazard events. Earth-quakes were one of the extreme natural hazards considered in this PRA.
Structural Mechanics Associates, Inc. (SMA), under subcontract to Pickard, Lowe and Garrick, provided the required information on the response of plant structures and equipment to earthquake (seismic) events.
The original version of this report was included as part of the Seabrook I Station Probabilistic Safety Assessment (SSPSA) report, Ref. 48, to document the seismic fragilities that were used to help estimate the risk contribution due to seismic events. While seism.c events were found to make a small contribution to risk, this contribution became more visible as a result of subsequent risk management efforts that reduced the risk l
contributions of non-seismic events. In addition, NRC conducted a review of the SSPSA including the portion dealing with seismic risk analysis, (Ref. 47). To account for new information about the Seabrook design, the NRC review comments and the greater visibility of the seismic risk I contribution in light of risk management activities, it was decided to reevaluate the seismic fragilities of selected key components. The purpose of this revision of our report is to document these updated fragility analyses for the Seabrook Station.
The frequency of seismically-induced failare as a function of peak ground acceleration for both safety-related structures and equipment has been developed by SMA for the Seabrook facility. Also included is the expected variability in the frequency of failure. The determination of the seismic hazard is being conducted by others. The information for E-1-1 I
I both the frequency of occurrence of different levels of peak ground acceleration and the frequency of failure of the safety-related systems and components will then be incorporated into the risk models by Pickard, Lowe and Garrick, to determine the frequency of seismic-induced radio-active release from the site.
I In order to correctly interpret the fragilities derived in this report, it is necessary to define the effective acceleration to which I these fragilities are anchored. It is recognized that the damage poten-tial of an earthquake depends on many f actors, among which are magnitude, peak acceleration, and duration. For the Seabrook 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 site-specific spectra used to evaluate the fragilities. Because the I site-specific 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 if the magnitude range were higher, say 6.0 to 7.0, either a different set of median spectra and a different duration f actor (which will be discussed in Sections 3.3 and 4.1.3) would required, or else it would be necessary to anchor the fragilities to an effective acceleration that would be greater than the mean peak acceleration. Conversely, if the I magnitude range were lower and this set of fragilities were to be used, the effective anchoring acceleration would have to be less than the mean peak acceleration in order to accurately predict the damage potential.
The Seabrook Station was designed in the late 1970's and early 1980's in accordance with criteria and codes in effect at that time (Reference 1). The Seabrook systems and components which are t.ssential to the prevention or mitigation of consequences of accidents which could affect the public health and safety were designed to enable the facility I to withstand the effects of natural forces including earthquakes. The design criteria included the effects of simultaneous earthquake and I
1-2 I
loss-of-coolant-accident (LOCA) conditions. The plant was designed to withstand both an Operating Basis Earthquake (0BE) and a Safe Shutdown l Earthquake (SSE). The structural design criteria for the SSE was based on 0.25g and the OBE on 0.1259 peak horizontal ground accelerations for l
all Seismic Category I structures.
Almost all Seismic Category I structures are founded on competent rock or concrete fill to rock. Some safety-related electrical manholes I are founded on engineered backfill consisting of offsite borrow or tunnel cuttings. The maximum depth of the backfill to rock for these manholes is 18 feet. The manholes are small structures and soil-st>ucture interac-l tion effects for these structures is expected to be insignificant. The shear wave velocity of the bedrock is from 8,000 to 10,000 fps, and the l
compression velocity is 16,500 to 18,500 fps (Reference 1). Consequently, the effects of soil-structure interaction are considered to be negligible for the Category I structures. The ground response spectra used in the design are those recommended in USNRC Regulatory Guide 1.60 scaled to I 0.259 for the SSE and 0.125g for the OBE. Horizontal response spectra used for the SSE design analyses of Category I structures are shown in Figure 1-1. Both modal response spectrum and modal time-history analyses l were conducted for the Seabrook Category I structures. In general, the response spectrum analysis results were used for evaluation of the struc-l ture seismic loads and stresses while time-history results were used to generate in-structure response spectra for the design and evaluation of piping and equipment. Three synthetic time-histories were generated based on the ground response spectra. Comparisons of the ground response I spectra generated by these artificial time-history records compared to the design spectra are shown in Figures 1-2 through 1-7 for 7 and 10 percent damping (Reference 1).
l The plant structures 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. Seabrook Station structures, systems and components 1-3 I
I 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. These plant features are those necessary to assure:
- a. The integrity of the reactor coolant pressure I boundary,
- b. The capability to shut down the reactor and maintain it in a safe shutdown condition, or
- c. The capability to prevent or mitigate the I consequences of accidents which could result in potential offsite exposures, comparable to the guideline exposures of 10 CFR Part 100.
I Seismic Category I structures include the following:
Containment Structure and Internal Structures Containment Enclosure Building Containment Equipment Hatch Missile Shield Containment Enclosure Ventilation Area Control and Diesel Generator Building Control Room Makeup Air Intake Structures I Emergency Feedwater Pump Building, Including Electrical Cable Tunnels and Penetration Areas (Control Building to Containment)
Enclosure for Condensate Storage Tank Fuel Storage Building
. Main Steam and Feedwater Pipe Chase (East),
I Including East Penetration Area Main Steam and Feedwater Pipe Chase (West),
I Including Mechanical Penetration Area and Personnel llatch Arca Piping Tunnels l Pre-Action Valve Building I Primary Auxiliary Building, Including Residual Heat Removal (RHR) Equipment Vault I
1-4
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b Safety-Related Electrical Duct Banks and Manholes Service Water Cooling Tower, Including Switchgear Rooms Service Water Pumphouse Tank Farm (Tunnels), Including Dikes and Foundations for Refueling Water Storage Tank (RWST) and Reactor Makeup Water Storage Tank Waste Processing Building
[
In addition, the foundations and supports for all Category I
[ structures and supports are designed for Category I criteria. Some structures such as the waste processing building, although classed as
( Seismic Category I, are not essential to the safe shutdown of the reactor and were, therefore, not evaluated in these analyses.
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 structures. An example of a non-Category I structure is the turbine building. Several structures, such as the service and
[ circulating water pumphouse, are classed as partially Category I.
Seismic Category I structures are sufficiently isolated or protected from non-Category I structures to ensure that their integrity is maintained
{ for the design SSE. Several non-Category I structures are designed against collapse onto Category I structures due to SSE loads.
For the most part, results of existing analyses and evaluations
. of structures and equipment for the Seabrook 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 this 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 response at failure and, hence, the median peak ground acceleration for
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I failure. It is known that earthquakes with only one or two high accelera-tion spikes are not as damaging to structures and equipment as longer duration earthquakes with multiple peaks at close to the maximum accelera-tion level. The reason for this is that the shorter duration earthquakes do not have sufficient energy content to develop resonances. For this reason, the fragility evaluations described in this report are keyed to a I mean peak acceleration belonging to an earthquake of short duration that develops narrow band response spectra.
An evaluation of the individual important structures and some of the equipment was conducted in this manner. However, much of the piping and equipment were evaluated on the basis of a number of generic catego-ries. Although inelastic energy dissipation is included in determining the f actors of safety, no nonlinear analyses have been conducted for either the structures or equipment for Seabrook, and all evaluations were I based on elastic analysis and load distributions.
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 failure for each safety-related structure or component in the plant. In the total study, these conditional component f ailure frequencies are used with systems models to determine 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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- 2. GENERAL CRITERIA FOR DEVELOPMENT OF MEDIAN SEISMIC SAFETY FACTORS
{_ c The factor of safety of a structure or component is defined as the resistance capacity divided by the response associated with the Safe Shutdown Earthquake (SSE) of 0.25g peak acceleration. The development of
( seismic safety factors associated with the SSE is based on consideration of several variables. The variability of dynamic response to the specified accrieration and the strength capacity of the structure or
{ equipment coniponent are the two basic considerations in determining the variability in the factor of safety. Several variables are involved in determining both the structural response and the structural capacity, and each such variable, in turn, has a median factor of safety and b variability associated with it. The overall factor of safety is the product of the factors of safety for each variable. The median of the
(
- overall factor of safety is the product of the median safety factors of a ll the variables. The variabilities of the individual variables also
{ combine to determine that of the overall safety factor.
Variables influencing the factor of safety on structural capac-ity to withstand seismic induced vibration include the strength of the 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 structural response for a
( given peak free-field ground acceleration is made up of many factors.
The more significant factors include variability 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) combination of modes, (6) combination of earthquakecomponents,and(7) soil-structureinteraction. The ratio between the median value of each of these factors and the value used in b design of the Seabrook plant and the variability of each factor are E
{ 2-1
l I
quantitatively estimated in Chapters 4 and 5 for various structures and components. These estimates are based on available test data for Seabrook, limited analysis, and engineering judgment and experience in the analysis of nuclear power plants and components.
2.1 DEFINITION OF FAILURE In order to estimate the median factor of safety against the structure or component failure for the SSE peak acceleration (0.25g), it is necessary to define what constitutes failure.
2.1.1 Seismic Category I Structures For purposes of this study, Category I structures are considered to fail functionally when inelastic deformations of the structure under 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) chosen for Category I structures are estimated to correspond to the onset of significant structural damage. For many potential modes of failure, this is believed to represent a conservative bound on the level of inelas-tic structural deformation which might interfere with the operability of components housed within the structure. It is important to note that considerably greater margins of safety against structural collapse are believed to exist for these structures than many cases reported within I this study. Thus, the conditional probabilities of failure for a given free-field ground acceleration presented in this report for Catetory I structures are considered appropriate for equipment operability limits and should not necessarily be inferred as corresponding to structure l collapse.
2.1.2 Seismic Category I Equipment and Piping Piping, electrical, mechanical and electro-mechanical equipment vital to a safe shutdown of the plant or mitigation of an accident are considered to fail when they will no longer perform their designated functions. Rupture of the pressure boundary on mechanical equipment is I 2-2
1 l
also considered a failure. Therefore, for mechanical equipment, a dual l failure definition exists: failure to function and pressure boundary rupture. Depending upon the equipment type, one or the other definition will govern. For active equipment, the functional failure definition l will usually govern as equipment pressure boundaries are usually very conservatively designed for equipment such as pumps and valves. For l
piping, failure of the support system or plastic collapse of the presure boundary are considered to represent failure. The inelastic energy absorption limits (ductility limits) associated with these failure modes g have been conservatively estimated in order to define the margins of u safety.
2.1.3 Non-Category I Structures l In the Seabrook plant, no components identified as important to safety are located within non-Category I buildings. The service and j circulating water pump house and waste processing building are partially Category I. The entire pump house structure was evaluated as part of this PRA. However, no equipment essential for the safe shutdown of the reactor is located in the waste processing building, and its capacity was not determined. Non-Category I buldings are separated from the Category I structures by seismic gaps. The non-Category I structures were either designed to Category I criteria or designed so that their failure would l not damage any Category I structures. Since it was judged that failure t of non-Category I buildings would not affect the seismic capacities of l the Seabrook Category I structures, fragility evaluations were not conducted for the non-Category I buildings as part of this evaluation.
l 2.1.4 Non-Seismic Category I Equipment and Piping I Failure of Non-Seismic Category I piping, electrical, mechanical and electro-mechanical equipment is defined as for Category I equipment; i.e., f ailure to perform its intended function or failure of the pressure boundary.
2-3
lI 2.2 BASIS FOR SAFETY FACTORS DEPIVED IN STUD _Y, There was a general lack of detailed information available for this study on seismic fragility of specific Seabrook structures and equipment. This occurs because existing codes and standards do not require determination of ultimate seismic capacities, either for structures or equipment qualified by analysis, or for equipment or components qualified by testing. Therefore, most median safety factors, estimates of variability, and conditional 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 of the important structures. The additional analyses were based on the original design analyses which were available, however.
2.2.1 Structural Response and Capacity The results from existing dynamic analyses of the important structures (Reference 1), which were used in the design, were extensively I used in this study. These were supplemented as required to provide estimates of load redistributions resulting from localized failures, etc.
Levels of conservatism associated with the method of analysis used in design were estimated such that safety f actors reflecting this analysis could be estimated for the building structures and for the seismic excitation of equipment mounted within the building.
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.
2.2.2 Seismic Category I Piping and Equipment Response and Capacity For most of the safety-related equipment, information on analysis methods was available in summary form in the FSAR. Seismic response information was obtained from the seismic qualification I
2-4 I
reports for specific components. In some cases such as for piping, only the seismic analysis requirements and stress acceptance criteria were known. Safety factors for response and structural or functional capacity were estimated from existing information. No new analyses were conducted.
In-structure response spectra for all Category I structures were generated during the design process. From these typical floor response spectra and 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 static coefficient used in design to determine a median safety factor on response.
Capacity factors 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 considered in developing capacity factors for piping and equipment:
g structural and functional. Equipment and piping design reports delineate ur stress levels for the specified seismic loading plus normal operating conditions. Where the equipment fails in a structural mode (i.e.,
pressure boundary rupture or loss of support), the median capacity f actor and its variability are derived in the same 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. There are some fragility test data on generic classes of equipment that have been utilized in hardened military installations.
I The equipment was off-the-shelf without special shock resistant design and is similar to nuclear power plant equipment. These data provide estimates of the fragility levels, and thus, safety factors can be developed for the specified design earthquake. Fragility levels are not normally determinable from equipment qualification reports, but the achieved test levels can be utilized to update generic fragilities derived from the military data.
2-5 I ,
1 2.3 FORMULATION USED FOR FRAGILITY CURVES Seismic-induced fragility data are generally unavailable for specific plant components and are certainly unavailable for the specific Seabrook 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 g in all subsequent analyses. Because of this uncertainty, great precision B in attempting to define the shape of these curves is unwarranted. Thus, a procedure which requires a minimum amount of information, incorporates uncertainty into the fragility curves, and easily enables the use of engineering judgment, was used in this study.
I The entire fragility curve for any mode of failure and its I uncertainty can be expressed in terms of the best estimate of the median ground acceleration capacity, E, times the product of random variables.
Thus, the ground acceleration, A, corresponding to failure is given by:
A=dcR *U (2-1) in which cR and cu are random variables with unit median representing the inherent randomness (failure fraction) about the median and the uncertainty (probability) in the median value, respectively. Equation I 2-1 enables the fragility curve and its uncertainty to be represented as shown in Figure 2-1; i.e., as a set of shifted curves with attached g uncertainty levels. Thus, it is assumed that all uncertainty in the 3 fragility curves can be expressed through uncertainty in the median alone.
l Next, it is assumed that both cR and cu are lognormally distributed with logarithmic standard deviations of BR and BU '
respectively. The advantages of this formulation are:
I 1. The entire fragility curve and its uncertainty can be expressed by three parameters - A, BR .
and BU . With the very limited available data on i
2-6
I fragility, it is much easier to only have to I estimate three parameters rather than the entire shape of the fragility curve and its uncertainty.
- 2. The formulation in Equation 2-1 and the lognormal 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" fragility curve (i.e., one which does not separate out uncertainty from underlying randomness) defined by:
A=dc c (2-2)
I where c c is a lognormal random variable with unity median and logarithmic standard deviation SC given by:
I l SC=
SR+8 J (2-3)
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 failure fraction and does not desire an estimate of uncer-I tainty. In this study, the guidelines used to estimate the values of BR and SU for each variable affecting A were based on considering the I inherent randomness, RS , to be associated with the earthquake character-istics themselves, and BU to be associated with other lack of knowledge.
Thus, such variability as resulting from earthquake response spectra shapes and amplification, earthquake duration, numbers and phasing of peak excitation cycles, etc., together with their contributions to repeated structure ductility and response characteristics is attributed to randomness. In general, randomness is not considered to be significantly reduced from additional analysis or test based on current state-of-the-art techniques. Uncertainty is considered to result primarily from analytical modeling assumptions and other lack of knowledge concerning variables such as material strength, damping, etc. which could in many cases be reduced by additional study or test.
l 2-7
I The lognormal distribution can be justified as a reasonable distribution since the statistical variation of many material properties I (Reference 3 and 4) and seismic response variables may reasonably be represented by this distribution (Reference 5). In addition, the central limit theorem states that a distribution consisting of products and quotients of distributions of several variables tends to be lognormal even if the individual distributions are not lognormal. Use of this distribution for estimating failure fractions on the order of one percent or greater is considered to be quite reasonable. Lower fraction esti-mates which are associated with the extreme tails of distribution must be considered less accurate.
Use of the lognormal distribution for estimating very low failure 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 f arther from the median than actual structural resistance or response data might indicate since such data generally show cut-off limits beyond which there is essentially zero failure fraction. The degree of conservatism introduced into the probability of release is dependent not only on the conservatism I in the fragility description, but also on the seismic hazard description at low seismic levels. If the seismic hazard for low seismic input levels is large enough, it is apparent that very low level earthquakes can govern I the seismic-induced release. This is considered unrealistic for engi-neered structures and equi'pment found in nuclear power plants. Structures and equipment are subjected to low level dynamic loads from a number of sources including wind on a repetitive basis which have never been known to produce nuclear power plant structural failures. Similarly, for low level earthquakes, it is expected that below some threshold, there is virtually no chance of failure due to seismic excitation. Material strength data, for instance, normally does not fall 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.
I I 2-8 I
E 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 some 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 is lacking, this threshold value is expected to be at approximately minus
{ two lognormal standard deviations for the median curves using the "best estimate" or composite fragility variability. The composite lognormal standard deviation, B C
, is used for the basis of the cut-off rather than randomness or uncertainty since the composite value combines the effects of both dispersions. 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, j assumed consistent with the majority of the other variables encountered in the PRA. The following approximation is recomended for establishing l
the cut-offs for the various fragility curves:
t The cut-off on the lower tails of the median (50 percentile) fragility curve should be:
} d co =d exp (-28 )
C.
I l
where d co isthecut-offonthemediancurve,histhemedianpeak ground acceleration for failure, and B C is the composite lognormal standard deviation.
2-9 I
I The cut-off for the lower tails of the other fragility curves should be:
v -
Aco = Aco .exp(-xsC/1.65)
I 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 +38 C for all fragility curves. Similarly, for fragility curves involving only uncertainty, it is recomended that the cut-offs be set at -38 0for the lower bound and +380 for the upper bound, I respectively.
Some characteristics of the 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 Seabrook structures and equipment seismic capacities. In one exception to this, I ',
the possibility of a large throughwall flaw was considered as a lower bound for generic piping. In general, for a plant as new as Seabrook with current design and QA procedures, the possibility that design and construction errors which can affect the seismic capacity of a component may exist is considered remote. Although some discrepencies have been identified and others may be in the future, these items have been modified as necessary or shown to have no safety implications. Thus, these items are not expected to significantly affect the seismic capacity of the equipment or structures after they have been identified. However, I there is a possibility that unidentified design and construction errors may exist which can affect the seismic capacity.
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- 3. DIFFERENCES BETWEEN CRITERIA USED FOR DESIGN OF SEABROOK AND PARAMETERS USED IN THE EVALUATION OF THE SEISMIC CAPACITY I The seismic design of the Seabrook structures and equipment was I based for the most part on currently accepted methodology and criteria in conformance with NRC licensing requirements. Essentially, the same cri-teria exist for the design and analysis of the Seabrook Nuclear Steam I- Supply System (NSSS) and non-NSSS Category I components. 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 fac-tors of safety are introduced at various stages in the design procedure.
The exact magnitude of many of these safety factors is still a matter of considerable discussion. Nevertheless, in order to establish a realistic value of the actual seismic capacity of a structure or equipment compo-nent, the amount of conservatism along with its variability must be estab-lished as accurately as possible. In this chapter, the design basis of I the most important parameters affecting seismic capacity are identified, and the general methods used in obtaining more realistic values associated l with very high seismic response levels are discussed. The detailed j determination of these parameters is described in Chapters 4 and 5 for structures and equipment, respectively. The estimated seismic capacities of the most probable failure modes are also developed in Chapters 4 and 5.
I The general approach used in the evaluation of the Seabrook seismic capacity 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 overall factor of safety is typically composed of several important contributions such as strength, allowance for inelastic energy dissipation l
I 3-1 ;
I
[
(ductility), and differences in median structure response compared to design values resulting from such parameters as earthquake character-
{
istics, damping, and directional load components.
3.1 STRENGTH The design strength of a structure or component is typically
[ ,
determined from applicable codes and standards such as the ACI building codes for concrete or the ASME boiler and pressure vessel code. Inherent in these design codes is a factor of safety on material strength. Some-times this factor is known reasonably accurately, such as the design
[ allowable being one-half the minimum yield strength or some similar rela-tionship. At other times, it is less well defined or may be a function of the geometry or other physical characteristics of the component such
{ as for reinforced concrete shear . alls. For metal structures and compo-nents, the safety factor included in the codes is usually fairly accu-rately known as are the relationships between minimum and mean or median strengths. For concrete structures, the factor of safety is normally b less accurately known. In this case, the 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 eieraent geometry and 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 p tests provide a valuable basis for establishing the element strength 5 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 DUCTILITY In order to establish realistic seismic capacity levels for most
{ structures and components, an assessment of the inelastic energy absorp-tion must usually be considered. Exceptions to this are some modes involving brittle failure, functional f ailure or elastic buckling.
i ;
( 3-2
[ .
However, most failures due to seismic response involve at least some degree of yielding. This is true of reinforced and prestressed concrete as well as the 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 linear elastic techniques. In the design analysis of the Seabrook structures, all design analyses were based on linear elastic analyses. No nonlinear analyses of the structures were conducted. Although inelastic analysis would be 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 nonlinear analyses. This can be accomplished by the use of the ductility-modified response spectrum approach (References 6 and 7) together with a knowledge of the elastic model results and the
{ expected ductility ratios of the critical elements 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 nonlinear system comnared to the equivalent elastic system response is calculated. 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 or component can be made provided the results of the elastic analysis are available and a realistic evaluation of the system ductility can be made.
3.3 EARTHQUAKE DURATION The earthquake duration assumed for design was from 10 to 15 I seconds. This was used primarily to determine the number of response cycles for the OBE for ASME Code fatigue analysis. No fatigue analysis is required by the ASME Code for the SSE since it is a Service Level D (faulted) condition. For the non-NSSS equipment, 20 stress cycles were assumed for the analysis. For the NSSS equipment, an evaluation was 3-3
I conducted which indicated no more than 8 peak acceleration (above 90 I percent of the maximum) cycles occurred for flexible equipment, and no more than 3 peak cycles for rigid equipment. For design purposes, 10 cycles were used for flexible equipment, and 5 for rigid equipment. For the magnitude earthquakes expected at the Seabrook site,10 to 15 seconds of strong motion excitation is considered extremely conservative. Con-sequently, fewer cycles would be expected than calculated for the design earthquake since the design earthquake accelograms are approximately 15 seconds for all three components of motion.
I The seismic capacity of structures is affected by the duration and resulting number cf strong motion cycles since the expected available ductility of the controlling structural elements increases as the number of cycles is reduced. Element ductilities for concrete elements were developed from limited test data available in the literature. These data are considered applicable for reversed load cycles representative of earthquakes with magnitudes of approximately 6.2 or greater. Estimated effects in terms of equivalent ductility from lower magnitude earthquakes, such as are expected for the Seabrook site, have been developed from I limited nonlinear analyses of representative nuclear power plant struc-tures and observed damage to conventional structures. These effects are included in the seismic capacity evaluations conducted for Seabrook.
3.4 SYSTEM RESPONSE A number of parameters must be evaluated when considering the expected system response near failure compared to the design conditions.
Among these are the expected compared to the design earthquake character-istics, directional combinations, system damping, load combinations, and I system modeling approaches and assumptions. 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. Some 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 of the more important parameters I
3-4 I
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.
3.4.1 Earthquake Characteristics
( The Seabrook Seismic Category I structures are founded on rock or concrete poured against rock. Equipment within the structures were designed for an SSE of 0.25g defined by the USNRG Regulatory Guide 1.60 free-field ground response spectra shown in Figure 1-1. These spectra were developed from a number of earthquakes 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-dependent spectra are not available for Seabrook. The spectra chosen as site-specific spectra were derived from Reference 8. A-(
comparison between these spectra and the design spectra for different damping values is presented in Figure 3-1. Below 28 Hz, the design
{ spectra accelerations exceed those of the site-specific spectra. At frequencies below 8 Hz, the difference is substantial. Most of the
[ structures analyzed in this report have their fundamental frequency below 8 Hz. These effects, together with the higher expected damping
[ associated with seismic response levels at or near failure, provide a significant factor of safety compared to the Seabrook design criteria.
3.4.2 System Damping Damping values used for the SSE design analysis of the Seabrook plant are shown in Tables 3-1 and 3-2 for the non-NSSS and NSSS design, respectively. The values are typically the same as those specified in USNRC Regulatory Guide 1.61 (Reference 9), with the exception of the NSSS primary coolant loop system and large piping. The values of damping h specified in Regulatory Guide 1.61 are normally considered to be somewhat conservative. Therefore, the design values are considered to be quite conservative, particularly at response levels of structures and equipment near failure levels. Very little actual test data exist at failure N
3-5
L
[
levels, particularly for structures. However, the damping values recom-mended in References 6,10 and 11 are considered representative. These
{ damping values for structures and equipment at or near yield are shown in Tables 3-1 and 3-2 in comparison with those used for design analysis for the SSE. In accordance with the recommendations in Reference 10, the lower levels of the pairs of values shown in Tables 3-1 and 3-2 are con-sidered to be lower bounds while the upper levels are considered to be essentially average values. The values of damping used for this evalua-tion were taken from Tables 3-1 and 3-2 assuming the upper level to be a median value except in the case of piping. Review of piping damping values derived from experiments support the use of higher values (Reference 11). Composite modal damping ratios were developed based on strain energy weighting for structures constructed of different materials.
For subsystems constructed of different materials, the damping ratio of the lowest damped material was used for all modes. This introduces some b conservatism in the response results for these subsystems. This was considered in the evaluation of their seismic capacities.
3.4.3 Load Combinations Load combinations on which the design of the Seabrook station Category I structures were based are shown in Tables 3-3 through 3-6 (Reference 1). These load combination criteria define a large number of load combinations that must be considered in design. For the reactor building structure and much of the equipment contained within the reactor building, these load combinations include a combination of a loss of coolant accident (LOCA) and the SSE loads. Random LOCA events have an extremely low frequency of occurrence as do seismic events such that the frequency of both events occurring simulaneously is so small that their inclusion is judged to be not important to the risk analysis results.
{
Seismically-induced LOCA loads are considered to have a higher i probability of occurring coincident with earthquake loads. Thus, the
- effects of seismic-induced LOCA loading on the LOCA mitigating systems L (high pressure injection and low pressure injection, including their 1
3-6 r l
electrical power, control systems and supporting structures) were investigated. The conclusions of this investigation regarding the k Seabrook plant are:
( l. For PWR's, the major portions of each of the mitigating systems is contained within the auxiliary building. Equipment within the auxiliary building is not affected by transient
[ , LOCA loads; thus, their corresponding fragilities L are unaffected by a LOCA. The only portion of
/ these mitigating systems which would be affected L . by a LOCA are piping runs from the containment penetrations to the NSSS connections. Generic piping fragility derivations for Seabrook have resulted in very high capacities; thus, transient LOCA loads much higher than the SSE would be required in order to significantly alter these piping fragility levels. During a small LOCA,
[. the high pressure injection line would be slightly affected by LOCA loading. The change in fragility is judged to be inconsequential to the overall
( safety injection system fragility which is greater than 2.0 g's.
- 2. The steam generator has the lowest median ground
[ acceleration capacity (1.71g's) of any of the Seabrook components which could cause a large LOCA. The only active components of the required LOCA mitigation system which are located in containment are motor-operated valves, which are qualified for a LOCA environment. It is judged that the valves subjected to LOCA effects will C have greater than 2.0g seismic capacity.
- 3. In addition to the equipment adjacent to the NSSS system, LOCA's affect both the containment building and the containment internal structure.
The LOCA increases the internal pressure stress on the containment building, while transient LOCA loads are distributed directly into the internal structure. The ground acceleration capacity
( levels for both of these structures has been shown in Section 4.2.1 to be 7.6g's or greater.
[
[
[
3-7
These capacity levels are so great that the inclusion of seismic-induced loads does not significantly alter the computation of the capacity.
Therefore, special consideration of LOCA loading combined with seismic events in the development of fragility descriptions is not required for the Seabrook risk models.
l 3.4.4 Modal Combination The Seabrook seismic design analysis was conducted on the basis of loads determined by the square-root-of-the-sum-of-the-squares (SRSS) method for both the NSSS and non-NSSS structures and equipment. Closely spaced modes were considered in accordance with USNRC Regulatory Guide l 1.92 (Reference 12). The grouping method of Reference 12 was used for closely spaced modes for the non-NSSS structures while the double sum l method was used for the NSSS analysis. Both of these methods are considered to give approximately median centered results. Although some frequency shifts are expected as structures approach failure, these shif ts in frequency are normally not large unless very high ductility
.I ratios exist. Also, the relationship between loads developed from individual modes may be expected to change once nonlinear response levels are reached. In the absence of a nonlinear analysis, the changes in the l modal ratios are unknown. For the seismic evaluation of Seabrook, it is assumed that the load response relationships between modes does not change j significantly once the structure reaches the yield point. For systems where most of the response results from one mode, this assumption intro-duces negligible possibility for error. For systems with a large number of modes with significant response levels, some additional uncertainty is I introduced. The resulting assumed dispersion is discussed in Chapter 4 for structures.
E l
3-8 I
3.4.5 Combination of Responses for Earthquake Directional Components In the Seabrook plant design analyses of both the NSSS and non-NSSS systems, the responses for the earthquake directional components '
were combined for structures and equipment by the SRSS of the vertical and two horizontal components. This is in accordance with USNRC Regulatory Guide 1.92 (Reference 12). This approach requires that the effects of two horizontal directional responses be combined with the vertical response, but does not require that the maximum response in each direction occur at the same instant as the maximum response in the other two directions. The SRSS combination of the three orthogonal components of response is considered to be essentially median centered so that no significant factor of safety exists for this aspect of the design. Some i
variability exists, however, and this is included in the evaluation of the individual structures and components.
( 3.4.6 Structure Modeling Considerations, In the seismic design analysis of Seabrook, multi-degree-of-freedom lumped mass models were developed for most of the seismic
{ Category I structures. For structures where the centers of mass and centers of rigidity were not coincident, three-dimensional models were developed in order to compute the torsional response of the structure.
Due to the synnietry of the containment building shell, a two-dimensional lumped mass was developed. Because of the high relative stiffness of the foundation rock, fixed-base models were used. Since the containment internal structures are not connected to the containment shell structure above the base slabs, the high rock foundation stiffness allowed uncoup-
{ ling of the shell and internal structures into two separate models.
Separate models were also developed for the vertical analytical models for many of the structures. The models developed for the Seabrook buildings are considered to be able to characterize the seismic response consistent with the current state-of-the-art of seismic analysis and do not appear to introduce significant degrees of either conservatism or non-conservatism into the results.
[
[
3-9
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 re-evaluate the modal responses. Another area where modified responses are considered is in the load distribution through diaphragms containing relatively large cut-outs. Neglecting the cut-outs typically overesti-mates the stiffness of the diaphragm and may consequently overestimate the seismic load calculated. For a single stick horizontal model, typically no diaphragm loads are computed. However, an estimate of the stiffness of the diaphragm with cut-outs, and, if necessary, in the
( f ailed condition, may be used to redistribute the seismic loads if redundant load paths are available, and hence provide a more realistic
[ ultimate seismic capacity. The details of these and similar evaluations necessary to account for changes between parameter design values and values more representative of seismic response levels near failure are
{ discussed in the following chapters.
[
3-10
[ TABLE 3-1 COMPARISON OF CRITICAL DAMPING RATIOS FOR
( DIFFERENT MATERIALS (NON-NSSS)
Percent Critical Damping Structure or Component Seabrook SSE Fragility Evaulation*
[ Design (Ref. 1) (Ref. 6, 10)
D Equipment and large-diameter piping systems, pipe diameter greater than 12 in. 3 5
[ Small-diameter piping systems, diameter equal to or less than 12 in. 2 5 I
L Welded steel structures 4 5 to 7 Bolted steel structures 7 7 to 15 E Prestressed concrete structures 5 7 to 10**
Reinforced concrete structures 7 7 to 10
( OLower values are considered to be approximately lower bounds; upper values are L considered to be essentially median centered ooWith no prestress left e
E 3-11
b
( TABLE 3-2 b COMPARISON OF CRITICAL DAMPING RATIOS FOR DIFFERENT MATERIALS (NSSS)
[
E Percent Critical Damping Seabrook SSE Fragility Design (Ref.1) Evaluation
( Structure or Component (Ref.6.10)
F Primary coolant loop system components L and large piping (12" Diameter and 4 5 greater)
( Small piping 2 5 Welded steel structures 4 5 to 7 Bolted and/or riveted steel structures 7 10 to 15
- Lower values are considered to be approximately lower bounds; upper
( values are considered to be essentially median centered.
[
t r
[
[
E 3-12 F ------
k TABLE 3-3 DESIGN FACTORED LOAD COMBINATIONS FOR
[ CONTAINMENT INVOLVING EARTHQUAKES (REF. 1) k .
(1) U =.1.0D + 1.3L + 1.0T o+ 1.5Eo + 1.0Ro + 1.0P y
{
(2) U = 1.00 + 1.0L + 1.25Pa + 1.0Ta + 1.25Eo + 1.0Ra + 1.0Rrr +
1.0Rrj + 1.0R rm (3) U =
1.0D + 1.0L + 1.0To + 1.0Ess + 1.0Wt + 1.0Ro + 1.0P y
[ (4) U =
1.0D + 1.0L + 1.0Pa + 1.0Ta + 1.0Ess + 1.0Ra + 1.0Rrr +
1.0Rr j + 1.0R m where D = Dead Load L = Live Load T = Normal Temperature o
Eo
= Operating Basis Earthquake Ro
= Normal Pipe Reaction Py = Pressure Variation
( P a
= Accident Pressure T
a
= DBA Temperature Ra = DBA Thermal Pipe Reaction Rrr = Reaction of Ruptured High Energy Pipe J R rj = Jet Impingement Loads .
( Rrm = Impact of Ruptured High Energy Pipe
( .
/
5
[
3-13
TABLE 3-4 I ALLOWABLE STRESSES AND STRAINS IN THE CONTAINMENT STRUCTURE (REF. 1)
I Concrete Factored Loads CompressiveStress(ff=3000 psi)
Membrane 1.8 ksi Membrane + Bending 2.25 ksi CompressiveStress(ff=4000 psi)
Membrane 2.4 ksi Membrane + Bending 3.0 ksi I
Shear Stress
- Radial CC-3431.4.1 Tangential CC-3431.5.1 Punching CC-3421.6 &
Code Case N-219 Reinforcing (fy = 60 ksi)
I Tensile Stress 54 ksi I
- Allowable shear stress does not exceed 40 psi and 60 psi for load combinations (2) and (4) respectively from Table 3-3.
I I
I I
3-14
[
[
TABLE 3-5 DESIGN FACTORED LOAD COMBINATIONS FOR
{ CONCRETE INTERNAL STRUCTURES INVOLVING EARTH 0VAKES (Ref. 1) b (1) U = 1.4D + 1.7L + 1.9Eg
{
(2) U = 1.05D + 1.28L + 1.28Tg + 1.43Eg+ 1.28R g (3) U = 1.0D + 1.0L + 1.25P a
+ 1.0Ta + 1.25Eg + 1.0Ra +
1.0R rr + 1.0Rp ) + 1.0R rm (4) U = 1.00 + 1.0L + 1.0Tg + 1.0E ss + 1.0R g l
(5) U = 1.0D + 1.0L + 1.0Pa + 1.0Ta + 1.0E ss + 1.0Ra +
l 1.0R rr + 1.0Rrj + 1.0R rm + 1.0M where: M = Internal Missile Loads All other loads defined as in Table 3-3 Stresses in accordance with ACI 318-71 Criteria I
I I
I I
I 3-15 I
L
[ l l
[
TABLE 3-6 DESIGN FACTORED LOAD COMBINATIONS FOR CONCRETE
{ STRUCTURES OTHER THAN CONTAINMENT & INTERNALS FOR LOADS INVOLVING EARTHQUAKES (Ref.1)
[.
(1) U = 1.40 + 1.7L + 1.9Eg+ 1.7H + 1.9H,
{
(2) U = 1.05D + 1.28L + 1.28T o+ 1.43E g+ 1.28H +1.43Hg+ 1.28R g (3) U = 1.20 + 1.9E g+ 1.7H + 1.9H, b (4) U = 1.0D + 1.0L + 1.25E n+ 1.0H + 1.25H, + 1.25P, +
1.0Ra + 1.0Rrj + 1.0R, + 1.0R rr + 1.0T, (5) U = 1.0D + 1.0L + 1.0Tg + 1.0Ess + 1.0H + 1.0H3 + 1.0R g
[ (6) U = 1.0D + 1.0L + 1.0E ss + 1.0H + 1.0Hs + 1.0P, + 1.0R,
+ 1.0Rrj + 1.0R m + 1.0R rr + 1.0M + 1.0T, where: H = Lateral Earth Pressure
{ H, = Earth Pressure due to OBE Hs = Earth Pressure due to SSE b All other loads defined in Tables 3-3 and 3-5 Stresses in accordance with ACI 318-71 Criteria E
[
E
{ 3-16
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4.
I STRUCTURES In this chapter, the median factors of safety and logarithmic standard deviations for the important structures are developed. Based on these factors of safety, median acceleration levels associated with g seismic failure are presented. For these structures, existing dynamic a models and response analyses were used to determine the median factors of safety and logarithmic standard deviations for each of the variables involved in calculating building response. All original analyses were based on linear response model results, but some seismic loads were modified to more closely approximate the expected inelastic response at the high acceleration levels expected for failure.
I 4.1 MEDIAN SAFETY FACTORS AND LOGARITHMIC STANDARD DEVIATIONS As discussed in Section 2.3, the seismic fragilities of struc-I tures and components are described in terms of the median ground accelera-tion, A, and random and uncertainty logarithmic standard deviations, B R
and BU . 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 estimate the median factor of safety, F, and variability parameters, B R and BU , based upon the original SSE stress I analysis than it is to directly estimate the fragility parameters. Thus, d=F*ASSE (4-1)
From the existing analyses of the important structures together with a knowledge of the deterministic design criteria utilized, median factors of safety associated with the SSE ground acceleration of 0.25g can be estimated. These are most conveniently separated into those 4-1
~
L E
f actors associated with the seismic strength capacity of the structure, the inelastic energy absorption factor, the factor associated with earthquake duration, and those factors associated with the expected building response. -
The factor of safety for the structure seismic capacity consists
[ of the following parts:
p 1. The strength factor, Fs , based on the ratio of u actual member strength to the design forces, p 2. The inelastic energy absorption factor, Fy ,
L related to the ductility of the structure.
- 3. The earthquake duration factor, FED, used to
[ account for the expected duration compared to that implicitly assumed in the determination of F.
y E .
Associated with the median strength factor, is ,and the median ductility
{ factor, I ,yare the corresponding logarithmic standard deviations, B 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 within a given structure. Factors of safety for the most important modes of failure are summarized in subsequent sections.
I The earthquake duration factor, FED, as stated in Section 3.3, L reflects the additional capacity due to the shorter duration and fewer number of strong motion cycles present in the Seabrook median expected earthquake as compared to the earthquake which would generate the number
{
of cycles used in the determination of Fy . Limited experimental data were available for the determination of F y . For the most part, the l
available data for reversed-load tests of reinforced concrete shear walls consisted of three to six or more cycles. As discussed in Section 4.1.3, for a median magnitude earthquake expected at the Seabrook site, one to three strong motion cycles are expected. FED accounts for the expected increase in F, due to the above-mentioned items.
4-2
[ The factor 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 j multiple seismic events. )
r- 2. Damping used in the analysis compared with L damping expected at failure.
- 3. Modal combination methods.
E 4. Combination of earthquake components.
r 5. Modeling accuracy.
L
- 6. Soil-structure interaction effects.
Based on the characteristics of lognormal distribution, median factors of safety and logarithmic standard deviations for the various contributing effects can be combined to yield the overall estimates. For instance, the capacity factor of safety of a structure, Fcap, is b obtained from the product of the strength, ductility, and duration factors of safety which, in turn, may include effects of more than one
[ variable.
{ F cap = sF xFp xF ED (4-2)
The methods of determining these safety factors are discussed in the following sections. The logarithmic standard deviation on capacity, Scap, is found by:
L S
cap " 8 s
+8 u +8 ED (4-3)
As discussed in Section 2.3, the logarithmic standard deviations are composed of both an inherent randonmess and uncertainty in the median value.
E 4-3 E
E Median factor of safety, F, and variability, SR and sg ,
[ estimates are made for each of the parameters affecting capacity and response. These median and variability estimates are then combined using the properties of lognormal distribution (Equations 2-10 and 2-11) and in
{ accordance with Equations 4-2 and 4-3 to obtain the overall median factor of safety and variability estimates required to define the fragility curve for the structure.
b For each variable affecting the factor of safety, the random variability, B ,Rand the uncertainty, S ,U must be separately
[ estimated. The differentiation is based on the following guidelines.
Essentially, SR represents those sources of dispersion in the factor of safety which cannot be reduced by more detailed evaluation or by gathering
{
more data. S R is due primarily to the variability of an earthquake time history and, therefore, of a structure's response when the earthquake is only defined in terms of the peak ground acceleration. BU represents those sources of dispersion which could be reduced only through better b understanding or more knowledge of the behavior of the item. S U is due to such items as our lack of ability to predict the exact strength of
[ materials (concrete and steel) 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 of plant specific data on fragility levels.
The variables which are related to the structure response can be b grouped into several main categories for which factors of safety and the logarithmic standard deviations may be combined in a similar manner.
[ Each of the f actors presented in Chapter 3 will now be discussed in more detail. To help in understanding the methodology involved, failure modes for the control and diesel generator building will be derived at the same
{ time.
[
4-4
E 4.1.1 Structure Capacity 7
The primary lateral load carrying systems of the Category I L
structures that were analyzed are of reinforced concrete construction with the exception of the condensate storage tank which is constructed
( fro'n stainless steel. The containment buildings and the containment enelosure buildings are cylirders with hemispherical heads. The
[ condensate storage tank enclosure is also a cylinder, but is open at the top. The rest of the structures are composed of shear walls (typically
{* i two to three feet thick) with diaphragms supported by structural steel beams and girders. All structures are separated from adjacent buildings 7 by standard three-inch gaps except for the control building and the diesel h generator building which share a connon wall.
Since the lateral load carrying systems are composed of rein-forced concrete, the two most important material strengths to determine
[ are those for the concrete and for the reinforcing steel. The determina-tions 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, ff. Concrete compressive strength used for design is normally specified as some value at a specific time from mixing (for example, 28 or 90 days). This value is verified by laboratory testing of mix samples.
[ The strength must meet specified values allowing a finite number of failures per number of trials. As previously stated, there are two major p f actors which justify the selection of a median value of concrete strength N above the design strength.
- 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.
4-5 V -_ ----- --
For the Seabrook structures, results of concrete compression tests are available (Reference 13). These tests consist of 28 day strength tests F and are divided into tests for the various mix numbers. Table 4-1 shows the average values and numbers of samples taken from each mix.
l As concrete ages, its strength increases. This must also be j accounted for in determining the median strength compared to the design strength. Figure 4-1 from Reference 14 shows the increase of the 5 concrete compressive strength with time assuming the concrete poured in I
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 l 50 percent which approaches 60 percent asymptotically. The factor relating the strength of aged concrete to the 28 day strength is, therefore, 1.2. No information is available on the standard deviation l
expected for aging. The estimated logarithmic standard deviation for j
aging is 0.10. For a small standard deviation, the median may te taken g as approximately equal to the mean. Thus, the factor relating median a compressive strength including aging effects to design compressive strength for the Seabrook structures varies depending on the design strength and mix number. The average factor for 4000 psi concrete is approximately 1.65 and 1.9 fo'r the 3000 psi concrete.
t.?
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 g increase in strength resulting from rate of loading at the seismic n response frequencies of the structures. Although experimental data on these effects are extremely 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 I
I 4-6 I
I 4.1.1.2 Reinforcing Steel Yield Strength I Grade 60 reinforcing steel was used throughout the construction of the structures. Information pertaining to the strength of the rein-forcing steel used in the structures was supplied by Reference 15. A sumary of this information is presented in Table 4-2. All structures other than the containment building used No.11 bars or smaller. There-fore, for ease in calculating member strengths, an overall median yield strength encompassing these sizes (No. 4 through 11) was calculated. It is also presented in Table 4-2.
Two other effects must be considered when evaluating the yield strength of reinforcing steel. These are the variations in the cross-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 I concrete compression.
4.1.1.3 Shear Strength of Concrete Walls Recent studies have shown that the shear strength of low-rise concrete shear walls with boundary elements is not accurately predicted by the ACI 318-77 code provisions (Reference 17). This is particularly true for walls with height to length ratios in the order of 1 or less.
1 Barda (Reference 18) determined that the ultimate shear strength of low-rise walls they tested could be represented by the following I relationship:
I I
- I g 4-7 I
I
'I Vu"Yc+Ys
= 8.3 ( -3.4 ( (hg/fg -0.5) + p f uy (4-4)
I where:
I Vu = Ultimate shear strength, psi Vc = Contribution from concrete, psi V
s
= Contribution from steel reinforcement, psi fc = Concrete compressive strength, psi hw = Wall height, in tw = Wall length, in ou = Vertical steel reinforcement ratio fy = Steel yield strength, psi I The contribution of the concrete to the ultimate shear strength of the wall as a function of hg/t, is shown in Figure 4-2. Also shown I in Figure 4-2 are the applicable test values (References 18 through 21) and the corresponding AI 318-17 formulation. The tests included load reversals and varying reinforcement ratios and hg /tw ratios. Web crushing generally controlled the failure of the test specimens. Testing was performed with no axial loads, but an increase in shear capacity of N/41) was recommended, where N is the axial load in pounds, and h is the wall thickness in inches.
- I l
I 4-8 l
I
L The contribution of the steel to the ultimate shear strength according to ACI 318-77 is: ,
Vs"#fhy (4-5) where ph = horizontal steel reinforcement ratio.
Furthermore, one of the conclusions reached by Oesterle (Reference 21) is that for low-rise shear walls (specificallywh w/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 range of 0.5 < hw /2, < 2. Test data from the above references were used. The effective steel shear strength was assumed to be in the form:
Vse = AVsu + BVsh (4-6) where A, B are constants and l
l V = vertical steel contribution to shear su " Puy f
strength V
sh
- Phy f =
horizontal steel contribution to shear
" strength 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 shown to be:
6 I
4-9
A=1 B=0 h,/Eg < 0.5
=-2.0(hgt)+2.0 y = 2.0 (hg /y t ) - 1.0 0.5 s hg /I g s 1.0
=0 =1 1.0 s hg /ig and the median ultimate shear strength is given by:
E Vu"Vc+Vse
=8.3%-3.4( hg /t g -0.5 + 4gN , f se y where pse = Aou + Bo bwith A and B determined as shown above.
Based on an evaluation of the same experimental data, the I
l logarithmic standard deviation was calculated to be 0.15.
4.1.1.4 Example of Shear Wall Failure in Shear l A plan view of the control and diesel generator building is shown in Figure 4-3. The east wall governs the shear capacity of this building.
l This wall is two feet thick. The vertical reinforcing consists of No. 11
, bars every 12 inches on each face while the horizontal reinforcing con-sists of No.10 bars every 12 inches on each face. The design concrete g compressive strength was 3000 psi. From Table 4-1 and using the aging 3 factor of 1.2 mentioned in Section 4.1.1.1, a median concrete compressive strength of 5700 psi was calculated. From Table 4-2, the reinforcing steel yield strength is 69.8 ksi. The wall length is 90 feet. The effective wall height is the base moment for this wall divided by the wall's base shear. This gives an effective height of 42.5 feet. Since i
4-10
hw/1w < 0.5, the steel's contribution to shear strength is assumed to come only from the vertical reinforcing steel. Thus, the concrete shear strength is:
v
/42.5 c = 8.3 /5700 -3.4 /5700 (tyg g - =0.5) 634 psi = 91.3 ksf
(. The steel shear strength is:
v (69.8ksi) s= l, 144 1= 108.9 ksf The contribution due to axial load is typically very small and is usually neglected since the load is rarely known. Therefore, the ultimate shear capacity of this wall is:
[
Vu = (91.3 + 108.9) (2') (90') = 36,000 k The shear due to the design SSE is 7210 k. This gives a shear strength factor of 5.00. The variability due to randomness is negligible because the strength of the wall is independent of seismic events. The variability due to uncertainty is estimated to be 0.16 based on a steel strength variability of 0.04, a concrete compressive strength variability of 0.17, and an equation variability of 0.15. Thus, 0.04 (108.9)+(0.2 (91.3) 2 8 + Od5 = Od6 0= (108.9 + 91.3)2 Note that the concrete variability is divided by two. This is due to the concrete strength being a function of the square root of the concrete compressive strength.
4-11
I 4.1.1.5 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 I 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 small. The total moment capacity of reinforced concrete shear walls in flexure under in-plane I forces is then:
1 M= 2 1+Afy 1- +A chfy d-(4-8) where:
I c = Depth to neutral axis from extreme compression fiber As = Area of distributed steel Ach = Area of chord steel t
w = Wall length fy = Steel yield strength N = Axial load d = Distance from the extreme compressive fiber to the centroid of tensile chord steel 8
3
= Ratio of depth of equivalent rectangular
'E concrete stress block to depth to neutral 5 axis (c) i I
3 4-12 I
I 4.1.1.6 Example of Shear Wall Failure in Flexure I The west wall of the control and diesel generator building governs the flexural capacity of this structure. This wall is two feet l
l thick. The vertical reinforcing consists of No. 9 bars every 12 inches on each face. The overturning moment will be resisted by not only the west wall, but also by some of the north and the south walls acting as flanges. Reference 22 presents a procedure by which the effective flange width may be estimated. For this problem, an effective flange width of 13 feet (exclusive of the west wall thickness) is calculated. The neutral axis is contained within one of these flanges while the other I flange provides the chord steel. The vertical steel reinforcement in the flanges is No. 9 bars every 12 inches on each face.
From balancing the tensile and compressive forces, c = 1.645'.
The values used for the rest of the variables are as follows:
As =
2 (1.00 in2/ft) (90') = 180.0 in2 Ach =
2(1.00in2/ft) (13') = 26.0 in2 t
w = 90' fy = 69.8 ksi N = 0 (as with the shear strength) d =
90'-f(2')=89'
' =
B i 0.85 - 0.05 (5700 - 4000)/1000 = 0.765 E Using these values in Equation 4-8, the ultimate moment capacity for this wall is 718,000 k-ft. The moment derived from the design SSE is I 246,000 k-ft. The flexural strength factor is thus 2.92. The variability due to uncertainty is estimated to be 0.18 based on a steel strength variability of 0.04, an equation variability of 0.10, and a flange-width uncertainty of 0.15. Thus, I
4-13 5
2 B
U= 0.04* + 0.10* + 0.15 = 0.18 Note that there is no variability due to concrete strength in this B - U
( If the concrete strength was only half the calculated median value of 5700, the effect would be to roughly double the depth to the neutral axis, c. This, in turn, would lower the ultimate moment capacity by about one percent. Therefore, the concrete strength has no significant i impact on the ultimate moment capacity. l 4.1.2 Structure Ductility A much more accurate assessment of the seismic capacity of a j structure can be obtained if the inelastic energy absorption of the
[ structure is considered in addition to the strength capacity. One 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 acceleration region of the spectrum (i.e.,
approximately 2 Hz and above), Figure 4-4 from Reference 7 shows the deamplification function for several damping values as a functon of the ductility ratio.
4-14
i l
Actual tests on walls show that there is a wide spread in the l- amount of ductility present in any given wall. For example, Reference 23 perfonned tests with load reversals and obtained ductilities of 2 to 10.
Reference 24 allows a ductility of four for reinforced concrete shear j l walls in a bearing wall system. A ductility of 4 was used in these analyses for simple one- or two-story systems, and 3.5 was used for more l complex systems. When a ductility of 4 was used, the variabilities were estimated to be (Bu )R = 0.15 and (S p )g = 0.45. When a ductility of 3.5 l was used, (8p)R = 0.15 and (8 9 )U = 0.40 were estimated for the variabil-ities. The uncertainty was judged to be much higher than the randomness because the ductilities are derived for strong motions with at least 3 g strong cycles, and it is felt that the ductility will not vary by much B for any earthquake meeting these requirements.
l 4.1.2.1 Example of Inelastic Energy Absorption Factor l Figure 4-4 presents the ductility, p, versus the response spec-trum reduction factor, tu, for different damping values. The inelastic energy absorption f actor is then 1/4 y For the control and diesel l
generator building, a ductility of 3.5 and a damping value, 8, of 10 percent of critical were used. From Figure 4-4:
l q = 3.008-0.30 = 3.00 (10)-0.30 = 1.504 l
p = q + 1 = 2.504 l
r = 0.488-0.08 = 0.48 (10)-0.08 = 0.399 l
F y =f=(pp-q)r,~2.504(3.5)-1.504.
p .
0.399 = 2.21 I
, 4-15 i
l l
p p It can be shown that the effect of (S )R and (S )U On *u can be I represented by:
B rpu 8
4, pu-4 f u)R l
B /0 rpu l
\ _
l pu-4 u)g
' 4W }U ^
l For u = 3.5, (S p)R = 0.15 and (S p)U *" #"' ""
tuR" l (Bey) = 0.19. There are no other factors to take into account for randoraness, so BR " (64uR
= . . H wever, ee s an equadon uncertainty of an estimated 0.10 that must be combined with (84 )g to produce UB . Therefore, the total uncertainty on F is l
B U= 0.19 + 0.10 = 0.21 1
I l
4.1.3 Earthquake Duration The basis for this factor, as previously stated, is the expected increase in capacity due to the median expected earthquake being of less duration and lower energy content than that from which the ductility B
f actor was developed. The median expected earthquake has a Richter l magnitude of 5.8. Earthquakes of this size typically have a duration of 7 to 9 seconds and 1 to 3 strong motion cycles with an average of 2 l cycles. It is felt that the lower bound on the duration f actor is 1.0 and the upper bound is 3.0. This means that the expected median earthquake would have to be scaled by a factor between 1.0 and 3.0 in order to have the same damage potential as an earthquake with 3 to 6 cycles with both earthquakes having the same unscaled peak ground acceleration. This factor has an estimated median of 1.4. Note that B 4-16 1
I with lower and upper bounds of 1.0 and 3.0, respectively, this distribu-tion is not lognormal. However, since the region between 1.4 and 3.0 is of no concern, the variabilities were determined ac if it is a lognormal distribution, at least around the region 1.0 to 1.4. It was assumed that there is only a five percent chance of the actual factor being less than 1.0 and that this prediction is made with 95 percent confidence.
Therefore, 1.0 = 1.4 exp(-1.65FR) exp(-1.658)
U =1.4{exp[-1.65(B+8(f RU I Thus, BR+OU = 0.20. This factor is mainly an earthquake-dependent factor, but with a good deal of uncertainty, so BR was set to 0.12 with By set to 0.08.
I This factor is only used for failures that are ductile in nature. Brittle failures rely only on the acceleration reaching a given level. This level can theoretically be obtained in both large and small magnitude events.
I 4.1.4 Spectral Shape, Damping, and Modeling Factors As previously discussed, the important Seabrook structures were designed using the ground response spectra shown in Figure 1-1. For the design SSE, seven percent of critical damping was used for the reinforced I concrete structures. For the reinforced concrete comprising the lateral load carrying structures for Seabrook, ten percent of critical damping is considered to be the median value expected at response levels near failure (Reference 10). The frequencies of interest for the Seabrook structures are in excess of 4 Hz. As is evident from Figure 3-1, the response of these structures using the ten percent damped median centered response spectrum for rock sites is less than the seven percent damped design spectum at all frequencies below 27 Hz. For the Seabrook structures, only the frequencies were known so that the spectral shape I f actor of safety for the individual structures was calculated based on
- I 4-17 I
1
I the fundamental frequency. Basing this factor on the ratio of the spectral acceleration of the design spectrum to that of the site-specific l spectrum at the fundamental frequency is usually sufficient inasmuch as almost all of most structure's response is due to vibrating at the j fundamental frequency. The spectral shape factor of safety is represented by: i l
D F
c = 7%
33 - 3
' M c = 10%
l where S0c = 7g represents the 7 percent damped design spectral acceleration and S
M E " * "" "" * * * *E' # # #* ""# " ** #*
c = 10%
j the median site-specific response spectrum for 10 percent damping.
In computing the spectral shape factor of safety, it is g convenient to combine the damping and ground response spectrum effects.
5 In the development of logarithmic standard deviations on spectral shape, I
however, it is informative to consider the damping effects separately.
This implies a factor of safety of unity on damping alone since it has l already been included in the ' factor of safety on spectral shape.
I The logarithmic standard deviation on spectral acceleration, l
834, may be estimated from References 8 and 10. Reference 8 provided the mean site-specific spectrum and associated variabilities for five percent damping. It also presents a procedure by which mean spectra at other damping values could be calculated, but does not give the variabil-1 ities for these other spectra. These variabilities were estimated with the aid of Reference 10.
l l
l l
4-18
The deviation on spectral acceleration resulting from damping, Bg , can be estimated from:
[bMC " 7y" )
8 = En (4-10)
N
{ c=10%/
l 1
where SM = 7%
is the spectral acceleration from the median site-specific spectrum at seven percent damping, and SM = 10%
- E' * * * *~
tionfromthetenpercentdampedmediansfte-specificspectrum. Seven percent damping is estimated by Reference 10 to be one standard deviation below the median damping value of ten percent.
The modeling factor of safety is tsually taken to be unity.
Among the items that would change this are:
- 1. Story stiffnesses that did not compensate for large openings and are, therefore, too stiff; and
- 2. Diaphragm stiffnesses used to connect the various sticks in a multi-stick and lumped mass model that also do not account for openings.
Variability in modeling predominantly influences the calculated mode shapes and modal frequencies. Since the concrete strength and, consequently, the stiffness of the structures is above the design values, calculated frequencies would be expected to be somewhat less than actual values, at least for low to moderate levels of response. At response levels approaching failure, softening of the structures due to concrete cracking occurs, and for structures analyzed using uncracked section properties, some decrease in the actual frequencies compared to the calculated values is expected. As can be seen from Figure 3-1 for frequencies in the 5 to 9 Hz range and greater than 20 Hz, the response 4-19
l l
accelerations are fairly constant so that a small shift in frequency does I
l not result in much change in amplitude. Between 8 and 20 Hz, an increase
{
in frequency results in a decrease in amplitude. Calculated frequencies and mode shapes were assumed to be median centered unless material I properties used in the original analyses differed from the material properties calculated from test data enough to change the calculated l frequencies by at least 15 percent. The new frequencies were calculated based on the new material properties. The mode shapes were assumed to stay the same.
Modeling uncertainties from both the mode shapes and modal frequencies enter into the uncertainty on calculated modal response as defined by Sg . Thus, l
B l S g = fBk + Bhp (4-11)
B l
where Bg3 and BMF are estimated logarithmic standard deviations on structural response of a given point in the structure due to uncertainties g in mode shape and due to uncertainties in modal frequency, respectively.
3 Based upon experience in performing similar analyses, B MS is estimated I to be about 0.10. The modal frequency variability shifts the frequency at which spectral accelerations are to be determined, so that:
l B
)
M f,f)
EMF " E" (4-12)
(sM f,f M
E where fM is the median frequency estimate, and f 6 is the 84 percent exceedance probability frequency estimate. The logarithmic standard deviation on frequency is estimated to be approximately 0.20 for the structures.
4-20 E
4.1.4.1 Example of Spectral Shape, Damping, and Modeling Factors The fundamental frequency of the control and diesel generator building for the N-S direction was calculated to be 5.69 Hz (Reference 1).
The spectral amplification factor from the seven percent damped design spectrum at 5.69 Hz is 2.42. The spectral amplification factor from the ten percent damped site-specific spectrum at 5.69 Hz is 1.77. These amplification factors are obtained from Figure 3-1. Their ratio gives F33 = 1.37. The variability due to randomness is estimated to be 0.24 at this frequency. The variability due to uncertainty is estimated to be i
% of S R, or 0.08.
For damping, the spectral acceleration from the seven percent damped site-specific spectrum is 1.96. Therefore, 9
8g = En 7
= 0.10 Bg needs to be broken down into BR and 80 which are judged to be equal to each other.
Since 8g is an SRSS combination of SR and BU '
BR*8U*, Bz = 0.07 The model of the control and diesel generator building is judged to provide a median-centered representation of the structure response, so FM = 1.0. To calculate BMF' f8 (Equation 4-12) is 6.95 Hz. The spectral amplification factor from the ten percent damped site-specific spectrum at 6.95 Hz is 1.81. Thus, e
/1 81 gg = en p = 0.02 4-21
When combined with e gg, 8g=V0.02*+0.10*=0.10 4.1.5 Modal Combination The seismic design analysis of Seabrook structures was performed by response spectrum analysis; therefore, phasing of the individual modal responses was unknown. Most current design analyses are normally con-ducted using response spectra techniques. The current recomended prac- i tice of the USNRC as given in Regulatory Guide 1.92 (Reference 12) is to combine modes by the square-root-of-the-sum-of-the-squares (SRSS). This was the methodology used in the Seabrook 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 25) shows the actual time history calculated peak response versus SRSS combined modal responses for structural models with four predominant medes. Based
( upon these and other similar results, it is estimated that for ten percent structural damping, the SRSS response is median centered.
Therefore, FMC = 1.0 for Seabrook structures.
Where individual modal responses are known, the absolute sum of these responses can be used to estimate the coefficient of variation.
The absolute sum is an upper bound considered to be three standard
( deviations above the median SRSS response. Where the individual modal responses are not known, past experience with structures where one mode predominates indicates that the coefficient of variation is on the order of 0.05.
4-22
I 4.1.6 Combination of Earthquake Components I The design of the Seabrook structures was based on the current recomended practice of combining the responses for the three principal directions by the SRSS method. Alternatively, it is recomended (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.
The effect of SRSS combination of three components compared to g
the direct addition of two depends on the relative magnitudes of the two m horizontal load components together with the vertical component and the geometry of structure. For instance, if the two horizontal load components are approximately equal, and the vertical component is small, the SRSS method results in an increase in stress of from approximately 40
- percent for a square structure to 0 percent for a circular structure.
Combining the effects by the 100, 40, 40 percent method for the same case results in the same 40 percent increase in stress for a square structure as for the SRSS method and an increase of approximately 8 percent for a circular structure, such as the containment structure.
lI i
l Depending on the geometry of the particular structure under l consideration together with the relative magnitude of the individual load or stress components, the expected variation in stresses due to the 100, 40, 40 percent method of load combinations is from -5 to +10 percent when compared with the original design method. For shear wall structures where the shear walls in the two principal directions act essentially I independently and are the controlling elements, the two horizontal loads do not combine to a significant degree except for the torsional coupling.
,I Thus, only the vertical component affects the individual shear wall stress. A moderate amount of vertical load slightly increases the ultimate shear load carrying capacity of reinforced concrete walls.
However, there is an equal probability that the vertical seismic component will add to or subtract from the deadweight loads at the time of maximum horizontal loads. Thus, while the dead load is usually 4-23
- I
included in the analyses, the vertical seismic component is ignored.
Consequently, the factor of safety is not strongly influenced by the directional component assumptions.
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, assumed to be three standard deviations
{
above the median. Lacking the individual components, BR is assumed to be 0.05.
C 4.1.7 Soil-Structure Interaction Effects
( 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 soil and the dissipation of energy into the soil by radiation (geometric) damping. For structures founded on competent bedrock such as the
{ Seabrook 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 structures founded directly on the bedrock, essentially no amplification b occurs, and the motion is normally specified at the foundation level as was done in the design of the Seabrook structures. Thus, the design of
(, the structures at Seabrook was conducted using current state-of-the-art assumptions and methods of analysis in regard to the soil-structure interaction effects.
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 building 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 4-24 f -
[ occur. So long as significant rock or concrete crushing does not occur, relative motion sufficient to cause piping or electrical conduit failure is not considered a possible failure mode. The bedrock at the Seabrook site is considered to be of adequate strength to preclude failures resulting from base slab uplift.
[ 4.2 CONTAINMENT BUILDING The containment building is a reinforced concrete upright cylinder with a hemispherical dome roof. It is supported on a reinforced
{ concrete foundation mat which is keyed into the bedrock by a depression for the reactor pit and by continuous bearing around the periphery of the mat . The inside diameter of the cylinder is 140'-0". The cylinder wall thickness is typically 4'-6" including the /e" 3 thick liner. The dome thickness is 3'-6s/8" including the 1/" 2 thick liner. The foundation mat is
, 153'-0" in diameter with a thickness of 10'-0".
The containment wall is reinforced with No. 18, Grade 60 reinforcing bars at the inner and outer faces, each consisting of one
{ meridional and two hoop layers. Below Elevation (-)15'-0", there are two additional meridional layers on the inner face to resist discontinuity moments and radial shears caused by the restraint on the cylinder at the cylinder-base mat connection. There is also an orthogonal set of bars inclined at 45 degrees to the horizontal on the outer face. This set is provided to resist in-plane seismic shear forces and membrane tension from other loads. Where there are large openings in the cylinder, the bars are continued around the openings without interruption. No main reinforcement is terminated at any opening.
The liner plate is carbon steel conforming to ASME SA 516, Grade
- 60. It is provided with an anchorage system that will maintain leak tightness in the event of accidents. The anchorage system consists of vertical tees spaced every 20 inches around the circumference of the cylinder wall. The webs of the tees are welded to the liner plate with
]
continuous fillet welds.
7 4-25
I l
A number of structures important to safety are located within the containment. Among the most critical to seismic response are the reactor support system and the primary and secondary shield walls. The I internal structures are supported on and anchored to a 4-foot thick fill I
mat which is not anchored to the containment base mat. The internal structure is separated from the containment wall by a minimum 0.5" gap.
l Potential damage due to impact between the internals and the containment wall was considered in this analysis.
1 4.2.1 i
Containment Failure Modes The lowest level significant failure mode for the containment structure is failure of the wall due to flexure at Elevation (-)9'-0".
The median peak ground acceleration capacity is estimated to be 7.69 I
Median factors of safety and their variabilities are reported in Table 4-3. Four other failure modes were considered: failure due to shear, l failure due to impact, and failure of the internals due to flexure and shear.
l Failure of the containment due to shear is also critical at Elevation (-)9'-0"; however, the structure is stronger in shear than in flexure. The median ground acceleration capacity for shear is estimated to be 8.89 The factors of safety and variabilities for this failure I mode are presented in Table 4-4.
I l Containment impact was evaluated at three locations: one involving the internal structure and two involving the enclosure l building. These latter two will be discussed in the section pertaining to the enclosure building since any potential damage is to it and not to the containment building. The location of greatest concern for impact between the containment and the internal structure is at Elevation 25'-0" on the south side. There is a 0.5" seismic isolation gap between the two l
structures at this level. An estimated median peak ground acceleration of 1.09 is required to close this gap. It is expected that higher accelerations will lead to some penetration of the containment wall, 4-26 I
I o
L
[ but that the penetration will be insufficient to cause the liner to break. Spalling off the outer face of the containment wall is not considered possible since the collision velocity and penetration appear to be less than those required to cause spalling.
Failure of the concrete internal structure is expected at higher accelerations than the containment. The internal structure is a massive structure with a dead load equal to a third of the dead load of the containment. The primary shield wall was checked for both flexure and shear. For flexure, the factor of safety on strength is estimated to be 13.6; for shear the factor is 7.78. Note that both of these factors are greater than the strength factor of 7.28 reported in Table 4-3. The other factors for the primary shield wall would be the same as those listed in Table 4-3.
[ 4.3 CONTAINMENT ENCLOSURE BUILDING The purpose of the containment enclosure building is to provide
( leak protection for the containment and to protect it from certain loads such as wind loads and tornado loads. Due to its presence, there are also no dynamic soil effects on the containment.
{
The enclosure building has the same shape as the containment building. The inside diameter is 158'-0", and the wall varies in thickness from 15 inches above Elevation 45'-6" to 36 inches below Elevation (-)11'-0". The hemispherical dome roof is 15 inches thick.
The space between the containment and the enclosure building varies from 4'-6" between the cylindrical sides to 5'-6" between the domed roofs.
The enclosure building wall is supported on a spread footing that is
{ 10'-3" wide by 10'-0" deep. This footing abuts the containment base mat, but the two are not connected except by water stops. Everywhere else, the two structures are separated by at least 3 inch gaps.
4-27
4.3.1 Containment Enclosure Failure Modes Three failure modes were considered for this structure: failure of the wall due to shear and flexure and failure due to impact between this structure and other buildings. The lowest level failure mode is due to impact between the containment building and a concrete shield located at Elevation 49'-6" on the northwest face of the enclosure building. It is estimated that a median ground acceleration of 4.1g is necessary to initiate spalling of the outside of the containment enclosure. This failure mode is only a local failure and will not damage any safety-related equipment. The lowest level significant failure mode is failure of the wall at the base due to shear. The median peak ground accelera-tion capacity for this mode is estimated to be 8.29 Table 4-5 presents I the factors of safety and related variabilities for this failure.
Failure due to flexure has a median capacity of 10.4g. The median f actors of safety and their variabilities are listed in Table 4-6. In comparing the flexural capacity of the enclosure building to that of the containment building (Table 4-3), the main difference is in the strength factor. The fact that the strength factor is larger for the enclosure building does not mean that the enclosure building can withstand a greater overturning moment than can the containment building. At the critical sections in both buildings, the containment building can withstand a moment that is 78 percent greater than the maximum moment for I the enclosure building. However, the containment building is required to withstand a moment that is 2.54 times the moment required to be taken by the enclosure building. Hence, the strength factor, which is the ultimate moment capacity divided by the SSE moment, is greater for the g enclosure building by a f actor of 2.F/1.78 or 1.43.
1 Although an impact failure capacity of 4.lg has been discussed, 8 it is possible that due to phasing and directional components, impact will not occur at the shield at Elevation 49'-6". Thus, impact was also checked at Elevation 22'-0" where there are concrete shields on the east 4-28 I
1 and west faces of the enclosure building. A peak ground acceleration of ;
9.59 is necessary just to close the three inch gap at this level. Impact of the fuel storage building roof at Elevation 84'-0" against the enclo-sure building was also considered. To close the gap at this level, a peak ground acceleration of about 7.29 is necessary. This acceleration, however, is greater than the acceleration needed to cause significant f ailure in the fuel storage building. Therefore, this impact mode cannot I occur.
4.4 PRIMARY AUXILIARY BUILDING The primary auxiliary building is a four-story structure which contains such equipment as heat exchangers, pumps, demineralizers, filters, tanks, and ventilation equipment. The residual heat removal (RHR) equipment vault is located north of and shares a wall with the primary auxiliary building. The vault contains containment spray pumps, residual heat removal pumps, and heat exchangers. The main portion of I the auxiliary building is 79 feet wide,145 feet long, and extends from a maximum of 46 feet below grade to 88 feet above grade.
4.4.1 Primary Auxiliary Building Failure Modes Two failure modes were considered for this structure: failure of j the shear walls due to shear and due to flexure. Failure due to flexure is the lowest level significant f ailure mode with a median peak ground
,I acceleration of 2.69 The median factors of safety and their variabil-i g ities are given in Table 4-7. This f ailure mode pertains to the north W wall. Since this is the common wall with the RHR vault, this 2.69 acceleration can also be considered as the median capacity for the vault.
I
} Failure due to shear, the other failure mode that was analyzed, is not expected until the peak ground acceleration reaches 4.09 This j f ailure mode pertains to the south wall. Table 4-8 presents the safety f actors and variabilities for this failure mode.
I 4-29 I
{ .
i 4.5 SERVICE WATER PUMPHOUSE AND CIRCULATING WATER PUMPHOUSE G The service water pumphouse (SWPH) is a two-story structure that _
contains the service water pumps and screen wash pumps. The reinforced q
concrete basin under the SWPH is approximately 91 feet wide by 74 feet long. It extends from the operating floor 1 foot above grade to 63 feet below grade. The SWPH itself is approximately 118 feet wide by 78 feet a long and extends 28 feet above the operating floor. An electrical .
equipment room is attached to the west end of the building. .
The circulating water pumphouse (CWPH) is attached to and shares -
( a foundation with the SWPH. The concrete basin under the CWPH is
- approximately 110 feet wide by 123 feet long and extends to the sam'e depth as the SWPH basin. The CWPH itself is non-Category I and consists
{ of a steel frame covered with metal siding. It is approximately 119 feet '
wide by 123 feet long and extends 28 feet above the opere, ting floor. .It contains the circulating water pumps and screen wash pumps.
( Water is supplied to the CWPH by means of an intake tunnel bored through the bedrock at a depth of 150 to 250 feet below sea level. The .
[ tunnel is 19 feet in diameter and extends for over three miles. At a minimum, the tunnel is supported by patterned rockbolts. Where more support is needed, due to the presence of faults, diabase dikes, or closely spaced joints, 6- to 8-inch steel ribs at 2.5 to 5 foot intervals are used. The tunnel connects to a transition structure by means of a 200-foot vertical shaft. At this structure, the flow is separated into four sections and channeled into the CWPH basin via a flume.
4.5.1 Service Water Pumphouse Failure Modes
[ The lowest level significant failure mode is flexural failure of the shear walls due to N-S motion. The median peak ground acceleration is estimated to be 2.19 The median factors of safety and their varia-
{ bilities for this mode are listed in Table 4-9.
4-30
[ _- -
Due to the number of openings in the SWPH roof, its capacity was also analyzed. It was found to be slightly stronger than the shear walls, requiring a median peak ground acceleration of 2.4g to cause failure.
This type of failure is expected to be a local failure. It would not greatly affect the overall building response and would only cause damage to that equipment located imediately beneath falling debris. The median safety factors and variabilities associated with this failure are presented in Table 4-10.
The lowest significant failure for the CWPH-flume-transition siructure-intake tunnel system occurs in the intake tunnel. The intake tunnel capacity is based on the past behavior of tunnels during the San 5 Fernando earthquake of February, 1971, and during weapon tests at the l Nevada Test Site. It is estimated to have a median peak ground accelera-tion capacity of 4.6g with a variability due to uncertainty of 0.39 and a variability due to randomness of 0.49. The median was derived by comparing past ground velocities due to weapon tests at different stress regions in the rock to the damage in nearby tunnels. In a stress region of about 8700 psi, tunnel collapse has been fairly universal; at about 1800 psi, there has been almost no damage. The ground velocities at these points are 50.2 fps and 10.7 fps. The maximum ground velocity of
!I an earthquake was assumed to be 2.5 fps /1.09 The weapon test velocities were divided by two to try to correlate the pulsive blast accelerations to cyclic earthquake accelerations. These scaled velocities were then assumed to be the +28 and -28 bounds on the capacity. The variability due to uncertainty reflects the unknown rock strength while the variabil-j ity due to randomness contains the variabilities associated with the 2.5 fps /1.0g earthquake ground velocity and the factor of two used to scale j the weapon test ground velocities. This caoacity is based on the tunnel I
not having experienced rockfalls or showing signs of creep. If any of these assumptions is not correct, the tunnel capacity could be greatly diminished.
I 4-31 I
b
(
4.6 SERVICE WATER COOLING TOWER The cooling tower is a rectangular building approximately 300 by 54 feet in plan, extending 28 feet below grade and rising 57'-6" above grade. It serves as the ultimate heat sink in the event that the cooling
{
water tunnels are rendered inoperative. The cooling tower contains pumps, f ans, and a water distribution system. The water level in the tower is 16 feet above grade. The switchgear rooms that are attached to the east and west ends of the cooling tower are approximately 54 by 26 feet in plan and are located below the mechanical equipment rooms. They contain the switchgear, substation, and motor control center for the cooling
( tower.
4.6.1 Cooling Tower Failure Mode
( Two failure modes were investigated for this structure: flexural failure of the shear walls due to in-plane dynamic loads and due to out-of-plane hydrodynamic loads. Shear failure of the walls does not appear to be likely. Failure of the roof is considered most likely in the area between colu:r.n lines D to K. Failure of the roof in this region will not damage any equipment nor- affect the overall capacity of the
( structure. Flexural failure of the outside switchgear walls due to N-S motion is predicted at a median peak ground acceleration of 2.4 9 . The factors of safety and their variabilities for this failure mode are
( presented in Table 4-11.
Failure of the north and south walls above grade (El. 22'-0")
due to out-of-plane hydrodynamic forces was also analyzed. Depending on how f ailure is defined, different capacities can be calculated. For instance, if it is vital that very little, if any, water be allowed to
[ leak out, then the capacity must be based on the pressure that causes the wall to crack near grade. This capacity is estimated to have a median
{ peak ground acceleration of 0.74g with su = 0.43 and BR = 0.10. On the other hand, if larger amounts of water can be lost and failure is defined as the wall reaching its ultimate capacity, then the median peak ground acceleration is expected to be 3.75g with 80 = 0.24 and 4-32
SR = 0.20. Note that if it is possible for the water level to drop to Elevation 22'-0" without impairing any other safety-related function, then this failure mode becomes irmiaterial.
4.7 CONDENSATE STORAGE TANK AND ENCLOSURE c The condensate storage tank is a cylindrical stainless steel L tank with a diameter of 42'-0" and a height of 42'-7". It has a spherical dome roof that has a 42'-0" radius and rises almost 5'-8" above
( the tank. The tank walls vary in thickness from 0.500 inch at the base to 0.188 inch at the top. The roof is 0.455 inch thick. The bottom
{ plate is 0.25 inch thick. It connects to the tank wall through a 0.800-inch footer plate that extends 4.75 inches inside the tank and 7.25 inches outside the tank. There are 46 anchor bolts spaced typically at 8 degree intervals around the tank. These bolts have a diameter of 1.75 inches and are made from SA 193, Grade B7 steel. The tank'sf:apacity is 400,000 gallons.
The tank is enclosed in a reinforced concrete cylinder, 42'-11" in diameter, 2' thick and 42'-10" high. It surrounds the tank from the l base up to the springline and provides protection from horizontal tornado-generated missiles. It is capable of retaining the tank contents should the tank be ruptured.
4.7.1 Tank and Enclosure Failure Modes l
The lowest level f ailure mode is for the welds connecting the anchor bolt chairs to the tank to yield in tension; thus, permitting that l side of the tank to lift up and causing the bottom plate to bend. The weld connecting the footer plate to the bottom plate lies between the j edge of the tank and the point at which the plastic hinge will form; thus, causing bending across the weld. Since this weld is only a single lap fillet weld, this weld is expected to fail with loss of the tank contents through the base. The median peak ground acceleration for this failure is estimated to be 1.09 Failure of the tank, however, does not mean f ailure of the system since the contents will simply flow into the enclosure. At most, the water level in the tank would drop about 1.5',
4-33
leaving outlet nozzles still below the water level. Failure of the enclosure is not expected below a peak ground acceleration of 4.29 The f actors of safety and the variabilities for this failure mode are listed in Table 4-12. Note that the two factors dealing with ductility, the inelastic energy absorption f actor and the earthquake duration and cycles f actor, are absent from this table. The reason for this is that failure of the enclosure is defined to be that point at which the concrete begins to crack. This point is well below the yield point of the reinforcing.
4.8 CONTROL AND DIESEL GENERATOR BUILDING The control and diesel generator bulding is a rectangular struc-
{ ture approximately 233 feet long by 90 feet wide. A 4-foot thick wall separates the 138-foot long control building on the east side from the 95-foot long diesel generator building on the west. The control building has three floors and extends froin grade to about 79 feet above grade. It b contains the electrical switchgear, motor generator sets, battery rooms, cable spreading room, and the main control room. The diesel generator
( building has two floors and extends from 36 feet below grade to approxi-mately 59 feet above grade. This building houses diesel fuel storage
{ tanks, the diesel generators, air intakes for the generators and building ventilation equipment.
4.8.1 Control and Diesel Generator Building Failure Modes Two failure modes were checked for this building: flexural f ailure and shear failure of the shear walls. Flexural failure gives the lower median peak ground acceleration: 3.0g. At this acceleration, failure is expected in the west wall, which is the outer wall of the diesel generator building, due to N-S motion. The same motion results in the lowest level shear capacity, 5.29, this time at the east wall, which
{ is the outer wall of the control building. The median factors of safety and their variabilities for the flexural failure are given in Table 4-13; those for the shear failure are presented in Table 4-14.
[
4-34
Reference 26 provides an analysis of the control room ceiling.
{ Because the ceiling is wire-suspended, a nonlinear analysis had to be performed to account for the fact that the wire can carry only tensile loads. Thus, it is difficult to say, for instance, whether an earthquake with a peak ground acceleration of 10 times the one used in the analysis will generate stresses and displacements that are greater than or less than 10 times the reported values. However assuming the connections are as detailed in Reference 26, it does appear that the ceiling capacity
} ,
should exceed the lowest calculated structure acceleration of 3.0g.
4.9 FUEL STORAGE BUILDING I
I The fuel storage building is a two-story, square building approximately 98 feet on each side that extends approximately 44 feet below grade and rises 66 feet above grade. The building contains the new fuel storage area and the spent fuel pool. The spent fuel pool exists l entirely below grade and has walls of a minimum thickness of 6 feet. It is lined with stainless steel plates 0.188 inch thick on the walls and l 0.25 inch thick on the floor.
I l
4.9.1 Fuel Storage Building Failure Modes The lowest level significant failure mode for this structure is j flexural f ailure of the west wall due to N-S excitation. It is expected g to fail at a median peak ground acceleration of 4.99 The median safety 5
f actors and their variabilities are presented in Table 4-15 for this I mode. The only other significant f ailure mode that was considered was shear failure of the walls. The lowest level shear f ailure has a median l peak ground acceleration of 6.5g and also occurs to the west wall due to N-S motion. The factors of safety and variabilities for this mode are l
l listed in Table 4-16.
I 1
5 4-35 I
TABLE 4-1 SEABROOK CONCRETE COMPRESSIVE STRENGTHS
[ Average Number L Design Tested Standard of Mix Class Strength Strength Deviation Samples (psi) (psi) (psi) 4AWR67 (M.53) 3000 5260 487 414 4AWR67 (M.60) 3000 4327 484 405 4AWR67 (M.45) 4000 5859 582 57 4ftAWR67(M.45) 4000 6057 576 456 4AWR67 (M.48) 4000 5557 490 54
[ 4AWR67 (M.48)special 4000 5592 466 135 4AWR67 (M.50) 4000 5442 546 1599
{
4MN67 (M.45) 4000 6369 354 30 b 4AR67 (M.48)special 4000 5858 376 50 4AS67 (M.429) 4000 5747 406 207
[ 4 MAS 67 (M.44) 4000 5829 452 60 4AWR67 (M.48)
- 4000 5400 ** 78 4AWR67 (M.48)special* 4000 5360 ** 54
- 4000 **
4WR67 (M.50) 5560 75 4AS67 (M.429)
- 4000 5640 ** 30
- These four mixes were specifically for containment. The rest of the
[ mixes were assumed to apply to all other structures.
- Values not reported. A COV (see Appendix A) of 0.08 was assumed.
4-36
TABLE 4-2 SEABROOK REINFORCING STEEL STRENGTHS Number Median Yield Standard Bar Size of Tests Strength Deviation (ksi) (ksi)
- 4 20 70.5 2.18
- 5 12 67.9 2.11
- 6 96 67.9 2.66
- 7 32 70.0 2.45
{
- 8 128 69.6 2.37
( #9 80 70.3 2.81
- 10 84 70.9 2.65
- 11 136 70.6 2.82
- 14 16 73.6 2.32
{
- 18 92 72.3 2.04 Median yield strength of all bars except #14 and #18 = 69.8 ksi Standard deviation of all bars except #14 and #18 = 2.79 ksi
[
[
4-37
l TABLE 4-3 l
Structure: Containment Building Failure Mode:
Flexural Failure of Wall I Item Median F.S. B R
8 U
3 C
i Strength 7.28 0 0.16 0.16 I Inelastic Energy Absorption 2.21 0.07 0.21 0.22 E Earthquake Duration and Cycles l.4 0.12 0.08 0.14 Spectral Shape 1.46 0.24 0.08 0.25 f Damping 1.0 0.08 0.08 0.11 Modeling 1.0 0 0.10 0.10
} Modal Combination 1.0 0.05 0 0.05 Combination of Earthquake Components 0.93 0.09 0 0.09 Soil-Structure Interaction 1.0 0 0.05 0.05 Total 30.6 0.31 0.32 0.44 Median Acceleration Capacity = 30.6(0.25) = 7.6g l
l l TABLE 4-4 Structure: Containment Building l Failure Mode: Shear Failure of Wall Item F.S. 8 8 8 l R U C Strength 8.36 0 0.16 0.16 l Inelastic Energy Absorption 2.21 0.07 0.21 0.22 Earthquake Duration and Cycles 1.4 0.12 0.08 0.14 l Spectral Shape 1.46 0.24 0.08 0.25 Damping 1.0 0.08 0.08 0.11 Modeling 1.0 0 0.10 0.10 Modal Combination 1.0 0.05 0 0.05 Combination of Earthquake Components 0.93 0.09 0 0.09 Soil-Structure Interaction 1.0 0 0.05 0.05 Total 35.1 0.31 0.32 0.44 Median Acceleration Capacity = 35.l(0.25) = 8.8g 4-38 I
L TABLE 4-5 Structure: Containment Enclosure Building i Failure Mode: Shear Failure of Wall )
Median i Item F.S. 8 R
8 U
8 C
Strength 8.25 0 0.25 0.25 Inelastic Energy Absorption 2.21 0.07 0.21 0.22 ,
Earthquake Duration and Cycles l.4 0.12 0.08 0.14 Spectral Shape 1.39 0.24 0.08 0.25
( Damping Modeling 1.0 1.0 0.07 0
0.07 0.10 0.10 0.10 Modal Combination 1.0 0.05 0 0.05 Combination of Earthquake Components 0.93 0.09 0 0.09 Soil-Structure Interaction 1.0 0 0.05 0.05 Total 33.0 0.30 0.37 0.48 Median Acceleration Capacity = 33.G(0.25) = 8.2g
{
E TABLE 4-6 Structure: Containment Enclosure Building Failure Mode: Flexural Failure of Wall Median Item F.S. B 8 8 R 0 C Strength 10.4 0 0.25 0.25 Inelastic Energy Absorption 2.21 0.07 0.21 0.22 Earthquake Duration and Cycles 1.4 0.12 0.08 0.14 Spectral Shape 1.39 0.24 0.08 0.25 Damping 1.0 0.07 0.07 0.10 Modeling 1.0 0 0.10 0.10 Modal Combination 1.0 0.05 0 0.05 I Combination of Earthquake Components 0.93 0.09 0 0.09 Soil-Structure Interaction 1.0 0 0.05 0.05 Total 41.6 0.30 0.37 0.48 Median Acceleration Capacity = 41.6(0.25) = 10.49 4-39 I
l Table 4-7 ,
l L
Structure: Primary Auxiliary Building
[ Failure Mode: Flexural Failure of Shear Walls l Median Item F.S. B 8 8 R 0 C l
Strength 2.32 0 0.18 0.18 Inelastic Energy Absorption 2.21 0.07 0.21 0.22 l ~
Earthquake Duration and Cycles 1.4 0.12 0.08 0.14
, Spectral Shape 1.44 0.25 0.08 0.26 Damping 1.0 0.08 0.08 0.11 Modeling 1.0 0 0.10 0.10 Modal Combination 1.0 0.05 0 0.05 Combination of Earthquake Components 0.99 0.01 0 0.01
{ Soil-Structure Interaction 1.0 0 0.05 0.05 Total 10.2 0.30' i 0.33 0.44 l Median Acceleration Capacity = 10.2 (0.25g) = 2.69 I
i I Table 4-8 I
f Structure: Primary Auxiliary Building Failure Mode: Shear Failure of Shear Walls
,I Median l Item F.S. B S 8 R U C l
I Strength 3.66 0 0.16 0.16 I
Inelastic Energy Absorption 2.21 0.07 0.21 0.22 Earthquake Duraticn and Cycles 1.4 0.12 0.08 0.14 I Spectral Shape 1.44 0.25 0.08 0.26 Damping 1.0 0.08 0.08 0.11 Modeling 1.0 0 0.10 0.10 Modal Combination 1.0 0.05 0 0.05 Combination of Earthquake Components 0.99 0.01 0 0.01 Soil-Structure Interaction 1.0 0 0.05 0.05 I Total 16.1 0.30 0.32 0.43 Median Acceleration Capacity = 16.1 (0.259 ) = 4.0g 4-40 I
L Table 4-9
[
Structure: Service Water Pumphouse Failure Mode: Flexural Failure of Shear Walls Item F.S. 's R 8 0
8 C
Strength 3.05 0 0.18 0.18 Inelastic Energy Absorption I.62 0.04 0.14 0.15 l
Earthquake Duration and Cycles l.4 0.12 0.08 0.14 Spectral Shape 1.26 0.10 0.03 0.11
(, Damping 1.0 0.01 0.01 0.01 Modeling 1.0 0 0.14 0.14
[ Modal Combination Combination of Earthquake Components 1.0 0.97 0.05 0.02 0
0 0.05 0.02 Soil-Structure Interaction 1.0 0 0.05 0.05
{ Total 8.45 0.17 0.29 0.33 Median Acceleration Capacity = 8.45 (0.25g) = 2.lg
{
[
Table 4-10 Structure: Service Water Pumphouse
[ Failure Mode: Diaphragm Failure Median Item F.S.
{ 8 R
8 0
8 C
Strength 4.14 0 0.18 0.18
( Inelastic Energy Absorption 1.32 0.02 0.11 0.11 Earthquake Duration and Cycles 1.4 0.12 0.08 0.14 Spectral Shape 0.10 0.03
{ Damping 1.26 1.0 0.01 0.01 0.11 0.01 Modeling 1.0 0 0.14 0.14 Modal Combination 1.0 0.05 0 0.05 Combination of Earthquake Components 0.98 0.01 0 0.01 Soil-Structure Interaction 1.0 0 0.05 0.05 Total 9.45 0.17 0.27 0.32 Median Acceleration Capacity = 9.45 (0.259 ) = 2.4g 4-41
L Table 4-11 Structure: Service Water Cooling Tower Failure Mode: Flexural Failure of Shear Walls
{ )
Item F.S. B 8 8
[ Strength 2.23 0 R 0 0.19 C
0.19 Inelastic Energy Absorption 2.21 0.07 0.21 0.22
~
Earthquake Duration and Cycles 1.4 0.12 0.08 0.14 Spectral Shape 1.43 0.24 0.08 0.25 b Damping 1.0 0.08 0.08 0.11 Modeling 1.0 0 0.10 0.10
[ Modal Combination 1.0 0.05 0 0.05 Combination of Earthquake Components 0.98 0.05 0 0.05 Soil-Structure Interaction 1.0 0.05 0.05
{ Total 9.67 0
0.30 0.33 0.44
[ Median Acceleration Capacity = 9.67 (0.259 ) = 2.49
[ Table 4-12 Structure: Condensate Storage Tank Enclosure
{ Failure Mode: Flexural Failure of Wall Median
{ Item F.S. 8 R
S U
8 C
Strength 15 0 0.22 0.22 Inelastic Energy Absorption - - - -
Earthquake Duration and Cycles - - - -
[ Spectral Shape 1.20 0.06 0.02 0.06 Damping 1.0 0 0 0 Modeling 1.0
{ Modal Combination 1.0 0
0.03 0.12 0
0.12 0.03 Combination of Earthquake Components 0.93 0.09 0 0.09 Soil-Structure Interaction 1.0 0 0.05 0.05 Total 16.7 0.11 0.26 0.28 Median Acceleration Capacity = 16.7 (0.25g) = 4.2g 4-42
Table 4-13 I Structure: Control and Diesel Generator Building Failure Mode: Flexural Failure of Shear Walls I Item Median F.S. s R
8 0
8 C
Strength 2.92 0 0.18 0.18 I' Inelastic Energy Absorption 2.21 0.07 0.21 0.22 Earthquake Duration and Cycles l.4 0.12 0.08 0.14 Spectral Shape 1.37 0.24 0.08 0.25 Damping 1.0 0.07 0.07 0.10 Modeling 1.0 0 0.10 0.10 Modal Combination 1.0 0.05 0 0.05 Combination of Earthquake Components 0.98 0.05 0 0.05 Soil-Structure Interaction 1.0 0 0.05 0.05 Total 12.1 0.29 0.33 0.44 Median Acceleration Capacity = 12.1 (0.25g) = 3.0g I
Table 4-14 I Structure: Control and Diesel Generator Building Failure Mode: Shear Failure of Shear Walls Median Item F.S. B 8 3 R 0 C Strength 5.00 0 0.16 0.16 Inelastic Energy Absorption 2.21 0.07 0.21 0.22 Earthquake Duration and Cycles 1.4 0.12 0.08 0.14 Spectral Shape 1.37 0.24 0.08 0.25 Damping 1.0 0.07 0.07 0.10 Modeling 1.0 0 0.10 0.10 Modal Combination 1.0 0.05 0 0.05 Combination of Earthquake Components 0.98 0.05 0 0.05 Soil-Structure Interaction 1.0 0 0.05 0.05 Total 20.8 0.29 0.32 0.43
, . Median Acceleration Capacity = 20.8 (0.25g) = 5.29 4-43
Table 4-15 Structure: Fuel Storage Building Failure Mode: Flexural Failure of Shear Walls I Item Median F.S. S R
8 0
8 C l Strength 5.53 0 0.18 0.18 Inelastic Energy Absorption 2.08 0.06 0.20 0.21 Earthquake Duration and Cycles 1.4 0.12 0.08 0.14 l Spectral Shape 1.25 0.18 0.06 0.19 l Damping 1.0 0.05 0.05 0.07 Modeling 1.0 0 0.13 0.13 Modal Combination 1.0 0.05 0 0.05 Combination of Earthquake Components 0.97 0.02 0 0.02 Soil-Structure Interaction 1.0 0 0.05 0.05 Total 19.5 0.24 0.32 0.40 Median Acceleration Capacity = 19.5 (0.259) = 4.9g Table 4-16 I Structure: Fuci Storage Building Failure Mode: Shear Failure of Shear Walls I Item Median F.S. 8 R
8 U
8 C
Strength 7.33 0 0.22 0.22 It. elastic Energy Absorption 2.08 0.06 0.20 0.21 Earthquake Duration and Cycles 1.4 0.12 0.08 0.14 Spectral Shape 1.25 0.18 0.06 0.19 l Damping 1.0 0.05 0.05 0.07 Modeling 1.0 0 0.13 0.13 Modal Combination 1.0 0.05 0 0.05 Combination of Earthquake Components 0.97 0.02 0 0.02 Soil-Structure Interaction 1.0 0 0.05 0.05
, I Total 25.9 0.24 0.35 0.42 Median Acceleration Capacity = 25.9 (0.25g) = 6.5g I
4-44 ,
L p 80 L
IO .
p L
- Air cured, dry at test 60 -
,E 50 m m L =>
$ 40 -
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L 20 b 10 E o b 0 1 2 3 4 5 6 7 8. 9 10 11 12 Time (Months)
{
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E FIGURE 4-1.
{ EFFECTS OF TIME AND CURING CONDITIONS ON CONCRETE STRENGTH (FROM REFERENCE 14)
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4-45
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FIGURE 4-4. DEAMPLIFICATION FACTORS FOR ELASTIC-PERFECTLY PLASTIC SYSTEMS IN THE ACCELERATION AMPLIFIED RANGE (FROM REFERENCE 7)
E E
4-48 I
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SRSS COMPUTED RESPONSE FOR FOUR-DEGREE-0F-FREEDOM DYNAMIC MODELS (FROM REFERENCE 25)
[
4-49
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[
- 5. EQUIPMENT FRAGILITY This chapter describes the fragility development for the l seismically critical equipment within the Seabrook Nuclear Generating l Station. Pickard, Lowe and Garrick, Inc. have identified those equipment items which are essential to plant safety during and after a seismic
( event, and a fragility level and associated variabilities are determined for each of these components. Section 5.1 contains a general description of the equipment fragility methodology with a more in-depth treatment than was provided in Chapter 3. Section 5.2 presents a set of represen-tative example fragility derivations which provide the reader with further insight into the equipment fragility determination process. Section 5.3 presents the resulting equipment fragilities for the Seabrook plant.
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 input. In this case, the fragility of a component or system is defined
{
as the frequency of failure as a function of peak ground 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, earthquake duration and equipment response. These three 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.
F F F FE=FEC ER ED SR (5-1) 5-1
L F
EC is the capacity factor of safety for the equipment relative to the floor acceleration used for the design, FER is the factor of safety inherent in the computation of equipment response, F ED is the earthquake duration f actor of safety associated with the predicted number l of strong motion cycles within a seismic event, and F SR is the factor of safety in the structural response analysis that resulted in floor spectra for equipment design. Sections 5.1.1.1, 5.1.1.2, 5.1.1.3, and 5.1.1.4 of this report contain a more thorough explanation of these four factors (FEC, FER, F. ED, and FSR,respectively). The overall factor of safety, F ,E is then multiplied by the reference earthquake peak ground acceleration to obtain fragility in terms of peak ground acceleration.
=F E A (5-2)
SSE where:
5 = Median ground acceleration capacity ASSE
= Peak ground acceleration of the safe shutdown earthquake 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 criteria governed the equipment design.
The logarithmic standard deviation, 8, for each of these factors is obtained using the logarithmic standard deviations for each of the above f actors and based upon the lognormal model ( Appendix A).
l l B E " (SEC + 8ER + 8ED2 + 85R H E 5-2 l
l l
l L
where BEC' OER* OED, and SSR are the logarithmic standard ,
deviations of the equipment capacity, equipment response, earthquake I duration, and structural response, respectively. The logarithmic standard deviations are further divided into random variability, BR '
I and uncertainty, SU , as described in Chapter 3.
I l 5.1.1.1 Equipmen_t Capacity Factor The equipment capacity factor is defined as the failure l threshold divided by seismic design level. For the purposes of this i
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 I of the steam generator. Where several failure modes pertaining to the same component are found to have roughly the same capacity level, all j significant failure modes are analyzed and reported.
E The factor of safety for the equipment seismic capacity consists of two parts:
- 1. The strength factor, F 3, based on the components static strength and
{ 2. The ductility factor, Fu , related to the equipment's inelastic energy absorption I capability.
I FEC = F3Fu (5-4) l The logarithmic standard deviation on the capacity can be derived j by taking the SRSS of the logarithmic standard deviations on the strength f actor and the ductility f actor. 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 3 for the strength factor and the ductility factor (i.e., 6 3 for 83 and 8 9 for B y, p
etc.).
B EC"(85+g 2 (5-5) 5-3 I
L 5.1.1.1.1 Strength Factor - The strength factor, Fs , is derived from the equation:
P 1'C N p b b (5-6) l S- P T
P N
P D
VD
~
where CP is the median limit state load or stress, P is the normal N
operating load or stress, PT is the total normal plus seismic load or stress and PD is the code design allowable load or stress.
Alternatively, this equation can be written:
PC-Pg F (5-7) 3= p SSE where P is the seismic load or stress corresponding to the safe SSE 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 collapse load, PC , is a function of the failure mode for the specific equipment item. Equipment failures can be classified into three categories:
- 1. Elastic functional failures
- 2. Brittle failures
- 3. Ductile Failures.
1 e-.
l - - - - - -
Elastic functional failures involve the loss of intended function
( while the component is stressed below its yield point. Examples of this type of failure include:
- 1. Elastic buckling in tank walls and component supports.
- 2. Chatter and trip in electrical components. l
- 3. Excessive blade deflection in fans.
{
- 4. Shaft seizure in pumps.
The limit state load for this type of a failure is cefined as the median load or stress level where functional failure occurs.
Brittle failures are defined in this study as those failure modes which have little or no system inelastic energy absorption capability. Examples of brittle type failures include:
- 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 transmission structure, and thus, these bolts will fail in a brittle mode once the ultimate bolt strength is reached.
5-5
( 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
( include:
- l. Pressure boundary failure of piping
{
- 2. Structural failure of cable trays
[ 3. Structural failure of ducting
- 4. Polar crane failure.
The collapse load for ductile failure modes consists of the median yield
( strength of the material for tensile type loading conditions. For bending type failure modes, the yield point is defined as the limit load or stress to develop a plastic hinge. The ductility factor will then
{
quantify the inherent safety factor above the yield strength to the failure threshold.
{
Each variable within Equation 5-6 has an associated lognormal probability distribution to express its combined randomness and uncer-tainty. To find the overall variance on the strength factor, a technique comonly referred to as the "Second Moment Method" was 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 (Reference 27). The resulting equation for the logarithmic standard deviation on the strength factor is given below:
2 2 P P C 2 T 2
,g , ,g (PC-P) N (PT-P) N (5-8)
{ (PC-P) T P
N 2 Y2
, g"
. (PT-P) N -(PC-P) N
~
[
5-6
[ - - - -
I where:
l BC
= Logarithmic standard deviation on the I collapse load (stress).
= Logarithmic standard deviation on the total I load (stress).
SN
= Logarithmic standard deviation on the normal l load (stress).
5.1.1.1.2 Ductility Factor - The inelastic energy absorption capability I of a piece of equipment is quantified by the ductility factor. Brittle failure modes and functional failure modes typically hava a ductility I factor of 1.0, while ductile type failure modes have ductility factors which are a function of a deamplification factor (Reference 7). At moderate damping levels, the ductility f actor (Fy ) for equipment that responds in the amplified acceleration region of the design spectrum is approximately:
Fp = c(2p-1) 2 (5-9)
The symbol u represents the ductility ratio and c is a random variable I with a median value equal to 1.0 and a logarithmic standard deviation ranging from about 0.02 to 0.10 (depending on the ductility), which represents the uncertainty in the use of Equation 5-9. For rigid equipment, Reference 7 recommends that the ductilty factor be represented by:
0.13 Fy = cu (5-10)
Again, e is a variable of median equal to 1.0 with a logarithmic :;tandard deviation ranging from about 0.02 to 0.10, as a function of the ductility.
In both Equations 5-9 and 5-10, the logarithmic standard deviation on c increases with the ductility, p. Equation 5-9 applies to equipment with a fundamental frequency in the amplified acceleration
, 5-7 I
[
range (about 2 to 8 Hz) and Equation 5-10 applies to equipment with a
( fundamental frequency greater than about 30 Hz. Between about 8 and 30 Hz the ductility factor and the logarithmic standard deviation of are interpolated.
{
The ductility ratio, p, itself is based upon the recommendations ,
1 given in Reference 6. This reference gives a range of ductility values to be used for design. The upper end of this range is considered to be a I median value while the lower end of this range is considered to be about a -2 logarithmic standard deviation value. Engineering judgment was I
utilized to match the applicable category from Reference 6 to a particular failure mode for the equipment component.
5.1.1.2 Equipment Response Factor The response factors are an estimate of the conservatism or 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
{ perfomed for Seabrook 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:
[
- 1. Qualification Method (Fgg)
- 2. Spectral Shape (F33) 5-8
- 3. Modeling (effects mode shape and frequency results) (FM) ,
[ 4. Damping (FD ) s
- 5. Combination of Modal Responses (for response '
l
( spectrum method) (FMC)
- 6. Combination of Earthquake Components (FECC)
For equipment qualified by static analysis, two subdivisions must be considered. For rigid equipment, spectral shape, combination of
{ modal responses, damping,'and for the most part, modeling errors are -
} j eliminated. If the equipment is flexible and was designed via the static - I coefficient method, the dynamic characteristic variables and their variability must be considered. This involves 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
[ response f actor must take into account:
1.
Qualifiction Method (FQM) -
- 2. SpectralShape(Fss)
[
- 3. Boundary Conditions in the Test vs Installation (FBC)
- 4. Damping (FD )
- 5. 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 factor is provided below. A more detailed discussion is contained within Reference (28).
b 5-9
F 5.1.1.2.1 qu_alification 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.
e Analytical qualifications can be separated into static analysis and
[ dynamic analysis techniques. The inherent safety factor in using these qualification techniques is discussed below, while the variability on this factor is accounted for within the damping, modeling and mode
{ combination factors (i.e., e 8
=0.0).
c k -
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 L qualified. Typically, the peak spectral acceleration is multiplied by a coefficient and this product is multiplied by the, weight of the component
( to determine an equivalent static load to be applied at the subsystem center of gravity. If the component is comprised of more than one lumped
{ 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 component is rigid (i.e., its fundamental frequency is 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 zero 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 Analysis - 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 single b 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 integration time-history method, we would expect to obtain equal median centered results assuming that the
{ response spectrum and time-history inputs are compatible.
E 5-10
[
The response spectrum method was extensively used for dynamic analysis of components and systems within the Seabrook plant. If the applicable Seabrook floor response spectra were utilized in the design analysis, the qualification method factor, FQM, is equal to unity and the variability is zero. If a conservative generic spectra was used to seismically qualify a component, Fgg is the ratio of the spectral
{ acceleration from the generic spectra divided by the spectral acceleration p from the Seabrook site specific spectra evaluated at the components' L fundamental frequency.
5.1.1.2.1.3 Testing - In vibration testing, the test response spectrurn 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 strength factor, the qualification method factor (FQM) and variability (8QM) will be unity and zero, respec-tively. If the component fragility is being based on testing where the test response spectra are not available, FQM and Sgg account for the overtest safety factor and variability on a generic case-by-case basis.
5.1.1.2.2 Equipment Spectral Shape Factor - The Seabrook floor response spectra (Reference 29) were computed by means of a time-history (T/H)
{ '
seismic analysis. The overall dynamic response of each of the critical buildings was modeled by lumping the mass of the structure and rigidly attached components generally at each of the floor levels. Two artificial T/H's (each with a peak acceleration of 0.25g) were used in the T/H analyses. One T/H was applied horizontally in each of the N-S and E-W directions while the second T/H was applied in the vertical direction. The two time-histories were developed to envelope, as closely as possible, the ground response spectra for the Seabrook site. The conservatism /unconservatism involved in developing the floor response
{
spectra from the ground response spectra is quantified with the equipment spectral shape factor. The conservatism /unconservatism involved in using the specified Seabrook design response spectra in lieu of a median Safe Shutdown Earthquake spectra is quantified in development of the spectral shape f actor associated with the structural response f actor.
5-11
The response spectrum method is often referred to as being conservative, however, the conservatism compared to a time-history analysis is primarily due to the method of developing the spectrum. I Spectra used for design purposes are generally smoothed and the peaks are widened such that the resulting design spectrum is conservative. In addition, conservatism is generally introduced in the development of the I artificial time-history. The combined effect of the two conservatisms make up the equipment spectral shape factor.
5.1.1.2.2.1 Peak _ Broadening and Smoothing - The effect of smoothing and peak broadening varies with structure, elevation, frequency and damping.
Comparisons between broadened and unbroadened floor spectra for various elevations within the Containment Building, Primary Auxiliary Building, j Fuel Building and Control / Diesel Generator Building are contained within Section 3.7 of the Seabrook FSAR (Reference 1). Figure 5-1 shows a typical example of these spectra comparisons.
Factors of conservatism due to peak broadening and smoothing I
were generated for these four buildings based on these FSAR spectra. For any particular frequency, this safety factor can be computed from l Equation 5-11.
I F =
Sa (broadened and smoothed) 33 (5-11) ba (unbroadened and unsmoothed)
I where:
l FSS1
= Spectral shape factor due to peak broadening and smoothing Sa = Spectral acceleration value l
5-12
[ Due to the inexact nature of predicting fundamental frequencies, these safety factors were computed for frequency bands of roughly 5 Hz incre-
{ ments. The median ratio within these 5 Hz bands was used as a factor, F
33 and a minus two logarithmic standard deviations were estimated tobx,istbetweenthemedianandtheminimumratioswithina5Hzband.
Therefore, SS I(median)\
( Bss1 = 1/2 in (pSS3(minimum))
(5-12) where:
8 = Logarithmic standard deviation on the ssi peak broadening and smoothing factor Since the variability in 8 33 is due to the shift in the frequency, it is considered to be all uncertainty.
For equipment located in buildings other than the four which were analyzed, average median spectral shape factors from the four
[ buildings were used and the variability 8 33 was computed by taking a factor of unity as a -28 lower bound. Table 5-1 shows the peak broadening and smoothing factors for each of these buildings together with the loga-rithmic standard deviation due to uncertainty. These values are appli-cable to equipment on any floor level except the basemat. Equipment on
{ the basemat were qualified to the ground spectra, and have a factor of p 1.0 and a variability of 0.0 since floor spectra were not generated at L this elevation.
( 5.1.1.2.2.2 Artificial Time-History Generation - Studies have been con-ducted which show that conservatism is involved in the current practice
{ of generating floor spectra in structures using artificial time-histories.
These artificial time-histories result in response spectra that conserva-
~
tively envelope the applicable ground spectra. For instance, Reference 30 indicates that the average industry-generated artificial time-history tends to introduce about 10 percent conservatism except at high frequen-5-13
cies for which the conservatism is about 20 p'ercent at 33 Hz. Our own experience is compatible with these numbers. Since Seabrook structures have fundamental frequencies in the amplified region of the spectra, an artificial time-history f actor of 1.1 is applied. This relatively low f actor of conservatism is a reflection of the substantial industry effort to reduce this arbitrary source of conservatism.
It has also been observed that two different artificial time-histories, both of which result in response spectra which adequately envelope the Regulatory Guide 1.60 response spectra, can lead to floor
{ spectra which may differ by a factor of 2 or more (for instance, see Reference 31). Use of the artificial time-histories method for testing
{ and analysis can result in a small arbitrary amount of conservatism on the average and considerable dispersion in the resultant response.
I Reference 31 reports that a coefficient of variation of 0.2 is reasonable l
based on a comparison study of 44 synthetic time-histories. This vari-ability on the artificial time-history generation factor is classified as I being all randomness since it represents the variety of possible earth-quakes.
l The overall spectral shape factor was generated by taking the j product of the peak broadening and smoothing factor times the artificial time-history f actor. Table 5-1 shows the spectral shape f actors and i
their variabilities for each of the seismically critical buildings as a l
function of the frequency interval. Note that a 5 to 20 Hz interval has been included to reflect the most possible frequency ranges for complex I mechanical systems such as piping and cable trays.
l 5.1.1.2.3 Modeling Factor - In any dynamic analysis there is uncertainty in resonse due to assumptions made in modeling the structure, modeling j 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 5-14
I 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 treating nonlinear gap effects linearly cannot be quantified generically and each model must be treated specifically to determine a response factor for modeling. Assuming that the analyst does his best job of modeling, modeling accuracy could be l
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.
I For complex state-of-the-art dynamic analysis, the coefficient of variation on response (approximate logarithmic standard deviation) is about 0.20. For simple single-frequency systems the coefficient of variation is about 0.10, and for systems of medium complexity the coefficient of variation is about 0.15. These variabilities are considered to be all uncertainty and are based on past experience and engineering judgment.
I 5.1.1.2.4 Damping Factor - The basis for the damping factor has ceen addressed in Section 3.4.2 of this report. Tables 3-1 and 3-2 show the damping values used for the SSE design analysis of Seabrook equipment.
Median damping values and their variabilities are a function of the l material, construction details, size and stress level. Reference (28) 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 Seabrook equipment is:
I S (qual)
F (5-13)
D" I S- (median)
I 5-15
[
where:
E Sa (qual) = Spectral acceleration using the qualification design analysis damping and evaluated at the equipment
[ fundamental frequency l
r Sa(median) = Spectral acceleration using the L expected median damping and evaluated at the equipment fundamental frequency.
For multi-degree-of-freedom systems, Equation 5-13 can be altered to reflect the summation of the spectral accelerations at each of the frequencies multiplied by their associated mass participation factors.
L There is variability in damping and associated response that must be considered. It is indicated within Reference 28 that for a I 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 deviation in response equal to:
}
l S = An (5-14)
D c=5.0%)
1 where Sa e e n n n a c = 5% c = 3.5%
is the 3.5 percent damped spectral acceleration taken at the equipment I fundamental frequency using the applicable floor response spectra. The resulting logarithmic standard deviation on the damping response factor, from Equation 5-14 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.
5-16
( 5.1.1.2.5 Mode Combination Factor - The modal combination technique utilized within the Seabrook seismic design analysis was described in general in Section 3.4.4 of this report. A square-root-of-the-sum-of-the-squares (SRSS) methodology was used for all Seabrook equipment. This
( SRSS method (allowing for absolute sum for closely spaced modes) is in accordance with current Regulatory Guide 1.92 (Reference 12) recommended 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 (28) recomends that the coefficient of variation due to mode combination is approximately 0.15. For single-degree-of-freedom flexible
( systems, the coefficient of variation due to mode combination is estimated within Reference 28 to be approximately 0.10. For a single-degree-of-freedom rigid system, the COV is by definition zero. The variability due
{
to mode combination is considered to be all random due to the random phasing of modes.
5.1.1.2.6 Earthquake Component Combination Factor - The Seabrook plant design analyses earthquake components were required to be combined by the SRSS of the vertical and the two horizontal components. This approach
( requires that the effects of two horizontal directional responses be combined with the vertical response, but does not require the maximum response in each direction occur at the same instant as the maximum
[
response in the other two directions. Reference 10 recommends that the median 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. Comparing this suggestion to the Seabrook design criterion results in a response factor for combination of earthquake components. The magnitude of the factor depends, however, on
( the orientation and response characteristics of the component under consideration.
[ .
5-17
[
[ A generic study was conducted to develop earthquake component combination response factors and their variabilities for connon two- and three-dimensional equipment idealizations. The amount of conservatism /
unconservatism and the associated variability on this factor are a function of the following:
[ 1. The number and direction of earthquake components which affect the failure mode under consideration (e.g., piping failures are influenced by all I three directional responses, but a particular L relay can fail due to a particular horizontal seismic excitation while remaining unaffected by the vertical and the other horizontal directions)
- 2. The amount of coupling that exists between directional response (i.e., does an x direction f excitation cause a response in the y and z directions)
- 3. The attachment configuration for anchor bolt l failures (rectangular anchor bolt patterns will I
l behave differently than circular patterns when combining directional responses)
- 4. The end item of response which was combined by SRSS (i.e., different safety factors exist for l
the design analysis where the directional loads were combined by SRSS and then aplied to the model to find the resulting stress, than for the design analysis where stresses were calculated l for each of the three earthquake excitations separately and then combined by SRSS).
l Table 5-2 contains the earthquake component combination response I factors for those cases which were applicable to Seabrook equipment. The variability involved in the phasing of the three earthquake directional g components was considered to be all random, while the variability due to l the degree of coupling involved between directions was considered to be all uncertainty.
5-18
g 5.1.1.2.7 Boundary Conditions Factor (Testing) - The boundary conditions a 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 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 experience little variability in response factor due to boundary conditions. Carelessness on the part of the various organizations involved in design, f abrication, testing and installation can result in a I
significant variability. For instance, the lack of a specified bolt 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 mode shape and frequency shift. The variability of mode shape and frequency and resulting response due to boundary conditions varies considerably for different generic types of equipment. For a large majority 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 cases where the component to test table attachment mechanism is not representative of the actual in-plane condition. 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 currently developed directly from the Required Response -trum at most testing laboratories. A much better approach, as recormiended in Reference 32, 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 I 5-19
[ mode to coincide with a significant peak or valley. Reference 28 recomends a spectral test method factor of unity and a total variability of 0.11. This variability is entirely uncertainty since the use of better equipment and techniques could eliminate most of the uncertainty.
I L
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. Seabrook 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 L 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 required for all
{ plant specific equipment qualified for the Seabrook plant. The shock tests conducted during the SAFEGUARD program were, in many cases, single axis tests with complex waveforms consisting of superimposed sine beats.
Some biaxial testing data were included when deriving the generic SAFE-GUARD fragilities, but were scaled to an equivalent uniaxial input.
Thus, multi-directional effect f actors were developed for biaxial testing (used for fragilities developed for plant specific Seabrook testing) and
[ uniaxial testing (used for fragilities based on generic SAFEGUARDS test data).
E 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 F
three-dimensional. This unconservatism along with its associated variability is a function of both the phasing and the coupling between I earthquake directional components. Assuming that the median acceleration vector can be defined as recommended in Reference 10 as 100 percent of l 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 5-20
[
vector for biaxial testing divided by the median three-axis response.
The resulting response factor based on both phasing and coupling is calculated to be 0.86. The variability due to phasing is a function of the earthquake, and thus, is all random. The phasing variability is b identical to that which has been calculated for the general three-dimensional condition (case No. 1 of Table 5-2) for the earthquake i I component combination factor and is equal to 0.12. The variability due to coupling is very small since median coupling in testing exists by l
definition for the two input directional components. Using the uncoupled case and the 100 percent coupling case as 138 extremes on coupling, an uncertainty logarithmic standard deviation of 0.01 is calculated.
The multi-directional effects factor and its associated 8's for l random vibration biaxial testing is:
l FMDE
= 0.86 EMDER
= 0.12 l B MDEg
= 0.01 l 5.1.1.2.9.2 Uniaxial Testing - A uniaxial test is, in general, unconserva-tive in that coupling and phasing between the three-directional earthquake l components is not accounted for. Again, assuming the median acceleration vector can be defined as recommended in Reference 10 as 100 percent of the j acceleration in one direction plus 40 percent of the acceleration in the other two orthogonal directions, 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 l 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 133 extremes, is calculated to be 0.07.
5-21
I Thus, the multi-directional effects factor and its associated 8's for uniaxial testing is:
NMDE = 0.735 EMDER
= 0.12 B = 0.07 MDEU 5.1.1.3 Structural Response Factors
. Structural response factors as they relate to structural capacity for the safety-related structures within Seabrook are derived in Chapter
- 4. These structural response factors were computed assuming the structure was at or above its yield point. For equipment whose seismic capacity level has been reached while the structure is still within the elastic range, these structural response factors are optimistic. Reference 10 recomends seven percent damping for reinforced concrete at the yield condition and five percent damping for reinforced concrete at the one-I half yield condition. Thus, a second set of structural response factors which reflect the one-half yield condition of the structure (using five percent damping) were calculated. The variables pertinent to the struc-tural response analyses 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 appilcable variables from those analyses are:
- 1. Spectral Shape
- 2. Damping
- 3. Modeling
- 4. Soil-Structure Interaction.
The explanation of these variable effects are contained in Chapter 4 and will not be repeated here. Note, the combination of earthquake components is not included in structural response since that 5-22
E variable is addressed for specific equipment orientation in the treatment of equipment response. The resultant structural response factors derived from each of the above variables that pertain to equipment fragilities
[ are included in Table 5-3.
[ Equipment capacities were compared to capacities of the struc-tures that housed the equipment in order to determine the appropriate damping factor of safety to use in developing the structural response factor. 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 factor. For those cases where the equipment was
{ detennined to fail at a level where the structure remained elastic, the spectral shape factor appropriate for five percent damping was r substituted for the seven percent damped spectral shape factor.
It should be noted that equipment that is located on the base mat have had their structural response factors calculated on a case by case basis. Since the ground spectrum was utilized in their qualifica-b tion, the spectral shape f actor reflects the conservatism /unconservatism involved in using the ground spectra as opposed to the site specific
[ median spectra. In this instance, only the spectral shape and soil structure interaction factors apply. The structure modeling factor and the damping f actor do not apply since the equipment response is
{ independent of the building response.
5.1.1.4 Earthquake Duration Factor The earthquake duration factor has previously been addressed in Section 3.3 and 4.1.3. The basis for this factor is the increase in capacity due to the median expected earthquake being less severe than the earthquake on which the equipment ductility factors were based. Equipment ductility f actors were taken from the recommendations in Reference 6 and are based on three to five cycles of strong seismic motion. The median expected earthquake for the Seabrook site has a duration of seven to nine seconds and one to three strong motion cycles. The seismic capacity of 5-23
I equipment that fails in a structural mode is affected by the duration and resulting number of strong motion cycles since the expected available l ductility of the controlling structural elements increases as the number of cycles is reduced.
l As derived in Section 4.1.3, the duration factor and its l
logarithmic standard deviations for equipment that fails in a ductile manner is:
= 1.40 I B OR
= 0.12 S " 0 08 g Du l
For equipment that fails in a brittle manner or for functional g
E failure modes within the elastic range, the duration factor and its variability are unity and zero, respectively. ~
l 5.1.2 Information Sources Several sources of information are utilized in a PRA from which j to develop plant specific and generic fragilities for equipment. These sources include:
l
- 1. Seismic Qualification Design Reports
- 2. Seismic Qualification Test Reports
- 3. Final Safety Analysis Report (FSAR) l 4. Seismic Qualification Review Team (SQRT)
Submittals -
)
l
- 5. Seismic Qualification Report Summaries
- 6. Vendor drawings from which new analyses are 1 conducted
- 7. Past Earthquake Experience
- 8. Specifications for the Seismic Design of Equipment 5-24
0 I
The first 6 of these information sources are termed " plant specific" since they pertain to specific equipment within the Seabrook plant. The remaining information sources are termed " generic" since they constitute data generated for similar types of equipment or are definitions of design requirements, in lieu of actual design results.
I Plant specific sources are preferred since they have been generated for the specific items in question and their uncertainty level is reduced i from that of the generic sources.
5.1.2.1 Seismic Qualification Analysis Reports The majority of the fragility levels for critical Seabrook equipment were developed from the review of seismic qualific Ation analysis reports. Westinghouse provided qualification report summa les for most of the equipment items which they had supplied to Seabrook, and fragility I levels were calculated based on these sumaries. In scme cases, the Westinghouse supplied data was based on a generic analysis where generic spectra, which enveloped the response spectra for several plant sites, I had been used for the loading. In these cases, the stresses have been scaled down to reflect the response for the Seabrook site, and thus, these cases essentially constitute a plant specific analysis.
5.1.2.2 Seismic Qualification Test Reports Several examples of test reports for equipment qualified by I testing were reviewed. Qualification test reports, by themselves, cannot be utilized to directly develop full fragility relationships unless the equipment has been tested to increased vibration levels up to failure.
I Fragility at levels greater than design criteria can, however, be inferred from test data and if the test levels were sufficiently high, the inferred fragility levels may be such that there is high confidence failure will not occur below the maximum vibration level postulated for the site.
I 5.1.2.3 Final Safety Analysis Report & SQRT Sunmaries The Seabrook FSAR contained very few SSE stress summaries on critical equipment; thus, was not significantly utilized within the g 5 25 I
b seismic portion of the PRA. Seabrook SQRT summaries were used to a limited degree to demonstrate that selected items of equiment had median
[ ground acceleration capacities exceeding 2.09 .
5.1.2.4 Vendor Drawingsor Design Reports from Which New Analyses are
{ Conducted Occasionally, it is fruitful to conduct new analyses for critical components in order to remove hidden conservatisms inherent in the original design analysis and to reduce the uncertainty in the fragility derivation. New analyses were conducted for the diesel fuel oil day tank and the refueling water storage tank.
5.1.2.5 Past Earthquake Experience Past earthquake experience is valuable for establishing fragilities for equipment which have historically been vulnerable. Most equipment survives without any apparent damage and the historic experience must be treated the same as a qualification test. Earthquake experience was used to estimate fragility levels for non-vital AC power.
5.1.2.6 Specification for the Design of Equipment Specifications for seismic qualification of Seabrook equipment were provided by United Engineers and Constructors, Inc. In cases where plant specific qualification reports were not reviewed, knowledge of the vendor requirements plus generic fragility and qualification test data were combined to develop fragility descriptions.
E r
1 5-26
I 5.1.3 Equipment Categories Depending 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 fragility description may be appropriate. The factors of safety relative to the Safe Shutdown Earthquake are widely variable. In general, flexible equipment such as piping, which possesses the ability to undergo large inelastic deformation, will have a factor of safety against failure of 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 I 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.
Fortunately, most rigid equipment stress response is very much less than the allowable and large safety factors are present.
I The extensive number of safety-related equipment items within a I nuclear power plant, coupled with practical limits on resources available with which to perform a PRA analysis, necessitates limiting the amount of detailed analysis devoted to any single piece of equipment. Experience gained as to relative component fragility levels must be utilized in deciding which components to treat generically and which components to treat specifically. Those components which have been shown to possess a high degree of resistance to seismic loading can be treated in more of a generic fashion. The higher degree of uncertainty which results from the use of generic analysis can be accepted due to the inherently high fragility level for components of this type. Likewise, components which can be shown through experience to possess low fragility levels should have a more thorough analysis undertaken to provide as much accuracy as possible. Note that often after a preliminary risk analysis has been I
I 5-27 I
I conducted, components which contribute heavily to the overall risk of the plant are reevaluated in more detail to reduce sources of uncertainty that may have arisen from an approximate or generic derivation of fragility. Table 5-4 contains a listing of the relative fragility level l
for general equipment categories based on the data provided in Reference 1
- 33. The information provided within Table 5-4 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.
I
. 5.2 EQUIPMENT FRAGILITY EXN4PLES Because of the amount of equipment to be included within the risk model, it is impractical to describe the specific fragility deriva-tion for each piece of equipment. This section contains selected examples of fragility derivations which are judged to be representative of the different types of analyses which had to be undertaken for Seabrook equipment. The equipment fragility derivation categories applicable to the Seabrook PRA are:
- 1. Equipment whose fragility descriptions are based on plant specific design reports.
- 2. Equipment whose fragility descriptions are based on qualification test reports
- 3. Equipment whose fragility descriptions are based on knowledge of the design specifications and the I factors of safety inherent in the governing codes and standards h 4. Equipment whose fragility descriptions are based E on new analysis Equipment whose fragility descriptions are based I 5.
on engineering judgment and past earthquake experience (non-seismically qualified components).
I An example of Seabrook equipment whose fragility derivation stems from each of the above categories is included in this section.
I 5-28 I
( 5.2.1 Example of a Plant Specific Design Reptrt Fragility Derivatirn The majority of the fragility derivations for the Seabrook PRA fall within the plant specific design report category. United Engineers
{
and Constructors, Inc. (UE&C) supplied the seismic qualification reports for all of the critical equipment for which they were responsible in the Seabrook plant development. These UE&C supplied reports were used to derive fragilities for components except for those cases where a generic fragility development was deemed appropriate (expected high capacity) or where the qualification report was not descriptive enough to accurately derive a capacity.
The example chosen for the plant specific design report
{
fragility derivation is the spray additive tank. The spray additive tank has a 6.67-foot diameter, is 44.25 feet high and holds 10,700 gallons.
It is located at Elevation 25' within the Tank Farm. The tank is constructed of SA 240 Type 304 stainless steel and was designed to ASME Code Section III Subsection ND Class 3 criteria. The qualification analysis (Reference 34) was performed by the Pittsburg, Des Moines Steel Company using a response spectrum approach.
{
A review of Reference 34 reveals the critical areas during
{ seismic loading are:
- 1. Buckling of the tank walls
- 2. Anchor bolts
- 3. Anchor Bracket.
[ Strength factors were calculated for each of these failure modes and the resulting governing case was the anchor bolts. The other two failure h modes had strength factors significantly above that of the anchor bolts; thus, only the anchor bolts were utilized in the fragility derivation.
( Table 5-5 contains all of the factors which make up the final fragility values for the spray additive tanks. Each of these factors is discussed briefly.
5-29
( - - - - - - - - - -
I 5.2.1.1 Spray Additive Tank Capacity Factor The anchor bolt pattern consists of eight, two-inch diameter SA193 87 bolts on a 7'-25 /a" diameter bolt circle. Reference 34 states the faulted condition maximum load to be a tensile load of 214.9 kips and a shear load of 18.53 kips. The state of stress in the most highly stressed bolt can be calculated as:
s I o=
2.50 in 18.53 kips
= 85.96 ksi (tensilestress)
T = = 8.65 ksi (shear stress) o' 3.142 in' These stresses are essentially all due to the safe shutdown earthquake (SSE) since the normal stress in the anchor bolts is negligible.
Anchor bolt failures are considered to be a brittle type of failure mode. The system inelastic energy absorption capability for anchor bolts is negligible in comparison to the amount of kinetic energy which is input into the system by the earthquake. There exists only a small region in the bolt which goes inelastic and when the median I ultimate strength of the bolt is reached, failure occurs. Therefore, in using Equation 5-7 to derive the strength factor, the collapse load is defined as the median ultimate strength.
For SA 193 B7 bolts, the ASME code specified ultimate strength l
is 125 ksi. For high strength steel, Reference 35 reports that the average strength is about a factor of 1.1 above the ASME code specified lI ultimate tensile strength. Considering the ASME code specified tensile strength to be a 95 percent probability of exceedance value (i.e., -1.658) we can calculate the logarithmic standard deviation for uncertainty in bolt strength as:
I 8
1.1 U
= Rn h-)=0.06 (5-15)
I g 5-30 I
I Since the state of stress within the anchor bolt includes both i shear and tensile stresses, an interaction equation was utilized in order to calculate the strength factor. The AISC code (Reference 36) recommends that the shear and tension stresses be combined utilizing Equation 5-16 below:
I 2 2 f f d+is1.0 F F (5-16) t y I where:
ft = Computed tensile stress fy = Computed shear stress I Ft = Ultimate tensile stress Fy = Ultimate shear stress Using a shear ultimate of 60 percent of the tensile ultimate and i inserting values into Equation 5-16:
2 2 85.96 , 5.9
= 0.396 (1.1 x 125)2 (1.1 x 125 x 0.6)2 Since the normal stress in zero, the strength factor becomes:
I S= 1/(0.396) /2 = 1.59 This states that the tensile and shear stresses could be scaled up by a factor of 1.59 before bolt failure will occur. The variability on this strength factor was calculated using Equation 5-8. Since the normal stress and its variability have been stated to be negligible, the e n term drops out of the equation. In addition, the SSE stress has been I
5-31 1
given in the qualification report and its variability is accounted for in the equipment response factor. Therefore, the variability on the applied stress is zero and drops out of Equation 5-8 since the B T term is a function of BN and BSSE. What remains from Equation 5-8 is:
[
83=BC The variability on the capacity factor is made up of the 0.06 material l strength variability from Equation 5-15 together with an uncertainty l k variability associated with the actual failure mechanism of the bolts, 8pg. This latter uncertainty, B g, p accounts for miscellaneous conditions such as prying action, load paths to the bolt pattern, corrosion, etc. which are difficult to include within the analysis. The 95 percent confidence bound on failure is judged to be the yield point, and the resulting logarithmic standard deviation is 0.11. The SRSS combination of these two variabilities gives the strength factor logarithmic standard deviation of:
Bs = (0.06* + 0.11 ) 2 = 0.13 This variability is all uncertainty and the resulting strength factor and variability for the spray additive tank are:
is = 1.59
( 8 5
R
= 0.0 B,S
= 0.13 As stated previously, the ductilty factor will be unity and the variability will be zero since the anchor bolts are considered to fail in a brittle mode. Therefore, the capacity factor and its variability are are equivalent to the strength factor and its associated variability.
5-32 r
I NC "N S = 1.59 BCR"OSR = 0.0 B
CU"OSU = 0.13 5.2.1.2 Spray Additive Tank Equipment Response Factor The response spectrum method was used to qualify the spray additive tank using Seabrook site specific spectra. As stated in Section I 5.1.1.2.1.2, the qualification method response factor is unity and its variability is zero for this case.
The spray additive tank is located at Elevation 25' in the tank farm building. The tank has a sloshing frequency of 0.67 Hz and a constrained frequency of 3.3 Hz. Since the tank has a high slenderness ratio, the sloshing effect is negligible and the fundamental frequency was treated as being 3.3 Hz. The applicable equipment spectral shape factor is contained within Table 5-1 in the "All Other Buildings" I category for the 3 to 10 Hz range.
Iss = 1.43 BSSR
= 0.20 BssU
= 0.13 The modeling of the spray additive tank is considered to be median centered; thus, a f actor of 1.0 is applicable. The tank model is judged to be of median complexity, and as stated in Section 5.1.1.2.3, the applicable variability is:
I 8R = 0.0 and BU = 0.15.
The damping factor was computed as the ratio of the spectral accelerations for the design damping value of three percent and the I median damping value of five percent taken at the tank fundamental I
g 5 33 I -- - - -- -
L frequency of 3.3 Hz (Equation 5-13). The three percent damped response used in the analysis was 1.14g's and the average between the two
( horizontal five percent damped spectra was 0.96g's. Therefore,
[ i D" " l'19
[.
The variability on this damping factor was calculated from Equation 5-14 considering three percent damping to be about a minus one logarithmic l l
standard deviation value.
[.
[ e ou " *" 0:0 " ' '
C Section S.1.1.2.5 recommends a mode combination factor of unity and a random logarithmic standard deviation of 0.15 for a multi-degree-of-freedom system such as the spray additive tank. Table 5-5 reflects these values.
The spray additive tank is anchored via a circular bolt pattern.
For a tank of these proportions, the vertical earthquake component does not significantly affect the anchor bolt failure mode. Thus, earthquake component combination case number 5 from Table 5-2 applies and:
{
NECC = 0.926
[ = 0.06 BECCR 0.0
[ B ECCg
=
The combined equipment response factor is then:
ER
= 1.43 x 1.19 x 0.926 = 1.58 k
5-34 r - _ -- -- -
L The random and uncertainty variabilities are:
2 BERR
=
(0.202 + 0.152 + 0.06 )V2 = 0.26
' 2 BERU
=
(0.132 + 0.152 + 0.16 )V2 = 0.25
( 5.2.1.3 Spray Additive Tank Structural Response Factors The structural response factors for equipment are based on the data presented in Chapter 4 and are tabulated in Table 5-3. The tank farm building was assumed to remain elastic at the spray additive tank fragility level. The structural response factors must be updated to the inelastic level on a trial and error basis if the fragility level of the tank exceeds the approximate structural yield level of 1.2g's. In this j case, it did not and the appropriate structural response factor and its l variability from Table 5-3 are:
fSR = 1.20 B
SRg
= 0.31 B
SRg
= 0.16 5.2.1.4 Spray Additive Tank Earthquake Duration Factor The anchor bolt failure on the spray additive tank is a brittle
{ type of failure with very little system ductility. Therefore, a short duration earthquake is nearly as damaging as a longer duration earthquake and the appropriate duration factor is unity with a variability of zero.
( 5.2.1.5 Syray Additive Tank Ground Acceleration Capacity The ground acceleration capacity for the spray additive tank was calculated using Equations 5-1 and 5-2.
{
4 = 1.59 x 1.58 x 1.20 x 1.0 x 0.25g's = 0.75g's
[
The variability was calculated by taking the SRSS of the variabilities for each of the four factors contributing to overall capacity (Equation 5-3).
2 B
R= (0.02 + 0.262 + 0.312+0.0) = 0.40 (randomness)
BU=(0.132 + 0.252 + 0.162+0.0')2=0.32 (uncertainty) k 5-35
[
( -- - - - - - - - -
I l
g The combined variability, CB , is a measure of the overall variability B contributed by earthquake randomness and uncertainty and can be obtained l
by taking the SRSS of SR and 89 l 2 l B C = (0.402+0.32)h = 0.51 I
j This value of BC , along with the four factors making up the overall fragility (FEC, FER, FSR, FED) are tabulated in Table 5-12 along with the rest of the equipment which were addressed in the Seabrook PRA study.
l 5.2.2 Example of Qualification Test Report Fragility Derivation The battery chargers will be used as an example of a fragility l derivation based on a plant specific test report. The battery chargers were qualified by subjecting them to 30-second duration simultaneous horizontal and vertical phase-incoherent inputs of random motion consisting of frequency band widths spaced one-third octave apart over I
l the frequency range of 1 Hz to 40 Hz. The chargers were subjected to generic required response spectra which were designed to envelop the requirements for a number of nuclear power generating stations.
l 5.2.2.1 Battery Charger Capacity Factors l During the seismic qualification testing of the battery charger, the indicator lights went out and the alarm relay contact opened. The explanation given within the qualification report (Reference 37) was that g the indicator light filament broke and made intermittent contact causing B both a fuse and a relay contact to open. In spite of this anomaly, the Wyle Laboratories test report states that the battery charger demonstrated sufficient integrity to withstand, without compromise of structural or l electrical functions, the prescribed simulated environment. Due to the indicator light failure and the relay tripping, it is judged that the l seismic SSE test level provided in Reference 37 is a fragility level for the battery chargers. It is estimated that any further increase in the loading would cause additional anomalies which could cause the functional failure of the chargers.
5-36 l
l 1 - - - - - - _ - -
The battery chargers are located at Elevation 21'-6" within the
]
control Suilding. Their fundamental frequencies are not specified within the qualification report, but past experience has shown these electrical components to be in the 5 to 15 Hz range. The capacity factor was, there-fore, based on average spectral acceleration values in the 5 to 15 Hz j range.
The test response spectra, from the test report, have the following average spectral accelerations in the 5 to 15 Hz range:
Horizontal = 6.0g's
( Vertical = 7.5g's
( These loads were utilized to define the failure load, Pc, in Equation ,
5-7. The normal loads on the battery charger are very small and were neglected. The seismic loading, PSSE, was taken from the ground
{ response spectra which are the appropriate floor spectra for the battery I
chargers. Two percent damped ground spectra were utilized for comparison i to the test spectra since the test response spectra were given for two percent damping. The average spectral accelerations from the ground spectra between 5 and 15 Hz are:
Horizontal = 0.86g's Vertical = 0.879's ,
Assuming that each earthquake directional component contributes equally to the functional failure mode of the battery chargers, the test level and the required level were ratioed by their resultant peak vectors.
2 p , (62 + 7.5 )V2 = 6.41 (0.862 + 0.862 + 0.872 )y
(
Note that the test level has only two components since biaxial testing
{ was conducted.
[ 5-37 b
f
l The variability on the computed strength factor has two separate I components. The first variability component pertains to the uncertainty in the fundamental frequency of the battery charger. The strength factor was calculated based on average salues in the 5 to 15 H: range. From
( '
inspection of the spectra, a 5 Hz frequency will produce the lowest corresponding strength factor (F3 = 5.38) within this frequency range.
Treating this as a 95 percent probability of exceedance (-1.658) value, the variability is calculated to be:
= I 8 * ""
3 1.65 .38)=0.11 ,
The second component of the strength factor variability, 85' 2
stems from uncertainty in the exact failure threshold of the battery charger. No anomalies were reported during the OBE testing which was at one-half the level of the SSE tests; thus, the OBE test level was treated as a lower bound for fragility. Estimating this OBE test level to represent a -28 lower bound on strength:
8 3 =finh)=0.35 i
The overall strength factor variability due to uncertainty is L then:
8 3 . Bhl + k 2 c
The ductility factor is unity and the variability on this factor b is zero since the battery charger failure mode is an acceleration sensitive functional failure. Thus, the capacity factor and its
( variability are equal to the strength factor and its variability.
E 5-38 r
I 5C "N S = 6.41 I
BCR "SR = 0.0 SCU "OSU = 0.37 5.2.2.2 Battery Charger Equipment Response Factors I The battery chargers were qualified to generic spectra whose safety factor and variability were accounted for in the strength factor.
Thus as described in Section 5.1.1.2.1.3, the qualification method factor and variabilties are:
I .
FqM = 1.0 8QMR"8QMU = 0.0 The battery chargers are located on the basemat in the control building and were qualified to the ground response spectra. The spectral shape factor and its variablity are unity and zero, respectively, for I this condition since the ground spectra conservatism and variability are included in the structural response factor. Therefore, f SS = 1.0 SSSg = BSSU = 0.0 The qualification test report states that the battery chargers were installed onto the test table exactly as they are anchored in the field. Thus, as is discussed in Section 5.1.1.2.7:
V FBC = 1.0 8BCR=BBCU = 0.0 I
I 5-39 I
The test response spectra (TRS) at two percent damping was compared to the required response spectra (RRS) at two percent damping to develop the strength factor. Even though actual damping is expected to be much higher, approximately the same ratio exists between the TRS and RRS for median damping. Therefore, the damping factor is considered to be unity and the variability equal to zero.
iD = 1.0 EDR"8Du = 0.0 I The fectral test methods factor quantifies the variability involved in synthesizing a time-history to represent the RRS.Section I 5.1.1.2.8 discussed this subjected and the recommended values are:
i STM = 1.0 BSTMR = 0.0 85TMu = 0.11 Multi-directional effects of using biaxial testing was accounted for in the development of the strength factor. In the strength factor development, the vector resulting from two components of biaxial excita-tion were compared directly to the vector resulting from three components of the median earthquake response. Thus, the difference between biaxial and three directional effects was accounted for and the factor, I MDE' equals unity. The uncertainty associated with the degree of coupling between earthquake directional components has also been accounted for within the strength factor derivation. There still exists the variability I due to random phasing of the earthquake which was stated in Section 5.1.1.2.9.1 to be about 0.12.
I i MDE = 1.0 BMDE R
= 0.12 BMDE
- U I
5-40 I
The overall equipment response factor,ER# , and its logarithmic standard deviations, P ER and BE% , were calculated by taking the n
product of the factors and the SR3s of the logarithmic standard deviations of each of the contributing variables (Section 5.1.1.2).
N ER = 1.0 8
erg = 0.12 B
erg = 0.11 5.2.2.3 Battery Charger Structural Response Factors The structural response factors listed in Table 5-3 are not
{
applicable for the battery chargers since the chargers are located on the base mat and were qualified to ground spectra. Building response does not affect the response of equipment mounted on the basemat. Only the effects of soil-structure interaction and the spectral shape of the ground spectrum affect the response. From Chapter 4, the soil-structure interaction modeling for buildings at the Seabrook site resulted in a SSI factor of 1.0 and variabilities of SR = 0.0 and 80 of 0.05.
The spectral shape f actor, in this case, is a measure of the conservatism involved in qualifying the battery chargers to the ground spectra instead of median site-specific spectra (Figure 3-1). The spectral shape factor was evaluated at the equipment fundamental frequency and for an estimated median damping level of five percent. The average spectral acceleration in the 5 to 10 Hz range is 0.70g's. The average spectral acceleration in the 5 to 10 Hz range is 0.50g's.
Therefore, the spectral shape factor is:
p g3 = 0.70g's 0.50g s
= 1.40
[
[
5-41
l 5
Methodology utilized in deriving the random and the uncertainty portion I of the variability on this spectral shape factor was developed in Chapter 4 for seismically critical buildings and are applicable to equipment mounted on the base mat. The resulting variabilities for the spectral shape factor on the battery chargers are BR = 0.30 and BU = 0.10.
The overall structural response factor and its variability for the battery chargers was calculated by combining the soil-structure interaction factor with the spectral shape factor.
FSR = 1.40 BSRR = 0.30 2
SSRg = (0.10 2 + 0.05 )Y2 = 0.11 5.2.2.4 Battery Chargers Earthquake Duration Factor Testing on battery chargers and similar electrical equipment has I shown that failures due to seismic loads consists of chatter, breaker trip and similar electrical malfunctions. These functional type failures have no ductility associated with them; thus, the earthquake duration f actor is unity and the variability is zero.
5.2.2.5 Battery Chargers Ground Acceleration Capacity The ground acceleration capacity for the battery chargers was I calculated using Equations 5-1 and 5-2:
E = 6.41 x 1.0 x 1.40 x 1.0 x 0.25g's = 2.24g's The variability was calculated using Equation 5-3:
2 BR = (0.122 + 0.30 )Y2 = 0.32 2 2 2 BU = (0.11 + 0.11 + 0.37 )Y2 = 0.40 I
I I 5-42 l
I
~
L Note that since is greater than 2.0g's, Table 5-12 will contain "NA" (not applicable) for the individual response factors and their variabili-ties and ">2.0 g's" for the ground acceleration capacity. Equipment with ground acceleration capacities greater than 2.0 g's do not contribute significantly to the overall risk of the plant; thus, do not necessitate a detailed derivation and subsequent inclusion in Table 5-12.
l 5.2.3 Examle of Generic Fragility Derivation Based on Design Specifications In the majority of cases in risk studies, all detailed informa-tion 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 equip-ment whose failure modes are structural and for which design reports or sunmaries were not reviewed. Balance of plant piping and miscellaneous pressure vessels and heat exchangers are typically addressed in this manner. Seismic capacities of Class 2 and 3 piping and supports were derived in a generic manner and have been chosen as the example for this section. Tables 5-7 and 5-8 contain the fragility derivation parameters l
for the balance of plant piping and the piping supports, respectively.
I 5.2.3.1 Failure Modes of a Piping System In order to determine the most probable failure mode for piping, I
I the design margins inherent for various pipe fittings, when designed to the governing code, must be compared to those for supports designed to the applicable codes. The fragility description for piping systems is l based upon the single component type most likely to fail (i.e., pipe fittings, straight pipe, pipe support, etc.). Failure of a pipe support l does not necessarily mean failure of a piping system pressure boundary; however, the scope of this study does not permit side studies to deter-mine the increased probability of a piping system failure, given a support failure. Consequently, it is assumed that a support failure results in a failure of the piping system.
I l 5-43
I !
5.2.3.1.1 P,iping Failure Modes - References 38 and 39 compare pipe fitting I collapse loads to code allowable load for Class 1, 2 and 3 piping for Service Levels C and D. Both studies used almost identical data bases and both studies were based on current code criteria which are essentially identical to the Seabrook piping design criteria. For illustration purposes, development of generic capacities for Class 2 and 3 piping is portrayed. Capacities for the Class 1 piping systems were developed in a similar manner.
Equation 9 for Class 2 piping was the governing equation of I Seabrook piping design for seismic induced loading combined with other loading and is:
P D 0.75i M
+ '"S (5-17)
I "$n Z h I The equation accounts for the axial stress due to pressure and the bending stress due to deadweight, hydrodynamic and earthquake induced moment, M .
a is a constant that depends upon the classification of the load combina-tion (i.e., normal, upset, emergency or faulted) and Sh is a basic code allowable stress intensity. The criteria only take credit for 75 percent of the combined deadweight and earthquake momcat; however, the combina-tion of 0.751 cannot be less than 1.0, where i is a stress intensification factor. This can have a slight effect on the most critical type of pipe iI fitting selected, Reference 38 ranks pipe fittings in order of least to most conservative design as:
- 1. Straight pipe
- 2. Elbows and bends
- 3. Branch connections
- 4. Tees 5-44
.I
Review of the data base reveals, however, that at room tempera-ture the elbows have a slightly les conservative design basis than
[ straight pipe. The same conclusior, can be drawn from Reference 39 .
However, two factors must be considered in the ranking. First, for elevated temperatures, straight pipe has a slightly less conservative design basis than elbows. This is due to a change in the governing criterion for establishing the allowable Sh as temperature increases (i.e.,S is based upon yield strength instead of ultimate strength).
h Secondly, the largest moments usually occur at terminal points in piping (anchors). Butt weld joints are then a logical candidate to define fragility descriptions for piping since they occur at almost all terminal points, in most cases have less margin against failure if stressed to code allowables, and are most likely to contain flaws.
5.2.3.1.2 Support Failure Modes - Supports for restraint of seismic inertial loads can be in the form of snubbers or rigid rod type supports and can be both horizontal and vertical. Vertical rigid rod type supports must also carry deadweight; thus, they would carry proportionally less seismic load than theoretically allowed for lateral supports or vertical snubbers. If it is assumed that the resulting stresses in each support type are at code allowable, a larger seismic margin would exist for vertical rigid supports than for lateral rigid supports or vertical snubbers. Thus, the fragility description for supports is based on supports that carry only seismic load. In the case of snubbers, the snubbers themselves would be less likely to fail structurally under the seismic loading than attachments to the pipe or the building.
5.2.3.2 Piping Capacity Factor p The steps utilized in establishing a median factor of safety on L piping capacity are:
- 1. Establish a range of piping capacity
- 2. Estimate the range of loading on piping due to weight, pressure and seismic events
{
E 5-45
- 3. Estimate the range of ductility
- 4. Estimate the threshold of piping system collapse
[ vs individual pipe element collapse.
( The range of piping system collapse is based on two extreme case models of piping failure. The upper bound on capacity can be represented by modeling the piping failure mechanism as occurring when the entire cross-section of the pipe is at the flow stress level. The flow stress is defined as midway between the yield strength and the tensile strength
~
of the material. This value has been shown from tests to be an upper bound on capacity.
The lower bound on capacity can be represented by modeling the piping failure mechanism as occurring on a flawed piece of straight pipe with a circumferential1y oriented flaw length equal to six times the pipe wall thickness. A flaw of this size is estimated to bound the possible flaws which could occur at butt welded joints. The theory for analyzing the moment capacites of through-wall flawed piping has been developed in Reference 40.
5.2.3.2.1 Piping Strength Factor - Strength factors were calculated for both of these extreme cases for a piping configuration that was estimated to be typical of the Seabrook plant critical piping. The assumptions made for this analysis were:
[ 1. Flow stress around the cross-section of an unflawed pipe represents the +2 logarithmic standard deviation (+28) upper bound
{
- 2. A flawed pipe configuration with the net section at flow stress represents the -2 logarithmic standard deviation lower bound (-28)
- 3. A 10-inch pipe model was used
- 4. Two pipe thicknesses bound the possibilities, high energy lines Schedule 160) and low energy lines (Schedule 40 5-46
[
- 5. Pipe material was assumed to be 304 stainless i steel type SA 312
[ 6. The upset load combination governed piping design (i.e., OBE + Press + DW)
A ten-inch pipe is considered representative of typical Seabrook piping, and the schedule 160 and the schedule 40 piping thicknesses are estimated to be the thickest and the thinnest piping commonly used for safety-related lines. In addition, past PRA studies on plants with piping design criteria similar to the Seabrook Plant have shown that the collapse capacity of stainless steel fittings is more critical than for carbon steel, and that the upset (0BE) load case always governs the design in the absence of pipe break loading coupled with the SSE.
The median collapse load for piping, based on the values calculated from the +28 bounding cases (i.e., the flow stress model and the through wall flaw model), was calculated to be 3.11 times the ASME code yield strength,oy (code) with a logarithmic standard deviation of
( 0.16. These values are used later in Equations 5-7 and 5-8 to derive the strength factor and its variability.
For essential Class 2 and 3 subsystems, the resulting stresses from normal loading plus OBE are held to upset allowables (1.2 Sh )*
The normal loading due to pressure and weight, combined with seismic loading, will vary considerably among piping systems. In a generic
[ treatment of piping, fragility estimates for loading ranges must be made. In a piping system, the axial pressure stress typically will be less than 1/2 Sh and will never exceed this value. Weight supports are nominally spaced to result in deadweight bending stress of about 1500
( psi. The combination of pressure plus weight stress is generally much less than the allowable value of Shin order to acconnodate seismic loading.
[
5-47
Expressing the pressure and weight stress approximations in terms of the allowable stress and allowing for variations, the normal loading stress range for piping systems will typically be from about 0.35 to 0.7 times the allowable stress, S . This translates to a median h
normal stress of 0.5 x Sh and a logarithmic standard deviation of 0.17. The total stress (oN+ OBE) for Seabrook piping systems are assumed to typically vary from 0.65 to 1.0 times the allowable design stress of 1.2 Sh . This translates to a median total stress of l approximately 0.80 x (1.2 x Sh ) with a logarithmic standard deviation of 0.13.
I For SA 312 Type 304 stainless steel, the ratio of the code yield strength of oy (Code) to the allowable value of Sh varies from 1.60 to 1.14 (depending on the operating temperature) with a median value of 1.35.
I Thus, we can put the components of the strength factor all in like terms.
Collapse Load =
C = 3.11 x cy (Code) = 3.11 x l (Sh x 1.35) = 4.20 x Sh 8co11 apse = 0.16 l
Normal Stress =
N = 0.5 x Sh SN = 0.17 Total Stress =
T = 1.2 x 0.8 x Sh = 0.96 x Sh BT = 0.13 5
l Using Equation 5-6, R
S* 4.20 0.96 -- 0.5 0.5 _- 8.04 Using Equation 5-8, 83 = 0.36 5-48 5
This strength factor of 8.04 was calculated based on the pipe
( being capable of reaching the flow stress. Piping capacity tests strnmarized in Reference 38 have shown that thick-walled pipe are capable of reaching this flow stress, but that thin-walled pipe (schedule 40 or
[
schedule 80) buckles before this flow stress is realized. Thus, the calculated strength f actor of 8.04 is not applicable to thin-walled piping. For piping with D/t ratios (diameter to thickness) between 25 and 50, which is representative of the standard weights of pipe (schedule 40), the median shape f actor for both stainless steel and carbon steel ranges from about 1.4 to 1.7. Since a broad range of pipe sizes,
( materials and schedules is being considered, a shape factor of 1.5 is selected as a median value for all piping within this D/t range. This median pipe capacity under static load is then 1.5 times the yield
{ moment. Considering that the median yield strength is about 1.25 times the ASME code specified yield strength, the median moment capacity is about 1.87 times the yield moment determined from code yield properties.
The strength factor for thin-walled piping is calculated using Equation 5-6:
F 2.52 x Sh - 0.5 x Sh 3 = 0.96 x Sh - 0.5 x Sh where the Collapse Load = C = 1.87 x (1.35 x Sh ) = 2.52 x Sh The logarithmic standard deviation, 8 Collapse, remains the same at a 0.16 value; thus, the strength factor variability will be identical to that which was previously calculated (i.e., Bs = 0.36).
The overall peak ground acceleration capacity of the Seabrook plant critical piping is conservatively based on the buckling of the thin-walled piping.
N = 4.39 3
B s = 0.36 5-49 a
5.2.3.2.2 Piping Ductility Factor - Reference 6 recommends a ductility b of 1.5 to 3 for design of critical piping systems. These are design recommendations; thus, the value of 3 is considered to be a median value
( with 1.5 representing an approximate lower bound or approximately a minus two logarithmic standard deviation value. Using these assumptions and applying Equation 5-9, the median factor of safety for ductility was computed to be 2.24 with a logarithmic standard deviation, sy , of 0.24.
The random portion and the uncertainty portion of the ductility variability are considered to be about 0.16 each.
b 5.2.3.2.3 Piping "Three-Hinge" Factor - For complex piping systems, there is an additional source of design conservatism. In order for a piping
{ system to completely collapse, usually more than one collapse mechanism must form in the system; thus, basing fragility on the moment capacity of one fitting is conservative. A lower threshold of collapse could be likened to a simple beam where only one hinge is necessary for collapse.
An upper threshold of collapse could be likened to a fixed-fixed beam F where three hinges must form. The elastically calculated maximum moment in the latter case would be 1.5 times the pipe element collapse moment.
l These bounds were considered to be approximately a +2s range and the median system collapse factor was computed to be 1.22. The logarithmic l standard deviation, which is all uncertainty, is approximately 0.1.
I l Combining all the f actors and variabilities results in a median capacity factor of safety relative to the OBE and variability expressed in terms of logarithmic standard deviations of:
FC = 12.0 BCR = 0.16 BCU = 0.41 5-50
5.2.3.3 Piping Equipment Response Factors l The equipment response factors for piping are contained within Table 5-7 and are explained briefly below. The bulk of the piping was qualified by response spectrum analysis; thus, a factor of unity and a
[ variability of zero are applicable for qualification method. The spectral shape factor was taken from Table 5-1 in the 5 to 20 Hz l
l F frequency range for the "All Other Buildings" category. This category was used from Table 5-7 for the example, while individual factors based on the location of the piping system were used on a piping system by piping system basis.
The modeling of the piping systems is felt to be median centered and of median complexity, thus, NM = 1.0 BMg = 0.0 B
Mg = 0.15 The damping factor was computed by comparing response for a two percent damped spectrum to response for an expected median damping value of five percent at or near failure. Two percent damping was utilized in designing large diameter piping to the OBE event. For the example problem, spectra for Elevation 53' in the Primary Auxiliary Building was used. Applying Equations 5-13 and 5-14:
kD = 1.34
" S DR = 0.03
{
B og = 0.17 The mode combination factor is unity with random variability of 0.15 as suggested in Section 5.1.1.2.5 for multiple degree-of-freedom systems.
5-51 1
l
b
[ The earthquake component combination factor for piping is considered to be the general case (Case No.1 in Table 5-2) since all three directions of earthquake motion generally excite the piping system.
( The overall equipment response factor, IER and the variability, BR and SU for piping were computed to be:
f ER = 2.14
(, BERR = 0.28 S
ERu 0.28 5.2.3.4 Piping Structural Response 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 5-3. Piping systems are typically in the 5 to 20 Hz frequency range and values in Table 5-3 corresponding to this frequency band were used. The structural response factor used as an example in Table 5-7 for piping is the most conservative value within Table 5-3, and is for the containment internals.
5.2.3.5 Piping Earthquake Duration Factor Piping is a very ductile system and the duration factor and associated logarithmic standard deviations are specified in Section 5.1.1.4 to be:
ED " 1.4 8
EDR = 0.12 B
{ EDu = 0.08
(
[
[
5-52 F
L
[ 5.2.3.6 Piping Ground Acceleration Capacity The ground acceleration capacity for piping was obtained by multiplying the four factors within Equation 5-1 by the OBE level of 0.125g's, since the capacity factor was developed based on the OBE and L not the SSE as is generally the case.
d = 4.99g's
% = 0.43 BU = 0.53
[ 5.2.3.7 Piping Supports Capacity Factor It was stated previously that for supports stressed to their design limit under seismic conditions, the minimum margin would occur if
{ the load were all seismic (i.e., the support carried no normal load).
The fragility description for supports was developed on this basis.
{
In order to apply Equation 5-7 to compute a strength factor or upper and lower bound factors, the range of material properties, the support failure mode, the allowable design load and a range of applied load for the seismic event must be established.
( Piping supports are generally constructed of carbon steel, and three of the most comon carbon steels were utilized for this generic study. The three carbon steels are SA 36, SA 675-G70 and SA 516-G70.
{ The ratio of the allowable stress value, Sh , to the yield strength was evaluated for each of these materials with a resulting median ratio of 0.53 and logarithmic standard deviation of 0.11.
( Almost all piping supports in a modern nuclear power plant such as Seabrook are welded carbon steel structures, and from analytical experience the most critical section of these supports due to seismic
{ loading is the welds. Since the pipe supports at Seabrook were designed
[
5-53
L to current ASME Code criteria contained in Appendix XVII of the Code for
[ linear type supports. Appendix XVII specifies that for Service Level B (Upset Condition):
I OBE + Deadweight + Thermal s 0.4 Sy (shear in welds)
I where Sy = ASME Code specified yield strength.
L For Service Level D (Faulted Condition) the allowable of 0.4 Symay be increased up by the lessor of "1.2 x (o y / allowable)" or "0.7 x ult / allowable)" where in this case allowable is the tension allowable of 0.6Sy . Using the properties of A36 carbon steel, the l lesser of these factors is 1.88. Thus, the allowables for Level D conditions are:
SSE + Deadweight + Thermal + Hydrodynamic s 0.75 S y
F L Since deadweight and thermal are taken to be zero, the OBE loading condition governs, just as it did for the piping.
A classical strength of materials analysis of fillet welds which are subjected to a combined state of shear and tensile loads, as are typically produced in pipe supports, has shown that yield will occur in the weld throat when the principal stress is 73 percent of the material yield strength. The variability on this 73 percent factor can be quantified by estimating the pure shear condition (shear yield is L approximately 60 percent of the yield strength) to be 95 percent probability of exceedance value (-1.658) and a logarithmic standard
[ deviation of 0.12 results. The yield level in the weld throat was utilized as the collapse load in determining the strength factor
{ (Equation 5-7), realizing that the ductility f actor will quantify the supports' capacity past the yield level and into the plastic region.
oC = Collapse Stress = 0.73 x cy i 5-54 I
WII II.I It was assumed that the median seismic stress is 0.7 times the allowable design load for welds, 0.4 x Sy , with 1.0 times the design
[ load being about a +1.658 (90 percentconfidenceupperbound). Thus, the median OBE stress and its logarithmic standard deviation are:
"0BE = 0.7 x 0.4 x Sy = 0.28 Sy b
8 0BE = in = 0.22 j For the most limiting case, the normal stress is zero and Equation 5-7 becomes:
f= C
( OBE References 35 and 41 have established that the median yield strength of
( both carbon and stainless steels is about 25 percent above the ASME code specified yield strength with a variability of 0.14. Therefore.
r NS " 0.73 x 1.25 x S = 3.26 0.28 x S y L
The overall logarithmic standard deviation on the strength factor was computed using Equation 5-8 to be 0.29.
The system ductility for piping systems is considered applicable to supports since piping may be well into the inelastic range prior to
{ failure of a support. The median ductility factor, F y, is then about 2.24 with logarithmic standard deviations due to both randomness and
[ uncertainty of B U R
.B Ug = 0.16.
( Combining the strength and ductility factors and their varia-bilities, the resulting capacity factor relative to the OBE and its variabilities were computed to be:
{
E 5-55
[ f EC = 7.30
{ BECR = 0.16 .
SECU = 0.33 Pipe supports have a much lower capacity factor than piping and would be the governing element in piping systems.
Concrete anchors used to attach the pipe supports to the surrounding walls are not qualified with the supports themselves; thus, must be addressed separately. The NRC has required a factor of safety of
( four for wedge anchors and a factor of safety of five for shell anchors (Reference 42) to be used in the anchorage design of piping and equipment.
These safety factors are based on the median ultimate capacity of the
{ particular anchor bolt in question in relation to the design allowable.
In the design of a piping system, the load on a pipe support will generally be less than the allowable and it is estimated that the median load on a support is 70 percent of the design allowable. Thus, strength factors of 5.7 and 7.1 exists for the wedge anchors and the shell anchors, respectively.
Effective ductility for the anchorage pullout depends. upon the
( degree of inelasticity in the piping system. If the piping system remains elastic up to the point of anchor pullout, the failure mode is brittle, the elastica 11y calculated load is valid and the ductility
{ factor would be 1.0. On the other hand if the piping system were highly inelastic, the calculated support loading would not develop and the ductility factor computed for piping systems would be appropriate. The effective ductility factor can then be assumed to range from 1.0 to
[ 2.24. The median ductility factor is about 1.5 with a logarithmic standard deviation of 0.2. Combining the median strength and ductility factors results in:
{
[
E 5-56 E
[ (EC = 8.55 (for wedge anchors) fEC = 10.65 (for shell anchors) l Thus, the concrete anchor bolts will not govern the fragility description i
[ of piping systems since piping supports have a lower capacity factor.
( L 5.2.3.8 Ground Acceleration Capacity of Piping Supports The equipment response factor, the structural response factor and the duration factor for piping supports are identical to those which were
{ developed for piping. Table 5-8 contains all of the fragility f actors for pipe supports. The ground acceleration capacity of pipe supports and
[ its variability are:
d = 3.03g's BR = 0.43 EU = 0.47 Pipe supports are then the governing failure mode for piping systems and were utilized in their fragility descriptions. However, since the ground
( acceleration capacity of the pipe supports is greater than 29 's they will not contribute significantly to the overall plant risk.
5.2.4 Example of Fragility Derivation Based Upon New Analysis A new analysis was conducted for the refueling water storage
{ tank in order to remove some of the conservatisms and uncertainties that are inherent in scaling from the vendor's design analysis.
The RWST is 44'-0" inside diameter and is composed of six rings
( of different thicknesses. The tank has a spherical dome roof and is anchored to a slab in the tank farm area at EL 20'. Amplified response spectra applicable to the tank location in its supporting structure were
{ specified by UE&C and are contained in the vendor design report, Reference 46. The tank is anchored by 46, 2-inch diameter SA 193 Grade B-7 high strength bolts.
5-57
L The tank was analyzed using computer program TANK. TANK computes the fundamental frequency and base shear and overturning moment for a
( specified input acceleration. The program was developed around the methodology of Veletsos, Reference 46. The fundamental flexural frequency
{ of the tank was computed to be 7.0 Hz. The first 2 modes of sloshing frequency were computed to be 0.26 Hz and 0.44 Hz. The tank was assumed to be rigid in the vertical direction. l The base shear for the specified design spectrum was 2100 kips
, and the overturning moment was computed to be 53,700 ft/ kips. These loads were used to assess the potential failure modes in the tank.
Several potential failure modes were examined to determine the governing capacity. Failure Modes examined included:
{
Anchor bolt tension in threads Anchor bolt shear and tension in unthreaded shank Shell buckling Anchor bolt chair gusset welds Anchor bolt chair gusset capacity
( Anchor bolt chair tcp plate
{ It was determined that the minimum capacity was controlled by the anchor bolt chair gussets. They are subjected to a combination of compression and bending and when a fully plastic section (compression plus bending) was formed, the gussets were assumed to become unstable, allowing tank lift-off and subsequent buckling of the compression side.
5.2.4.1 RWST Capacity Factor
[ The tensile bolt load at failure of the bolt chair gussets was computed to be 266 k. The computed tensile load from the specified SSE amplified response spectrum was 106 k. The resulting strength factor is
{ computed as:
F 3 = 266/106 = 2.51 5-58
[
Tnere are two sources of uncertainty in the bolt chain capacity, the uncertainty in the strength calculation and the uncertainty in the
[ material properties. Failure level of the bolt chair gussets is a complex problem to assess. The failure model assumed that when the free edge of the bolt chair gusset was fully plastic, i.e., the combination of
{ axial load and bending produced a fully plastic section, the increased eccentricity would result in the gussets buckling. The next higher failure mode was computed to be tensile failure in the anchor bolt in the thread area. Vedian tensile capacity was calculated to be 344 kips. It
( was reasoned that plastic buckling of the gussets would possibly either not occur or that the deformed bolt chairs would not result in tank
[ failure until the ultimate strength of the bolts was reached. The bolt ultimate strength was assumed to be a 95% confidence upper bound. The uncertainty,BU , on the failure strength was computed to be:
{
[ BU strength=(1/1.65)in (344/266) = 0.16 The uncertainty on gusset material strength is well defined. Median
( strength is about 25% above the code specified strength, where code strength is a 95% confidence value, Reference 41. The uncertainty on
[ material strength is then:
Su = (1/1.65) in 1.25 = 0.14 matl.
The resulting uncertainty on strength is:
e s
u
'C+ 4U'*
There is no random variability assigned to strength thus, 8 = 0.
3 R
The failure mode, whether gusset buckling or bolt tension, will occur with very little displacement and is considered a brittle failure; thus, there is no credit taken for ductility.
E 5-59
5.2.4.2 RWST Equipment Response Factor The variables that must be addressed in deriving an equipment L response factor and its uncertainty include:
[ Qualification Method Spectral Shape p Damping Modeling Mode Combination L Earthquake Component Combination r"
L 5.2.4.2.1 Qualification fkthod - The dynamic analysis was conducted by the response spectrum method which is considered to be median-centered.
{ The uncertainty in the response analysis is defined by other variables;.
thus, the qualification method factor and its variability are considered r to be unity and zero, respectively.
L 5.2.4.2.2 Spectral Shape Factor The amplified response spectra, ARS, I used in the analysis were peak broadened 10% and smoothed. The ARS peaked at 2.5 Hz wherein the tank fundamental frequency was 7.0 Hz; thus, l there should not be a large factor of conservatism well away from the spectral peak. Comparisons of raw and smoothed spectra were not readily l available for the tank locations and the spectral shape factor was conservatively assumed to be 1.1. This is consistent with factors in Table 5-1 for frequencies well away from the peak of the ARS. Since the tank was mounted very low in its supporting structure, the ARS ZPA was only amplified about 20%, thus it was assumed that there was virtually no additional conservatism applied in generating the ARS. The uncertainty in the spectral shape factor was computed to be:
1 8
33 U
l Random variability,e SS , is considered zero for the equipment spectral R
shape factor.
5-60
[ 5.2.4.2.3 Damping Factor - The ARS used in the response analysis was for 3% damping. Median damping is considered to be 5%. Five percent damped
( ARS were not specified for the tank location. The ratio of 3% to 5%
amplified response was, therefore, estimated from ground motion amplifica-tion f actors contained in Reference 10. The ground motion amplification
{
factors are applied at the tank fundamental frequency. Use of ground motion amplification factors is reasonable, since the ARS spectral shape is similar to that for the ground motion input at the tank fundamental frequency. The resulting factor is conservatively estimated as:
(
Sa3% -
F " l'ID D
" Sa 5%
{
Three percent damping was assumed to be an approximate 95% lower bound; thus:
{
eg = (1/1.65) in 1.15 = 0.09 The actual equipment damping is considered to be all uncertainty; thus,
[ eo = 0.
R
( 5.2.4.2.4 Modeling Factor - The dynamic model was considered to be median-centered,
[
FM = 1.0
[ The geometry is simple and the error in calculating the fundamental frequency was estimated to be no greater than 15%. A 15%
error in frequency at the tank frequency results in very little difference in spectral acceleration due to the shallow slope of the ARS
( at 7 Hz. The resulting uncertainty, Bg , was only about 0.01. SM is !
U R considered zero for modeling.
[ 5.2.4.2.5 Mode Combination Factor - Sloshing and tank flexural mode response were combined by the square-root-of-the-sum-of-the-squares, SRSS, rule which is considered to be median and the response factor is considered to be unity. The tank response is dominated by the flexural
( mode response; thus, the variability is very small. Mode combination variability is considered random and:
[
eMC R
= 0.03 5-61
5.2.4.2.6 Earthquake Component Combination Factor - The base shear and overturning moment were computed for one direction of response. The SRSS
[ response combination for vertical, circular components would result in no increase in bolt load. There is, however, a possibility of having two
[ orthogonal acceleration vectors in-phase, in which case, the resulting vector would be d times the specified horizontal acceleration for each direction. An estimate of the most probable phasing is taken from Reference 10 where it is suggested that 100% of the load in one direction be combined with 40% of the load in the other two orthogonal directions.
L verticai ecceieration contributes very iittie to tne tanx feiiure mode; thus, the resulting response factor for the horizontal resonse is:
I F
ECC = 1/(1 + 0.4 )b = 0.93 l
The phasing is all random variability. Considering the ratio of completely in-phase vectors to out-of-phase vectors to be a three log standard deviation spread, l S = (1/3) in 1.4 = 0.14 I
l ECC a
5.2.4.2.7 Overall Equipment Response Factor - The overall equipment response factor and its variability reflects the degree of conservatism l
and uncertainty in the tank response analysis that was conducted using the specified SSE ARS.
l F
ER
= (1)(1.1)(1.15)(1.0)(1.0)(0.93) = 1.18 l s gg = (0 + 0 + 0 + 0 + 0.032 + 0.19 ) = 0.12 p
l B ER
= ( 0 + 0.062 + 0.09 2 + 0.012 + 0 + 0) = 0.11 U
5.2.4.3 RWST Structural Response Factor The RWST is mounted in a Tank Farm structure for which ARS were generated. The ARS peaks at 2.5 Hz reflecting the fundamental frequency 5-62 I
I of the structure. Concrete structures were analyzed for a damping level of 7%. The variables to be considered in quantifying the conservatism and uncertainty in the structural response are:
j Spectral Shape Damping Modeling Soil-Structure Interaction 5.2.4.3.1 Spectral Shape Factor - At the 2.5 Hz fundamental frequency of the structure, there is a pronounced difference in the amplification l between the Reg. Guide 1.60 spectrum specified for design and the site-specific spectrum considered to be median for fragility analysis. Figure 3-1 compares these two spectra. The spectral shape factor is defined as:
Sa F
R.G. 1.60 j
33 = Sa
= 1.81 I site-specific The variability of the amplification in the site-specific spectrum varies with frequency. From data in Reference 29, at 2.5 Hz, the random variability is:
8 = 0.38 33 p The uncertainty in the spectral shape,8 33U' approximately 1/3 833 R
I S Ss u
" (1/3)( '38) " *13 l 5.2.4.3.2 Damping - Structure response was calculated using 7% damping.
For structures that are below yield, 7% is considered to be median. The supporting structure is considered to be below yield and the design I
damping is considered to be median with the resulting damping factor being unity (FD = 1.0). Ten percent (10%) damping is considered to be an approximate plus one log standard deviation value, thus:
S D
= = 0.10 V 7%
5-63 I
[ There is some random variability assigned to damping that is a function of the earthquake time history input. The 80 is estimated to
{ be equal to S D*
g R
5.2.4.3.3 Modeling Factor - The structural model was considered to be
^
median-centered.
- F M
= 1.0
. The structural model is simple and the uncertainty, 8g is estimated to be 0.1. B M is taken as zero. U R
5.2.4.3.4 Soil-Structure Interaction - Seabrook is a rock site and all structures are either founded on rock or on concrete fill. Therefore,
]
uncertainty in using fixed-base structural models is very low and estimated to be:
u B 33;U 5.2.4.3.5 RWST Structural Response Factor - The overall structural j response factor and its variability are:
I F SR = 1.81 (1.0)(1.0)(1.0) = 1.81 s
39 =(0.382 + 0.102 + 0 + 0) = 0.39 8
3p U
= M M + d + d + 0. M = M 5.2.4.4 Earthquake Duration Factor
} The tank failure mode is considered to be essentially brittle.
The duration factor is accordingly considered to be unity with zero variability.
I 5-64
s
! 1 5.2.4.5 RWST Capacity '
The peak ground acceleration capacity of the RWST is the product of the four factors time the SSE peak ground acceleration.
A = (2.51)(1.18)(1.81)(1.0)(0.25) = 1.34g The variability is the SRSS of the variabilities of the four factors:
{
B R = (0 + 0.122 + 0.392 + 0)b = 0.41 s
U =(0.212 + 0.112 + 0.202 + 0)b = 0.51 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 Seabrook 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 l previous examples of developing capacity factors, response factors, duration factors, etc., is ' generally not applicable for unqualified components. The fragility levels for components must be derived based on earthquake experience and engineering judgment. The example which has l been chosen in this category is the reserve auxiliary transformer.
This transformer is a large steel structure which sits unanchored on a concrete slab. It is located on the base mat, so building amplifica-tion will not be a consideration. Inspection of the transformer during the Seabrook site visit led to the judgment that sliding of the trans-former relative to the slab would occur before overturning of the trans-former. A static coefficient of friction between steel and concrete of
{ 0.4 is recommended in Reference 43. Due to uplift effects from the vertical portion of the earthquake combined with the horizontal components, an acceleration level of about 0.39's could be tolerated
[
5-65
before transformer sliding will occur. The derivation of this 0.3g ground acceleration fragility level was based on engineering judgment combined with seismic analysis using simplified models.
As a check of the transformer fragility level which was derived in the previous paragraph, some earthquake experience data exists for transformers which are'unanchored. Reference 44 reports that an
{
unanchored two station auxiliary transformer sustained significant damage during the 1971 San Fernando Earthquake. This transformer experienced as much as 18 inches of movement relative to its concrete pad and the resulting damage included broken 4.16 KV bushings, damaged bushing F
L terminal plates, and terminals, control box malfunction and surface conduit failures. Reference 44 reports that the San Fernando Valley
{ earthquake which caused this transformer damage had an estimated peak ground acceleration in the range of 0.3g to 0.59 Thus, actual experience confirms the 0.3g capacity calculated by approximate methods. There is
{ considerable variability on this capacity due to both the uncertainty involved in the failure mechanism and the randomness of the earthquake.
3 Earthquake experience has shown that for numerous small earthquakes in the 0.lg peak ground acceleration range very little damage has occurred
[ to unanchored equipment. Thus, the 0.lg level was used as a 98 percent probability of exceedance value (-2.08) which results in an overall 8 =
0.55.
{ Based on engineering judgment this can be broken down to S R*
0.25 and BU = 0.50. Table 5-9 shows the ground acceleration capacity and its associated logarithmic standard deviations for loss of offsite power which would include the reserve auxiliary transformer as well as other high voltage electrical equipment in the switchyard as well as on the grid.
[ 5.3 EQUIPMENT FRAGILITY RESULTS Table 5-9 contains fragility descriptions for all of the equip-
{ ment which were included in the PRA. Fragility derivations were conducted for each of the components and are reported for those items which have a ground acceleration capacity less than 29's. Pickard, Lowe and Garrick, Inc. has stated that equipment which possess ground acceleration capaci-ties greater than 2g's will not contribute to the overall plant risk because of the extremely low frequency of events causing this level of
[ 5-66
I acceleration; thus, detailed fragility descriptions need not be included.
Equipment which fall into this category have been labeled with a
"> 2.0g's" in the ground acceleration capacity column, and have "NA" (not applicable) in the response factor and variability columns. In addition, for those components which have capacities less than 2.0g's, only the capacity f actor, equipment response factor, structural response f actor I and the earthquake duration factor are given in Table 5-9. Intermediate factors which make up these four main factors were determined but not included in the table.
5.3.1 General Results The following are some general results on the equipment portion of the PRA:
- 1. The majority of the equipment within the Seabrook I plant which were seismically qualified have rela-tively high ground acceleration capacities. This is due to the relatively high SSE (0.25g ZPA)
I coupled with the more sophisticated qualifi-cation techniques and applicable codes which are associated with equipment in a modern plant.
- 2. Non-seismically qualified components listed in Table 5-9 generally have relatively low capacities and relatively high uncertainties.
These results are understandable due to the lack of a requiremeqt for seismic design.
I 3. The category of " instrument sensors" within Table 5-9 represents a group of information gathering devices (thermocouple probes, pressure trans-I ducer:, flow transmitters, etc.) which have been shown during vibration testing to be inherently rugged. The weak link in theN ' instrument sensor systems is estimated to be Le : 1all tap lines which connect the piping fr :w" .nent to the transmitters. These liaq ry a idged to have a capacity similar to that of sma rt piping which is greater than 29's.
- 4. Where failure modes are listed in Table 5-9 as
" chatter," the consequences of chatter should be I determined by the systems analyst by examining the electrical circuits and capability of the operators to recover from any spurious signals or trips resulting from chatter.
5-67 I
l TABLE 5-1: EQUIPMENT SPECTRAL SHAPE FACTORS l
I Peak Broadening Overall Spectral Shape I Building Equipment Frequency and Smoothing Factor (Hertz) F 33 8
33 F
33 8
33 8
33 i
1 1 U R i Containment 3-10 1.23 0.10 1.35 0.10 0.2
) Building 10-15 1.24 0.11 1.36 0.11 0.2 15-20 1.16 0.07 1.28 0.07 0.2 20-33 1.05 0.02 1.16 0.02 0.2 5-20* 1.21 0.11 1.33 0.11 0.2 Rigid 1.0 0.0 1.1 0.0 0.2 Primary 3-10 1.47 0.19 1.62 0.19 0.2 Auxiliary 10-15 1.24 0.11 1.36 0.11 0.2 l Building 15-20 1.35 0.15 1.48 0.15 0.2 l
20-33 1.30 0.13 1.43 0.13 0.2 5-20* 1.35 0.19 1.48 0.19 0.2 Rigid 1.0 0.0 1.1 0.0 0.2 Control / Diesel 3-10 1.25 0.11 1.37 0.11 0.2 Generator 10-15 1.13 0.06 1.24 0.06 0.2 Building 15-20 1.09 0.04 1.20 0.04 0.2 i 20-33 5-20*
1.17 0.08 1.29 0.08 0.2 1.16 0.11 1.28 0.11 0.2 Rigid 1.0 0.0 1.1 0.0 0.2 Fuel Buildings 3-10 1.25 0.11 1.37 0.11 0.2 10-15 1.60 0.23 1.76 0.23 0.2 j 15-20 1.11 0.05 1.22 0.05 0.2 20-33 1.10 0.05 1.21 0.05 0.2 5-20* 1.32 0.23 1.45 0.23 0.2 Rigid 1.0 0.0 1.1 0.0 0.2 All Other 3-10 1.30 0.13 1.43 0.13 0.2 I Buildings 10-15 15-20 20-33 1.30 1.18 1.15 0.13 0.08 0.07 1.43 1.30 1.26 0.13 0.08 0.07 0.2 0.2 0.2 5-20* 1.26 0.13 1.39 0.13 0.2 Rigid 1.0 0.0 1.1 0.0 0.2
- Piping, Cable Tray and Conduit are typically in the 5-20 Hz range depending on the support configuration.
I i
5-68 I
t m m J v M v _m v n v r TABLE 5-2: EARTHQUAKE COMPONENT COMBINATION FACTORS Case Directional Number Responses Description F 8 8 ECC R 0 1 2 Horizontal + General Case (Piping) 1.15 0.12 0.10 Vertical 2 2 Horizontal General Case, Coupled 1.11 0.10 0.08 3 2 Horizontal Rectangular Anchorage Failure Mode, Uncoupled, 1.01 0.12 0.0 Designed by SRSS of the resultant stresses 4 2 Horizontal Circular Anchorage Failure Mode, Uncoupled, 1.31 0.06 0.0 Designed by SRSS of the applied moments m 5 2 Horizontal Circular Anchorage Failure Mode, Uncoupled, 0.926 0.06 0.0
& Designed by SRSS of the resultant stresses
, 6 1 Horizontal + Coupled 1.04 0.07 0.05 l
Vertical 1 Horizontal +
7 Uncoupled 1.15 0.03 0.0 Vertical 8 1 Horizontal General Case 1.0 0.0 0.0 I Refers to the earthquake directional components which affect the failure mode under consideration
TABLE 5-3: STRUCTURAL RESPONSE FACTORS FOR EQUlPMENT Approximate Elastic Structure Inelastic Structure Building Yield p Level) F SR 8 8 F 8 8 R U SR R U L
(g's)
Waste Processing /
Tank Farm 1.2 1.20 0.31 0.16 1.45 0.24 0.16 Containment Internals high 2 1.11 0.26 0.16 NA 2
NA 2
NA 2
Fuel Storage 2.15 1.14 0.22 0.16 1.25 0.19 0.16 Containment 2.87 1.22 0.30 0.16 1.46 0.25 0.16 Control / Diesel 1.15 1.16 0.31 0.14 1.37 0.23 0.16 Primary Auxiliary 1.2 1.20 0.31 0.16 1.45 0.24 0.16
, service Water Pump Structure 1.28 1.24 0.14 0.16
{ 1.26 0.10 0.15 RHR/ Containment Spray Vault I 1.2 1.20 0.31 0.16 1.45 0.24 0.16 Cooling Tower 0.90 1.19 0.30 0.16 1.43 0.25 0.15
[ Pipe Chase high 2
1.17 0.30 0.16 NA 2
NA 2
NA 2
Emergency Feed-water Pumphouse 0.90 1.24 0.33 0.16 1.50 0.28 0.17 Containment Enclosure Ventilation Area 1.2 1.15 0.22 0.13 1.26 0.18 0.13 I
The approximate yield level estimates the ground acceleration level at which yielding is reached in the building. Equipment with capacities less than this value should
[ 2 utilize the elastic structural response factors.
The containment internals and the pipe chase have very high yield levels, and thus the 1/2 yield structural response factors will always be appropriate.
C 5-70 V - - - - - - - -
E I
TABLE 5-4: NUCLEAR POWER PLANT EQUIPMENT CATEGORIES I Relative Capacity Equipment Categcry Level High 1. Piping, Ducting, Cable Trays and Electrical Conduit
- 2. All Valves (Except small motor operated valves)
Medium-High 3. Small Vessels and Heat Exchangers
- 4. Horizontal Pumps, Compressors and Turbines I 5.
6.
7.
Fans and Air Conditioning Units Diesel Generator Reactor Coolant Loop Components I Medium 8. Small Motor Operated Valves
- 9. Large Vessels and Heat Exchangers I 10. Batteries and Racks
- 11. Vertical Pumps
- 12. Reactor Internals and Control Rod Drive Mechanism Low-Medium 13. Motor Control Centers, Switchgear, Control Panels, Instrument Racks I 14. Non-seismically Qualified Components (e.g. Offsite PowerSystem)
I I
I I
I I
5-71 I
TABLE 5-5: FRAGILITY DERIVATION OF THE SPRAY ADDITIVE TANKS i
[ Factors Median Safety Random Variability Uncertainty Variability Factor B 8 R U Capacity Factor (FEC)
- 1. Strength Factor 1.59 0.0 0.13
- 2. Ductility Factor 1.0 0.0 0.0 Combined -.- F 1.59 0.0 0.13 EC Equipment Response Factor (FER) f 1. Qualification Method 1.0 0.0 0.0 L 2. Spectral Shape 1.43 0.20 0.13
- 3. Modeling 1.0 0.0 0.15
- 4. Damping 1.19 0.0 0.16
- 5. Combination of Modes 1.0 0.15 0.0
- 6. Earthquake Component Com-bination 0.926 0.06 0.0 Combined - F 1.58 0.26 0.25 EC Structural Response Factor (FSR) 1.20 0.31 0.16 l
Earthquake Duration Factor (FED) 1.0 0.0 0.0 I
Ground Acceleration Capacity (A) 0.75 g's 0.40 0.32 l
l l
l 1
l 1
5-72
[
b TABLE 5-6: FRAGILITY DERIVATION OF BATTERY CHARGERS
[ Median Random Uncertainty Factors Safety Variability Variability Factor S R
8 U
Capacity Factor (FEC)
- 1. Strength Factor 6.41 0.0 0.37
- 2. Ductility factor 1.0 0.0 0.0 Combined-. FEC 6.41 0.0 0.37 EquipmentResponseFactor(FER)
- 1. Qualification Method Factor 1.0 0.0 0.0
- 2. Spectral Shape Factor 1.0 0.0 0.0
- 3. Boundary Conditions Factor 1.0 0.0 0.0
- 4. Damping Factor 1.0 0.0 0.0
- 5. Spectral Test Method Factor 1.0 0.0 0.11
- 6. Multi-Directional Effects Factor 1.0 0.12 0.0
( Combined - F ER 1.0 0.12 0.11 Structural Response Factor (FSR) 1.40 0.30 0.11 Earthquake Duration Factor (FED) 1.0 0.0 0.0 Ground Acceleration Capacity (A) 2. 24 g 's 0.32 0.40
[
[
[ !
[
[ 5-73
L
(
TABLE 5-7: FRAGILITY DERIVATION OF BALANCE OF PLANT PIPING
[
{ Factors Median Safety Random Variability Uncertainty Variability
. Factor 8 R
8 U
[
Capacity Factor (FEC)
- 1. Strength Factor *
{ .
- 2. Ductility Factor 4.39 2.24 0.0 0.16 0.36 0.16
- 3. 3 Hinge Factor 1.22 0.0 0.10 Combined--. EC F* 12.0 0.16 0.41 Equipment Response Factor (FER)
( 1. Qualification Method 1.0 0.0 0.0 L 2. Spectral Shape 1.39 0.20 0.13
- 3. Modeling 1.0 0.0 0.15
- 4. Damping 1.34 0.03 0.17
{ 5. Combination of Modes
- 6. Earthquake Component 1.0 0.15 0.0 Combination 1.15 0.12 0.10 Combined -F ER
{ 2.14 0.28 0.28 Structural Response Factor (FS R )** 1.11 0.26 0.16 Earthquake Duration Factor (FED) 1.40 0.12 0.08 Ground Acceleration Capacity (A) 4.99 g 's 0.43 0.53
- Based on OBE (0 125 g's) .
- Based on Containment Internals Structural Response Factor and 8 's which are the Most Conservative
{ 5-74
( TABLE 5-8: FRAGILITY DERIVATION OF PIPING SUPPORTS b Median Random Uncertainty Factors Safety Variability Variability Factor S R
8 U
l Capacity Factor (FEC)
( 1. Strength Factor *
- 2. Ductility Factor 3.26 2.24 0.0 0.16 0.29 0.16 Combined--. F EC
- 7.30 0.16 0.33 EquipmentResponseFactor(FER)
Qualification Method 1.0 0.0 0.0
{ l.
- 2. Spectral Shape 1.39 0.20 0.13
~
- 3. Modeling 1.0 0.0 0.15 r 4. Damping 1.34 0.03 0.17 L 5. Combination of Modes 1.0 0.15 0.0
- 6. Earthquake Component Combination 1.15 0.12 0.10
[ Combined -F ER 2.14 0.28 0.28 Structural Response Factor (FSR)*
- 1.11 0.26 0.16 Earthquake Duration Factor (FED) 1.40 0.12 0.08 Ground Acceleration Capacity (A) 3.03 g's 0.43 0.47
- Based on OBE (0.125 g's)
( ** Based on Containment Internals Structural Response Factors which are the Most L Conservative
[
W 5-75
(
['
[
TABLE 5-9
{
[. 1
SUMMARY
OF SEABROOK COMPONENT FRAGILITIES The following pages (5-77 through 5-78) comprise Table 5-9
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8 HORIZONTAL (E W) RESPONSE,EL.75' a-I o 9
AMPLIFIED RESPONSE SPECTRA - SSE CONTROL / DIESEL GENERATOR BUILDING 7% STRUCTURAL DAMPING; 2% EQUIPMENT DAMPING
,I 6
o FINAL SAFETY ANALYSIS REPORT I -
w FIGURE 3.7(B)-29, SH. 2 o
I ~
z9 o
o ua H
T e
we
,I a o dE" g Smoothed and Broadened
>a u C
e8 I F-u {
w I 0.
Woo s
C
=
l 1. 0 i S A $ $ i $ $ '10" 5 $ i $ $ i $ $ '10 NATURAL PERTOD (SECONDS) 1 I FIGURE 5-1: COMPARISON OF A SM0OTHED AND BROADENED SPECTRA TO AN UNSM00THED AND UNBROADENED SPECTRA 5-79 ,
I I i REFERENCES I 1. Seabrook Station Final Safety Analysis Report, Public Service Company of New Hampshire, Revision 45, June,1982.
- 2. USNRC, " Design Response Spectra for Seismic Design of Nuclear Power Plants", USNRC Regulatory Guide 1.60, Revision 1, December,1973.
- 3. Freudenthal, A. M., J. M. Garrelts, and M. Shinozuka, "The Analysis of Structural Safety", Journal of the Structural Division, ASCE, ST 1, pp. 267-325, February, 1966.
- 4. Kennedy, R. P., A Statistical Analysis of the Shear Strength of .
Reinforced Concrete Beams, Technical Report No. 78, Department of I Civil Engineering, Stanford University, Stanford, 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.
I 6. Newmark, N. M., " Inelastic Design of Nuclear Reactor Structures and 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, I 8.
1979.
Bernreuter, D. L., " Seismic Hazard Analysis, Application of I Methodology, Results, and Sensitivity Studies", NUREG/CR-1582, Vol. 4, Lawrence Livermore National Laboratory, October,1981.
I 9. USNRC, " Damping Values for Seismic Design of Nuclear Power Plants",
USNRC Regulatory 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 Engineering and Design, Vol. 59, No. 2, pp. 315-338.
- 12. USNRC, " Combining Modal Responses and Spatial Components in Seismic Response Analysis", USNRC Regulatory Guide 1.92, Rev.1, February, 1976.
I R-1 I
L
[ REFERENCES (Continued)
[
l
- 13. Letter from H. L. Ruffner, Pittsburgh Testing Laboratory Seabrook
[ Site Manager, to R. A. Rebel, Resident Construction Manager for United Engineers and Constructors, Inc., September 7, 1982.
{ 14. Troxell, G.E., H.E. Davis and J.W. Kelly, Composition and Properties ,
of Concrete, McGraw-Hill, 1968. '
(L 15. United Engineers and Constructors, Inc., Calculation Set No. MA-29 (final), sheets 62 through 137 of 162, Revision 0, May 27, 1981.
- 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 318-77, " Building Code Requirements for Reinforced Concrete",
{ American Concrete Institute,1977.
- 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.
T., A. Shibata and J. Tabahashi, " Experimental Study on
( 19. Shiga 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", Construction Technology Laboratories (Division of PCA), Skokie, Illinois, October,1979.
- 22. Hadjian, A. H., and T. S. Atalik, " Discrete Modeling of Symmetric Box-Type Structures", International Symposium on Earthquake Structural Engineering, St. Louis, Missouri, August, 1976.
{
- 23. " Earthquake Resistant Structural Walls - Tests of Isolated Walls",
PB-271 467, Portland Cement Association, prepared for National
( Science Foundation, November, 1976.
- 24. " Tentative Provisions for the Development of Seismic Regulations for Buildings", ATC 3-06, prepared by Applied Technology Council for National Science Foundation, June, 1978.
- 25. Merchant, H. C., and T. C. Golden, " Investigations of Bounds for the
[ Maximum Response of Earthquake Excited Systems", Bulletin of the Seismological Society of America, Vol. 64, No. 4, pp.1239-1244, August, 1974.
R-2 r - - - -
I REFERENCES (Continued)
I I 26. " Final Report, Testing and Seismic Qualification of the Seabrook Control Room Ceiling", prepared by CYGNA Energy Services, San Francisco, California, Revised April, 1982.
- 27. Ang, Alfredo H. and Wilson H. Tang, Probability Concepts in Engineering Planning and Design, John Wiley and Sons, Inc.,1975.
I 28. NUREG/CR-1706, UCRL-15216, " Subsystem Response Review, Seismic Safety Margin Research Program", October, 1980.
- 29. " Amplified Response Spectra for Seismic Category I Structures", J.0.
9763.006, Public Service Company of New Hampshire, February 15, 1980.
- 30. Smith, P. D. and 0. R. Maslenikov "LLNL/ DOR Seismic Conservatism Program, Part III: Synthetic Time Histories Generated to Satisfy NRC Regulatory Guide 1.60", UCID-17964 (draft report), Lawrence Livermore Laboratory, Livermore, California, April, 1979.
l
- 31. Smith, P. D., S. Bumpus and 0. R. Maslenikov, "LLNL/ DOR Seismic Conservatism Program, Part VI: Response to Three Input Components",
I UCID-17959 (draft report), Lawrence Livermore Laboratory, Livermore, California, April, 1979.
- 32. " Seminar on Understanding Digital Control and Analysis in Vibration Test Systems", sponsored by Goddard Space Flight Center, Jet Propulsion Laboratory and The Shock and Vibration Information Center held at Goddard Space Flight Center on 17-18 June 1975 and at the I JPL on 22-23 July 1975.
- 33. Hardy, G.S. and R. D. Campbell, " Development of Fragility I 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.
- 34. " Seismic Qualification Report for the Seabrook Spray Additive Tanks", by Pittsburgh-Des Moines Steel Company, July,1981, Foreign Print No. 52802-08.
- 35. NUREG/CR-2137, " Realistic Seismic Design Margins of Pumps, Valves and Piping", by E.C. Rodabaugh and K. D. Desai, June, 1981.
- 36. Manual of Steel Construction, Seventh Edition, American Institute of Steel Construction, Inc.
- 37. " Qualification Program for the Class lE Battery Chargers for the Seabrook Nuclear Generating Station", by Power Conversion Products, Inc., Document No. QR-15629UE&C Foreign Print No. 31601.
R-3 I
L
[ REFERENCES (Continued) r 38. NUREG/CR0261, ORNL/SUB-2913/8, " Evaluation of the Plastic L Characteristics of Piping Products in Relation to ASME Code Criteria", by E. C. Rodabaugh and S. E. More, Battelle Columbus p Laboratories, July, 1978.
- 39. Sargent and Lundy Report, " Evaluation of the Functional Capability of ASME Section III, Class 1, 2 and 3 Piping Components, MARK I f Containment Program, Task 3.1.5.4", September 21, 1978.
- 40. Witt, F. J., W. H. Bamford and T. C. Esselman, " Integrity of the Primary Piping Systems of Westinghouse Nuclear Power Plants During l Seismic Events", WCAP No. 9283, Westinghouse Electric Corporation, March, 1978.
l 41. ASTM D5-5S2, "An Evaluation of the Yield, Tensile, Creep and Rupture Strengths of Wrought 304, 316, 321 and 347 Stainless Steels at I Elevated Temperatures", American Society of Testing Materials.
- 42. IE Bulletin No. 79-02, " Pipe Support Base Plate Designs Using Concrete Expansion Anchor Bolts."
l 43. PCI Design Handbook, Published by Prestressed Concrete Institute, First Edition, Second Printing 1971.
j 44. " San Fernando Earthquake of February 9, 1971: Effects on Power System Operation and Electrical Equipment", Prepared by the Design and Construction Division of the Department of Water and Power of the City of Los Angeles, October, 1971.
I 45. Pittsburg-Des Moines Steel Company Design Report, Refueling Water Storage Tank for Seabrook, New Hampshire, June 1981, UE&C Foreign Print Number FP 52801.
- 46. Veletsos, A. S. and J. Y. Yang, Dynamics of Fixed-Base Liquid Storage Tanks, presented at U.S.-Japan Seminar for Earthquake Engineering Research with Emphasis on Lifeline Systems, Tokyo, Japan, I November 8-17, 1976. .
- 47. USNRC letter dated April 4,1985,
Subject:
Seabrook PRA Review, G. W. Knight to R. J. Harrison.
- 48. Pickard, Lowe and Garrick, Inc., Seabrook Station Probabilistic Safety Assessment, Report PLG 0300, December 1983, prepared for I Public Service of New Hampshire.
R-4 I
L
[
APPENDIX A
[ CHARACTERISTICS OF THE LOGNORMAL DISTRIBUTION b Some of the characteristics of the lognormal distribution which are useful to keep in mind when generating estimates of , BR , and SU are
( sumarized in References Al and A2. A random variable X is said to be lognormally distributed if its natural logarithm Y given by:
[ Y = in (X) (A-1) is normally distributed with the mean of Y equal to in i where i is the median of X, and with the standard deviation of Y equal to 8, which will b be defined herein as the logarithmic standard deviation of X. Then, the coefficient of variation, COV, is given by th.e relationship:
b 2
COV=Mexp(8)-1 (A-2)
{
For 8 values less than about 0.5, this equation becomes approximately:
b C0V = 8 (A-3)
( and C0V and 8 are often used interchangeably.
For a lognormal distribution, the median value is used as the
{ characteristic parameter of central tendency (50 percent of the values are above the median value and 50 percent are below the median value).
The logarithmic standard deviation, 8, or the coefficient of variation, COV, is used as a measure of the dispersion of the distribution.
E A-1
{
[ .
The relationship between the median value, X, logarithmic standard deviation, 8, and any value x of the random variable can be
{ expressed as:
x=i exp (n 8) (A-4) b where n is the standardized Gaussian random variable, (mean zero, standard deviation one). Therefore, the frequenc) that X is less than any value x' equals the frequency that n is less than n' where:
(
- n. , in(x'/i) (A-5)
B Because n is a standardized Gaussian random variable, one can simply enter b 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 i
- 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 X 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 b that if A, B, and C are independent lognormally distributed random vari-ables, and if A" BS 0= t 4 (A-6)
[
[
[
A-2
b
[
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 80, which is the square of the logarith-mic standard deviation, 80 , of D, are given by:
( 6= q (A-7)
C
[
and
( g 2 22 22 22 D=rBA+sBB+tBC -
(A-8) where d 5, and C are the median values, and B A ' 88, and BC are the loga-rithmic standard deviations of A, B, and C, respectively.
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 failure fraction is not 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
( sunnarized below.
With perfect knowledge (i.e., only accounting for the random
{ variablity, BA), the failure fraction, f(a), for a given acceleration a can be obtained from:
[
f(a) = eI ln(a/d)\
t (A-9)
( R )
{
[
A-3
{
i L
I L
in which t(-) is the standard Gaussian cumulative distribution function,
{ and S is the logarithmic standard deviation associated with the R
underlying randomness of the capacity.
l F
L For simplicity, denote f = f(a). Similarly, f' is the failure fraction associated with acceleration a', etc. Then, with perfect I knowledge (no uncertainty in the failure fractions), the ground acceler-ation a' corresponding to a given frequency of failure f' is given by:
1 L .
a' = A exp B e -1(f')- (A-10)
.R .
The uncertainty in ground acceleration capacity corresponding to a given frequency of failure as a result of uncertainty of the median L capacity can then be expressed by the following probability statement:
E P A > a"l f' =l0 (A-ll)
U 7 . .
I I 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 I 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 l in symbols P[f s f'la']. This probability is also shown shaded in Figure l A-1. It follows that:
l P[f s f'la"] = P[A > a" l f '] (A-12) l Thus, from Equations A-10 and A-ll:
ina"/dexp BR* II')
P[fsf'la"] = l- C 6 U
(A-13)
E A-4 I
L e
u from which:
F ' -
L_ [in(a"/k exp -s R *_i (f')-
P[f > f' la"] = 0 g (A-14) l
( U )
' which is the basic statement expressing the probability that the failure
, fraction exceeds f' for a ground acceleration a" given the median ground acceleration capacity 5, and the logarithmic standard deviations BR and SU associated with randomness and uncertainty, respectively.
u As an example, if:
A = 0.77, SR = 0.36, SU = 0.39 L 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.
l I
1 I
I I A-5 I
q~ .. -. - - - - _
,/
/
/
/
Failure Frequency /
/
/
f(a) = e En(a/5)- B - /j n .
/
/
/
/
/
/
/
C
/
_ _ _ _ - - - . f 3
c 0.5 . - _ _ _ _ _
/
l 9 8 0
> E l /
c'n E f,, --.. -- . --- / Probability
= 1-0 .in(a"/A) u 5 / P A > a"lf' g /I _ - B y .
/ -
f' - - - _
. I f I I / ;
I 3/ # I I .
I P
-f s f' la".
= P A>a"lf' l . / l l
'p # lI I I l
I l
i
- l 0
- ,/e I I
E I
g e
a' a" A Ground Acceleration, a FIGURE A-1. RELATIONSHIP BETWEEN UNCERTAINTY IN GROUND ACCELERATION FOR A GIVEN FAILURE FRACTION AND UNCERTAINTY IN FAILURE FRACTION FOR A GIVEN GROUND ACCELERATION
L
[
REFERENCES
[
A.1 Benjamin, J. R., and Cornell, C. A., Probability, Statistics and
{ Decision for Civil Engineers, McGraw Hill Book Company, New Yo W ,
1970.
b A.2 Kennedy, R. P., and Chelapati, C. V., " Conditional Probability of a Local Flexural W311 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.
E
[
[
[
[
[
[
r I .
I I
I A-R-1 I
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/ %' \
. - SBN-ll67.
k 4
) ATTACHMEffr 2 3
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