ML20012G335
| ML20012G335 | |
| Person / Time | |
|---|---|
| Site: | 05200002 |
| Issue date: | 02/16/1993 |
| From: | ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY, ASEA BROWN BOVERI, INC. |
| To: | |
| Shared Package | |
| ML20012G334 | List: |
| References | |
| NUDOCS 9302240272 | |
| Download: ML20012G335 (46) | |
Text
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_ SYSTEM:80+ ALWR A PRA-BASED SEISMIC MARGIN EVALUATION
~
h ADDITIONAL CLARIFICATIONS IN RESPONSE TO ;
NRC REQUESTED ITEMS :
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i Prepared By: l ABB Combustion Engineering l 1
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l 9302240272 930216 i PDR ADOCK 05200002 A PDR l
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L System 80+ ALWR A. PRA Based Seismic Marcin Evaluation CONTENTS L
_Page No.
1.0 NRC ~ Request: Provide an overview of the 1-1 general approach ABB Response: Overview of General approach is provided in section 1.0 2.0 NRC Request: Provide details of the approach 2-1 developed by Dr. R.P. Kennedy to develop approximate fragilities using the EPRI CDFM methodology i
ABB Response: Details of'this approach is provided in cection_2.0 3.0 NRC Request: Provide justification for 3-1 selection of spectral shape to be used in the margin evaluation ABB Response: Justificatio, provided in !
section 3.0 \
4.0 NRC Request: Provide a position regarding 4-1 applicability of the margin evaluation insights to soil conditions as well as rock conditions ABB Response: Position is stated in section 4 0 5.0 NRC Request: Provide clarification on the 5-1 notation HCLPFe4 versus CDFMHCLPF ABB Response: Clarification provided in section 5.0 ABB Combustion Engineering Pagei
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System 80+ ALWR A PRA-Based Seismic Marcin Evaluation SECTION 1.0 NRC Request: Provide an overview of the general approach ,
Below is a description of an overview of the general approach for performance of a PRA-Based seismic margin analysis of the System '
80+ design. This approach consists of 5 main tasks described below:
TASK 1- DEVELOP INITIAL SEISMIC EVENT AND FAULT TREES: Under this task, initial event and fault trees assuming an earthquake as an initiating event will be developed. These models will consider secondary failure effects which could impact functionality of equipment in various branches. Examples are failure of structures or system interaction concerns.
The construction of these trees will result in an initial set of Structures, Systems and Components (SSCs), whose seismic fragility levels will need to be evaluated.
TASK 2- PRUNNING OF THE SEISMIC EVENT AND FAULT TREES: Under this task, both systems engineers as well as seismic fragility engineers will review the models developed under task 1, for prunning purposes. For this purpose, the experience of the seismic .
fragility engineers will be relied upon to modify the models, if for instance based on past experience it would be obvious that certain components in certain paths will have excessively low seismic fragilities, hence contributing to low sequence or plant level HCLPFs. For such cases alternate routes will be considered if acceptable by the system engineer. By the same token, the opposite may be true, i.e. some components or systems not included in the initial model may exhibit large HCLPFs, thus improving sequence or plant level HCLPFs, once included in the model as an alternate path.
To the extent possible, prunned out SSCs will be represented in the model by surrogate fragilities. For this purpose, generic fragilities based on past PRAs as summarized in the EPRI Utility Requirements Document (Appendix A, Table A.3-4) will be used to represent rugged SSCs.
1 The outcome from this task will be a revised SSC list for which seismic HCLPFs and fragilities will be computed.
4 ABB Combustion Engineering Page 1-1
i System 80o ALWR A PRA-Based Seismic Maroin Evaluation l i
SECTION 1,0 (Cont.)
Significant interaction between the system engineers and the !
seismic fragility engineers will take place during the execution of this task. :
TASK 3- DETAILED SEISMIC FRAGILITY ASSESSMENT: Under this task -
detailed fragility evaluations will be performed for SSCs identified under. task 2 above. ;
SSC fragilities will be determined based on a 2-phase approach.
Initially, approximate fragilities will be developed using an approach recently developed by Dr. R. P. Kennedy. This approach makes use of the EPRI Conservative Deterministic Failure ,
Methodology (CDFM) as outlined in EPRI-NP-6041-SL, Rev.1 report.
The CDFM methodology will be used to compute HCLPF values for all SSCs on the list. Using these HCLPFs and assumed value of Bc (composite uncertainty), approximate fragility curves' will be computed. The details of this method are given in section 2.0.
Once approximate fragilities are computed, the PRA~ model will use :
these values to determine dominant contributors to seismic risk. For these dominant contributors, detailed fragilities will be computed '
using rigorous techniques and the PRA model will be re-evaluated.
Initially, plant SSC HCLPFs will be evaluated using a Review Level .
Earthquake of 0.6g. The CMS 3 spectral shape (modified NUREG 0098 spectral shape) will be anchored to 0.6g. Rock conditions are chosen initially, since for any given site condition, they provide a broad-band input and hence it is likely to cover a wide range of frequencies of interest. Once HCLPF values for this site condition are computed, the effects of potential soil conditions on altering certain SSC HCLPFs as well as their effect on changing ranking of dominant ,
contibutors will be addressed. Further discussion on this subject is provided in section 4.0.
TASK 4- CONTAINMENT EVALUATION: Under this task, seismic failure modes, sequences and vulnerabilities involving containment, containment functions, and containment systems will be evaluated.
Gross structural failures as well as penetration stresses will be determined.
l 1
ABB Combustion Engineering Page 1-2
' System 80+ ALWR A PRA-Based Seismic Marcin Evaluation SECTION' 1.0 (Cont.l~
The NRC suggested approach for evaluation of containment isolation and Bypass will be used in the margin analysis.'This. approach requires identification of' each cutset. whose HCLPF .is less than 0.6g considering random failures 'using either the Min / Max 'or the -
convolution approach. If such cutsets are . identified, then active and passive systems important to containment isolation whose failure would lead to an unscrubbed release.will be identified. In addition, the ruggedness of- potential containment bypass paths will be determined to see if they exhibit HCLPF below:0.6g.- ,
The rescit will be reporting of any systems or components identified l above, and discur., sing the potential effects associated with- the .l combination of ' sequences identified in- the original .cutsets with those of containment bypass and isolation. ,
TASK 5- DETERMINATION OF PLANT VULNERABILITIES: Under this task, various path,. sequence and plant. level seismic vulnerabilities will be identified by both the Min / Max and the convolution' approach.
Since component fragilities will be determined using the:CDFM approach utilizing the approximation technique suggested by Dr.
Kennedy, the option of using both. the Min / Max. approach and the convolution approach will be. open.
Since System 80+ detailed design is not complete at this stage, should this exercise result in' plant SSC .HCLPFs below the. desired level of 0.6g, or certain SSCs contributing to unacceptably high seismic risk numbers, then the insights from this evaluation will be; used to provide committments in design in order to achieve desired HCLPF values.
ABB Combustion Engineering Page 1-3
System 80+ ALWR .A PRA-Based Seismic Marcin Evaluation j SECTION 2.0 NRC Request: Provide details of the -approach developed by Dr. R. P. Kennedy to develop approximate fragilities using the EPRI CDFM methodology This section provides an overview of this approach. Attachment 1 to this section provides the presentation slides and reference material used by Dr. Kennedy to present this approach.
OVERVIEW ,
Approximate seismic fragility curves can be computed using deterministic HCLPF evaluation assuming that the fragility is lognormally distributed. It can be shown that this approximate methodology will in general result in risk numbers which are conservative by a factor of no more than 2, assuming a reasonable range of variabilities (when compared with risk numbers from exact fragilities).
In a rigorous fragility evaluation, once median acceleration estimates as well as estimates of randomness (Br) and uncertainty (Bu) are determined, one can compute HCLPF as follows:
HCLPF = (Median acc.) exp (-1.65 (Br + Bu)) (1)
To determine the mean risk only, and relative ranking of components that contribute to the mean risk, one does not need to separate variability into randomness and uncertainty. As such, both variabilities are lumped into a composite variability, Bc. For the typical range of Bc, equation (1) can be approximated as:
HCLPF = (Median acc.) exp (-2.3 Bc) (2)
Assuming a range on Bc = 0.3 to 0.5 (typicall of computed values for Bc), the corresponding range on (Median /HCLPF) ratio from (2) above will be in the 2.0 to 3.2 range. ,
Using an average Bc = 0.4 (half way between 0.3 and 0.5), equation (2) wil! result in:
Median (acc.) = 2.5 HCLPF (3)
ABB Combustion Engineering Page 2-1
System 800 ALWR A PRA-Based Seismic Maroin Evaluation SECTION 2.0 (Cont.)
This HCLPF is usually denoted as HCLPFso corresponding to an earthquake response spectrum which has 50% probability of being exceeded at any frequency. In contrast, the HCLPF value computed using the EPRI CDFM approach is denoted by HCLPF84. This corresponds to an earthquake response spectrum which only has 16%
probability of being exceeded at any frequency. The relationship between these two HCLPFs is given by:
HCLPF84 = HCLPFso exp (Besa) (4)
Where, Bcsa corresponds to the composite variability associated with spectral shape.
Using the value of Besa of 0.18 which was used to develop the CDFM ,
methodology, one can estimate: ,
HCLPFso = HCLPF84/1.2 (5)
= CDFM/1.2 Therefore, using equations (3) and (5), one can determine:
Median (acc.) = 2.1 CDFM (6)
Having determined Median (acc.) and an assumed value of Bc = 0.4 for composite variability, one can construct approximate fragility curves for various SSCs based on CDFM HCLPF only.
It can be shown by either exact or approximate convolution '
techniques, that the resulting risk numbers from these approximate fragilities are generally on the conservative side when compared with exact values by no more than a factor of 2. Example problems
- demonstrating this conclusion are g;ven in attachment 1. Even with extremely large Bc, approximate risk numbers are shown to be less than a factor of 2 too large.
ABB Combustion Engineering Page 2-2
]
1 System 80o ALWR A PRA-Based Seismic Maroin Evaluation l SECTION 3.0 NRC REQUEST: Provide justification for selection of ;
spectral shape to be used in the margin evaluation This section provides the justification for using CMS 3 as the ;
spectral shape in margin evaluation of System 80+ design.
i Control Motion Spectrum 3 (CMS 3) is a modified NUREG 0098 spectral shape. The modification is done by extending the flat '
portion of the spectrum from 8 Hz to 15 Hz in order to introduce more high frequency content typical of what might be expected from ,
~
an Eastern U.S. earthquake. This spectrum is shown in figure 3.1 anchored to a PGA of 0.3g. CMS 3 is one of the 3 control motions used in the design of System 80+.
For margin evaluation using the guidelines of the EPRI SMA approach, the SME (or RLE) is defined at an 84% Non Exceedance Probability (NEP). Two components contribute to this definition. First, is the .
level at which the PGA is set. Second, is the spectral shape once the PGA is defined. To approximately achieve an 84% NEP SME, one can either set the PGA level at 84% NEP and use a median spectral shape, or alternatively set the spectral shape at 84% NEP and use a median C
PGA. However, it is generally believed that in order to obtain 84%
NEP at all frequencies, the first alternative is desirable. Setting both the PGA and the spectral shape at 84% NEP results in excessive NEP (approximately > 95% NEP). ,
The design basis of 0.3g for ALWRs is defined at 84% NEP. Since the RLE is set at twice the design basis PGA, it also represents an 84%
- NEP PGA for margin evaluation. The NUREG 0098 spectral shape is generally viewed as a median spectral shape, where as R.G.1.60 spectral shape was developed based on an 84% NEP constructed through the records which formed its basis.
Therefore, it is concluded that in order to meet the intent of the margin evaluation philosophy, the demand is to be defined as 84% '
NEP consistently at all frequencies. By choosing a NUREG 0098 '
spectral shape (representing 50% NEP) anchored to a PGA of 0.6g (representing 84% NEP) one arrives at an approximate 84% NEP RLE at all frequencies.
ABB Co 1bustion Engineering Page 3-1 a
System 80+ ALWR A PRA-Based Seismic Maroin Evaluation {
SECTION 3.0 (CONT.)
By choosing a R.G.1.60 spectral shape anchored to 0.6g, one would have an RLE with approximate NEP in excess of 95% in the lower frequencies (2.5 to 9 Hz), gradually reducing to an 84% NEP at PGA levels.
The choice of a NUREG 0098 spectral shape for margin et'aluation of ;
System 80+ is also consistent with the spectral shape recommended '
in NUREG-1407 for Seismic IPEEE for existing plants, if the seismic margin methodology is chosen.
t i
r L
ABB Combustion Engineering Page 3-2
F System 80+ ALWR A PRA-Based Seismic Marcin Evaluation FIGURE 3.1: CMS 3 Spectral Shape anchored to both 0.3g (Design 4 Basis) and 0.6g (RLE),5% Damped Damping - 5%
1.6 7 ;
q ;
i l-r- r* "4-r-e'-e 1.4 ~
- r-i i l A-""-- -'i-'r* \ -- + -
1.2 r--' - " ' - * --?
\
5 1,o -++, i ~~ -,-e+t. +---
C O
% 0.8 . 2 , q-}g--
l ,l l !p J
5 ! ! D.6Q
-'---*---*i*+
' d 8 0.6 + +-*-
-+t -
'xi---l-s
- / i i 0.4 ' - -b--t - 5--j r- ;pg -
0.2 / /r* "---"--" " 4
/ '
0.0 2
O.10 1.0 10 10 Frequency (Hz)
ABB Combustion Engineering Page 3-3
System 80+ ALWR A PRA-Based Seismic Marain Evaluation i
SECTION 4.0 ;
NRC REQUEST: Provide a position regarding applicability of -
the margin evaluation insights to soil conditions as well as rock conditions This section provides the requested position on the applicability of the margin evaluation insights to soil site conditions as well as rock conditions.
The System 80+ seismic margin evaluation will be performed in two stages. Initially, the margin evaluation will be performed using rock .
site conditions. As such, initially a broad-band input motion is used l to determine SSC HCLPFs , . approximate fragilities, and seismic risk numbers for components covering a wide frequency range of interest.
At this stage,'the natural frequencies of all SSCs of interest, as well as the contribution to HCLPF from the capacity side. for each of these SSCs will also be available. Once this data is available, the effect of soil conditions on potentially reducing HCLPFs due to higher demands, or altering the relative ranking of the domirnnt contributors will be adressed in the following manner.
The initial margin evaluation corresponding to rock conditions, is exnected to result in HCLPF values in the range of 0.7g to 0.8g or hiper (probably in excess of the desired HCLPF level of 0.6g). This is due to the observation that the System 80+ design basis spectra are fairly high (about 0.5g ZPA at foundation elevation). The high design basis spectra is primarily due to the convolution process associated with shallow soil sites when the control motion is defined at top of a hypothetical rock outcrop. Figure 4.1 shows the design basis broadened spectra at foundation elevation superimposed ,
with the design basis CMS 3 rock spectrum as well as RLE CMS 3 rock j spectrum anchored to 0.6g. Included in the same plot are the results of one of the soil cases which contributes to the highest spectral ,
peaks at some narrow frequency (about 2.0 Hz.).
For the initial margin evaluation, it is therefore desirable to have a broad-band input in order to cover a wide frequency band of interest.
Any one soil site is liable to have spectral peaks in a narrow ,
frequency range, because of filtering effects associated with SSI phenomenon (e.g. soil case shown in Figure 4.1).
ABB Combustion Engineering Page 4-1
System 80o ALWR A PRA-Based Seismic Marcin Evaluation SECTION 4.0 (CONT.)
Once the margin assessment is completed using the rock site .
conditions, HCLPF values and natural frequencies for all SSCs of interest will be available. Using this data as well as the design basis demand data available for the envelope of all cases (12 soil and 1 rock case) versus rock case, allowing for frequency shifts resulting from higher RLE motions going through soil, and allowing for spectral peak clipping and pick shifting, one can approximately determine in what frequency range and for which components, soil site conditions could result in higher demand and hence potentially lower HCLPFs. If this estimation of reduced HCLPFs is below the desired level of 0.6g for any SSC, then margin assessments corresponding to the governing soil conditions will be repeated resulting in accurate estimation of H.CLPFs for soil site conditions.
If detailed margin. evaluations are required to be performed for one or mora soil site conditions, then these will also utilize a NUREG 0098 spectral shape adjusted to represent soil conditions (i.e. more low frequency content). This control motion will also be anchored to 0.6g PGA. ,
in this fashion, the effects of soil site conditions potentially affecting HCLPFs for certain components will be considered and evaluated.
L ABB Combustion Engineering Page 4-2
System 80+ ALWR A PRA-Based Seismic Marain Evnfuation Figure 4.1: Comparison of Example Design Basis Spectra with CMS 3 Raw Spectra for Both Design Basis and RLE and a Typical Individual Soil Case Response Spectrum (Elev. +50', Top of Basemat, E-W Direction, 5% Damped) 3.00 i S
2.50 Design Basis Typical soil Case (0.3g)
CMS 3 Rock Site (0.3g) 2.00
- -* - CMS 3 Rock Site (0.6g) -
S ""
/ +.
5 1.50 g , , ,
~, ,
f A
f '.j ., '
. \,, , , \ L .,
p 's./ '
8 bi,
< J!
,.', \
1.00 g
!l, ! ..
r A/Vu,rvW l
0.50 - -
f .... i , pi v- x A qr .,
/ *\ M'hN -
m g .... n ~ 7 l o 00 WWC - - l toom ' 1.00 10.00 l o io Frequency (liz) ABB Combustion Engineering Page 4-3 _ _ _ _ . . , . . . _ . _ . _ . _ . _ , _ . _ . . . . - . _ . _ . . . - . - . . _ , . . . . _ . . . . ~ . . _ . . ._ . _ . . , . . ~ . - . _ _ . _ . . . - . . - _ . _ . . ~ ___ . . . . . _ . - _ . _ .
I System 80+ ALWR A PRA-Based Seismic Marcin Evaluation SECTION 5.0 , NRC REQUEST: Provide clarification on the notation of i HCLPFat versus CDFM HCLPF This section provides clarification on the subject. The term HCLPF refers to High Confidence of Low Probability of Failure. This term is refered to a 95% (high)' confidence level that the probability of failure will not exceed 5% (Iow probability of failure). Hence HCLPF is sometimes denoted as the 95/5 failure acceleration threshold. Using the EPRI CDFM approach one computes HCLPF. However, , inherent in the CDFM approach is the definition of ground motion which is defined as 84% Non-Exceedance Probability (NEP). Hence, HCLPF as computed by the EPRI CDFM approach is sometimes denoted as HCLPF84. When one computns median fragility estimates, all parameters are assumed as median. This includes the definition of control motion meaning that at all frequencies of interest (if fragility is defined in terms of PGA), there is 50% NEP. In defining a family of fragility curves, one usually presents a number of curves ranging from 5% to 95% confidence level. On these plots, the acceleration level which represents the 5% probability of failure on a 95% confidence curve is denoted as HCLPF also. However, due to the definition of the input motion being 50% NEP, this HCLPF value is sometimes denoted as HCLPFso (see Figure 5.1). , The difference between this HCLPFso and HCLPFs4 as obtained from EPRI CDFM approach is purely due to the definition of the input motion, specifically whether it is defined at 50% NEP or.84% NEP. The relationship between these two HCLPF values is given as: HCLPFs4 = HCLPFso exp (Bcsa) Where, Besa is the composite variability associated with spectral , shape. i i ABB Combustion Engineering Page 5-1
System 80+ ALWR _ A PRA-Based Seismic Marcin Evaluation Figure 5.1: Typicall Fragility Curves ILLUSTRATION OF FRAGILITY CURVES 1.00 --
.. liEAtt -
9- . _
- 0.75 -
95% Cot 1FIDEllCE Z .. . O _ 50% C0!iFIDEliCE . I-O N 5% C0!! FIDEL 1CE
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4 - . D' O.50 - - LL _ _ w . y _ 3 . - 0.25 -
<C _
L' .
~
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0.00 1ICLPFyo MEDIAN GROUND ACCELERATION PARAMETER ABB Combustion Engineering Page 5-2
'i
-i ATTACHMENT 1 TO SECTION 2.0 Additional - Presentation Slides - in Support' of L the j Proposed M ethodology '- .l f
l l
'i Presented At:
Post-Symposium Seminar . I on 3 FRAGILITY EVALUATION FOR PROBABILISTIC RISK' !
- ASSESSMENT FOR NUCLEAR POWER PLANTS q.
I 1 i Presented- By: : i Dr. R. P. Kennedy 'l
'RPK Structural Mechanics. Consulting, Inc.
10871 Villa Terrace - ". 3 Yorba Linda, CA 92686 [ i 1
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b Session K14 Suggestec Simplifications ) , Vugrag1s F i
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l t I i h r l Suggested Simplifications i Robert P. Kennedy i l
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Treatment oP Variabilities : i To Determine Mean Risk and Components Which 1 Dominant Contribution to Mean Risk, One Doesn't Need to Separate Variability into Randomne'ss and ' Uncertainty 3
= Both Variabilities Can Be Lumped Into Composite Variability i
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T , Fragility Analysis (Cont.) l I l.
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= l-ICLPFs can be calculated as follows:
1ICLPF - ao -1.65([lr + Ilu) I Dc , HCLPF = ao I i . l 1 t
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. . . . . , . _ . _ _ , . _ , _ _ _ - . ~ , . _ . . - . _ . . . _ . , . . _ , _ , . . . _ . _ - . . _ - _ . . _ . ,_ . , _ . . . . . . . , _ . _ . . - . _ _
?
Screening :
= Aggressively Screen-Out Higher Capacity Components From Fragility Development Using EPRI-NP-6041-SL '
= Set Screening Level SufTiciently High That Either:
I Several Important- Components Have HCLPF34 Levels Below Screening Level e Seismic Risk Based' on Screening Level is Adequately Low
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3 ConservativeSurrogate FragUlty CDFM 0.8g HCLPF50 = = = 0.67g 1.2 1.2
# c = 0.3 (Conservative Surrogate)
) 2 Median Sa = HCLPF50 e . sac = 2.0(0.67g) = 1.33g F 3 e I I4 d :
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f s e 1 i Approximate Probability of Failure Estimate (ie., Convolution of Hazard and Fragility Curves) , i _I t
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f 1 l 9 -) J4.10
i UCRL-CR-111478 BASIS FOR SEISMIC PROVISIONS ! OF UCRL-15910 i Prepared by: , Robert P. Kennedy RPK Structural Mechanics Consulting and Stephen A. Short EQE Engineering Consultants i Prepared for: U.S. Department of Energy , f v f t September 1992 DRAFT l l l 4 4 l1. ll
; " Exact" Convolution i
The probability, Pp, of unacceptable performances is obtained by a convolution of ; the seismic hazard and fragility curves. This convolution can be expressed by either: t
+= f d Hg*3 ' .
Pp = - Ppja da' Sa 0 g da j ;
.i oi
*+CO / T Pp = F /a '
H(a)l da Sb ! 0 ( da j where PF/a is the conditional probability of failure given the ground motion level "a" which is defined by the SSC fragility curve.
) :
t
~
where H(a) is the annual frequency of exceedance of ground' motion level "a," t i i
= Solve by Numerical Integration [
I i
. t i
I
///. /I i
l Approximate Convolution I Figure 1 presents two representative probabilistic seismic hazard curves expressed i in. terms of mean annual probability of exceedance versus peak ground acceleration. Curve A represents a hazard estimate for a western higher seismicity site. Curve B represents a typical hazard estimate for an eastern lower seismicity site. Over any ten-fold difference in exceedance probabilities, such hazard curves may be approximated by: 1
-k H (3)
H(a) = K 13 Defining HD as the annual frequency of exceedance of the DBE ground motion level, from Equation (3'- i i K 3
=
Ho {DBE] H Sg : l i 1 (4) Kg = log ( Ag) se in which A R is the ratio of ground motions corresponding to a ten-fold reduction in exceedance probability. DBE = Reference Ground Motion Level (Preferably Midway Between Median and HCLPF on Fragility Curve) J G. B h 3 rw- - -
--v-9--+t rw--+w rrmye er-w e- e de y e-g ew+e *
, .s - >
i
~
i 2 10 ' ' ' ' ' ' '
!~
- [
Curve A (Western) . .; e o -3 = -= c 10 : A r
- 3 8 Curve B (Eastern) _
g _ _- .; U' -4 _ o 10 i E x : : t 3 3 - a - O .. o -5 b j j E 10 ,
~ ~
6 10 ' ' ' ' ' ' ' ' O.1 0.2 0.3 0.5 1 2 i i Peak Acceleration (g)
- s 1
r ( I
?
i i 1 l Figure 5-1: Typical Probabilistic Seismic Hazard Curves .i .l - H1123nblusdoech5 5-6
.g-1 I
- i
. i. a
'[
I Table 5-3 l Typical Ground Motion Ratios and Hazard Slope Parameters . Probability Range Ag K Hazard curve H A (Western) 10-3 to 10-4 2.O' ' 3.32 A (Western) 10-4 to 10-5 1.67 4.49 B (Eastern) 10-3 to 10-4 2.31 2.75 B (Eastern) 10-4 to 10-5 2.13 3.05 l t 1 e 9 e i 0 i r i
/g./5 :
_. 3 Approximate Convolution (Cont.) H De Pp ~ ' 5 (C50 /DBE)KH Equation (5) is exact so long as the fragility is lognormally distributed and the hazard curve is defined by Equation (3), (i.e., is linear on a log-log plot). Median Ca.nacit.y ; i C 50 % =Cep P (10) . where Xpis the factor associated with the f ailure probability "P" for the standard l normal distribution, i.e.: P Xp P Xp 1% 2.326 15% 1.037 4 5% 1.645 20 % 0.842 10 % 1.282 50% 0 ' I
= Therefore given the capacity Cp at any failure '
probability and the composite a one can obtain P.p J pl.Il }
F . Approximate Convolution (Cont.) Range on #c = 0.3 to 0.5 Corresponding Range (Median /HCLPF) = 2.0 to 3.2- . Approximate Fragility
- 1. Estimate HCLPF 50 By EPRI CDFM Method CDFM HCLPF50 =
1.2
- 2. Use Average #c
# c = 0.4 C,y, = HCLPF50 Median = 2.5 HCLPF50 = 2.1.CDFM IT.l]
i Approximate Convolution (Cont.) : i
- 3. Set DBE at C ygg DBE = -1.5 HCLPF50 = 1.25 CDFM w
- 4. Find H g Corresponding to DBE from Hazard Curve l 0
2 '
- 5. Pg =
H g(0.6)^He '08KH (Approximate) ; i l I i t 6 i
- l l
f f h
-) !
/4. /P 4
I J
. Approximate Convolution (Cont.) )
Hazard Slope Factors A, K, P,/F3 3.75 1.74 0.52 3.25 1.95 0.50 t 2.75 2.28 0.47 2.25 2.84 0.45 i l 2.05 '3.21 0.44
. 1.85 3.74 0.45 I
l 1.65 4.60 0.52 . 1.50 , 5.68 0.73 l l r l m Except for Very Steep Hazard Curves ( A, < 1. 6 5 ) ' , P, = H 3 /2
?
I i
/4. /9
x
- Annroximate Convolution (Cont.1 l
'Alternatelv if Know B;. ~One can Slichtiv Improve ;
i DBE = HCLPF * .To 2 ! P, = H (3 F )y
- H c"# M
-Me ~
Parameter 0.3 0.4 0.5 ; F3 ! 1.35 1.50 1.65
. .I Fg i 0'.68 0.60 l
0.53 . i .
+
a 0.045 0.080 - 0.125 : i
~
't I
e f
'5 e
k t C t 3 h a G l
. 1 +. 20. 1
& 4 % .- .r.
.3 Approximate Convolution (Cont.)
1 Ha;:ard Shape Factor P,/4 A, K, #g = .3 Se = .4 Se = . 5 3.<~ 1.74 0.59 . 0.52 0.48 3.25 1.95 0.56 0.50 0.47 ! f 2.75 2.28 0.52 i 0.47 i 0.45 i
!- l l
2.25 2.84 0.48 i 0.45 l 0.45 2.05 3.21 0.46 ! : 0.44 0.47 ! a i l I
. 1.85 3.74 0.44 5 0.45 0.53 ;
1.65 4.60 0.44 0.52 0.76 1.50 5.68 0.48 0.73 1.53 l I , 1 a Except for Steep Hazard Curves And Large Se F P = 4/2 9 3
+
6 l4.2 I
-i l
t
-2 10 _
' ' i i ' i i i* i =
~
Curve A (Western) _" -l a> o -3 = _ c 10 : m - _5 , o -
. . t E : Curve B (Eastern)
~
-W .
LU 4 T:5 10 5 ! . d
=
f 25 - e c - . .t
.O i o -5' dC 10 2 E -)
i
~
-)
~ ~
-6 10 ' ' ' ' ' ' '** -'
l 0.1 0.2 0.3 0.5 1 2 i Peak Acceleration (g) , i k I t
'i
.i f
f i Figure 51: Typical Probabilistic Seismic Hazard Curves ! H1123nb/vsdo ech5 5-6 l
/ 4. 21- .
I Example Bat Bottom Tank Apy_os: . EPRI CDFM = 0.31g DBE = 0.39g i Median = 0.68 A c
= 0'A1 Parameter Curve A Curve B d
Hg 4.6x10 4.6x10-5 . Approx Pg - 2.3x10~4 ~ 2.'3x10-5 . ,
~
. " Exact" Pg 1.6x10~4 1.7x10-5 a
i
= Slight Conservatism is Introduced Because ;
Actual Hazard Curves Are Concave Downward , and Not Linear and Because- 0.5 Factor is Conservative ;
~
14.23
.Enmple ARD Relay In Cahinct Approx:
EPRI CDFM = 0.26g i DBE = 1.25(0.26) = 0.32g i Median A = 0.81g sc = 0.65 ,
; Parameter Curve A Curve B !
Hg 8.3x10~# 8.3x10-5 Approx Pg 4.1x10~# 4.1x10-5 ,
"Exac.1" Pg 2.4x10~# 3.2x10-5
- Even With Extremely Large s c, Approximate Pg is Less Than a Factor of Two Too Large
/4. 2 (
i Example High Variability Case i i Median = 0.Sg i A c
= 00 HCLPF50 = -0.25g Approx: DBE = 1.5 HCLPF50 = 038g F
~
Parameter Curve A Curve B > Hg 5.0x10-4 5.0x10-5 Anurox
^'
Pg 2.5x10-# 2.5x10-5
" Exact" Pg 1.4x10~# 1.5x10-5 .
(
= Additional Consentatism Because of High sc, But Still Within Factor of Two .
l l 1(1. 2 f
m l Example Low Variability Case i Median = 0.5g
#c = 0.3 HCLPF50 = 0.25g Approx: DBE = 1.5 HCLPF50 = 0.38g Parameter Cun'e A Cun'e .B
~
Hg 5.0x10-4 5.0x10-5
.Annrox
'^
) Pg 2.5x10-4 2.5x10-5 "Ex a c t'_' Pg 3.0x10~4 3.3x10-5
= Slightly Unconservative Because of Low s c = Failure Probabilities Differ By Only a Factor of Two for e c from 0.3 to 0.5
)
- 14. 2 4
WW i Conclusions t i To: !
- 1. Approximately Estimate Mean Seismic Core Damage Risk
- 2. Determine Dominate Contributions to Seismic '
Risk Can Use Approximate Approach: . Median = 2.1 CDFM i HCLPF50 = CDFM/1.2
#c
= 0.4 DBE = 1.5 HCLPF50 frH g f l
b I Pg = 0.5 H g i I 6 1 % 17 .
F w Suggestec: Simplifiec Seismic PDA s 1 l Approach for Seismic IPE ! i
+
- 1. Set Screening Limit at NRC Defined RLE-
- 2. Screen Out All Stronger . Components Using EPRI
[ NP-6041-SL Screening Tables and Walkdown {
- 3. Add A Surrogate Fragility Element to Replace All Screened Out Components
- 4. Compute EPRI CDFM Capacities for All-Non-Screened Components . -
- 5. Obtain Approximate Fragility Curves from:
Median = 2.1 CDFM p c = 0.4
- 6. Use Approximate Fragility Curves in Systems Analyses to Define Approximate Seismic Risk and Dominant Contributors' '
- 7. For About 5 Components Which- Dominate Seismic Risk Generate Accurate Fragilities and Repeat Step
# 6.
I4. 2V
Session K12-
.Snggested Simp. iications e
Reference Materia W}}