ML19309B446
| ML19309B446 | |
| Person / Time | |
|---|---|
| Site: | Vallecitos File:GEH Hitachi icon.png |
| Issue date: | 03/21/1980 |
| From: | Jeffrey Reed JACK R. BENJAMIN & ASSOCIATES, INC. |
| To: | |
| Shared Package | |
| ML19309B433 | List: |
| References | |
| NUDOCS 8004040153 | |
| Download: ML19309B446 (10) | |
Text
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I-PROBABILITY ANALYSIS OF SURFACE RUPTURE OFFSET BENEATH GENERAL ELECTRIC TEST REACTOR REACTOR
- BUILDING by John W. Reed Jack R. Benjamin and Associates, Inc.
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l PURPOSE OF PROBABILISTIC ANALYSIS l
1.
To determine the probability of occurrence of a future surface rupture offset of any size greater than zero beneath the Reactor Building foundation 2.
Then to determine whether the probability of occurrence is sufficiently low so that surface rupture offset should not be considered as a design basis event l
I l
Jack R. Benjamin & Associates. Inc.
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Consulting Engineers
)
PROBABILITY ACCEPTANCE CRITERION
.... a conservative calculation showing that the probability of occurrence of potential exposures in excess of the 10CFR Part 100 guidelines is approxi-mately 10-6 per year is acceptable if, when combined with reasonable qualitative arguments, the realistic probability can be shown to be lower."
USNRC Standard Review Plan Section 2.2.3 E
Jack R. Benjamin & Assoclotos,Inc.
Consulting Engineers B
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l RESULTS AND CONCLUSION OF ANALYSIS RESULTS Calculated probability of occurrence of a future e
surface rupture offset of any size greater than zero beneath.the ' Reactor Building foundation complies with the criterion Probabilistic analysis is conservative CONCLUSION Surface rupture offset should not be considered e
as a design basis event l
I Jack R. Benjamin & Associates,Inc.
E Consulting Engineers
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OUTLINE OF PRESENTATION OF PROBABILISTIC ANALYSIS Simplified approach Confidence level probability analysis e
Detailed model analysis e
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l BASIC PROBABILITY PARAMETERS Annual probability of occurrence of an offset beneath' Reactor Building foundation, P:
P=P xP 3
2 Where:
P, = annual probability that an offset will occur between shears B-2 and B-1/B-3 P2 = probability that an offset will occur beneath the Reactor Building foundation, given that an offset occurs between the shears I
Jack R. Benjomin & Associates,Inc.
Consulting Engineers B
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SIMPLIFIED APPROACH t = 128,000 years t = 195,000 years P
a 1/128,000 P.3 a 1/195,000 3
P a 72/1320 P
a 72 /1320 2
2 P=P3xP2 P = 1/128,000 x 72/1320 P = 1/195,000 x 72/1320 ny
$a 55 l sf F = 4.3 x 10-7 P = 2.8 x 10-7 gg I
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CONFIDENCE LEVEL PROBABILITY ANALYSIS P = - 2n (1-C)/t i
Where:
C = Confidence level probability Number of years without an offset t
=
between the shears P = (2+b)/(L-b) 2 Where:
2
= Width of Reactor Building L = Distance between two existing shears b = Width of offset at ground surface P=PxP 3
2 I
Jack R. Benlomin & Associates,Inc.
Consulting Engineers E
PROBABILITY OF OFFSET OCCURRING BENEATH REACTOR BUILDING FOUNDATION Confidence Level No. of yrs. without an event Probability t = 128,000 yrs t = 195,000 yrs 0.95 1.4 x 10-6 8.9 x 10-7 0.90 1.0 x 10-6 6.8 x 10-7 g
in 0.50 3.1 x 10-7 2.1 x 10-7
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DETAILED MODEL ANALYSIS P = $ Ae4 i
Where:
A = Mean time rate of occurrence of offsets
$ = Probability that an offset will occur between the two shears given that an offset occurs P = (2+b)/(L-b) 2 Where the parameters are the same as the confidence level probability analysis P=PxP i
2 i
I Jack R. Benjamin & Associates,Inc.
Consulting Engineers B
METHOD FOR OBTAINING PROBABILITY DENSITY FUNCTION FOR A AND c p(A,$) = $ L(A, Idata) p'(A, )
Where:
$ = normalizing constant p'(A,$) = prior probability density function 4 (At )"i e At; i
L(A, Idata) = Il n;l
,1 i=
1; = tinae period (years) n; = number of events in time period t; pI A,4) " t"+ 1 A" e-A t nl Where:
4 t= E t; i=1 4
n= In;
,1 i=
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Jack R. Benjomin & Associates,Inc.
Consulting Engineers B
ESTIMATED VALUES FOR PROBABILITY P 3 Weighted estimate 1
=
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Confidence limits 4
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PROBABILITIES OF OFFSET BENEATH REACTOR BUILDING FOUNDATION Detailed Model*
Confidence Level Prob. Analysis Analysis Basis t = 128,000 yrs.
t = 195,000 yrs.
t = 128,000 yrs.
t = 195.000 yrs.
Weighted estimate 4.5 x 10 7 3.0 x 10-7 NA NA 0.95 Confidence level 1.3 x 10 6 8.4 x 10'7 1.4 x 10 8 8.9 x 10 7 O.90 Confidence level 1.0 x 10 6 6.7 x 10-7 1.0 x 10-8 6.8 x 10 7 0.50 Confidence level 2.9 x 10-7 1.9 x 10'7 3.1 x 10-7 2.1 x 10 7
- Based on n = 15 l
l E
Jock R. Benjamin & Associates,Inc.
Consulting Engineers D
CONFIDENCE LEVELS FOR OFFSET BENEATH REACTOR BUILDING FOUNDATION FOR 10-s CRITERION PROBABILITY VALUE Detailed Model*
Confidence Level Prob. Analysis t = 128,000 yrs t = 195,000 yrs t = 128,000 yrs t = 195,000 yrs 0.91 0.97 0.89 0.96
- Based on n = 15 E
Jack R. Benjamin & Associates,Inc.
Consulting Engineers D
EVALUATION OF CONSERVATISM Probability of potential consequences are at least one order e
of magnitude lower Offsets can occur outside of area between the two shears Conclusion is based on t = 128,000 years. An average value between 128,000 years and 195,000 years is more appropriate.
Furthermore, the age of unfaulted soil material is probably older than 195,000 years I gu
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Prior distribution for A and $ was conservatively assumed e
iy in Detailed Model oa I [g Two-dimensional geometric model is conservative aa 80 n!
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SUMMARY
AND CONCLUSION Weighted estimate probability value is less than 10-6 0.90 Confidence level value is essentially equal to 10-6 Probabilistic analysis is conservative Analysis and results comply with criterion l gg Hence 4
E iaj Surface rupture offset of any size should not be considered e
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GENERAL ELECTRIC TEST REACTOR (GETR)
DOCKET NO. 50-70 REVIEW 0F REPORTS SUBMITTED IN RESPONSE TO NRC ORDER TO SHOW CAUSE DATED 10/24/77 STRUCTURAL ISSUES 1.
You state that containment shell stresses exceed critical buckling stresses on the first floor level. Specify the extent of local as well as overall failure.
2.
Discuss in detail the final orientation, support conditions and locations, and status of all structural portions of the reactor building and core structure resulting from the most severe surface offset conditions.
3.
For the cases of vibratory motion during and after the worst case surface offset conditions, provide the factor of safety against overturning, discuss how it was determined, and justify its acceptability 4.
If, due to a surface rupture under the plant, the mat cantilevers off the edge of the soil, describe the load path through which all loads are trans-mitted from the reactor building to its support. Quantify any increase in stresses which result from the absence of support originally provided directly by the mat and soil.
5.
Specify the type of concrete in the basement and upper levels walls.
U 6.
Discuss how a dip of 60 in the surface offset, rather than the 15 assumed in your analysis, will affect the analysis procedures and results.
Include a discussion of the support conditions, and provide a diagram indicating forces acting on the core structure.
7.
For surface offset cases 2 and 3 (Figure 3-2 of the Phase 2 Report), quantify the maximum possible cantilever and unsupported lengths. Provide bases justifying these lengths, and verify that they were used in the offset analyses.
A shear strength of 6 { jor cracking and failure. representing the first crack thresh 8.
indicates the onset of ma Justify why some allow-able strength less than this should not be used to provide an acceptable level of safety.
9.
Vertical excitation should be included in the sliding and uplift analyses.
In addition, sliding between the basement slab and foundation mat must be accounted for in the reactor building model.
- 10. Address the issue of the reactor building impacting the mat during the surface rupture and simultaneous vibratory motion, f
- 11. Discuss the findings of your program to verify that the piping restraints and anchors are in the correct locations.
Indicate all deviations.
BAYESIAN ANALYSIS EVALUATION FOR i
" PROBABILITY ANALYSIS OF SURFACE RUPTURE OFFSET BENEATH REACTOR BUILDING - GENERAL ELECTRIC TEST REACTOR" In both the Bayesian and classical statistical analyses performed in the report, a Poisson distribution is used to describe the number of offsets, of any size, which can occur in a given time period.
In both analyses, of the total number of offsets which occur in a given time period, a fixed fraction is assumed to occur between the shears (instead of on them) and a specific offset which occurs between the shears is assumed to be equally likely to be located at any point on a line between the shears.
For the classical statistical analysis, an upper 95% confidence bound can be derived for PjxP2 which does not depend upon the location distribution assumption (using 128,000 years recorded without an offset _ occurring beneath the reactor building).
In the Bayesian analysis in the report, two parameters are trcated as being random variables:
(1) the occurrence rate for the Poisson distribution, and (2) the fraction of offsets occurring between the shears.
This random variable treatment is standard for a Bayesian analysis.
The random variables are assigned prior probability distributions which are supposed to describe the previous state of knowledge about these parameters before a specific set of observed data are assessed.
By utilizing the observed set of data, the prior p.robability distributions are updated to new distributions (the posterior probabi-lity distributions) which now incorporate the previous state of knowledge as well as the observed data.
In the report, a gamma distribution is assumed as the prior distribution for the Poisson occurre.ce rate and a beta distribution is assumed as the prior distri-bution for the fraction occurring between the shears.
There is no justification
2-given for these distribution assumptions other than mathematical tractab'ility.
As sensitivity studies in the report,-different parameters are selected for the gamma and beta distributions.
However, as part of the sensitivity studies, entirely different distributions are not examined to s50w the effect on the results (such as using the log-normal and the log-beta for the occurrence rate prior and fraction prior).
The statement on page 5-3 that ignorance is represented by using uniform distributions as the priors for the occurrence rate and the fraction between l
2 shears is simply not true (see for example C. R. Rao and R. A. Evans ).
Because no firm physical or engineering bases are given for the choice of prior distribu-tions in the report and because the prior distributions can completely bias and dominate any results (see G. C. Canavos3 4
and J. Aitchison and J. P. Dunsmore )
comprehensive sensitivity studies must be performed in the report utilizing very different prior distributions.
These comprehensive sensitivity studies are not performed and hence the report's Bayesian results are not credible.
(The report's Bayesian results are summarized in Table 5-1 on page 5-10 under the heading entitled, "Model Approach.")
A second deficiency in the Bayesian analysis performed in the report, which is as important as the lack of sensitivity studies, is the use of data which were not observed but were "made-up."
Instead of using the observed data in Table 4-1 on page 4-2 to modify the prior distributions, the report assumed that the numbers of offsets occurring in the four time periods were observed.
This untrue assumption was " justified" by varying the numbers assumed and stating that no significant effect was observed for the specific prior distributions and variations utilized in the report.
I
. In reality, as stated in the report, the numbers of offsets were not bbserved.
Only the total sizes of the offsets were observed.
It is one thing to have observed the number with some uncertainty (as was assumed) but it is another thing to not have observed the number at all (as was reality).
If the actual data in Table 4-1 are used to update the prior distributions, and not some fictitious observed numbers of offset occurrences, very different results for P xP can be obtained. The utilizing of the actual data is straightforward, j
2 although a computer may be required (the likelihood would consist of a Poisson compounded with a convolution for the offset size distribution).
The use of
" fictitious" data in the report appears to be a lazy, short-cut way of obtaining mathenatically simple equations - a way by which data are fictitiously generated to fit the simple mathematical model assumed (to allow natural conjugate distributions in the Bayesian analysis). The report should treat the real data.
==.
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References 1.
C. R. Rao, Linear Statistical Inference and Its Applications, Wiley and Sons, New York, 1965, 2.
R. A. Evans, " Bayes in Theory and Practice,".The Theory and Application of Reliability, ed._ by C. P. Tsokos and I. N. Shimi, Academic Press, New York,1977.
3.
G. C. Canavos, " Robustness and the Prior Distribution in the Bayesian Estimation," The Theory and Application of Reliability, ed. by C. P.
Tsokos and I. N. Shimi, Academic Press, New York, 1977.
4.
J. Aitchison and I. P. Dunsmore, Statistical Prediction Analysis, Cambridge Press, Cambridge,1975.
1 I
GENERAL ELECTP.IC TEST REACTOR (GETR)
DOCKET NO. 50-70 REVIEW 0F REPORTS SUBMITTED IN RESPONSE TO NRC ORDER TO SHOW CAUSE DATED 10/24/77 STRUCTURAL ISSUES 1.
You state that containment shell stresses exceed critical buckling stresses on the first floor level. Specify the extent of local as well as overall failure.
2.
Discuss in detail the final orientation, support conditions and locations, and status of all struttural portions of the reactor building and core structure resulting from the most severe surface offset conditions.
4.
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4.
If, due to a surface rupture under the plant, the mat cantilevers off the edge of the soil, describe the load path through which all loads are trans-mitted from the reactor building to its support. Quantify any increase in stresses which result from the absence of support originally provided directly by the mat and soil.
6.
Discuss how a dip of 60 in the surface offset, rather than the 15 assumed 0
t in your analysis, will affect the analysis procedures and results.
Include a discussion of the support conditions, and provide a diagram indicating forces acting on the core structure.
7.
For surface offset cases 2 and 3 (Figure 3-2 of the Phase 2 Report), quantify the maximum possible cantilever and unsupported lengths. Provide l
' m s justifying these lengths, and verify that they were used in the offset a v:fses.
8.
A shear strength of 6 ( representing the first crack threshold strength indicates the onset of major cracking and failure. Justify why some allow-able strength less than this should not be used to provide an acceptable level of safety.
9.
Vertical excitation should be included in the sliding and uplift analyses.
In addition, sliding between the basement slab and foundation mat must be accounted for in the reactor building model.
- 10. Address the issue of the reactor building impacting the mat during the surface rupture and simultaneous vibratory motion.
- 11. Discuss the findings of your program to verify that the piping restraints and anchors are in the correct locations.
Indicate all deviations.
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12.
Provide a detailed discussion verifying that a seismic design basis of 0.8 EPGA combined with some small amount of surface offset has been considered, and will not be as severe as the design bases used in your surface offset or post-offset analyses.
Include a discussion verifying that any structural i
degradation resulting from surface. offset effects has been considered and accounted for in your post-offset analysis.
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MEETING
SUMMARY
DISTRIBUTION ORBf4 Mr. R. W. Darmitzel, Manager Irradiation Processing Product Section Vallecitos Nuclear Center General Electric Company P. O. Box 460 Pleasanton, California 94566 Docket File NRC PDR V. Noonan L PDR P. Check ORB #4 Rdg G. Lainas NRR Rda G. Knighton E. G. Case OELD OI&E (3)
R. Ingram R. Vollmer R. Fraley, ACRS (16)
W. Russell Program Support Branch B. Grines TERA T. J. Carter J. R. Buchanan A. Schwencer Meeting Summary File D. Ziemann T. Ippolito L. Shao i
J. Miller AE0D 1
1 THIS LIST IS IN ADDITION TO THOSE LISTED IN ENCLOSURE 1 (LIST OF ATTENDEES) 4
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