ML19312D870
| ML19312D870 | |
| Person / Time | |
|---|---|
| Site: | Vallecitos File:GEH Hitachi icon.png |
| Issue date: | 04/30/1980 |
| From: | Darmitzel R GENERAL ELECTRIC CO. |
| To: | Eisenhut D Office of Nuclear Reactor Regulation |
| References | |
| NUDOCS 8005050294 | |
| Download: ML19312D870 (21) | |
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I aenfa I GENER AL h ELECTRIC E N G E N E E R I N Gf GENERAL ELECTRIC COMPANY, P.O. BOX 400, PLEASANTON, CALIFORNIA 94566 DIV1S1ON i
50 - VO i
April 30, 1980 t
l 1,
Mr. Darrell G. Eisenhut, Director Division of Operating Reactors 4
Office of Nuclear Reactor Regulation U. S. Nuclear Regulatory Commission Washington, D.C.
20555 4
Subject:
Responses to NRC Questions on " Additional Probability Analyses of Surface Rupture Offset Beneath Reactor Building - General Electric Test Reactor"
Dear Mr. Eisenhut:
i Enclosed are responses to comments and questions received from the Nuclear i
Regulatory Commission with respect to the report " Additional Probability i
Analyses of Surface Rupture Off ait Beneath Reactor Building - General Electric Test Reactor".
One of the suggestions made was that additional sensitivity analysesbeperformed,andinresponsetothistheparametgrvalueswere 4
allowed to vary so as to produce probability values of 10- and 10 It is interesting to note that the bounding values are generally out of the range of realistic geology parameter values.
In several instances the selected prooability limits could not be reached.
Thus, the probability of an offset i
beneath the reactor building is insensitive (in the sense of an order of magnitude) to realistic parameter values.
Very truly yours, i
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l AFFIRMATION The General Electric Company hereby submits the attached responses to NRC questions on " Additional Probability Analyses of Surface Rupture Offset Beneath Reactor Building - General Electric Test Reactor".
To the best of my knowledge and belief, the information contained herein is accurate.
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Irradiation Processing Operation Submitted and sworn before me this 30th day of April,1980.
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, Notary Public in and for the County'of Alameda, State of California.
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RESPONSES TO NRC QUESTIONS ON
" ADDITIONAL PROBABILITY ANALYSES OF SURFACE RUPTURE OFFSET BENEATH REACTOR BUILDING - GENERAL ELECTRIC TEST REACTOR" Questions and comments were received from the United States Nuclear Regulatory Commission (USNRC) concerning the report:
" Additional Probability Analyses of Surface Rupture Offset Beneath Reactor Building
- General Electric Test Reactor" (Ref 1). A telephone meeting was held on 10 April 1980, between reptasentatives of the USNRC, General Electric Co. (GE), and GE's consultant's to discuss the questions and coninents.
Based on that conversation, it was agreed that GE would provide information for the following areas.
e Separation of probability results into component terms e Sensitivity of procedures for selecting N for Analysis Approach '.
e Justification for selecting prior distribution for p(N) e Confidence Intervals for o/E e Procedure for selecting maximum bounda for Analysis Approach 2, cases 7 and 8 e Additional Sensitivity Analyses The remaining coninents by the USNRC are in the nature of observations and do not require a response. These were discussed in the telephone meeting, and it was agreed that they were resolved.
Responses for each of the areas are given below. The reader is i
directed to Reference 1 for the development of the probabilistic methodology and definitions of terms.
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r SEPARATION OF PROBABILITY RESULTS INTO COMPONENT TERMS In the JBA report (Ref 1), the first term in Equation 2-1 (i.e.
Pg PBSl g PRBlBS) produces the same results as the alternate probability analysis given in the first report (Ref 2). Table 1 gives the breakdown of the probability values presented in Reference 1 for the various analysis cases. The probability values for the two terms in Equation 2-1 of the JBA report along with the total probability values are given in the table.
Note that in most cases the first term is larger than the second term.
In a few cases the second term is larger; however, in all cases the difference between the two terms is less than an order of magnitude.
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SENSITIVITY OF PROCEDURE FOR SELECTING N FOR ANALYSIS APPROACH 1 The value of N used in Analysis Approach I was selected as the mode ofp(NlT),whichistheposteriordistribution. Becausep(NlT)isa x
x relatively " tight" distribution, the results of the analysis are not sensitive to the procedure for selecting N.
For example, Table 2 gives the cumulative distribution for N given T for the best estimate x
case. As presented in Table 2, the 95 percent, 90 percent, and mode values for N are 209, 211, and 221, respectively. Relative to the mode value, the 90 percent and 95 percent values increase the probability P
by only 6 percent and 5 percent, respectively, which are BS ON insignificant compared to variations caused by other effects.
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o JUSTIFICATION FOR SELECTING PRIOR DISTRIBUTION FOR p(N)
Incalculatingp(NlT),whichisusedinAnalysisApproach1,a x
geometric distribution was selected for the prior mass function p(N),
and the results compared to the probabilities obtained using a diffuse prior distribution. Parametric analyses were perfonned for values of f (the mean of the geometric distribution) between 2 and infinity.
It was found that the prior geometric distribution did not significantly increase the probability of offset between the shears (see Table 4-2 in the JBA report).
Since the geometric distribution is defined by only one parameter, the coefficient of variation of N cannot be independently controlled as the mean is varied. Alternate distributions such as the binomial or negative binomial could be used; however, the real question concerns the range of values for N to be simulated by the prior distribution.
From a geological perspective (prior to obtaining data from the recent trench excavations at GETR) the average number of offsets in 1,600,000 years (the time period for the best estimate case for which Table 4-2 in the JBA report is based) would be on the order of 50 to 16,000, with an average value close to 10,000. This is based on experience with faults in California which have return periods for surf ace rupture offset on the order of 100 to 30,000 years, with likely values closer to the 100-year value. Thus, one would expect higher values of N as compared to 221 which was the mode value selected fro:n the p(NlT ) p sterior distribution based on a diffuse prior x
distribution. Since high values of N produce lower values of the probability P for Analysis Approach 1, it is conservative to use a diffuse distribution for the prior mass function p(N).
The effect of using a bounded prior distribution, which is highly skewed to the right, is closely approximated by a geometric distribution with a small mean. As discussed above, the principal concern is the minimum value for the upper bound on N.
The uncertainty in the upper bound value is accounted for by using a diffuse geometric distribution with a mean value equal to infinity.
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Note that the impact of using a prior distribution which is highly skewed to the left can be approximated by using single large values of N.
There is no adverse impact on the final probability results for large values of N.
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CONFIDENCE INTERVALS FOR a/I Approximate confidence intervals were calculated for Sieh's trench excavation data given in Table 3-4 of the JBA report. The procedure used consisted of calculating 95 percent confidence bounds on the mean value using the t-distribution (which asswes the underlying distribution is nonnal with both mean and standard deviation unknown) and on the standard deviation using the Chi-square distribution (which assunes the underlying distribution is normal). The values were paired to produce maximun ranges on the coefficient of variation, which approximately represents 90 percent confidence values.
The results of the computation are given in Table 3.
The lower value is greater than the bound used in the parametric analyses (i.e.
a/E=0.2).
The upper bound value of 1.72 exceeds the analysis bound of 0.7.
However, for the range of parameter assignments which produces large, values of the probability P, increasing c/T decreases P.
An example of a case where P increases for increasing values of a/E is given in Table 7, where for Analysis Case 2 the maximum probability for all values of c/E occurs for a/E equal to 1.0, which is slightly larger than the upper bound value of 0.7 given in Reference 2.*
However, the corresponding probability P is only 1.0 x 10-6 In general, for cases where the probability P increases for increasing values of c/t, the increase in P is always small. This is true since for these cases t is always less o
than (ts - t )/(N-1), and for these combinations of parameter values o
PON (and hence P) is relatively small.
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r PROCEDURE FOR SELECTING MAXIMUM BOUNDS FOR ANALYSIS APPROACH 2, CA5E5 / AND 8 In Analysis Approach 2, the time period for offsets on existing shears, t and the number of offset values for N were selected for 3
analysis cases 7 and 8 (see Table 4-3 in the JBA report) to produce maximtsn bounds based on a three-parameter sensitivity analysis. The maximum bounds were determined from the ranges of values for T, r, x
and x given in Tables 3-2 and 3-3 of the JBA report. Table 4 summarizes the ranges of values for the three parameters used in the analysis. The variables t and N are a function of the three parameters as given s
below.
t = T /r s
x N = T /x x
For Analysis Approach 2, P increases while P decreases as N ON BSl0N increases; hence, it is not obvious which combination of parameters T, r, and x produce the maximum bounds. Thus, all combinations of x
the ranges were investigated to determine the maximum bounds.
It was assuned that the two shears were perfectly correlated and that high and low extreme values occurred together for the two shears. Table 5 gives the results for the cases which were analyzed to determine the maximum bounds. Each of the two bounds was investigated further to determine whether a slight change in the parameters (within the limits of Table 4) would widen the bounds.
It was found that the cases considered in Table 5 produced the maximum bounds.
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ADDITIONAL SENSITIVITY ANALYSES Additional sensitivity analyses were conducted to determine the effects of varying the parameters on the probability of an offset beneath the reactor building. Tables 6 and 7 give the values for each parameter which cause the calculated annual probability of an offset to equal the 1 x 10-5 and 1 x 10-4 limits. Table 6 presents the results of varying one parameter at a time (except as noted below) for Analysis Approach 1, while Table 7 gives corresponding results for Analysis Approach 2.
Note that each parameter was varied only in the direction which increased the value for P.
Changing the parameter in the other direction only decreases P.
Note that in several instances the probability limits (i.e. 1 x 10-5 and 1 x 10-6) could not be obtained as discussed below. The bases for the sensitivity analyses for the two analysis approaches are also given below.
Analysis Approach 1 Parameters a/Y and C (cases 1 and 6):
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by systematically decreasing the parameters individually unti
,.hhEi fidence level on the parameters associated with PBSlNIandPBS y y, %
the two probability levels were obtained.
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As parameter t was increased, the strain rate, r, was also
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o increasedaccordingly(e.g.seeTable3-3oftheJBAreport),untilj h f t reached 97,500 years. Higher values of t imply negative j
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strain rates with corresponding total number of events, N, undefined. Thus t cannot exceed 97,500 years. The corresponding o
probability P is given in Table 6.
Parameter t* (case 3):
As t* was decreased the strain rate, r, was increased accordingly l
by assuming that the age on the shears for the third time period (see Table 3-1 in JBA report) was equal to t*.
t* was decreased 8
i until the third time period age reached 8,000 years.
Lower values of t* (hence the third time period age) inply negative strain rates with corresponding number of events, N, undefined. Thus t* cannot be less than 8,000 years.
Parameter Tx (case 4):
Decreasing T increases the probability, P.
Since it was x
positively established in the recent trench excavations that a minimum of 52 ft and 88 ft of offset has occurred on shears B-1/8-3 and B-2, respectively, these values were selected as lower bounds.
Parameter r (case 5):
The strain rate, r, was increased until the probability of an offset reached 1 x 10-5 In attempting to reach the 1 x 10~4 probability limit, strain rates corresponding to 1 event on each shear were found to constrain the value for r since higher values do not change the probability P.
Thus, the maximum annual probability for P is 2.8 x 10-5 for the corresponding strain rates shown in Table 6.
Analysis Approach 2 Parameters t;, t* and C (cases 2, 3, and 7):
Parameter bounds were obtained for t,
t*, and C by systematically o
varying the parameters individually until the two probability limits were obtained.
In an analogous manner to the parameter calculations for Analysis Approach 1, the strain rate was increased as t was increased. Hence t decreased accordingly (e.g. see g
s Table 3-3 of the JBA report).
Values for t* were found to be less than 70,000 years.
In order to be consistent with the observed geological data the number of offsets were conservatively based on 12 ft and 8 ft (rather than 52 ft and 88 ft) for the B-1/8-3 and B-2 shears, respectively.
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The values of the parameter a/T for the best estimate case (i.e.
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0.5) produces essentially the maximum annual probability, P.
A very small increase occurs as a/E is increased to 1; however, by rounding off the values of P as given in Table 7, the best estimate case and case 1 give the same results for P.
Parameters t and N (cases 4, 5, and 6):
3 The parameters t and N were asstned to be related as given by s
the following equations:
t = T /r s
x N = T /x x
where T = total accumulated offset on the existing shears x
r = strain rate on existing shears x = characteristic offset size.
The best estimate values for the three underlying parameters are given in Table 8.
These values were varied one at a time which produced the analysis bound cases 4, 5, and 6 in Table 7.
These cases correspond to varying T r, and x, respectively. For case x
4, the values for T were limited to minimum values of 52 and 88 x
feet, respectively, for shears B-1/B-3 and B-2 as discussed above for Analysis Approach 1, case 4.
It was found for case 6 that the value of x corresponding to N equal to 12,000 produced the maximum annual probability P.
The probability P increases as N increases up to 12,000. For values of l
N greater than 12,000 (i.e. lower values of x) lower values of P l
are obtained. Table 9 gives the values of T, r, and x x
corresponding to cases 4, 5, and 6 for the two probability levels.
Note that the bounding parameter values are given in Table 9, but only one parameter was varied at a time. Thus the other two l
corresponding best estimate values for each case are given in Table 8.
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a The bounding values in Tables 6 and 7 are generally out of the range of realistic geologic parameter values.
In several instances, the selected probability limits could not be reached (i.e. the probability P reached a maximum value).
In conclusion, the prcbability of an offset beneath the reactor building is insensitive (in the sense of an order of magnitude) to realistic parameter values.
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REFERENCES 1. Jack R. Benjamin and Associates, Inc., " Additional Probability Analyses of Surface Rupture Offset Beneath Reactor Building - General Electric Test Reactor," Report to General Electric Co., San Jose, California, March 12, 1980. 2. Engineering Decision Analysis Co., " Probability Analysis of Surface Rupture Offset Beneath Reactor Building - General Electric Test Reactor," Report to General Electric Co., San Jose, California, April 12,1979. i i l a- - ~, waw?O -. - eg,. ~_ orw OFFICIAL ' ) th:,1(l'y VIRGINIA C. CAEC' : '9 r l i .( .- s -c. t " NOTARY PUBLIC CALINRN'A l 3 {g (l -ffbjI ALAMED A COUNTY 4 (, J' f.ty ccom. errirss MAR 8, ":' '-
e 9 TABLE 1. SEPARATION OF PROBABILITY RESULTS GIVEN IN REFERENCE 1 6 Probability in one year (x 10 ) Analysis Analysis Approach Case First Terml Second Term 2 Total Probability, P 1 Best Estimate 0.835 0.315 1.15 1 0.835 0.270 1.11 2 0.835 0.911 1.75 3 0.835 0.223 1.06 4 0.835 0.340 1.18 5 0.835 0.303 1.14 6 1.04 0.315 1.36 7 0.685 0.315 1.00 8 0.835 1.42 2.26 9 0.835 0.117 0.95 10 1.09 0.409 1.50 11 0.038 0.015 0.053 2 Best Estimate 0.835 0.132 0.97 1 0.835 0.040 0.88 2 0.835 0.152 0.99 3 0.835 0.351 1.19 4 0.835 0.062 0.90 5 1.04 0.132 1.17 6 0.685 0.132 0.82 7 9.835 6.37 7.21 8 0.835 0.083 0.92 9 1.09 0.171 1.26 10 0.038 0.006 0.044 I (same as alternate probability analysis in Pg PBS g PRBlBS Reference 2) 1 (PbN PjSj0N+P BSl0N) PRBlBS P ON ' 75 '~3fidEiAE, Akin vmmu c. cxn ~ - (%#gu:/df pl1 NOTARY PUBUC
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TABLE 2. CUMULATIVE PROBABILITY DISTRIBUTION P(NlTx) AND PBSl0N PUR THE BEST E5TIMATE CASE N P(NlTx)* PBSION Comment 190 3.4 x 10-6 1r ir 209 0.048 0.010957 95% confidence value 210 0.064 211 0.084 0.010853 90% confidence value 212 0.107 213 0.136 214 0.168 215 0.205 216 0.247 217 0.292 218 0.341 219 0.392 220 0.445 221 0.498 0.0103648 Mode 222 0.551 223 0.604 224 0.653 225 0.701
- P(NlT ) is the ctmulative prrtah414ty distribution for N given T.
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a e i TABLE 3. CONFIDENCE INTERVALS FOR SIEH'S TRFNCH EXCAVATION DATA Confidence Lower Bound Upper Bound Level Mean, Y 93.841 226.661 0.95 Standard Deviation, a 52.712 161.643 0.95 I Coefficient of Variation, a/T 0.23 1.72 0.904 1k.025,7=2.365 Xh.025, 7 = 16.01 Xb.975, 7 = 1.69 Approximate confidence level TABLE 4.
SUMMARY
OF PARAMETRIC VALUE RANGES Shear B-1/8-3 Shear B-2 Parameter Lower Bound Uoper Bound Lower Bound Upper Bound Tx(ft) 52 420 88 280 r x 104 (ft/yr) 0.99 2.18 0.66 1.45 x (ft) 0.328 3.28 0.328 3.28 OFFICIAL k ~ O I"m,-T/- VIRGINTA C. CAFC'.No.l [ 313 r;otARY PUGUC - CAUFORN: A y w%i$d' n,7"y^3,j f.yf3, y.n $; 15
c TABLE 5. ANALYSIS CASES FOR DETERMINING MAXIMUM B0UNDS FOR ANALYSIS APPROACH 2, CASES 7 AND 8 Shear B-1/B-3 Shear B-2 T r x 104 x t t r x 104 t P x 106 s x s (f() (feet / year) (feet) N (years) (ft) (feet / year) (feet) N (years) (in one year) 52 0.99 0.328 160 530,000 88 0.66 0.328 270 1,300,000 2.22 52 0.99 3.28 16 530,000 88 0.66 3.28 27 1,300,000 0.93 1 52 2.18 0.328 160 240,000 88 1.45 0.328 270 610,000 7.21 52 2.18 3.28 16 240,000 88 1.45 3.28 27 610,000 1.30 420 0.99 0.328 1280 2,000,000* 280 0.66 0.328 850 2,000,000* 1.06 2 420 0.99 3.28 128 2,000,000* 280 0.66 3.28 85 2,000,000* 0.92 420 2.18 0.328 1280 1,900,000 280 1.45 0.328 850 1,900,000 2.03 420 2.18 3.28 128 1,900,000 280 1.45 3.28 85 1,900,000 0.93
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TABLE 6. ANALYSIS APPROACH 1 -- PARAMETER B0UNDS Tv (feet) r x 104 (feet / year) t t* P o Analysis Case Distribution a/t (years) (years) B-1/8-3 B B-1/B-3 B-2 C (in one year) Best Estimate Weibull 0.5 8,000 160,000 210 140 1.34 0.89 0.90 1.2 x 10-6 10-5 Probability 1.0 x 10-6 1 0.023 3.1 x 10-6 2* 97,500 = = 3 62,000 2.22 1.48 1.0 x 10-5 4* 52 88 1.7 x 10-6 5 35 35 1.0 x 10-5 6 1-10-9 1.0 x 10-5 0 10-4 Probability 1 0.00218 1.0 x 10-4 3.1 x 10-6 2* 97,500 = = 1.0 x 10-4 3 8,000 = = 4* 52 88 1.7 x 10-6 5* 300 200 2.8 x 10-5 6 1-10-96 1.0 x 10-4 Nate that values not shown are the same for the Best Estimate Analysis Case
- See text for explanation.
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s TABLE 7. ANALYSIS APPROACH 2 -- PARAMETER BOUNDS te (years) N t t* P o Annlysis Case Distribution o/E (years) (years) B-1/B-3 B-2 B-1/B-3 B-2 C (in one year) Best Estimate Weibull 0.5 8,000 160,000 1,600,000 1,600,000 128 85 0.90 1 x 10-6 10-5 Probability 1* 1.0 1.0 x 10-6 2 62,000 621,000 621,000 1.0 x 10-5 3 51,000 8 5 t.0 x 10-5 4* 388,000 989,000 32 54 1.3 x 10-6 5 273,000 182,000 1.0 x 10-5 6 7,000 7,000 1.0 x 10-5 7 1-10-12 1,0 x 10-5 ca 10-4 Probability 1* 1.0 1.0 x 10-6 2 80,000 306,000 306,000 1.0 x 10-4 3 21,000 8 5 1.0 x 10-4 4* 388,000 989,000 32 54 1.3 x 10-6 5 84,000 56,000 1.0 x 10-4 6* 12,000 12,000 1.6 x 10-5 7 1-10-113 1.0 x 10-4 Nnto that values not shown are the same for the Best Estimate Analysis Case OSee text for explanation. .; u ~., _ _,.. _ )((-'sk VIRGIN!A C. CAC~mo lk OFFICIAL.. 1 .. ;g f;OTARY PU2UC - CAurORPaA / J"G-
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a. TABLE 8. BEST ESTIMATE PARAMETER VALUES T r x 104 x Shear (feet) (feet / year) (feet) B-1/8-3 210 1.34 1.64 B-2 140 0.89 1.64 TABLE 9. PARAMETER VALUES FOR TWO PROBABILITY LEVELS 1 x 10-5 Probability Level 1 x 10-4 Probability Level T r x 104 x T r x 104 x Shear (feNt) (feet / year) (feet) (feNt) (feet / year)_ (feet) B-1/8-3 52* 7.7 .03 52* 25 .018* B-2 88* 7.7 .02 88* 25 .012* Analysis 4 5 6 4 5 6 Case
- See Table 7 for Probability Level P corresponding to parameter values.
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