ML19290E584
| ML19290E584 | |
| Person / Time | |
|---|---|
| Site: | Vallecitos File:GEH Hitachi icon.png |
| Issue date: | 03/12/1980 |
| From: | JACK R. BENJAMIN & ASSOCIATES, INC. |
| To: | |
| Shared Package | |
| ML19290E581 | List: |
| References | |
| JBA-111-013-01, JBA-111-13-1, JPA-111-013-01, JPA-111-13-1, NUDOCS 8003140239 | |
| Download: ML19290E584 (32) | |
Text
J B A-111-013-01 Additional Probability Analyses of Surface Rupture Offset Beneath Reactor Buildirig General Electric Test Reactor prepared for
*~"'"""^^^^W i
OFF:CIAL :
.L
?
General Electric Company y;' :. '
vmmin c. c4: ~
San Jose, California
-1
- a g w=y ruer - u
, un n n
..f,
,'n.',',
e ;f e-
[
I' k,
y ttr ; *..., " +,... '. ' '
s.
-=.n;
-.w._.
Jack R. Benjamin & Associatos, Inc.
Dj Consulting Engineers Dh D
f' car "xxm naa Euma w o,
- q w sn
.a m m, tuo y.o com.o,a ;4 j;gp hed t.$ :
c) a 8003140 237
ADDITIONAL PROBABILITY ANALYSES OF SURFACE RUPTURE OFFSET BENEATH REACTOR BUILDING GENERAL ELECTRIC TEST REACTOR Prepared for General Electric Company San Jose, California
~w
.<-~~ ~ m wwxm OFFICIAL E AL
[
v!c7N' A C. CVO~m I; Marcr 1, 1980 nmiw puu: - caut cem,
i
,,?>,c
.\\
- y tern. eri.as ;2 : :. :: $
_o.
,_-,w -
Jack R. Benjamin & Associates,Inc.
3 Consulting Engineers Court House fMoro Bu l ding hte 205 b
260 Shendon Ae Fuo A:fo. Cohfornia 94306
TABLE OF CONTENTS Page EXECUTIVE
SUMMARY
ii 1.
INTRODUCTION 1-1 2.
PROBABILISTIC MODEL 2-1 Model Formulation 2-1 3.
GE0 LOGICAL DATA 3-1 4.
PROBABILISTIC ANALYSES 4-1 Analysis Approach 1 4-1 Analysis Approach 2 4-4 5.
CONCLUSIONS 5-1 REFERENCES R-1 y-v f
O.
Vf i'Q,' A ( CA i_'
'.OTisky N 't!: - C J, 1
' E p.; r (',, ;
[x f'
cc e f M s } r,71 (
hv-~~y comm
~n _ _,.., A i
O Jack R. Benjamin & Associates,Inc.
Consulting Engineers D
EXECUTIVE
SUMMARY
Additional probability analyses were conducted to determine the likelihood of a surface rupture offset occurring beneath the General Electric Test Reactor (GETR) reactor building, which is located at the Vallecitos Nuclear Center. The analyses considered that offsets of geologic strata have been observed in the vicinity of the reactor building and that these offsets are either faults or ancient landslides.
These analyses were performed at the request of the United States Nuclear Regulatory Commission (USNRC) in response to their review of the first probability analysis (Ref. 1). Based on the findings in the first analysis, it was concluded that surface rupture offset of any size beneath the GETR reactor building was sufficiently remote that it should not be considered as a design basis event.
In the prior analysis for determining the probability of an offset beneath the reactor building, the oossibility of offsets occurring either on existing shears or between shears was investigated.
The remote possibility of offsets occurring on an existing shear and between shears simultaneously was judged to be relatively small and was not considered. After reviewing the first report, the USNRC requested that additional analyses be conducted to include the possibility of surface rupture offsets occurring on and off the shears simultaneously during the same event.
A strain-rate accumulation model was developed and used in the current analyses to calculate the probabiiity of such events, and two approaches were used to obtain values for the probabilistic model.
The computed probabilities were compared to an acceptance criterion of 10-6 annual probability of occurrence, which was selected for the first analysis (Ref. 1).
ii p._
.__.c._
r OTRCL\\L,
,e f
- ) VWGi? M C CA
4 noncy po=x - cm; mn{
Jack R. Benjamin & Associates,Inc.
O
%-~, w 1.g [M,,, k l'
Consulting Engineers B
___r
The results of the current analyses show that the best estimate annual probability values for a future surface rupture offset beneath the GETR reactor building are 1.2 x 10-6 and 1.0 x 10-6 for the two approaches.
These values compare closely to the values obtained from the first analysis (Ref. 1).
Values calculated from parametric sensitivity computations range between 0.04 x 10-6 and 7.2 x 10-6,
The latter value is very conservative since there is less than a 4 x 10-4 probability that the assumed values for the geologic parameters would occur.
The best estimate probability values and most of the values obtained from the parametric calculations are close to the 10-6 annual probability criterion value.
Because the criterion is based on the occurrence of potential exposure, the probability calculations for an offset beneath the reactor building are very conservative.
Consideration of other elements leading to potential adverse consequences (i.e.
damage, release, dispersion, and exposure) would likely decrease the calculated probabilities by at least one order of magnitude.
The results confirm that surface rupture offset of any size beneath the reactor building still should be excluded as a design basis event.
CI F.'C! AL ;
', " }'M ;u c; m v ;
.cn u, g ra
.m
~
g pp..
,[
{-
' ' ~ '
iii O
Jack R. Benjamin & Assoclofes,Inc.
Consulting Engineers D
1.
INTRODUCTION Additional probability analyses were conducted to determine the likelihood 'f a surface rupture offset occurring beneath the General Electric Test Reactor (GETR) reactor building, which is located at the Vallecitos Nuclear Center.
The analyses considered that offsets of geologic strata have been observed in the vicinity of the reactor building and that these offsets are either faults or ancient landslides.
These analyses were performed at the request of the United States Nuclear Regulatory Commission (USNRC) in response to their review of the first probability analysis (Ref. 1).
Based on the findings in the first analysis, it was concluded that surface rupture offset of any size beneath the GETR reactor building was sufficiently remote that it should not be considered as a design basis event.
In the first analysis for determining the probability of an offset beneath the reactor building, the possibility of offsets occurring either on existing shears or between shears was investigated.
The remote possibility of offsets occurring on an existing shear and between shears simultaneously was judged to be relatively small and was not considered.
The USNRC requested that additional analyses be conducted to include the effect of such events.
Since an offset occurring between existing shears may be linked to simultaneous occurrence of offsets on existing shears, the USNRC requested that a model which takes into account strain-rate accumulation be used to calculate the probability for this type of event.
Hazard functions which monotonically increase with time due to the underlying constant strain rate assumption were used to model the time between offsets. Thus the probability of a future offset on existing shears (and similtaneously between shears) increases with the amount of time since :he occurrence of the last offset on an existing shear.
~ _ n w.w
,3+ ywalt !:n rOFFICI AL l e
co c f s y;:n r; x - c '
y 1-1 Jack R. Benjamin & Assocloies, Inc.
Consulting Engineers B
The probabilities computed in the first analysis were compared to a criterion of 10-6 annual probability of occurrence, which was selected based on USNRC Standard Review Plan (Ref. 2), which states in Section 2.2.3:
"Accordingly, a conservative calculation showing that the probability of occurrence of pctential expnsures in excess of the 10CFR Part 100 guidelines is approximately 10-6 per year is acceptable if, when combined with reasonable qualitative arguments, the realistic probability can be shown to be lower."
The 10-6 annual probability criterion is very conservative for surface rupture offset beneath the GETR reactor building because this criterion is intended for potential exposures.
It is estimated that the probability of adverse consequences (which include damage, release, dispersion, and exposure) is at least one order of magnitude lower than the probability of surface rupture offset beneath the reactor building.
The 10-6 criterion value was used for judging the results of the current probability analyses to determine whether sJrface rupture offset should be considered as a design basis event.
This report consists of five sections.
In Section 2, the conceptual model used to perform the current probability analyses is presented.
Section 3 sumarizes the geological data pertinent to the analyses.
Two approaches for conducting the analyses using the alternate probabilistic model are discussed, and computational results are given in Section 4.
Finally, the conclusions of the current analyses are presented in Section 5.
Y OFF!CIAL '
>^
\\ vlPcM A C C *-
- Nort cY Neuc - cc.
y n.,
e.. cc.
3,,
= * - w., %
,__s O
Jack R. Benjamin & Associates,Inc.
1-2 Consulting Engineers D
2.
PROBABILISTIC MODEL The 1 cation of shears in relation to the GETR site and a cross-section of the site are shown in Figures 2-1 and 2-2, respectively.
It is assumed that if surf ace rupture offsets occur in the future they will be located either on the existing shears 8-1/B-3 and B-2, or between the shears, or on a shear (s) and between the shears simultaneously.
It is more likely that a future offset will occur on the existing shears since this has been the state of nature for the past 128,000 to 195,000 years and probably much longer (Ref. 3).
If an offset occurs away from the existing shears, it is conservative to assume that it will occur between the two shears where there is some possibility that it may occur beneath the reactor building.
It is assumed that the area in the direction perpendicular to the model will behave similarly to the model.
This assumption is supported by the geological evidence which is discussed in References 1 and 3.
Thus, it is appropriate to use a two-dimensional model as shown in Figure 2-2.
It is possible that a future event off the existing shears could occur outside the area between the two shears.
If this occurs, the reactor building would not be affected by surface rupture offset since the reactor building is located between the shears.
Indications of the presence of shear s outside the area of the model (e.g., in Trench H, see Ref. 3) support the belief that future offsets could occur outside the area of the model.
Thus, it is conservative to assume that a future offset will occur in the area bounded by and including the two existing shears shown in Figures 2-1 and 2-2.
MODEL FORMULATION The probability, P, of the occurrence of a future surface rupture offset beneath the reactor building is defined by the following equation.
k. x. _--
OF FICI AL '
4 L i VUsrP/sC CA 7' ',
i
~
2-1 Jack R. Benjamin & Associates, Inc.
O.
' ', emu pumx - couren A
)
.v m m.
Consulting Engineers D
r3 wry.cir > n ' ' "
y,.,,-.%--
~
(-
P
- PBSl0N + P
- PBSl0N) '
RBlBS g
BSIM RBlBS + (P P=P P
ON N
where:
Pg
= probability of an offset on unknown undiscovered shears g s conservatively set equal to unity.)
in the region (P i
BSIDII = probability of an offset between existing shears 8-1/B-3 P
and B-2, given an offset on unknown undiscovered shears in the region P
= probability of an offset on existing shear i (i = 1,2 for N
shears B-1/B-3 and B-2, respectively).
Sl0N
= probability that an offset will occur between shears P
8-1/B-3 and B-2, given that an offset occurs on existing shear i (i = 1,2 for shears B-1/B-3 and B-2, respectively)
P
= probability that an offset will occur beneath the reactor RBlBS building, given that an offset occurs between shears 8-1/B-3 and B-2.
Conceptually, the PRBIBS pr bability is different for the two terms in equation 2-1.
However, a common term which is conservative is used as discussed later in this section.
The first term (i.e., Pg BSl0ii RBlBS ) is essentially the
- P same as the probability calculated in the first analysis (Ref. 1), where it was assumed that offsets could occur either on or off the existing shears. The second term includes the probability of simultaneous events on and off the existing shears.
It is assumed that occurrences of offsets on shears B-1/B-3 and B-2 are independent and the probabilities are added.
This is conservative since the product of the probabilities for offsets occurring on both existing shears simultaneously is not subtracted.
As discussed in Section 4, the possibility of offsets occurring on both shears ar.d between the shears simultaneously was also considered, and it was founo that using the geologic data to calculate the probabilities of an offset between the existing shears, due to each shear separately and then combining, is conservative.
.m
'j r OFI !CI AL !
. A ' o VIPGINIA C CA&' m Jack R. Benjamin & Associates,Inc.
O
~ "cuy pac. c;,
,{y 2-2 Consulting Engineers D
, en
{- m uin, et
.s m r-
g s conservatively assumed to be unity.
i As indicated above, P This probability is believed to be small, but it is difficult to rationally estimate its value.
In calculating the probability PBSIM is assumed that offsets, which occur due to unknown undiscovered shears, are independent with respect to time and fit a binomial distribution.
The parameter, p, of the binominal distribution was selected at a confidence level, C, based on observing zero offset events in t* years, that is:
p = 1 - (1 - C)
The probability, PBSIM, is the probability in the neat year of an offset occurring between the shears given an offset occurs on unknown undiscovered shears in the region.
Thus PBSlg is just the probability of success of a Bernoulli trial as given below.
PBSIM " P BSlg becomes:
PBSlM "
where p is determined at confidence level C.
Similarly, the probability PBSl0N (note that the superscript "i" is dropped for convenience but that two analyses, one for each existing shear, were conducted) is determined based on zero offsets between the shears for N trials (i.e., offset events) on the existing shears.
Thus the probability P BSl0N is given as follows:
PBSION ' 1 - (
)
(2-3) where the underlying parameter, p, is determined at confidence level C.
The probability PON (note that the superscript "i" is dropped for convenience) is determined from the distribution of time between offsets,F(t).
Figure 2-3 shows a hypothetical density function f(t),
which is the probability that the time between offsets on the existing shears is equal to t.
The hazar function is the probability of an offset in the next years given ti.at no offsets have occurred in the
- ~ w.m
[,
OFFICI AL '
s 3 VQGWIA C. C~V ^
S r-
>m 3
2-3 Jack R. Benjamin & Associates,Inc.
O m'un ruwc - ce,, -
{
kODijN'y l " '
Consulting Engineers D
i n.m
prior t years.
As shown in Figure 2-3, PON can be expressed in the g
following form.
Q(t + T)
(2-4)
PON*1-Qt) g where Q(t) = probability that the time between the last and the next offset will be equal to or greater than t.
Both the normal (Gaussian) and the Weibull distributions were used to calculate P The standard deviation, o, was varied to ON.
investigate different shapes for the Weibull distribution.
The normal distribution has been shown to fit certain types of experimental failure data (i.e., concrete cylinder compression tests where the strength is the sum of individual element strengths).
The alternate Weibull distribution fits failure data for components where strength is dependent on the strength of the weakest link (Ref. 4).
The Weibull distribution also is intuitively appealing since all permissible values are greater than zero which is not true for the normal distribution.
Both distributions can be used to produce hazard functions which increase monotonically with time.
The probability PRBlBSwasderivedbasedonthegeometrical relationships between the existing shears and the reactor building.
Geological data obtained from the recent trench excavations at the GETR site (Ref. 3) indicate that future offsets, which occur on shears B-1/B-3 and B-2, are equally likely to occur on either shear.
Similarly, if future off.ets occur between the existing shears, it is geologically reasonable to assume that the probability of location is symmetrical between the shears; thus, various symmetrical shapes of probability density functions were investigated to determine the sensitivity on PRBl0N.
Because the reactor building is located one-quarter of the distance between the existing shears, the different density functions which were investigated produce values of PRBIBS which are always less than or equal to the value produced by a uniform distribution.
Because of this finding, it was assumed that PRBlBS should be based on a uniform distribLtion to produce maximum conservatism.
<; 45)Ivar cw n Jack R. Benjamin & Associates,Inc.
O i
. nomy puede - cmc 2-4 Consulting Engineers D
}
Ld uacx s
W.$A1 22 ~
Since an offset may have a width greater than zero, the probability that an offset will intersect the foundation of the reactor building is given by the following equation which is based on a uniform density function as discussed above.
RBlBS*L-b (2-5)
P where:
1 = width of the reactor building L = distance between the two shears b = width of the offset at the ground surface It was estimated from the geological observations of existing shears in the trench excavations that the width of a future surface rupture offset at the ground level will vary between 2 and 4 feet (Ref. 1); thus, it was conservatively assumed in the analysis that the effective (i.e., in terms of affecting the structural response of the reactor building) offset width, b, is 4 feet.
For values of 72 feet and 1,320 feet for 1 and L, respectively, P is calculated to be 0.058.
RBlBS The data used in the analyses of the probabilistic model discussed above are given in the next section.
The approaches for obtaining parameter values and the results of the analyses are presented in Section 4
~'
~
- m.,.
, - c
..y.
c..
- a
,.-.b
%.J
'~-
Jack R. Benjamin & Associates,Inc.
O 2-5 Consulting Engineers D
% \\ N w
% %N l
i s
B '.
B-3
/
B-1/g'3 shear y
GETR e,44, B-2 & side trenches o
20,00 feet c:..u n v' 'T C. CJ '
':c ' W r -
.*C - c A cr
,af.
s,.
y.. cc, s
~
~n~...,
FIGURE 2-1.
LOCATION OF SHEARS IN RELATION TO GETR.
Jack R. Benjamin & Associates,Inc.
O 2-6 Consulting Engineers D
272' I
- 1320, Trench B-1 Trench 8-2 A
w UB-3 REACTOR BUILDING 72 w
Shear 8-2 SCALE: Horizontal = Vertical
?
2g0 400 600 800 10,00 feet O! F'CIAL i vir,w:^ C. c/c-
-. m ruuc.ca_
L.C..._Sjb~A.m i'.. r.:tm e g
~.
FIGURE 2-2.
CROSS-SECTION OF GETR SITE.
Jack R. Benjamin & Assoclofes,Inc.
O 2-7 Consulting Engineers 3
1 f(t)
Pon = 1. O(to +f) l O(to) where Q(t) = probability that the time between the Icst
-a
+o and next offset will be equal to or greater than t co f f(t)dt
=
l z time, t i
to to + T
--ww-=m e-cay OF F'CIAL E: AL
,),
CA50"!RO )}
i"i m NI A.-
!s O TA 4Y PUBL C. CAi, c q y. g D
t J 's, ',,n,
, 3
(
Nir y
,c.-,.
~ ~. ~
- ~.
FIGURE 2-3.
DERIVATION OF THE HAZARD FUNCTION, Pgy, Jack R. Benjamin & Associates,Inc.
O 2-8 Consulting Engineers D
3.
GE0 LOGICAL DATA The geological data used in the current probability analyses are discussed in Appendices A and B of the previous probability analysis report (Ref. 1). A sumary of the geological data and the determination of the model parameters are given in the following text.
Table 3-1 gives the offsets in feet during the past 128,000 to 195,000 years at shears B-1/B-3 and B-2.
These data were found during the recent trench excavations (Ref. 3).
Data from Trenches B-1 and 8-2 (see Figure 2-1) establish that there are nc offsets between shears B-1/B-3 and B-2 for at least the last 128,000 to 195,000 years.
It is conservatively assumed in the model that unknown shears parallel to shears B-1/B-3 and B-2 may be present in both directions away from the existing shears. Therefore the segment between the shears B-1/8-3 and B-2 is typical of the geological process, and it is appropriate to define this region as the area for analysis.
Thus the model includes shears B-1/B-3 and B-2 and the 1,320 feet space in between (see Figure 2-2).
Tables 3-2 and 3-3 give values for the geologic parameters used in the current probability analyses.
In Table 3-2, the coefficient of variation of the time-between-offsets distribution is defined as the standard deviation, c, divided by the mean time between offsets, T (see Figure 2-3 for a schematic representation of a and t).
The best estimate value of c/t equal to 0.5 is based on recent data obtained from Sieh's trench excavations on the San Andreas fault in Southern California (Ref. 5).
Table 3-4 gives the data used to obtain the best estimate value for the coefficient of variation.
A lower bound of 0.2 was assumed which is conservative when compared to standard deviation values obtained from concrete cylinder tests.
In other words, it would be surprising if the strength of a shear is as consistent as the strength of concrete. Values for c/t at the GETR, if they could be determined, would be higher. The 0.7 upper bound value was assumed Y-
. m:.nu,
i OFRCI AL I
)s h vmc.nM c.cr 3-1 Jack R. Benjamin & Associates,Inc.
O ramw rucuc - cm, A '
Consulting Engineers D
o
- x y
e.m cm YO I'v ce :m. evpq,yg g, $ ^
~~~_ 3
1 since higher ve.oes of c/t would oecrease the probability of a future offset beneath the reactor building for the assumed geological parameter values.
The time si. ice last offset, t, and the age of soil beneath the o
eactor building, t*, were obtained from the range of values givea in Table 3-1 The total cumulated offset on existing shears, T, is based on values of minimum total offset of the Livermore formation measured in the recent trench excavations (lower bound values) and the differences in elevation between the valley floor and the height of the hills surrounding the GETR (best estimate and upper bound values).
The values in Table 3-2 for characteristic offset size, x, range from an upper bound of 1 meter to a lower bound of 0.1 meter.
It is geologically reasonable that the shears have some characteristic offset size within this range (there appears to be no basis for applying a "M versus log N" seismological concept to the distribution of offset sizes on specific faults or shears).
These values were used with the values for total cumulated offset on existing shears to obtain parameter estimates for the number of offsets, N, on the existing shears.
Note that the lower and upper bound values for number of offsets, N, have been obtained by pairing extreme lower and upper bound values for the total cumulated offset and characteristic offset sizes (i.e., for the upper bound values, the largest total cumulated offsets and the smallest characteristic offset sizes were used and vice versa for the lower bound values).
Table 3-3 gives tne values for strain rates and geologic time periods for the two existing shears.
The values for strain rate, r, were obtained by dividing the total cumulated offset during the middle two time periods (see Table 3-1) by the amount of time during the two periods.
Bounding strain rate values were obtained by using the extreme age values at the beginning and end of each time period.
The offset Cime period, t, associated with each strain rate is s
also given in Table 3-3.
These values were obtained by dividing the total cumulated offset by the strain rate.
Note that the values of total cumulated offset displacements and strain rate values, used to j)
'6H !cIE 3-2 Jack R. Benjamin & Assoclotos,Inc.
O
.j', virc. w r crc Consulting Engineers D
- r. m r rw uc - c.
.t y r,
g
~--
.hm my
obtain the lower and upper bound value.
were selected to produce extreme bounds for the calculated probab' ' ties of surface rupture offset beneath the reactor building.
Because of this procedure the offset times for the calculated lower strain rate values exceed a reasonable geological limit for offset time in the region.
Accordingly a more reasonable value of 2,000,000 years was used in the current probability analyses.
However, the 4,200,000 year value produces even lower probabilities than the 2,000,000 year value; thus, the 2,000,000 year value is conservative.
.w
, w.: <., _ - -
h ym mtnr. c.
c'.<:~
j
" r.om ruttc - c.
3-3 Jack R. Benjamin & Associates,Inc.
O w m c':,, ' '
Consulting Engineers D
g
" c c. - -
- i
p%.
]_,,.,..
. - nc.. ~ - ;nn. -
TABLE 3-1.
OBSERVED OFFSET DATA Offset During Time Period (ft)**
Time Period (Before Present in Years)
Shear B-1/8-3*
Shear B-2*
0-8,000 to 15,000 0
0 8,000 to 15,000 - 17,000 to 20,000 2
3 17,000 to 20,000 - 70,000 to 125,000 10 5
70,000 to 125,000 - 128,000 to 195,000 and greater 40+
80+
- See Figure 2-1 for location of shears
- Each offset shown is maximum measured value which the geologists believe resulted from several events
(<. ~.enn OFF:CI AL f' # 'u xQ v' e.~,:N!^ C. C A' ~
~'
l,
- f.OTARY PU6L iC - C S a $
}.
j x. A " -
} n.-..
o m %
<f s - -
3-4 J ek R. Benjamin & Associates,Inc.
O Consulting Engineers D
7 :...na ~
t,_
TABLE 3-2.
GEOLOGIC PARAMETER VALUES j,
{ 5,
(
Parameter Lower Bound Best Estimate Upper Bound 5'-
- a o t.
S pi Q j Coefficient of variation of time-j,jc{@
between-offset distribution, c/t 0.2 0.5*
0.7 o di
- S ~ '
Time sirce last offset, t 4000 yrs 8000 yrs 15,000 yrs o
'i g 3, 4
Total accumulated offset on existing shears, Tx B-1/B-3 Shear 52 ft.
210 ft.
420 ft.
.3,.
B-2 Shear 88 ft.
140 ft.
280 ft.
Age of soil beneath reactor building, t*
128,000 yrs 160,000 yrs 195,000 yrs Characteristic offset size, x 0.328 ft 1.64 ft.
3.28 ft.
(0.1 meter)
(0.5 meter)
(1 meter)
Number of offsets on existing shears, N B-1/B-3 Shear 16 128 1280
@y B-2 Shear 27 85 854 8"g[
Strain rate on existing shears, r See Table 3-3 o3 Time period for offsets on existing S_ g m
3 shears, t See Table 3-3 s
aa
$ S*
- ?
- See Table 3-4.
O.
?
59 F. g g
TABLE 3-3.
STRAIN RATE AND OFFSET TIME PERIOD PARAMETER VALUES f... n.-
t
^
Strain Rate, r Offset Time Period, t s
Parameter Bound (feet per year)
(years) j,,
,.l E'5 Lower Bound Strain Rate la bd 9' j'
- iE 5 }
B-1/B-3 Shear 12/(125,000-4,000) = 0.99x10-4 420/r = 4,200,000*
B-2 Shear 8/(125,000-4,000) = 0.66x10-4 280/r = 4,200,000*
l.J.,>0J n-x lI b9 dest Estimate y ()
' 9 to = 4,000 years B-1/B-3 Shear 12/(97,500-4,000) = 1.28x10-4 210/r = 1,600,000 B-2 Shear 8.(97,500-4,000) = 0.86x10-4 140/r = 1,600,000
~'
to = 8,000 years Y
B-1/B-3 Shear 12/(97,500-8,000) = 1.34x10-4 210/r = 1,600,000 B-2 Shear 8/(97,500-4,000) = 0.89x10-4 140/r = 1,600,000 t = 15,000 years o
B-1/8-3 Shear 12/(97,500-15,000) = 1.45x10-4 210/r = 1,400,000 u
n$
g B-2 Shear 8/(97,500-15,000) = 0.97x10-4 140/r = 1,400,000 Em y6 Upper Bound Strain Rate o8 b"li B-1/8-3 Shear 12/(70,000-15,000) = 2.18x10-4 52/r = 240,000 yl-B-2 Shear 8/(70,000-15,000) = 1.45x10-4 88/r = 610,000
% a'
- k 5
n-0
- This value exceeds the geologic time period for development of the topography in the vicinity of the GETR.
The more reasonable bound of 2,000,000 years was used in the y
analyses.
t UU
Table 3-4 SAN ANDREAS FAULT RUPTURE DATA Time Interval Rupture Date*
Between Ruptures (year AD)
(years) 1857 2
1745 275 1470 1245 55 1190 225 965 105 860 665 90 575 mean, E 160.25 standard deviation, a 79.42 coefficient of variation c/t 0.50 (Best Estimate Value)
- Reference 5.
- = ~ - ~,,,
O! iCI,it,
\\"M WI A C. car.e
,~,,
3 j
U %f rucac. c;,
Jack R. Benjamin & Assoclofes* Inc' D
.'/
3-7
- e ca,.,n Consulting Engineers D
- +
,,* y. _: c,. r - c c.
4.
PROBABILISTIC ANALYSES The geological data (Sect ion 31 was used to determine the parameters for the probabilistic model (Section 2) to calculate annual probabilities of surface rupture offset occurring beneath the GETR reactor building.
Two different approaches were used to evaluate the variables in the probabilistic model, because there is a surplus of parameters obtained from the geological data. This led to two separate analysis procedures for determining probabilities from the model.
The two approaches and the results of the current probability analyses are given.below.
ANALYSIS APPROACH 1 In the first approach the following assumptions were made, e Probability distribution type for time intervals between offset events (i.e., Weibull or normal) e Coefficient of variation of the d'stribution for time between offsets, c/t e Time since last offset, t g e Age of soil beneath reactor building, t*
e Total cumulated offset on existing shears, T x e Strain rate on existing shears, r e Specified confidence value, C The hazard function, PON, given by equation 2-4, is a function of the complementary cumulative distribution function Q(t), which is given below for both the Weibull and normal distributions.
Weibull:
Q(t) = e (4-1)
Normal:
Q(t) = 1 - F (w)
(4-2) where:
a.n u l
'" qt!M C.CA" ~ m 01 F!CI AL '
]
O f F Uf'.!C - CA r'?*
T
)$ \\
...cc,fc('.,m'(.x7j';
Jack R. Benjamin & Associates,Inc.
O b.m e,
4-1 Consulting Engineers D
.w m e.
t
= time between offsets t
= u r (1 + 1/k)
[gj7)2, f(1 + 2/k)
_y 2r (1 + 1/k) r(.)
= gamma function F (w)
= standardized cumulative normal distribution w
w
= (t - t)/c Since c is assumed, u and T must be estimated based on data for the Weibull and normal distributions, respectively.
Using the fact that no offset has been observed in the last to years, maximum likelihood estimates for u or I were obtained.
In a strict sense, the time of the next offset is required to properly use the maximum likelihood approach.
However, since t is varied between a wide range of values o
in the parametric studies it was deemed appropriate to use to directly in obtaining estimates for u and t.
Using the maximum likelihood approach, u and I are equal to t for the Weibull and normal g
distributions, respectively.
In order to compute PBSl0fi,avalueforNisrequired.
Assuming that the strain rate, r, is constant with time and that all strain accumulated since the last event is released with each offset event, the probability density function for time between offsets (see Figure 2-3) can be transformed to a density function for size of offset, x, where:
x " rt (4-3)
The mean, x, and standard deviation o are also directly related to the x
parameters of the time-between-offsets distribution as follows:
x = rf (4-4) x = ra (4-5)
The total cumulated offset, T, is equal to the sum of individual x
offsets, x.
Thus, T is given by the following equation:
j x
.n~: --
O! i'!CI AL ocr,; ; C. CA O - -
Jack R. Benjamin & Associatec,Inc.
g
\\
}
rmutu Ntac-c,'uiew a 4-2 Consulting Engineers D
4 i
y N* n-a -,,
wn,ect u 3
f.fi ccm crices f/AR R,
_'C! 5
- --- n= wnmn,,.L
N x$
(4-6)
T
=
x i=1 Assuming that all offset are identically distributed and independent, the mean and standard deviation of the total offset are just Nx and /II c, respectively.
The distribution for the total x
cumula' ad offset, T, can be reasonably assumed to be normally x
distributed for a number of offsets greater than five, if the Weibull distribution for x is used.
The normal distribution for T is exact x
if the underlying distribution for x is also normal.
Hence knowing the number of offsets, N, the probability for total cumulated offset, p(T lN) is given by the following equation, x
p(TlN)=f(w)
(4-7) x w
where:
f (w) = Standardized normal density function T - Nrt x
W
=
ro /II Using the identity (from the multiplicative law of probability):
p(NjT)p(T)=p(TlN)p(N) x x
x The following equation for the probability of number of offsets given thetotaldisplacement,p(NlT)canbedirectlystated.
x p(T lN) p(N) x p(NlT)=
(
}
x p(T )
x where (from the extension law of probability):
N p(T ) =
p(T !I)Pfi) x x
i=1 The probability mass function, p(N), depends on the amount of time t '
s which is the time period for offsets on the existing shears.
A geometric distribution for p(N) was assumed and the effect on p(NlT )
was calculated.
A geometric distribution is conservative since the mean O W,R Jock R. Benjamin & Associates,Inc.
D l
E
<Nc 4-3 Consulting Engineers D
e, y a g. 7,
.,
=-
can be selected to give relatively high probabilities to low values of N.
It was found that assuming p(N) to be diffuse as compared to using the geometric distribution did not significantly affect the calculations; thus a diffuse distribution was used.
The effects of using the geometric distribution are discussed later in this section.
Once the probability mass function p(NIT ) was determined for x
each analysis, a value of N was selected using the maximum likelihood approach, which selects the mode (or value with the highest probability) as the best value to use.
Using this approach, annual probability values for surface rupture offset beneath the reactor building were calculated.
Table 4-1 presents the results of the calculations.
The first line in the table gives the input data and the annual probability for the best estimate analysis case.
Note that the best estimate annual probability using analysis approach 1 is 1.2 x 10-6 Analysis cases 1 through 11 give probability values based on parameter sensitivity variation of the geologic and probabilistic assumptions.
For this approach, the annual probability of an offset beneath the reactor building varies between 0.05 x 10-6 and 2.3 x 10-6,
Table 4-2 gives the results of assuming a geometric distribution for p(N) for the B-1/B-3 shear.
The mean of the geometric distribution, N, was varied between 2 and infinity.
The latter value corresponds to a diffuse distribution for p(N).
As seen in Table 4-2 the effect of assuming a diffuse distribution for p(N) is small; thus using a diffuse distribution in the analysis is appropriate.
ANALYSIS APPROACH 2 in the second approach, the following conditions were assumed.
e Weibull probability distribution for time between offsets e Coefficient of variation of the distribution for time between offsets, c/t e Time since last offset, t g Age of soil beneath reactor building, t*
e e Time period for offsets on existing shears, t s
_m~
' yO)f
',,.3 Jack R. Benjomin & Assoclotes,Inc.
D r m ruwe - c1 w a{
4_4 Consulting Engineers D
me K%.
W b
e Number of offsets on existing shears, N e Specified confidence value, C The effect of these assumptions were investigated using the model.
Since the number of offsets occurring on the existing shears is assumed in this analysis approach, the probability PBSION can be computed directly using equation 2-3.
Rather than computing a single value for the mean of the time-between-offset distribution, as was done in the first analysis approach, a weighted value (marginal probability) for P was computed as given by the following equation.
ON Q(t +1)-
=-
PON Q( gF o'
s' b
~
In a sin 'lar manner used to derive the equation for p(NIT ), the x
conditional probability for I can be expressed in the following form, p(t, t j, N, t) p(tlo, N) g s
p(Ilt, t,
N) =
( -10) g s
(t, t lc, N) g 3
where:
p(t, t ic, N) =
p(t, t lc, N, t) p(tlc, N) di g
s g
3 o
A diffuse distribution was assumed for p(tic, N).
The effect of this assumption was checked using an exponential distribution which is conservative since the mean of the exponential distribution can be selected to give relatively high probabilities for low values of I.
The results of this check calculation are given after the results for Analysis Approach 2 are presented.
The Weibull distribution was used for time between off:ets, which allowedtheprobabilityp(t,tlc,N,i)tobeexpressedbythe o
s following equation:
t k p(t, t l, N, t) = e (
)
f (w)
(4-11) g s
g where:
wm. ~x, O! F!CIAL <
Dj c,-
Jack R. Benjamin & Associates,Inc.
' ' ~
e
-c 4-5 Consulting Engineers D
L
f(w) = standardized normal density function (t - t ) - (N-1)t s
g c/N-1 The first cerm on the right-hand side of equation 4-11 is the probability that the time since last offset equals or exceeds t.
The g
second term is the prcbability of the total time period on the existing shears being t -t, which approaches a normal distribution independent s g of the underlying distribution on t.
Using this approach, annual probability values for surface rupture
, offset beneath the reactor building were calculated.
Table 4-3 presents the results of the calculations. The first line in the table gives the input data and the annual probability for the best estimate analysis case.
Note that the best estimate annual probability using analysis approach 2 is 1.0 x 10-6 Analysis cases 1 through 10 give probability values based on parameter sensitivity variation of the geologic and probability assumptions.
The time period for offsets on existing shears, t and the number of offset values for N were 3
selected for analysis cases 7 and 8 to produce maximum bounds on the best estimate case.
The number of offsets were selected to be a maximum.
for case 7 and a minimum for case 8.
Values for N are consistent with the total cumulated offset, T, values used to compute the time ceriod x
for offsets on existing shears, t.
That is, the same value for total s
cumulated offset, T, was used to compute the values for t and N x
s (see Chapter 3).
The computed annual probability value for case 7 is very conservati.ve as discussed in the following text.
Equivalent f values, which are defined as the.alues for t which when used directly in the hazard function give the same results as equation 4-9 were calculated for the B-1/B-3 and the B-2 shears.
Values of 1460 years and 2340 years were calculated, respectively, for the tso shears for an assumed value of t equal to 8000 years.
Using the associated hazard functions, the g
probability of observing 8000 yeau or more without an offset are less than 4 x 10-5 for both shearc ;or these conditions; thus, the combination of geologic parameters used for case 7 is highly unlikely.
~ {IOwe V "9 Nil c Jack R. Benjamin & Associates,Inc.
y
, % m r n i.C/
a-6 Consulting Engineers D
-ce, m 1
f,
<n r e (s :w >:
My cc r -
- m. y to,, n a.
.w m%.ww.
Using Analysis Approach 2, the annual probability of an offset beneath the reactor building varies between 0.04 x 10-6 and 7.2 x 10-6 for the parametric analysis cases.
Table 4-4 gives the results of assuming an exponential distribution for p(tla, N) for the best estimate case for shear B-1/B-3.
By decreasing the mean of the exponential distribution the effect of assuming a diffuse distribution was investigated.
As can be seen in Table 4-4, if the mean of the exponential distribution is 1000 as compared to the diffuse case with the mean equal to infinity, only a 5 percent error occurs. An extreme value of 10u ror the mean causes only a 27 percent difference, which is small compared to the range of probability values obtained from th: parametric studies.
The possibility of interpreting the data observed on the existing shears as indicating that both shears have had simultaneous offsets in the past was considered.
In terms of the probability analysis, if all of the past offsets were considered to have occurred simultaneously on the two shears, the number of offsets, N, would be about the same, but only one hazard function value would be computed (as compared to two for the two shears).
The computed probability of an offset beneath the reactor building would be less than for the analyses which were performed assuming that the offsets on the shears occurred separately.
Thus the results given in Tables 4-1 and 4-3 are conservative.
b! i 'O \\L "3ME 3,.
a -
Jack R. Benjamin & Assoclotes,Inc.
D 4_7 l.
Consulting Engineers D
n.,, <,,,
g m,.= ; - -.., m,
,.c..
- t..,,
s
.p,.s,9
TABLE 4-1.
RESULTS OF ANALYSIS APPROACH 1
-s.
I
- 1 to t*
--Ty (feet) rx104 (feet / year)
P x 106 4
Analysis Case Distribution a/t (years)
(years)
B-1/B-3 B-2 B-1/B-3 B-2 C
(in one year) l Best Estimate Weibull 0.5 8:000 160,000 210 140 1.34 0.89 0.90 1.2
@) o *
-y 1
Normal 1.1
,;s-
' <f( E,
2 0.2 1.8
- ?>
l:
3 0.7 1.1 4
15,000 1.45 0.97 1.2 5
4,000 1.28 0.86 1.1 7
6 128,000 1.4 cn 7
195,000 1.0 8
52 88 2.18 1.45 2.3 ok 9
420 280 0.99 0.66 1.0 o5x i 5
10 0.95 1.5
! c$ l 8:
5' o i 11 0.10 0.05
- c. i !
ao i f $ Q*
I i
j
- g Note that values not shown are the same as for the Best Estimate Analysis Case.
I o
O.
O_
TABLE 4-2.
COMPARISON OF RESULTS OF ASSUMING A GE0 METRIC OISTRIBUTION FOR p(N) FOR THE B-1/B-3 SHEAR Geometric Distrit'ution 1
2 Mean,Ti N
PBSION 3
221 0.0104 221 221 0.0104 100 221 0.0104 10 216 0.0106 5
210 0.0109 2
191 0.0120 1Computed using equation 4-8 and selecting N to be equal to the mode of the p(NlT ) distribution x
2Computed for C = 0.90 3Corresponds to diffuse distribution for p(N)
. xu - ~2-OFFICIAL
, w n",v.;;; c_ Ct: c '
Jack R. Benjamin & Associates,Inc.
O
- r.s..:v r m ac - c.-
4-9 Lv(., ',,..c,
- n..
C,:/,,
Consulting Engineers D
n..
TABLE 4-3.
RESULTS Of ANALYSIS APPROACH 2 te (years)
N y...,
t t*
P x 106 y,
(years)
(years)
B-1/B-3 B-2 B-1/B-3 B-2 C
(in one year) o Analysis Case Distribution a/t p
\\.<
es'.Best Estimate Weibull 0.5 8,000 160,000 1,600,000 1,600,000 128 85 0.90 1.0
.i. r 2: k
/#
E' h
1 0.2 0.9
? 6 n t S 9 5
2 0.7 1.0
{f j5 AL i, ? - 5" M 3
15,000 1,400,000 1,400,000 1.2 ygW
., n c.,
.'d-4 4,000 0.9 L,
5 128,000 1.2 v4
[
6 195,000 0.8 o
7 240,000 610,000 160 270 7.2 8
2,000,000 2,000,000 128 85 0.9 Oa Rw 9
0.95 1.3 SP e{
10 0.10 0.04 F
gir os 55 Note that values not shown are the same as for the Best Estimate Analy::is Case.
gn 8
9.
O
~C."
9 50-
TABLE 4-4 COMPARISON OF RESULTS OF ASSUMING AN EXPONENTIAL DISTRIBUTION FOR p(tlo, N) FOR THE B-1/B-3 SHEAR Exponential Distribution Mean, 1/A P
Error 1 ON 2
0.0000785 0
12,535 0.0000785 0
1,000 0.0000822 0.05 100 0.0000997 0.27 PON("
}
ON (at 1/A = =)-
7 P
2 orresponds to diffuse distribution case C
.._w..
Of F'CIAL '
s,
-,e p 7s q c3.-~
,sq Jack R. Benjamin & Associates,Inc.
O
, : < nuc..c - cermc,.
.?!
5.
CONCLUSIONS The best estimate annual probability values for a future surface rupture offset beneath the GETR reactor building are 1.2 x 10-6 and 1.0 x 10-6 for the two analysis approaches presented in Section 4 These values compare closely with the values obtained from the first analysis (Ref. 1). The annual probability values obtained in the parametric computations range between 0.04 x 10-6 and 7.2 x 10-6, The latter value is very conservative since a very unlikely combination of geologic parameters is assumed.
The best estimate probability values and most of the results from the parametric calculations are close to the criterion value of 10-6 annual probability.
Consideration of other elements leading to potential adverse consequences (i.e., damage, release, dispersion, and exposure) would likely decrease the calculated probability by at least one order of magnitude, or well belove the criterion specified in USNRC Standard Review Plan Section 2.2.3.
Based on the results of the current probability analyses, it is still concluded that surf ace rupture offset of any size beneath the GETR reactor building should be eliminated as a design basis event.
01 F!CIAL i a
- ~m'HA C. CA T '~ ' ' '
- e.. em rueuc-cn us Jack R. Benjamin & Associates,Inc.
O
)... j.
5-1 nu cc Consulting Engineers D
._ U!Cl[,l'd "
^*
REFERENCES 1.
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.
2.
USNRC, " Standard Review Plan for the Review of Safety Analp is Reports for Nuclear Power Plants," LWR Edition, September 19,'s.
3.
Earth Sciences Associates, "Geologicu' Investigation, Phase 2, General Electric Test Reactor Site, Va
'citos, California," Report to General Electric Co., Vallecitos, Ca fornia, February 1979.
4.
Weibull, W.,
"A Statistical Distribution o.: Wide Applicability,"
Journal of Applied Mechanics, Vol. 18, p. 293-297, 1951.
5.
Kerry Sieh, "A Study of Holocene Displacement History Along the South-Central Reach of the San Andreas Fault," Ph.D. Thesis at Stanford University, August 1977.
OF ie!Q AL s
,((ruhcbc,(,;,3.[,s{
Jack R. Benjamin & Associates,Inc.
O R-1 Consulting Engineers D
4
, m,, m: n
{e, ny cer, e.,,..,. n. - - -
~ve r ew n ars n n a gem,,
.-----....