ML13066A436

Email from J. Mitman, NRR to J. Philip, RES Et Al on NSAC/60

ML13066A436
Person / Time
Site:	Oconee
Issue date:	06/01/2010
From:	Jeffrey Mitman Office of Nuclear Reactor Regulation
To:	Jacob Philip, Thomas Nicholson Office of Nuclear Regulatory Research
References
FOIA/PA-2012-0325
Download: ML13066A436 (19)

Text

Mitman, Jeffrey From: Mitman, Jeffrey , 4 -

Sent: Tuesday, June 01, 2010 3:08 PM To: Philip, Jacob; Nicholson, Thomas

Subject:

NSAC/60 Attachments: NSAC-60.pdf The pertinent sections of NSAC/60 are in the attached. The document vitals are:

NSAC/60 Oconee PRA A Probabilistic Risk Assessment of Oconee Unit 2 The Nuclear Safety Analysis Center of EPRI and Duke Power Company 1984 1

9.4 ANALYSIS OF EXTERNAL FLOOD EVENTS This section presents results of analyses performed to evaluate the contribution of external floods to the core-melt frequency estimated for Oconee Unit 3. It also explains in detail the methods used in these analyses.

Two potential sources of external flooding of the Oconee plant were iden-tified. The first is a general flooding of the rivers and reservoirs in the area due to rainfall in excess of the probable maximum precipitation (PMP).

Since the Oconee site is inland, the effects of hurricanes were not consid-ered. The second source is a random failure of the upstream Jocassee Dam.

(Random failure includes all causes other than a rain-induced overtopping and an earthquake-induced failure, which were analyzed explicitly).

9.4.1 PRECIPITATION The PMP postulated for the Oconee site would be 26.6 inches within 48 hours5.555556e-4 days <br />0.0133 hours <br />7.936508e-5 weeks <br />1.8264e-5 months <br />. The effects of this PMP on reservoirs and spillways were evaluated in a study performed by the Duke Power Company (1966). The results of this study demonstrated that the Keowee and Jocassee reservoirs are designed to contain and control the floods that could result from a PMP. Thus in order to flood the plant site, rainfall exceeding the PMP must occur. The frequency of exceeding the PMP was obtained from the analysis presented in this section and was used as a bounding estimate of the frequency of core melt caused by rain-induced extcrnal flooding.

9.4.1.1 Precipitation Data The U.S. Weather Bureau (1961, 1964) has compiled a series of rainfall intensity-duration-frequency curves derived from meteorological data collected throughout the continental United States over a period of 50 years. The isopluvial maps published in these technical papers were interpolated for the Oconee site to obtain the amount of precipitation (inches) given the rainfall duration (hours) and its annual frequency of occurrence. The interpolated data for the Oconee site (see Table 9-18) are the basis for all the results derived in this section.

9.4.1.2 Method The method used in deriving the probability distribution of the frequency for a PMP is an extension of the technique of Bayesian extrapolation first developed by S. Kaplan (personal communication, 1981). This method extrapo-lates the known trend to values outside those experienced to date. It is particularly suitable for probabilistic analyses because it establishes the degree of confidence in the extrapolation--providing that the trend continues.

The validity of the assumption of a continuing trend is discussed in Sec-tion 9.4.1.5.

9-110

Table 9-18. Input Data for the Oconee External Flood Analysisa Number Observed of observed Rainfall Precioitation storm storms 0

Data duration, Tm depth, hm frequency, 1m in 50 years point, m (hours) (inches) (yr-1) Vp = mm50 -o 1 12 3.5 1.0 48 2 12 4.2 0.5 24 3 12 4.8 0.2 10 4 12 5.8 0.1 5 5 12 6.7 0.04 2 6 12 7.5 0.02 1 7 12 8.1 0.01 1 8 24 4.2 1.0 48 9 24 4.7 0.5 24 10 24 6.5 0.2 10 11 24 6.8 0.1 5 12 24 8.5 0.04 2 13 24 9.2 0.02 1 14 24 10.5 0.01 1 15 48 6.0 0.5 24 16 48 7.0 0.2 10 17 48 8.0 0.1 5 18 48 9=5 0M04 2 19 48 10.0 0.02 1 20 48 11.5 0.01 1 21 96 7.0 0.5 24 22 96 8.5 0.2 10 23 96 10.0 0.1 5 24 96 11.0 0.04 2 25 96 12.0 0.02 1 26 96 14.0 0.01 1 27 168 8.5 0.5 24 28 168 10.0 .0.2 10 29 168 13.0 0.04 2 30 168 14.0 0.02 1 31 168 16.0 0.01 1 anaineh v internpoation of U.S. Weather Bureau

...... Sy.......... ....

isopluvial maos.

9-111

A plot of the data presented in Table 9.18 is shown in Figure 9-56. This plot shows that there is a family of curves predicting the frequency of a rainstorm for the Oconee site in terms of the cumulative precipitation and the duration of the storm. The family of curves suggest that the frequency can be expressed as an exponential function of the form cf( ,h) = a exp{-[B(T)h]} (9.4-1) where cf(Th) S calculated frequency of storm (yr h S maximum cumulative precipitation (in)

T E duration of rainfall (hr) a 5 constant cumulative precipitation (in)

B(T) F a function of T Analysis of the B(T) values obtained by fitting each individual curve of Figure 9-56 suggests that B(T) can be expressed as n

B(t) = b/T (9.4-2) where n is a constant.

Substituting Equation 9.4-2 into Equation 9.4-1 gives cf(T,h,a,b,n) = a exp{-[b(h/Tn)1} (9.4-3) where for emphasis f is expressed as a function of a, b, and n.

Equation 9.4-3 expresses a mathematical model for the frequency of a complicated meteorological process involving many random variables. This model along with the data in Table 9-18 was used to derive probabilities for the various combinations of values for a, b, and n.

This set of probabilities permits the derivation through Equation 9.4-3 of the probability distribution for the frequency of PMP (TpMp = 48 hr; hpMP = 26.6 in.).

Table 9-18 consists of 31 data entries. Each entry (m) represents the observed number of storms (vm) exhibiting particular values of cumulative precipitation (hm) and duration (Tm) over the 50-year observation period. The quantity Vm is defined by Vm = 50 fo (9.4-4) where fO is the observed frequency for entry (m).

For each of these entries, a doublet, Em = <VYm,50>

can be formed to characterize the experience Em.

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C S10-1 0r 65 2 4 6 86 10 12 14 16 Cumulative precipitation h (in.)

Figure 9-56. Plot of the data in Table 9-18. (Solid lines are a fit of data to Equation 3.)

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The collective experience E of all 31 data points can be characterized by E E {<v°,50>} all m (9.4-5)

In light of this evidence E and Eouation 9.4-3 (which models the fre-quency f), a probability was assigned to the various combinations of different values for the three unknown parameters a, b, and n, using Bayes' theorem:

p(Ela,b,n) p(a,b,n!E) = p(a,b,n) (9.4-6)

E p(Ela,b,n) all a,b,n where p(a,b,n) probability of a, b, and n prior to experience E p(Ela,b,n) likelihood of a, b, and n after the experience E p(a,b,nIE) probability of a, b, and n after the experience E To obtain information on the probability of a, b, and n, several steps must he taken. The first is to define the calculated number of storms (cv) during the 50-year observation period:

cv(T,h,a,b,n) = 50cf(T,h) (9.4-7) where cf(T,h) is qiven by Equation 9.4-3.

The likelihood nf observing the doublet Em < \P,,,50>

given the values a, b, and n, can now be formulated. A process describing events that occur randomly in time is characterized by the Poisson distribu-tion. This distribution predicts the likelihood of observing the doublet E given a, b, and n: m p(Emla,b,n) = [cv(to,hm,a,b,n)jvP exp[-cV(Tm,hm,a,b,n)] (9.4-8) vmo The likelihood of the total experience E is the product of the likeli-hoods of all the individual Em terms--that is, p(Eia,b,n) = fl p(Emia,b,n) all m

[C (Tm,hm,a,b,n) ° m

=n exp-cV(Tmhmabn)l]

(9.4-9)

V(m, ma,n all m M5 With the p(Ela,b,n) defined, the prior probability distribution p(a,b,n) is needed before applying Equation 9.4-6 to calculate p(a,b,niE). Since there was no knowledoe prior to experience E on the probability of the different 9-114

__ ~ - ____--

-~- ___ ~ - ___ ~ -- ~ -~. -__ __

possible combinations of values for a, b, and n, a uniform prior was assumed, and Equation 9.4-6 is rewritten as P(EIa,b,n) p(a,b,nIE) = p(Eabn) (9.4-10) p(Ela,b,n) all a,b,n where p(Ela,b,n) is given by Equation 9.4-9.

9.4.1.3 Numerical Analysis Equation 9.4-3 expresses the frequency of a storm of duration (Tm) and cumulative precipitation depth (hm) for any given combination of a, b, and n.

Equation 9.4-10, on the other hand, establishes the probability of a specific combination of values a, b, and n in light of the available data. The objec-tive of the numerical analysis was to obtain from these two equations the probability distribution for storm frequencies for a specific t and h (i.e.,

at the PMP conditions).

The numerical procedure requires establishing a grid of a., b., nk values for a discrete evaluation of p(Ela,b,n) and subsequently p(a,bnJEi. A judi-cious choice of grid points is essential in obtaining accurate results without excessive computation. The following grid was used in evaluating the data of Table 9-18:

((a i} 1 {=0, is15,20,25,30,35,40,45,50,55,60}

1[b,]} = {i.0,1A.,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2.0.2.1,2.2,2.3,2.4, 2.5,2.61

{[nk] }= {0.10,0.12,0.14,0.16,0.18,0.20,0.22,0.24,0.26,0.28,0.30, 0.32,0.34,0.36,0.38,0.401 For each specific combination of ai, b,., nk Values from this grid one can evaluate Equation 9.4-9, the likelihood functionwhich when expressed in its discrete form is given by

[cV( m,,hm,,ai,bj,nk)1]vm p(Elaihjnk) = al  ! exp1-cv(Thm,hmai,bjnM) ] (9.4-11)

The posterior probability for each ai, b., nk combination can now be obtained from a discrete form of Equation 9.4-8:

p(ai,bj.,nkIE) = P(E P iab In k) (9.4-12)

Z E E o(Elai, Ib.n k

all all all i j k 9-115

- ____ ____J

The last step of the analysis is the evaluation of the discrete version of Equation 9.4-3 at each one of the grid points cf,ijk = ai exp (- b )(941 nk(9.4-13)

T PMP where TPMP is the duration of a PMP rainfall (48 hours5.555556e-4 days <br />0.0133 hours <br />7.936508e-5 weeks <br />1.8264e-5 months <br />) and hpMp is the maxi-mum cumulative precipitation of a PMP rainfall (26.6 inches).

Note that for each cf,ijk there is a corresponding p(a ,b.,nk E). In probabilistic languaqe this correspondence is called a "dou le." The entire set of

{<p(aibjnkIE), cfijk>P doublets forms the probability distribution for the frequency of the PMP storm at the Oconee site. The cumulative of this discrete probability distribution indicates the confidence when postulating a particular storm-frequency value.

9.4.1.4 Results The numerical analysis described in Section 9.4.1.3 was carried out with the objective of calculating the probability distribution for the PMP fre-quency. A computer program specifically designed to carry out this analysis was written in the Basic language. The results of these calculations are given in Table 9-19: the PMP storm-frequency intervals, the discrete prob-ability distribution (DPD) for each interval, and finally, the cumulative probability from zero to the end of each frequency interval.

Table 9-19. Probability Distribution for the Frequency of PMP Stormsa Storm-frequency ranqe Cumulative From To DPD probability 0 3 .5- 8 b 0.0253 0.0253 3.5-8 6.0-8 0.0429 0.0682 6.0-8 1.0-7 0.1413 0.2096 1.0-7 1.7-7 0.2283 0.4380 1.7-7 3.0-7 0.2850 0.7230 3.0-7 5.0-7 0.1104 0.8334 5.0-7 8.0-7 0.0941 0.9276 8.0-7 1.3-6 0.0428 0.9704 1.3-6 2.2-6 0.0267 0.9972 aDuration t = 48 hours5.555556e-4 days <br />0.0133 hours <br />7.936508e-5 weeks <br />1.8264e-5 months <br />; precipitation depth h = 26.6 inches.

b 3 .5- 8 = 3.5 x 10-8.

9-116

A least-squares fit of the Table 9-19 storm frequency versus cumulative probability yields the frequencies of a PMP associated with the lower, median, and upper bounds of the probability distribution:

Cumulative PMP frequency probability (year-I 0.05 4.9-8 0.50 2.9-7 0.95 8.9-7 The cumulative probability for a particular frequency interval is to be interpreted as the degree of certainty that the PMP frequency observed over a long period of time will be less than or equal to the upper value of that frequency interval.

9.4.1.5 Discussion and Conclusions Three questions concerning the validity of this analysis come to mind.

First, since the data on which the analysis is based were collected during a relatively short period, 50 years, how can we be sure that the climatic condi-tions prevailing today will continue indefinitely?

For the purpose of this analysis there is no need to know that the pre-vailing climatic conditions will continue any longer than the plant life (about 40 years). The PMP frequency results are then based on the expectation that no dramatic change in climatic conditions will occur over the next 40 years. Historical data on climate show this assumption to be reasonable.

Second, we have formulated a mathematical model, Equation 9.4-3, which predicts the frequency of a storm given the duration of rainfall (hours) and the cumulative precipitation (inches). How can we be certain that this expo-nential model still applies at the precipitation level of a PMP storm?

We have no way of being certain that the exponential model continues to apply at the precipitation level of a PMP storm. The amount of precipitation during a period of time is dependent on a variety of random meteorological variables. The severity of the rainstorm is related to the probability of occurrence of increasingly adverse conditions (exponential model). There are, however, physical limits on these adverse conditions; at those limits the exponential model breaks down. If we continue to use the exponential model beyond those limits, we will overpredict the frequency of the storms. Since there is no information beyond the recorded data as to where the exponential model breaks down, the results of this analysis are an upper-bound, conserva-tive estimate of the frequency of a PMP storm.

Third, there is an implicit assumption that the most severe condition that can affect the area around the Oconee site is the one where the storm lasts 48 hours5.555556e-4 days <br />0.0133 hours <br />7.936508e-5 weeks <br />1.8264e-5 months <br /> with a cumulative precipitation of 26.6 inches. Is this truly the limiting storm, or could other storms of shorter or longer duration pos-sibly cause flooding at the Oconee plant?

9-117

The duration, cumulative precipitation, and frequency resulting from this analysis have been reviewed by the plant designers and they share the belief of the Duke Power Company (communication from S. B. Hager, August 18, 1981),

that the PMP storm is the most frequent storm that could exceed spillway capacities and result in flooding of the plant site.

Since the conservatively calculated mean frequency of flooding of the Oconee plant due to the PMP storm is more than an order of magnitude less than that due to a random failure of the Jocassee Dam, it was concluded that precipitation-induced external flooding is a negligible contributor to core-melt frequency and public risk.

9.4.2 DAM FAILURE The Oconee site has a yard grade elevation a few feet below the full-pond level of Lake Keowee, which serves as the source of its condenser circulating water. Lake Jocassee has a full-pond elevation about 300 feet above Lake Keowee. If a sudden failure of the Jocassee Dam were to occur, and a rapid enouqh release of the impounded water from Lake Jocassee into Lake Keowee resulted, the flood wave generated in Lake Keowee would overtop the Keowee Dam and the Oconee intake dike, flooding the plant. This section presents the analysis performed to estimate the frequency of such a flood.

9.4.2.1 --

Frequency -- ofa Failure The Jocassee Dam is an earth-rockfill structure approximately 400 feet high. The dam was completed in 1972, and the reservoir was filled by April 1974. The spillway lies along one of the abutments, about one-quarter of a mile from the dam, and is a concrete structure founded on granite.

An analysis was performed to determine an annual frequency of failure for earth, earth-rockfill, and rockfill dams due to events other than overtopping and earthquake ground shaking, which were considered in separate analyses.

Also, based on dam design information, structural failure of the spillway during discharge and failure associated with seepage along an outlet works have been eliminated as a possible failure mechanism. The following principal modes of failure were considered:

1. Piping.

2. Seepage.

3. Embankment slides.

4. Structural failure of the foundation or abutments.

These failure mechanisms are referred to collectively as random failures.

Only failures resulting in the complete collapse of the structure and the uncontrolled release of the reservoir's contents were considered to have the potential for flooding the Oconee plant.

Previous investigations into the frequency of dam failure indicate that it decreases with later years of construction (Baecher et al., 1980). This is 9-118

generally attributed to improvements in the methods of design and construc-tion. Therefore, another criterion considered in developing a data base and failure-frequency estimate was the period of construction.

The age of a dam is another factor that has been identified as having an effect on the rate of dam failure. Approximately half the dam failures occur during the first 5 years of operation (Baecher et al., 1980). Therefore, age was also considered in developing a data base.

Size, type of construction, realistic failure modes, period of construc-tion, and age were the major considerations used to define a data base for use in estimating the failure frequency of the Jocassee Dam.

The data-base characteristics that were attributed to the Jocassee Dam are:

Characteristic Jocassee Dam Location (country) United States Year completed 1972 Age (years in operation) 7 Height (feet) 400 Type Earth-rockfill 9.4.2.1.1 Data Various catalogs were used to develop the data groups that were studied.

Each goau consisted of la earth; earth-rockfi!!, or r-ckfi! as (more than 45 feet high, USCOLD, 1975) in the United States that were in operation 6 or more years when they failed. Of the references used in this study (Middle-brooks, 1953; Gruner, 1964; Babb and Mermel, 1968; USCOLD, 1975), not one is a complete catalog, and therefore they were used collectively. At present, these references represent the best readily available information. From the various listings of failures, cross-checks were made when possible.

A data base uniquely suited in every major respect to the Jocassee Dam was unattainable because of a scarcity of the number of the earth-rockfill type.

The data base ultimately developed reflects discussions with Duke Power engineers familiar with the characteristics of the Jocassee Dam. It was decided that the data base should include only the failure modes that could occur at Jocassee. The two major failure types excluded from the data set were failures resulting from piping at a conduit passing through the dam and structural failures of the spillway during the flood discharge. Neither of these failures can occur because the necessary physical conditions do not exist at Jocassee. (Note, however, that dams in the data base do include those that can fail in either or both of these modes. This is proper because the experience from these dams represents realizations of nonfailure for other failure modes, such as embankment piping, foundation failure, and slope fail-ure.)

Because of limitations in the historical record, it is possible only to develop a data set that takes into account a limited number of the specific 9-119

properties of the Jocassee Dam. Since Jocassee is a structure designed and constructed in recent times, it can be assumed that state-of-the-art techno-logy was used in its design. In addition, because of its role as a critical facility of large size and importance, other aspects of the dam, such as seepage monitoring and inspection programs, are important factors that de-crease the likelihood that the dam will fail. The following specific charac-teristics of Jocassee are identified as relevant factors that will affect the frequency of failure:

1. Quality maintenance and inspection programs.

2. Monitoring of the dam (i.e., seepage, settlement, etc.).

3. Presence of personnel at the site.

4. Responsiveness of the owner to potential problems (i.e., implementation of emergency plans).

5. Detailed geologic investigations conducted before site selection.

6. Experience of earth-rockfill dams in Jocassee's class (with respect to random failures).

7. Design techniques.

These factors notwithstanding, the data were examined, and the best available data base for application to Jocassee Dam was extracted (Benjamin and Associates, 1982) and used.

The data base was divided into three overlapping periods of dam construc-tion: 1900 to 1975, 1940 to 1975, and 1960 to 1975. In each category, U.S.

dams in operation 6 or more years at the time of failure and 45 feet or more in height were considered. The dams were of three types--earth, earth-rock-fill, or rockfill--and only catastrophic failures were includcd. Table 0-20 lists the failures considered in the analysis.

The number of dam-years of operation was determined from data on the rate of construction provided in the USCOLD (1975) report. Table 9-21 lists chronologically for the three periods of construction the year a failure oc-curred, the interval between each failure in years, the cumulative number of dam-years to the year of failure, and the number of dam-years between fail-ures.

The data in Table 9-21 show a historically upward trend in the dam-years between catastrophic failures. The reciprocal of these dam-year periods between failures represents the frequency of dam failures. Allowing for statistical variations, this number has been steadily declining since the beginning of this century. This change reflects a steady improvement in the state of the art for the design, construction, and maintenance of dams and dikes (i.e., a "learning curve").

In order to realistically represent the failure rate for a dam of modern design, construction, and operating practice, an analytical method was devel-oped to use the data obtained, including the chronological order of dam fail-ures. The method outlined below is adapted from one first developed by S. Kaplan (personal communication, 1981).

9-120

Table 9-20. Dar Failures Used in This Study Year Year Dam completed failed Goodricha 1900 1956 Lake Toxawayb 1902 1916 Sinker Creekc 1910 1943 Baldwin Hillsa 1951 1963 Walter Boudind 1967 1975 aData from Babb and Mermel (1968) and USCOLD (1975).

bData from Babb and Mermel (1968),

USCOLD (1975), and Middlebrooks (1953).

CData from Babb and Mermel (1968),

Middlebrooks (1953), and USCOLD (1975).

dData from Jansen (1980).

Table 9-21. Chronological Order of Dam Failures Year of Years Cumulative Dam-years failure between failures dam-years between failures Period of Construction: 1900-1975 1916 a 1,560a 1,560a 16 1943 27 15,254 13,694 1956 13 29,236 13,982 1963 7 42,486 13,250 1975 12 82,709 40,223 1981 No failure 107,270 No failure Period of Construction: 1940-1975 1963 b 12 , 157b 12,157b 23 1975 12 43,308 31,151 1981 No failure 67,869 No failure Period of Construction: 1960-1975 1975 15c 18,014c 18,014c 1981 No failure 42,575 No failure aFrom 1900.

bFrom 1940.

CFrom 1960.

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9.4.2.1.2 Method for Estimating Frequency The data in Table 9-21 can be regarded as the random realization of a learning process in which the dam-failure frequency evolves with 'time' t (measured in dam-years) according to the functional form described by L(t) = at-b In this equation a and b are fitted probabilistically by means of Bayes' theorem. More specifically, a probability distribution on the space of <a,b>

doublets, that is, the probability {p(a,btv)} (defined later) was derived.

Using this probability distribution, the trend to the "time" (dam-years) accu-mulated by 1981 was extrapolated to obtain the present-day probability distri-bution for the frequency of random dam failures.

Method The functional form chosen to describe the time-dependent (dam-years) failure rate was L(t) = at-b (9.4-14)

The probability of no failure between tkI and tk, and subsequently a failure at tk + dt is (tk P(tkI + tk) = exp[-j] L(t) dtj [L(tk) dtj k-1 a (1-b) (1-b) -bat)b (9.415)

Sexp (--b) L - k-1 The probability of experiencing a sequence of K failures is given by the product of the K dam-failure probabilities, where to is the time from which the failure and success data have been counted.

K p(to ÷ tk) = ii P(tk_1 + tk) k=1

= K R1 expl- a- [t1T1_b) - ~ b)j a k= - (1 - b) -

(9.4-16)

= aK a tk)-b expj- a Lt~ lb) - tl b) (dt)K k= 1 Furthermore, the probability of experiencing a sequence of K failure incidents and subsequently a period of time without failure between the K-th failure time (tk) and the present time (tp) is given by t

p (BIa,b) = p(t° + tk exp [-f t L(t) dt9 K (9.4-17)

K

= aK 11ntk)-b expj- 1,a t4 1 -b) - to (1 -b)] (d t) K k =1  :: b) 9-122

Equation 9.4-17 represents in Bayesian languaqe the likelihood function--

that is, the probability of the evidence B (data) given a combination of values for a and b.

Bayes' theorem can be expressed as

= p(a,b) p(Blab) p(a,bIB) (9.4-18)

Z E p(a,b) p(BIa,b) all all a b where p(a,b) is the probability of a particular combination of a.and b prior to having the evidence B and p(a,bIB) is the probability of a particular combination of a and b posterior to the evidence B (i.e., a measure of the confidence we have in the values of a and b).

Given that prior to evidence B there was no particular preference toward any particular values of a and b, Equation 9.4-18 is then

= p(Blab) p(a,bIB) (9.4-19)

E E p(Bla,b) all all a b with p(Bla,b) qiven by Equation 9.4-17.

Numerical Aualysis The numerical procedure involves forming a grid of a. and b. values to be used in evaluatinq p(Bla,b). The process of selecting the grid is somewhat iterative. For the purpose of this analysis, the following grid was arrived at:

{[a.] }5 {0.0002,0.0004,0.00075,0.0015,0.003,0.006,0.012,0.016,0.02, 0.024,0.03,0.04,0.05, 0.06,0.075,0.1,}

{[(bj]} {0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65,0.7, 0.75,0.81 For each combination a , b. from one of these grids, a likelihood J

p(Bla.,b.) can then be calculated from Equation 9.4-17, which we can now express in discrete form:

p(Bli~b Bab a i ~=K1 (k1t ]-bj tk, exp{-

aK (I ai-bj) tb]o (tl-bj) I(- to(l-bj) (9.4-20)

Finally, a posterior probability for each ai, b. can be obtained through a discretely expressed Equation 9.4-19.

P(Blai,bj) p(ai'bjlB) = 16 (9.4-21) 15 p(Bla.,b.)

i=1 j=1 9-123

The last step required for completing the analysis is to evaluate Equa-tion 9.4-14 at each one of the grid points (i,j) and time t -- that is, the dam-years as of 1981 since the last failure in the data base. Again in dis-crete form Equation 9.4-14 can be written as L.j(t) = aitp (9.4-22)

Note that for each L. .(t ) there is a corresponding P(aibjIB). These

.. . .op .13 p correspondino ordered pairs are doublets. The set of i<P(ai,bjlB),Lij(tp)>}

doublets form a discrete probability distribution that describes the proba-bility of any individual value of dam-failure frequency.

9.4.2.1.3 Results The numerical analysis outlined in the preceding section was carried out with the objective of estimating the frequency of occurrence and the asso-ciated probability for dam failure in 1981. A computer program specifically designed to perform this analysis was written in the Basic language. The results are shown in Table 9-22. The parameters shown are the dam-failure frequency intervals, the discrete probability distribution (DPD) for each frequency interval, and, finally, the cumulative probability from zero to the upper end of each frequency interval.

Table 9-22. Discrete Probability Distribution for Random Dam Failures Frequency Cumulative From To DPD probability 0 8 .- O6 a 0.0519 0.0519 8.0-6a 1.0-5 0.0473 0.0993 1.0-5 1.4-5 0.1259 0.2253 1.4-5 1.75-5 0.1199 0.3452 1 .75-5 2.2-5 0.1476 0.4928 2.2-5 2.8-5 0.1645 0.6573 2.8-5 3.5-5 0.1188 0.7761 3.5-5 4.4-5 0.1248 0.9010 4.4-5 5.5-5 0.0527 0.9538 a 8 .0 6 = 8.0 x 10-6.

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A plot of the Table 9-22 dam-failure frequency versus cumulative proba-bility yields the 1981 dam-failure frequencies associated with the lower, median, and upper bounds of the probability distribution:

Cumulative 1981 annual probability frequency 0.05 7.9 x 10-6 0.50 2.3 x 10-5 0.95 5.5 x I0-5 The mean annual dam-failure frequency obtained from this distribution is 2.5 x 10.

The analysis indicates that the 1981 mean failure frequency for the class of large U.S. built earthen dams included in the data base described in Sec-tion 9.4.2.1.1 is 2.5 x 10-5. To the extent that this class is representative of the Jocassee Dam, these results can be interpreted as the predicted annual failure frequency of the Jocassee Dam from causes other than earthquakes or overtopping.

In using the data base of Table 9-22 to quantify the dam-failure fre-quency probability distribution, a fundamental assumption was made: the failure frequency in a particular year for a certain dam (regardless of its age) is identical with the failure frequency of a new dam built in that same year. in other words, the dams that survive up to a given yeaL ate jusL as "good" as the dams built in that year. As a check on the validity of this assumption, a complete learning-curve analysis was done on the subsets of the data base given in Table 9-22. These subsets are represented by the failures of dams built after 1940 and after 1960. The results of these analyses, showing the annual 1981 frequency, are as follows:

Cumulative probability After-1940 dam After-1960 dam 0.05 3.2 x 10-6 1.0 x 10-6 0.50 1.6 x 10-5 1.4 x 10-5 0.95 5.0 x 10-5 7.7 x 10-5 Mean 2.0 x 10-5 2.2 x 10-5 The median and the mean values of the 1981 dam-failure frequencies ob-tained by using different subsets of the failure data base compare closely. As expected, the hounds of the distribution are tighter as more data are included.

These comparisons indicate that the above-mentioned assumption is reasonable.

9.4.2.2 Contribution to Core-Melt Frequency In order to evaluate the contribution of random failure of Jocassee Dam to the frequency of core melt at Oconee Unit 3, three factors must be quanti-9-125

fied. The first factor, the frequency of random dam failures, was estimated in the preceding section. The remaining two factors are the following:

1. The conditional probability of flooding of the Oconee site given a failure of the Jocassee Dam.

2. The conditional probability of core melt given flooding at the Oconee site.

The conditional probability of flooding at the Oconee site given a failure of the Jocassee Dam is a complex function of several variables. The level of the Jocassee Lake at the time of failure determines the amount of impounded water that will be released into Lake Keowee; the level of Lake Keowee deter-mines how much flow can be received from Lake Jocassee before Keowee Dam and the Oconee intake dike are overtopped. The time available for warning of an impending dam failure will determine the likelihood that effective action can be taken to lower the levels of the Jocassee and Keowee Lakes and whether an action like notching the east side of the Keowee Dam, allowing the flood to bypass the Oconee site, could be conceived and implemented. The conditional probability of flooding given a dam failure also depends on the mode of fail-ure, the rate of erosion (time to failure), the vertical depth to which the failure penetrates (fraction of the impounded water released), and whether either Keowee Dam or the east intake dike fails rapidly when overtopped (allowing the flood to bypass the Oconee site).

The data base includes only catastrophic failures by modes believed appli-cable to Jocassee. Most of the catastrophic failures reported in the liter-ature for earth or earth-rockfill dams were total (i.e., the entire reservoir emptied), and most times to failure were in the range of 1 to 2 hours2.314815e-5 days <br />5.555556e-4 hours <br />3.306878e-6 weeks <br />7.61e-7 months <br />.

However, the failures in the data base (Table 9-20) occurred only in earthen dams; thus, there is some question as to how applicable their rates of erosion and depths of failure are to the Jocassee Dam, an earth-rockfill structure.

The Hell Hole Dam, an earth-rockfill structure, failed during construction in 1964 when extreme precipitation caused overtopping. Since construction had not been completed and since the dam was overtopped, it did not satisfy the data-base characteristics and was not included in the failure set. However, its material of construction and size were very similar to those of Jocassee, and its failure behavior can therefore be used as one point of reference in judgments about the possible failure behavior of Jocassee. The overtopping of this partly constructed dam lasted for more than 40 hours4.62963e-4 days <br />0.0111 hours <br />6.613757e-5 weeks <br />1.522e-5 months <br /> before a catastrophic failure occurred. This suggests that a long warning time may be available, at least in some cases, before the failure of an earth-rockfill dam. Once the dam was breached, however, the breach propagated the full depth of the dam, down to the foundation, in about 2 hours2.314815e-5 days <br />5.555556e-4 hours <br />3.306878e-6 weeks <br />7.61e-7 months <br />. Thus, though more warning time may have been available, once failure began, the time and depth to complete breach were quite similar to those observed for earthen dams.

In addition to the uncertainty in the important parameters described above, a spectrum of calculated flood levels is not available. Thus it is not possible to determine where the sensitive range for the key parameters lies.

Given this lack of information, a bounding value of 1 was used for the condi-tional probability of flooding of the Oconee site given a catastrophic failure of the Jocassee Dam.

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The conditional probability of core melt given flooding at the Oconee site is also a complex function depending on the warning time, the action taken by the plant staff (e.g., hot shutdown vs. cold shutdown; whether the standby shutdown facility is manned), the depth of flooding, the survival time for various plant equipment (e.g., steam-driven emergency feedwater pump, standby shutdown facility), and other factors. A scoping of this problem indicates that all means of core cooling are likely to be lost for more than 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />, and a conditional probability of 1 was assigned to core melt given flooding.

Combining the three factors yields a bounding estimate of 2.5 x 10-5 for the mean annual frequency of core melt due to a random failure of the Jocassee Dam. It is possible that a more detailed analysis could provide estimated conditional probabilities of site flooding and core melt less than unity.

However, core melt due to flooding in the turbine building from CCW failures clearly dominates the contribution from dam failure, and further analysis was judged to be not warranted.

A scopinq analysis was performed to investigate whether or not an interfacing-system LOCA could be caused by a loss of decay-heat removal due to the flood, and subsequent RCS heatup and pressurization. Assuming core cooling is lost at about 8 hours9.259259e-5 days <br />0.00222 hours <br />1.322751e-5 weeks <br />3.044e-6 months <br /> after a reactor trip with the plant in a cooled-down condition and the PORV reset to lift at approximately 500 psig, decay heat could be matched with liquid relief at system pressure on the order of 100 psia. Several hours would be required to heat up the primary and sec-ondary systems. In steady state at about 12 hours1.388889e-4 days <br />0.00333 hours <br />1.984127e-5 weeks <br />4.566e-6 months <br /> after a trip and after significant RCS inventory has been lost through liquid relief, saturated steam relief out of the RCS via the PORV at ahnut 500 psia nnujnd match the decay heat, and the RCS would stabilize at a pressure below that estimated to cause a rupture in the 388-psig design RHR suction piping. Therefore it was con-cluded that a core melt caused by the flooding of the plant and a prolonged loss of core cooling would not directly breach the containment. Since this sequence would be a late core melt (on the order of 12 hours1.388889e-4 days <br />0.00333 hours <br />1.984127e-5 weeks <br />4.566e-6 months <br />) with the RCS at moderate pressure (about 500 psig), it was assigned to core-melt bin II.

Flood effects would cause a failure of the reactor-building sprays and cooling units (i.e., containment-safeguard state C). Thus these sequences were assigned to plant-damage bin IIC.

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