ML20135D248

Rev 1 to Probability of Burst Model for ANO-2 Tts Circumferential Cracks

ML20135D248
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Site:	Arkansas Nuclear
Issue date:	10/16/1996
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ML20135D238	List: 2CAN029707, Forwards non-proprietary Repts Re ANO-2 SG Cycle 12 Operational Assessment ML20135D243 ML20135D248 ML20135D255 ML20135D259 ML20135D262
References
TR-96-005(NP), TR-96-005(NP)-R01, TR-96-5(NP), TR-96-5(NP)-R1, NUDOCS 9703050151
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l TR-96-005(NP), Rev.1 l

Probability of Burst Model l for ANO-2 TTS Circumferential Cracks Prepared for Entergy Operations, Inc.

16 October,1996 D DOK05b368 P PDR W Tetra Engineering Group, Inc.

USA: 110 Hopmeadow Street, Suite 800, Weatogue, CT, 06089 (1).860.651.4622 France:Immeuble Petro B, B.P. 272, 06905 SOPHIA ANTIPOLIS (33).92.96.92.54

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Non-Proprietary Information f

4 This is a non-proprietary version of a Tetra Engineering  ;

Group report. Proprietary information has been removed at locatic: s indicated by a heavy vertical bar in the right ,

margin. This report is submitted in confidence and is to be used solely for the purpose for which it is furnished. This report, parts thereof, or the information contained within, may not be transmitted, disclosed, or reproduced in any form without the written permission of Tetra Engineering Group, Inc.

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@ Copyright,1996 l 3

Tetra Engineering Group,Inc.  ;

Copyright under International Copyright Conventions  !

and under PAN AMERICAN Conventions. l 4

ALL RIGHTS RESERVED A

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TR-96-005, Rev.1 Overview a li

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Contents Overview 1 Introduction.. . .1 ;

Safety Analysis Considerations . .2 l SGTR Events. . .2 )

Conditional Burst Probability.. .3

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Conditional Burst Probability for TTS Circumferential Cracks 5 Description of Approach.. .5 j Circumferential Flaw Population.. . .6 <

Burst Correlation for Tubes with Circumferential Cracks.. .8 Burst Correlation . . . .8 Treatment of Uncertainty in Tube Mechanical Properties.. . .9 Treatment of Uncertainties in Correlation Parameters. . . .I1 Treatment of Data Scatter.. .13 Conditional Probability of Burst for Specified PDA . . .15 Definition of Probability Burst.. .15 Monte Carlo Simulation Algorithm.. . .16 Probability of k Bursts for M Cracks.. . . . . .19 Total Conditional Burst Probability.. . . 20 Probability of Zero Bursts. . . . 20 Probability of Exactly One Burst.. . 21 Conditional Probability of Multiple Tube Bursts . . 22 Application to ANO-2 Cycle 12 23 Conclusions 26 References -

26 TR.96-005, Rev.1 Overview e ill

Overview I

l Introduction This topical report describes the methodology for calculating the conditional l probability of one or more tube bursts for a population of circumferential cracks on the outside diameter of the steam generator tube at the top of tube sheet elevation. It is assumed that these flaws possess the OD-initiated stress conosion crack morphology typical of the explosively expanded tubes of CE-design steam generators.

Therefore, the approach described in this report has generic applicability to CE-designed steam generators. While the methodology is general in its applicability to CE-designed steam generators, plant specific data have been used to apply the methodology to the Arkansas Nuclear One Unit 2 (ANO-2) steam generators for their  ;

current operating cycle of 16 EFPM. The next scheduled refueling outage is designated 2R12.

Caution should be exercised, h'owever, to ensure that assumptions and data used to define specific model elements for the ANO-2 steam generators are adequate for application to other plants. Speci5cally, plant-specific data from ANO-2 were used including: tube mechanical proper:ies, NDE detection capability and sizing uncertainties specific to the technology deployed for recent tube inspections.

Elements of the overall methodology are described, with particular attention to the treatment and characterization of uncertainties in predicted flaw populations, in tube mechanical properties and in the correlation of tube burst with flaw size. Appropriate methods are described for combining uncertainties so that the probability of burst can be calculated for a specified population of cracks.

The approach described in this report closely follows the approach described in the proposed draft Regulatory Guide for Steam Generator Tube Integrity (Reference 1) and Generic Letter 95-05 (Reference 2).

An overview of safety analysis considerations relevant to assessing the probability of an event occurring which might lead to the postulated conditions of a main steam line break or feed line break transient is provided to place the conditional burst probability analysis in its proper context. This overview is from an evaluation performed for TR-96-005, Rev.1 Overview e 1

I ANO-2. Details of the assessment for ANO-2 and an assessment ofits generic l applicability to other CE-design plants are, however, beyond the scope of this j document.  :

1 Safety Analysis Considerations Section 6 of the Attachment to Reference 3 contains a Safety Assessment which was l performed prior to ANO-2 cycle 11; the previous operating cycle. The Safety Assessment applied best-estimate methodologies to validate emergency operating procedures, confirm acceptable control room and off-site dose consequences in accordance with 10CFR100 and to establish the adequacy of refueling water tank inventory to shut down and de-pressurize the plant. A brief overview of that document is provided in this section of the report. .

l The Safety Assessmc! dso addressed the potential severe accident impact to )

ANO-2 due to differem proposed steam generator inspection intervals. The l

assessment considered the impact attributable to both spontaneous and induced steam generator tube rupture (SGTR) events.

The purpose of this report is to provide an improved approach for calculating i conditional probability of burst. It takes advantage of additional burst test data, the ANO-2 burst correlation for circumferential cracks at TTS and statistical treatment of correlation uncertainties and tube mechanical properties. These elements of the conditional burst probability model when combined with the probability ofinitiating events yield the probability of zero, one and two or more tube bursts under postulated accident conditions. The conditional probability of burst addresses in this report is  !

limited to the contribution from the population of circumferential cracks at the top-of-tubesheet. Any contributions fror other degradation mechanisms are not included.

An acceptably low probability of burst is required to justify continued for a specified operating cycle (equivalently, steam generator inspection interval.) l SGTR Events Three events were considered in the Safety Assessment described in Reference 3:

1. Single SGTR i

2. Multiple SGTR

3. MSLB induced leak (s) or ruptures (limiting event)

A probabilistic safety analysis (PSA) was performed to assess the impact of the steam generator tube degradation mechanism on the probability of a severe accident. l l

In order to account for plant response dependencies on the steam line break location 1 and to distinguish the feedwater line break from the SLB, the SLB/FLB initiating  !

evmt was split into four parts:

i TR-96-005, Rev.1 Overview e 2

1 l

1. (T5-1) steam line piping outside of the main steam isolation valves (MSIVs) 1

2. (T5-2) steam line piping inside of MSIVs and outside of the containment on both j SGs l 4

3. (T5-3) steam line inside of containment on both SGs l

4. (T5-4) feedwater line inside of the feedwater check valves on both SGs l Reference 3 lists the following initiating event frequencies for spontaneous and i induced SGTRs.

l Table 1 ANO-2 SGTR Initiating Event Frequencies  ;

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Initiating Event ANO-2 Fraction of SGTR Analysis Frequency Total SL/FL Frequency (/rx-yr) l

(/rx-yr) Length R 9.77 x 10-' NA 9.77 x 10-2 d

T5-1 1.10 x 10-' O.699 7.69 x 10 T5-2 1.10 x 10 4 0.107 1.18 x 10" l d

T5-3 1.10 x 10-5 0.114 1.26 x 10 I 4

T5-4 1.10 x 10-' O.079 8.71 x 10 These initiating event frequencies are not necessarily applicable to other plants.

The probability of a tube burst induced by a main steam line break (MSLB) is calculated from the product of the initiating event frequency and the conditional burst  !

probability. The conditional burst probability is a conservative estimate of the conditional tube rupture probability and its consequences since not all tubes with circumferential cracks which might burst under postulated accident conditions would necessarily rupture in the sense of a double-ended guillotine rupture.

Conditional Burst Probability The conditional probability of tube burst is determined by statistically combining the probability of burst for specified extents of tube degradation with the predicted population of degraded tubes. The assessment can be performed at the beginning of cycle (BOC) following the inspection and repair campaign to support condition monitoring activities or at the projected end-of-cycle (EOC) to support operational assessments.

Flaw population projections typically account for the probability ofdetection (POD) for the inspection technclogy, NDE sizing uncertainties (and for EOC projections, a conservative treatment of crack growth (/EFPM) over the proposed interval of full-power reactor operation.) These uncertainties, when combined statistically, yield the TR-96-005, Rev.1 Overview e 3

projected crack population. Reference 4 describes the methodology for projecting end-of-cycle populations for circumferential cracks at the top-of-tubesheet in explosively expanded steam generator tubes of CE design. The flaw projection methodology takes into account POD, NDE sizing capability and the potential for flaw growth.

Extent of tube wall degradation for circumferential cracks is measured either by percent degraded area, PDA, or a conservative equivalent loosely termed " average" depth. Average depth has been calculated as the product of the maximum depth of the crack times the measured crack length; it tends to significantly overestimate the crack PDA.

Reference 3 refers to " fragility" curves which were developed to assess the tendency for a tube with a specified amount of degradation to burst when subjected to the differential pressure of a postulated MSLB. The fragility curves were developed based on the experimental burst pressure test data available m early 1995.

Subsequently. ational test data applicable to the ANO-2 SGs, have been identified.

These data were used to develop a burst correlation model, a key element of the conditional burst probability methodology for circumferential cracks.

The methodology described in this report contains some of the elements of the fragility curve concept; however, the current approach fully accounts for uncertainties in elements of the burst probability analysis following the guidance of Generic Letter 95-05 and the draft Reg. Guide for Steam Generator Tube Integrity.

TR-96-005, Rev.1 Overview e 4

I Conditional Burst Probability for l TTS Circumferential Cracks l

Description of Approach This section describes the elements of the approach for calculating the conditional probability of burst given that a MSLB has occurred in the steam generators.

Reference 3 cites the maximum credible differential pressure as PSdP=2500 psid.

The primary elements of the approach are:

1. crack population (total number and statistical distribution of flaw sizes at either BOC or EOC),

2. tube mechanical properties and uncertair.ty,

3. burst model, parameter uncertainty and the treatment of data " scatter" A number of computational methods exist for determining the total probability of burst for a specified flaw population; the method described in this report provides an adequate level of rigor with an efficient algorithm which results in acceptable computer implementation. Monte Carlo simulation will be used to statistically combine the tube mechanical properties uncertainty with the burst correlation parameter uncertainty and the data scatter uncertainty in order to determine the conditional probability of burst per crack for a single circumferential crack of PDA=Q%.

Standard statistical methods are then used to systematically combine the projected crack population with the conditional probability of burst per crack; the result being the total conditional probability of burst for the entire crack population.

The basic approach for calculating the conditional probability of burst per crack is to determine, for any crack size Q, the probability that the burst pressure will be less than or equal to the maximum credible differential pressure (PSdP):

Pg = P psu,sg & PSdPl flaw af size Q (1)

TR-96-005, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks e 5

1 1

In words, the conditional probability of burst per crack is the probability that the burst ,

pressure for a tube with a circumferential crack of size Q will be less than PSdP. ' '

From a knowledge of the total number of tubes projected to have cracks of PDA=Q (+ i dQ), the conditional probability of burst per crack can be determined. The total  ;

conditional burst probab.lity is then determined from the contribution from all crack size intervals.

The total number of tubes with cracks of size Q is calculated using the circumferential crack population (evaluated at BOC for condition monitoring, at EOC for operational assessments); refer to Reference 4 for details on the development of EOC crack j populations.

Circumferential Flaw Population l

The population of circumferential cracks in the steam generator at the top-of- l tubesheet is described by two quantities: the total number of cracks of all sizes ]

(detected + undetected ), M, and the statistical distribution of crack sizes. The total l number of cracks is determined by adjusting the as-found distribution to account for '

POD. The total number of cracks projected after operation for a specified cycle is typically characterized by a Weibull distribution (Reference 4.)

The distribution of crack sizes for OD-initiated stress corrosion cracks at the top-of-tubesheet in explosively expanded tubes of CE design is characterized by a common i shape (References 5,6).

The number of cracks in a particular size interval, (for example, Mg in the interval Q + 2.5%) is then:

L+2.5%

Mg = M lf(g)do m g-2.5%

wheref(g) is the statistical distribution for crack size: percent degraded area, PDA or its approximation " average" depth. Mg is the actual number in the interval; the relative frequency in the interval is designatedpg and represents the proportion of all cracks whose size is between Q + 2.5%. _

So-called average depth has been calculated as measured maximum depth times length; typically, a very conservative measure of PDA. In the case of ANO-2, the largest cracks were subjected to more detailed " profiling" to establish more accurate l values for PDA. A typical projected EOC population of circumferential cracks is provided in Figure 1.

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' Note: lower case p will be used to represent pressure; upper case P to represent probability expressions.

TR-96-005, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks e 6  ;

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3 Figure 1 Typical Circumferential Crack Population If out of a total of M cracks there are M nwhich are of size Q, then the conditional j j probability of k (>0) burst tubes for size interval GidQ is:

P[k > 0] = 1-(1- g P [" (3)

{ Related expressions are provided in later sections to calculate the probability of zero l bursts for all crack sizes, the probability of one burst for all crack sizes and the i probability of 2 or more bursts for all crack sizes.

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{ Monte Carlo simulation is used to calculate the conditional probability of burst per

! crack for each crack size interval; the results are then systematically combined to

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.h determine the total conditional burst probability.

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] TR 96-005, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks . 7 I

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Burst Correlation for Tubes with Circumferential Cracks Burst Correlation Reference 8 describes the data and corrections for temperature and material properties which were applied to develop a burst correlation for CE-design steam generator tubes with outside diameter stress corrosion cracks with a circumferential orientation. The result of that work was a burst correlation which relates the percent degraded area (PDA), Q, to the average burst pressure,Pburst:

in units of psi. Refer to Reference 8 for additional information on the development of this structural model. Figure 2 provides a comparison of the burst pressures predicted by the burst correlation with the actual bmst test data. The burst pressure correlation is labeled Circumferential Burst Regression.

Circumferenllal Burst Data 12000 11000 -

10000 -

9000 - .

I 8000 - # /

j "~

g 6000 -

1-- : r_,_e._._

x x 3000 - ZUC~

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2000 - [ [" [,,T,,, a,,,, ,,,

1000 -

0 i , , , , , , , i i 0 10 20 30 40 50 60 70 80 90 100 Percent Degraded Area (PDA)

Figure 2. Circumferential Crack Burst Correlationfor Explosively Expanded Tubes The burst test data were obtained for a large number of EDM notch specimens which conservatively characterize the burst potential for alloy 600 tubes which have stress corrosion cracks with a circumferential orientation. Recently developed analytical models of the structural integrity of tubes with circumferential cracks (References 9, 10), while conservative in their treatment of degraded tube integrity, provide support TR-96-005, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks 8

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for the adequacy of the burst correlation model. Reference 8 contains a comparison of results between the empirical burst correlation and conservative analytical tube

, integrity models.

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4 Treatment of Uncertainty in Tube Mechanical Properties l

Steam generator tube mechanical properties tend to be plant-specific due to the heat- l i to-heat variations. While a given steam generator often has a large number of heats l

. (20 or more),the number of tubes per heat is not uniform. This results in a relatively l small number of heats typically defining the overall population of mechanical

properties. Consequently, significant differences in mechanical properties are

expected from steam generator to steam generator.

l j Reference 11 describes the mechanical properties data for the ANO-2 steam )

generators. Figure 3 provides a typical graph of the statistical distribution of tube l mechanical properties for the limiting steam generator "A". At ANO-2, the nu'nber of tubes in a given heat is known, so the distribution labeled " Tubes" is the actual 1 l distribution of tube flow stress in the steam generator. l

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{ I slleats

, _ . . .._._._m aTubesl g _._ _. . . _ _. _ . _ . . . . _ . . _ . ~ . _ . _ _ . _ _ . . _ . _ . _ . . . _

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g. _ _ . _ _ _ _ _ _ . _ _ . . . _ _ . . _ . . _ . _ _ ~ _ . _ _ _ _ _

$ $ $ k $ $ $ $ $ k $ $ $ $

2 s = c s s te .: u  :: , i: e a Flow stress (psi)

Figure 3. Mechanical Properties Distributionfor ANO-2 SG "A "

This discrete distribution is used in the Monte Carlo simulation of conditional burst probability per crack. Values are randomly sampled from this distribution and then used to scale the predicted burst pressure from the burst correlation (the burst TR-96-005, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks e 9

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correlation was developed by normalizing the test data to lower bound 95/95 l mechanical properties).  !

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l' TR-96-006, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks .10

Treatment of Uncertainties in Correlation Parameters f

Ordinary least-squares linear regression methods were used to calculate the coefficients of the linear relationship between PDA and burst pressure defined by equation (3). Table 2 presents the standard analysis of variance results for the linear l

regression; the burst correlation is seen to be statistically significant at better than the

p=5% level. A 'no-intercept' model was used to force the correlation through 0 at

! 100% PDA.

. Table 2 Circumferential Crack Burst Correlation - Linear Regression Statistics l

l Regression Statistics Multiple R 0.88 R Square 0.78 1

Adjusted R 0.75 Square Standard 1016 l

34 i

ANOVA Degrees of SS MS F Sigmficance l Freedom F 42 Regression 1 l 121084436 l 121084436 l 117.36 l 3.0910 l Residual 33 l 34048236l1031765 l l l f

[ l Total 34l155132672l l l l

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j Coefficient Standard t Stat P-Value l Error Intercept 0. lN/A lN/A lN/A l l PDA, Q% -197.1 l 5.85 l 33.7 l 3.87 x 10 2' l l l For PDA's less than 50%, a correlation with zero slope is used and only data scatter i uncertainty is applied to burst pressure predictions. The treatment of the data scatter l

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TR-96-005, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks .11 l l

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4 j uncertainty is described later in this report. For PDA's greater than 50%, standard

. methods (Reference 12) were used to incorporate the uncertainty in the slope of the l burst correlation. The uncertainty in the slope of the burst correlation is treated as a l l

j normally distributed variation about the value listed in Table 2 with a standard l l

j deviation given by:

S ,

! ap = r I

i E(a -U)2 i

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! where: S is the standard error of the regression and Q represents PDA. Random l values of the burst correlation slope are then obtained by calculating:

I bi = /S + Zcrp i pi = -197 j j where a random normal deviate Z is used to approximate a random Student's t j deviate. Figure 4 provides a graph of the correlation uncertainty distribution. )

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Burst Correlation Slope, bl i

j Figure 4. Circumferential Crack Burst Correlation Parameter Uncertainty l

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4 TR-96-005, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks e 12

Treatment of Data Scatter The difference between the " scatter" of the burst pressure test results used to define the correlation and the predicted average burst pressure obtained by applying the correlation to a crack with a specified PDA is termed the residual variation of the data. That is, the residual variation in the test results which is not explained by the linear relationship of burst pressure with PDA.

Th'is common statistical model arises from a consideration of the probability distribution for the statistical population. For example, the superposition of the resistance to burst imparted by a number of remaining crack ligaments, each of which might have a normal distribution, is expected to have this model. It is common for this distribution to represent phenomenon in structural reliability analysis (Reference 13.) This probability distribution is defined in terms of a standardized variable z :

where a, p are two parameters calculated from the burst test data. This equation gives the probability of varying amounts of data scatter relative to the average burst pressure predicted by the burst correlation. Figure 5 compares the with I a normal distribution with the same mean and standard deviation. l l

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The standard method for calculating the model parameters is to solve the maximum likelihood equations (Reference 14) :

This was accomplished using the SOLVER utility in Microsoft Excel (Reference 15).

The results were u=-0.4, p=0.75. Figure 6 compares the frequency of residual variations from the burst tests with those predicted by the model with these coefficients. Good agreement between the data and the inodel is indicated.

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Figure 6. Comparison ofBurst Correlation Data Scatter with Model The fitted model is seen to F wervative relative to the calculated residuals in the region ofinterest (negativ > .aal values.) Figure 6 indicates the tendency of the burst pressure data scatte ' slightly negative, although there exists a " tail" on the positive side. 2 Standard statistical goodness-of-fit tests were applied to the burst correlation residuals to confirm the apparent adequacy of the model; results from these tests follow. l Two standard statistical tests (K-S and the Cramer-Von Mises) were applied to assess l the adequacy of the distribution as a model for data scatter of the burst  !

l 2

A negative value corresponds to an overestimation of the measured burst pressure by the correlation, a positive value corresponds to an underestimation of the measured burst pressure by the correlation. l l

TR-96-005, Rev.1 Conditional Burst Probability for TTS Circumferentini Cracks .14 l

._ - _ - -. - .-- . = _ _ - - . _ _ _ _ ___ _ __

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The standard method for calculating the model parameters is to solve the maximum l likelihood equations (Reference 14) :

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This was accomplished using the SOLVER utility in Microsoft Excel (Reference 15).

The results were u=-0.4, p=0.75. Figure 6 compares the frequency of residual variations from the burst tests with those predicted by the model with these coef6cients. Good agreement between the data and the model is indicated.

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A C C IC A C C C C C iC C C Residual Burst Pressure (ksi)

Figure 6. Comparison ofBurst Correlation Data Scatter with Model The fitted model is seen to be conservative relative to the calculated residuals in the ,

I region ofinterest (negat > tesidual values.) Figure 6 indicates the tendency of the i burst pressure data scatt ' to be slightly negative, although there exists a " tail" on the i positive side. 2 Standard statistical goodness-of-fit tests were applied to the burst correlation residuals to confirm the apparent adequacy of the model; results from these tests follow. I Two standard statistical tests (K-S and the Cramer-Von Mises) were applied to assess j I

the adequacy of the distribution as a model for data scatter of the burst i

2 A negative value corresponds to an overestimation of the measured burst pressure by the correlation, a positive value corresponds to an underestimation of the measured burst pressure by the correlation.

TR-96405, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks 14

l correlation data set. Both tests are based on calculating the difference between the l empirical probability distribution of the residual burst correlation data scatter and the l

l proposed extreme value probability distribution. Refer to Reference 16 for details of these procedures.

For both these tests, if the value of the statistic calculated from the burst data is less than the acceptance criterion, we conclude that there is not enough information to contradict the assumption that the residual burst correlation data are from ,

distribution. Table 3 lists the results of the goodness-of-fit tests.

l Table 3 Goodness-of-Fit of Model to Burst Correlation Data Scatter l j Test Statistic Critical p Value Confirms Model?

(5%) i K-S fp = 0.66 0.85 Yes Cramer-Von Mises g,2 = 0.24 0.46 Yes These results indicate that both tests confirm the model as statistically I valid for representing the burst correlation data scatter at a p level better than 5% .  !

Conditional Probability of Burst for Specified PDA Definition of Probability Burst The maximum credible difTerential pressure for the ANO-2 steam generators is PSdP=2500 psid as specified in Reference 3. The probability that the burst pressure will be less than PSdP for a circumferential crack of Q% degraded area is defined to be the conditional probability of burst for such a defect. This probability can be expressed as:

P Pburst s;PSdP (6) l where the burst pressure,Pbursi, is dependent on the size of the crack; Q.

The burst correlation defined by equation (3) predicts the avuage value ofpbury, for a i

defect of size Q%; however, to account for the uncertainties in the tube mechanical l properties, in the burst correlation parameters and the burst data scatter, it is necessary

( to .

The burst pressure for a cracked tube can be represented as the sum of the average (predicted) burst pressure, j(,,,, determined from equation (3) plus a random component, z, which corresponds to the residual deviation for a specific tube from the l

TR-96405, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks e 15 l

i

! average correlation. It was shown in a previous section of this report that this deviation of tube burst pressures from the average is described by the probability distribution. A Monte Carlo procedure will be described for incorporating

• the mechanical properties and burst correlation parameter uncertainty into the probability of burst analysis.

Equation (6) can be expressed as:

P psu,,, s PSdP' =P ps,,,, + (psu,,, - ps,,,,) s PSd?

which is equivalently:

P Pbuy,, sPSdP =P z s PSdP - Pbuy,, = P(z s Z] (7) where z is a random variable described by the distribution. Equation (7) is dependent on the PDA since the predicted burst pressure depends on the crack degraded area Q%. This equation is used to calculate the conditional burst probability for a given PDA size interval by systematically combining the uncertainty distributions for mechanical properties, the burst correlation and the data scatter via a Monte Carlo procedure.

Monte Carlo Simulation Algorithm Monte Carlo simulation will be used to calculate the conditional burst probability per crack for a specified size. One Monte Carlo simulation (N trials) is used for each crack size interval. Each Monte Carlo trial yields a random value for the probability .

of burst for the specified crack size; the simulation is repeated many times and the l 95/95 value of conditional probability is determined the size interval. That value is used as the conditional burst probability per crack.

The probability of specific numbers of bursts for a population of cracks of specified size can be calculated easily for each size interval. The contribution to the conditional probability from all size intervals is then determined by systematically  ;

combining the results for each of the individual crack size intervals. Figure 7 l illustrates the Monte Carlo algorithm developed for this purpose. l i

TR-96-005, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks .16

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) Figure 7. Monte Carlo Algorithmfor Conditional Probability ofBurst Per Crack I

TR-96-005, Rev.1 Conditional Burst Probability forTTS Circumferential Cracks .17

. . _ - . . - - . - . _ _ _ . _ _ - ~- -- . . _ _ _ . . . - . . -.--- -_. _ . - - _ _ - . - - - . . _

i i Figure 8 provides a graph of the 95/50 conditional probability of burst calculated I

from equation (7) vs. PDA with an accident PSdP value of 2500 psid using 10,000

Monte Carlo trials per crack interval. These results include the effects of mechanical properties uncertainty, burst correlation uncertainty and data scatter. This is essentially a 'best-estimate' of the probability of burst. Average values of the

^

conditional probability of burst will be used to determine the total probability for all crack size intervals; the average values from the Monte Carlo simulations tend to be slightly higher than the 95/50 values.

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1. 2 ~7 a I , / 7 4 4 PDA, Q%

I Figure 8. Conditional Probability ofBurst per Crack vs. PDA As seen in Figure 8, the steep decrease in the burst pressure with increasing PDA l yields a rapid increase in the conditional probability of burst per crack for l circumferential cracks in excess of 75% PDA. However, below 75% there is a negligible probability of burst per crack. Table 4 lists average values of the

, conditional probability of burst per crack for increasing PDA based on 10,000 Monte  ;

Carlo trials per interval.

I l

l TR-96-005, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks 18

Table 4 Conditional Probability of Burst Per Crack (Circumferential Cracks at Top-of Tubesheet in CE-Design Steam Generators)

PDA, Q% Probability of Burst per Crack 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 The total conditional burst probability must account for the contribution from all cracks in the population. A method for calculating the probability of multiple bursts follows.

Probability of k Bursts for M Cracks A steam generator inspection interval may be as long as a conventional refueling outage, or a shorter "mid-cycle" interval. The total conditional burst probability for the steam generator at the end of the inspection interval is determined by summing the contributions from all the cracks. The conditional burst probability per crack is used to calculate the probability of specific numbers of tube bursts under the PSdP load when Mg tubes have cracks of a specified size Q%.

TR-96-005, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks = 19

c l

l l

l To simplify the calculations, the number of projected indications are grouped by I increments of 5% PDA; the conditional probability per crack for the largest PDA in l

each interval is used as the value for the interval, thereby bounding the probability for

[ all Afg cracks in the interval. l Designate the average conditional probability of burst for a single crack of size Q as l

calculated from equation (7) by Pp. Then the probability of zero, one and two or 1 more bursts for Afp tubes can be calculated from the standard binomial distribution:

P[k = 0] = (1- g P)0 P[k = 1] = Af g Pg(1- Pg) Afp-l (8) i l

M p-l P[k 2 2] = l- {P[k = 0] + P[k = 1]} = 1- 1+(Alp-1 Pg 1-Pg Equation (8) describes the probability of 0, I and 2 or more bursts, respectively when the Afg tubes with cracks of size Q e.re subjected to the accident load of PSdP.

Calculations of the total conditional probability of burst due to varying numbers of cracks of all sizes combine the conditional probabilities for a specific size with the predicted numbers of cracks of that size and determine the total by summing the contributions over all crack size intervals. A method for performing these calculations is described in the following section.

Total Conditional Burst Probability Probability of Zero Bursts The conditional probability of zero bursts for the crack population is equivalent to the probability that there will be zero bursts contributed from all crack size intervals.

Equation (8) for k=0 gives the probability of zero bursts for a specified crack size, Q.

The probability of zero bursts for all M cracks where there are Afg in the crack interval Q+2.5% is determined from the product of repeated applications of equation (8) for all size intervals:

P[0] = P,0lQ = 5% P 0lQ = 15%..P 0lQ = 95%

since 0 bursts for the entire population can only occur if there are 0 bursts in each of the crack size intervals. Substituting equation (8) for k=0 yields:

P[0]= (1 - P5%) ^ ^ (1i - P s% ) ^ -(I - P95%)

• or using the " product" operator, ] , to designate term by term multiplication:

TR-96-005, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks = 20 l

l

i P(0)= h(1-Pg ) # (9) l 0 l l Equation (9) will be used to calculate the conditional probability of zero bursts for a specified crack population.

Probability of Exactly One Burst ,

1 The ennditional probability of one burst for the crack population is equivalent to the probarn(ty that there will be a total of one burst in all crack size intervals. In other words, tne probability of one burst is equivalent to the probability due to one burst in a specific crack size interval with 0 bursts in all other intervals - systematically determined for all the intervals and then summed to determine the total.

Equation (8) for k=1 gives the probability of one burst for a specified crack size, Q.

The probability of one burst for all M tubes is determined by considering the systematic combinations of contributions from the K=10 crack intervals:

P[1] = P 1lG=5% P 0lQ = 15%..P 0lQ = 95%+

l P O!G = 5%P 1lG=15% ..P 0lQ = 95%+ l

> 1 P 0lG = 5%P 0lG = 15%...P 1lQ = 95%

since 1 burst for the entire population can occur only if there is I burst in one of the crack size intervals. Substituting equation (8) for k=0, k=1 yields:

P(1]= Af 3 .,, P5%(1 - P5%)"*~'](1-P)#+ g O*5%

Af is% Pi s%(1- P15%) '*~' h(1-g P ) " + (10) etis% ,

i Af95 % E95%(1- P95%)# (1- Pg )"

Q*95%

Equation (10) can be calculated fairly easily by use of a spreadsheet program.

Values obtained from the Monte Carlo analysis are substituted for each Pg value.

The values of Afg are obtained from the projected crack population.

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i TR 96-005, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks e 21 l

e---- -- h 1

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Conditional Probability of Multiple Tube Bursts  !

The probability of exactly one burst is related to the probability of one or more bursts .

I by: l P(21] = P(1]+ P(2 2]

Once the probability of 0 and exactly I burst are determined, the probability of two or more burst follows. It is immediately possible to calculate the probability of 2 or more tube bursts from:

P[2 2] = 1-(P[0]+ P[1]) (l1) j lt is possible to develop equations, analogues to (9) and (10) which express the probability of higher multiple tube bursts (> 3, > 4, ...) in terms of systematic l combinations of the probability ofindividual numbers of bursts for specific crack  ;

sizes. However, the equations rapidly become cumbersome and innplementation j rather difficult, although some simplifications are possible.

If the probabilities of one or more burst are relatively small (< 10 2) then the probability oflarge numbers of multiple bursts will be insignificant. Monte Carlo 1 simulation of multiple tube burst probabilities is the preferable method ifit is )

necessary to calculate the probability oflarge numbers of multiple bursts.

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TR-96-005, Rev.1 Conditional Burst Probability for TTS Circumferential Cracks e 22

I Application to ANO-2 Cycle 12 l

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1 l

The most recent steam generator exam at ANO-2 was the 2R11 inspection in l November,1995 where the largest circumferential crack was d<,termined to have a l PDA of 73. Data from the 2R11 inspection will be used to d:termine the conditional  !

probability of burst for the population of circumferential cracks predicted after 16 months of full-power operation at the next scheduled inspection - 2R12 l

Reference 4 describes the methodology for projecting the EOCl2 population of l circumferential cracks at the top-of-tubesheet in ANO-2 SG "A"; the limiting steam generator. Reference 17 contains the calculation of the EOCl2 population. Figure 9 is a tabulation of these results in 5% increments.

l l

160 "

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20 gg

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60

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,0 E Es._

E b U b, U N U b N fd b (5 h b U ($ E EoCl2 Percent Degraded Area

Figure 9. Projected ANO-2 Circumferential Crack Population at EOCl2 1

TR-96-005, Rev.1 Application to ANO-2 Cycle 12 e 23

l The typical size of a circumferential flaw at 2R12 is about 20% PDA. The frequency of flaws is seen to decrease exponentially with increasing PDA.

l An accident differential pressure of PSdP = 2500 was specified in Reference 3 as appropriate for the ANO-2 plant for these assessments. Equations (9)-(11) were I applied to the number of cracks for both steam generators for 2R11.

Results from calculating the conditional probability of burst for this population of cracks are provided in Table 5. The calculated conditional probabilities of burst for the limiting population of circumferential cracks at ANO-2 at EOCl2 is acceptably low relative to the guidance of Reference 1.

Table 5 Conditional Hurst Probabilities for ANO-2 SG "A" at 2R12 Number of Bursts Conditional Probability Performance Criteria for Individual Degradation Mechanism 0 99.9 % 3 95 %

1 1.2 103 1.0 10-2

>2 5.2 10-' 5.0 10-2

> 10

<5.2 10 2.0 10" Conditional probability of burst for the projected EOCl2 population of TTS circumferential cracks at ANO-2 following 16 months of full-power operation satisfies all of the performance criteria from Reference 1.

l l

TR-96-005, Rev.1 Application to ANO-2 Cycle 12 24

1 Conclusions The conditional burst probability model for explosively expanded tubes with circumferential cracks at the top-of-tubesheet was developed from the burst test data from ANO-2 and other plants with CE-design steam generators and laboratory specimens.

A methodology has been developed to combine statistically the uncertainties associated with tube mechanical properties, the burst correlation parameters and the data scatter of the burst tests. The approach follows the general guidance of the draft Steam Generator Tube Integrity Reg. Guide and Generic Letter 95-05. This approach provides a suitably rigorous statistical methodology for assessing the risk to tube integrity from applying postulated accident loads to projected EOC steam generator conditions.

Results from the application of the methodology to the ANO-2 EOCl2 crack population after 16 months of full-power operation indicates acceptable conditional probabilities of one or more bursts for a postulated accident PSdP of 2500 psid. Therefore, the performance criteria for circumferential cracks at the top of tubesheet have been satisfied.

l TR-96-005, Rev.1 Conclusions = 25 l

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References i I

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1. " Steam Generator Tube Integrity", NRC preliminary draft Reg. Guide X.XX, September,1996.

2. " Voltage-Based Repair Criteria for Westinghouse Steam Generator Tubes Affected by Outside Diameter Stress Corrosion Cracking", NRC Generic i Letter 95-05, August 3,1995. )

3. D. C. Mims to USNRC, "2P95-1 Steam Generator Inspection Results and Circumferential Cracking Evaluation", Docket No. 50-368, Entergy Operations Letter 2CANO29505, February 17,1995.  ;

1

4. 1

5. ,

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6. "ANO-2 Steam Generator Circumferential Cracks: 2R10 Inspection", Tetra Engineering Report TR-94-7203, June,1994.

7. " Statistical Modeling of Millstone 2 Circumferential Crack Extents and l Depths", Tetra Engineering Group Report TR-90-0602, Revision 1, April i 1990.

1

9. P. Hernalsteen,"Circumferential Cracks in Steam Generator Tubes: Structural Analysis Model and Integrated Burst Pressure Data Base", Tetra Engineering Group Report TR-95-030, Revision 3, October,1996.

10. P. Hernalsteen, "Circumferential Flaws Burst Data - Evaluation of Foil Reinforcement Effects", Tetra Engineering Group Report TR-96-016, Rev. O, l

October,1996.

1

! 11. "ANO Unit 2 Steam Generator Tubes: 95/95 Mechanical Properties", Tetra Engineering Group Report TR-95-025, Rev. O, March,1996.

12. N. Draper and H. Smith, Applied Regression Analysis, Second Edition, John Wiley,1981 I

l TR-96-005, Rev.1 References 26 l

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13. F. Casciati and B. Roberts, Mathematical Modelsfor Structural Reliability l Analysis, CRC Press, Inc.,1996.

14. N.L. Johnson and S. Kotz, Continuous Univariate Distributions, Vol.1, Second Edition, John Wiley,1994. j

15. Excel Version 7.0 for Windows NT, Microsoft Corporation,1995. l

16. R.B. D' Agcstino, Goodness-of-Fit Techniques, Marcel Dekker, Inc.,1986 17.

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TR-96405, Rev.1 References e 27 l

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ATTACIIMENT 5 TR-95-024 NON-PROPRIETARY l

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