ML071970083

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Draft a EPRI Report: Advanced Fea Industry Corres Presentation Studies
ML071970083
Person / Time
Site: Wolf Creek Wolf Creek Nuclear Operating Corporation icon.png
Issue date: 07/14/2007
From: Dedhia D, Harris D, Riccardella P
Electric Power Research Institute, Structural Integrity Associates
To:
Office of Nuclear Reactor Regulation
Sullivan E, NRR/DCI, 415-2796
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DRAFT Page 1 of 26 1/11/07 1 2 3 4 5 6 7 8 9 10 Evaluation of Pressurizer Alloy 82/182 11 Nozzle Failure Probability 12 13 (Including Effect of the Fall-06 Wolf Creek NDE Indications) 14 15 16 17 18 19 20 Peter C. Riccardella 21 Dilip Dedhia 22 David O. Harris 23 24 25 Structural Integrity Associates, Inc.

26 27 July 14, 2007 28 29 DRAFT Page 2 of 26 1/11/07 Table of Contents 1 2 3 1.0 Introduction 4 5 2.0 Flaw Distributions 6 7 2.1 Inspection Data 8 2.2 Statistical Fits to the Data 9 10 11 3.0 Critical Flaw Size Distribution 12 13 3.1 Applied Load Distribution 14 3.2 Compilation of Full Scale Pipe Tests 15 3.3 Development of Fragility Curve 16 17 4.0 Crack Growth 18 19 4.1 Summary of Advanced FEA Results 20 4.2 Adaptation to Probabilistic Analysis 21 22 5.0 Monte Carlo Analysis 23 24 5.1 Methodology 25 5.2 Cases Analyzed 26 5.3 Results 27 28 6.0 Conclusions 29 30 DRAFT Page 3 of 26 1/11/07 1 Introduction 1 2 To complement the deterministic analyses being performed under the advanced FEA 3 project [1], the MRP also performed a probabilistic evaluation of the Alloy 82/182 4 pressurizer butt welded nozzles, considering current inspection data, to assess the effect 5 of various inspection options on probability of a nozzle failure in the time interval until 6 all nozzles are inspected or mitigated. There are three major elements to the probabilistic 7 analysis approach:

8 9 1. Flaw Distribution - As discussed in the Section 2 of this report, considering 10 inspections performed through Spring of 2007, data exists for a total of 51 Alloy 11 82/182 nozzles that either have been inspected as part of the MRP-139 inspection 12 program [2], or in which leaks, cracks or UT indications have been detected prior 13 to the commencement of MRP-139 examinations in 2006. These data, 14 summarized in Table 2-1, and illustrated graphically in Figure 2-1, are used to 15 estimate probable flaw distributions that might exist in uninspected nozzles.

16 17 2. Fragility Curve - A second important aspect of the analysis, discussed in Section 18 3, is the critical flaw size to cause a nozzle failure. For any given flaw size, 19 characterized in terms of percentage of cross section lost to the crack (denoted in 20 this report as the Criticality Factor, CF%), there is a probability that the flaw will 21 cause a pipe rupture under operating loads and internal pressure. This probability 22 of rupture versus flaw size is called a "fragility curve" which can be combined 23 with a probable flaw distribution to estimate the probability of a nozzle failure in 24 the time period up to the time of the recent inspections.

25 26 3. Crack Growth - The flaw distribution discussed in 1 above represents a snapshot 27 at the time of the inspections. In order to make meaningful comparisons of future 28 probabilities of rupture under various inspection scenarios, one must also make 29 estimates of the probability of future flaw growth. The deterministic results of the 30 advanced FEA project [1] are used, as discussed in Section 4, to produce a series 31 of flaw distributions similar to those discussed in 1 above, but which increase 32 with time. These time-varying crack size distributions are used in conjunction 33 with the fragility curve to produce estimates of the probability of rupture versus 34 time into the future (at six month intervals).

35 36 The analysis process is illustrated in Figure 1-1. A typical flaw distribution (Weibull) at 37 the time of the recent inspections is illustrated by the heavy black curve on the left hand 38 side of the graph. This curve is estimated to shift to the right due to crack growth during 39 each six-month period between outage seasons, as illustrated by the series of parallel 40 colored curves in the figure. Finally, the fragility curve is illustrated by the heavy red 41 curve, on the right hand side of the figure. Figure 1-1b zooms in on the low probability 42 region of the same graph.

43 44 45 DRAFT Page 4 of 26 1/11/07 The failure probability is actually simulated by a process of Monte Carlo sampling from a 1 flaw distribution and the fragility curve, as discussed in detail in Section 5. Each time a 2 trial yields a flaw size from the flaw distribution that is greater than the critical flaw size 3 from the fragility curve; it represents a predicted nozzle rupture. The number of 4 predicted ruptures divided by the total number of trials performed represents the 5 cumulative probability of rupture (per nozzle) up to the time of the flaw distribution. The 6 Monte Carlo simulation process is performed for each time period for which a flaw 7 distribution has been determined, and the incremental probabilities of failure (per nozzle, 8 per time interval) are computed by subtracting the cumulative probabilities for adjacent 9 time intervals. Finally, the incremental probabilities are multiplied by the number of 10 nozzles, divided by the number of plants, and then combined by calendar year to produce 11 the common units of probability per plant year for various inspection scenarios.

12 DRAFT Page 5 of 26 1/11/07 00.10.20.30.40.5 0.60.70.80.9 10%10%20%30%40%50%60%70%80%90%100%CF(%)ProbabilityWeib Flaw distFragility6 Mo Growth12 Mo Growth18 Mo Growth 1 Figure 1-1a - Complementary Cumulative Distribution of Crack Area Fraction 2 at Different Times, along with Complementary Cumulative Distribution of 3 Critical Crack Area Fraction (CF, %)

4 00.0050.010.0150.020.0250.030.0350.040.0450.050%10%20%30%40%50%60%70%80%90%100%CF (%)ProbabilityWeib Flaw distFragility6 Mo Growth12 Mo Growth18 Mo Growth 5 Figure 1-1b - Enlargement of Low Probability Region of Figure 1-1a.

6 DRAFT Page 6 of 26 1/11/07 2 Flaw Distributions 1 2 The flaw size distribution is estimated from inspection data.

3 2.1 Inspection Data 4 5 A compilation of the inspection data used to develop the flaw distributions is provided in 6 Table 2-1. There are a total of 51 data points listed, in approximate chronological order, 7 with a total of 7 axial indications (or leaks), and 8 circumferential indications. The early 8 data (2005 and earlier) are legacy data that preceded MRP-139 inspections, and in some 9 cases include non-pressurizer nozzles such as hot and cold leg drains, as well as overseas 10 plants. The 2006 and 2007 data are from inspections performed in response to MRP-139.

11 The circumferential indications include the three Wolf Creek indications observed in 12 Fall-2006.

13 14 The data were updated to reflect recent inspections performed in Spring 2007. These 15 include a total of ten new data points, nine clean and one moderate-sized circumferential 16 indication. These new data did not indicate any new trends that weren't apparent from 17 the prior data.

18 19 Figure 2-1 presents a locus plot of the data in which crack length as a percentage of 20 circumference is plotted along the abscissa, and crack depth as a percentage of thickness 21 on the ordinate. Axial indications plot along the vertical axis (l/circumference = 0) in this 22 plot, with leaking flaws plotted at a/t = 100%. Circumferential indications plot at non-23 zero values of /circumference, at the appropriate a/t. Clean inspections are plotted 24 randomly in a 10% box near the origin, to give some indication of inspection uncertainty.

25 26 Also shown on this plot are loci of critical flaw sizes from the fragility curve discussion 27 in Section 3. 50 th and 99.9 th percentile plots are shown. It is seen from this figure that all 28 of the flaw indications detected were far short of the sizes needed to cause a rupture.

29 However, the analysis must address the small but finite probability that larger flaws may 30 exist in uninspected nozzles, plus the potential for crack growth during future operating 31 time until all the nozzles are inspected (or mitigated).

32 33 There exist a total of about 280 Alloy 82/182 pressurizer nozzles in 50 PWRs affected by 34 this concern. Under the industry inspection program in accordance with MRP-139 (and 35 approved deviations) 83 nozzles were inspected or mitigated, by the end of 2006, at the 36 time that the Wolf Creek indications were observed. An additional 74 were performed in 37 Spring 2007, and 70 are scheduled for Fall 2007. (Note that many of the nozzles were 38 preemptively overlaid without inspection prior to the overlay, and the post-overlay 39 inspections cover a limited volume, explaining why the numbers of inspections in Table 40 2-1 are much less than these totals.) The issue being addressed in this report, and the 41 advanced FEA project of [1] concerns a total of 51 nozzles in 9 plants for which 42 inspections or mitigation will not be performed until Spring 2008 under the industry 43 program. 44 DRAFT Page 7 of 26 1/11/07 Table 2 Plant Data used in Flaw Distribution 1 Plant Inspection Date Nozzle OD (in) Thick (t, in) Type of Indication Indication Depth (a, in) Indication Length ( in) a/t /circ Criticality Factor Tihange 2 2002 Surge 14 1.4 Axial 0.600 0.000 43% 0% 0.00% TMI 2003 Surge 12 1.3 Axial 0.585 0.000 45% 0% 0.00% Tsuruga 2003 Relief 6 1 Axial 1.000 0.000 100% 0% 0.00% Tsuruga 2003 Safety 6 1 Axial 0.900 0.000 90% 0% 0.00% Calvert 2 2005 CL Drain 2 0.56 Circ 0.056 0.628 10% 10% 1.00% Calvert 2 2005 HL Drain 2 0.56 Axial 0.392 0.000 70% 0% 0.00% DC Cook 2005 Safety 8 1.4 Axial 1.232 0.000 88% 0% 0.00% Farley 2 2005 Safety 8 1.1 Clean 0.000 0.000 0% 0% 0.00% Farley 2 2005 Spray 6 0.83 Clean 0.000 0.000 0% 0% 0.00% Millstone 3 2005 Spray 6 0.9 Circ 0.220 3.750 24% 20% 4.86% Calvert 1 2006 HL Drain 2.875 0.375 Circ 0.100 0.450 27% 5% 1.33% Calvert 1 2006 Relief 6.0675 1.3 Axial 0.100 0.000 8% 0% 0.00% Calvert 1 2006 Surge 12.75 1.3 Circ 0.400 2.400 31% 6% 1.84% Davis Besse 2006 CL Drain 2 0.56 Axial 0.056 0.000 7% 0% 0.00% D-B 2006 Relief 4.5 0.8125 Clean 0.000 0.000 0% 0% 0.00% D-B 2006 Safety 4.5 0.8125 Clean 0.000 0.000 0% 0% 0.00% D-B 2006 Safety 4.5 0.8125 Clean 0.000 0.000 0% 0% 0.00% D-B 2006 Spray 5.125 0.625 Clean 0.000 0.000 0% 0% 0.00% D-B 2006 Surge 11.5 1.125 Clean 0.000 0.000 0% 0% 0.00% Prairie Is. 2006 Surge 15 1.5 Clean 0.000 0.000 0% 0% 0.00% SONGS 2 2006 Safety 8 1.4 Axial 0.420 0.000 30% 0% 0.00% SONGS 2 2006 Safety 8 1.4 Axial 0.420 0.000 30% 0% 0.00% SONGS 2 2006 Safety 8 1.4 Clean 0.000 0.000 0% 0% 0.00% SONGS 2 2006 Spray 5.5 0.75 Clean 0.000 0.000 0% 0% 0.00% SONGS 3 2006 Relief 8 1.1875 Clean 0.000 0.000 0% 0% 0.00% SONGS 3 2006 Safety 8 1.1875 Clean 0.000 0.000 0% 0% 0.00% SONGS 3 2006 Safety 8 1.1875 Clean 0.000 0.000 0% 0% 0.00% SONGS 3 2006 Spray 5.5 0.75 Clean 0.000 0.000 0% 0% 0.00% SONGS 3 2006 Surge 13 1.437 Clean 0.000 0.000 0% 0% 0.00% Watts Bar 2006 Relief 7.75 1.29 Clean 0.000 0.000 0% 0% 0.00% Watts Bar 2006 Safety 7.75 1.29 Clean 0.000 0.000 0% 0% 0.00% Watts Bar 2006 Safety 7.75 1.29 Clean 0.000 0.000 0% 0% 0.00% Watts Bar 2006 Safety 7.75 1.29 Clean 0.000 0.000 0% 0% 0.00% Watts Bar 2006 Spray 6 0.9 Clean 0.000 0.000 0% 0% 0.00% Watts Bar 2006 Surge 15 1.5 Clean 0.000 0.000 0% 0% 0.00% Wolf Creek 2006 Relief 7.96 1.32 Circ 0.340 11.500 25.8% 46% 11.85% Wolf Creek 2006 Safety 7.96 1.32 Circ 0.297 2.500 22.5% 10% 2.25% Wolf Creek 2006 Safety 7.96 1.32 Clean 0.000 0.000 0% 0% 0.00% Wolf Creek 2006 Safety 7.96 1.32 Clean 0.000 0.000 0% 0% 0.00% Wolf Creek 2006 Spray 6 0.9 Clean 0.000 0.000 0% 0% 0.00% Wolf Creek 2006 Surge 15 1.45 Circ 0.465 8.750 32.1% 19% 5.95% Farley 2 2007 Safety 8 1.1 Clean 0.000 0.000 0% 0% 0.00% Farley 2 2007 Safety 8 1.1 Clean 0.000 0.000 0% 0% 0.00% Farley 2 2007 Safety 8 1.1 Clean 0.000 0.000 0% 0% 0.00% Farley 2 2007 Safety 8 1.1 Clean 0.000 0.000 0% 0% 0.00% Farley 2 2007 Spray 6 0.83 Clean 0.000 0.000 0% 0% 0.00% Farley 2 2007 Surge 15 1.52 Circ 0.500 3.000 33% 6% 2.12% Calvert 2 2007 Safety 8 1.1875 Clean 0.117 1.886 0% 0% 0.00% Calvert 2 2007 Safety 8 1.1875 Clean 0.052 1.681 0% 0% 0.00% Calvert 2 2007 Spray 5.5 0.75 Clean 0.066 1.475 0% 0% 0.00% Calvert 2 2007 Surge 13 1.437 Clean 0.030 3.107 0% 0% 0.00%

2 3 4 5 DRAFT Page 8 of 26 1/11/07 0%10%

20%

30%

40%

50%60%70%80%90%100%0%10%20%30%40%50%60%70%80%90%100%l/circumferencea/thicknessDMW IndicationsWOLF Creek IndicationsCrit-surgeCrit-reliefFarley Surge NozzClean Inspections Axial IndicationsCircumferenial Indications 1 Figure 2-1: Plot of Indication Sizes along with 50 th and 99.9 th Percentiles 2 of Fragility Curve.

3 4 2.2 Statistical Fits to the Data 5 6 The "Criticality Factor" (CF = percentage of cross section lost to the assumed crack) was 7 computed for each of the nozzles in Table 2-1 (last column), by multiplying the reported 8 indication circumferential lengths times their depths, and dividing the product by the 9 approximate cross sectional area of the nozzle at the flaw location. CF corresponds, 10 approximately, to the percentage of circumferential cross sectional area that is lost due to 11 the observed indications, assuming that they are cracks with a depth equal to their 12 maximum reported depth over the entire length of the indication. A cumulative 13 distribution of criticality factors was then developed, by sorting the data from smallest to 14 largest CF and assigning each data point a rank of i/N (where i = the inverse rank of each 15 data point and N = the total number of data points, 51). The individual data points are 16 listed in Table 2-2, which also shows the estimated cumulative probability (i/N) of an 17 indication exceeding each CF value. Note that Table 2-2 only lists the eight nozzles that 18 had circumferential indications. The other 43 nozzles had a CF of zero (clean or axial 19 indications only) and were not included in curve fitting the distribution, although N was 20 assigned as the total number of data points (51).

21 22 23 DRAFT Page 9 of 26 1/11/07 1 Table 2-2: Axial Indications from Table 2-1 Including 2 Estimates of Cumulative Probability 3 4 5 6 7 8 9 10 11 12 13 14

  • N = 51 15 16 17 Weibull, Log-Normal and Exponential fits to the data of Table 2-2 are shown on a log-18 log scale in Figure 2-2. The fits to the data were made by fitting a straight line to the data 19 after transforming it to scales that would result in a straight line if the random variable 20 had that distribution (equivalent to plotting it on probability paper appropriate for each 21 distribution type). The resulting distributions and the data are shown in Figure 2-2.

22 Table 2-3 summarizes the parameters of the fits.

23 10-3 5x10-3 10-2 5x10-20.1 1 2 5 10 20 50CF (%)ProbabilityDataExponentialWeibullLog NormalFits Compared (Rank = i/N)E:\EPRI248\Rev 2\StatsDD4.plt 24 25 Figure 2 Complementary Cumulative Distributions of CF showing each of the 26 Three Fits along with the Data.

27 28 CF Rank, i F, i/N* 1-F 1.00% 8 0.1568630.8431371.33% 7 0.1372550.862745 1.84% 6 0.1176470.8823532.09% 5 0.0980390.9019612.25% 4 0.0784310.921569 4.86% 3 0.0588240.941176 5.95% 2 0.0392160.96078411.85% 1 0.0196080.980392 DRAFT Page 10 of 26 1/11/07 1 2 Table 2 Parameters of the Fitted Distributions 3 4 5 6 From Figure 2-2 it is seen that the Weibull and Log-Normal distributions are excellent 7 fits within the range of the actual data (up to ~12% CF). The exponential distribution fit 8 is not as good, but still reasonable. Figure 2-2 also shows the distributions extrapolated 9 out to large flaw sizes, from which it is seen that there are substantial differences between 10 the distributions at large sizes, even though they all agree well in the range of the data.

11 For this reason, the probabilistic analysis will not be used to estimate absolute failure 12 probabilities, but rather to compare relative probabilities for various inspection scenarios, 13 under a common set of assumptions. Results of Monte Carlo simulations for the three 14 distribution types are presented in Section 5.

15 16 Distribution Type Complementary CumulativeDistribution Values of Parameters R 2 Exponential b x Ce/ 1/b = 18.608, C= 0.1524 0.9349 Weibull )/(x e =0.3034, =0.001321 0.9772 Log-Normal 2 1 erfc2)/ln(m x m = 0.0009785, = 2.36058 0.9765 DRAFT Page 11 of 26 1/11/07 1 3 Critical Flaw Size Distribution 2 3 There are two sources of statistical variability in the critical flaw size calculations. One is 4 the variability in the applied loads for the different plants and nozzle types, and the 5 second relates to uncertainty in ability to predict critical flaw size (CF%) when the 6 applied loading is known. These two sources of variability are addressed separately and 7 then combined statistically to produce a single fragility curve as discussed in the 8 following subsections.

9 3.1 Applied Load Distribution 10 Applied loads for the 51 PWR pressurizer nozzles scheduled for Spring 2008 inspections, 11 plus the Wolf Creek pressurizer nozzles, have been compiled as part of the advanced 12 FEA project [1]. Figure 3-1 presents a summary of this compilation, in terms of ASME 13 Code membrane and bending stress levels (Pm and Pb) computed using standard Code 14 formulas and nozzle dimensions for each plant. The loads include pressure and dead 15 weight primary loading plus sustained thermal expansion (Pe) loads, which are secondary 16 or displacement controlled. Thermal stratification loads, which are also secondary, are 17 not included. Analyses were performed in the advanced FEA project [1] which 18 demonstrate that secondary loads do not need to be included in critical flaw size 19 computations for the ductile Alloy 82/182 weld materials being addressed in these 20 nozzles, thus justifying the exclusion of both thermal expansion and stratification loads.

21 However, an agreement was reached under the project to include sustained thermal 22 expansion loads in the critical flaw size computations, since they are used to support leak 23 rate predictions. For consistency these thermal expansion loads are also included in 24 critical flaw size calculations performed for the probabilistic evaluation.

25 26 Safe shutdown earthquake (SSE) loads are also included in Figure 3-1, as indicated by 27 the dashed lines in the plot. For the probabilistic evaluation, the load data were analyzed 28 separately, with and without SSE loads, permitting seismic loads to be considered with a 29 reduced probability of occurrence (typically 0.001 per year or less) relative to normal 30 operating loads.

31 32 DRAFT Page 12 of 26 1/11/07 0 5 10 15 2001 A - Re (7.75x5.17)02 A - SA (7.75x5.17)03 A - SB (7.75x5.17)04 A - SC (7.75x5.17)05 E - Re (7.75x5.17)06 E - SA (7.75x5.17)07 E - SB (7.75x5.17)08 E - SC (7.75x5.17)09 H - Re (7.75x5.17)10 H - SA (7.75x5.17)11 H - SB (7.75x5.17)12 H - SC (7.75x5.17)WC1 J - Re (7.75x5.17)WC1a J - Re/Sa (7.75x5.17)WC2 J - SA (7.75x5.17)WC3 J - SB (7.75x5.17)WC4 J - SC (7.75x5.17)13 F - Re (8x5.19)14 F - SA (8x5.19)15 F - SB (8x5.19)16 F - SC (8x5.19)17 B - Re (7.75x5.62)18 B - SA (7.75x5.62)19 B - SB (7.75x5.62)20 B - SC (7.75x5.62)21 G - Re (7.75x5.62)22 G - SA (7.75x5.62)23 G - SB (7.75x5.62)24 G - SC (7.75x5.62)25 C - Re (7.75x5.62)26 C - SA (7.75x5.62)27 C - SB (7.75x5.62)28 C - SC (7.75x5.62)29 D - Re (8x5.19)30 D - SA (8x5.19)31 D - SB (8x5.19)32 D - SC (8x5.19)33 I - Re (8x5.188)34 I - SA (8x5.188) 35 I - SB (8x5.188)36 A - Sp (5.81x4.01)37 E - Sp (5.81x4.01)WC5 J - Sp (5.81x4.01)38 B - Sp (5.81x4.25)39 G - Sp (5.81x4.25)40 C - Sp (5.81x4.25)41 F - Sp (8x5.695)42 D - Sp (5.188x3.062)43 I - Sp (5.188x3.25)44 A - Su (15x11.844)45 E - Su (15x11.844)46 H - Su (15x11.844)WC6 J - Su (15x11.844)47 B - Su (15x11.844)48 G - Su (15x11.844)49 C - Su (15x11.875)50 D - Su (13.063x10.125)51 I - Su (13.063x10.125)

P m , P b , P m+P b Stress Loading (ksi) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.00 0.75 1.50 2.25 3.00 3.75 4.50 5.25 6.00 6.7 5 7.50 8.25 9.00 9.75 1 0.50 1 1.2512.0012.75 1 3.50 1 4.25 1 5.0015.7516.5017.25 1 8.00 1 8.75 1 9.5020.2521.00 2 1.75 2 2.50 2 3.2524.0024.75 2 5.50 2 6.25 2 7.00 27.7528.50 2 9.25 3 0.00 3 0.75 31.5 0 32.25 3 3.00 3 3.75 3 4.50 35.2 5 36.0 0 3 6.75 3 7.50 3 8.25 39.0 0 39.7 5 4 0.50 4 1.25 4 2.00 42.7 5 43.5 0 44.2 5 4 5.00 4 5.75 4 6.50 4 7.25 48.0 0 4 8.75 4 9.50 5 0.25 5 1.00 5 1.7552.50 5 3.25 5 4.00 5 4.75 5 5.5056.2557.00 5 7.75 5 8.50 5 9.2560.00 PmPm with SSE PbPb with SSEPm+PbPm+Pb with SSE 1 Figure 3 Compilation of Applied Stresses (Pm + Pb + Thermal Expansion) in 51 2 Pressurizer Nozzles scheduled for Spring 2008 Inspection plus Wolf Creek 3 4 5 6 The data in Figure 3-1 were sorted by increasing stress level, and were found to be well 7 fit by Log-Normal statistical distributions, as illustrated in Figures 3-2 and 3-3 for Pm +

8 Pb + Pe, with and without SSE loads, respectively. The fitting accuracy and parameters 9 of the Log-normal fits are included on the figures.

10 11 12 DRAFT Page 13 of 26 1/11/07 Log Norm Fit (w/o SSE)

R 2 = 0.97520.0000.5001.000 1.5002.000 2.5003.000 3.500-2.500-2.000-1.500-1.000-0.5000.0000.5001.0001.5002.0002.500Norm Dist.LN (Pm + Pb+ Pe) w/o SSEMedian = 8.9 ksiMean (ln) = 2.166Std. Dev. (ln) = 0.395 1 Figure 3 Log-normal Fit and Parameters of Applied Load Distribution without 2 Seismic Loads 3 4 Log Normal Fit w/SSE R 2 = 0.98220.0000.500 1.000 1.500 2.000 2.500 3.000 3.500-2.500-2.000-1.500-1.000-0.5000.0000.5001.0001.5002.0002.500Norm Dist.LN (Pm + Pb + Pe) w/ SSE)Median = 9.4 ksiMean (ln) = 2.298Std. Dev. (ln) = 0.412 5 Figure 3 Log-normal Fit and Parameters of Applied Load Distribution without 6 Seismic Loads 7 8 DRAFT Page 14 of 26 1/11/07 3.2 Compilation of Full Scale Pipe Tests 1 The statistical fits of figures 3-2 and 3-3 can be sampled to provide estimates of the 2 distribution of applied loading on the pressurizer nozzles in the study. However, even if 3 the applied loading were known with complete accuracy, uncertainty exists in our ability 4 to predict the critical flaw size, in terms of CF%. To help characterize this uncertainty, a 5 review was performed of test data from the NRC-sponsored Degraded Piping Program 6 conducted at Battelle Columbus Laboratories [3, 4]. Approximately 60 full scale pipe 7 tests were conducted in this program, of pipes containing three types of circumferential 8 defects: through-wall cracks, surface cracks, and complex cracks (see Figure 3-4). Pipe 9 sizes ranged from 4" to 42" and loadings included 4-point bending, combined bending +

10 internal pressure and pure axial load. The majority of the pipes tested were in the 6" to 11 16" range which is directly relevant to the pressurizer nozzles being evaluated. Pipe 12 materials in the tests included 304 stainless steel, Alloy 600 and Carbon Steel, but no 13 pipes containing A-82 or 182 weldments were tested. Therefore the results of the 14 predominantly base material pipe tests must be translated to DMWs on the basis of 15 relative material properties for use in this evaluation. Fortunately, the piping materials 16 used in the program were extensively characterized in terms of tensile properties and 17 fracture toughness (J-R curves). Recent data also exists on the J-R properties of a large 18 A-182 weldment, which can be used for comparison to the test materials.

19 20 21 22 23 Figure 3 Illustration of Circumferential Flaw Types Tested in Degraded Piping 24 Program Full Scale Pipe Tests 25 26 Figure 3-5 is a plot of test data from 31 of the pipe tests, performed on Austenitic 27 materials only (304SS plus A-600). The data are plotted in terms of maximum loading 28 achieved in the pipe tests (i.e. failure load) vs. % of pipe cross section cracked (CF %).

29 The maximum load is plotted in terms of applied stress at the cracked cross section 30 normalized by the ASME Section III design allowable stress for the appropriate material 31 and temperature: (Pm + Pb) / Sm.

32 DRAFT Page 15 of 26 1/11/07 0.0000.5001.0001.5002.0002.5003.0003.5004.0000.0%10.0%20.0%30.0%40.0%50.0%60.0%70.0%80.0%90.0%100.0%

CF(Pm+Pb)/SmComplexSurfaceThru-wallWOL (Surf)Fity = 0.4061x ^ (-1.4613)R2 = 0.8988 1 Figure 3 Plot of Full Scale Pipe Test Data from Degraded Piping Program.

2 Austenitic Materials Only; Various Flaw Types, 3 4 5 The large majority of the tests in Figure 3-5 were conducted under bending loading (Pb) 6 only, and those tests yielded a very consistent trend. However, in order to include pipes 7 tested under combined membrane plus bending (Pm + Pb), and since the applied nozzle 8 loadings in Section 3.1 include both membrane and bending loads, a correction factor 9 was developed based on net section collapse analyses plus data from similar pipes tested 10 under varying amounts of membrane and bending stress. It results in a correction of the 11 form: 12 13 (Pm + Pb)/Sm adjusted = [(Pm + Pb)/Sm] x [0.9817 + 0.4311 x Pm/(Pm + Pb)]

14 15 which varies from ~1 for pure bending loading (Pm/(Pm + Pb) = 0) to ~1.4 for pure 16 membrane loading (Pm/(Pm + Pb) = 1).

17 18 Plotting the test results in this manner yields a monotonic trend with relatively little 19 scatter, indicating that CF% is a reasonable parameter for characterization of the effect of 20 cracking on pipe failure load, at least for the configurations tested.

21 DRAFT Page 16 of 26 1/11/07 1 3.3 Development of Fragility Curve 2 Also shown on Figure 3-5 is a power law fit of the data:

3 4 (Pm + Pb)/Sm = 0.4061 (CF)-1.4613 5 6 In order to develop a statistical distribution for this curve, residuals were calculated based 7 on the difference between the actual CF for each data point and that predicted by the 8 power law fit (CF - CFpredicted). The residuals were then sorted from lowest to highest, 9 and were found to be reasonably represented by a normal distribution, as illustrated in 10 Figure 3-6. CF% was selected as the dependent variable in this correlation, since applied 11 loading is the independent variable in the analysis (i.e. applied loads determined from the 12 plant loading distributions are used to determine critical CF% from Figures 3-5 and 3-6).

13 14 y = 0.0403x + 0.0027 R 2 = 0.9801-10.00%-8.00%-6.00%-4.00%-2.00%0.00%2.00%4.00%6.00%8.00%10.00%12.00%-2.50-2.00-1.50-1.00-0.500.000.501.001.502.002.50Norm Dist.CF% Residual 15 Figure 3 Normal Probability Plot of the CF% Residuals between Test Data and 16 Power-Law Curve in Figure 3-5 17 18 Consistent with the advanced FEA project, the applied loads are first multiplied by a Z-19 factor [5] before entering Figures 3-5 and 3-6 which accounts for potentially lower 20 toughness of Alloy-182 weldments relative to the austenitic base materials tested in the 21 pipe tests. J-Resistance testing of a typical Alloy-182 weldment showed little or no 22 reduction in toughness relative to the pipe test materials [5]. Sm for stainless steel base 23 metal at pressurizer operating temperature was used to normalize the plant loads.

24 DRAFT Page 17 of 26 1/11/07 1 The final step in developing the fragility curve was to perform Monte Carlo sampling 2 from the load distribution of Figure 3-2, and then independently sample the critical flaw 3 size distribution of Figures 3-5 and 3-6 for critical CF % for each load. Consideration 4 was given to occasionally sampling from the SSE distribution of Figure 3-3 (e.g. once in 5 every 1000 simulations), however, the two distributions are so close that this was judged 6 to have an insignificant effect. 1000 samples were performed, resulting in the critical 7 flaw size distribution shown in Figure 3-7. Both the sampling results and a Log-Normal 8 fit to the distribution are plotted. The Log-Normal fit was found to give a very accurate 9 representation of the fragility curve distribution. Parameters of the Log-Normal fit are 10 also listed in Figure 3-7.

11 12 13 0.000.10 0.200.300.40 0.500.600.700.800.90 1.000.00%10.00%20.00%30.00%40.00%50.00%60.00%70.00%80.00%90.00%100.00%CF % at FailureProbabilitySampled DataLognormal Dist.Parameters of Log-Normal Fit:Median CF% = 76.4%Mean (ln) = -.2748 Std. Dev. (ln) = .27215 R^2 of Fit = 0.9992 14 Figure 3 Resulting Fragility Curve and Associated Log-Normal Fit 15 16 17 One anomaly exists in the fragility curve in Figure 3-7: it yields a probability of failure of 18 less than one for CF = 100%, which is physically impossible. This effect results from 19 sampling the tails of the two distributions, which occasionally yields unrealistically small 20 applied loads or unrealistically high critical flaw sizes (For example, the right hand side 21 of the power law curve in Figure 3-5 doesn't go through zero.) However, this anomaly is 22 corrected in the Monte Carlo analyses of Section 5 by discarding and re-sampling any 23 trials in which the critical flaw size is predicted to be greater than 100%.

24 DRAFT Page 18 of 26 1/11/07 1 4 Crack Growth 2 3 4.1 Summary of Advanced FEA Results 4 The advanced FEA analyses addressed a total of 53 cases with variations of each 5 resulting in over 100 individual crack growth analyses. Over half of the analyses 6 demonstrated stable crack arrest prior to penetrating through-wall or reaching critical 7 size,. The remainder exhibited varying degrees of crack growth. The first 20 cases were 8 denoted base cases, and include cases that envelope all geometries and loads for the 51 9 Spring 2008 pressurizer nozzles. The 20 base cases and their resulting crack growth 10 rates, in terms of CF% per year are summarized in Table 4-1. (Note that a total of 22 11 analyses are actually reported in the table since two cases were run with two sets of weld 12 residual stresses each.) The crack growth rates naturally divide into two regimes: crack 13 growth from initial assumed flaw size until through wall (TW) penetration, denoted 14 "Rate1" in the table, and crack growth following TW penetration, denoted "Rate2".

15 Rate2 can be seen to be on average about an order of magnitude greater than Rate1, 16 indicating significant acceleration in crack growth once the assumed crack breaks 17 through and becomes through wall.

18 19 Another observation from Table 4-1 is that all but two base cases exhibit relatively small 20 pre-TW crack growth rates (~1%/yr < Rate1 < 3.5%/yr) with the exception of Case 6 21 (9.85%/yr) and Case 17 (14.97%/yr). A similar trend is seen in the post-TW growth rates 22 (Rate2), albeit at much higher rates. Thus for the geometries enveloped, the high crack 23 growth rates predicted for cases 6 and 17 are relatively rare. The remainder of the cases 24 (21 through 53) for the most part started with cases 6 and 17 and looked at the effect of 25 various analysis parameters and assumptions on these bounding cases. For this reason, it 26 was judged not appropriate to include these remaining cases in the statistical distribution 27 of crack growth rates, since they would bias the distribution very much to the high side.

28 Instead, only the base cases were used, but the spread in the distributions was combined 29 with the experimental scatter in crack growth rates from MRP-115 [6], as described in the 30 next section.

31 32 DRAFT Page 19 of 26 1/11/07 Table 4 Summary of Base Case Crack Growth Results from Advanced FEA Project [1]

Case Number Nozzle Type CF% Initial CF% @ TW Time to TW (yrs) Rate1 CF%/yr CF% @ 1GPM Time (days) Time to 1 GPM (yrs)

CF% @ LF =1.2 Time (yrs) Comb Time (yrs) Rate2 CF%/yr 1 S&R 10.00% 40.00% 17.4 1.72% 46.60% 114 0.312 56.80% 0.299 0.611 27.50% 2 S&R 10.00% 39.50% 21.3 1.38% 47.00% 142 0.389 57.40% 0.323 0.712 25.13% 3 S&R 10.00% 38.30% 26.3 1.08% 47.20% 182 0.499 58.00% 0.342 0.841 23.42% 4 S&R 10.00% 40.00% 18 1.67% 46.20% 107 0.293 55.80% 0.307 0.600 26.33% 5 S&R 10.00% 38.10% 25.7 1.09% 46.60% 180 0.493 57.40% 0.375 0.868 22.22% 6 S&R 10.00% 43.50% 3.4 9.85% 47.10% 31 0.085 52.90% 0.112 0.197 47.65% 7 S&R 10.00% 44.00% 10.5 3.24% 49.10% 70 0.192 57.30% 0.195 0.386 34.43% 8 S&R 10.00% 39.90% 13.4 2.23% 45.90% 94 0.258 55.30% 0.271 0.529 29.12% 9 S&R 10.00% 36.40% 32.2 0.82% 47.00% 229 0.627 58.60% 0.395 1.022 21.72% 10 spray 10.00% 38.90% 21.2 1.36% 49.70% 195 0.534 58.20% 0.200 0.734 26.29% 11 spray 10.00% 37.80% 25.3 1.10% 50.60% 260 0.712 58.70% 0.200 0.912 22.91% 12 spray 10.00% 43.60% 10.5 3.20% 50.70% 110 0.301 57.50% 0.132 0.433 32.11% 13 spray 10.00% 42.70% 13.6 2.40% 51.20% 130 0.356 58.20% 0.148 0.504 30.75% 14 spray Arrest 15 spray Arrest 16 spray Arrest 17a surge Arrest 17b surge 6.03% 24.00% 1.2 14.97% 24.30% 0 33.10% 0.096 0.096 94.90% 18a surge Arrest 18b surge 10.00% 49.90% 11.5 3.47% 52.30% 0 59.10% 0.118 0.118 78.09% 19 surge Arrest 20 surge Arrest Average 9.74% 39.77% 16.8 3.31% 46.77% 0.337 55.62% 0.234 0.571 36.17% Std. Dev. 1.03% 5.53% 8.8 3.92% 6.55% 0.214 6.43% 0.102 0.288 21.66% Maximum 10.00% 49.90% 32.2 14.97% 52.30% 0.712 59.10% 0.395 1.022 94.90% Minimum 6.03% 24.00% 1.2 0.82% 24.30% 0.000 33.10% 0.096 0.096 21.72%

DRAFT Page 20 of 26 1/11/07 4.2 Adaptation to Probabilistic Analysis The base case crack growth results identified in Section 4.1 were used to define statistical distributions of crack growth rates for the probabilistic analysis. Figure 4-1 presents the sorted data for pre- and post-penetration crack growth rates plotted versus cumulative probability. Bilinear fits to the data were developed for the two regions of each of the curves. These bilinear distributions properly characterize the dichotomy observed in the FEA results (i.e. about an 80% probability that the crack growth rate will be relatively small, and about a 20% probability of large crack growth rates as observed in Cases 6 and 17). The high portion of te crack growth distributions also extrapolate out to even higher crack growth rates than those predicted for Cases 6 and 17, thereby covering to some extent the remaining sensitivity cases that weren;t included in the distribution.

00.1 0.20.30.40.50.6 0.70.80.9 10.00%10.00%20.00%30.00%40.00%50.00%60.00%70.00%80.00%90.00%100.00%Rate (CF%/Yr)Cumulative ProbabilityRate 1 (before TWPenetration)Rate 2 (after TWPenetration)

`` Figure 4-1: Data for Pre- and Post-penetration Area Growth Rates Illustrating the Bilinear Nature of the Distributions.

The distributions in Figure 4-1 do not include the scatter in the crack growth rate itself; All the base case computations used the 75 th percentile of the MRP-155 crack growth rate distribution that describes material crack growth rate scatter (Figure 4-2).

DRAFT Page 21 of 26 1/11/07 0.000.250.500.751.000.101.0010.00CGR MultiplierProbabilityLogNormData Figure 4 MRP-115 Distribution Characterizing Material Crack Growth Rate Scatter for PWSCC in Alloy 182 Weld Metal

The material crack growth rate scatter needs to be combined with the above analytical distributions to obtain the overall statistical description of the crack growth rate. This was accomplished by Monte Carlo simulation employing the following steps:

1. Sample from the bilinear distributions of Figure 4-1.
2. Divide the sampled value by the ratio of the 75 th to the 50 th percentile of the MRP-115 distribution of Figure 4-2(i.e. adjust to the median).
3. Sample from the MRP distribution (with a median of 1 and lognormal shape parameter of 0.6069) to determine a multiplier for the analytical crack growth rate.
4. Multiply the sample from Step 2 by the sample from Step 3.

This provides a set of samples from which a cumulative distribution can be derived. The cumulative distribution for pre-TW penetration is shown in Figure 4-3 on lognormal scales (as data points) along with a lognormal distribution that was fit to the data. The line is seen to provide a good description to the Monte Carlo results. The constants describing the line are the parameters of the lognormal distribution of crack growth rate for pre-penetration.

DRAFT Page 22 of 26 1/11/07 2-1 0 1 2 30.10%1.00%10.00%100.00%CGR before TW Penetration (CF%/yr)Normal Dist Lognormal Parameters:Mean (ln) = -4.30984STD (ln) = 0.992779Median Growth Rate = 1.34%/yr Figure 4-3: Monte Carlo Simulation Results of Pre-TW Penetration Crack Growth Rates with Fitted Lognormal Line.

A similar analysis was performed for the post-TW penetration data. Figure 4-4 provides the corresponding results. 2-1 0 1 2 31.00%10.00%100.00%1000.00%CGR afterTW Penetration (CF%/year)Normal Dist.Lognormal Parameters:Mean(ln) = -1.49254STD (ln) = 0.745357Median Growth Rate = 22.48%/yr Figure 4-4: Monte Carlo Simulation of Post-TW Penetration Crack Growth Rates with Fitted Lognormal Line DRAFT Page 23 of 26 1/11/07 5 Monte Carlo Analysis Monte Carlo simulation was used to generate results of the probability of a nozzle failure as a function of time. 5.1 Methodology The following steps were used in each trial of the Monte Carlo simulation.

1. Sample crack size (CF%) from one of the flaw size distributions (Weibull, Log-Normal, Exponential) developed in Section 2. Truncate the CF at 100% (if the sampled CF is greater than 100%, then discard it and sample again). Separate Monte Carlo analyses were conducted for each of the distribution types, and results are presented for each.
2. Sample pre-penetration crack growth rate from a log-normal distribution using the same percentile as the sampled crack size (based on the observation that the larger cracks likely were associated with high crack growth rates, either due to material, high loads, or both). This crack growth rate was used for crack sizes up to CF = 40%, which corresponds to the mean crack size at through-wall penetration in Table 4-1.
3. Sample post-penetration crack growth rate from a lognormal distribution using an independent sample. This crack growth rate was used to grow cracks beyond CF=40%.
4. Sample Fragility CF. Truncate the Fragility CF at 100% (if the sampled Fragility CF is greater than 100%, then discard it and sample again).
5. Grow the cracks in steps of 6 months at a time for up to 18 months. The pre-penetration crack growth rate is used for cracks of size less than 40%. The post-penetration crack growth rate is used once the crack size exceeds 40%. (If the initial size of the sampled crack is greater than 40 %, it will always grow at the post-penetration rate.) Failure at a given time step (0, 6, 12, 18 months) is defined as the cracking CF exceeding the fragility CF.
6. Check for crack arrest. Probability of arrest is an input, and only applies to sampled cracks of initial size that are smaller than 40% CF. If the sampled crack is less than 40%,

a random sample is taken from the uniform distribution. If this sample is less than the probability of arrest, then that crack does not grow beyond 40% CF. This crack could still cause a failure if the sampled Fragility CF is less than the cracking CF. If the sampled crack size is greater than 40%, arrest is not assumed. Based on the results of the advanced FEA crack growth analyses, a probability of arrest = 0.57 was used in the Monte Carlo analyses.

7. The probability of failure is computed as the number of failures divided by the number of trials.

DRAFT Page 24 of 26 1/11/07 5.2 Cases Analyzed Monte Carlo results were generated for all three distribution types (Weibull, exponential, lognormal) for times up to the present and for 6, 12, and 18 months into the future. Since the majority of the inspection data reported in Table 2-1 were from 2006, and the Wolf Creek inspection findings were observed in Fall 2006, the inspection data were treated as a snapshot in time at end of the Fall 2006 outage season, and that date was assumed to be the present, or time = 0 in the time-based probability of failure results. 5.3 Results The results of the Monte Carlo simulations are presented in Table 5-1. 10 7 trials were used in each case. The cumulative probabilities are directly from the Monte Carlo simulation and are given for each of the three distribution-types. The incremental probabilities are the differences in the cumulative probabilities for each six-month time span. These correspond to the probability of a nozzle rupture (per nozzle) during each six-month time interval.

The number of nozzles column corresponds to the number of remaining, PWSCC-susceptible pressurizer nozzles that will not have been inspected or mitigated at the end of each outage season, assuming that the industry inspection plans are implemented. The next column reflects the number of plants containing those uninspected/unmitigated nozzles. The probability of a nozzle failure in the time increment is given by the expression Pnoz=1-(1-p 1)N , where p 1 is the incremental failure probability for a single nozzle and N is the number of nozzles. The per plant probability of a nozzle failure is then obtained by dividing by the number of plants in which those nozzles exist.

It may be observed from Table 5-1 that the incremental probabilities of nozzle failure are remaining about constant for each of the six month intervals, especially for the analyses performed with the Weibull and lognormal flaw distributions (which from Figure 2-1 were the better fits of the data). The analyses with the exponential distribution show some increase in incremental probability of failure versus time, but those start at much lower present values (time = 0), since the exponential fit produced less conservative extrapolations of probabilities of larger flaw sizes. Since the numbers of susceptible nozzles and plants are being removed from the population at a steady rate, the industry inspection plan results in an essentially constant probability of a nozzle failure per time interval, until the time when all nozzles will have been inspected or mitigated, at the end of the Spring 2008 outage season.

DRAFT Page 25 of 26 1/11/07 Table 5-1: Results of Monte Carlo Simulation Distribution/ Outage Season Time (months) Time Increment (months) Cumulative Prob. Incremental Prob. # Nozzles # Plants Nozzle Failure Probability Total per Plant Weibull Fall-06 0 7.57E-04 278 50 Spring-07 6 6 1.47E-03 7.13E-04 195 34 0.1299 0.0038 Fall-07 12 6 2.18E-03 7.09E-04 121 21 0.0822 0.0039 Spring-08 18 6 2.93E-03 7.49E-04 51 9 0.0375 0.0042 Log Normal Fall-06 0 1.12E-03 278 50 Spring-07 6 6 2.03E-03 9.09E-04 195 34 0.1624 0.0048 Fall-07 12 6 2.84E-03 8.17E-04 121 21 0.0941 0.0045 Spring-08 18 6 3.60E-03 7.56E-04 51 9 0.0379 0.0042 Exponential Fall-06 0 5.90E-06 278 50 Spring-07 6 6 7.03E-05 6.44E-05 195 34 0.0125 0.0004 Fall-07 12 6 2.59E-04 1.89E-04 121 21 0.0226 0.0011 Spring-08 18 6 6.58E-04 3.99E-04 51 9 0.0201 0.0022 DRAFT Page 26 of 26 1/11/07 6 Conclusions The following observations are apparent from the results of the probabilistic evaluation presented in Table 5-1:

  • Pressurizer nozzle failure probabilities (per plant, per six months) for the Spring-08 Plants are approximately the same as what has existed in PWRs due to PWSCC susceptible pressurizer nozzles during the Fall and Spring of 2007 (on the order of 4 x 10

-3 per plant, per six months).

  • The absolute failure probabilities (on the order of 8 x 10

-3 per plant, per year) are greater than the generally accepted 1 x 10

-3 per plant, per year. However, these results assume no leakage or plant response to leakage. For comparison to pipe break probability limits, they should be factored by the probability of non-Leak-Before-Break (or failure to react to leakage) from the advanced FEA analysis, which was shown to be very small.

  • If there is just a 90% probability that leakage would be detected (i.e. a 10% or less probability that it would be missed), then the predicted failure probabilities are within the generally accepted limits. Since essentially all cases evaluated in the advanced FEA analysis demonstrated leak before break, including agreed upon margins on load, leak rate and time to failure, the probability of a significant crack/leak in one of these nozzles going undetected is considered to be much less than 10%.

Therefore, it is concluded that there is no significant risk benefit to accelerating the scheduled Spring 2008 inspections.

7 References

1. DEI Advanced FEA Program Report
2. MRP-139 3. NUREG/CR-4082, Volume 8, "Summary of Technical Results and Their Significance to Leak-Before-Break and In-Service Flaw Acceptance Criteria, March 1984- January 1989
4. Pipe Fracture Encyclopedia, U.S. NRC, 1997 (A collection of NUREG Reports and Data Files from the DP2 and other programs distributed on CDs)
5. G. Wilkowski et al, "Determination of the Elastic-Plastic Fracture Mechanics Z-Factor for Alloy 82/182 Weld Metal Flaws for Use in the ASME Section XI Appendix C Flaw Evaluation Procedures", (Draft) ASME PVP2007-26733
6. MRP-115
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