Journal of Mechanical Science and Technology 26 (7) (2012) 2055~2058

www.springerlink.com/content/1738-494x DOI 10.1007/s12206-012-0514-4

Benchmark analysis on PFM analysis codes

for aged piping of nuclear power plants† Hiroto Itoh1, Yinsheng Li1,*, Kazuya Osakabe2, Kunio Onizawa3 and Shinobu Yoshimura4

1Japan Nuclear Energy Safety Organization, 4-1-28 Toranomon, Minato-ku, Tokyo, 105-0001, Japan 2Mizuho Information & Research Institute, Chiyoda-ku, Tokyo, 101-8443, Japan

3Japan Atomic Energy Agency, Tokai, Ibaraki, 319-1195, Japan 4The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

(Manuscript Received February 22, 2012; Revised March 16, 2012; Accepted April 10, 2012)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract Probabilistic fracture mechanics is a rational methodology in structural reliability evaluation and risk assessment for aged piping in nu-

clear power plants. Several probabilistic fracture mechanical analysis codes have been improved or developed in Japan. To verify the reliability and applicability of two of these codes, we did a benchmark analysis using their basic functions in consideration of representa-tive piping systems in nuclear power plants and typical aging mechanisms. Based on the analysis results, we concluded that the analysis results of these two codes are in good agreement.

Keywords: Aged piping; Benchmark analysis; Probabilistic fracture mechanics; Stress corrosion cracking ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction

About one-third of the nuclear power plants in Japan have been operating for more than 30 years, and during this time some flaws have been detected within some of these plants’ piping systems. Therefore, structural reliability evaluation and risk assessment of such aged piping have become increasingly important. Probabilistic fracture mechanics (PFM) is recog-nized as a rational methodology for evaluating structural reli-ability and assessing the risk of aged piping because it can take the influence parameters into consideration with their inherent probabilistic distributions. Several PFM analysis codes for aged piping have been developed in Japan: one such code, PRAISE-JNES [1], was improved by JNES (Japan Nu-clear Energy Safety Organization) based on pc-PRAISE [2], and another is PASCAL-SP [3] which was developed at JAEA (Japan Atomic Energy Agency). Although these two codes were developed for different purposes, both have the same basic functions for conducting failure probability analy-ses of piping.

In this study, we conducted a benchmark analysis on PRAISE-JNES and PASCAL-SP using their basic functions to verify their reliability and applicability to the failure prob-ability analysis of aged nuclear piping. As the analysis exam-

ple, the primary loop recirculation system (PLR) piping in the boiling water reactor (BWR) plant was selected. Stress corro-sion cracking (SCC) and fatigue crack growth were consid-ered to be the typical aging mechanisms. Among the input parameters, pipe size and the amount of seismic stress were treated as the major variables in the case studies. The analysis results on pipe failure probabilities were compared as a func-tion of operation years.

2. PFM codes for benchmark analysis

PRAISE-JNES and PASCAL-SP were used to evaluate failure probabilities for aged piping by Monte Carlo methods. Each code was developed for a specific purpose. For example, PRAISE-JNES [1] has been improved primarily to evaluate the seismic safety margin of aged components as well as to provide information on fragilities for seismic PSA and seismic risk assessment related to huge earthquakes. Several analysis models that consider the response of seismic motion and its uncertainty as well as the crack growth due to seismic stress are included. When the analysis is conducted, the crack is sampled in consideration of its location and the crack size distribution at first. Next, the crack growth is calculated in consideration of the aging mechanisms, such as SCC and fa-tigue, in addition to the stress conditions, including residual stress, seismic response stress and their uncertainties. If a pre-service inspection (PSI) or in-service inspection (ISI) is per-formed, the probability of crack detection is evaluated in con-

*Corresponding author. Tel.: +81 3 4511 1542, Fax.: +81 3 4511 1598 E-mail address: li-yinsheng@jnes.go.jp

† This paper was presented at the ICMR2011, Busan, Korea, November 2011. Recommended by Guest Editor Dong-Ho Bae © KSME & Springer 2012

2056 H. Itoh et al. / Journal of Mechanical Science and Technology 26 (7) (2012) 2055~2058

sideration of the type and size of the crack as well as the de-tection performance of the non-destructive test team. If the crack grows through the wall thickness, the leak rate will be calculated. If the applied stress exceeds the failure stress based on the elastic-plastic fracture mechanics or net-section col-lapse method, the pipe will be recognized as failure. Finally, the results of the leak and failure probabilities are obtained by Monte Carlo methods.

PASCAL-SP [3] was developed as an original Japanese code in order to contribute to the provision of probabilistic considerations as well as to serve as a technical basis for pos-sible revisions to codes and standards in Japan. Several analy-sis models original to Japan are considered. As the important driving force for SCC growth, the probabilistic analysis model of residual stress has also been incorporated in a sophisticated way considering the uncertainties.

Although these codes were originally developed for differ-ent purposes as described above, both have nearly identical basic functions and probabilistic models (such as those for initial crack distributions, crack growth rates due to SCC and fatigue, and failure criteria), which are based on the models published for or prescribed in the Japanese regulations and standards [4, 5]. In this study, benchmark analyses were con-ducted using those functions of these two codes.

3. Analysis conditions of the benchmark analysis

The PLR piping in the BWR plant has been selected to serve as the representative example. SCC and fatigue are con-sidered to be the typical aging mechanisms. A crack due to SCC detected in a PLR piping can be illustrated in Fig. 1. The crack initiates in the heat-affected zone (HAZ) of the weld joints. L is the distance between the location of the initiated SCC and the fusion line of the weld metal. The crack can be characterized as a semi-elliptical shape according to the JSME Code [5]. Crack size distribution models proposed by Ma-chida [6] based on measured data from actual PLR pipes were used in the two codes. In his study, the distribution of crack depth, a, was represented as a normal distribution. For the half length, c, of the semi-elliptical surface crack, a log-normal distribution was proposed.

The crack initiated in a PLR pipe first grows in the HAZ, as shown in Fig. 1. After it exceeds a depth of dc, it may expand into the weld metal. The data on the relationship between L and dc is taken from the NISA (Nuclear and Industrial Safety Agency) report [4] and shown in Fig. 2. Based on the data shown in Fig. 2, the relationship between L and dc was ob-tained as follows, as the result of a statistical analysis:

c cd L L= + (1)

where L and Lc represent normal distributions. The mean value and the standard deviation of L are 2.246 mm and 2.152 mm, and the mean value and the standard deviation of Lc are 3.017 mm and 1.314 mm, respectively.

For cracks initiated in PLR pipes, the deterministic crack growth rate due to SCC and fatigue can be evaluated in accor-dance with the NISA report [4]. Based on the data provided in the JSME Code [5], the probabilistic model of the crack growth rate due to SCC was obtained from statistical analysis. The crack growth rate was represented in units of m/s as fol-lows:

m

sda C Kdt

= (2)

where K is the stress intensity factor in units of MPa√m, m is the exponent of the crack growth rate and CS is evaluated as a probabilistic variable following log-normal distribution. If the crack tip is located in the HAZ of the weld joints under the BWR normal water environment, the median value of CS is 9.27 × 10−14 and the standard deviation of ln (CS) is 0.2167. The maximum crack growth rate is 9.2 × 10−10 m/s and the minimum one is 2.0 × 10−12 m/s. If the crack tip is located in the weld metal of the weld joints under the BWR normal wa-ter environment, the median value of CS is 7.04 × 10−15 and the standard deviation of ln (CS) is 0.7983. The maximum crack growth rate is 2.1 × 10−10 m/s and the minimum one is 2.0 × 10−12 m/s.

Based on the data provided in the JSME Code, we also ob-tained a probabilistic model for fatigue crack growth rate. For austenitic stainless steel used in the BWR water environment, the fatigue crack growth rate can be expressed in units of m/cycle as follows:

0.5 3.0

2.12(1 )f rC t Kda

dN RΔ

=−

(3)

where ΔK is the stress intensity factor range in units of MPa√m, R is the stress ratio and Cf is evaluated as a probabil-

HAZ 溶接金属

Base metal

Outside of pipe

Inside of pipe

Weld metal

HAZ

SCC

L

dc

Fig. 1. Geometry of the weld joint and the location of the crack.

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10

L (mm)

d c (m

m)

Fig. 2. Relationship between L and dc.

H. Itoh et al. / Journal of Mechanical Science and Technology 26 (7) (2012) 2055~2058 2057

istic variable following log-normal distribution. The median value of Cf is 1.59 × 10−12 and the standard deviation of ln(Cf) is 0.355. tr is defined as the load increasing time in seconds. If the precise value is unclear, tr = 1000 s is assumed.

The failure criterion based on elastic-plastic fracture me-chanics in the JSME Code [5] was used for cracks existing in the weld joints of pipes. The load multiplier factor Z as a func-tion of the nominal outer diameter of the pipe was applied to determine the critical bending stress based on the net-section collapse criterion.

The base metal material of the PLR pipes under considera-tion is Type 316L low-carbon austenitic stainless steel. For the flow stress of Type 316L, the previously proposed [1] log-normal distribution based on the statistical analysis of experi-mental data was used. The median value of the flow stress σf is 302 MPa and the standard deviation of ln(σf) is 3.69 × 10−2. The stress intensity factor K provided in the JSME Code [5] was used, which is expressed by a third-order polynomial equation.

For PSI and ISI, the probability of crack detection proposed by Khaleel and Simonen [7] was applied. The detection prob-ability for ultrasonic testing was modeled by considering the diameter of the ultrasonic beam and so on. In this analysis, a parameter set for the outstanding level of detection perform-ance and crack type of SCC was used.

The nominal pipe sizes taken into account in this analysis are 300A and 400A, as listed in Table 1.

The stresses due to normal operating loads, transient stress-es, seismic stresses and residual stresses are shown in Table 1, Table 2, Table 3 and Fig. 3, respectively. In the benchmark analysis, seismic stress is hypothetically applied to the pipes to

calculate the effect of an earthquake at the time of evaluation. The stratified Monte Carlo simulation technique was used

in these analyses for both PRAISE-JNES and PASCAL-SP. The crack sampling numbers were in the range of approxi-mately 400,000 to 5000,000.

4. Analysis results

Based on the analysis conditions described above, the cu-mulative failure probabilities of PLR pipes in consideration of SCC and fatigue were calculated using PRAISE-JNES and PASCAL-SP. For 300A and 400A pipes, the relationships between the cumulative failure probabilities and the operation years are shown in Figs. 4 and 5, respectively.

Figs. 4 and 5 indicate that pipe failure probabilities increase as the operation years due to the progress of SCC and fatigue without PSI and ISI. When an earthquake is concerned, the

Table 1. Nominal pipe sizes and stresses used in this analysis. Nominal pipe size

Inner radius (mm)

Wall thickness (mm)

Internal pres-sure (MPa)

Membrane stress (MPa)

300A 141.9 17.4 9.0 66.9

400A 181.8 21.4 9.0 74.2

Table 2. Transient stresses used in this analysis.

Internal pressure (MPa)

Membrane stress (MPa) Pipe

size Event No.

Number of transients (40 years) Min. Max. Min. Max.

400A

1 2 3 4 5 6 7

40 85 85 85 85 85 300

0.00 0.00 1.18 1.18 0.15 0.00 9.00

7.83 7.43 9.00 1.18 1.18 0.15 9.00

3.7 4.5 20.3 15.6 8.4 4.5 72.3

35.6 70.4 76.0 20.3 15.6 8.4 76.1

300A

1 2 3 4 5 6 7

40 85 85 85 85 85 300

0.00 0.00 1.18 1.18 0.15 0.00 9.00

7.83 7.43 9.00 1.18 1.18 0.15 9.00

1.6 1.6 16.0 16.0 8.3 1.6 63.7

34.2 63.0 70.0 47.0 31.0 8.3 70.1

Table 3. Seismic stresses used in this analysis.

Seismic acceleration (gal)

Seismic stress (MPa)

Equivalent number of cyclic stress ( - )

450 90

750 150

1100 220

60

-300

-200

-100

0

100

200

300

400

500

0.0 0.2 0.4 0.6 0.8 1.0Distance from inner surface / Wall thickness (-)

Res

idua

l stre

ss (

MPa

) 300A pipe

400A pipe

Res

idua

lstre

ss (

MPa

)

Distance from inner surface/Wall thickness (-) Fig. 3. Residual stress distributions used in this analysis.

1.0E-10

1.0E-08

1.0E-06

1.0E-04

1.0E-02

.0E+00

0 5 10 15 20Operation time (year)

Cum

ulat

ive

failu

re p

roba

bilit

y

10-10

10-8

10-6

10-4

10-2

100

Cum

ulat

ive

failu

re p

roba

bilit

y (-

)

1100 gal

750 gal

450 gal

Without earthquake

PASCAL-SPPRAISE-JNES

1100 gal

750 gal

450 gal

Without earthquake

PASCAL-SPPRAISE-JNES

Fig. 4. Cumulative failure probabilities for 300A pipe.

2058 H. Itoh et al. / Journal of Mechanical Science and Technology 26 (7) (2012) 2055~2058

failure probabilities of cracked pipes increase with increasing seismic stresses.

For 300A pipe in consideration of the effects of PSI and ISI in its tenth year, the relationships between the cumulative failure probabilities and operation years are shown in Fig. 6. By comparing Fig. 6 with Fig. 4, it is found that the failure probabilities for the tenth year decrease by about one order of magnitude when PSI is considered. The effects of inspections on failure probabilities after 10 years become much greater when ISI is considered.

As previously described, these two codes were independ-ently developed by different organizations. Therefore, there are many differences in the simulation techniques, such as the algorithm for generating random numbers and the approach on the residual stress distribution. Despite these differences, it can be seen from Figs. 4 to 6 that there are only slight differ-ences between the analysis results from the two codes.

To date, many benchmark analyses have been conducted on PFM analysis codes for aged piping: for example NURBIM in EURATOM for nuclear piping integrity [8]. Compared to the differences among the numerical solutions obtained by differ-ent organizations using different analysis codes, as shown in these previous studies, the degree of the differences shown in Figs. 4 to 6 is sufficiently small. In particular, the results with high failure probabilities when the seismic motion is assumed to be 1100 gal agree very well for both codes in all cases. Therefore, considering the feature of the PFM, it can be con-

cluded that the failure probabilities obtained from the two codes are in good agreement.

5. Conclusions

Two PFM analysis codes, PRAISE-JNES and PASCAL-SP, which were developed by different Japanese organizations, were used to conduct a benchmark analysis by applying their common functions to verify their reliability and applicability. As the representative piping system, PLR pipes were analyzed in terms of cumulative failure probability as a function of op-eration years considering the typical ageing mechanisms, SCC and fatigue crack growth, and inspection. Based on the results of the benchmark analysis, we conclude that the analysis re-sults of the two analysis codes agree well for the analysis con-ditions under consideration.

References

[1] Y. Li, M. Nakagawa, K. Ebisawa, S. Yoshimura and H. Kameda, Failure probability of degraded pipes based on probabilistic fracture mechanics for seismic safety margin assessment on NPP, Proc. of ASME Pressure Vessels and Piping Division Conference, USA, PVP2010-25203 (2010).

[2] D. O. Harris and D. D. Dedhia, Theoretical and user’s man-ual for pc-PRAISE, NUREG/CR-5864 (1992).

[3] K. Onizawa, H. Nishikawa and H. Itoh, Development of probabilistic fracture mechanics analysis codes for reactor pressure vessels and piping considering welding residual stress, International Journal of Pressure Vessels and Piping, 87 (2010) 2-10.

[4] Nuclear and industrial safety agency, http://www.meti.go.jp/ report/downloadfiles/g41012a02j.pdf (in Japanese) (2004).

[5] JSME, Code for nuclear power generation facilities: Rules on fitness-for-service for nuclear power plants (in Japanese), JSME S NA1-2008, Tokyo (2008).

[6] H. Machida, Reliability assessment of PLR piping based on domestic SCC data, Proc. of ASME Pressure Vessels and Piping Division Conference, USA, PVP2007- 26059 (2007).

[7] M. A. Khaleel and F. A. Simonen et al., The impact of in-spection on intergranular stress corrosion cracking for stainless steel piping, Proc. of ASME Pressure Vessels and Piping Conference 296 (1995) 411-422.

[8] H. Schulz, T. Schimpfke and B. Brickstad et al., Final report on nuclear risk-based inspection methodology for passive components, NURBIM Final Report (ftp://ftp.cordis.europa.eu/ pub/fp5euratom/docs/nurbim_projrep_en.pdf) (2004).

Hiroto Itoh, received his Ph.D from Chuo University in 2000. He is a re-searcher in the Japan Nuclear Energy Safety Organization (JNES), Seismic Safety Division. His major subjects are structural integrity evaluation and risk assessment.

1.0E-10

1.0E-08

1.0E-06

1.0E-04

1.0E-02

1.0E+00

0 5 10 15 20Operation time (year)

Cum

ulat

ive

failu

re p

roba

bilit

y

10-10

10-8

10-6

10-4

10-2

100

Cum

ulat

ive

failu

re p

roba

bilit

y (-

)

1100 gal

750 gal

450 gal

Without earthquake

PASCAL-SPPRAISE-JNES

1100 gal

750 gal

450 gal

Without earthquake

PASCAL-SPPRAISE-JNES

Fig. 5. Cumulative failure probabilities for 400A pipe.

1.E-10

1.E-08

1.E-06

1.E-04

1.E-02

1.E+00

0 5 10 15 20Operation time (year)

Cum

ulat

ive

failu

re p

roba

bilit

y

10-10

10-8

10-6

10-4

10-2

100

Cum

ulat

ive

failu

re p

roba

bilit

y (-

)

1100 gal

750 gal

450 gal

Without earthquake

PASCAL-SPPRAISE-JNES

1100 gal

750 gal

450 gal

Without earthquake

PASCAL-SPPRAISE-JNES

Fig. 6. Cumulative failure probabilities for 300A pipe with PSI and ISI.