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Recent Japanese research activities on probabilistic fracture mechanics for pressure vessel and piping of nuclear power plant
International Journal of Pressure Vessels and Piping 87 (2010) 11–16
Contents lists available at ScienceDirect
International Journal of Pressure Vessels and Piping journal homepage: www.elsevier.com/locate/ijpvp
Recent Japanese research activities on probabilistic fracture mechanics for pressure vessel and piping of nuclear power plant Y. Kanto a, *, K. Onizawa b, H. Machida c, Y. Isobe d, S. Yoshimura e a
Department of Mechanical Engineering, Ibaraki University, Japan Nuclear Safety Research Center, Japan Atomic Energy Agency, Japan c TEPCO Systems Corporation, Japan d Nuclear Fuel Industries Ltd., Japan e The University of Tokyo, Japan b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 October 2008 Accepted 26 January 2009
This paper describes a review of recent Japanese activities on probabilistic fracture mechanics (PFM) analyses. Japan Atomic Energy Agency (JAEA: previously JAERI) had sponsored research committees on PFM organized by Japan Society of Mechanical Engineers (JSME) and Japan Welding Engineering Society (JWES) for more than a decade. This work still continues with the same members in JWES. The purpose of the continuous activity is to provide probabilistic approaches in several fields of integrity problems of nuclear power plant. This paper shows some of the newest results of the JWES research committee. First topic is evaluation of the new JSME code case with rules of Fitness-For-Service from the view of PFM, including reactor pressure vessel subject to pressurized thermal shock loading, piping with a crack of the allowable size and effect of sizing accuracy for piping integrity. The next one is development of new PFM techniques including reliability assessment of piping with domestic (Japanese) SCC data and maintenance optimization of LWRs based on risk and economic models. The last topic is the international round robin program just starting from 2008. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction In design and integrity evaluation processes for nuclear structural components, deterministic approaches have been mainly employed. All kinds of uncertainty related to operating history, material property change and damage mechanisms are taken into account in so-called safety factors. It is easily expected that the results obtained are too conservative to perform a rational evaluation of plant safety and to make judgment of life extension because of the accumulation of conservatism of all related factors. Probabilistic approaches have gained an important position in this area these days. Japan Atomic Energy Agency (JAEA: previously JAERI) had sponsored research committees on Probabilistic Fracture Mechanics (PFM) organized by Japan Society of Mechanical Engineers (JSME) and Japan Welding Engineering Society (JWES) for around two decades. This work still continues with almost the same members in JWES. The purpose of the continuous activity is to provide probabilistic approaches in several fields of integrity problems of nuclear power plant. These Japanese research activities
* Corresponding author. E-mail address: [email protected] (Y. Kanto). 0308-0161/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2009.11.010
on PFM before 2001 have been summarized in the previous paper [1] and summarized in Table 1. Here more recent activities are shown, such as evaluation of the new JSME code case from the view of PFM, reliability assessment with the domestic SCC data, combination of PFM and economic models, and the international round robin program newly planned among Asian countries. 2. Some recent results of Japanese research group 2.1. PFM evaluation of acceptable crack size in the new JSME code case A standard for screening small flaws which are detected by ultrasonic examination during ISI (In-Service Inspection) and have no significant influence on the structural integrity of class 1 vessel through plant life is prescribed in the flaw acceptance standard of ASME B&PV Code Sec. XI [3] and JSME Code SNA1-2002 [4]. Some concerns from the viewpoint of probabilistic methodology against the deterministic flaw acceptance standard in Sec. XI are whether or not the failure probability is uniform for each flaw with different aspect ratio, failure frequency is small enough, and how the nondetection probability of inspection compares against acceptable flaws. Furthermore, the use of probabilistic approaches in
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Y. Kanto et al. / International Journal of Pressure Vessels and Piping 87 (2010) 11–16
Table 1 Progress of PFM researches sponsored by JAEAa (formerly JAERI) (reproduced from Ref. [2]). Period
Executing organization
Components
1988–1990
JWESb PFM WG under LE sub-committee
RPV
Survey of existing PFM code and numerical and fracture mechanics models for PFM analysis PFM round robin analysis of RPV Research on numerical algorithm
1991
MRIc PFM committee
RPV Piping
Survey of input data Survey of analysis model
1992–1994
JSMEd RC111 committee
RPV Piping
Survey of input data Survey of analysis model and research on numerical algorithm Round robin analysis of RPV under operating load and PTS Round Robin Analysis of Piping
Proposal of a standard guideline for PFM analysis
1996–2000
JWES PFM sub-committee
RPV Piping SG
Refinement of PFM methodology: input seismic load, SIF database, treatment of embedded crack Application to ISI code Application to RII, cost/benefit analysis in inspection strategy Utilization of PASCAL by round robin analyses Survey of application in other fields, need in structural integrity issues in LWR components
Practical application to structural integrity issues of LWR components
2001–Present
JWESa PFM sub-committee
RPV Piping SG
Refinement of PFM methodology: input seismic load, SIF database, treatment of embedded crack Application to ISI code Application to RII, cost/benefit analysis in inspection strategy Utilization of PASCAL by round robin analyses Survey of application in other fields, need in structural integrity issues in LWR components
Practical application to structural integrity issues of LWR components
a b c d
Main activities
Remarks
PFM researches sponsored by JAERI were completed in 2000. PFM Sub-Committee in JWES has succeeded the research activities as a voluntary research. The Japan Welding Engineering Society. Mitsubishi Research Institute Incorporation. The Japan Society of Mechanical Engineers.
determining failure may provide more rational basis for the acceptable flaws. The failure probability based on the probabilistic approach may be a good index for determining the acceptable flaws. From the above points, the round robin analyses were carried out on the failure probability of an RPV with an initial flaw specified by the standard. Case studies were performed by different analysis conditions such as the influence of simulation method of semielliptical crack extension, material properties (Cu and Ni contents, and initial RTNDT), and so on. As a typical result, the influence of semi-elliptical crack extension method is shown in Fig. 1. Conditional failure probabilities of RPV were calculated under a severe
PTS loading with the acceptable size of initial flaws defined by ASME Sec. XI and JSME Code for various flaw aspect ratios. In the Method 1, the crack initiation and extension are evaluated at both the deepest and the surface points. On the other hand, in the Method 2, the crack initiation is only evaluated at the deepest point, and after the initiation, the semi-elliptical initial flaw is replaced by an infinite edge crack. As seen in the figure, Method 2 gives underestimation above aspect ratio of 0.6. It shows that the crack
Fig. 1. Conditional failure probability of RPV with an initial flaw by JSME Code [2].
Fig. 2. An example of defect sizing accuracy.
Y. Kanto et al. / International Journal of Pressure Vessels and Piping 87 (2010) 11–16
13
Table 2 Crack sizing performance parameters. Case
0
1
2
3
4
5
6
A0 A1 B0 B1
Without FFS
0.0 1.0 1.0 0.0
0.0 1.0 2.0 0.0
0.0 1.0 3.0 0.0
0.0 1.0 1.5 0.0
1.0 1.0 1.5 0.0
2.0 1.0 1.5 0.0
Case
7
8
9
10
11
12
13
A0 A1 B0 B1
3.0 1.0 1.5 0.0
1.0 0.9 1.5 0.0
1.0 0.8 1.5 0.0
1.0 0.7 1.5 0.0
1.0 1.0 1.5 0.1
1.0 1.0 1.5 0.2
1.0 1.0 1.5 0.3
initiation at the surface point becomes significant under a severe PTS loading above aspect ratio of 0.6. This result indicates that the fluctuation of failure probability depends on an applied transient and that the selection of a transient for determining the acceptable flaws is very important. Furthermore, non-uniform failure probabilities may suggest existence of the other optimal acceptable flaw size than those defined by ASME or JSME Codes. Fig. 4. Fitting curves of POD [9].
2.2. Reliability of nuclear power plant piping considering defect sizing accuracy Applying rules of ‘‘Fitness-for-Service (FFS)’’ determined in the new JSME Code [4], integrity of components with defects will be evaluated during some period decided by a plant user, and the nuclear power plant (NPP) will be operated continuously if the integrity of the flawed components is secured. When defects were detected in the NPP components, all the defects were repaired until FFS was established, and the structural integrity of the repaired portion was evaluated based on the Rules on Design and Construction of an NPP [5]. Consequently, the failure probability was calculated based on the scenario that all the detected defects will be repaired in the conventional PFM analysis. In such analyses, the effect of in-service inspection (ISI) on the failure probability was only considered as the probability of defect detection. However, since the plant will be operated continuously with the defect when the defect size is small enough to maintain the integrity of the components in case applying FFS, not only the probability of defect detection but also the defect sizing accuracy is important on the evaluation of reliability of the components. The failure probability might increase in case of low defect sizing accuracy, especially
Fig. 3. Relation between defect sizing accuracy and safety factor for leak probability (16 inches pipe) [7].
when thermal expansion stress – safety factor is not considered – is large. The effects of defect sizing accuracy on probability of failure are evaluated supposing the case when FFS is applied to the primary loop recirculation system (PLR) piping of BWR. SCC conditions are set using observed data in some BWR plants, and loading conditions are determined referring actual BWR operational experience. The defect sizing accuracy of the non-destructive tests can be defined as the difference between the recognized crack size and the actual crack size obtained by destructive observation. As a typical example, SCC cracks measured by ultrasonic test can be plotted as a function of the actual crack size as shown in Fig. 2 [6]. Lower accuracy will give a higher failure probability because of the existence of underestimated defects. However, since the safety factor (SF) is considered in the crack stability assessment in FFS, failure probability may not increase if the SF covers the defect sizing
Fig. 5. Postulated step function of POD curves [9].
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Y. Kanto et al. / International Journal of Pressure Vessels and Piping 87 (2010) 11–16
Fig. 6. Cumulative probability of 12 inches pipe for each POD curve with ISI in every 5 years [9].
accuracy. In this paper, the SF value was supposed from 1 to 3, and a mean value (m(a)) and standard deviation (s(a)) of the recognized crack size were supposed by linear function of the actual crack depth (a) as follows, and the parametric survey was performed for the parameters shown in Table 2.
mðaÞ [ A0 D A1 a
(1)
sðaÞ [ B0 D B1 a
(2)
The cumulative break probabilities are seldom influenced by the safety factor and defect sizing accuracy. On the other hand, the effect of the defect sizing accuracy appears greatly in leak probabilities, and the safety factor cannot cover influence of the defect sizing accuracy in many cases even if SF ¼ 3.0 as shown in Fig. 3.
Fig. 8. Evaluated costs for various inspection accuracies [10].
Fig. 7. Relation between percentage of oversight of a crack and cumulative failure probability (12 inches pipe, after 40 years operation) [9].
Fig. 9. Net Present Value for various inspection accuracies (I600 case) [10].
Y. Kanto et al. / International Journal of Pressure Vessels and Piping 87 (2010) 11–16
15
Fig. 11. Net Present Value for various inspection intervals (I600 case) [10].
NPP. Many studies on the crack detection performance by UT have been continuously carried out for the fatigue crack and the stress corrosion crack. The typical study in Japan is that which was performed by Japan Power Engineering and Inspection Corporation (JAPEIC) from 1995 to 2004; the detection performance and the sizing performance of the crack by UT were examined [8]. Fitting of the JAPEIC’s results to three equations has been carried out as shown in Fig. 4. In this evaluation, 40 years of plant operational life is assumed. Pre-service inspection (PSI) and in-service inspection (ISI) every 5 years by UT are performed. There is oversight of a crack in the inspection and oversight of a deep crack has a great influence on the failure probability. Then, failure probability is evaluated using postulated step function of POD curves shown in Fig. 5 in addition to the three POD curves to grasp the effect of detectable crack depth. From 0% to 5% of oversight probability of the crack is considered in the PFM analysis to grasp the effect of human error. Fig. 6 shows the cumulative probabilities of 12 inches pipe for each POD curve with ISI in every 5 years. The oversight in ISI is not considered in these analyses. The results of fitting equations are similar to those of the step function POD with the critical flaw size of 2 mm and 3 mm. This suggests that the estimation of effective detectable crack depth (POD z 100%) is more important than the slope of the estimate POD curves. The effect of the oversight probability in ISI on the failure probabilities after 40 years operation is shown in Fig. 7. If the oversight probability is greater than 0.5%, the reliability of piping scarcely depends on POD curves, but depends on the value of the oversight probability. This shows that Fig. 10. Evaluated costs for various inspection intervals [10].
2.3. Reliability of PLR piping based on domestic SCC data Many stress corrosion cracks have been observed in the weld joints of piping in primary loop recirculation system (PLR) of Japanese BWR from 2000. The crack is generated in heat affected zone (HAZ) and propagates into weld metal. For this reason, detection of the stress corrosion crack is difficult comparing with the fatigue crack, and some examples of oversight of a comparatively large crack have been reported. Since performance of detection of the crack greatly depends on the inspector’s skill, accessibility, etc., the relationship between the crack size and the probability of detection has to be taken into consideration in reliability assessment of the flawed pipe. Ultrasonic testing (UT) is used for Non-destructive test (NDT) for the weld joint of piping in an
Fig. 12. Three inspection models to be used in the sensitivity analyses.
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Y. Kanto et al. / International Journal of Pressure Vessels and Piping 87 (2010) 11–16
Table 3 Parameters for sensitivity analyses for POD.
No inspection (base) C: marginal B: good A: very good
Ac
PODmax
– 24 mm 12 mm 6 mm
0.0 0.75 0.85 0.95
the oversight probability is more important than the slope of the estimate POD curves, as well. From these results, POD curve could be expressed using simple function like a step or lamp curve considering detectable crack depth and oversight probability, because the reliability of piping scarcely depends on slope of POD curves. 2.4. Maintenance optimization of LWRs based on PFM analysis A number of PSA (Probabilistic Safety Assessment) studies have been applied to the optimization of maintenance activities in nuclear power plants from a viewpoint of safety focusing on the risks of core meltdown. However, even a small-scale incident of component, which never causes the core meltdown, resulted in the reactor shutdown and economic losses. The economic losses due to this kind of incident become enormous when including the losses that are not officially counted. Accordingly, in addition to the safety analysis focusing on the risk of core meltdown, it is very practical and useful to establish a model that can plan maintenance strategies in terms of availability and economic efficiency of nuclear power plants. With the background above mentioned, an integrated simulator for the maintenance optimization of LWRs based on PFM has been developed [10]. The concept of the simulator is to provide a method to optimize maintenance activities for representative components and piping systems in nuclear power plants totally and quantitatively in terms of safety, availability and economic efficiency (both from cost and profit). As an example of application of the model, it was applied to the maintenance of Inconel 600 SG tubes in PWRs for the purpose of quantitative evaluation of effectiveness of various maintenance strategies, including inspection accuracies (Figs. 8 and 9), inspection intervals (Figs. 10 and 11). Fig. 8 shows the change of cost with various inspection accuracies, (a) D40 (Base), (b) D20(Better), (c) D10(Best). The cost for leakage failure is the most of the total cost, and reduces very much with higher inspection accuracy. The Net Present Value (NPV) as an important financial index is also evaluated as shown in Fig. 9. The better inspection could increase the benefit in spite of higher cost of inspection because of lower failure probability. The longer interval of inspection will increase the rupture cost but scarcely affect the leakage cost as shown in Fig. 10. In spite of the increase of the total cost, the NPV increases because of the increase of net operation hours as shown in Fig. 11. 3. International round robin analysis program Some round robin analysis programs were conducted in the Japanese research group repeatedly to evaluate the precision of PFM programs and to raise the level of analyzers’ technique in two decades. The international round robin program in Asian countries
was planned to develop international communication and cooperation of PFM technique in this area where the nuclear power development seems to be activated rapidly. The object of the newly planned RR problem is to evaluate inspection effects for failure probabilities at PTS event of pressure vessel. Sensitivity analyses will be conducted on (1) the level of maximum probability of detection (PODmax), (2) the critical crack size (Ac) and (3) the timing and frequency of inspection. POD curves and values of above parameters used in the analysis are shown in Fig. 12 and Table 3. The base problem is to evaluate failure probabilities of a pressure vessel at PTS event. Temperature transients employed here are PTS and SGTR, which were used in the previous NRC/EPRI benchmark problem. Several other problems are set and provided to research groups in Korea, Taiwan and Japan. JAEA solved a part of the problems in advance by using PASCAL ver. 2 [11] (updated from PASCAL ver. 1 [2]) and is giving some advises to the groups. 4. Concluding remarks Recent activities of Japanese PFM research group are summarized. Around 20 years research efforts started from literature survey have produced fruitful results and several original PFM programs. These activities have extended the field of PFM applications to many components and problems in nuclear power plants, and up to economic based analysis. These results show that PFM could provide a rational index for complicated and uncertain problems and could be usefully utilized to optimize some decision making. Several round robin analysis programs were conducted to raise the level of knowledge and experience of new PFM techniques among the members of the group. This effort is still continuing and extended to the international research groups of Korea and Taiwan in 2008. References [1] Yagawa G, Kanto Y, Yoshimura S, Shibata K. Recent research activity of probabilistic fracture mechanics for nuclear structural components in Japan. In: 16th International conference on structural mechanics in reactor technology, MG01/5, 455, Washington DC, USA; Aug 2001. [2] Shibata K, Kanto Y, Yoshimura S, Yagawa G. Recent Japanese probabilistic fracture mechanics researches related to failure probability of aged RPV. Solid State Phenomena 2007;120:49–67. [3] ASME boiler and pressure vessel code section XI, rules for in-service inspection of nuclear power plant components; 2001. [4] Code for nuclear power generation facilities – rules on fitness for service for nuclear power plants. JSME S NA1; 2002. [5] Code for nuclear power generation facilities – rules on fitness for service for nuclear power plants. JSME S NC1; 2005. [6] Ultrasonic test & evaluation for maintenance standards. 2002 FY report, Japan Power Engineering and Inspection Corporation; 2002. [7] Machida H. Study on reliability of nuclear power plant piping considering defect sizing accuracy. ASME PVP2006-ICPVT11-93775; July 2006. [8] Development on standards and guides for formation of up-graded inspection system on NPP – ultrasonic test & evaluation for maintenance standards – synthesis report. Japan Nuclear Energy Safety Organization (JNES); April 2005. [9] Machida H. Reliability assessment of PLR piping based on domestic SCC data. In: Proc. ASME PVP-2007; July 2007. [10] Yoshimura S, Furuta K, Isobe Y, Sagisaka M, Noda M, Wada T, et al. Integrated maintenance optimization of LWRs based on PFM analysis. In: Kanda, Takeda, Furuta, editors. Applications of statistics and probability in civil engineering; 2007. [11] Onizawa K, Osakabe K, Shibata K, Suzuki M. Structural integrity analysis of reactor pressure vessel using probabilistic fracture mechanics analysis code. PROSIR WS; 2006.
Contents lists available at ScienceDirect
International Journal of Pressure Vessels and Piping journal homepage: www.elsevier.com/locate/ijpvp
Recent Japanese research activities on probabilistic fracture mechanics for pressure vessel and piping of nuclear power plant Y. Kanto a, *, K. Onizawa b, H. Machida c, Y. Isobe d, S. Yoshimura e a
Department of Mechanical Engineering, Ibaraki University, Japan Nuclear Safety Research Center, Japan Atomic Energy Agency, Japan c TEPCO Systems Corporation, Japan d Nuclear Fuel Industries Ltd., Japan e The University of Tokyo, Japan b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 October 2008 Accepted 26 January 2009
This paper describes a review of recent Japanese activities on probabilistic fracture mechanics (PFM) analyses. Japan Atomic Energy Agency (JAEA: previously JAERI) had sponsored research committees on PFM organized by Japan Society of Mechanical Engineers (JSME) and Japan Welding Engineering Society (JWES) for more than a decade. This work still continues with the same members in JWES. The purpose of the continuous activity is to provide probabilistic approaches in several fields of integrity problems of nuclear power plant. This paper shows some of the newest results of the JWES research committee. First topic is evaluation of the new JSME code case with rules of Fitness-For-Service from the view of PFM, including reactor pressure vessel subject to pressurized thermal shock loading, piping with a crack of the allowable size and effect of sizing accuracy for piping integrity. The next one is development of new PFM techniques including reliability assessment of piping with domestic (Japanese) SCC data and maintenance optimization of LWRs based on risk and economic models. The last topic is the international round robin program just starting from 2008. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction In design and integrity evaluation processes for nuclear structural components, deterministic approaches have been mainly employed. All kinds of uncertainty related to operating history, material property change and damage mechanisms are taken into account in so-called safety factors. It is easily expected that the results obtained are too conservative to perform a rational evaluation of plant safety and to make judgment of life extension because of the accumulation of conservatism of all related factors. Probabilistic approaches have gained an important position in this area these days. Japan Atomic Energy Agency (JAEA: previously JAERI) had sponsored research committees on Probabilistic Fracture Mechanics (PFM) organized by Japan Society of Mechanical Engineers (JSME) and Japan Welding Engineering Society (JWES) for around two decades. This work still continues with almost the same members in JWES. The purpose of the continuous activity is to provide probabilistic approaches in several fields of integrity problems of nuclear power plant. These Japanese research activities
* Corresponding author. E-mail address: [email protected] (Y. Kanto). 0308-0161/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2009.11.010
on PFM before 2001 have been summarized in the previous paper [1] and summarized in Table 1. Here more recent activities are shown, such as evaluation of the new JSME code case from the view of PFM, reliability assessment with the domestic SCC data, combination of PFM and economic models, and the international round robin program newly planned among Asian countries. 2. Some recent results of Japanese research group 2.1. PFM evaluation of acceptable crack size in the new JSME code case A standard for screening small flaws which are detected by ultrasonic examination during ISI (In-Service Inspection) and have no significant influence on the structural integrity of class 1 vessel through plant life is prescribed in the flaw acceptance standard of ASME B&PV Code Sec. XI [3] and JSME Code SNA1-2002 [4]. Some concerns from the viewpoint of probabilistic methodology against the deterministic flaw acceptance standard in Sec. XI are whether or not the failure probability is uniform for each flaw with different aspect ratio, failure frequency is small enough, and how the nondetection probability of inspection compares against acceptable flaws. Furthermore, the use of probabilistic approaches in
12
Y. Kanto et al. / International Journal of Pressure Vessels and Piping 87 (2010) 11–16
Table 1 Progress of PFM researches sponsored by JAEAa (formerly JAERI) (reproduced from Ref. [2]). Period
Executing organization
Components
1988–1990
JWESb PFM WG under LE sub-committee
RPV
Survey of existing PFM code and numerical and fracture mechanics models for PFM analysis PFM round robin analysis of RPV Research on numerical algorithm
1991
MRIc PFM committee
RPV Piping
Survey of input data Survey of analysis model
1992–1994
JSMEd RC111 committee
RPV Piping
Survey of input data Survey of analysis model and research on numerical algorithm Round robin analysis of RPV under operating load and PTS Round Robin Analysis of Piping
Proposal of a standard guideline for PFM analysis
1996–2000
JWES PFM sub-committee
RPV Piping SG
Refinement of PFM methodology: input seismic load, SIF database, treatment of embedded crack Application to ISI code Application to RII, cost/benefit analysis in inspection strategy Utilization of PASCAL by round robin analyses Survey of application in other fields, need in structural integrity issues in LWR components
Practical application to structural integrity issues of LWR components
2001–Present
JWESa PFM sub-committee
RPV Piping SG
Refinement of PFM methodology: input seismic load, SIF database, treatment of embedded crack Application to ISI code Application to RII, cost/benefit analysis in inspection strategy Utilization of PASCAL by round robin analyses Survey of application in other fields, need in structural integrity issues in LWR components
Practical application to structural integrity issues of LWR components
a b c d
Main activities
Remarks
PFM researches sponsored by JAERI were completed in 2000. PFM Sub-Committee in JWES has succeeded the research activities as a voluntary research. The Japan Welding Engineering Society. Mitsubishi Research Institute Incorporation. The Japan Society of Mechanical Engineers.
determining failure may provide more rational basis for the acceptable flaws. The failure probability based on the probabilistic approach may be a good index for determining the acceptable flaws. From the above points, the round robin analyses were carried out on the failure probability of an RPV with an initial flaw specified by the standard. Case studies were performed by different analysis conditions such as the influence of simulation method of semielliptical crack extension, material properties (Cu and Ni contents, and initial RTNDT), and so on. As a typical result, the influence of semi-elliptical crack extension method is shown in Fig. 1. Conditional failure probabilities of RPV were calculated under a severe
PTS loading with the acceptable size of initial flaws defined by ASME Sec. XI and JSME Code for various flaw aspect ratios. In the Method 1, the crack initiation and extension are evaluated at both the deepest and the surface points. On the other hand, in the Method 2, the crack initiation is only evaluated at the deepest point, and after the initiation, the semi-elliptical initial flaw is replaced by an infinite edge crack. As seen in the figure, Method 2 gives underestimation above aspect ratio of 0.6. It shows that the crack
Fig. 1. Conditional failure probability of RPV with an initial flaw by JSME Code [2].
Fig. 2. An example of defect sizing accuracy.
Y. Kanto et al. / International Journal of Pressure Vessels and Piping 87 (2010) 11–16
13
Table 2 Crack sizing performance parameters. Case
0
1
2
3
4
5
6
A0 A1 B0 B1
Without FFS
0.0 1.0 1.0 0.0
0.0 1.0 2.0 0.0
0.0 1.0 3.0 0.0
0.0 1.0 1.5 0.0
1.0 1.0 1.5 0.0
2.0 1.0 1.5 0.0
Case
7
8
9
10
11
12
13
A0 A1 B0 B1
3.0 1.0 1.5 0.0
1.0 0.9 1.5 0.0
1.0 0.8 1.5 0.0
1.0 0.7 1.5 0.0
1.0 1.0 1.5 0.1
1.0 1.0 1.5 0.2
1.0 1.0 1.5 0.3
initiation at the surface point becomes significant under a severe PTS loading above aspect ratio of 0.6. This result indicates that the fluctuation of failure probability depends on an applied transient and that the selection of a transient for determining the acceptable flaws is very important. Furthermore, non-uniform failure probabilities may suggest existence of the other optimal acceptable flaw size than those defined by ASME or JSME Codes. Fig. 4. Fitting curves of POD [9].
2.2. Reliability of nuclear power plant piping considering defect sizing accuracy Applying rules of ‘‘Fitness-for-Service (FFS)’’ determined in the new JSME Code [4], integrity of components with defects will be evaluated during some period decided by a plant user, and the nuclear power plant (NPP) will be operated continuously if the integrity of the flawed components is secured. When defects were detected in the NPP components, all the defects were repaired until FFS was established, and the structural integrity of the repaired portion was evaluated based on the Rules on Design and Construction of an NPP [5]. Consequently, the failure probability was calculated based on the scenario that all the detected defects will be repaired in the conventional PFM analysis. In such analyses, the effect of in-service inspection (ISI) on the failure probability was only considered as the probability of defect detection. However, since the plant will be operated continuously with the defect when the defect size is small enough to maintain the integrity of the components in case applying FFS, not only the probability of defect detection but also the defect sizing accuracy is important on the evaluation of reliability of the components. The failure probability might increase in case of low defect sizing accuracy, especially
Fig. 3. Relation between defect sizing accuracy and safety factor for leak probability (16 inches pipe) [7].
when thermal expansion stress – safety factor is not considered – is large. The effects of defect sizing accuracy on probability of failure are evaluated supposing the case when FFS is applied to the primary loop recirculation system (PLR) piping of BWR. SCC conditions are set using observed data in some BWR plants, and loading conditions are determined referring actual BWR operational experience. The defect sizing accuracy of the non-destructive tests can be defined as the difference between the recognized crack size and the actual crack size obtained by destructive observation. As a typical example, SCC cracks measured by ultrasonic test can be plotted as a function of the actual crack size as shown in Fig. 2 [6]. Lower accuracy will give a higher failure probability because of the existence of underestimated defects. However, since the safety factor (SF) is considered in the crack stability assessment in FFS, failure probability may not increase if the SF covers the defect sizing
Fig. 5. Postulated step function of POD curves [9].
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Y. Kanto et al. / International Journal of Pressure Vessels and Piping 87 (2010) 11–16
Fig. 6. Cumulative probability of 12 inches pipe for each POD curve with ISI in every 5 years [9].
accuracy. In this paper, the SF value was supposed from 1 to 3, and a mean value (m(a)) and standard deviation (s(a)) of the recognized crack size were supposed by linear function of the actual crack depth (a) as follows, and the parametric survey was performed for the parameters shown in Table 2.
mðaÞ [ A0 D A1 a
(1)
sðaÞ [ B0 D B1 a
(2)
The cumulative break probabilities are seldom influenced by the safety factor and defect sizing accuracy. On the other hand, the effect of the defect sizing accuracy appears greatly in leak probabilities, and the safety factor cannot cover influence of the defect sizing accuracy in many cases even if SF ¼ 3.0 as shown in Fig. 3.
Fig. 8. Evaluated costs for various inspection accuracies [10].
Fig. 7. Relation between percentage of oversight of a crack and cumulative failure probability (12 inches pipe, after 40 years operation) [9].
Fig. 9. Net Present Value for various inspection accuracies (I600 case) [10].
Y. Kanto et al. / International Journal of Pressure Vessels and Piping 87 (2010) 11–16
15
Fig. 11. Net Present Value for various inspection intervals (I600 case) [10].
NPP. Many studies on the crack detection performance by UT have been continuously carried out for the fatigue crack and the stress corrosion crack. The typical study in Japan is that which was performed by Japan Power Engineering and Inspection Corporation (JAPEIC) from 1995 to 2004; the detection performance and the sizing performance of the crack by UT were examined [8]. Fitting of the JAPEIC’s results to three equations has been carried out as shown in Fig. 4. In this evaluation, 40 years of plant operational life is assumed. Pre-service inspection (PSI) and in-service inspection (ISI) every 5 years by UT are performed. There is oversight of a crack in the inspection and oversight of a deep crack has a great influence on the failure probability. Then, failure probability is evaluated using postulated step function of POD curves shown in Fig. 5 in addition to the three POD curves to grasp the effect of detectable crack depth. From 0% to 5% of oversight probability of the crack is considered in the PFM analysis to grasp the effect of human error. Fig. 6 shows the cumulative probabilities of 12 inches pipe for each POD curve with ISI in every 5 years. The oversight in ISI is not considered in these analyses. The results of fitting equations are similar to those of the step function POD with the critical flaw size of 2 mm and 3 mm. This suggests that the estimation of effective detectable crack depth (POD z 100%) is more important than the slope of the estimate POD curves. The effect of the oversight probability in ISI on the failure probabilities after 40 years operation is shown in Fig. 7. If the oversight probability is greater than 0.5%, the reliability of piping scarcely depends on POD curves, but depends on the value of the oversight probability. This shows that Fig. 10. Evaluated costs for various inspection intervals [10].
2.3. Reliability of PLR piping based on domestic SCC data Many stress corrosion cracks have been observed in the weld joints of piping in primary loop recirculation system (PLR) of Japanese BWR from 2000. The crack is generated in heat affected zone (HAZ) and propagates into weld metal. For this reason, detection of the stress corrosion crack is difficult comparing with the fatigue crack, and some examples of oversight of a comparatively large crack have been reported. Since performance of detection of the crack greatly depends on the inspector’s skill, accessibility, etc., the relationship between the crack size and the probability of detection has to be taken into consideration in reliability assessment of the flawed pipe. Ultrasonic testing (UT) is used for Non-destructive test (NDT) for the weld joint of piping in an
Fig. 12. Three inspection models to be used in the sensitivity analyses.
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Y. Kanto et al. / International Journal of Pressure Vessels and Piping 87 (2010) 11–16
Table 3 Parameters for sensitivity analyses for POD.
No inspection (base) C: marginal B: good A: very good
Ac
PODmax
– 24 mm 12 mm 6 mm
0.0 0.75 0.85 0.95
the oversight probability is more important than the slope of the estimate POD curves, as well. From these results, POD curve could be expressed using simple function like a step or lamp curve considering detectable crack depth and oversight probability, because the reliability of piping scarcely depends on slope of POD curves. 2.4. Maintenance optimization of LWRs based on PFM analysis A number of PSA (Probabilistic Safety Assessment) studies have been applied to the optimization of maintenance activities in nuclear power plants from a viewpoint of safety focusing on the risks of core meltdown. However, even a small-scale incident of component, which never causes the core meltdown, resulted in the reactor shutdown and economic losses. The economic losses due to this kind of incident become enormous when including the losses that are not officially counted. Accordingly, in addition to the safety analysis focusing on the risk of core meltdown, it is very practical and useful to establish a model that can plan maintenance strategies in terms of availability and economic efficiency of nuclear power plants. With the background above mentioned, an integrated simulator for the maintenance optimization of LWRs based on PFM has been developed [10]. The concept of the simulator is to provide a method to optimize maintenance activities for representative components and piping systems in nuclear power plants totally and quantitatively in terms of safety, availability and economic efficiency (both from cost and profit). As an example of application of the model, it was applied to the maintenance of Inconel 600 SG tubes in PWRs for the purpose of quantitative evaluation of effectiveness of various maintenance strategies, including inspection accuracies (Figs. 8 and 9), inspection intervals (Figs. 10 and 11). Fig. 8 shows the change of cost with various inspection accuracies, (a) D40 (Base), (b) D20(Better), (c) D10(Best). The cost for leakage failure is the most of the total cost, and reduces very much with higher inspection accuracy. The Net Present Value (NPV) as an important financial index is also evaluated as shown in Fig. 9. The better inspection could increase the benefit in spite of higher cost of inspection because of lower failure probability. The longer interval of inspection will increase the rupture cost but scarcely affect the leakage cost as shown in Fig. 10. In spite of the increase of the total cost, the NPV increases because of the increase of net operation hours as shown in Fig. 11. 3. International round robin analysis program Some round robin analysis programs were conducted in the Japanese research group repeatedly to evaluate the precision of PFM programs and to raise the level of analyzers’ technique in two decades. The international round robin program in Asian countries
was planned to develop international communication and cooperation of PFM technique in this area where the nuclear power development seems to be activated rapidly. The object of the newly planned RR problem is to evaluate inspection effects for failure probabilities at PTS event of pressure vessel. Sensitivity analyses will be conducted on (1) the level of maximum probability of detection (PODmax), (2) the critical crack size (Ac) and (3) the timing and frequency of inspection. POD curves and values of above parameters used in the analysis are shown in Fig. 12 and Table 3. The base problem is to evaluate failure probabilities of a pressure vessel at PTS event. Temperature transients employed here are PTS and SGTR, which were used in the previous NRC/EPRI benchmark problem. Several other problems are set and provided to research groups in Korea, Taiwan and Japan. JAEA solved a part of the problems in advance by using PASCAL ver. 2 [11] (updated from PASCAL ver. 1 [2]) and is giving some advises to the groups. 4. Concluding remarks Recent activities of Japanese PFM research group are summarized. Around 20 years research efforts started from literature survey have produced fruitful results and several original PFM programs. These activities have extended the field of PFM applications to many components and problems in nuclear power plants, and up to economic based analysis. These results show that PFM could provide a rational index for complicated and uncertain problems and could be usefully utilized to optimize some decision making. Several round robin analysis programs were conducted to raise the level of knowledge and experience of new PFM techniques among the members of the group. This effort is still continuing and extended to the international research groups of Korea and Taiwan in 2008. References [1] Yagawa G, Kanto Y, Yoshimura S, Shibata K. Recent research activity of probabilistic fracture mechanics for nuclear structural components in Japan. In: 16th International conference on structural mechanics in reactor technology, MG01/5, 455, Washington DC, USA; Aug 2001. [2] Shibata K, Kanto Y, Yoshimura S, Yagawa G. Recent Japanese probabilistic fracture mechanics researches related to failure probability of aged RPV. Solid State Phenomena 2007;120:49–67. [3] ASME boiler and pressure vessel code section XI, rules for in-service inspection of nuclear power plant components; 2001. [4] Code for nuclear power generation facilities – rules on fitness for service for nuclear power plants. JSME S NA1; 2002. [5] Code for nuclear power generation facilities – rules on fitness for service for nuclear power plants. JSME S NC1; 2005. [6] Ultrasonic test & evaluation for maintenance standards. 2002 FY report, Japan Power Engineering and Inspection Corporation; 2002. [7] Machida H. Study on reliability of nuclear power plant piping considering defect sizing accuracy. ASME PVP2006-ICPVT11-93775; July 2006. [8] Development on standards and guides for formation of up-graded inspection system on NPP – ultrasonic test & evaluation for maintenance standards – synthesis report. Japan Nuclear Energy Safety Organization (JNES); April 2005. [9] Machida H. Reliability assessment of PLR piping based on domestic SCC data. In: Proc. ASME PVP-2007; July 2007. [10] Yoshimura S, Furuta K, Isobe Y, Sagisaka M, Noda M, Wada T, et al. Integrated maintenance optimization of LWRs based on PFM analysis. In: Kanda, Takeda, Furuta, editors. Applications of statistics and probability in civil engineering; 2007. [11] Onizawa K, Osakabe K, Shibata K, Suzuki M. Structural integrity analysis of reactor pressure vessel using probabilistic fracture mechanics analysis code. PROSIR WS; 2006.