The surge line is one of the base case systems.

F.3.3.1 Dimensions and Welds — From the piping isometric available to the panel members, the surge line is a 14 inch line (14 inch outer diameter) with a thickness of 35.7 mm (1.406 inches). The material is SA376 Type 304, which is an austenitic stainless steel. There are some 13 welds in the line.

F.3.3.2 Stresses and Cycles — The stresses at the surge line elbow are provided in Reference F.5, which is evidently the highest stressed location in the line. These stresses include seismic events and are given in Table F.8. The stress amplitude is contained in this table, which is one-half the stress range (peak-to-peak value).

Load Pair	Amplitude	Number/	Load Pair	Amplitude	Number/
	(ksi)	40 yr		(ksi)	40 yr
HYDRO-EXTREME	190.17	6	9D-LEAK TEST	52.20	50
8A-OBE	163.18	14	8G-LEAK TEST	52.20	65
9B-OBE	162.06	14	8G-UPSET3	51.00	30
8B-HYDRO	138.05	4	8G-12	50.96	90
8B-OBE	127.94	10	8G-16	50.93	90
9A-OBE	127.04	14	8E-8G	50.92	13
8C-OBE	64.76	68	8E-OBE	43.38	77
9F-OBE	64.17	68	9H-OBE	42.79	500
8F-18	63.40	68	8H-13	39.82	90
9C-11	63.38	68	8H-OBE	37.43	203
8D-OBE	54.02	72	8H-UPSET4	35.42	40
9G-OBE	53.42	400	8H-9E	33.94	90
8G-18	52.38	22	2A-8H	33.94	77
9D-11	52.35	22	3A-10A	33.10	4120
8G-17	52.35	90	6-10A	33.10	200
9D-LEAK TEST	52.20	50	3B-10A	33.10	4120
8G-LEAK TEST	52.20	65	7-10A	33.10	4580
8G-UPSET3	51.00	30	2B-SLUG1	32.87	100
8G-12	50.96	90	2B-SLUG2	32.87	500
			4B-10A	29.90	17040

To estimate the influence of seismic events, it is necessary to also have the stress history without such events. It is not possible to remove seismic events knowing only the information in the above table. This information was provided in Reference F.14 and is summarized in Table F.9.

Load Pair	Amplitude	Number/	Load Pair	Amplitude	Number/
	(ksi)	40 yr		(ksi)	40 yr
HYDRO-EXTREME	190.17	6	8G-16	50.93	90
9B-HYDRO	149.86	4	8G-9H	50.92	128
8A-UPSET 4	140.42	14	2A-8E	40.10	90
9B-UPSET4	139.43	10	8H-9H	40.09	100
8B-UPSET4	105.89	14	9H-10A	40.09	272
9A-UPSET4	105.13	2	9E-13	39.82	90
9A-LEAK	103.86	12	3A-10A	33.10	4120
8F-18	63.40	68	6-10A	33.10	200
9C-11	63.38	68	3B-10A	33.10	4120
9F-LEAK	63.37	68	7-10A	33.10	4580
8C-LEAK	63.37	35	2B-SLUG1	32.87	100
2A-8C	62.30	33	2B-SLUG2	32.87	500
8G-18	52.38	22	5-10A	29.90	9400
8G-17	52.35	90	4A-10A	29.90	17040
9D-11	52.35	22	4B-10A	29.90	17040
2A-8D	51.20	72	2B-10A	20.60	14400
8H-9G	51.18	400	2A-10A	20.60	14805
8G-UPSET3	51.00	30	10A-UPSET1	20.59	70
9D-12	50.96	50	10A-UPSET5	20.59	30
8G-12	50.96	40	10A-UPSET6	20.59	5
			10A-UPSET2	20.59	95
			1B-10A	20.59	1533
			1B-10B	20.00	87710

The cyclic stress amplitudes of Tables F.8 and F.9 provide the information for the initiation analysis, but additional information is required for the growth portion of the analysis. The spatial gradient (primarily radial) is required. Also, when analyzing the stability of a through-wall crack, the steady normal operating stress is needed. This stress is considered to be the sum of the pressure, deadweight and restraint of thermal expansion stresses. The values of these latter two are given in Reference F.5 as

Cdw = 0 Ote = 102.6 MP (14.88 ksi).

Many of the high stress contributors in Tables F.8 and F.9 are from rapid excursions of the coolant temperature. The largest stress amplitude (half the peak-to-peak) is 1,310 MPa (190 ksi), so the stresses are large (but localized). These are the stresses at the peak stress location, which is not at weld. The spatial stress gradients (both along the surface and into the pipe wall) are required for a thorough analysis. The radial gradient (into the pipe wall) can be estimated by the procedure given in Section 5.3 of Reference F.5, i. e.,

The following specific rules were applied to assign stress to the uniform and gradient categories:

• Cyclic stresses associated with seismic loads were treated as 100 percent uniform stress.

• Cyclic stresses greater than 310 MPa (45 ksi) were treated as having a uniform component of 310 MPa (45 ksi), and the remainder were assigned to the gradient category.

• For those transients with more than 1000 cycles over a 40 year life, it was assumed that 50% of the stress was uniform stress and 50% a through-wall gradient stress. In addition, for these transients, the uniform stress component was not permitted to exceed 69 MPa (10 ksi).

The gradient stress mentioned above is assumed to vary through the thickness as

= &o — 3£ + 3 £2 j [F.6]

In this equation, co is the stress at the inner wall of the pipe, £ = x / h, x is the distance into the pipe wall from the inner surface, and h is the wall thickness. The stresses and cycles are high enough that fatigue crack initiation is important, which has been considered in Reference F.5, which shows a probability of 0.981 of a leak in 40 years for this component. The LOCA probabilities will be less. The use of the gradient along the surface will reduce this.

A refined stress analysis was available as part of the efforts reported in Reference F.6. These stresses included details of the variation of the stress in the circumferential direction, and are referred to as the “refined stresses”. The stresses used in the surge line evaluation were based on the actual stress analysis for a CE-designed plant in response to NRC Bulletin 88-11 dealing with surge line stratification. The loadings were based on the methods approved by the NRC staff in the CE Owner Group Report CEN 387-NP, "Pressurizer Surge Line Flow Stratification Evaluation," Rev. 1-NP, December 1991. Additional evaluations of the local stress distributions in the elbow were conducted to get the detailed stress distribution around the circumference of the elbow. The critically stressed location that produced the highest probability of cracking was the circumferential stresses in the side of the elbow due to stratification bending. Detailed stresses are not provided, because they belong to the plant that allowed us to use them.

F.3.3.3 Results — PRAISE runs were made using the versions that can treat fatigue crack initiation. No inspections were considered. Since crack initiation is considered, there will be no effect of a pre-service inspection. The results are summarized in Table F. 10.

Table F.10 Cumulative PRAISE Results for the Surge Line Elbow Condition Ref. F.5 Table F.8 Stresses Table F.9 Stresses Refined Stresses Seismic yes yes no yes ^DL no no no no О A 25 0.372 0.233 40 0.982 0.772 0.587 8×10-7 60 0.998 0.968 0.882 3.3×10-5 CENC4H1 О о л 25 — 1.6×10-5 7.5×10-6 <10-7 40 — 3.11×10-4 7.1×10-5 <10-7 60 1.33×10-3 2.51×10-4 <10-7 — CENC4D01 CENC4A3 20 hrs >1500 25 — <10-7 <10-7 40 — <10"’ <10"’ 60 — 2.0×10"7 1.0×10-7 CENC4D15 CENC4A4 axisymmetric seismic axisymmetric nonseismic strain rates and bivariate stresses

It is seen that the seismic stresses do not have a large effect, roughly a factor of 3. The use of the refined stresses greatly reduces the calculated failure probabilities. The computer run for 380 lpm (100 gpm) took about 20 hours and resulted in no failures in 107 trials. The runs for > 5,700 lpm (1,500 gpm) with the stresses from Tables F.8 and F.9 had 2 and 1 failures in 107 trials, respectively, and these runs each took many hours. Hence, it is evident that the Monte Carlo simulation with multiple fatigue crack initiation sites does not allow definition of the small probabilities of large leaks in the surge line elbow, and an alternate procedure was developed. Stratified sampling is not used for fatigue crack initiation.

F.3.3.4 Alternate Procedure — In cases where the dominant degradation mechanism is fatigue crack initiation with subsequent growth, PRAISE currently has no way of generating low probability results other than conventional Monte Carlo simulation. This is the dominant mechanism for three of the base line components; the surge line elbow, the HPI make up nozzle and the BWR feedwater line elbow. Excessive computer time is needed to generate probabilities of various size leaks for these components, with some runs taking 4 days on a 3 GHz pc, with no leaks of even 380 lpm (100 gpm). An alternate procedure is needed to estimate leak probabilities for the large leaks of interest, and such a procedure is described below.

As part of a standard analysis, the PRAISE software computes the crack opening area and leak rate as functions of the length of through-wall cracks. Hence, this information is readily available, and can be used to determine the length of a through-wall crack needed to produce a given leak rate, such as 380 lpm (100 gpm), 5,700 lpm (1,500 gpm), etc. The probability of having a leak of a given magnitude is then the probability of having a through-wall crack exceeding that length. The half-crack length, b, is considered, which is a function of the desired leak rate, q. Hence, b(q) can be considered as known.

The probability of a double-ended-pipe-break (DEPB) is also of interest. In the cases of interest here, the critical net section stress failure criterion is used. For a through-wall crack, the value of b for a DEPB is given by the expression

where R[ is the inside radius, aflo is the flow stress (average of yield and ultimate) and aLC is the load controlled stress, which is equal to the pressure plus deadweight stress.

The version of PRAISE that performs Monte Carlo simulation of fatigue crack initiation and growth commonly provides information on the probability of having any leak and a leak exceeding a given magnitude. In order to have a nonzero number for the latter, a leak exceeding that magnitude must occur during the simulation. The problem is that this often does not occur within a number of trials that can be reasonably performed. In order to overcome this, PRAISE was modified to print out the length of any crack resulting in a leak and the time at which it first became through-wall. This was then used to estimate the size distribution of through-wall cracks as a function of time. The complementary cumulative distribution, denoted as Pb(>b), is concentrated upon. Then the probability of a leak greater than q is given by

PlK (> q) = Pb [> b(q)] [F.8]

Table F.11 summarizes the information from a PRAISE run using the stresses from Table F.9 for the crack opening area (A) and leak rate (q) for a given half-length of a through-wall crack (b).

Table F.11 Half Crack Lengths and Areas for a Given Leak Rate
(Surge Line Elbow, Table F.9 Stresses)

Q, gpm	b, inches	b nRi	A, in2	A A • Apipe
100	5.981	0.445	0.936	0.010
1500	10.379	0.591	10.028	0.143
5000	11.791	0.671	46.762	0.476
DEPB	15.95	0.907	—	—

A table of lengths of through-wall cracks was generated from the modified version of PRAISE using 104 trials using the stresses of Table F.9 (no seismic). In this run, there were 2,162 leaks within 25 years, 5,932 within 40 years and 8,890 within 60 years. Dividing these numbers by 104 provides leak probabilities that are nearly the same as obtained from the Monte Carlo simulation with 107 trials. Figure F.2 is the complementary cumulative distribution of leaking crack sizes for the three times of interest.

The upper curve is for 60 years, because there is a higher probability of encountering a longer crack at this longer time. The lines in this figure are least squares curve fits, which are discussed later.

6.0

Figure F.2 Complementary Cumulative Distribution of Half-Crack Length of Through-Wall
Cracks in Surge Line Elbow at 25, 40 and 60 Years

Figure F.2 shows changes in slope, and the “lumpiness” of the distribution is readily apparent. This “lumpiness” is representative of a multi-modal probability density function of crack length, which is most likely due to the fatigue crack initiation sites being taken as 50 mm (2 inches) in length. That is, each two-inch segment around the circumference is taken as an independent initiation site. The surface length of an initiated crack is also a random variable. Once a crack initiates, it grows, and can link with neighboring cracks. This growth and linking can lead to sudden increases in crack length (by linking) and evidently is responsible for the multi-modal nature of the probability density function of crack length.

The multi-modal nature of the probability density function is clearly shown in Figure F.3.

Figure F.3 Histogram of the Half-Length of Through-Wall Cracks at 60 Years for the Surge Line

Elbow

Pleasing curve fits to the lines in Figure F.2 are not possible. A good fit could perhaps be obtained by assuming that the histogram of Figure F.3 consists of a sum of lognormals with medians to match the

location of the modes and relative weights adjusted to match the relative heights of their modes. This is believed to be unwarranted, since the multi-modal nature of the density function is an artifact of the modeling assumption of a 50 mm (2 inch) long initiation site. It is better to just smooth out the cumulative distribution, and this was accomplished by a linear least squares curve fit to the cumulatives on log-linear scales. Since it is desired to represent the curve at long cracks, the fit was performed only for cracks corresponding to a probability less than 0.2. This eliminates the numerous cracks at higher probabilities that would skew the curve fit if included in the least squares calculations. The lines in Figure F.2 are the curve fits obtained in this manner.

The assumed functional form was

P(> b) = 0.2e“c(b"b°-2) [F.9]

The values of C and b0.2 depend on the time. Once they are evaluated, the leak probabilities of a given size are obtained using the crack sizes in Table F.11. Table F.12 summarizes the results.

Table F.12 Summary of Results for Surge Line Elbow (Table F.9 Stresses)

Time, years	25	40	60
Number of cracks	2162	5932	8890
Cracks above 0.2	1730	4744	7109
b0.2	2.072	2.089	2.108
C	1.876	1.597	1.425
P(>5.981)	1.31×10-4	4.00×10-4	8.02×10-4
P(>10.379)	3.41×10-8	3.56×10-7	1.52×10-6
P(>11.791)	2.42×10-9	3.73×10-8	2.04×10-7
P(>15.95)	9.86×10-13	4.86×10-11	5.43×10-10

Table F.13 summarizes the results along with corresponding ones obtained directly from the Monte Carlo simulation. The conventional Monte Carlo simulation used 106 trials for 380 lpm (100 gpm) and 107 trials for 5,700 lpm (1,500 gpm).

Table F.13 Cumulative PRAISE Results for the Surge Line Elbow as Obtained from the Alternate
Procedure and Directly from Monte Carlo Simulation
(Table F.9 Stresses)

	Direct Monte Carlo	Alternate Procedure
	25	0.233	0.216
О A	40	0.587	0.593
	60	0.882	0.889
>100	25	7.5×10-6	1.31×10-4
40	7.1×10-5	4.00×10-4
60	2.51×10-4	8.02×10-4
О	25	<10-7	3.41×10-8
m	40	<Ю7	3.56×10-7
A	60	1.0X10-7	1.52×10-6
о	25	—	2.42×10-9
о о	40	—	3.73×10-8
л	60	—	2.04×10-7
DEPB	25	—	9.86×10-13
40	—	4.86×10-11
60	—	5.43×10"1U

Table F.13 shows that the alternate procedure is able to greatly extend the leak rates whose probabilities can be estimated. In cases where direct comparisons are possible, the alternate procedure gives higher leak probabilities. The direct Monte Carlo for 5,700 lpm (1,500 gpm) employed 107 trials and took 36 hours of computer time. The alternate procedure used 104 trials, so took about 2 minutes. Even in this era of fast cheap computer time, it would still be prohibitive to use direct Monte Carlo to generate the results obtained by the alternate procedure. It would take 1010 trials to produce the DEPB results in the above table. This translates to 36,000 hours of computer time, or about 4 years.