ML20247F132
| ML20247F132 | |
| Person / Time | |
|---|---|
| Site: | Wolf Creek, Callaway, 05000000 |
| Issue date: | 03/23/1989 |
| From: | Johnson T, Saeung S, Eric Thomas BECHTEL POWER CORP. |
| To: | |
| Shared Package | |
| ML20247F099 | List: |
| References | |
| ULNRC-1950, NUDOCS 8904030327 | |
| Download: ML20247F132 (54) | |
Text
.. _ . _ - _ _ _ _ _ _ _ _ . __ _ ________
, . e Attachment 2 ULNRC-1950 54 Pages SNUPPS CALLAWAY UNIT 1 UNION ELECTRIC COMPANY, MISSOURI WOLF CREEK UNIT 1 WOLF CREEK NUCLEAR OPERATING CORPORATION-i POST TENS 10NING SYSTEM EVALUATION CALLAWAY UNIT 1 CONTAINMENT WOLF CREEK UNIT 1 CONTAINMENT 0
Prepared by: M MWM ((< S.See #"1h6 Art S. Sae-Ung/M'rwan Daye/C. C. Fu" gq Reviewed by: cc . .
f.W.' Thomas 3 2qBS Approved by: 7* t= 3 as\e3 i T. p ohnson Bechtel Power Corporation Gaithersburg, MD U.S.A. ,
March 1989 8904030327 890323 PDR ADOCK 05000482 P PDC
- .' e
]
TABLE OF CONTENTS
- 1. INTRODUCTION' II. DESCRIPTION OF THE POST-TENS 10NING SYSTEM l
IV. NUMERICAL COMPUTATIONS AND RESULTS V. '
SUMMARY
VI. CONCLUSIONS ii
.., c-LIST OF FIGURES l ~ TITLE l ' FIGURE Tendon Galleries in the Callaway and Wolf Creek Containment 1
Buildings Post Tensioning System for the Callaway and Wolf Creek 2
Containment Shells Horizontal Prestressing as a function of Time for Callaway Unit 3a 1 Containment (Actual Data Only)
Horizontal Prestressing as a Function of Time for Wolf Creek 3b Unit 1 Containment (Actual Data Only)
Vertical Prestressing as a Function of Time for Callaway Unit 1 4a Containment (Actual Data Only)
Vertical Prestressing as a Function of Time for Wolf Creek Unit 4 4b 1 Containment (Actual Data Only)
Horizontal Prestressing as a Function of Time for Callaway Unit Sa 1 Containment (Actual and Simulated Data)
Horizontal Prestressing as a Function of Time for Wolf Creek 5b Unit 1 Containment (Actual and. Simulated Data)
Vertical Prestressing as a Function of Time for Callaway Unit 1 6a Containment (Actual and Simulated Data)
Vertical Prestressing as a function of Time for Wolf Creek Unit 6b 1 Containment (Actual and Simulated Data) l iii
7_ _ _
. T l
l l
- LIST OF TABLES l
I TABLE TITLE la Actual Prestress Force Data for Horizontal Tendons for Callaway Unit 1 Containment Ib Actual Prestress Force Data for Horizontal Tendons for Wolf Creek Unit 1 Containment 2a The Average, Lower Bound, and Upper Bound Prestress Force of the Horizontal Tendon for Callaway Unit 1 Containment (Actual Data Only) 2b The Average, Lower Bound, and Upper Bound Prestress Force of the Horizontal Tendon for Wolf Creek Unit 1 Containment (Actual Data Only) 3a Actual Prestress Force Data for Vertical Tendons for Callaway Unit 1 Containment 3b Actual Prestress Force Data for Vertical Tendons for Wolf Creek Unit 1 Containment 4a The Average, Lower Bound, and Upper Bound Prestress Force of the Vertical Tendon for Callaway Unit 1 Containment (Actual Data Only) 4b The Average, Lower Bound, and Upper Bound Prestress Force of the Vertical Tendon for Wolf Creek Unit 1 Containment (Actual Data Only)
Sa Actual and Simulated Prestress Force Data for Horizontal Tendons for Callaway Unit 1 Containment 5b Actual and Simulated Prestress Force Data for Horizontal Tendons for Wolf Creek Unit 1 Containment 6a The Average, Lower Bound, and Upper Bound Prestress Force of the Horizontal Tendon for Callaway Unit 2 Containment (Actual and Simulated Data) 6b The Average, Lower Bound, and Upper Bound Prestress Force of the Horizontal Tendon for Wolf Creek Unit 1 Containment (Actual and Simulated Data) 7a Actual and Simulated Prestress Force Data for Vertical Tendons ,
for Callaway Unit 1 Containment 7b Actual and Simulated Prestress Force Data and Vertical Tendons for Wolf Creek Unit 1 Containment iv
I
.. r LIST OF TABLES Continued)
TITLE TABLE The Average, Lower Bound, and Upper Bound Prestress Force o 8a Vertical Tendon for Callaway Unit 1 Containment (Actual and Simulated Data)
The Average, Lower Bound, and Upper Bound Prestress Force o ;
8b Vertical Tendon for Wolf Creek Unit 1 Containment (A Simulated Data)'
1 e
v
, r )
l REFERENCES i 1
P., "A Study of Stress Relaxation
- 1. Magura, D. D. Sozen, M. A. and Siess, C.
Proceedings Paper Pages 13 thru 57, in Prestressing Reinforcement,"
Journal of the Prestressed Concrete Institute, April 1964.
S., and Boullion, T. L., " Statistical Methods for
- 2. Bethea, R. M., Duran, B.
Engineers and Scientists," Marcel Dekker, Inc., New York, New York.
]
Benjamin, J. R., and Cornell, C. "A., Probability, Statistics, andMcGraw-Hilll 3.
Decision for Civil Engineers,"
York, 1970. >
" Statistical Models in Engineering," John
- 4. Hahn, G. J., and Shaprio, S. S.,
Wiley & Sons, Inc., New York, New York,1967. ]
i 5.
Calc. No. C-1989-107, "The Tendon Prestressed on the Containment ;
time Functions", Wolf Creek Unit 1 Containment, Bechtel Power <
Corporation.
I 6.
Calc. No. C-1989-106, "The Tendon Prestressed on the Containment Time Functions", Callaway Unit 1 Containment, Bechtel Power Corpor l
Technical Report, ASCO Unit 1, '
- 7. " Post Tensioning system Evaluation",
Spain, Bechtel Power Corporation, September, 1988 8.
"In-service Tendon Surveillance Procedure - Reactor Building Post-Tensioning System", SNUPPS Callaway Unit 1 in Missouri, Bechtel Pow Corporation, Maryland, Nay, 1985.
9.
"In-service Tendon Inspection Program - Reactor Building Post-Tens System", Rev.1, SNUPPS Wolf Creek Generating Station in K Power Corporation, Maryland, December, 1985 E
i vi I. - - - - - - - - . _ _ _ _ . _ . _ _ ""-"--~~_u
. f I. INTRODUCTION Union Electric and Wolf Creek Nuclear Operating Corporation have proposed the U. S. NRC a revision to their respective nuclear power plant Technical c
Specification.
The proposed revision is related to the action plan for the containment post-tensioning system surveillance and reflects a change The shutdown is required if the present 72 hour8.333333e-4 days <br />0.02 hours <br />1.190476e-4 weeks <br />2.7396e-5 months <br /> plant shutdown to 15 days.
surveillance results do not meet certain conditions stated lat section.
In response to Union Electric the U. S. NRC "USNRC letter (Alexion) to U Electric (Schnell) dated May 16, 1988" and U.S. NRC "USNRC Letter (O' Conner) to requested statistical backup justification I WCNCC (Withers) dated May 24, 1988" for the proposed revision to show continued structural integrity of the pos tensioning system during the requested 15 day no shutdown period.
This report is generated to provide the requested backup justification.
Post-tensioning systems for containment structures are subjected to time For this reason, the dependent losses during the service life of the system.
system design incorporates allowances for such losses so that service life the remaining prestressing force is equal to or exceeds t requirement.
1
. t Time dependent losses are in the form of tendon material relaxation un
-Since the amount of losses are tension and concrete creep under compression.
lts, material dependent and can only be estimated based on experimental resu The assumed values are assumed values are used in the design of the system.
The actual usually conservative and exceed the actual experienced losses.
i performance of the system is verified by the results obtained from m the tendon forces as part of the periodic tendon surveillance requirem ld The aforementioned NRC to UE letter They addresses are as three be indicative of gross containment capacity deterioration.
follows:
1.
The average prestressing forces of the sampled tendons falling minimum required prestress.
2.
More than one tendon force out of three adjoining tendons fallin their predicted lower bound force and 90% of the lower bound.
d 3.
Any of the sampled tendons falling below 90% of its predicI The purpose of this evaluation is to verify that even with the co 4 i their outlined above, the containment post-tensioning systems mainta n The results clearly indicate structural capacity above design requirements. is that the structural integrity of the Callaway and Wolf Creek systems; maintained past their service life.
2
. t The Callaway and Wolf Creek Unit I containments have been subjected to two surveillance programs each in the last 3 years. The results from these four surveillance plus two initial prestress data sets have been statistically evaluated and used to predict the system performance from the immediate future until the end of the 40 year design life. The statistical evaluation is based on the regression analysis approaches.
This statistical evaluation is composed of two major steps. The first step is to determine the time functions of the average, lower bound and upper bound prestress levels based on the actual prestress data from the two surveillance plus the initial prestress data. The second step utilizes the statistical result obtained from the first step to probabilistically simulate prestress outcomes. Each set of outcomes is so conservatively simulated that the probability of actually obtaining a set of outcomes being worse than the simulated set is insignificant 1y small and yet the performance of the prestress system remains adequate. The study then used the combination of the actual prestress data obtained from the initial prestressing,1st and 2nd surveillance plus the simulated prestress data for the next surveillance to I
determine the time functions of the average, lower and upper bound prestress levels. I i
l
- 11. DESCRIPTION OF THE POST-TENS 10NING SYSTEM l
The post tensioning system for the Callaway and Wolf Creek Unit I containment The hoop structures consist of the vertical tendons and the hoop tendons.
tendon system consists of the cylinder tendons and the dome tendons.
3
l Vertical tendons consist of 86 inverted U-shaped tendons, which extend through j the full height of the cylindrical shell over the dome and are anchored in the f tendon gallery at the bottom of the foundation slab as shown in Figure 1.
Hoop tendons located in the cylindrical shell consist of 135 tendons anchored l
by three buttresses equally spaced around the exterior surface of the Reactor Building. Each tendon is alternately anchored at buttresses located 240 degrees apart. Three tendons constitute two complete circumferential tendons.
Prestressing of the hemispherical dome is achieved by the two-way pattern of the inverted U-shaped tendons and 30 additional hoop tendons which start at the spring line of the dome and continue to an approximately 45 - degree vertical angle from the spring line. Figure 2 illustrates the arrangements of the hoop tendons in the post-tensioning system.
III. EVALUATION The results collected from the two tendon surveillance programs on tendon samples have been utilized to predict the system behavior for the 40 year service life and the level of prestressing force in each tendon group at the end of 40 year service.
Regression analysis and simulation outcomes have been employed using the existing information collected at three points in time, i.e., initial installation and the two consecutive surveillance. The details of the regression analysis and the simulation are provided in Sections 111.1 and IV.3, respectively.
4
. t Rearession Analysis _
III.1 Per the shape of the curves of the relaxation loss at time functions exhibited in Fig. 5 of Ref.1 and per the functional form of Eq. 3 Ref. 1, it can be assumed that the tendon prestress force, Y at any time, T can be expressed as the logarithmic function of T given bel ow.
(1)
Y = Bo + B1 In T Where Bo and B 1 are constants to be estimated by regression analy Let x = In T, then Eq. I becomes (2)
Y = Bo + Bi x Per Eq. 2, Bo and B 1 can be determined by the linear regression and 81, analysis. Letbo and $1 be the estimates for Bo -
Per Eqr 9-12 and 9-13 on Pgs, 275 and 276 of Ref. 2, respectively.
n (3)
. E (xi-s)(yi-9)
B1 - _i - 1 n
E. (xi-i)2 i=1 (4) bo = 9 $1x 5
( ._ _______-______ - _ -
. J'-
+, _ . ,
)-
Where n = number of. data points.
xj = In Tj where Tj is the' time at which the tendon prestress force is being measured, e.g., the initial time, the 1st surveillance, the 2nd surveillance, etc. Note that i = 1, 2,..., n.
2,..., n yj = the tendon prestress force at time, Tj for i = 1, n
. 1 E xi x = n i=1 n
1 E yi y = n i=1 Let y be the estimate of y, then by Eq. 2 y can be expressed as:
A A A A A (5) y- Bo +l B1 x = Bo + B ilnT
^
Physically y represents the averaae tendon prestress force at any time T.
The degree of functional relationship between the data xj and yi for i =
1,2,..., n, and the increasing Tj or xj leading to decreasing yi will be verified as follows: Let r xy denote the correlation coefficient between xj's and yj's, then from Eq.1.3.2 on Pg.15 of Ref. 3, rxy is as follows:
Sxy I n ry = = { 1 Y (xj-i) (yj-9) ) (Sa) x SxS y SxS y n i=1 where Sx and Sy (per Eq. 1.2.2a on Pg. 11 of Rev. 3) are:
n 1/2 ..
(6)
=
( nl Ei=1 (xj-i)2 )
Sx n 1/2 (7)
=
{ nl Ei=1 (yi-5)2 )
Sy 6
. t The higher the degree of relationship between the data xi and yj, the c l' Normally, lrl 20.6 indicates a good relationship the value of lrl to unity.
In order to have increasing xj leading to decreasing between.two sets of data.
yj, r must be negative.
denote the lower and upper bound prestress force of a tendon at Let yt and y u In the calculation, yL is associated with 97.5%
any time T, respectively.
I probability that the actual value of the tendon prestress force is la t l value of the is associated with 2.5% probability that the ac ua yt; and y u Per Eq. 9.29 on Pg. 265 of Ref. 2, tendon prestress force is larger than yu .
yt and y ucan be determined from A
(8) yt = y - S y3 tn-2, 1 12 A
(9) yu " Y + S^ y in-2, 1.a2 d two sided where i n -2, l.a is the t-statistics with n-2 degrees of freedom, an In this case 8 = 0.025. The value of 2
confidence level of 100 (1-a)%.
tn-2,1-)canbeobtainedfromTableIIonPg.312ofRef.4.
From Eq. 9.25 on Pg. 284 of Ref. 2, i.e., yS is:
(x-x)2 - (10)
Ss
.([]+1+ n n
) 2 31/2 y E (Xi-X)2 i=1 7
2 js:
where from Eq. 9.18 on Pg. 281 of Ref. 2, i.e.,
n , n E. (yj-y)2 ,B 1
-(xi-i) (vj-y) (11) al _f =1 n-2 1-1 In the next section, Eqs, 5, 8 and 9 will be used to compute, at any time.T the average prestress forces (y), lower bound (yt), and upper bound (yu) fo the dome, cylinder, and vertical tendons based on (a) the corresponding l
initial, first, and second surveillance tendon prestress levels, and (b corresponding initial, first, and second surveillance tendon prestress lev plus the simulated tendon prestress levels for the next (third) surveilla IV. NUMERICAL COMPUTATIONS AND RESULTS Based on the methodology for regression analysis technique provided III.1, the average (y), lower bound g (y ), and upper u bound (y ) prestress at any time T for the dome and cylinder horizontal tendons, and the Note that tendor,s will be computed in Sections IV.1, and IV.2, respectively.
due to (a) ine geometrical similarity between the dome tendons and tendons, ane (b) only few samples of dome tendon prestress availab d for the tendons are considered to be equivalent to the cylinder ten ons Hereinafter, the dome and cylinder tendons will be statistical evaluation. I raferred to as horizontal tendons.
for prestressing the dome Per Eq. 5 in Section 111.1, the initial time, To )
tendon can not be assumed zero because the natural logarithm, in T Based on the study in Ref. 7, it is conservative to use To=0.001 undefined. )
year.
Therefore, in this investigation, To 0.001 year will also be used.
8
- r. ,
IV.I Norizontal Tendon Prestress Force as Time function B QDlY s
The horizontal tendon prestress force data associated with To = 0.001 year, and the 1st and 2nd surveillance are tabulated in Columns of Tables la and Ib for the Callaway and Wolf Creek Unit I containments respectively.
Based on these data and by using Eqs. 5, 8 and 9, and other related equations in Section III.1, the average (y), lower bound (yt),
upper bound u
-(y ) prestress forces of the horizontal tendons as func of time T, and the correlation coefficient x (r y) are derived in Refs. 5 and 6, namely for the Callaway containment, (12) y = 164.049 - 1.840 In T 2 (13) yg = 164.049 - 1.840 In T - 2.624 (i5.836 + 0.03951 (In T + 2 2
(14) y u
= 164.049 - 1.840 In T + 2.624 (19.836 + 0.03951 (In T +
ryx
= -0.88 For Wolf Creek containment, t
(15) y = 167.987 - 1.213 int 2
(16) yt = 167.987 - 1.213 int - 2.624 (20.581 + 0.04194 (int + 2.5 (17) l y
u
= 167.987 - 1.213 int + 2.624 (20.581 + 0.04194 (lnT ryx
- -0.76 Based on Eqs. 12 thru 14, Figure 3a provides 3 curves exhibiting the and the time T up to 40 years for relationship between y, yL, and y u i 9
Callaway containment.
Based on Eqs. 15 thru 17 Figure 3b provides 3 and the time T up curves exhibiting the relationship between y, yj , and yu to 40 years for Wolf Creek containment.
IV.2 Vertical Tendon Prestress Force as Time Function Based on Actual Data O o
The vertical tendon prestress force data associated with T =0.001 year, and the 1st and 2nd surveillance are tabulated in Columns 5 and Tables 2a and 2b for the Callaway and Wolf Creek (Jnit I containments, respectively. Based on these data and by using per Eqs. 5, 8 and 9, and
~
other related equations in Section 111.1, the average (y), lower bound (yg), and upper bound u(y ) prestress forces of the vertical tendons as functions of time T, and the correlation coefficient (r y) x are derived in Refs. 5 and 6, namely, for Callaway containment, (18) y = 173.245 - 0.994 In T (19) yt = 173.245 - 0.994 In T - 2.162 (5.134 + 0.01787 (In T +
(20) yu - 173.245 - 0.994 In T + 2.162 (5.134 + 0.01787 (In T +
ry x
= -0.90 for Wolf Creek containment, (21) y = 170.454 - 1.163 In T yg = 170.454 - 1.163 In T - 2.162 (10.325 + 0.03662 (In 2 (23) y u
- 170.454 - 1.163 In T + 2.162 (10.325 + 0.03662 (In T + 2.42 ryx
= -0.86 10
' Figure 4a provides 3 curves exhibiting the relationship between y, yg, and y y and the time T up to 40 years for Wolf Creek containment based on Eqs. 18 thru 20. Figure 4b also provides 3 curves exhibiting the relationship between y, yg , and yu and the time T up to 40 years for Callaway Unit I containment based on Eqs. 21 thru 23.
IV.3 SIMULATION OF THE NEXT SURVEILLANCE TENDON PRESTRES Four sets of tendon prestress outcomes are simulated for the next (or third) surveillance of the Callaway and Wolf Creek Unit I containments, i.e., one (simulated set) for the Callaway horizontal prestress system, one for the Callaway vertical prestress system, one for the Wolf Creek horizontal prestress system, and one for the Wolf Creek vertical prestress system. To satisfy the requirement described in Section I that the probability of actually obtaining a set of outcomes being worse than the corresponding simulated set is insignificant 1y small and yet the performance of the prestress system remains adequate, the simulation is performed as described below. .
Assume that the outcomes deviate normally about its average time function.
Thus This assumption is typically made in regression analysis (Ref. 2).
at any time, T the tendon prestress outcomes, yj (T) can be generated by (24) yi(T) = zj S 3(T) + y(T) y where y(T) and S (T) represent the average tendon prestress (Eq. 5) and y Zj is standard deviation of the tendon (Eq. 10) at time T, respectively.
the standard normal variate which can be obtained from Table V]ll on Pg. ,
329 of Rev. 4.
11
In this analysis, assume that the next surveillance takes place at 7 years after the init,31 prestressing, i.e., T-7 years. y(T) and S,(T) y at 7 years are calculated based on initial, the 1st and 2nd surveillance data as shown in Refs. 5 and 6.
For the horizontal prestress system of each containment, 7 tendons will be Herein, only 3 tendon prestress inspected in the next surveillance.
The remaining 4 prestress outcomes are simulated based en Eq. 24.
outcomes are arbitrarily set equal to the design requirement specified in References 8 and 9 that the averace prestress shall be greater than or For the horizontal equal to the minimum effective design prestress. '
For prestress system, the minimum effective design prestress.is 147 ksi.
the Callaway and Wolf Creek containments, the simulated horizontal tendon prestress outcomes are listed in rows 28 thru 34 of Tables 5a and 5b, respectively.
denote the probability of obtaining one or more outcomes from 7 Let rh samples (tendons) to be drawn in the next surveillance being less tha ksi. Because more than half of the simulated outcomes are arbitrarily set at the lower allowable limit (147 ksi), rh practically prepresents the probability of a set of actual outcomes being worse than the simulate Based of outcomes. Mathematically, rh follows the binomial distribution.
Hence, on the result of the calculation in References 5 and 6, rh =1.05%.
the probability of a set of actual outcomes being worse than the sim set is insignificantly low.
12
- For the vertical prestress system of each containment, 4 tendons will be In this. case, only 2 tendon prestress inspected in the next surveillance.
outcomes are simulated based on Eq. 24. The reraining 2 prestress outcomes are arbitrarily set equal-to the design requirement specified in References 8 and 9.that the averace prestress shall be greater than or equal to the minimum effective design prestress.
For the vertical For prestress system, the minimum effective design prestress is 139 ksi.
the Callaway and Wolf Creek containments, the simulated vertical tendon prestress outcomes are listed in Rows 16-thru 19 of Tables 6a and 6b, respectively.
Similar to the simulated sets of horizontal prestress outcomes, it has been shown in References.5 and 6 that the probability of a set of actual vertical prestress outcomes being worse than the simulated set is extremely low (virtually zero).
IV.4 Horizontal Tendon Prestress Forces As Time Function Based On Plus Simulated Data The actual prestress data of the horizontal tendons associated with To=0.001 year, and the 1st and 2nd surveillance plus the simulated prestress data for the horizontal tendons associated with the next (3rd) surveillance are tabulated in Tables 5a and 5b for the Callaway and Wolf Creek Unit I containments, respectively. Based on these data and by using Eqs. 5, 8 and 9, and other related equations in Section 111.1, the average (y), lower bound (yL), and upper bound (yu) prostress forces of the 13
, t
! ~~. .
horizontal tendons as functions of time, T are derived in Refs 5 and 6 namely:
For Callaway Containment, (25) k-162.288-2.110 int (26)
Y t - 162.288 - 2.110 int - 2.038 (36.26 + 0.059222 (int (27)
Yu - 162.288 - 2.110 int + 2.038 (36.26 + 0.059222 (i For Wolf Creek Containment, (28) h-164.829-1.702 int (51.20 + 0.084834 (int + 1.637)2 (29)
Y L - 164.829 - 1.702 int - 2.038 (30)
(51.20 + 0.084834 (int + 1.637)2 Yu - 164.829 - 1.702 int + 2.038 Figure 5a provides 3 curves exhibiting the relationship between y, yt, yu and time, T up to 40 years for Callaway containment based on Eqs. 25 thru 27. In the same manner, Figure 5b provides 3 curves exhibiting the and time, T up to 40 years for Wolf relationship between y, yL, and yu Creek containment based on Eqs. 28 thru 30.
14 i
i g
IV.5 VERTICAL TENDON PRESTRESS FORCE AS TIME FUNCTI PLUS SIMULATED DATA i o ]
The actual prestress data of the vertical tendons associated with T =0.001 I year, and the 1st and 2nd surveillance plus the simulated prestress data for the vertical tendons associated with the next (3rd) surveillance a tabulated in Tables 7a and 7b for the Callaway and Wolf Creek Unit I containments, respectively. Based on these data and by using Eqs. 5, 8 and 9, and other related equations in Section 111.1, the average (y),
lower bound (yt), and upper bound (yu) prestress forces of the vertical '
tendons as functions of time (T) are derived in Refs. 5 and 6 namely:
For Callaway Containment, (31) k-168.814-1.672 int (32)
Y L - 168.814 - 1.672 int - 2.110 /110.72 + 0.32027 (int +
1.470)4 (33)
Yu - 168.814 - 1.672 int + 2.110 /110.72 + 0.32027 (ini s For Wolf Creek Containment, (34) h-166.09-1.839 int (35)
/)2.11+0.26956(int +1.502)2 Y L - 166.09 - 1.839 int - 2.110 (36)
Yu - 166.09 - 1.839 int + 2.110 (92.11+0.26956(int +1.502)2 Figure 6a provides 3 curves exhibiting the relationship between y, yL' and yu and time, T up to 40 years for Callaway containment based on Eqs. 31 thru 33. In the same manner, Figure 6b provides 3 curves and time, T up to exhibiting the relationship between y, yt, and yu ,
40 years for Wolf Creek containment based on Eqs. 34 thru 36.
15
V.
SUMMARY
As discussed in Section 111.1, the tendon prestress force, y at any time, T can be expressed as the logarithmic function of T described by Eq. 1.
For all the prestressing system groups of the Callaway and Wolf Creek Unit I containment shells, the functional relationship between y and T based on the actual tendon prestress data is strong. As indicated in Section IV, the magnitude of the correlation coefficient'between y and T are -88% for Callaway horizontal tendons, -90% for Callaway vertical tendons -76% for Wolf Creek horizontal tendons and -86% for Wolf Creek vertical tendons.
By applying the linear regression analysis on Eq. I and using the actual tendon prestress data described in Section IV, the following results are obtained:
(a)
For t.he horizontal tendons, the time functions of its average, lower bound, and upper bound prestress forces are respectively given by Eqs. 12 through 17, and are exhibited in Figures 3a and 3b for the Callaway and Wolf Creek containments, respectively.
(b)
For the vertical tendons, the time functions of its average, lower bound and upper bound prestress forces are respectively given by Eqs.
18 through 23, and are exhibited in Figures 4a and 4b for the Callaway and Wolf Creek containment, respectively.
has a 97.5% probability that the actual tendon prestress Note that yt force is larger than yt; and y uhas a 2.5% probability that the actual tendon prestress force is larger than yu '
16
Based on the statistical prediction (using the actual tendon prestress data only) exhibited in Figures 3a, 3b, 4a and 4b, all post tensioning prestress systems for both the Callaway and Wolf Creek containments are shown to maintain their average prestress level much above their minimum offective arestress requirements throughout the plant operating life span of 40 years. Namely per i> fs. 8 and 9, the design requirement specifies that the averaae prestressed shall be greater than or equal to the minimum effective design prestress. For both Callaway and Wolf Creek containments, the minimum effective pres +.resses required are 147 ksi and 139 ksi, for the horizontal and vertical tendon, respectively. ,
Utilizing the result of the regression analysis based on the actual tendon prestress data from the initial,1st and 2nd surveillance records, the In this tendon prestress outcomes are probabilistically simulated.
simulation, for at least half of the samples (tendons) to be inspected in the next surveillance, their prestress outcomes are arbitrarily set equal to the minimum effective design prestress i.e.,147 ksi for the horizontal '
For the remaining samples tendon and 139 ksi for the vertical tendon.
(tendons) to be inspected in the next surveillance, their prestress outcomes are generated using normal variate about the average (mean) obtained from the regression analysis using the actual tendon prestress l
data. For each set of outcomes simulated using the above procedure, it has been shown that its probability of being worse t',an the set of actual i.e.,
data to be obtained in the next surveillance is insignificantly low, This implies that each set of simulated tendon its maximum is 1.05%.
prestress outcomes for the next surveillance is significantly conservative.
17 l
By applying the linear regression analysis on Eq. I and using 'the a tendon prestress data plus the simulated prestress data, the following results are obtained:
For the horizontal tendons, the time functions of its average, lower (a) bound and upper bound prestress forces are respectively given by Eq 25 thru 30, and are exhibited in Figures 5a and 5b for the Callaway and Wolf Creek containments, respectively.
For the vertical tendons, the time functions of its averagr, lower (b) bound and upper bound prestress forces are respectively given by E 31 thru 36 and are exhibited in Figures 6a and 6b for the Callaway and Wolf Creek containment, respectively.
Based on the statistically predicted (using the actual tendon prestress data plus the simulated data) exhibited in Figures Sa, 5b, 6a an post tensioning prestress systems for both the Calla *>ay and W containments are shewn to maintain the average prestress level mu their minimum effective prestress requirements throughout the plant operating life span of 40 years.
For each set of the simulated outcomes associated with th surveillance, (a) at least half of the outcomes are arbitrarily set e to the minimum effective design prestress, (b) the probability of obtaining a set of actual outcomes being worse than the set of si outcomes is insignificant 1y low, and (c) all the average prestres 1B
are much higher than their minimum effective design prestress throughout the plant operating life span.
VI. CONCLUSION For all the prestressing system groups of the Callaway and Wolf Creek Unit I containment shells, the tendon prestress force, y at any time, T can be expressed as the logarithmic function of T described by Eq. I which As discussed in adequately represent the relaxation of prestress force.
Section IV, the dome tendons can be considered equivalent to the cylinder tendons for statistical analysis. Both the cylinder and dome tendons are referred to as horizontal tendons.
The statistical prediction of the performance of each post tensioning prestress is obtained by applying the linear regression analysis on Eq At first, the regression analysis is performed using only the actual tendon prestress data from the initial prestressing, the 1st and 2nd surveillance. The result of this analysis is then utilized to '
probabilistically simulate the tendon prestress outcomes as described Section IV.3.
The regression analysis is then performed using the actual tendon prestress data from the initial prestressing stage, the 1st and 2n These analyses surveillance plus the simulated tendon prestress data.
lead to the foTTowing conclusion.
The analysis indicates with 97.5% confidence level that the remaining prestressing level in the tendons at 40 years will exceed the design requirement. Based on References 8 and 9, this design requirement 19
specifies that the averaae prestress shall be greater than the minimum-effective design prestress of 147 ksi for the horizontal tendons and 139 ksi for the vertical tendons.
In this regard the following margins were computed based on utilizing the initial and measured first and second surveillance data:
(a)
The prestress level provided by the Callaway horizontal tendons at 40 years exceeds the design requirement by 6.98%
(b)
The prestress level provided by the Wolf Creek horizontal tendons at 40 years exceeds the design requirement by 11.2% l (c)
The prestress level provided by the Callaway vertical tendons at 40 years exceeds the design requirement by 22.0%
(d)
The prestress level provided by the Wolf Creek vertical tendons a years exceeds the design requirement by 19.5%
I For each set of the simulated outcomes for both the Callaway and Wol Creek containments, (1) at least half of the tendon prestress outcones are arbitrarily set equal to there minimum effective design prestress (i.e.,
147 ksi for the horizontal tendon and 139 ksi for the vertical tendon),
(2) the probability of obtaining a set of actual outcomes being w the set of simulated outcomes is insignificant 1y low (i.e., the maximum probability is 1.05%), and (3) all the average prestress levels ar higher than their minimum effective design prestress throughou <
20
_ _ _ - _ _ _ _ _ _ _ _ _ _ _ - _ _ - _ _ _ = _ _ _ _ _ _ - _ _ _ _ _ _ _ _ - _ - _ - _ _ _ _ - ______-____ ______ -__-__ . _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __________-_________
(Note that per Refs. 8 and 9, the design operating life span of 40 years. t specifies requirement for both the Callaway and Wolf Creek containmen the minimum that the averace prestressed shall be equal .to or greater than effective design prestress.)
i ,
In this regard, the following margins were computed i lated based the initial, and measured first and second surveillance and s mu third surveillance data:
t (e)
The prestress level provided by the Callaway horizontal t !
40 years exceeds the design requirement by 5.1%
d at (f)
The prestress level provided by the Wolf Creek horizonta 40 years exceeds the design requirement by 7.86%
40 (g)
Th prestress level provided by the Callaway vertical ten years exceeds the design requirement by 17.0%
t 40 (h)
The prestress level provided by the Wolf Creek vertica years exceeds the design requirement by 14.6%
21
1 e ., ,
Based on the above projections, the post tensioning system is shown to maintain an average stress level above the minimum prestressing The data ;
requirements even with simulated low lift-off measurements.
clearly supports that there is a greater than 95% confidence factor and -
less than 5% chance for gross deterioration of containment capacity for Wolf Creek and Callaway. In addition, the rate of change in prestressing is extremely slow such that if occasional low lift-off readings are encountered an immediate reduction in the prestressing system capacity is not expected.
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s' TABLE ja - RECORDED PRESTRE55 FORCE' DATA AND RELATED STATISTIC CALCULATION (CALLAWAY WIT 1)
DATA TENDON TOTAL TENDON TENDON TIME K= (X1 Xavg (Yi Yavg (Xi-Xavg)
NO. NO. W1RE FORCE STRESS (YEAR) LnTi )*2 )*2 (Yi Yavg)
AREA (K) (KS1) ist trd 3r 4fh sth 6 fh 7fh 8 th N IN 1 1.CB 8.345 1480.04 177.36 0.001 -6.908 19.282 75.271 -38.097 2 9 CB 8.296 1484.27 178.91 0.001 -6.908 19.282 104.721 -44.936 3 9 AC 8.345 1496.51 179.33 0.001 -6.908 19.282 113.413 -46.764 4 26 AC 8.345 1496.51 179.33 0.001 6.908 19.282 113.413 -46.764 5 5 BA 8.345 1488.07 178.32 0.001 -6.908 19.282 92.894 -42.323 6 45 8A 8.247 1489.34 180.59 0.001 -6.908 19.282 141.875 -52.303 7 51 BA 8.345 1393.71 167.01 0.001 -6.908 19.282 2.786 7.330
- 8 5 AC 8.345 1454.38 174.28 0.001 -6.908 19.282 31.371 -24.595 9 11 CB 8.345 1495.26 179.18 0.001 -6.908 19.282 110.245 -46.106 10 14 BA 8.345 1476.26 176.90 0.001 -6.908 19.282 67.617 36.108 11 18 BA 8.345 1478.79 177.21 0.001 -6.908 19.282 72.695 37.439 12 3F BA 8.345 1500.33 179.79 0.001 -6.908 19.282 123.372 -48.774 13 4nBA 8.345 1420.67 170.24 0.001 -6.908 19.282 2.438 -6.857 14 1-CB 8.345 1371 164.29 3.847 1.347 14.930 19.277 -16.965 15 9 CB 8.296 1324 159.59 3.847 1.347 14.930 82.548 35.106 16 9 AC 8.345 1339.5 160.52 3.872 1.354 14.980 66.672 -31.603 17 26 AC 8.345 1339 160.46 4.031 1.394 15.293 67.655 -32.166 18 5 BA 8.345 1357 162.61 3.889 1.358 15.014 36.824 -23.513 19 45 BA 8.247 1312.5 159.15 3.692 1.306 14.614 90.856 -36.438 20 51 BA 8.345 1283.5 153.80 3.733 1.317 14.698 221.293 57.032 21 45 BA 8.247 1337.66 162.20 5.828 1.763 18.31 42.00 -27.73 22 5 AC 8.345 1320.18 158.20 5.997 1.791 18.56 109.84 -45.15 23 11 CB 8.345 1323.52 158.60 5.983 1.789 18.54 101.62 -43.40 24 14 BA 8.345 1389.44 166.50 5.900 1.775 18.42 4.76 -9.36 25 18 BA 8.345 1381.10 165.50 5.897 1.774 18.41 10.12 -13.65 35-BA 8.345 1421.15 170.30 5.872 1.770 18.38 2.62 6.94 26 27 47-8A 8.345 1285.80 154.20 5.847 1.766 18.34 209.69 -62.01 Yavg= Xavg= SW1= SW2= SW3=
168.681 -2.517 484.081 2117.877 -890.92 BETAl-
-1.840 BETA 0 164.049 to 2.624 19.126 i
1 s j TABLE lb - RECORDED PRESTRE55 FORCE DATA AND RELATED STATISTIC CALCULATION (WOLFCREEKGENERATIONSTATION)
DATA TENDON 101AL TENDON TENDON TIME A= (Xi Kavg (Yi Yavg (It Xavg)
NO. NO. WIRE FORCE STRESS LnT) (Yi Yavg)
(YEAR) )^2 )*2 AREA (K) (K51) ist and 3 4th sn an 7 th Sih 4 th to th 1 1.CB 8.345 1480.15 177.37 0.001 -6.908 18.855 39.327 27.231 2 9 C8 8.345 1491 98 178.79 0.001 -6.908 18.855 59.117 33.387 3 9 AC 8.345 1488.83 178.41 0.001 '-6.908 18.855 53.455 31.748 4 26-AC 8.296 1500.43 180.86 0.001 -6.908 18.855 95.323 -42.395 5 5 8A 8.296 1511.54 182.20 0.001 -6.908 18.855 123.266 -48.210 -
6 45 BA 8.345 1457.86 174.70 0.031 -6.908 18.855 12.961 15.633 7 51-BA 8.345 1387.41 166.26 0.001 -6.908 18.855 23.446 21.026 8 5 AC 8.345 1493.87 179.01 0.001 -6.908 18.855 62.651 -34.370 i 9 11 C8 8.345 1498.74 179.60 0.001 -6.908 18.855 72.230 -36.904 1 10 14 BA 8.345 1459.54 174.90 0.001 -6.908 18.855 14.451 -16.507 l 11 18 8A 8.345 1476.31 176.91 0.001 -6.901 18.855 33.768 -25.233 l 8.345 12 35 BA 1477.99 177.11 0.001 -6.908 18.855 36.148 -26.107 l 13 47-BA 8.345 1392.44 166.86 0.001 -6.908 18.855 17.972 18.408 14 1 CB 8.345 1422 170.40 3.686 1.305 14.977 0.486 2.698 15 9 CB 8.345 1387 166.21 3.706 1.310 15.019 23.924 -18.956 16 9 AC 8.345 1358 162.73 3.708 1.310 15.023 69.996 32.428 17 26 AC 8.296 1359 163.81 3.792 1.333 15.197 53.066 28.398 18 5 BA 8.296 1381 166.47 3.708 1.310 15.023 21.462 -17.957 19 45 BA 8.345 1409 168.84 3.383 1.219 14.321 5.085 -8.533 20 51-BA 8.345 1348 161.53 3.469 1.244 14.511 91.483 -36.435 21 45 BA 8.345 1430 171.36 4.967 1.603 17.375 0.068 1.090 22 5 AC 8.345 1395 167.17 5.278 1.664 17.885 15.465 16.63) 23 11-CB 8.345 1385 165.97 5.258 1.660 17.853 26.326 21.679 24 14 BA 8.345 1393 166.93 5.089 1.627 17.578 17.407 17.492 25 18 BA 8.345 1420 170.16 5.567 1.717 18.339 0.878 -4.011 !
26 35 BA 8.345 1408 168.72 5.056 1.621 17.523 5.639 9.941 27 47 8A 8.345 1305 156.38 5.006 1.611 17.440 216.604 -61.462 Yavg= Xavg= $ UNI. SUM 2= $UM3-171.099 2.566 473.182 1192.004 -573.821 SETAL-1.213 BETA 0 167.987 t-
, 2.424 19.846 l
h* . ;
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TABLE ta - The Average Lower Bound, and Upper Sound Prestress Force of the Horizontal Tendon for Callaway Unit 1 Containment i
DATA Ti Xi. Sy*2 AVG. LOWER UPPER ND. (yr.) LnTi PRE- BOUND BOUND STRESS PRE. PRE-(KSI) STRESS STRESS 1 0.001' -6.90775 20.59828 176.76 164.853 188.671 2 0.01 -4.60517 20.00873 172.52 160.787 184.262 3 0.5 -0.69314 19.96775 165.32 153.599 177.050 4 1 0 20.08662 164.05 152.289 175.809 5 2 0.693147 20.24346 162.77 150.967 174.579 6 4 1.386294 20.43827 161.50 149.635 173.360 7 6 1.791759 20.56983 160.75 148.850 172.652 8 8 2.079441 20.67105 160.22 148.292 172.152 9 10 2.302585 20.75407 159.81 147.857 171.765 10 15 2.708050 20.91498 159.06 147.065 171.065 11 20 2.995732 21.03704 158.54 146.500 170.571 12 25 3.218875 21.13621 158.12 146.061 170.188 -
13 30 3.401197 21.22017 157.79 145.702 169.877 14 35 3.555348 21.29320 157.51 145.397 169.614 15 40 3.688879 21.35798 157.26 145.133 169.387 .
AVG 1= AVG 2= AVG 3=
162.133 150.199 174.067 l
1*. l
\
l 7ABLE 2b The Average, Lower Bound, and Upper Bound Prestress Force of the Horizontal Tendon for Wolf Creek Unit 1 Containment FA 11 Xi= sya2 AVG. - LOWER NO. (yr.) LnTi J.;- BOUND UPPER BOUND STRESS PRE- PRE-(K51) STRESS STRESS 1 0.001 -6.90775 21.37138 176.36 164.234 188.495 2 0.01 -4.60517 20.75507 173.57 161.618 3 0.5 185.526
-0.69314 20.72762 168.83 156.882 180.774 4 1 0' 20.85663 167.99 156.004 179.971 5 2 0.693147 21.02594 167.15 155.115 179.179 6 4 1.386294 21.23556 166.31 154.214 178.398 7 6 1.791759 21.37685 165.81 153.682 177.947 8 8 2.079441 21.48548 165.47 153.303 177.629 9 10 2.302585 21.57451 165.20 153.007 177.383 10 15 2.708050 21.74697 164.70 152.467 -176.940 11 20 2.995732 21.87770 164.35 152.081 176.628 12 25 3.218875 21.9838B 164.08 151.781 176.387 13 30 3.401197 22.07374 163.86 151.535 176.191 14 35 3.555348 22.15188 163.68 151.326 176.026 15 40 3.688879 22.22119 163.51 151.145 175.883 AVGl= AVG 2= AVG 3-166.725 154.559 178.890 4
1 .
1 l
l TABLE 31 - RECORDE0 PRESTRE55 FORCE DATA AND RELATED STATISTIC CALCULATION (CALLAWAYUNIT1)
DAlA 1ENDON 101AL TENDON TENDON TIME X= (Xi Xavg (Yt Yavg (Xplavg)
ND. NO. W1RI FORCE STRESS (YEAR) LnT1 )*2 )*2 (Yi Yav9)
, AREA (K) (K51) 11 and .a r 4% Sth 46 ~
7th in 40 le th 3 V 20 8.296 1495.51 7DF 0.001 -6.908 20.4BB 22.832 21.625 2 V 35 8.296 1482.57 178.71 0.001 -6.908 20.488 9.598 -14.023 3 V 65 8.345 1515.08 181.56 0.001 6.908 20.488 35.336 -26.906 4 V-74 8.296 1508.3 181.81 0.001 -6.908 20.488 38.434 28.061 5 V1 8.345 1488.07 178.32 0.001 6.90B 20.488 7.332 12.256 6 V 18 8.345 1515.08 181.56 0.001 6.908 20.488 35.336 26.906 7 V 47 8.345 1488.07 178.32 0.001 6.908 20.488 7.332 -12.256 8 V 20 8.296 1411 170.08 3.747 1.321 13.708 30.570 -20.471 9 V 35 8.296 1418 170.93 4.083 1.407 14.351 21.952 -17.749 10 V 65 8.345 1449.5 173.70 3.764 1.325 13.741 3.664 7.096 11 V 74 8.296 1451 174.90 4.083 1.407 14.351 0.500 2.6SO 12 V 65 8.345 1446.19 173.30 5.917 1.778 17.299 5.341 9.612 13 V1 8.345 1412.81 169.30 6.289 1.839 17.810 39.829 -26.634 14 V 18 8.345 1451.20 173.90 5.917 1.778 17.299 2.928 -7.117 15 V 47 8.345 1396.95 167.40 5.919 1.778 17.302 67.421 34.155 Yav9= Kavg= SUMI. SUM 2= SUM 3=
175.611 2.381 269.276 328.404 267.549 BETAl-0.994 BE1A0 173.245 t.
2.162 4.813
)
. i
. j i
TABLE 3b - RECORDED PRISTRESS FORCE DATA AND RELATED STAT 1571C CAttulATION l (WOLF CREEK GENERATION STATION)
. 1 DATA lENDON 101AL lENDON lEN00N IlME 1 NO. NO. W1RE FORCE (Kj-Kavg (yj.ynyg (xj.Xavg)
STRESS (YEAR) LnTi )at ja2 (YiYavg)
AREA (K) l (K51) 1 (IN^3) ist td s ed 4% y% s% ph 60 M% n6 t
1 V 20 8.345 14B4.7 177.91 0.001 -6.908 20.125 21.574 -20.837 2 V-35 8.345 1486.55 178.14 0.001 -6.908 20.125 3 V 65 8.345 23.683 -21.832 1491.41 178.72 0.001 -6.908 20.125 4 V 74 8.345 1517.02 29.691 -24.444 181.79 0.001 -6.908 20.125 72.553 5 V1 8.296 1480.15 -38.212 178.42 0.001 -6.908 20.125 26.494 6 V-18 8.345 23.091 1483.02 177.71 0.001 -6.908 20.125 7 V-47 8.345 19.745 -19.934 1 1476.31 176.91 0.001 -6.908 20.125 13.246 8 V-20 8.345 1400 167.77
-16.327 l 3.608 1.283 13.726 30.305 20.395 !
9 V 35 8.345 1339 160.46 4.053 1.399 14.601 10 V-65 8.345 164.217 -48.967 1 1432 171.60 3.619 1.286 13.748 11 V-74 8.345 2.790 .-6.193 1404 168.24' 4.075 1.405 14.643 25.257 -19.231 V 65 12 8.345 1417 169.80 5.203 1.649 13 , V-1 16.572 12.026 -14.117 j 8.296 1385 166.95 5.531 1.710 17.074 14 - V-18 8.345 39.970 -26.123 1437 172.20 5.200 1.649 16.568 15 V-47 8.345 1.147 -4.360 1439 172.44 5.192 1.647 16.555 0.691 -3.383 Yav9= Xav9= SUMla SUM 2= SUM 3 173.270 -2.422 264.361 483.388 307.446 BETAl=
-1.163 BITAD.
170.454 t.
2.162 9.680 l
l
{
- )
1 p..
A B
TABLE 4s - The average, Lower Sound, and Upper Sound Prestrest Force of the Vertical Tendon for Callaway Unit 1 Containment L
l
- DATA 11 11= 5y'2 AVG. LOWER UPPER NO. (yr.) LaTi PRE- 80WD 80WD STRESS PRE- PRE-(KSI) STRESS STRESS 3 D 00T -6.90775 5.500175 180.11 175.037 185.180 2 0.01 -4.60517 5.222363 177.82 172.879 182.762 3 0.5 0.69314 5.184923 173.93 169.010 178.857 4 1 0 5.235344 173.24 168.297 178.193 5 2 0.693147 5.302942 172.56 167.577 177.536 6 4 1.386294 5.387715 171.87 166.848 176 887 7 6 1.791759 5.445266 171.46 166.419 176,H1 8 8 2.079441 5.489663 171.18 166.112 176.
- 7-9 10 2.302585 5.526138 170.96 165.874 176.040 10 15 2.708050 5.596970 170.55 165.438 175.670
!! to 2.995732 , 5.650791 170.27 165.128 175.409 12 25 3.218875 5.694575 170.05 164.886 175.207 13 30 3.401197 5.731670 169.87 164.688 175.042 14 35 3.555348 5.763961 169.71 164.521 174.904 15 40 3.688879 5.792619 169.58 164.375 174.784 AVGl. AVG 2= AVG 3=
172.211 167.139 177.282 9
0
1 l
TABLE (b - The average, Lower Sound, and Upper Bound Prestress Force of the Vertical Tendon for Wolf Creek linit 1 Containment DATA Ti 21= Sy^2 AVG. LOWER UPPER (yr.)
NO. LnTi PRE - BOUND BOUND 4 STRESS PRE- PRE-(K51) STRESS STRESS 1 0.001 -6.90775 11.06185 178.49 171.295 185.679 2 l 0.01 -4.60517 10.49954 175.81 168.803 182.816 3 0.5 -0.69314 10.43437 171.26 164.275 178.245 , ;
4 1 0 10.53970 170.45 163.f14 177.474 5 2 0.693147 10.68022 169.65 162.581 176.714 l 6 4 1.386294 10.85592 168.84 161.717 175.966 7 6 1.791759 10.97500 168.37 161.206 175.534 8 8 2.079441 11.06680 168.04 160.842 175.229 9 10 2.302585 11.14218 167.78 160.558 174.994 10 15 2.708050 11.28847 167.30 160.039 174.570 Il 20 2.995732 11.39957 166.97 159.669 174.271 12 25 3.218875 11.48992 166.71 159.380 174.040 13 30 3.401197 11.56645 166.50 159.144 173.852 14 35 3.555348 11.63305 166.32 158.944 173.694 15 40 3.688879 11.69215 166.16 158.770 173.558 AVGl= AVG 2= AVG 3-169.243 162.044 176.442 i
e
l c
TABLE 51 - ACTUA!. AHD SIMULATED PRESTRISS FOR:" OATA AMD RELATED STAT 15 TIC CALCULATION (CALLAWATUNIT1) t DATA TENDON T01Ai TENDON TENDON TIME A. '(11 lav9 (ft favg (Ai lavg)
MD. h0. W1RE FORCE STRESS (7IAR) LnTi )*2 )*2 (11 Yavg)
ARIA (K) (151)
(IM'3)
T T 8.345 1480.04 7"3T 0.001 -6.908~ 28.195 136.831 62.113 2 9.C8 8.296 1484.27 378.91 0.001 6.908 28.195 175.693 70.382 3 9 At 8.345 1496.51 179.33 0.001 6.908 28.195 186.900 72.592 4 26 AC 5.345 1496.51 179.33 0.001 6.908 28.195 186.900 72.592 5 5 8A 8.345 1488.07 178.32 0.001 -6.908 28.195 160.269 67.222 6 45 BA 8.247 1489.34 180.59 0.001 6.908 28.195 222.986 79.291 7 51 BA 8.345 1393.71 167.01 0.001 6.908 28.195 1.829 7.181 8 5 AC 8.345 1454.38 174.28 0.001 6.908 28.195 74.349 45.785 9 11 C8 8.345 1495.26 179.18 0.001 6.908 28.195 182.827 71.797 10 14.BA 8.345 1876.26 176.90 0.001 .l.908 28.195 126.439 59.707 11 18 8A 8.345 1478.79 177.21 0.001 6.908 28.195 133.350 61.317 12 35 8A 8.345 1500.33 179.79 0.001 6.908 28.195 199.626 75.023 13 47 BA 8.345 1420.67 170.24 0.001 6.908 28.195 21.004 24.336 14 1 C8 8.345 1371 164.29 3.847 1.347 8.674 1.874 -4.032 15 9 CB 5.296 1324 159.59 3.847 1.347 8.674 36.772 17.859 16 9 AC 8.345 1339.5 160.52 3.872 1.354 8.712 26.458 15.182 17 26 AC 8.345 1339 160.46 4.031 1.394 8.951 27.078 15.569 18 5.BA 8.345 1357 162.61 3.889 1.358 8.738 9.282 9.006 19 45 8A 8.247 1312.5 159.15 3.692 1.306 8.433 42.383 18.906 20 51 8A 8.345 1283.5 153.80 3.733 1.317 8.498 140.525 34.556 21 45 8A 8.247 1337.66 162.20 5.828 1.763 11.29 11.96 11.62 22 5 AC 8.345 1320.18 158.20 5.997 1.791 11.49 55.64 25.28 23 11 C8 8.345 1323.52 158.60 5.983 1.789 11.47 49.83 23.91 24 14.BA 8.345 1389.44 166.50 5.900 1.775 11.38 0.71 2.84 25 18.BA 8.345 1381.10 165.50 5.897 1.774 11.37 0.03 -0.54 26 35-8A 5.345 1421.15 170.30 5.872 1.770 11.34 21.54 15.63 27 47 8A 8.345 1286.80 154.20 5.847 1.766 11.32 131.31 38.55 28 51 1 162.28 162.28 7.000 1.946 12.56 11.42 11.97 29 52 1 164.31 164.31 7.000 1.946 12.56 1,82 4.78 30 53 1 16L44 163.44 7.000 1.946 12.56 4.92 7.85 31 54 1 147.00 147.00 7.000 1.946 12.56 348.16 66.12 32 55 1 147.00 147.00 7.000 1.946 12.56 348.16 66.12 33 56 1 147.00 147.00 7.000 1.946 !!.56 348.16 66.12 34 57 1 147.00 147.00 7.000 1.946 12.56 348.16 66.12 Yavg. Xavg. SUMI. SUM 2- 5U".3 -
165.659 1.598 594.780 3775.183 1254.99
$(TAl-2.110 SETA0-162.288 t.
2.038 35.224 Neie 5-1 thru S-7 are simulaird data.
=. .
- s TABLE fb - ACTUA!. AND SlWULATED PAISTAI53 FDR:I DATA AND St uTED STATIST (WOLF CREEK 01%1 RAT 10M STATION)
OATA TEhDON TOTAL TENDON IENDON IIME 1 (Ai Aavg NO. NO. WIRI (11 favg (Ai Aavg)
ARIA FORCE STRESS (Y[AR) Lnit )*2 )*2 (YiYavg)
(K) (K51)
(IN'3)
""T l'"G~ 8.345 1480.15 177.37 0.001 6.908 27.784 2 9 CB 8.345 1491.98 95.148 51.416 178.79 0.001 6.908 27.784 124.814 3 9.A; 8.345 1488.83 58.818 178.41 0.001 . 6.908 27.784 116.522 4 26 At 8.296 1500.43 180.86 56.855 0.001 6.908 27.784 175.471 69.824 5 5 SA 8.296 1511.54 182.20 0.001 6.908 27.784 212.744 76.813 6 45.BA 8.345 1457.86 174.70 0.001 6.908 27.784 50.173 37.337 7 51.BA 8.345 1387.41 166.26 0.001 5 At 6.908 27.784 1.846 7.163
- 8 8.345 1493.87 179.01 0.001 6.908 9 ll CB 8.345 27.784 129.925 60.0!!
1498.74 179.60 0.001 6.908 27.784 10 14.BA B.345 1459.54 174.90 143.570 63.!!8 0.001 6.908 27.784 53.066 38.358 11 18 8A 8.345 1476.31 176.91 0.C01 6.908 27.784 86.383 48.911 12 35 BA 8.345 1477.99 177.11 0.001 4' BA
-6.908 27.784 90.165 50.052 13 8.345 1392.44 166.86 0.001 6.908
' CB 27.784 0.572 3.985 14 8.345 1422 170.40 3.686 1.305 15 A CE 8.345 8.651 7.763 8.195 1387 166.21 3.706 1.310 16 9A 8.345 8.683 1.962 -4.149 1358 162.73 3.708 1.310 8.686 17 26 At 8.296 1359 23.845 14.351 163.81 3.792 1.333 8.818 14.451 10 5.BA B.296 1381 166.47 11.289 -
3.708 1.310 8.686 1.321 3. 3f ?,
19 45 BA B.345 1409 168.84 3.383 to 51 BA 1.219 8.154 1.509 3.56 8.345 1348 161.53 3.469 1.244 21 45 BA 8.345 8.298 36.9B4 17.51t 1430 171.36 4.967 1.603 10.494 22 5 At 8.345 14.024 12.131 1395 167.17 5.278 1.664 23 ll CB 8.345 10.892 0.202 -1.483 1385 165.97 5.258 1.660 10.866 24 14 BA 8.345 2.715 5.411 1393 166.93 5.085 1.627 25 18-8A 8.345 10.652 0.475 2.249 1420 170.16 5.567 1.717 11.246 8.54; 26 35.BA 8.345 6.485 1408 168.72 5.055 1.621 10.610 27 47 BA 8.345 1.229 3.511 1305 156.38 5.006 1.611 10.545 28 51 126.20B 36.481 1 160.37 160.37 7.000 1.946 12.835 29 52 52.454 25.957 1 167.55 167.55 7.000 1.946 12.835 30 53 0.004 0.234 1 163.34 163.34 7.000 1.946 12.835 31 54 1E.278 15.317 1 147 147.00 7.000 1.946 12.835 32 55 424.991 73.t56 1 147 147.00 7.000 1.946 12.835 424.991 33 56 1 147 147.00 73.856 7.000 1.946 12.835 424.991 73.856 34 5-7 1 147 147.00 7.000 1.946 !!.835 424.991 73.856 Yav9 Xavg. SUM). SUM 2 SUM 3 167.615 1.s37 186.320 3290.330 998.106 BE7A1
-1.702 817A0
- 164.829 t.
2.038 49.726 Note : S-t thns 6-8 see simulnied drin .
l -
1 TABLE 6a- The Average Lower Bound, and Upper Bound Prestress Force of the Horizontal Tendon for Callaway Unit 1 Containment DATA h Kim Sy'2 AVG., lower UPPER NO. (yr.) LnTI PRE.
a0VND BOUND STRESS PRE. PRE.
(K51) STRESS STRESS T N 6.90775 37.92964 176.86 164.311 189.414 2 0.01 4.60517 36.79548 172.00 159.642 184.367 3 0.5 0.69314 36.30836 163.75 151.470 176.030 4 0 36.41108 1 162.29 149.990 174.585 5 2 0.693147 36.57072 160.82 148.500 173.150 6 4 1.386294 36.78726 159.36 147.001 171.723 7 6 1.791759 36.94031 158.51 146.120 170.894 8 8 2.079441 37.06071 157.90 145.493 170.307 9 10 2.302585 37.16085 157.43 145.005 169.853 10 15 2.708050 37.35790 156.57 144.117 169.030 11 20 2.995732 37.50952 155.57 143.485 168.448 12 25 3.218875 37.63388 155.50 142.993 167.998 13 30 3.401197 37.73987 155.!! 142.591 101.631 14 35 3.555348 37.83255 154.79 142.250 167.321 15 40 3.688879 37.91510 154.50 141.955 167.053 AVGl. AVG 2= A(G3 160.091 147.662 172.520
S TABl.E 66 - The Average, Lower Bound, and Upper Bound Prestress Force of the Horizontal Tendon for Wolf Creek Unit 1 Containment CaiA- Ti 11 5f2 Ave. . LCa!R 16 0 . (y r. ) OPPER Ln11 PRI. BOUND BOUND STRESS FRI- PRE-(K51) STRISS STRISS
~T M 6.50775 13.54464 176.5i 161.675 191.501 2 0.01 -4.60517 51.93579 172.67 157.981 187.356 3 0.5 0.65314 51.25395 166.01 151.417 4 180.601 1 0 51.41563 164.83 150.216 179.443 5 2 0.693147 51.64881 163.65 149.003 178.296 6 4 1.315294 51.95348 162.47 147.778 177.160 7 6 1.751759 52.18533 161.78 147.057 176.501 8 8 2.079441 52.35564 161.29 146.542 176.036 9 10 2.302585 52.50452 160.91 146.142 175.677 10 15 2.7C!:50 52.78535 160.22 145.412 175.027 11 20 2.995732 53.008:1 159.73 144.891 12 174.567 25 3.218875 53.18797 159.35 144.486 174.213 13 30 3.401197 53.34095 155.04 144.155 173.924 14 35 3.555348 53.47469 158.78 143.874 173.680 15 40 3.688679 53.55380 158.55 143.630 173.469 Aycl. AVC2 AVC3 163.057 148.264 177.830 s.
i
', I i
1ABLE 7a - ACTUAL A@ SIMULATED P8tSTRESS FOR t DATA AND 8 ELATED STATISTIC CALCULATION i
(CALLAWAYUNIT1)
L 1
l DATA TENDON TOTAL TENDON TENDON TIME I. (11 14vg (Yt favg (11 lavg)
FORCE STRESS LaTi )*2 )*2 (Yi Yavg)
NO. NO. WIRE (YEAR)
ARIA (K) (K51)
(IN'3) 6 905 29.565 83.109 49.56i "T W B.296 1496.51 180.39 178.71 0.001 0.001 -6.908 29.565 55.296 40.433 l 2 V-35 8.296 1482.57 1515.08 181.56 0.001 -6.908 29.565 105.730 55.909 3 v.65 8.345 57.296 4 V 74 8.296 1508.3 141.01 0.001 6.908 29.565 111.041 -
178.32 0.001 6.908 29.565 49.644 38.311 5 v.1 8.345 1488.07 181.56 0.001 6.908 29.565 105.730 55.901 6 V 18 8.345 1515.08
-7 V 47 8.345 1488.07 178.32 0.001 6.908 29.565 49.644 38.311 l 170.08 3.747 1.321 7.792 1.418 3.324 8 V 20 8.296 1411 0.999 9.296 1418 170.93 4.083 1.407 8.279 0.121 .
9 V 35 6.777 j 8.345 1449.5 173.70 3.764 1.325 7.817 5.875 10 V 65 174.90 4.083 1.407 8.279 13.182 10.446 11 V 74 8.296 1451 6.584 0.345 1446.19 173.30 5.917 1.778 10.551 4.109 12 V 65 6.529 169.30 6.289 1.839 10.951 3.892 13 V1 8.345 1412.81 10.551 6.902 4.533 14 V-18 8.345 1451.20 173.90 5.917 1.778 5.919 1.778 10.553 14.999 12.581 15 V 47 8.385 1396.95 167.40 7.000 1.946 11.671 7.469 9.337 16 51 1 168.54 168.54 11.671 4.871 7.540 17 52 1 173.48 173.48 7.000 1.946 139.00 7.000 1.946 11.671 1041.541 110.255 18 53 1 139.00 7.000 1.946 11.671 1041.541 110.255 19 54 1 139.00 139.00 Yavg. Invg. SUMI. SUM 2 $UM3 ,
1.470 328.410 2706.114 549.137 171.273 SETA1 1.672 SITA0 168.814 t.
2.110 105.170 Not e : S-14hru S~4 are simulnied.
i 1
I
\
a t ;
s' !
", I s
l 1ABLE 7b - ACTUAL AND SIMULATED Pat!TRI53 FOR0! DATA AND RELi.TED STATISTIC CALOULAT10N 1 (WOLF CR((K C[NI d" T10f4 STATION)
(
l Qai A TIGN 101AL TEND 0h lE G N TIME f40. NO. W1RE FOR0E STRESS 3 (Ki Xavi (Ti'Yav9 (1. law;,
(YEAR) LnTi )*2 )*2 ARIA (K) (Yt Ya.9)
(K51) ,
(1h*3) -
7 V 20 8.345 1464.7 177.9) 0.001 6.506 25.220 82.161 41.004 2 v.35 8.345 1426.55 178.14 0.001 6.908 29.220 86.250 10.202 3 V 65 8.345 1891.41 178.72 0.001 6.908 4 V 74 29.220 97.406 13.310 8.345 1517.02 181.79 0.001 6.903 29.220 5 V1 8.296 167.401 -59.919 1880.15 178.42 0.001 6.906 29.220 6 V 16 8.345 1483.02 177.71 91.542 !!.719 0.001 6.906 29.22e 78.572 -47.915 7 V 47 8.345 1476.31 176.11 8 V 20 8.345 0.001 6.90! 29.h. 64.963 43.!!i 1400 167.77 3.60B 1.2B3 7.756 V 35 1.176 -3.020 9 8.345 1339 160.46 4.053 1.399 8.420 V 65 70.462 24.357 10 8.345 1432 171.60 3.619 1.2E6 7.775 V 74 7.564 7.611 11 8.345 1404 168.24 4.075 1.405 8.451 V 65 0.366 1.759 12 8.345 1817 169.80 5.203 1.649 9.931 V1 0.901 3.002 13 8.295 1385 166.95 5.531 1.710 10.321 la V 12 3.616 -6.109 8.345 1437 172.20 5.200 1.649 9.925 15 V 47 8.345 11.21! 10.511 1439 172.44 5.192 1.647 9.918 16 51 12.t11 11.301 1 363.95 163.95 7.000 1.946 11.889 24.006 17 52 -16.894 1 167.14 167.14 7.000 1.946 11.889 2.923 18 53 5.895 1 139 139.00 7.000 1.946 11.889 890.915 102.924 19 54 1 139 139.00 7.000 1.946 11.869 890.995 -102.924 Yavg. Xavs- SLH1 = SUM 2= SiH3 168.850 1.502 324.600 2585.425 557.053 EI7A1 1.239 E! TAO.
Hofe : s-2 thea s-t see simulated daia .
___ . _ _ . _ _ _ - _ - - - - " - - - - - - ' - - - - - - - - - - - - ' - " " ' - - - - ' - - - - " ' - - ._ = -
, i ;
e
. . =
s TABLE Ba - The average Lower Sound, and Upper Sound Prestress Force of the Vertical Tenden for Callaw8y Unit 1 Containment DATA Ti Kia Ey*2 AVG. LOWER UFFER NO. (yr.) LnT1 PRE. SOUND SOUND STRESS PRE- PRE-(K31} STRESS STRESS
- T N 6.90775 120.1736 180.36 157.234 203.495 2 0.01 4.60517 113.8526 176.51 154.000 199.029 3 0.5 0.69314 110.8992 169.97 147.753 192.193 4 1 0 111.3981 168.81 146.544 191.084 5 2 0.693147 112.2048 167.66 145.305 190.006 6 4 1.386294 !!3.3192 166.50 144.035 188.957 7 6 1.791759 114.1137 165.82 143.278 188.358 8 8 2.079441 114.7413 165.34 142.735 187.939 9 10 2.302585 115.2645 164.96 142.311 187.617 10 15 2.708050 116.2970 164.29 141.532 187.041 Il 20 2.995732 117.0934 163.81 140.973 186.637 12 25 3.218875 117.7477 163.43 140.536 186.328 13 30 3.401197 118.3059 163.13 140.177 186.077 14 35 3.555348 118.7945 162.87 139.872 185.867 15 40 3.688879 119.2300 162.65 139.606 185.686 AVGl= AVG 2= AVG 3 167.074 144.393 189.754 ,
1 i
1
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l c .. .
t 1
TABl.E Bb - The average, Lower Bosmd, and Upper Sound Prestress Force of the Vertical Tendon for Wolf Creek Unit 1 Containment CaIA' h 11= 5y'2 AVG. . LOWER NO. (yr.) LnTi PRE- SOUND UFFER BOUND STRESS PRE- PRE-(K51) STRESS STRESS r (35T Timr TERTIT 178.7s ~m .ss6 19s.esa 2 0.01 4.60517 94.62401 174.56 154.025 195.089 3 0.5 -0.69314 92.26540 167.35 147.094 4 187.629 1 0 92.69717 166.09 145.772 5
186.401 2 0.693147 ~ 93.38791 164.81 144.421 6 4 185.202 1.326294 94.33764 163.54 143.043 7 6 164.031 1.791759 95.01325 162.75 142.224 8 8 183.352 2.079441 95.54634 162.25 141.637 9 182.825 10 2.302525 95.99056 161.85 141.179 1C 182.524 15 2.702050 96.86643 161.!! 140.339 11 20 181.872 2.995732 97.54112 160.52 139.737 12 25 181.415 3.218875 St.09505 160.17 139.268 181.064 13 30 3.401197 SE.56292 14
!!9.83 138.882 180.779 35 3.55534B St.98222 !!9.55 138.555 180.539 15 40 3.685579 99.35165 15 .30 138.270 180.333 AVGl. AVG 2= AVG 3-164.172 143.476 184.857
_ _ _ _ _ . _ _ _ _ _ _ . _ _ _ _ . _ . _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ . _ . _ _ _ _ _ _ _ _ . _ _ . _ __ ._ . _ . . . _ . . _ _ _ _