ML20247L552

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Revised Tech Specs Re Containment Vessel Structural Integrity
ML20247L552
Person / Time
Site: Wolf Creek Wolf Creek Nuclear Operating Corporation icon.png
Issue date: 03/29/1989
From:
WOLF CREEK NUCLEAR OPERATING CORP.
To:
Shared Package
ML20247L304 List:
References
NUDOCS 8904050487
Download: ML20247L552 (60)
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{{#Wiki_filter:- ATTACHMENT I i 8904050487 890329 PDR ADOCK 0500048'2 p PDC

.. y Attachment I to WM 89-0097'. ( Page 1 of 3 Aat.s s oc cdAmc faam 141ML N(tC 9.G,R@ o betb ex A /ps ene c4eubsb.

  • CONTAINMENT SYSTEMS C,0,NTAINMENT VESSEL STRUCTURAL INTEGRITY LIMITING CONDITION FOR 0?ERATION
3. 6.1. 6 The structural integrity of the containment vessel shall be maintained

. at a level consistent with the acceptance criteria in Specification 4.6.1.6. su u aesuvo urr. ore APPLICABILITY: MODES 1, 2, 3, and 4. .mcu ser mecn,% rue. j ACTION: Accermua. enerusa er 1 ,4 sj, g, g, s, g, g, a. With more than one tendon with an observed lift-off forc between l l the predicted lower limit and 90% of the predicted lowet limi ee-with one tendon below 90% of the predicted lower limit, restor e i tendon (s) to the required level of integrity within 15 days and i perform an engineering evaluation of the containment and provide,a l Special Report to the Commission within~30 days in accordance with l Specification 6.9.2 or be in at least HOT STANDBY within the next 6 hours and in COLD SHUTDOWN within.the following 30 hours, b. "ith cay-obnomal dcgredetion cf -thc structurci.ategrity cther then AGHON-e-et e level belcw the occepte..ce c. iterio ef Specifico^ ( gg tien '.5.1.5, rc:;t+rc thc conte 4nment vcssci tc the re@ ired lewei ( sf-4ntegrity ithin 72 heurc cad-perform on cnginccring cveluction "t'i r";"'-""d P r; id; " SP"i'i '3 P' "' '+*-""i" i"" d A p* ithir 15 dcy; in accordancc with pccificctic? C.O.2 cr bc in ct leest-HM-STAN00Y within the next 0 hcers end in COLO SUUT00WN within the fcilcwing 30 hcurs. l ii SURVEILLANCE RE001REMENTS 4.6.1.6.1 Containment Vessel Tendons. The containment vessel tendons' struc-tural integrity shall be demonstrated at the end of 1, 3, and 5 years following l the initial containment vessel structural integrity test and at 5 year intervals thereafter. The tendons' structural integrity shall be demonstrated by: Determining that a random but representative sample of at least 11 a. tendons (4 inverted U and / hoop) each have an observed lif t-of f force within predicted limits for each. For each subsequent inspec-tion one tendon from each group may be kept unchanged to develop a history and to correlate the observed data. If the observed lift off force of any one tendon in the original sample population lies between the predicted lower limit and 90% of the predicted lower limit, two tendons, one on each side of this tendon should be checked for their lift off forces. If both of these adjacent tendons are found to be within their predicted limits, all three tendons should be restored to the required level of integrity. This single deficiency may be conside. red unique and acceptable. Unless there is abnormal degradation of the containment vessel during the first three inspec-tions, the sample population for subsecuent inspections shall inciuoe least 6 tendons (3 inverted U and 3 hoop); al Wolf CREEr. - UN11 1 3/4 6-8

Attachment I to WM 89-0097 Page 2 of 3. I 1 CONTAINMENT SYSTEMS 1 SURVEILLANCE REQUIREMENTS (Continued) ) b. Performing tendon detensioning, inspections, and material tests on a previously stressed ter. don from each group (inverted U and hoop). A-randomly selected tendon from each group shall be completely deten - stoned in order to identify broken or damaged wires and determining that over the entire length of the removed wire that: 3 1) The tendon wires are free of corrosion, cracks, and damage, l ~ 2) There are no changes in the presence or physical appearance of I the sheathing filler grease, and 3) A minimum tensile strength of 240,000 psi (guaranteed ultimate-strength of the tendon material) exists for at least three wire samples (one from each end and one at mid-length) cut from each removed wire.. Failure of any one of the wire samples _to meet l the minimum. tensile strength test is evidence of abnormal degradation of the containment vessel structure. Performing tendon retensioning of those tendons detensioned for. j c. inspection to their observed lif t-off force with a tolerance limit 4 of +6%. During retensioning of these tendons, the changes in load and elongation should be measured simultaneously at a minimum of three approximately equally spaced levels of force between zero and the seating force. If the elongation corresponding to a specific load differs by mere than 5% from that recorded during installation, i g an investigation should he made to ensure that the difference is not related to wire failures or slip of wires in anchorages; d. Assuring the observed lift-off stresses adjusted to account for elastic losses exceed the average minimum design value given below: Inverted U 139 ksi Hoop: Cylinder 147 ksi Dome 134 ksi l Verifying the OPERABILITY of the sheathing filler grease by assuring: e. Lw, ld No-veitts-Qi n scc 35 of p L a

  • . _J *. w _ / a., _. s aL y-A c f-- die-net-dttet vc ! =c,

1) 2) Minimum grease coverage exists for the different parts of the anchorage system, and 3) The chemical properties of the filler material are within the tolerance limits as specified by the manufacturer. de vaan on tact.ss or fi% or ner bu:r veuome ANb No MsOLSn*RCAb (antasL LLA b4A C,L bu A**l G1 Vi s sea % orH PCL re s N oc v4L CuransumKonT* EdrgtU c4. L [L UNil ) 3/4 (r 9 E.,. m u m., % n,,,p.m em e m Nsute,wg,p gr afg, g g,gg 4 og g gg gps.,cw,saissg $4.Gim8 W Ggfe$( LggggA(,g, 7WADsdf,sf NCT W N 4J IMLT 444Ls.4, Yeet (Meestasht 8dlJ e adA E Se/# woe Of lh*)C.h en rWL Mces tr y Awe NAfo f4 # THL GAEMC l c-____________-_____-

v I AttachmentItoWd 89-009'7 ^b ~ Page 3 of 3 l 1 INSERP A b. With any apparent abnormal degradation to a level below the acceptance. criteria of Specification 4.6.1.6.1.b @, er.d,- perform. an engineering evaluation to demonstrate continued i I containment structural integrity 'ni tirovide a Special Report to the Comission within 30 days in accordance with Specification 1 6.9.2, or be in at least WI SWIDOWN within the next 6 hours and in COID SWiDOWN within the following 30 hours. c. With' the structural integrity of the containment otherwise not conforming to the requirements of Specification-4.6.1.6, prcpcr-cr.d -indt : Spccici "cp^rt tc the 0c =i0010.. pursuant t Specification 6.9.2 within 90 days after conpletion of the inspection describing the tendon condition, the condition of the concrete (especially at tendon anchorages), the inspection procedures, the tolerances on cracking, and the corrective actions

taken, d.

The provisions of Specification 3.0.4 are not applicable. ' be mehrstarreAl '"*"a ru #Ast n gOgny.,ft rng 64dfC ## NoHCeNfetl4** Alt-0 M WC w!Kc.ito1*y of n/L consen retracgr-Y NAS A'os" bCNIL,0ftp7X), }$ fettum,ugav /tc.gst.r og vvr INvrerturiost snow.h DC PAwoch n l TM Os.wnessoost.//1"*N bo Onts R<ttsamr rz. Socc,,,w r,,g 6. 9. 2. ,4 s % ei Atseier sMoaa.;st saatserrch rsrwr G e<rius.,. l l l l i 1 ~

4 9 ATTACHMENT II

m Attachment-II to WM 89-0097 SNUPPS CALLAWAY UNIT 1 UNION ELECTRIC COMPANY, MISSOURI WOLF CREEK UNIT 1 WOLF CREEK NUCLEAR OPERATING CORPORATION 1 l. l POST TENSIONING SYSTEM EVALUATION CALLAWAY UNIT 1 CONTAINMENT l WOLF CREEK UNIT 1: CONTAINMENT q 1 l i i 1 1

a.. TABLE OF CONTENTS 1. INTRODUCTION

11. DESCRIPTION OF THE POST-TENS 10NING SYSTEM III. EVALUATION IV. NUMERICAL COMPUTATIONS AND RESULTS i

V.

SUMMARY

VI. CONCLUSIONS l ii L-___-__________

~ LIST OF' FIGURES q i FIGURE TITLE Tendon Galleries in the Ca11away' and Wolf Creek Containment ~ l 1 Buildings Post Tensioning System for the Callaway and Wolf. Creek ] 2-Containment Shells Horizontal Prestressing as a function of Time for Callaway Unit .l 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 l_ 4a Containment (Actual Data Only) Vertical Prestressing as a Function of Time for Wolf Creek Unit 4b 1 Containment (Actual Data Only) Horizontal Prestressing as a Function of Time for Callaway Unit 5a 1 Containment (Actual and Simulated Data) Horizontal Prestre:ising as a function of Time for Wolf Creek 5b Unit 1 Containment (Actual and Siraulated Data) i 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

LIST OF TABLES 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 l Only) 2b The Average, Lower Bound, and Upper Bound 'Prestress Force of the Horizontal Tendon for Wolf Creek Unit 1 Containment (Actual Data Only) I 3a Actual Prestress Force Data for Vertical Tendons for Callaway Unit 1 Containment 3b Actual Prestress Force Data for Vertical Tendens for Woif Creek Unit 1 Containment 4a The Average, Lower Bound, and Upper Bound Prestress Force of.the Vertical Tendon for Callaway Unit'l Containment (Actual Data Only) i i 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 J Horizontal Tendon for Callaway Unit 2 Containment (Actual and Simulated Data) 6b The Average, Lower Bound, and Upper Bound Prestress force of the Horizental Tendon for Wolf Creek Unit 1 Containment (Actual and j SimulatedData) i 1 7a Actual and Simulated Prestress Force Data for Vertical Tendons ) for Callaway Unit 1 Containment j 7b Actual and Simulated Prestress Force Data and Vertical Tendons ) for Wolf Creek Unit 1 Containment j ) iv 1 l

w lf LIST OF TABLES Continued) TITLE TABLE The Average, Lcwer Bound, and Upper Bound Prestress Force of the Vertical Tendon for Callaway Unit 1 Containment (Actual and t 8a Simulated Data) L, - The Average, Lower Bound, and Upper Bound Prestress Force of the 4 l Vertical Tendon for Wolf Creek Unit 1 Containment (Actual 8b Simulated Data) l l l 1 V ^ ~ - - - - ~ _. _ _ _ _ _ _ _ _ _ _

v i 1 REFERENCES l Magura, D.. D. Sozen, M. A. and Sicss, C. P., "A Study of Stress Relaxation in Prestressing Reinforcement," Proceedings Paper Pages 13 thru 57,' 1. Journal of the Prestressed Concrete Institute, April 1964. Bethea, R. M., Duran, B. S., and Boullion,'T. L., " Statistical Methods for Engineers and Scientists," Marcel Dekker, Inc., New York, New York. 2. Benjamin, J. R., and Cornell, C. A., " Probability, Statistics, andMcGraw-Hill 3. Decision for Civil Engineers," l-York, 1970. Hahn, G. J., and Shaprio, S. S., "St'atistical Models in Engineering," John 4. Wiley & Sons, Inc., New York, New York,1967. Calc. No. C'-1989-107, "The Tendon Prestressed on the Containment Shell as 5. Wolf Creek Unit 1 Containment, Bechtel Power time Functions", Corporation. Calc. No. C-1989-106, "The Tendon Prestressed on the Containment Shell as Time Functions", Callaway Unit 1 Containment, Bechtel Power Corporation 6. " Post Tensioning system Evaluation", Technir.a1 Report, ASCO Unit 1, 7. Spain, Bechtel Power Corporation, September, 1988 "In-service Tendon Surveillance Procedure - Reactor Building Post-Tensioning System", SNUPPS Callaway Unit 1 in Missouri, Bechtel Power 8. Corporation, Maryland, May,1985. "In-service Tendon Inspection Program - Reactor Building Post-Tensioning System", Rev.1, SNUPPS Wolf Creek Generating Station in Kansas, Bec 9. Power Corporation, Maryland, December,1985 l l vi i

m 1. 1HTRODUCTION Union Electric and Wolf Creek Nuclear Operating Corporation have proposed to the V. S. NRC a revision to their respective nuclear power plant Technical' The proposed revision is related'to the action plan for.the Specification. containment post-tensioning system surveillance and reflects a change from the The shutdown is required if the present 72 hour plant shutdown to 15 days. l surveillance results do not meet certain conditions stated later on section. In response to Union Electric the U. 5. NRC "USNRC letter (Alexion) to Union l Electric (Schnell) dated May 16, 1988" and U.S. NRC "USNRC Letter (O' Conner) WCNOC (Withers) dated May 24, 1988" requested statistical backup justificat for the proposed revision to show continued structural integrity of the post-tensioning system during the requested 16 day no shutdown period. This report is generated to provide the requested backup justification. Post-tensioning systems for containment structures are subjected to time I For this reason, the dependent losses during the service life of the system. i system design incorporates allowances for such losses so that at the end o service life the remaining prestressing force is equal to or exceeds the design requirement. h 1

Time dependent losses are in the form of tendon material relaxation u Since the amount of losses are tension and concrete creep under compression. material dependent and can only be estimated based on experimentf The assumed values are assumed values are used in the design of the system. The actual usually conservative and exceed the actual experienced losses. l performance of the system is verified by the results obtained from the tendon forces as part of the periodic tendon surveillance requiremen l The aforementioned NRC to UE letter addresses thre They are as' be indicative of gross containment capacity deterioration. i i l follows: The average prestressing forces of the sampled tendons falling belo 1. minimum required prestress. More than one tendon force out of three adjoining tendons falling betwe i 2. their predicted lower bound force and 90% of the lower bound. Any of the sampled tendons falling below 90% of its predicted 3. The purpose of this evaluation is to verify that even with the conditions l outlined above, the containment post-tensioning systems maintain their The results clearly indicate structural capacity above design requirements. that the structural integrity of the Callaway and Wolf Creek systems is maintained past their service life. 2

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 determine the time functions of the average, lower and upper bound prestress levels.

11. DESCRIPTION OF THE POST-TENSIONING SYSTEM The post tensioning system for the Callaway and Wolf Creek Unit I containment structures consist of the vertical tendons and the hoop tendons. The hoop tendon system consists of the cylinder tendons and the dome tendons, a

3

v Vr:rtical tendons consist of 86 inverted U-shaped tendons, which extend through the full height of the cylindrical shell over the dome and are anchored in the tendon gallery at the bottom of the foundation slab as shown in Figure 1. a Hoop tendons located in the cylindrical shell consist of 135 tendons anchored by three buttresses equally spaced around tne exterior surface of the Reactor Building. Each tendon is alternately anchored at buttresses located 240 Three tendons constitute two complete circumferential tendons. degrees apart. i Prestressing of the hemispherical dome is achieved by the two-way pattern of I 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 I i tendons in the post-tensioning system. q I III. EVALUATION I l The results collected from the two tendon surveillance programs on tendon samples have been utilized to. predict the system behavior for the 40 year l service life and the level of prestressing force in each tendon group at the end of 40 year service. i l Regression analysis and simulation outcomes have been employed using the l l 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 III.1 and IV.3, l l respectively. } 4 i l

m-111.1 Rearession Analysis Per the shape of the curves of the relaxation loss at time functions exhibited in Fig. 5 of Ref. I and per the functional form of Eq. 3 of 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 below. (1) Y = Bo + B1 In T 1 are constants to be estimated by regression analys Where Bo and B Let x = In T, then Eq. I becomes I (2) Y = Bo + B x 1 Per Eq. 2, Bo'and B1 can be determined by the linear regression and $ be the estites for Bo and 8, 1 analysis. Let$o 1 Per Eqs. 9-12 and 9-13 on Pgs, 275 and 276 of Ref. 2, - respectively. n (3) E. (Xi-5)(yi-5) a 81 1 n E. (xi-i)2 i=1 (4) Bi B0-i-l l 1 l 5 I ^~^ ^^---- - - -

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. yj = the tendon prestress force at time, Tj for i = 1, 2,..., n n 1 E xi .x = n i=1 n 1 E yi .y - n 1-1 Let y be the estimate of y, then by Eq. 2 y can be expressed as: A A A A A y-Bo + B x = Bo + B 1nT (5)- 1 1 l 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 = l 1,2,..., n, and the increasing Tj or xi leading to decreasing yi will be verified as follows: Let r y denote the correlation coefficient between xj's x and yj's, then from Eq. 1.3.2 on Pg. 15 of Ref. 3, r y is as follows-x l Sxy I n { 1 X~. (xj-x) (yj-9) ) (Sa) ry = = x SxSy SxSy n i=1 where Sx and Sy (per Eq. 1.2.2a on Pg. 11 of Rev. 3) are: n 1/2 ( l E. (xj-i)2 ) (6) n 1-1 S = x n 1/2 ( 1 E (yj-9)2 ) (7) n 1-1 S y 6

The higher the degree of relationship between the data xj and yj, the closer l Normally, lrl 10.6 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. l i denote the lgwat and uppgr bound prestress force of a tendon at and y Let yg u any time T, respectively. In the calculation, yt is associated with 97.5% { probability that the actual value of the tendon prestress force is larger tha f the f is associated with 2.5% probability that the actual value o y ; and yu g Per Eq. 9.29 on Pg. 285 of Ref. 2, tendon prestress force is larger than y. u r J and y can be determined from yg u I ( (8) t -2* 1 1 yg=y-S n 3 y 2 i 1 (9) l A yu " Y + b^ tn-2 1 A y 2 is the t-statistics with n-2 degrees of freedom, and two sided where tn-2, 1 A 2 confidence level of 100 (1-a)%. In this case A = 0.025. The value of 2 in 2,1-) can be obtained from Table II on Pg. 312 of Ref. 4. I is: From Eq. 9.25 on Pg. 284 of Ref. 2, i.e., S3 y .2 -{[l+1+ ] 2 )1/2 (10) I***I n n S E.(xj-x)2 3 y 1-1 7 l l 1'

v l where from Eq. 9.18 on Pg. 281 of Ref. 2, i.e., M is: a n n (yj-y)2 - B E (xi-x) (yi-y) (11) E. l y - i-1 1-1 i n-2 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) for ' the dome, cylinder, and vertical tendons based on (a) the corresponding initial, first, and second surveillance tendon prestress levels, and (b) the corresponding initial, first, and second surveillance tendon prestress levels plus the simulated tendon prestress levels for the next (third) surveillance. IV. NUMERICAL COMPUTATIONS AND_RESULTS Based on the methodology for regression analysis technique provided in Section 111.1, the average (y), lower bound (y ), and upper bound (y ) prestress forces g u at any time T for the dome and cylinder horizontal tendons, and the vertical Note that tendons will be computed in Sections IV.1, and IV.2, respectively. due to (a) the geometrical similarity between the dome tendons and the cylinder tendons, and (b) only few samples of dome tendon prestress available, the dome tendons are ccr.sidered to be equivalent to the cylinder tendons for the l statistical evaluation. Hereinafter, the dome and cylinder tendons will be referred to as horizontal tendons. Per Eq. 5 in Section 111.1, the initial time, To for prestressing the dome tendon can not be assumed zero because the natural logarithm, In T at T-0 is bssed on the study in Ref. 7, it is conservative to use T =0.001 o undefined, Therefore, b this investigation, To=0.001 year will also be used. year. 8

v l IV.1 Horizontal Tendon Prestress Force as Time Function Based on 911h The horizontal tendon prestress force data associated with To = 0.001 year, and the 1st and 2nd surveillance are tabulated in Columns 5 and 6 l of Tables la and Ib for the Callaway and Wolf Creek Unit 1 containments, l Based on these data and by using Eqs. 5, 8 and 9, and other respectively. related equations in Section III.1, the average (y), lower bound (y ), and g upper bcund (y ) prestress forces oT the horizontal tendons as functions u of time T, and the correlation coefficient (r y) are derived in,efs. 5 r x and 6, namely for the Callaway containment, 1 (12) h = 164.049 - 1.840 in T = 164.049 - 1.840 In T - 2.624 (19.836 + 0.03951 (In T + 2 yt = 164.049 - 1.840 in T + 2.624 (19.836 + 0.03951 (In T + 2.517) (14) yu -0.88 ry = x 1 For Wolf Creek containment, (15) h = 167.987 - 1.213 int = 167.987 - 1.213 int - 2.624 d i.581 + 0.04194 (int + 2.566)4 (16) yL = 167.987 - 1.213 int + 2.624 (20.581 + 0.04194 (int + 2.566)4 (17) yu -0.76 ry = x Based on Eqs. 12 thru 14, Figure 3a provides 3 curves exhibiting the relationship between y, yL, and y and the time T up to 40 years for u 9

v Callaway containment. Based on Eqs. 15 thru 17 Figure 3b provides 3 and the time T up-curves exhibiting the relationship between y, y), and yu to 40 years for Wolf Creek containment. IV.2 Vertical Tendon Prestress Force as Time Function Based on Actual Data Only The vertical tendon prestress force data associated with To=0.001 year, and the 1st and 2nd surveillance are tabulated in Columns 5 and 6 of Tables 2a and 2b for the Ca11 sway and Wolf Creek Unit I containments, respectively.. Based on these data and by using per Eqs. 5, 8 and 9, and other related equations in Section III.1, the average (y), lower bound (y ), and upper bound (yu) prestress forces of the vertical. tendons as g functions of time T, and the correlation coefficient (r y) are derived x l in Refs. 5 and 6, namely, for Callaway contair, ment, 9 (18) 173.245 - 0.994 In T y = 173.245 - 0.994 In T - 2.162 (5.13(B.01787 (In T + 2.399) A (19) yt 1 = 173.245 - 0.994 in T + 2.162 (5.134 + 0.01787 (In T + 2.381)' (20 ).. yu = -0.90 ry x For Wolf Creek containment, (21) y = 170.454 - 1.163 In T = 170.454 - 1.163 in T - 2.162 (10.325 + 0.03662 (In.T + 2.422)2 yt = 170.454 - 1.163 In T + 2.162 00.325 + 0.03662 (in T yu - -0.86 ry x 10 1 -__-----l--_._-_-_-_-_-_-___--_..__.-_.

^ Figure 4a provides 3 curves exhibiting the relationship between y, yL' and y and the time T up to 40 years for Wolf Creek containment based on y Eqs. 18 thru 20. Figure 4b also provides 3 curves exhibiting the relationship between y, yt, and y and the time T up to 40 years for u Callaway Unit I containment based on Eqs. 21 thru 23. IV.3 SIMULATION OF THE NEXT SURVEILLANCE TENDON'PRESTRESS OUTCOMES For sets of tendon' prestress outcomes are simulated for the next (or third) surveillance of the Callaway and Wolf Creek Unit I containments, l' 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, tnd 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 desiate normally about its average time function. This assumption is typically made in regression analysis (Ref. 2). Thus at any time, T the tendon prestress outcomes, yj (T) can be generated by yj(T) - zg S,(T) + y(T) (24) y l where y(T) and Sx(T) represent the average tendon prestress (Eq. 5) and l y standard deviation of the tendon (Eq. 10) at time T, respectively. Zi is l the standard normal variate which can be obtained from Table VIII on Pg. l 329 of Rev. 4, 11

v In this analysis, assume that the next surveillance takes place at 7 years after the initial prestressing, i.e., T-7 years. $(T) and S (T). at 7 y 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 j inspected in the next surveillance. Herain, only 3 tendon prestress outcomes are simulated based on Eq. 24. The remaining 4 prestress 4 outcomes are arbitrarily set equal to the design requirement specified in References 8 and 9 that the averace prestress shall be greater than or l equal to the minimum effective design prestress. For the horizontal 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. Let rh denote the probability of obtaining one or more outcomes from 7 samples (tendons) to be drawn in the next surveillance being less than 147 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 simulated set of outcomes. Mathematically, rh follows the binomial distribution. Based on the result of the calculation in References 5 and 6, rh =1.05%.

Hence, the probability of a set of actual outcomes being worse than the simulated set is insignificant 1y low.

12 1

For the vertical prestress system of each containment, 4 tendons will be inspected.in the'next surveillance. In this case, only 2 tendon prestress outcomes are simulated based on Eq. 24. The remaining 2 prestress outcomes 'are arbitrarily set equal to the design requirement specified in References 8 and 9 that the averaae prestress shall be greater than or For the vertical equal to the minimum effective design prestress. For prestress system, the minimum effective design prestress is 139 ksi. the Callawhy 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 Actual Data l 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 prestrass 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 uring 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 13

horizontal tendons as functions of time, T are derived in Refs. 5 and 6 namely: For Callaway Containment, 4 (25) $=162.288-2.110 int (26) L = 152.288 - 2.110 int - 2.038 (36.26 + 0.059222 (int + 1.598)4 Y Yu = 162.288 - 2.110 int + 2.038 (36.26 + 0.059222 (int +38 (27) For Wolf Creek Containment, (28) Y = 164.829 - 1.702 int YL = 164.829 - 1.702 int - 2.038 (51.20 + 0.084834 (int + 1.63 (29) 1 Yu - 164.829 - 1.702 int + 2.038 (51.20 + 0.084834 (int + 1.637)4 (30) 1 Figure Sa provides 3 curves exhibiting the relationship between y,~yL, and and time, T up to 40 years for Callaway containment based on Eqs. 25 yu thru 27. In the same manner, Figure 5b provides 3 curves exhibiting the relationship between y, yL, and yu and time,'T up to 40 years for Wolf Creak containment based on Eqs. 28 thru 30. t I 14

IV.5 VERTICAL TENDON PRESTRESS FORCE AS TIME-FUNCTION BASE PLUS SIMULATED DAB l ' The actual prestress data of the vertical tendons associated with To=0.001 year, and the 1st and.2nd' surveillance plus the simulated prestress data for'the vertical tendons associated with the next-(3rd) surveillance are tabulated in Tables 7a and 7b for the Callaway and Wolf Creek Unit I i containments, respectively. 8ased on these data anci by using Eqs. 5,'8 l and 9, and other related equations in Section III.1, the average (y), lower bound (yt), and upper bound (yu) prestress forces-of the. vertical 1 tendons as functions of time'(T) are derived in Refs. 5 and e namely: For Callaway Containment, (31) k=168.814-1.672 int L = 168.814 - 1.672 int - 2.110 (110.72 + 0.32027 (int + 1.470)4 (32) Y (33) Yu=168.814-1.672 int +2.110(110.72+0.32027(int +1.470)4 For Wolf Creek Containment, (34) = 166.09 - 1.839 int YL = 166.09 - 1.839 int - 2.110

  1. 92.11 + 0.26956 (int + 1.502)4 (35)

Yu = 166.09 - 1.839 int + 2.110 (92.11+0.26956(int +1.502)4 (36) Figure 6a provides 3 curves exhibiting the relationship between y, yt, and time, T up to 40 years for Callaway containment based on l and yu Eqs. 31 thru 33. In the same manner, Figure 6b provides 3 curves exhibiting the relationship between y, yL, and.yu and time, T up to 40 years for Wolf Creek containment based on Eqs. 34 thru 36. 15 l =

m 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 ';ie 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 l 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 dats described in Section IV, the following results are obtained: (a) For the horizontal tendons, the time functions of its average, lower l bound, and upper bound prastress forces are respectively given by Eqs. 12 through 17, and are exhibited in Figures la and 3b for the l 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 da and 4b for the Callaway and Wolf Creek containment, respectively. Note that yt has a 97.5% probability that the actual tendon prestress force is larger than yt; and y has a 2.5% probability that the actual u tendon prestress force is larger than y ' u 16

~- 1 1 Based on the statistical prediction (using the actual tendon prestress I data only) exhibited in Figures 3a, 3b, 4a and 4b, all post' tensioning ( l i 'prestress systems for both the Callaway and Wolf Creek containments are shown to maintain their average prestress level much above their minimum effective prestress requirements throughout the plant operating life span Namely per Refs. 8 and 9, the design requirement specifies-of 40 years. 1 that the averaae prestressed shall be greater than or equal to the minimum 1 effective design prestress. For both Callaway and Wolf Creek containments, the minimum effective prestressed required are 147 ksi and 139 ksi, for the horizontal and vertical tendon, respectively. i Utilizing the result of the regression analysis based on the actual tendon prestress data from the initial, 't and 2nd surveillance records, the i l In this tendon prestress outcomes are probabilistically simulated. simulation, for at least half of the samples.(tendens) 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 tendon and 139 ksi for the vertical tendon. For the remaining samples (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 data. For each set of outcomes simulated using the above procedure, it has been shown that its probability of being worse than the set of actual data to be obtained in the next surveillance is insignificant 1y low, i.e., its maximum is 1.05%. This implies that each set of' simulated tendon prestress outcomes for the next surveillance is significantly conservative. 17

j 4 By applying the linear regression. analysis on Eq. I and using the actual tendon prestress data plus the simulated prestress data, the following results are obtained: I i l For the horizontal tendons, the time functions of = its average, lower (a) l bound and upper bound prestress forces are respectively given by Eqs. 25thru30,andareexhibitedinFigures5aand5bfortheCallaway i and Wolf Creek containments, respectively. For the vertical tendons, the time functions of its average, lower l (b) bound and upper bound prestress forces are respectively given by Eqs. 31 thru 36 and are exhibited in figures 6a and 6b for the callaway and Wolf Creek containment, respectively. Based on the statistically prt.dicted (using the actual tendon prestress data plus the simulated data) exhibited in Figures Sa, 5b,.6a and 6b, all post tensioning prestress systems for both the Callaway and Wolf Creek containments are shown to maintain the average prestress level much above their minimum effective prestress requirements throughout the plant operating life span of 40 years. t For each set of the simulated outcomes associated with the next i j surveillance, (a) at least half of the outcomes are arbitrarily set equal to the minimum effective design prestress, (b) the probability of obtaining a set of actual outcomes being worse than the set of simulated outcomes is insignificant 1y low, and (c) all the average prestress levels l I 18 i I b _j

v_-_-__-_. f are much higher than their minimum effective design prestress throughout the plant operating life span. t e VI. CONCLUSlQH 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 j 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 dame tendons are i referred to as horizontal tendons. l The statistical prediction of the performance of each post tensioning prestress is obtained by applying the linear regression analysis on Eq.1. At first, the regression analysis is performed using only the actual tendon prestress data from the initial prestressing, the 1st and 2nd j l surveillance. The result of this analysis is then utilized to probabilistically simulate the tendon prestress outcomes as described in Section IV.3. The regression analysis is then performod using the actual tendon prestress data from the initial prestressing stage, the 1st and 2n.d surveillance plus the simulated tendon prestress data. These analyses \\ lead to the following 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 l l l 19

'E specifies that the averace prettress shall be greater than the minimum a effective design prestress of 147 ksi for the horizontal tendons and 139 ksi for the vertical tendons. j In this regard the following margins were computed based on utilizing the initial and measured first and second surveillance data: The prestress level provided by the Callaway horizontal tendons at 40 (a) years exceeds the design requirement by 6.98% a ' The prestress level provided by the Wolf Creek horizontal tendons at (b) 40 years exceeds the desi n requirement by 11.2% i I The prestress level provided by the Callaway vertical tendons at 40 (c) years exceeds the design requirement by 22.0% i The prestress level provided by the Wolf Creek vertical tendons at 40 (d) years exceeds the design requirement by 19.5% For each set of the simulated outcomes for both the Callaway and Wolf Creek containments, (1) at least half of the tendon prestress outcomes 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 worse than i the set of simulated outcomes is insignificantly low (i.e., the maximum probability is 1.05%), and (3) all the average prestress levels-are much higher than their minimum effective design prestress throughout the plant 20

v (Note that per Refs. 8 and 9, the design operating life span of 40 years. requirement for both the Callaway and Wolf Creek containment sp that the averace prestressed shall be equal to or greater than the m effective design prestress.) In this regard, the following margins were computed based on utilizin the initial, and measured first and second surveillance and simulate ) third surveillance data: The prestress level provided by the Callaway horizontal tendons a (e) 40 years exceeds the design requirement by 5.1% The prestress level provided by the Wolf Creek horizontal tendo (f) 40 years exceeds the design requirement by 7.86% The prestress level provided by the Callaway vertical tendons at (g) years exceeds the design requirement by 17.0% The prestress level provided by the Wolf Creek vertical tendon (h) years exceeds the design requirement by 14.6% l J 21 j

v l l l l Based on the above projections, the post tensioning system is shown to { maintain an average' stress level above the minimum prestressing r requirements even with simulated low lift-off measurements. The data l 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. l i WC:006.0B 22

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4v TABLE f a RECORDED PRESTRESS FORCE ' DATA AND RELATED STATISTIC CALCULATIO (CALLAWAYUNIT1) DATA TENDON TOTAL TENDON TENDON TIME X= (Ki Kavg (Yi Yavg (Xt-Xavg) N0. N0. W1RE FORCE STRESS (YEAR) LnTi )^2 )*2 (Yi-Yavg) AREA (K) (K51) at an/ 4# sth 6% 7% s th 6 800 1 TIG~ 5.345 1480.04 177.36 0.00F 6.RT 19.252 75.271 38.097 2 9 C8 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 1496.51 179.32 -0.001 -6.908 19.282 113.413 46.764 5 5 8A 8.345 1488.07-178.32 0.001 -4.908 19.282 92.894 -42.323 6 45 8A 8.247 1489.34 180.59 0.001' -5.908 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 C8 8.345 1495.26 179.18 0.001 -4.904 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 8A 4.345 1478.79 177.21 0.001 -6.908 19.282-72.695 -37.439 12 35 BA 8.345 1500.33 179.79 0.001 -6.904 19.282 123.372 -48.774 13 47 8A 8.345 1420.67 170.24 0.001 -6.908 19.282 2.438 -6.857 14 1 C8 8.345 1371 164.29 3.847 1.347

14. % 0 19.277

-16.965 15 9 C8 8.296 1324 159.59 3.847 1.347 14.930 82.548 35.106 4 16 9 AC 8.345 1339.5 160.52 3.872 1.354 14.980 66.672 -31.603 1 17 26 AC 8.345 1339 160.46 4.031 1.394 15.293 67.655 -32.166 18 5 8A 8.345 1357 162.61 3.849 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 66 162.2C 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 C8 8.345 1323.52 158.60 5.983 1.789 18.54 101.62 43.40 24 14 8A 8.345 1389.44 166.50 5.900 1.775 18.42 4.76 9.36 25 18 8A 8.345 1381.10 145.50 5.897 1.774 18.41 10.12 -13.65 26 35 8A 8.345 1421.15 170.30 5.872 1.770 18.38 2.62 6.94 27 47-8A 8.345 1286.80 154.20 5.847 1.766 18.34 209.69 62.01 168.g.Yev _1 Xav9 SUM 1= SUM 2= $UM3-6s -2.517 484.081 2117.877 890.92 BETAl= 1.840 SETA0 164.049 to 2.624 19.*28 ____m________

.. ~ l s i TABLE !b RECORDED PRESTRE55 FORCE DATA AND RELATED STATISTIC CALCULATION (WOLF CREEK GENERATION STATION) DATA TENDON 10TAL TENDON TENDON TIME %= (11 Xavg (Y1 Yavg (X1 Xavg) NO. No. WIRE FORCE STRESS (YEAR) Lnit )*2 )*2 (YlYavg) AREA (K) (KSI) ist and 3 49h sth Af6 f fb Sfh 4 th te th 1 IIII'~ 8.345 1480.15 177.37 0.001' -6.96I" 18.855 39.327 -27.231 2 9 C8 8.345 1491.98 178.79 0.001 6.904 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 13.855 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 SA 8.345 1457.86 174.70 0.001 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 82.651 -34.370 9 11 CB 8.345 1498.74 179.60 0.001 6.908 18.855 72.230 -36.904 to 14 8A 8.345 1459.54 174.90 0.001 -6.908 18.855 14.451 16.507 11 18 8A 8.345 1476.31 176.91 0.001 -6.908 18.855 33.768 25.233 12 35 8A 8.345 1477.99 177.11 0.001 -6.908 18.855 36.148 -26.107 13 47-84 8.345 1392.44 166.86 0.001 -6.908 18.855 17.972 18.408 14 1 C8 8.345 1422 170.40 3.686 1.305 14.977 0.486 2.6?8 15 9 C8 8.345 1347 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 At 8.296 1359 163.81 3.792 1.333 15.197 53.066 28.398 18 5 8A 8.296 1381 166.47 3.708 1.310 15.023 21.462 17.957 19 45 8A 4.345 1409 168.84 3.383 1.219 14.321 5.085 0.533 20 51 SA 8.345 1348 161.53 3.469 1.244 14.511 91.483 36.435 21 45 5A 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 16,631 23 11 C8 8.345 1385 165.97 5.254 1.660 17.853 26.326 21.679 24 14.lA 8.345 1393 166.93 5.089 1.627 17.578 17.407 17.492 25 18 SA 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 1.811 17.440 216.604 61.462 Yav9 Xavt= SUM 1= SUM 2= SUM 3-171.M9 -2.H6 473.182 1192.004 573.821 BETA 1 -1.213 BETA 0 167.987 to 2.624 19.846'

TA8LE 2a-The Avera9e, Lower Sound, and Upper Bound Prestress Force of the Horizontal Tendon for Callaway Unit 1 Containment DATA Ti Xie Sy'2 AVG. LOWER UPPER NO. (yr.) LnTi PRE-BOUND B0UND STRESS PRE-PRE-(K51) STRESS STRESS ~~Y- 0.001- -6.90775 20.59828 176.76 364.553 188.671 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 AVGl= AVG 2= AVG 3 162.133 150.199 174.067

7 TABLE tb The Average Lower Bound, and Upper Bound Prestress Force of the i Horizontal Tendon for Wolf Creek Unit 1 Containment DATA Ti 11= 5y*2 AVG.. LOWER UPPER NO. (yr.) LnTi PRE-BOUND 80dND STRESS PRE-PRE- {KSI) STRESS STRESS 1 0.001 -6.90775 21.37138 176.36 164.234 188.495 2 0.01 -4.60517 20.75507 173.57 161.618 185.516 3 0.5 20.69314 20.72762 168.83 156.882 180.774 4 1 0 20.85663 167.99 156.004 179.971 l 5 2 0.693147 21.02594 167.15 155.115 179.179 6 4 1.386294 21.23556 166.31 154.214 178.398 l 7 6 1.791759 21.37686 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 21.98388 164.08 151.781 176.387 13 30 3.401197 22.07374 163.86 151.535 176.191 14 35 3.555348 22.15138 163.68 151.326 176.026 15 40 3.688879 22.22119 163.51 151.145 175.883 AVG 1= AVG 2= AVG 3 166.725 154.559 178.890 l _________--_-_-_O

i TABLE 31 RECORDED PRESTRE55 FORCE DATA AND RELATID STATISTIC CALCULATION (CALLAWAYUNIT1) DATA TECON TOTAL TENDON TENDON TIME A= (Ki Kavg (Yt fav9 (Xt Xavg) I NO. NO. W1RI FORCE STRESS (YEAR) LnTi )^2 }^2 (YtYavg) AREA (K) (K31) i 1:1 ad .a r) 4% 5% 6 th 7 th 8% 4th no th i 1 W 8.296 1496.5T 180.39 0.001 -6.908 20.488 22.832 ' 21.626 2 V 35 8.296 1482.57 178.71 0.001 -6.908 20.488 9.528 14.023 i 3 V 65 8.345 1515.08 181.f* 0.001 6.908 20.488 35.336 26.906 4 V 74 8.296 1508.3 181.Bi 0.001 6.908 20.488 38.434 28.061 5 V1 8.345 1488.07 178.32 0.001 -6.908 20.488 7.332 12.256 6 V 18 8.345 1515.08 181.56 0.001 6.908 20.488 35.336 k6.906 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 20.570 20.471 9 V 35 8.296 1418 170.93 4.083 1.407 14.351 21.952 17.749 10 V 55 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 -2.680 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 t Vav9= Kavl. SUM 1= SUM 2= $UM3= 175.611 2.381 269.276 328.404 267.549 BETAl= 0.994 i BETA 0= 173.245 t= 2.162 4.813 I I

l i [ l I 1 I 1ABLE 3b RICORDID PRI57RI55 FORCE DATA AND RELATED STATISTIC CALCU (WOLFCREEK6ENERATIONSTAT10N) DA1A TENDON TOTAL TEfCON TENDON TIME K= (Xi Xavg (Yi Yavg (Xi Xavg) l NO. NO. W1RE FORCE STRESS (YEAR) LnT1 )*2 )*1 (TiYavg) l AREA (K) (K51) (IN'3) sf taJ sed 4M se en in stk en soth 1 W 8.345 1484.7 177.91 0.001 6.905 20.125 21.574 20.537 2 V 3% 8.345 1486.55 178.14 0.001 -6.908 20.125 23.683 21.832 3 V 6; 8.345 1491.41 178.72 0.001 6.908 20.125 29.691 24.444 4 V 74 8,345 1517.02 181.79 0.001 6.908 20.125 72.553 38.212 1 5 V1 8.296 1480.15 178.42 0.001 -6.908 20.125 26.494 23.091 k 6 V-18 8.345 1483.02 177.71 0.001 -6.908 20.125 19.745 19.934 7 V 47 8.345 1476.31 176.91 0.001 -6.908 20.125 13.246 16.327 4 V 20 8.345 1400 167.77 3.608 1.283 13.726 30.305 -20.395 9 V 35 8.345 1339 160.46 4.053 1.399 14.601 164.217 -48.967 j 10 V 65 8.345 1432 171.60 3.619 1.286 13.748 2.790 . 6.193 Il V 74 8.345 1404 168.24' 4.075 1.405 14.643 25.257 -19.231 12 V 65 8.345 1417 169.80 5.203 1.649 16.572 12.026 -14.117 13 V1 8.296 1385 166.95 5.531 1.710 17.074 39.970 -26.123 14 V 18 8.345 1437 172.20 5.200 1.649 16.568 1.147 4.360 15 V 47 8.345 1439 172.44 5.192 1.647 16.555 0.691 3.383 Vavg= Xavg= SUM 1= $UM2= SUM 3= 175.270 -2.422 264.361 483.388 307.446 BETAl= 1.163 SETAD. i 170.454 t. 2.162 9.680 e l l 1 1

l. l TABLE 4s - The average Lower Sound, and Upper Sound Prestress Force of the Vertical Tendon for Callaway Unit 1 Containment DATA Ti 11 syal AVE. LOWER UPPER h0. (yr.) LaTi PRI-SOUND SOUND STRESS PRE-PRE-(K51) STRESS STRESS 3 5"MT 6.90775 5.500175 150.11 175.037 155.130 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 173.14 168.297 178.193 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 171.44 166.419 176.511 8 8 1.079441 5.489663 171.18 166.112 175.245 9 10 2.302585 5.526138 170.96 165.874 176.040 i 10 15 2.708050 5.596970 170.55 165.438 175.670 i Il to 2.995732 5.650791 170.27 165.!!8 175.409 12 25 3.218875 5.694575 170.05 164.886 175.207 13 30 3.401197 5.731570 169.07 164.688 175.042 14 35 3.555348 5.763961 169.71 164.521 174.904 l 15 40 3.688879 5.792619 169.58 164.375 174.784 ~ AVG 1 AVG 2 AVG 3 172.211 167.139 177.282 l l i l l I

4 TABLE (b - The average, Lower Bound, and Utper Bound Prestress Force of the Vertical Tendon for Wolf Creek linit 1 Containment DATA T1 21= Sy^2 AVG. LOYER UPPER NO. (yr.) LnTi PRE - SOUND SOUND STRESS PRE-PRE-5 (K51) STRESS STRESS 1 b 5bT -6.90775 11.06185 178.49 171.295 185.679 2 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 10.5'1970 170.45 163.434 177.474 5 2 0.693147 .10.68022 169.65 162.581 176.714 6 4 1.386204 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 2.3025t5 11.14218 167.78 160.558 174.994 10 15 2.706050 11.28847 167.30 160.039 174.570 11 20 2.995732 11.30557 166.97 159.669 174.271 12 25 3.218875 !!.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 AVG 1= AVG 2= AVG 3 169.243 162.044 176.442 O

l l TA8LE Sa - ACTUAL AND SIMULATED PatsTRtis FotCI caTA AMD 81 LATED STAtl5 Tit CALCULATION I (CALLAEAT W if 1) j I 's DATA TINDON TOTAL TENDON TEMDON TDE 3 (11 lavg (Yt favg (11.Zavg) M0. h0. WIRE FORCE 578I55 (7tAA) Lnit )*2 )*t Ot.Yav9) ARIA (K) (151) (IR*3) l 7 W 8.345 1480.M ~Tf73f c.001 J.908 28.195 136.831 62.113 l 6 2 9 C8 8.296 14nt.27 178.91 8.001 6.908 28.195 175.693 70.382 3 9.AC 8.345 1496.51 179.33 8.001 6.908 28.195 186.900 72.592 4 26 AC 8.345 1496.51 179.33 8.001 4.904 28.195 IH 900 72.592 5 5 8A 3.345 1488.07 178.32 8.001 6.908 28.195 160.269 67.222 l 6 45 8A 8.247 1489.34 180.59 0.001 6.908 ft.195 222.986 79.291 i 7 51 8A 8.345 1393.71 147.01 0.001 4.904 28.195 1.829 7.181 8 5 At 8.345 1454.34 174.28 0.001 6.908 28.195 74.349 45.785 9 11 C8 8.345 14!5.26 179.18 0 Gal 4.908 28.195 182.827 71.797 l 10 14 8A 8.345 1476.26 176.90 0.001 6.908 28.195 126.439 59.707 11 18 IA 3.345 1478.79 177.21 0.001 6.908 28.195 133.350 81.317 12 35 8A 8.345 1500.33 179.79 0.001 6.908 28.195 159.626 75.023 13 47 8A 8.345 1420.67 170.24 0.001 6.908 28.195 11.004 24.336 14 1 t8 8.345 137) 164.29 3.847 1.347 8.674 1.874 -4.032 15 9 C8 8.296 1324 159.59 3.H7 1.347 8.674 36.772 17.459 16 9.AC 8.345 1319.5 160.52 3.872 1.354 8.712 26.458 -15.182 17 26 AC 8.345 1339 160.46 4.031 1.394 8.951 17.078 15.549 16 5 8A 8.345 1357 162.61 3.889 1.154 8.738 9.282 -S.006 19 45 8A 8.247 1312.5 159.15 3.652 1.306 8.433 42.303 18.906 20 ll BA 3.345 1283.5 113.80 3.733 1.317 8.498 140.525 34.556 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 1.997 1.791 11.49 55.64 25.28 23 11 C8 8.345 1323.52 158.60 B.983 1.789 11.47 49.83 23.91 24 14 8A 8,345 1389.44 164.50 B.900 1.775 11.38 0.71 t.84 25 18.lA 8.345 1381.10 165.50 5.897 1.774 11.37 8.03 -0.54 26 35 8A 8.343 1421.15 170.30 5.il72 1.770 11.34 11.54 15.63 27 47 8A 8.345 1286.80 154.20 5.847 1.7H 11.32 131.31 38.55 Il 51 a 162.28 162.28 7.800 1.946 12.54 11.42 .!!.97 29 52 1 164.31 164.31 7.000 1.946 12.56 1.82 4.78 ( 30 53 1 163.44 163.44 7.000 1.945 12.54 4.92 7.86 31 54 1 147.,00 147.00 7.000 1.946 12.54 344.16 66.12 l 32 55 1 147.00 147.00 7.900 1.946 12.54 318.16 66.12 33 56 1 147.00 147.00 7.000 1.946 12.54 31.16 66.12 j 34 57 1 147.00 147.00 7.800 1.946 12.54 348.16 46.12 1 t fav Xavg= SUMla SUM 2 SUM 3 f 165.g.559 1.598 594.780 3775.183 1254.99 8tTA1 2.110 SETAD. 162.288 1.834 35.224 i L Neie : 5-1 thru S-7 are simultitel data.. l

1 1

l 1 l 1 l l l l l i

TABLt !b - ACTUAL AND $WULATED P8E37At13 708CI 847A AND 8

  • a (WOL7 CREEK $1ntRA710N37Afl0N)

DATA IIiGON TOTAL TENDON ILNUQN IIME I+ (1).Xavg 11)*favg (RDI4vgf NO. NO. VIRE FORCE STRESS (YEAA) Lnft )*t )'I (VI.Y4v9) ARIA (K) (K31) (IM*3) T I !T-s.345 14so.15 i n. 37 - c.oct

e. sos a7.isa 93.14 si.4;s 9.C8 8.345 1491.98 178.79 0.001 6.908 27.784

!!4.814 88.882 3 9 AC 8.345 1488.83 178.41 8.001 . 6.908 27.784 116.522 54.815 4 26.AC 4.296 1500.43 180.84 0.001 6.908 17.784 175.471 89.824 5 5 la. 4.296 1511.54 182.20 0.001 6.908 27.784 212.744 -76.881 6 41.lA 8.345 1457.86 174.70 0.001 6.908 27.784 50.173 37.337 7 ll BA 8.345 1397.41 166.24 0.001 4.908 27.784 1.846 7.163 o 8 5.At 8.345 1493.87 179.01 0,001 6.908 27.784 129.925 60.012 9 ll.CB 8.345 1498.74 179.60 0.001 6.908 17.784 143.570 63.154 13 14 la 8.345 1459.54 174.90 0.001 6.908 27.784 53.066 30.398 11 II.BA 8.345 1476.31 176.91 0.001 6.908 27.744 86.383 48.911 12 M.BA 8.345 1477,95 177.!! 0.001 6.908 27.784 90.145 50.052 13 47.la 3.345 1392.44 164.86 0.001 6.908 27.784 0.572 3.945 14 1 CB 8.345 1422 170.40 3.686 1.305 8.651 7.763 4.195 Il 9 CB 8.345 1387 164.21 3.706 1.310 8.683 1.942 4.149 16 9.AC 8.345 '1358 162.73 3.708 1.310 8.686 23.845 14.391 17 26.AC 8.296 1359 163.41 3.792 1.333 8.818 14.451 11.tts 18 5.la 8.296 1381 166.47 3.708 1,310 8.685 1.321 3.38! 19 45.BA 8.345 1409 168.84 3.383 1.219 0.154 1.809 -3.507 to ll.BA 8.345 1348 161.53 3.469 1.244 8.198 36.984 17.51t 21 45 8A 8.345 1430 171.36 4.967 1.603 10.494 14.024' 12.131 22 5.AC 8.345 1395 147.17 5.178 1.664 10.892 0.102 1.483 13 II.C8 8.345 1385 145.97 5.258 1.660 10.864 2.715 1.431 to 14.lA 8.345 1393 166.93 5.081 1.627 10.452 0.475 2.249 25 18 8A 8.345 1420 170.14 5.547 1.717 11.246 6.485 8.54 26 35 8A 8.345 If04 168.72 S.058 1.621 10.610 1.229 3.511 27 47 BA B.345 1305 156.38 5.004 1.611 10.545 -124.208 34.481 28 l1 1 140.37 160.37 7.000 1.946 12.835 82.494 25.957 29 52 1 167.55 !$7.55 7.000 1.946 12.835 0.004 0.234 30 53 1 163.34 163.34 7.000 1.946 12.835 10.278 15.317 31 54 1 147 147.00 7.000 1.940 12.835 424.991 73.054 32 55 1 147 147.00 7.000 1.946 12.835 424.991 73.056 13 56 1 147 147.00 7.000 1.946 12.835 424.991 73.856 34 57 1 147 147.00 7.000 1.944 12.835 624.99) 73.856 Y4vt= 167.415 34vt=7 $UPile SUM 2= SUM 3 1.53 586.320 St90.330 998.106 StTAle 1.702 SETA0 164.829 to 2.838 49.726 Note : 51 thma S-8 are simaAlated d&it.

v TABLE 6a-The Averaqe, Lower Bound, and Upper Bound Prestress Force of the Horizonts' Tendon for Callaway Unit 1 Containment DATA It It. sy*2 AVG., Low [R ypptR E (yr.) Lnit P8t. SOUND SOUND STR!!$ PRE. PRt. (K51) STRt55 STRts! T N 5.90775 37.92964 175.55 Ibe.311 13g.414 2 0.01 4.50517 36.79548 172.00 159.642 184.357 3 0.5 0.69314 36.30836 163.75 151.470 176.030 4 1 0 36.41108 142.29 149.990 174.585 5 2 0.693147 36.57072 160.82 148.500 173.150 6 4 1.384294 36.78726 159.34 147.001 171.723 7 6 1.791759 34.94031 158.51 146.120 170.894 8 8 2.079441 37.06071 157.90 145.493 170.307 9 10 2.302185 37.16085 157.43 145.005 169.853 10 15 2.708050 37.35790 154.57 144.117 169.030 l t 11 20 2.995732 37.50952 155.97 143.485 368.448 12 25 3.218875 37.63388 155.50 142.993 167.998 13 30 3.401197 37.73987 155.11 142.191 167.631 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= AVG 3 160.091 147.662 172.520 l 1

TABLE 6b - The Average, Lower Bound, and Upper Bound Prestres5 Force of the Horizontal Tendon for Wolf Creek Unit 1 Containment CATA' It Ito 5j'2 AVG.. LCa[A UPPER h0. (yr.) Lnit PR[. BOUND SOUND 57AI55 PRE. PRE. (L51) STRESS STR155 7 N 6.f;771 13.54444 176.5i 161.675 791,5C1 2 0.01 4.60517 51.93579 172.87 157.981 187.356 3 0.5 0.63314 11.25395 166.01 151.417 180.601 4 1 0 11.41563 164.83 150.216 179.443 5 2 0.693147 51.64t41 183.65 149.003 178.296 6 4 1.3t5294 51.96343 162.47 147.773 177.160 7 6 1.?$1759 52.18533 181.78 147.057 176.501 8 4 2.079441 $2.35564 151.29 146.542 176.036 9 10 2.302585 52.50452 140.91 146.142 175.477 10 15 2.705050 52.74139 160.22 145.412 175.027 11 20 2.995732 53.00841 159.73 144.091 J74.567 12 25 3.214875 53.18797 119.35 144.486 174.213 13 30 3.401197 53.34095 159.04 144.155 173.924 14 35 3.555348 53.47469 158.78 143.874 173.680 15 40 3.6t8879 53.51380 158.55 143.630 173.019 AVal. AVC2 AVG 3 163.057 148.zt4 177.830 N.

y 6 TABLE 7a - ACTUAL AND SlWULATED PRtsTRts5 fontt DATA AMD SELATED STATISTIC CALCULATION (CALLAMAYUNIT1) DATA ILMDON TOTAL TENDON TENDON TIMI 3 (It Iavg (ft favg (11 1 avg) NO. No. WIRE FORet $1RE55 (YEAA) Lait )*2 )*2 (Yt Vavg) ARIA (E) (K$1) (th*3) ~~l" 7775"" 5.296 1494,51 150.39 0.001 6,905 29.555 53.109 49.563 2 V.35 8.296 1482.57 178.71 0.001 6.908 29.565 55.296 40.433 3 V.65 8.345 1515.08 181.56 0.001 6.90P 29.565 105.730 55.909 4 iv.74 8.296 1504.3 181.81 0.001 6.908 29.565 !!!.041 57.296 5f! 8.345 1488.07 178.32 0,001 6.908 29.565 49.644 38.311 5 V 18 8.345 1515.08 181.56 0.001 6.508 29.565 105.730 55.909 7 V 47 8.345 1488.07 178.32 0.001 6.908 29.665 49.644 38.311 8 V.20 8.296 1411 170.08 3.747 1.321 7.792 1.418 3.324 9 v.35 8.296 1418 170.93 4.083 1.407 8.279 0.121 0.999 10 V.65 8.345 1441.5 173.70 3.764 1.325 7.817 5.875 6.777 11 V.74 8.296 1451 174.90 4.083 1.407 8.279 13.182 10.446 12 V 65 8.345 1446.19 133.30 5.917 1.778 10.551 4.109 6.544 13 V1 8.345 1412.81 169.30 8.289 1.E39 10.951 3.492 4.529 14 v.18 8.345 1451.20 173.90 5.917 1.778 10.551 6.902 4.533 15 v.47 8.345 13D6.95 167.40 5.919 1.778 10.553 14.999 12.581 16 51 1 168.54 1 64.54 7.000 1.946 11.671 7.469 9.337 17 52 1 173.48 173.44 7.000 1.946 11.$71 4.871 7.540 18 53 1 139.00 139.00 7.000 1.946 11.671 1041.541 110.255 19 54 1 139.00 139.00 7.000 1.946 11.671 1041.541 !!0.255 Yevt. 14 4 SUMI. SUM 2 SUM 3 171.273 1.470 328.410 2706.!!4 549.137 BETA 1 1.672 BETA 0 168.814 t. 2.110 105.170 Note : s-11hru S-4 are simula.ted. r

m e 9 8 1A8tt 7b - ACTUAL AND SIMULATED PRESTA!$3 70R01 t*TA AND 8tLA7t0 STA (WOAT CRE!K lIN[4Afl0N STATION) C!.iA TL C N TOTAL TL40N T EEC4 11ML i A. (11.Zavg (fi.fav; (1 14v;, NO. me. H WIRZ FORet ITRE55 (YEAR) i Lnft )*2 )*2 (Yt.Yavg) AR(A (K) (K51) (IM*3) 7 T 3.J45' 1484,7 177.91 0.301 5.lCE 29.220 82.lti 45.004 2 V.35 8.345 14t6.55 178.14 0.001 6.909 29.220 86.210 50.2*2 3 V E5 8.345 1491.41 178.72 0.001 6.908 29.220 57.4C6 13.310 4 V.74 8.341 1517.02 181.79 0.001 6.908 29.220 167.401 59.521 5 V.1 8.296 1480.15 178.42 0.001 6.908 29.220 91.542 !1.719 6 V.18 8.345 14t3.02 177.71 0.001 6.905 29.220 78.572 47.9.! 7 V.47 8.345 1476.31 176.91 0.001 6.90! 29.220 64.943 43.!!i 4 V.20 8.345 1400 167.77 3.508 1.253 7.75C 1.176 3.02" 9 V.35 8.345 1339 160.46 4.053 1.399 8.420 70.462 24.317 10 V.65 8.341 1432 171.60 3.619 1.286 7.775 7.564 7.663 11 V.74 8.345 1404 168.24 4.075 1.405 8.451 0.366 1.719 12 v.65 8.34! 1417 169.60 5.203 1.649 9.931 0.905 3.002 13 V.) 8.2e6 1385 166.95 5.531 1.710 10.321 3.816 6.101 14 V*ll 8.345 1437 172.2' 5.200 1.649 9.928 !!.218 10.512 Il V.47 8.345 1439 172.44 5.192 1.647 9.918 12.881 11.303 16 51 1 163.95 163.95 7.000 1.946 11.889 24.006 16.8$4 17 52 1 167.14 167.14 7.000 1.946 11.889 2.923 .i.ht5 18 53 1 139 139.00 1.000 1.946 11.889 890.955 -iO2.924 19 54 1 139 139.00 7.000 1.946 11.849 H0.995 102.924 t ~ V4vg. 24vg. SUM 1 SUM 2= $7.3 168.stS 1.502 324.600 2585.425 557.053 ItTA). 1.835 !!7:0.,_ Noit 151 thea 5-4 set simultit0 OL$L. l l l l u

1 l TABLE Ba - The average, Lower Bound, and Upper Scund Prestress Force of the I Vertical Tendon for Callaway Unit 1 Containa8nt DATA 11 It= 5y*2 AVE. LOWER UPPEA N0. (pr.) LnTi PRt. SOUND 80VNO $TR!ll PRE. PRE. (E31) '. STREll $TR!ll T 5"WI~ TR77T T20.1736 150.34 1U.z34 "Y5031r l 2 0.01 4.60517 113.0526 176.51 154.000 199.029 l 3 0.1 0.69314 110.8992 149.97 147.753 192.193 i 4 1 0 111.3381 188.81 146.544 191.084 i 5 3 0.693147 112.2048 167.46 145.305 190.006 6 4 1.386294 113.3192 166.50 144.035 188.957 7 6 1.791759 114.1137 165.82 143.278 188.358 8 8 2.079441 114.7413 135.34 142.735 187.939 9 10 2.302585 !!l.2645 164.96 142.311 187.617 10 Il 2.708050 !!6.2970 164.29 141.132 187.041 11 to 2.995732 117.0934 143.81 140.973 186.637 12 Il 3.!!8875 117.7477 163.43 140.136 186.328 13 30 3.401107 !!8.30$9 143.13 140.177 166.977 14 35 3.555348 118.7941 142.87 139.872 185.867 15 40 3.684479 119.3300 142.45 139.806 185.486 Avtle AV82 AV83 167.074 144.393 189.754

l 1 t TABLE Bb - The average, Lower touM, ad Upper Sound Prestress Force < ' the Vertical Tendon for Wolf Creek Unit 1 Containment i i CaiA 11 21= 5y*2 AVE.. LOWER UPPER I HC. (pr.) Lnit PRE. SOUND SOUND STRESS PRE. PRE. (K51) STRESS STRI55 1 I T N 6.90775 95.96425 178.75 167.596 195.558 '+ 2 0.01 4.60517 94.68401 174.16 154.025 195.08) 3 0.5 0.69314 92.25540 167.36 147.094 197.629 4 1 0 92.69717 168.09 145.772 186.401 5 2 0.653147 93.38791 164.81 144.421 185.202 6 4 1.386294 94.33764 163.54 143.043 184.031 7 6 1.791759 95.01325 162.75 142.224 183.358 8 8 2.075441 95.54634 162.26 141.637 182.886 9 10 2.302585 95.99056 161.85 141.179 182.524 10 15 2.708150 96.86643 161.11 140.339 181.&72 11 20 2.995732 97.54162 160.58 139.737 181.415 12 25 3.2188?5 98.09605 160.17 135.268 181.064 13 30 3.40!!97 98.56 tit 159.83 138.882 130.779 14 35 3.555348 98.58282 159.55 138.555 180.539 15 40 3.688879 99.35165 !$9.30 138.270 180.333 l I AVGl. AVG 2 AVG 3 164.172 143.476 184.867 l \\ _ _ _ _ _ _ _. _ _. - - - - - " - -}}

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