Text

Rev 0 to Calculation 100031-C-04, Sliding & Overturning Factor of Safety
	ML20202B270
Person / Time
Site:	North Anna
Issue date:	06/12/1997
From:	; EQE INTERNATIONAL
To:	;
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ML20202B006	List: ML20202B001; ML20202B154; ML20202B185; ML20202B228; ML20202B270; ML20202B284; ML20202B318;
References
	100031-C-04, 100031-C-04-R00, 100031-C-4, 100031-C-4-R, NUDOCS 9712030085
	Download: ML20202B270 (90)
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CALCULATION COVER SHEET

w...,.. e Calculation No.

100031 C-04 Project:

North Anna SSI Analysis ofISFSI Pad Calculatlon

Title:

Sliding and Overturning Factor of Safety

References:

See page 48 Attachments:

See Table of Contents, page 2 Total Number of Pages (including Cover Sheet):

90 Revision Approval Numbe.'

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0/#ui7 JOB NO.10003101 JOB North Anna SSI Analysis ofISFSI Pad BY MA DATE CALC. NO.100031C04R0 SUBJECT Slidina and Overturnino Factor of Safety CHK'D N DATEkI2[9 TABLE OF CONTENTS Page C ALC U LATI O N C OVE R S H E ET.....................................................................................................

TA B L E O F C O NT E N T S...........................................................................................

1.0 PURPOSE....................................................................................................................................3 2.0 ANALYSES.....................................................................................................................4 3.0RESULTS........................................................................

.......................................5 4. 0 R E F E R E N C E S........................................................................................

ATTACHMENT A: COMPUTER INPUT AND OUTPUT FILES............................. 41 PAGES ATTACHMENT B: DIGITIZED FILES............................................................. 9 DIS KETTE S + 1 PAGE F

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1.0 Purpose The purpose of this calcu'.ation is to document the calculation of sliding and overturning factor of safety of the casks. SASSI [1,2] modules ANALYS and MOTION were used to calculate the acceleration time histories at the mass points of the beams modeling the casks.

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W DATE h M CALC. NO. 100031C04R0 SUBJECT Shdino and Overturnina Factor of Safety CHK'D 2.0 Analyses Modules ANALYS and MOTION were used to calculate the acceleration time histories at the nodal points corresponding to the center of the casks in the quarter model used for the SSI analysis of the 15FSI pad.

Program SASSI requires that one independent analysis should be performed for each input direction. Thus, the results for each direction need to be combined. In this case, due to the symmetry in the geometry, the results in the 2 directions orthogonal to the input direction are practically neglegible. However, for c: mpleteness, the time histories in one direction due to the input in the three directions were added (e.g., x due to x, x due to y, and x due to z).

To calculate the time histories of the factor of safety and casks base shear and moment, the following formulas were used:

Base Shear: Si = W'Al i=x,y Ai acceleration time history in g's, W = 230 kips Base Moment: Mxx = 8*W*Ay -lxx*Axx All rotational acceleration time history in g's Myy = 8*W'Ax + lyy*Ayy FS sliding: FSs = (Sx2 + sy2)i/2/(0.3*W*[1-Az]), coefficient of friction = 0.3 FS overturning: FSo = (Mxx2 + Myy2)t/2/(4*W*[1-Az])

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Figures 3-1,3-2, and 3-3 show, for the cask defined at node 231, the base shear load in the longitudinal direction, the base shear load in the transverse direction, and the vertical load due to the input in the 3 directions. Figures 3-4 and 3-5 show the time histories of the inverse of the sliding and overturning factors of safety (1/FS) based on these shear and axial loads.

Figure 3 6 to 3-10,3-11 to 3-15,3-16 to 3-20,3-21 to 3-25,3-26 to 3-30, and 3-31 to 3-35 show the same sets of results for nodes 232,233,234,235,236, and 237, respectively.

According to these figures, the lowest factor of safety for overturning is about 1/0.6 = 1.67 at /

3.71 seconds and higher than about 2 the rest of the time.

According to these figures, the lowest factor of safety for sliding occurs for the casks defined at node 231 (close to the center of the pad) at time 3.71 seconds and it is slightly higher than one. However,it should be noted that the ground motions in the x and y dire-tions have an extreme peak occurring at the same time at 3.71 seconds (Reference 4) eventhough they are statistically independent. This situation is very unrealistic and it is due to the fact that these motions correspond to artificially generated time histories. At any other time, the factor of safety is higher than 1.25. This value represents a more realistic factor of safety since it is calculated in a region with extreme peaks in both directions but they do not occur at the same time.

This higher than one value can be confirmed if this factor of safety is estimated by using the

-100-40-40 rule suggested in the ASCE Standard 4-86 (Reference 5) to combine the effects of the mnimum forces induced by each direction of the input motion. This combination rule recognize the fact that having a extreme peak in both input directions is unrealistic. At node 231 the maximum accelerations in each direction are:

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Assuming (100%x,40%y,40%z)

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PSs = 0.3'(1-0.050)/(0.2272 + 0.0912)1/2 = 1.165 Assuming (40%x,100%y,40%z)

FSs = 0.3'(1-0.050)/( 0.0912 + 0.2272)i/2 = 1.165 Assuming (40%x,40%y,100%z)

FSs = 0.3*(1-0.124)/(0.0912 + 0.0912)1/2 = 2.042 Thus, the use of this combination rule gives a minimum factor of safety for sliding of 1.165.

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l 198 0.2155 6.6400 0.0001 10.0300 0.0022 9.3800 t

203 0.2152 6.6400 0.0003 9.7400 0.0044 9.5500 208 0.2145 6.6400 0.0005 5.9100 0.0047 5.8300 I

213 0.2137 6.6400 0.0006 10.3400 0.0057 5.8200 t

218 0.2121 6.6400 0.0005 6.6600 0.0067 5.9500 223 0.2095 3.7100 0.0010 6.6600 0.0070 6.2700 228 0.2093 3.7100 0.0018 5.7900 0.0243 5.7300 231 0.2276 6.6400 0.0009 10.0300 0.0022 9.3800 232 0.2285 9.1000 0.0021 9.7400 0.0044 9.5500 233 0.2302 9.1000 0.0039 5.9100 0.0047 5.8300 234 0.2283 9.1000-0.0035 5.9000.

0.0057 5.8200 235 0.2259 6.6400 0.0034 6,1500 0.0067 5.9500 236 0.2178 9.1000 0.0091 5.8700 0.0070 6.2700 237 0.2411 9.1000 0.0142 5.7900 0.0244 5.7300

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Table 3-1(cont.) Maximum Absolute Angular Accelerations (Rads /Sec/Sec/g) i N.P.

XX AT TIME YY AT TIME ZZ AT TIME 198 0.0001 10.0300 0.0031 5.7100 0.0000 5.7200 l

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203 0.0002 9.2600 0.0029 5.7100 0.0000 5.7200 208 0.0004 5.9100 0.0030 5.7100 0.0000 5.7200 213 0.0004 5.9000 0.0031 5.7100 0.0000 5.7200 I

218 0.0004 6.1500 0.0028 5.7100 0.0000 5.7200 i

1 223 0.0010 5.8700 0.0026 5.7100 0.0000 5.7200 228 0.0015 5.7900 0.0056 5.7200 0.0000 5.7200 231 0.0001 10.0300 0.0035 5.7100 0.0000 5.7200 l

232 0.0002 9.2600 0.0033 5.7100 0.0000 5.7200 1

233 0.0004 5.9100 0.0034 5.7100 0.0000 5.7200 234 0.0004 5.9000 0.0035 5.7100 0.0000 5.7200 j

235 0.0004 6.1500 0.0032 5.7100 0.0000 5,.7200 i

236 0.0010 5.8700 0.0030 5.7100 0.0000 5.7200 237 0.0016 5.7900 0.0060 5.7200 0.0000 5.7200 l

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f 198 0.0005 8.0900 0.1960 3.7100 0.0366 14.2600

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l 218 0.0029 9.2300 0.1954 3.7100 0.0390 7.5100 223 0.0040 7.9400 0.1879 7.2400 0.0373 7.5000 228 0.0047 9.0900 0.1884 3.7100 0.0283 7.5000 231 0.0015 8.2500 0.2238 10.2200 0.0367 14.2600 232 0.0032 8.2500 0.2246 4.3500 0.0373 14.2600 1

233 0.0031 5.2000 0.2278 4.3500 0.0381 14.2600 2

234 0.0038 9.2400' O.2309 4.3500 0.0389 7.5100 235 0.0065 8.0800 0.2328 4.3500 0.0390 7.5100 i

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XX AT TIME YY AT TIhiE ZZ AT TIME 198 0.0069 14.2000 0.0001 8.2500 0.0001 4.4400 203 0.0070 14.2000 0.0003 8.2900 0.0002 4.4400 208 0.0072 14.2000 0.0003 4.9800 0.0003 8.0600 213 0.0073 14.2000 0.0003 7.6500 0.0003 9.2400 218 0.0070 14.2000 0.0006 7.6400 0.0004 4.6100 223 0.0067 7.4500 0.0010 7.5800 0.0006 5.2700 228 0.0061 7.4400 0.0016 7.5600 0.0007 14.2100 231 0.0074 14.2000 0.0001 8.2500 0.0001 4.4400 232 0.0075 14.2000 0.0003 8.2900 0.0002 4.4400 233 0.0076 14.2000 0.0003 4.9800 0.0003 8.0800 234 0.0077 14.2000 0.0004 7.6500 0.0003 9.2400 235 0.0075 14.2000 0.0007 7.6400 0.0004 4.6100 236 0.0071 7.4500 0.0011 8.0700 0.0006 5.2700 237 0.0065 7.4400 0.0017 7.5600 0.0007 14.2100 C nVORKWEPCOCALCSiC-04 DOC

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X AT TIME Y

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198 0.0006 3.7300 0.0033 7.9900 0.1335 7.2500 i.

203 0.0019 5.7200 0.0032 7.9900 0.1333 7.2500 l

208 0.0030 5.7200 0.0031 7.9900 0.1315 7.2500 213 0.0036 5.7200 0.0031 5.6800 0.1295 7.2500 1

218 0.0037 5.7200 0.0032 5.7400 0.1294 7.2500 223 0.0039 5.9400 0.0034 5.7400 0.1304 7.2500 l

228 0.0058 5.7300 0.0027 1,9800 0.1287 7.2500 t

231 0.0024 8.4500 0.0263 7.9900 0.1336 7.2500 3

232 0.0058 3.790 0.0255 7.9900 0.1334 7.2500 i

233 0.0062 3.7800 0.0244 5.6800 0.1316 7.2500 234 0.0066 5.7600 0.0243 5.6800 0.1295 7.2500 235 0.0064 8.2100 0.0253 5.7400 0.1294 7.2500 L

236 0.0087 5.8900 0.0268 5.7400 0.1304 7.2500 237-0.0221 5.6800 0.0205 1.9800 0.1288-7.2500 i

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Table 3-3 (cont.) Max.imum Absolute Angular Accelerations (Rads /Sec/Sec/g)

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XX AT TIME YY AT TIME ZZ AT TIME 198 0.0028 7.9900 0.0002 6.1000 0.0000 8.5100 203 0.0027 7.9900 0.0005 3.7900 0.0000 8.4600

- 208 0.0026 5.6800 0.0006 3.7800 0.0000 2.1000 213 0.0026 5.6800 0.0005 8.1200 0.0000 8.3400 218 0.0027

.5.7400 0.0006 8.1600 0.0000 2.3500 223 0.0029 5.7400 0.0009 8.1300 0.0000 2.0600 228 0.0022 5.6800 0.0021 5.6800 0.0000 5.7400 231 0.0029 7.9900 0.0002 6.0400 0.0000 8.5100 232 0.0028 7.9900 0.0005 3.7900 0.0000 8.4500 233 0.0027 5.6800 0.0006 3.7800 0.0000 2.1000 234 0.0027 5.6800 0.0006 S.1200 0.0000 8.3400 235 0.0028 5.7400_

0.0007 8.1600 0.0000 2.3500 236 0.0030 5.7400 0.0009 8.1300 0.0000 2.0600

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ECE INTET/ATIONAL I' 3

.2 SHEET NO. JOB NO.10003101 JOB North Anna SSI Analysis of ISFSI Pad BY U b DATE 7 CALC. NO.100031004RO SUBJECT.Slidina and Overturnina Factor of Safety - CHKD DM DATEb/2 "I 4.0 References

1. SUPER SASSI/PC Complete Dynamic Soil-Structure Interaction Analysis System on Personal Computers. May 1996.

4

2. EQE Calculation 100031-C-06 Rev 0, June 1997, Project Specific Verification of Computer Code SUPER SASSI/PC.

3. EQE Calculation 100031-C-03 Rev 0, June 1997, Pad Model and Input to Module HOUSE.

4. EQE Calculation 100031-C-01 Rev 0, June 1997, Development of Soil Profile.

5. ASCE Standard 4-86. Seismic Analysis of Safety-Related Nuclear Structures and Commentary on Standard for seismic Analysis of Safety-Related Nuclear Structures, September 1986.

J CTWoAKWEPCo\\CALCS\\C-04 Doc ~

~. 0 0 tot mrtcunow + SHEET NO. A1 JOB NO.10003101 - JOB _ North Anna SSI Ana'vsis of ISFSI Pad BY MA DATE UWO cal.C. NO.100031C04RO SUBJECT,Slidino and Overturnina Factor of Saferv CHK'D ? N DATE6/12fi] ATTACHMENT A COMPUTE!! INPUT AND OUTPUT FILES File Name Description Pages Date analysx Input to ANALYS, x direction 1 5/09/97 15:13 4 analysx.out Output of AN ALYS, x direction 2 5/13/97 20:57 motionx Input to MOTION, x direction 3 5/13/97 11:39 mxred.out Output

of MOTION, x direction 7

6/06/97 10:10 analysy input to ANALYS, y direction 1 5/09/97 15:13 analysy.out Output of ANALYS, y direction 2 5/13/97 23:59 motiony Input to MOTION, y direction 3 5/13/97 10:55 myred.out Output

of MOTION, y direction 7

6/06/97 10:01 analysz Input to ANALYS, z direction 1 5/09/97 15:14 analysz.out Output of ANALYS, z direction 2 5/14/97 03:15 motionz Input to MOTION, z direction 3 5/13/97 10:56 mzred.out Output

of MOTION, z direction 8

6/06 9710:19

Time histories have been deleted for printing purposes. The complete files (zipped) are in included diskettes.

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4
y---. o E0E INTERuTIONAL SHEET NO. B1 JOB NO.100031,01 JOB North Anna SSI Analysis of ISFSI Pad _BY M DATE bl/2/6) cat.c. NO.100031C04RO SUBJECT Slidino and Overturnina Factor of Safety CHKD T8D DATE M b ATTACHMENT B DIGITIZED FILES File Name Description Date analysx Input to ANALYS, x direction 5/09/97 15:13 analysx.out Output of ANALYS, x direction 5/13/97 20:57 motionx Input to MOTION, x direction 5/13/97 11:39 mxted.out Output
of MOTION, x direction 6/06/97 10:10 analysy input to ANALYS, y direction 5/09/97 15:13 analysy.out Output of ANALYS, y direction 5/13/97 23:59 motiony Input to MOTION, y direction 5/13/97 10:55 myred.out Output

cf MOTION, y direction 6/06/97 10:01 analysz Input to ANALYS,z direction 5/09/97 15:14 analysz.out Output of ANALYS, z direction 5/14/97 03:15 motionz Input to MOTION, z direction 5/13/97 10:56 mzred.out Output

of MOTION, z direction 6/06/97 10:19 mxzip. zip Zipped output of MOTION, x direction 6/06/97 09:19 myzip. zip Zipped output of MOTION, y duection 6/06/97 09:20 mzzip. zip Zipped output of MOTION, z direction 6/06/97 09:21 acc231.xis Excel fil:., node 231 6/09/97 13:20 acc232a xis Excel file, node 232 6/09/97 13:23 acc233a.xts Excel file, node 233 6/09/97 13:26 acc234a.xis Excel file, node 234 6/09/97 13:29 acc235a.xis Excel file, node 235 6/09/97 13:32 acc236a.xis Excel file, node 236 6/09/97 13:38 acc237a.xis Excel file, node 237 6/09/97 13:41 TOTAL PAGES, INCLUDING COVER 9 Diskettes and 1 SHEET Sheet Note: Signature at the top of this sheet signifies that all contained documents have been verified.
~~C WVORKWEPCoC ALCSC-04 Doc __}}~~

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