ML20147F058
| ML20147F058 | |
| Person / Time | |
|---|---|
| Site: | Sequoyah  |
| Issue date: | 12/02/1987 |
| From: | BECHTEL POWER CORP. |
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| References | |
| NUDOCS 8803070229 | |
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;g-TASK REPORT NONLINEAR TIME HISTORY SEISMIC RESPONSE ANALYSES FOR ERCW CELL
. Prepared for TENNESSEE VALLEY AUTHORITY 1
Sequoyah Nuclear Plant Knoxville, Tennessee - -- l by - Bechtel North American Power Corporation San Francisco, California December 2, 1987
~
8803070229 080302 7 DR ADOCK 050
TABLE OF CONTENTS Section Page
- 1. INTRODUCTION 1-1
- 2. NONLINER SEISMIC ANALYSIS METHODOLOGY FOR BASE UPLIFT 2-1
- 3. BENCHMARKING OF ANALYSIS METHODOLOGY AND COMPUTATION PROCEDURE 3-1
- 4. ANALYSIS MODEL FOR ERCW CELL 4-1
- 5. SEISMIC GROUND MOTION INPUT S-1 i ,
- 6. ANALYSIS CASES 6-1
- 7. ANALYSIS RESULTS 7-1
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- 8. ASSESSMENT OE RESPONSE _
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- 9. CONCLUSIONS . 9-1
- 10. REFERENCES 10-1 Tables Figures Appendix A Acceleration Response Spectral Values for ERCW Pipe E1. 681.5 ft.
l e e
. NONLINEAR TIME HISTORY SEISMIC RESPONSE ANALYSIS FOR ERCW CELL
- 1. INTRODUCTION This report presents the seismic analysis methodology, the analytical model, analysis cases and the analysis results obtained for the Essential Raw Cooling Water (ERCW) access roadway cell subjected to the Safe Shutdow Earthquak'e (SSE) for the Sequoyah Nuclear Plant. The objective of this anaysis is to determine the seismic displacement of the cell at the location of the ERCW piping for use in assessing the piping stresses, and to determine the bearing stresses at the cell base and rock interface, taking into account the nonlinear effect resulting from partial uplifting of base during the seismic response.
The seismic response analysis for the ERCW cell utilizes two-dimensional (2-0) nonlinear time history response analysis methodology and the associated UPLIFT coguter program developed for analysis of structures supported on the surface of the foundation medium (Reference 1). The methodology is. based on the Wink.ler. foundation. modal (uniformly- - distributed discrete foundation spr.ingss,and, damper,5), Wch.has;,no, tension. f.,,,,,,,,.; capability. Section 2 of this report presents the methodology for nonlinear seismic analysis of structure with base uplift. Section 3 presents the bench-marking of the methodology. Section 4 describes the soil-structure interaction (SSI) analysis model for the ERCW cell. Section S describes the seismic ground motion inputs. Section 6 discusses the analysis cases ccnsidered. Section 7 presents the analysis results. Section 8 presents the assessment of response. Section 9 sumarizes the conclusions. StaffGrp 30(b) 1-1
l l
- 2. NONLINEAR SEISMIC ANALYSIS METHODOLOGY FOR BASE UPLIFT For a structure supported directly on the underlying soil or rock by bearing, when the lateral inertia load on the structure induced by earthquake ground shaking produces a base overturning moment that exceeds the limit of foundation overturning resistance offered by the dead weight of the structure in combination with the transient vertical inertia load, a transient overload condition occurs. This condition, under the assumption of no tension capability at the interface between the structure base and the foundation, causes a transient, partial lift up of the base from its supporting foundation medium resulting in a nonlinear dynamic structural response behavior. Such a nonlinear response behavior results directly from the nonlinear constitutive relationships between the base overturning moment and rocking rotation, and between the base vertical force and displacement, that develop when partial base uplift occurs. A realistic analysis of the seismic response when significant base uplift occurs, thus, requires the application of a nonlinear time-history analysis procedure. - ~
Because' of the necessity of applying the time domain solution' procedure for a nonlineN dyn5miIbase upliftingNhs'pon' s e"a'nalysls,"the"foii$daNon"'~~ impedances that are, in general, frequency-dependent functions, cannot be directly incorporated in a nonlinear analysis of base uplifting response. To overcome this limitation, equivalent frequency-independent foundation impedances (constant foundation springs and dampers) are derived from the frequency-dependent impedance functions and used as the initial linear (before uplift occurs) foundation springs and dampers for the nonlinear analysis. Having established the equivalent constant foundation impedance model, these constant impedance values are then used as the initial values from which the nonlinear constitutive relations between the overturning moment and rocking rotation and between vertical force and displacement at the structure base, are derived as functions of the partial contact area between the base and the foundation as a result of base uplift. A StaffGrp 30(b) 2-1
l i l In this derivation, the structure base is assumed to be rigid; and the constant foundation springs and dampers are assumed to be uniformly distributed Winkler foundation with no-tension capability in the vertical direction. These assumptions lead to linear interface pressure distribution for base uplift condition. This linear pressure distribution assumption conforms to the normal engineering approach of evaluating the foundation bearing capacity. The assumption of rigid base is for simplicity in determining the linear foundation impedances. Deviation from th'e rigid base assumption results in softening of the foundation impedances which can be assessed through variation of SSI frequencies. For a surface-supported structure with a circular or rectangular base, the derivation of the nonlinear constitutive relations (foundction impedance matrix) based on the assumptions stated above is presented in detail in Reference 1. The Winkler foundation model and the geometry and soil pressure distribution of a partially uplifted circular base used in deriving the nonlinear constitutive relations are schematically shown in Figures 2-1 and 2-2, respectively. As a result of base uplifting, coupling occurs between the rocking and vertical responses of the structure due to shifting of the structural base rocking axis. This coupling effect appears as a coupling term in the nonlinear foundation impedance matrix and it results directly from the derivation of nonlinear constitutive relations as presented in Reference 1. Damping of the SSI system with base uplifting response is simulated by the composite of specified modal damping ratios for the fixed-base structural modes and the set of equivalent viscous foundation damping coefficients (soil dampers) for the Winkler foundation as shown in Figure 2-1. The foundation damping coefficients associated with the structure base are proportional to the base contact area when uplift occurs. StaffGrp 30(b) 2-2 6
Using the nonlinear constitutive relations (impedance matrix) for the foundation with base uplift, a set of nonlinear equations of motion for the SSI system is formed and a step-by-step time integration procedure is used to perform the time history response analysis. The Newmark constant acceleration step-by-step time integration algorithm and an equilibrium iteration scheme for each time step are used to ensure unconditional stability in the numerical integration and maintain system dynamic equilibrium at all time steps. The UPLIFT ~ computer program which implements the base uplift analysis procedure as described above is applied for the analysis of base uplifting responses of the ERCW cell.
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- 3. BENCHMARXING OF ANALYSIS METHODOLOGY AND COMPUTATION PROCEDURE The analysis methodology and computational procedure as implemented in the computer program UPLIFT has been verified against the comercially available nonlinear analysis computer programs ANSYS and ADINA. The program has also been verified for ifnear analysis capabilities against the standard (soil spring and damper type) linear SSI analysis computer program for cases where uplift does not occur. These verMications are documented in the Yalidation Report for the program (Ref. 2).
Due to the lack of available, suitable test results for base uplifting ' response, a direct validation of the base uplifting analysis methodology as implemented in the UPLIFT computer program based on test data is not currently feasible. Shaking table tests for uplifting response of a model structure are known to have been carried out in Japan by Nuclear Power Engineering Test Center (NUPEC). However, the results are not yet published and, therefore, are not available for validating the analysis methodology. ~ The SIMQUAXE II experime~nts '(Re'f. 3) on scal'ed cont'ainment models performed in 1977 by Electric Power Research Institute (EPRI), which used explosives to Menerate simulated "seYs'm'icTin'p'u't' toeth' model structures, ' -U ' "
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haveyieldresponse~ data'pertinenttobasIupliftingresponse. ~However, since the ground motions generated by explosives in the experiments were of such a short duration and high acceleration (e.g., the maximum vertical acceleration recorded in the free-field was of the order of 5 l g's), that the resulting responses were not typical of what would be expected of the base uplifting response of an actual structure. In fact, j due to the high vertical acceleration input, the model structure was temporarily debonded, i.e., completely separated from the foundation, during the tests. Thus, the SIMQUAXE II experimental results are considered to be unsuitable for the purpose of validating the base uplifting analysis methodology. An attempt of such an validation has been made by Miller (Ref. 4). However, the results were of limited success. StaffGrp 30(b) 3-1 e
In the lack of suitable experimental data, the nonlinear base uplifting response analysis methodology as described previously in Section 2, and the computational procedure as implemented in the computer program UPLIFT are validated by benchmarking the analysis results against the published analytical solutions for base uplifting response of a rocking block on a . flexible foundation which as been extensively studied by Psycharis (Ref. 5). The rocking block on a flexible foundation considered in Ref. 5 is shown in Figure 3-1. Two types of flexible foundation are studied, namely, the Winkler foundation and the two-spring foundation. The base uplifting response of a rocking block subjected to various strengths of acceleration impulse (measured by the parameter BETA), have been studied in detail and analytical solutions provided for three foundation cases, namely, (a) undamped flexible foundation; (b) damped flexible foundation; and (c) damped flexible foundation with simulation of plastic impact energy dissipation for base slapdown. The solutions as presented in Ref. 5 for the first two. cases with the input impulse strength of BETA = 8, are shown in Figures 2 and 3-3, respectively. -- - For benchmarking, the base tplifting-responses of the rocking Mock - . studied by Psycharis were analysed using the computer program UPLIFT, for the same first two foundation cases and the same input impulse strength of BETA = 8. The resulting responses as calculated by UPLIFT, corresponding to Phycharis' solutions shown in Figure 3-2 and 3-3, are respectively shown in Figures 3-4 and 3-5. By comparing Phycharis' ' solutions in Figures 3-2 and 3-3 with the corresponding solutions in Figures 3-4 and 3-5 obtained from the UPLIFT analyses, it can be concluded that the two solutions agree very well. Thus, the UPLIFT computer program is validated for the rocking block responses studied in Ref. 5. StaffGrp 30(b) 3-e
4. ANALYSIS H0 DEL FOR ERCW CELL i The structural configuration of a representative si shown in Fig. 4-1. ngle ERCW cell is concrete with a diameter of 32'-7-1/2"of and a heig supported on the surface of the rock foundationItatisEl
. 616'. The top elevation of the cell is at El. 691'.
water reservoir with the high reservoir level at ElThe cell is partia operating condition, and a low level at EL. 636' for th. 683' for normal downstream-dam condition. e loss-of-with the minimum embankment height of 25' above theT rock foundation. The cell concrete and the foundation rock properties: - have the following material Cell Concrete Rock Young's Modulus = 4.5 x 106 psi Poisson's Ratio = 0.25 Young's Modulus = 3.5 x 106 psi Unit Weight = 145 pcf Poisson's Ratio = 0.3 Unit Weight = 170 pcf In-place Strength = 4,000 psi Damping ratio "r 5% ' ~ Shear Wave Velocity = 6060 fps ~ Damping ratio ' - ="2%" ~ ' ~ ~~ ' For the purpose of assessing the seismic base high reservoir level (El. 683') is considered tuplifting response, the this condition results in largest buoyancy and o be more critical since mass for the cell, both of which are more critical fadded horizontal water response. or seismic uplifting For the analysis using the UPLIFT computer p stick model for the ERCW cell is developed n Fig. 4-2. as shown irogram, a 2-0 model consists of five lumped masses. The submerged portion of the cell include the tributary massThe lum concrete and the tributary masses of water es of cell equivalent t o one-displaced-volume of the cell for the horizontal hydrodynamic interaction between theaccount direction cell afordtheth to n i e surrounding water, StaffGrp 30(b) 4-1
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- 4. ANALYSIS H0 DEL FOR ERCW CELL The structural configuration of a representative single ERCW cell is shown in Fig. 4-1. This representative cell is a circular cylinder of concrete with a diameter of 32'-7-1/2" and a height of 75'. It is support >d on the surface of the rock foundation at E1. 616'. The top elevat :on of the cell is at El. 691'. The cell is partially submerged in water redarvoir with the high reservoir level at El. 683' for normal operating condition, and a low isvel at EL. 636' for the loss-of-downstream-dam condition. The cell is partially embedded in embankment with the minimum embankment height of 25' above the rock foundation. The cell concrete and the foundation rock have the following material properties: -
- Cell Concrete Rock Young's Modulus = 4.5 x 36 psi Young's Modulus = 3.5 x 106 psi Poisson's Ratio = 0.25 Poisson's Ratio = 0.3 Unit Weight = 145 pef Unit Weight = 170 pcf In-place Strength >= 4,000 psi Shear Wave Velocity = 6060 fps '~
Damping ratio- "r 5%
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-Damping ratio % ='2%"~ -" " '~"" '
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For the purpose of assessing the seismic base uplifting response, the high reservoir level (El. 683') is considered to be more critical since this condition results in largest buoyancy and added horizontal water mass for the cell, both of which are more critical for seismic uplifting response. For the analysis using the UPLIFT computer program, a 2-0 lumped mass stick model for the ERCW cell is developed as shown in Fig. 4-2. The model consists of five lumped masses. The lumped masses for the submerged portion of the cell include the tributary masses of cell concrete and the tributary masses of water equivalent to one-displaced-volume of the cell for the horizontal direction to account for the l hydrodynamic interaction between the cell and the surrounding water. l l . StaffGrp 30(b) 4-1
m l Added hydrodynamic water masses are not considered for the vertical direction. Based on this model and the concrete properties specified above, the fixed-base modal properties of the cell are summarized in Table 4-1. Based on the rock properties specified above, the initial linear constant-foundatic, springs and dampers associated with the horizontal and vertical trenslations, and the rocking rotation of the circular ERCW cell base are determined using the Bechtel CLASSI computer program (Ref. 6) as the average values of the CLASSI foundation impedance functions at the frequency range of 6 to 7. cps which is the range of the fundamental rocking frequency of the cell SSI system. The values for focadation springs and dampers 65 determined are shown in Table 4-2.. Although the ERCW cell is partially embedded in tre embankment, the effect of embedment is neglected for die seismic analysis of the cell. l This results in a conservative seismic model for the the cell since the embedmer,t contributes to stabilizing the rocking response of the cell. The total structural weight of the cell is 9,091 kips. This is reduced
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by the water buoyancy of 3,417 kips corresponding to the high reservofr level at El. 683', giving the buoyant weight of the cell at 5,674 kips. This buoyant weight is used as the effective structural dead weight for the seismic base. uplifting response analysis of the cell. StaffGrp 30(b) 4-2
- 5. SEISMIC GROUND MOTION INPUT The horizontal acceleration time histories for the SSE used as the control motion input for seismic response analyses of the ERCW cell are the four artifical earthquake acceleration time histories A, B, C, and D for the OBE of the Sequoyah Nuclear Plant scaled up by a factor of 2.
The vertical acceleration time histories used are 2/3 of the corresponding horizontal time histories for the SSE. The control motions are input at the' surface of the rock foundation. In order to simulate the realistic phasing between the horizontal and the vertical time history inputs, the horizontal time histories A, B, C, and D are input . simultaneously with the vertical time histories respectively in the order of D. A, B, and C. Furthermore, in order to assess the significance of the vertical time history input, analyses are also performed using only the horizontal time history as the input alone. 4
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StaffGrp 30(b) 5-1
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- 6. ANALYSIS CASES The ERCW cell nonlinear seismic response analyses have.been performed using the UPLIFT program for the following eight analysis cases, each with a different earthquake time history input condition:
Case 1: Artifical earthquake time history A Tor the SSE as the horizontal input coupled with 2/3 of horizontal artificial earthquake time history D for the SSE as the vertical input. Case 2: Artifical earthquake time history B for the SSE as the horizontal input coupled with 2/3 of horizontal artificial ; earthquake time history A for the SSE as the vertic.al input. Case 3: Artifical earthquake time history C for the SSE as the horizontal input coupled with 2/3 of horizontal artificial earthquake time history B for the SSE as the vertical 1
;,1nput. . . . ..
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Case 4: Artifical earthquake time history D for the SSE as the horizontal input coupled with 2/3 of horizontal artificial
- earthquake time history C for the SSE as the vertical input. F Case 5
- Artifical earthquake time history A for the SSE as the l horizontal input without vertical time history input. '
Case 6: Artifical earthquake time history B for the SSE as the horizontal input without vertical time history input. i
- j. Case 7: Artifical earthquake time history C for the SSE as the .
horizontal input without vertical time history input. Case 8: /,rtifical earthquake time history D for the SSE as the ! horizontal input without vertical time history input. , l StaffGrp 30(b) 6-1
- 7. ANALYSIS RESULTS The analysis results for the eight analysis cases described previously are sumarized in Table 7-1 in terms of the following key response parameters: -
(1) Maximum amount of base uplift measured in terms of percents of cell base diameter; (2) ~ Maximum horizontal and vertical displacements relative to rock at the ERCW pipe level and at the extreme edge of cell base; (3) Maximum cell base rotation in radians: c (4) Maximum toe compressive stress (pressure) at the concrete and rock interface resulting from the extreme uplifted position: The horizontal. and. vertical displaceme,n,t Jime hi, stories rel_a.tt.ve..t.o...the .. . . ..,
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rockattheERC[p'ip['lo'c'ationand.}t]heextremeedgeofceil'b'ase'for
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the eight analysis cases are plotted .and shown in Figs. 7.-ifthro. ugh 7,-16 __ 9
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The 1/2% and 1% damping horizontal and vertical accoleration response spectra at the location of ERCW pipe for the eight analysis cases are presented in Figs. 7-17 through 7-32. The arithmetic average of the horizontal and vertical response spectra for Analysis Cases 1 through 4 are presented in Figs. 33 and 34; the average spectra for Analysis Cases 5 through 8 are pre:ented in Figs. 35 and 36. The response spectral values are sumarized in Tables 1 through 8 in Appendix A. l. StaffGrp 30(b) 7-1
- 8. ASSESSMENT OF RESPONSE The results of analysis for all 8 analysis cases sumarized in Table 7-1 show that the maximum amount of base uplift is 77% of the cell base diameter. The maximum toe pressure at the cell base and rock interface is 637 psi. This maximum toe pressure is well within the allowable concrete compressive stress of 3000 psi and the allowable rock bearing stress of 1500 psi.
The maximum horizontal displacement of cell at the ERCW pipe elevation is under 0.2 inches. The maximum vertical displacement at the extreme edge of cell base is 0.06". These displacements are very small even with base uplift since both the concrete cell and the foundation rock are quite stiff. Based on the maximum toe pressure distribution corresponding to the extreme base uplifted position, the potential of progressive "chipping" (shear failure) of cell concrete at the extreme edge of contact area is evaluated by comparing the shear capacity of cell concrete.as a function ,.
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of the horizoi161 distance 'fYom'thel extreme ' edge 'of',liase contac
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versustheshearforcedemandresultingf,gmthetoe. pressure.,,,, distribution I6' the"contd5"ireii.' 'This evaluation. procedure is illustrated in Fig. 8-1. The shear capacity of cell concrete is determined for the diagonal tension shear mode based on a 450 diagonal shearplaneand'ashearstressallowableof4ff'e,where&isthe capacity reduction factor equal to 0.85, and f'c is the in-place concrete compressive strength equal to 4000 psi. As the shear demand exceeds the shear capacity, progressive chipping of cell concreto is assumed and the j toe pressure is redistributed within the new base contact area (excluding the assumed chipped area); and then, new shear demand is calculated and compared with the shear capacity. This process is repeated until the shear demand in the reduced contact area is enveloped by the shear capacity in the same area, at which point, the progressive chipping is considered stabilized, i.e., not extending further into the cell concrete. i
, StaffGrp 30(bT 8-1 i
Using the above procedure, the progressive chipping of cell concrete is determined to not exceed 12 inches from the extreme i:6gs of base for the worst case maximum toe pressure of 637 psi with the corresponding amount of base uplift area. In order to demonstrate that this amount of concrete chipping for the worst case has a neglible effect on the seismic response of the cell, the equivalent linear constant foundation springs and dampers are re-calculated for the cell base considering the cell base area reduced by the 12 inch maximum amount of chipping at both extreme edges of the base. The resulting values are shown in Table 8-1. Comparing the values in Table 8-1 with those shown in Table 4-2, one can observe that the maximum amount of chipping has a neglible effect on the foundation impedance values (less than 7% maximum) and, thus, has an insignificant
< effect on the seismic response of the cell (frequency variation less than 31 maximum).
The comparisons of, accelerat.fon,respons.e . spectra at the E,RCW pipe. .._ . ,. , , elevation resulting from the combined horizontal and vertical earthquake , time history input with the corresponding spectra resulting from the horizontal input only, indicate that the vertical input has a relatively insignificant effect on the base uplifting response of the cell. Since the ERCW pipes are surrounded by 3 inches of compressible material, the assessment of piping stress due to seismic response of cell should be based on the cell displacement at the pipe location induced by the seismic response, rather than based on the acceleration response spectra, i l StaffGrp 30(b) 8-2
.- _. .. - - . . - _ _ _ _ _ _ - _ _ -. - - - - - _ _ - - ..~
- 9. CONCLUSIONS The seismic response of the ERCW cell subjected to the SSE ground motion input for the Sequoyah Nuclear Plant has been analyzed using a 2-0 nonlinear time history dynamic analysis procedure considering the nonlinear geometry of cell base contact due to seismic base uplifting.
The analysis was based on a conservative reismic model for the cell which disregards the beneficial effect of the cell embedment. The analysis has been performed for eight different cases of seismic time history input to evaluate any significant effect on the response due to different time history inputs, different time phasing among horizontal and vertical inputs, and the presence and absence of vertical input. Based on the results of analysis as presented previously, the following conclusions can be drawn: (1) The seismic stability of ERCW cell under the SSE ground motion input of the Sequoyah Nuclear Plant is clearly demonstrated from the very ' small cell displacement resultfng-from the analysis'considert' ng the'"'- base uplift effect~. -- " ~
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(2) The amount of cell displacement at the ERCW pipe location induced by the seismic response of cell is limited to the order of 0.2 inches. (3) The maximum toe pressure induced by the seismic response of cell is 637 psi which is well within the allowable concrete compressive stress of 3000 psi and the rock allowable bearing stress of 1500 psi. The potential of chipping of cell concrete at the extreme edge of base contact area is limited to no more than 12 inches. This amount of chipping has an insignificant effect on he seismic response of cell. StaffGrp 30(b) 9-1
- 10. REFERENCES (1) Tseng, W. S., and Wing, D. W., "Seismic Soil-Structure Interaction Analysis with Basemat Uplift, "Theoretical Manual Revision 1, Computer Program CE444 (UPLIFT), Bechtel Power Corporation, July 1984.
(2) Tseng, W. S., and Wing, D. W., "CE444 (UPLIFT)-Seismic Soil-Structure Interaction Analysis with Basemat Uplift," Verification Manual, Revision 1, Bechtel Power Corporation, July 1984. (3) Higgins C. J., et al, "SIM0KE II - A Multiple Detonation Explosive Test to Simulate the Effects of Earthquake-Like Ground Motions on Nuclear Power Plant Models" EPRI NP-2916 Electric Power Research Institute, October 1983. (4) Miller, C. A., "Soil-Structure Int 1raction, Vol. 2, Incluence of Lift-Off," NUREG/CR-4588, BNL-NUREG-51983, Vol. 2, Brookhaven ; National Laboratory, April 1986. , (S) Psycharis, I. N., "Dynamic Behavior of Rocking Structures Allowed to UPLIFT, "Report No. EERL 81-02, Earthquake Engineering Research - Laboratory, California Institute of Technology, August 1981. (6) Wong, H. L. and Luco, J. E., "Dynamic Structure-to-Structure Interaction for Closely Spaced Buildings," Proceeding of the 3rd U.S. National Conference on Earthquake Engineering, Charleston, i South Carolina, August 24-28, 1986. i StaffGrp 30(b) 10-1
Table 4-1 FIXED-BASE MODAL PROPERTIES ' MODE FREQUENCIES MODAL MASSES (IN FRACTION) 0F TOTAL 3 NO. (CPS) HORIZONTAL (X) VERTICAL (Y)
)
1 7.92 .73 - 2 35.42 .22 - , 3 39.63 -
.90 Cumulative Total 0,95 0.90 t
Total Horizontal Mass = 337.8 k-s /f t Total Vertical Mass = 246.9k-sj/ft
- I I
f I L 9 StaffGrp 30(b) l
Table 4-2 FOUNDATION SPRINGS AND DMPERS FOR ERCW CELL BASE STIFFNESS COEFFICIENTS DMPING COEFFICIENTS CCHPONENT K C Horizontal (X) 1.495 X 107 k/ft .383 X 105 k-s/ft Translation Vertica' (Y) 1.844 X 107 k/ft .577 X 105 k-s/ft Translation , Rocking (4) 3.28 X 109 k-ft/ rad .328 X 107 k-ft-s / rad Rotation t 6 4
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Table 7-1 SUMARY OF MUIMUM ERCW CELL KEY RESPONSE PARAMETERS
.i +
Ah'ALYSIS CASE (JE1 CASE 2 CASE 3 CASE 4 Ut- r; SSE Earthquake Input A(H)+2/3 D(V) B(H)+2/3A(V) C(H)+2/3B(V) D(H)*2/3C(V) Max. Base Uplift Ratio (%) 77 74 74 76
- i
- Max. Horizontal Displacement (in)
ERCW Pipes at E1. 681.5' .160 .17 .17 Base Edge at E1. 616' .19 , O.002 0.002 0.002 0.002 4
, !!ax. Vertical Displacement (in)
- ERCW Pipes at E1. 681.S* .04 .04 .04 Base Edge at E1. 616' .04
.04 .04 .04 .06 Max. Base Rotation (10-4 rad) 1.562 1.761 1.694 1.963 Max. Pressure at Base Edge (psi) 470 604 584 633 1 .'
i StaffGrp 30(b) _. . , , i
Table 7-1 (Continued) SUpttARY OF MAXIMUM ERCW CELL KEY RESPONSE PARAMETERS i ANALYSIS CASE CASE 5 CASE 6' CASE 7 ' CASE 8 j SSE Earthquake Input A(H) 8(H) C(H) D(H) ! Max. Base Uplift Ratio (%) 74 76 75 76 1 l l Hax. Horizontal Displacement (in) l ERCW Pipes at E1. 681.5' .17 .18 .17 Base Edge at E1. 616' .19 O.002 0.002 0.002 0.002 i Max. ertical Displacement (in)
- ERCW Pipes at El. 681.5' .04 .04 .04 Base Edge at C1. 616' .04
.05 .04 .04 .06 Max. Base Rotetion (10-4 rad) 1.757 1.837 1.694 1.962 Max. Pressure at Base Edge (psi) 614 588 577 637 u
StaffGrp 30(b)
Table 8-1 FOUNDATION SPRINGS AND DAMPERS FOR-ERCW CELL BASE WITH BASE AREA REDUCED BY 12 INCH CHIPPING AT BOTH EDGES STIFFNESS COEFFICIENTS DAMPING COEFFICIENTS COMPONENT K C Horizontal (X) 1.480 X 107 k/f t
.378 X 105 k-s/ft Translation Vertical (Y) 1.820 X 107 k/ft .566 X 105 k-s/ft -
Translation Rocking ($) 3.09 X 109 k-f t/ rad .307 X 107 k-ft-s / rad - Rotation StaffGrp 30(b)
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Figure 7-19 1
8 , , , , ,,,,j , , , , , ,,,j , , , , , , ,,
.5I DAMPING VERTICAL
- -- 1 % DAMPING CASE 2 SSE r
, a I i s 6 m
- z -
o m t-g i W J W 4 , 4 U U :\
< ,. \
-t -
a i1 fr
. v4
}-
U
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- m .i l g l l l '
- o '
s i-
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~
'- i ' ' '
0 '
' ' ' ' 's ' i e ie s 'i n 10-1 10_ e 10 1 Ig 2 FREQUENCY-CPS ERCW CELL NONLINEAR ANAldSIS FQTH B(H)+2/3A(V) EL 681.~5' Figure M d .L d -
8, e i eisj i i i i i i i ie sij i i i i e i
.5% DAMPING HORIZONTAL
----- 1 % DAMPING CASE 3
- SSE i
l * , cm i I ! 2 6
- m Z
O e-e F-
- E .
W 5 a A t W u u "
)'l.
< l : f g :
m I :
- .t.
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- := =
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.- 's ..
~.. ; .
.. ./~ "a-2 0
f ~ l I i l l l I I I I I I l f I l I i 10-1 10 e 10 1 10 2 FRGQUENCY-CPS ERCW CELL NONLINEAR ANALYSIS EQTH CCH)+2/3BCV) EL 681.5' Fig,ure 7-21
.i
8 i i i i i i iij i aiij i i i i i iiii
,5% DAMPING l VERTICAL
-~~- 1 % DAHPING CASE 3 SSE G
I , .m 6 ! m I Z O H h x til 3 w 4 4 0
. O
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< i W
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y; . .. _ ~. . . . ~ ~ * .' ! O 10-1 10 e 10 1 10 2 i FR' #EQUENCY-CPS'
] ERCW CELL NONLINEAR ANALYSIS EQTH CCH)+2/38(V) .,
EL 681.5' Figure 7-22 u - _ _ _ _ _ _ _ _ _ _ _ _____ _ _ _ _ _ _ . _ . _ _ _ _ .
8 ieij i i e i e i i iiieii e i i iiii
.5% DAMPING HORIZONTAL 1% DAMPING CASE 4 SSE e
I a 6 m Z O I H 1-m .- W .i! J iir-w 4 * ** o !1:1 U i i
< } }\
;1 J i m -
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0 * ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' 10-1 10 e 10 1 10_2 FREQUENCY-CPS ERCW CELL NONLINEAR ANALYSIS EQTH DCH)+2/3CCV) EL 681.S' Fiqure 7-23
8 . , , , , ,,,j , , , , , ,,,j , , , , , , , ,
.5% DAMPING- VERTICAL
--- 1 % DAMPING CASE 4 l
SSE l cn i a 6 in Z o s F l w 3 w 4 U 1 0 1
]
l' E F !ii LJ ! w 2 e i G- l '. m : '.. J ' i .
- s. ~
' '-- I' ' ' ' ' ' ' ' ' '
0 . i i iii6 l 10-1 10 e 10 1 10 2 FGEQUENCY-CPS ERCW CELL NONLINEAR ANALYSIS-EQTH DCH1+2/3CCV) EL 681.S'
. ...... figure 7-24 e
8 i iiiij i iij i i i i i i i i i i ;r'
.5% DAMPING HORIZONTAL
----- 1 % DAMPING CASE 5
, SSE
.... 3..
CD I m 6 } ( Z O t-4 j b d Z . ttJ [I J :$ Lij 4 : : o i3 U l i.( I . *si i ! Ik j ir m ' F
. i a '} ii 1:
11J 2 ^
/.
n_ m t{. f: {a{ j (f Q.p.p -lr 1 8 !- 1 I I t i f f I I I i I I I I I I i1 10-1 10 e 10 1 10 2 FREQUENCY-CPS ERCW CELL NONLINEAR ANALYSIS EQTH ACH) EL 681.5'
. . . . . . . . . . . Figure 7 ,
8 i i i iiiij s i ij , i i i _i.i.
.5% DAMPING VERTICAL
--- 1% DAMPING CASE 5 SSE
~
cm l m 6 m Z o e-e t-E ' w 3 w 4 a
. o l
)
z t- {A U ^ \ w 2 . - .
~,
1' n_ '- - m 0 ' ' ' ' ' ' ' ' ' ' ' 10-1 10 e 10 1 4 10 2 ERbQUENCY-CPS ERCW CELL NONLINEAR ANALYSIS EQTH ACH)
, EL 681.5'
. t. Figure 7-26 -
O 5 5 I I I I I Il 5 5 5 5 5 5 5 5 h 5 .I 5 5 5 5 5 5
.5% DAMPING HORIZOtJTAL 1 %, D A M P It1 G CASE 6 SSE 7
On i e 6 in Z O H h
< i
, m - LLS !i _3 l\ 4 I : W
- _
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1 E
< j
- h Z i 1--
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N if , ,
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v '.
/
i n i i i i t I I f a f I I I t i i I 3 3 3 1
- 3-1 10 e 10 1 4
10 2 FREQUENCY-CPS ERCW CELL NONLINEAR ANALYSIS EQTH BCH) EL 681.S'
,,, figure 7-27
8 i i i i iiiij i i a i i ij i i e i i ii
.5% DAMPING VERTICAL
- 1r DAMPING CASE 6 SSE m
I a 6 tn z o e-a F-E La J 4 m u o J g . . . -.
;\
F-u : ./ \ LU 2 : D. - in i i
**. ,] '.
- m. _ ./ v_ _ _ . . ,,,
0 ' ' ' ' ' ' ' ' ' ' ' 10-1 10 e 10 1 10 2
. FREQUENCY-CPS ERCW CELL NONLINEAR' ANALYSIS EQTH BCH) EL 681.5'
, ...__ . .F.1qure 7-28
- u. I
i 8 i e i i i iasi i i i i i ainj i i i i iis
.5% DAMPING HORIZONTAL 1r DAMPING CASE 7 SSE
( 6 m j I
- a 6 in z
o H
- F i < -- -
i li T :. W _.1 ! : l W 4 J: t r: O u l. a: :
- < l' !
3
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,( . . V. '
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'sW.
/ c
~
m 0 - 10~1 10 e 10 1
, 10 2 FREQUENCY-CPS ERCW CELL NONLINEAR ANALYSIS EQTH C(H) EL 681.5'
_ .. -. _ Figure 7-29
, . - - - . r p 7- - - _ _ _ _ _ _ _ _ -_ - - - - - - - - - - - - -
.- . . ;. f " -
- g
( 8 i i i a i iisi i i i i i iiii , , , , , , , ,
.5% DAMPING VERTICAL 1r DAMPING CASE 7 SSE cn a
to 6 m z o e-. F-m w
/
~
J 4 w a U
< l-
- 4
-I /:
<C ! :
m ! l- ! U . l w 2 / u n_ . i m i i j.- __
=
0 ' ' ' ' ' ' - 'e ieis i i i , ,iin 10-1 19 a - 10 1 10 2 f FREQUENCY-CPS ERCW CELL NONLINEAR
- ANALYSIS EQTH C(H) EL 681.S' Figure 7-30
.r--
8 . . i i sij i e i iieiij i i i i , isi
.5% DAMPING HORIZONTAL
---- 1 r D AMP I NG CASC 8 j SSE I
e 6 l (n z o H 1--
< I E :
W 3 J 4 .x. I W U h*i i . U 4 . J ' I
< M E .
i l- i U W 2 *
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. v- .!a .y-I " ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '
O ' ' i 10-1 10 e 10 1 10 2 FREQUENCY-CPS ERCW CELL NONLINEAR ANALYSIS EQTH DCH) EL 681.S'
,, Figure 7-31
m L- - e ' 8 iij i i i i i , i i iii,j i i i i i ,i
.5% DAMPING VERTICAL I
---- 1r DAMPING CASE 8 l SSE r .
i I s 6 (n z o H 1-g . . _ . . . W J m 4 < 4 u a > I J s < it F-f-- o : :i W ! i 2 .' '~. tn :
\
- 1
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rs .
- v. ..~~._ .
~
- 0 ' ; ' ' ' ' ' ' ' ' ' ' ' ' '
10-1 10 e 10 1 10 2 FREQUENCY-CPS ERCW CELL NONLINEARnANALYSIS .c - EQTH D(H) EL 681.S' Figpre 7-32
,, 'a
8 : : : : : :j a j i i i : : ::
.5% DAMPING 4
' AVERAGE IIORIZONTAL
------- 1 r D AHP I NG SSE 05 I
a 6 in Z O t-6 W E l 11J 1 J tij 4 !i I-2
! U i !
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i pM ~ - 0 * ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' 10-1 10 e 10 1-10 2 FREQUENCY-CPS ERCW CELL NONLINEAR. ....- A'NALYSIS EQTH H+V EL 681.5' 6
' ,- Figu're 7-33 8
4 I 8 i i . . i i ij i i i i ii j , i i , , ei
.5% DAMPING AVERAGE' VERTICAL
---- 1 % DAMPING 3 SSE i
.. ._ e a,
I a 6 in 2 z O s t-i, < g . . . . . w _j - ta 4 U u '! _J
< e ^i a: ! i I-U ! i w 2 ! i-
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10-1 10 e 10 1 10 2 FRfQUENCY-CPS 1 ERCW CELL NONLINEAR. ANALYSIS EQTH H+V. EL 681.S' s
.. . . fiure7-34 9
8 : iiij i i i i i iiisi i i i i i ii
.5% DAMPING' AVERAGE HORIZONTAL
----- 1 r D AH P I N G SSE G
I a 6 (n z o e-o l-r 111 li 3 ILt 4 !*. u ii
. u :
< (!
I s i 3
< i !<! i)i m M l-i U ! i b# 10 m til 2
- n. g; i.n m : ./...\
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m 0 ' 10-1 10 e 10 1 10 2 FREQUENCY-CPS ERCW CELL NONLINEAR ANALYSIS EQTH H EL 681.S'
. . . ... . . F.f.gu re 7-35 l'
.I l b I I I I I I l lh 5 I I I I I l lh 3 I I I I I I I
.5% DAHPING AVERAGE VERTICAL
- II DAMPING SSE 1
cn i i a 6 in z o H
- F m
W . 3 w 4 U < U
< f a - .; :
m *; H ' .. . O l \ w 2 l < ['! i Q- I i tn !
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..=~~~.,
'I i 0 -
j 10-1 10 .e 10 1 - 10 2 l
' FREQUENCY-CPS ERCW CELL NONLINEAR ANALYSIS EQTH H EL 681.5' i-
. Figure 7-36
. _ __ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ . _ _ _ . _ _ _i__
8
% ~
i Ell 1otical Shea 'r Area Elevation View g 45 0 Cr
~,
;d-2R Chipped - - - -
1
' Area
~.
A':i-lk5
*:- M} ..
Base contac i -
- :... Area Plan Geometry of
. , . :.,. Contact Area 3.. ..c
. . . . . . .r.
j ("e,'-" ' , ' . , ' . c C ;"
-e %.- '
= J D '
a n vV Pressure Diagram
- For Determining P' P ,
Shear Demand i q e /,' Redistributed d Toe Pressure Ofagonal d Shear Capacity Capacity / Demand
' 1,0emand
. **, " Curve r
c .-- d i D . Figure 8-1 Evaluation of Cell Concrete Corner Chipping
APPENDIX A ACCELERATION RESPONSE SPECTRAL YALUES FOR ERCW PIPE EL. 681.5 FT. O f
'n ' i Tm
. L* : . .
, jet ' 4F
TABLE 1
. 5% DAMPING HORIZONTAL RESPONSE SPECTRAL VALUES FOR ERCW PIPES EL 681.5 FT.
SSE FREQ CASE 1 CASE 2 CASE 3 CASE 4 AVERAGE (cps) (g) (g) (g) -(g) (g)
.20 .03 .06 .03 .06 .05
.30 .06 .10 .06 . 11 .08
.40 .12 .13 .12 .11 .12
.50 .16 .12 .17 .20 .16
.60 .17 .29 .28 .26 .25
.70 .34 .30 .28 .19 .28
.80 .26 .27 .25 .23 .25
.90 .43 .28 .30 .44 .36 1.00 .27 .33 .38 .27 .31 1.10 .28 .32 .43 .23 .31 1.20 .31 .50 .38 .24 .37 1.30 .28 .56 .50 .25
~
.40 1.40 .36 .49 .71 .74 .57 1.50 .47 .48 .69 .58 .55 1.60 .58 .83 .52 .75 .67 1.70 .41 1.08 .51 1.05 .76 1.80 ;; .38 80 '
j68 f-i74
~
's.65 '
1.90 -- j90 1.30 .95 1.14
- 1.07 2.00 .77 .74 .84
~
-1.30 .91 2.10 -T62 .68 .85 2 1:11 ',.82 2 7 2.20 " ,
L. 6 4 .86 - f88 -.86
.81 2.30 .76 1.17 1.09 .77 .95 2.40 .95 .93 .87 1.28 1.01 2.50 1.08 .73 1.36 1.20 1.10 2.60 .71 .64 1.33 1.27 .99 2.70 1.47 1.30 1.04 1.19 1.25 2.80 1.73 1.13 1.25 1.37 1.37 2.90 1.16 1.53 1.71 1.46 1.46 3.00 1.52 1.59 1.24 2.10 1.61 i
3.15 1.56 1.28 1.57 3.30 1.33 1.44 1.25 1.46 2.31 1.48 1.62 ! 3.45 1.99 2.63 1.63 1.76 2.00 3.60 3.29 1.67 2.52 2.97 2.61 3.80 1.83 4.11 3.08 2.23 2.81 4.00 2.26 3.33 2.20 3.02 2.70 4.20 3.58 4.40 4.27 2.38 3.66 4.40 2.48 3.55 3.70 3.38 3.28 4.60 4.39 4.66 4.86 4.47 4.59 4.80 5.26 4.64 l 5.00 4.35 6.63 5.22 6.25 5.98 4.85 6.02 5.78 5.25 5.77 5.44 4.40 5.11 5.18 e w -
, - -na-----r- ,. , , , , , ,
~ TABLE 1 (continued)
.5% DAMPING HORIZONTAL RESPONSE SPECTRAL VALUES
- FOR ERCW PIPES EL 681.5 FT.
- SSE
= FREQ CASE 1 CASE 2 CASE 3 CASE 4 AVERAGE (cps) (g) (g) (g) (g) (g) T 5.50 5.57 6.31 5.54 5.68 5.77 5.75 4.39 5.51 6.77 3.65 5.08 I 6.00 5.03 4.41 3.70 3.54 4.17 I 6.25 3.95 2.99 2.74 3.26 3.24 6.50 2.63 2.05 3.25 2.50 2.61 6.75 3.02 2.38 3.48 2.40 2.82 7.00 1.93 1.94 2.77 1.74 2.10 7.2b 2.05 2.75 2.42 1.79 2.25 7.50 1.90 3.11 1.78 2.51 2.33 , 7.75 1.68 1.66 1.38 1.66' 1.59 8.00 1.23 2.24 1.64 1.89 1.75 $ 8.50 1.46 1.55 1.40 h 1.87 1.57 9.00 1.19 1.45 1.51 1.41 1.39 9.50 1.34 1.37 1.16 1.65 1.38 g 10.00 1.47 1.28 1.11 1.47 1.33 10.50 1.54 1.32 1.57 1.42 P= 1.45 11.00 1.45 1.86 1.42 1.80 1.63 11.50 1.83 1.44 1.49 1.36 1.53 12.00 1;67 2.18 1;"i4 1.54 if79 12.50 1.44 1.83 1.51 1.43 ~1.55 13.00 1.96 1. 3'6 1:46 1.55 1.'58 13.50 1.73 1:42 1;55 1.10 1."45 s 14.00 1.50 1.35 1.71 li3( 1.'47 14.50 1.46 1.52 1.47 1.80 [ 15.00 1.55 1.55 1.39 1.33 1.56 1.45 16.00 1.54 1.25 1.42 1.43 1.41 E 17.00 1.77 1.09 1.12 1.11 5 18.00 1.27 1.86 1.58 1.43 1.31 1.54 f 20.00 1.51 2.61 1.59 1.59
- 1.83 22.00 2.28 2.52 2.01 1.51 25.00 2.08 2.00 2.12 1.92 2.07 2.03 28.00 1.46 2.02 1.27 1.49
- 31.00 1.56
.79 .83 .77 .70 .77 34.00 .66 .54 .54
- 40.00
.48 .55
.59 .49 .48 .41 .49 L 50.00 .55 .46 .46 .39 .47 i- 70.00 .56 r
.55 .52 .44 .52 100.00 .54 .45 .44 .39 .45 5
E_ m F.O q M
TABLE 2 1% DAMPING HORIZONTAL RESPONSE SPECTRAL VALUES FOR ERCW PIPES EL 681.5 FT. SSE , FREQ CASE 1 CASE 2 CASE 2
- CASE 4 (cps) AVERAGE (g) (g) (g) (g) (g)
.20 .03 .06 .03
.30 .06
.05 .04
.09 .0' .10 .08
.40 .11 .12 .12 .10 .11
.50 .15 .11 .15 .17 .15
.60 .16 .27 .25
.70 .30
.23 .23
.26 .24 .17 .24
.80 .21 .24 ,21
.90 .34
.21 .22
.24 .26 .37 .30 1.00 .23 .29 .35 .25 .28 1.10 .24 .31 .37 .20 .28 1.20 .28 .47 .35 .25 1.30 .24
, .25 .50 .38 .27 .35 1.40 .31 .45 .55 .60 .48 <
1.50 .42 .46 .56 .54 .50 1.60 .48 .75 .49 .66 .60 1.70 .37 .95 .47 .93 .68 1.80 .34 . 73 ? 262 :.e73 . a.61 1.90 .- .64 '1: 03 ??8 .91
.87 2.00 ._ .60 . .66 .79 ;1,10
.79 2.10
;54 . 57 .65 .;93 .67 2.20 ; *. ;60 1.a77 -
169 2.30 '- ;71 (79 .71 - - i
.98 .95 .71 .84 i-2.40 .90 .71 .83 1.15 .90 2.50 .85 .60 1.02 1.15 .90 2.60 .70 .62 1.09 1.09 .87 2.70 1~07 .96 .83 1.11 .99 2.80 1.41 1.00 1.12 1.21 2.90 1.18 1.01 1.35 1.43 . 1.15 1.24 3.00 1.20 1.29 1.03 1.65 3.15 1.29 1.44 1.03 1.29 1.21 1.24 3.30 1.19 1.32 1.70 1.28 3.45 1.37 1.55 1.99 1.31 1.67 1.63 3.60 2.53 1.67 1.74 2.45 2.10 3.80 1.45 3.21 2.48 1.95 2.27 4.00 2.27 2.94 1.70 2.32 2.31 4.20 2.72 3.61 3.13 2.17 2.91 y 4.40 2.20 2.91 3.15 2.94 2.80 '
4.60 3.38 3.84 3.69 3.49 3.60 4.80 3.91 3.77 3.69 4.51 3.97 5.00 4.58 4.42 3.81 4.63 4.36 5.25 4.65 4.35 3.91 3.79 4.18 e 4
TABLE 2 (continued) 1% DAMPING HORIZONTAL RESPONSE SPECTRAL VALUES FOR ERCW PIPES EL 681.5 FT. SSE FREQ CAS * .1 CASE 2 CASE 3 CASE 4 (cps) (g) AVERAGE (g) (g) (g) (g) 5.50 4.27 4.48 4.06 4.56 5.75 4.34 3.33 4.09 4.62 3.01 6.00 3.76 3.57 3.57 3.10 2.73 6.25 3.24 2.81 2.15 2.11 2.79 2.46 6.50 2.13 1.68 2.61 2.24 2.17 6.75 2.29 1.91 7.00 2.46 1.74 2.10 F 1.75 1.56 2.23 1.33 1.72 9 7.25 1.74 2.21 1.62 1.56 1.78 7.50 1.59 2.44 1.38 1.89 7.75 1.43 1.83 1.56 1.16 1.39 1.38 8.00 1.10 1.70 1.22 1,49 8.50 1.38 1.21 1.34 1.21 1.28 9.00 .98 1.26
, , 1.09 1.33 1.12 1.13 9.50 1.11 1.06 .99 1.30 10.00 1.11 1.16 1.09 .97 1.24 1.12 10.50 1.25 1.22, 11.00 1.23 1.04 '
1.18 1.23 1.54 1.27 1.34 1.35 11.50 1.45 1.29 1.32 1.20 -1.31 12.00 ,1. 2,5 1.,72 1{46 1.-24 1.42 12.50 1.21 1.61 1.44 1.17 1.36 13.00 1.52 1.31 1.29 1.20 1.33 ~ 13.50 'li,41 1.;2.8 1.228 14.00 .l97
. III,2 3 ~
-1:18 1.17 1.38 1.23 14.50 1.24 1.15 1.22 1.04 1.42 15.00 1.25 1.23 1.17 1.23 1.16 1.20 16.00 1.26 1.11 1.17 1.22 1.19 17.00 1.35 1.01 1.10 .95 1.10 18.00 1.45 1.37 1.33 20.00 1.31 2.24 1.20 1.34 1.57 1.51 1.66 22.00 1.69 2.19 1.65 1.40 25.00 1.67 1.73 1.93 1.58 1.63 1.70 28.00 1.25 1.56 1.04 1.24 1.27 31.00 .73 73 .66 .60 34.00 .68
.66 .54 .53 .47 .55 40.00 .59 .48 .48 .41 50.00 .55 .46 .46 .39
.49 70.00 .56 .47
.52 .46 .43 100.00 .54 .49
.45 ti .;; . *,5
- g. -.
?
v hd ( e.
;,b
i l
)
TABLI 3
.5% DAMPING VERTICIL RESPONSE SPECTRAL VALUES FOR ERCW PIPES FL 681.5 FT.
SSE FREQ CASE 1 CASE 2 CASE 3 (cps) CASE 4 AV'. RAGE (g) (g) (g) (g) (g)
. 7 ,$ .04 .02 .04 .02
.30 .03
.07 .04 .07 .04 .05
.40 .08 .08 .08 .08 .08
.50 .13 .10 .08
, F 's .17 .11
.11 .11
.19 .19 .16
.70 .12 .22 .19 .19 .18
.80 .14 .17 .17 .16
.90 .28 .28
.16
.17 .19 .23 1.00 .16 .16 .21 .24 .19 1.10 .14 .18 .19
'. .27 .19 1.20 .14 .19 .33 .23 1.30 .15 .22
.17 .34 .31 1.40 .42 .25
.20 .28 .42 1.00 .34 .33
.26 .27 1.60 .41 .33
.41 .32
.46 .29 .37 1.70 11 .60 2.24 1,59 1.80 s28 943 i .39 .21 '.41 1.90 '.39 '. 3 5
.64 .51 .72 2.00 . . .63 .40
.49 .59
.37 .41 "'45 2.10 ' ' .56 .31
.37 .40 :.41 2.20 .45 .31 .38- .45 .40 2.30 .36 .35 2.40 .58
.57 .53 .45
.40 .47 .41 2.50 .54 .39 .46
.31 .65 .48 2.60 .52 .34 2.70 .30 .54 .43
.47 .60 .57 .44 2.80 .55 .71 .52 2.90 .49
.37 .51 .53
.43 .49 .62 3.00 .60 .59 .51 3.15 .42
.51 .41 .53 3.30
.43 .33 .51 .42
.39 .44 .37 .73 3.45 .44 .48
.60 .66 .56 3.60 .61 .57 3.80
.81 .54 .61 .64
.45 .49 .63 4.00 54
.53 .53
.55 .57 .54 .55 4.20 . 37 .59 4.40 55
.50 .54 .50
.46 .57 .43 4.00 52 .50
.84 .52 .59 .62 4.80 . 64
.41 .58 .69 .58 5.00 .68 .52 5.25 .60
.56 .46 .56
.69 .55 .64 .62 i
e I
,, ,,,-r-- --------.. - _ , - - - - - , . + , . - , , . , - - - - , - - - - . - - - - -
TABLE 3 (continued) 5% DAMPING VERTICAL RESPONSE SPECTRA .L VALUES FOR ERCW PIPES EL 681.5 FT. SSE FREQ CASE 1 CASE 2 CASE 3 CASE 4 AVERAGE (cps) (g) (g) (g) (g) (g) 5.50 .68 .58 .67 .76
.67 5.75 .48 .66 .80 .58 6.00 .63
.58 .58 .95 .89 6.25 .75
.76 .83 .61 .87 .77 6.50 .85 .78 .95 1.36 6.75 .98
.99 1.25 .83 .74 7.00 .95
.79 .90 .94 .98 7.25 .90
.88 .88 1.01 1.32 7.50 1.02 1.03 1.18 .89 .85 .99 7.75 . 97 .71 .90 1.44 S.00 1.00 1.34 1.64 1.49 1.36
". 8.50 1.46 1.47 .80 1.40 1.47 9.00 1.29
; 1.31 1.36 1.40 9.50 1.43 1.57 1.11 1.30 1.41 1.09 1.37 10.00 1.52 1.49 1.86 1.02 10.50 1.47 1.22 1.43 1.51 11.00 1.58 1.56 1.43 1.57 1.01 1.29 1.36 11.50 1.16 1.05 1.18 1.20 12.00 1.15
.89 1,27 1.12 1.07 12.50 1.09
, 1.02 1.01 .85 1.55 13.00 1.11
.82 .89 .79 .91 13.50 ; .89 .85
.96 .74 .8.7 i87 -
14.00 1.10 .68 .64 .85 14.50 .82 1.07 .70 .83 1.05 15.00 .91 1.10 1.37 1.17 16.00 1.23 1.21 1.21 1.60 1.05 1.00 1.22 17.00 1.04 2.19 1.28 1.10 18.00 1.15 1.40 1.04 .90 1.08 1.04 20.00 1.65 1.70 1.34 1.24 22.00 2.42 1.92 1.48 2.50 2.07 2.23 25.00 3.30 4.99 3 13 2.83 28.00 3.46 3.56 4.16 3.29 3.72 3.66 31.00 4.01 3.28 2.94 2.87 34.00 3.27 2.61 3.21 2.57 2.48 40.00 2.72 1.61 1.77 1.34 50.00 .80 1.64 1.59 1.00 .56 .93 .82 70.00 1.26 1.13 1.05 1.48 100.00 1.23
.56 .54 .39 .60 .52 4
i TABLE 4 ' 1% DAMPING VERTICAL RESPONSE SPECTRAL VALUES FOR ERCW PIPES EL 681.5 FT. SSE FREQ CASE 1 CASE 2 CASE 3 CASE 4 AVERAGE (cps) (g) (g) (g) (g) (g)
.20 .04 .02 .04 .02 .03
.30 .07 .04 .06 .04 .05
.40 .07 .07 .08 .08 .07
.50 .11 .10 .07 .10 .10
.60 .15 .10 .18 .17 .15
.70 .11 .20 .17 .16 .16
.80 .13 .14 .15 .14 .14
.90 .23 .22 .15 .16 .19 1.00 .15 .14 .18 .23 .17 1.10 .12 .15 .18 .23 .17 1.20 .15 .17 .28 .21 .20 1.30 .16 .15 .30 .24 .21 1.40 .35 .18 .25 .33 '
.28 1.50 .31 .23 .26 .34 .28 1.60 .38 .28 .41 .28 .34 1.70 .53 .20 .50 .26
.37 1.80 -
.39 18 .38 .35
') .33 1.90 '.' 4 8 .' 3 7 .58 ;45 2.00
".47 iS6
.31 .33 .39 -
-~.40 2.10 - 342 .27 330 .31 -
.33 -
t 2.20 237 .29 i32 .' 3 2 '".33 2.30 -- .32 .32 .48 .- 4 6 ~1.39 2.40 .52 .37 .39 .39 .42 , 2.50 .51 .32 .27 .47 .39 2.60 .46 .27 .28 .44 .36 2.70 .43 .42 .41 .34 .40
'2.80 .49 .58 .33 .45 .46 2.90 .39 +38 .38 .51 .41 3.00 .48 .49 .41 .34 .43 3.15 .35 .40 .28 .43 .36 3.30 .34 .39 .32 .51 .39 i 3.45 .39 .49 .50
! .42 .45 3.60 .53 .59 .39 .44 .49 3.80 .39 .s. .52 .45 .44 4.00 .41 .48 .50 .41 .45 4.20 .34 .49 .43 .41 .42 4.40 .44 .45 .43 .41 .43 4.60 .41 .67 .41 .48 .49 4.80 .54 .38 .45 .56 .48 5.00 .49 .42 .45 .38 .43 5.25 .49 .53 .45 .46 .48
*#^.Y
TABLE 4 (continued) - 1% D.0! PING VERTICAL RESPONSE SPECTRAL VALUES FOR ERCW PIPES EL 681.5 FT. SSE FREQ: CASE 1 CASE 2 CASE 3 CASE 4 (cps) AVERAGE
.(g)' (g) (g) (g) (g) 5.50 .53 .49 .59 .55 .54 5.75 .44 .57 .64 .52 .54 6.00 . 4 5. .43 .69 .68 .56 6.25 .63 .67 .48 .77 .63 6.50 .62 .59- .73 1.03 .74 6.75 .85 1.06 .75 .59 .81 7.00 .66 .80 .85 .73 .76 7.25 .75 .71 .78 1.01 .81 7.50 .81 .98 .66 .78 .81 7.75 .75 .74 .86 1.11 .87 8.00 1.01 1.33 1.17 1.14 1.16 8.50 1.17 .77 1.19 1.11 9.00 1.06
' 1.10 1.06 1.10 .98 1.06 9.50 1.11 1.28 1,05 .94 10.00 1.10 1.14 1.18 1.36 .89 1.14 10.50 1.16 1.17 1.09 1.35 11.00 1.19 1.28 1.11 .93 .98 1.07 11.50 .99 .91 . 93' 1.07 '
12.00 . 98
.83 .93 3.92 .89 .89 12.50 .79 . 7 3. .79 1.23 .88 13.00 .72 .80 .59 .77 .
.<72 13.50 < .7 L .76 .63
.69 .70 14.00 -.88 .61 .57 .74 14.50 .70
.85 .61 .75 .87 15.00 .77
.95 1.1) 1.01 .87 16.00 .99 1.02 1.45 .94 .89 17.00 1.07
.89 1.80 .85 .93 18.00 .95 1.12
.96 .75 .97 .91 20.00 1.28 1.21 1.06 1.23 22.00 1.19 1.93 1.44 1.80 1.74 1.73 25.00 2.38 4.10 2.42 2.19 28.00 2.77 2.96 3.08 2.69 2.90 31.00 2.91 3.21 2.99 2.50 2.71 34.00 2.00 2.85 3.15 2.33 1.91 2.35 40.00 1.47 1.59 1.08 1.45 50.00 1.40
.80 .99 .55 .93 70.00 1.16
.82 1.11 1.36
.83 1.11 '
100.00 .56 .54 .39 .60 .52 4
- . . . - . . , - - - - . , . . . . , . _ - ,,._.,..-_m.._ ,_.__ , _ . - , . , _ , . . _ _ . . , , -
i TABLE 5 l
.5% DAMPING HORIZONTAL RESPONSE SPECTRAL VALUES FOR ERCW PIPES EL 681.5 FT.
SSE FREQ CASES I CASE 6 CASE 7 CASE 8 (cps) (g) AVERAGE -{ (g) (g) (g) (g) l
.20 .03 .06 .03
.30 .06
.06 .05
.10 .06 .11 .08
.40 .12 .13 .12 .11 .12
.50 .16 .12 .17
.60 .17
.20 .16
.29 .29 .26 .25
.70- .34 .30 .28 .19 .28
.80 .26 .27 .25 .23 .25
.90 .43 .28 .30 .44 .36
- 3. 00 .27 .33 .38 .27 1.10 .28 31
.32 .42 1.20 .31 .5G
.23 .31
.38 .24 .37 1.30 .28 .56 .50 .25 .40 1.40 .36 .49 .71 1.50 .46
.73 .57
.48 .69 .58 .55 1.60 .58 .82 .49 1.70
.74 .66
.42 1.10 .51 1.03 1.80 .76
.38 .80 .68 .73 .65 1.90 --' 590 ,1732 -
- 92 lii2 - -1.06 '
2.00
.79 .72 .82 1.28 .90 2.10 _ .' 6 3 .69 l .87
1.12 . 83 2.20 764 , ,
- '86 !85 t-i87 ".80 2.30 .75 1.20 1.10 .76 .95 2.40 .94 .95 .88 2.50 1.10 1.23 1.00
.72 1.36 1.18 1.09 2.60 .71 .63 1.29 1.29 .98 2.70 1.46 1.32 1.02 2.80 1J3 1.15 1.24 1.13 1.22 1.38 1.36 2.90 1.16 1.51 1.63 3.00 1.54 1.J6 1.44 1.55 1.31 2.13 1.63 3.15 1.53 1.22 1.53 3.30 1.26 1.31 1.40 1.40 2.17 1.33 1.54 3.45 2.02 2.52 1.86 1.85 2.06 3.60 3.29 1.88 2.51 3.05 2.68 3.80 1.77 3.83 2.55 2.06 2.55 4.00 2.37 3.27 1.87 2.75 2.57 4.20 3.66 4.20 4.42 2.17 2.61 4.40 2.53 3.19 3.89 3.23 3.21 4.60 4.56 4.64 4.81 4.80 5.23 3.69 4.42 5.22 3.92 6.23 5.15 5.00 5.95 5.35 4.05 4.92 5.07 5.25 6.19 5.88 4.97 4.64 5.42
pr - . . a r y+ 1-i
- l
.p.
TABLE 5 (cor.lin d
.5% DAMPING HORIZONTAL RESPONSE SPECTRAL VALUES FOR ERCW PIPES EL 681.5 FT.
SSE FREQ CASE 5 CASE 6 CASE 7 CASES (cps) (g) AVERAGE (g) (g) (g) (g) 5.50 4.76 5.91 6.67 5.67 5.75-5.75 4.18 5.15 6.51 3.72 4.89 6.00 5.43 4.43 3.90 3.73 4.37 6.25 3.94 3.26 2.87 3.38 6.5G 2.70 3.36 2.36 3.32 2.84 2.81 6.75 3.16 3.26 3.38 2.36 3.04
' .00 1.91 2.09 2.71 1.72 2.11 7.35 2.07 1.81 2.22 1.96 7.53 2.27 1.71 2.67 1.68 2.58 7.75 2.16
_1.72 1.90 1.10 1.33 8.00 1.23 1.51 2.25 1.42 1.72 1.66 8.50= 1.50 1.40 1.65 1.99 1.63 9.00 1.16 1.43 1.42 1.35 1.34 9.50 1.43 1.49 1.07 1.54 1.38 10.00 1.40 1.28 1.19 1.53 1.35 10.50 1.52 1.33 1.58 1.34 1.44 11.00 1.42 1.99 1.44 1.47 1.58 11.50 1.66 1.23 12.00 1.t5 L.2 6 l'.40 1.69 2.14 ~1.81 1.53 1.79 12.50 1 22 1,84 1..49 1.60 1.54 13.00 1. 8.8 L.44 1A8 1 54 1.59 13.50 1. .'/O 1.14 1.90 1.48 1150 14.00 1.36 1.21 14.50 1.67 1.24 1.37 1.56 1.71 1.73 2.11 15.00 1.55 1.78 1.29 1.35 1.60 1.45 16.00 1.86 1.37 1.51 17.00 1.79 1.63 1.90 1.58 1.21 1.22 18.00 1.42 1.48 1.59 1.48 1.01 20.00 1.90 1.38 1.72 1.86 1.39 22.00 2.37 1.72 2.63 1.63 2.02 25.00 2.62 2.16 2.12 1.74 2.02 2.13 28.00 1.18 1.30 1.46 31.00 .80 .64 1.00 1.24
.70 .77 .73 34.00 .54 .56 .59 .59 40.00 .51 .57
.48 .49 .49 50.00 .49 .49
.46 .47 .46 70.00 .52 .47
.46 .57 .50 100.00 .51
.44 .44 .46 .46 .45 1
i 1 0 P
TABLE 6 1 1% DAMPING HORIZONTAL RESPONSE SPECTRAL VALUES ! FOR ERCW PIPES EL 681.5 FT. l SSE FREQ CASE 5 CASE 6 CASE 7 CASES (cps) (g) AVERAJE (g) (g) (g) (g)
.20 .03 .06 .03 .05 .04
.30 .06 .09 .05 .10 .08
.40 .11 .12 .12 .10 .11
.50 .15 .11 .15 .17 .15
.60 .16 .27 .25
.70 .30
.23 .23
.26 .24 .17 .24
.80 .21 .24 .21 .21 .22
.90 .34 .24 .26 .37 .
.30 1.00 .23 .29 .35 .25 .28 1.10 .24 .31 .36 .20 .28 1.20 .28 .47 .34 .25 1.30 .34
.26 .50 .38 .27 1.40 .35
.31 .45 .55 1.50 .42
.60 .48
.46 .56 .54 .49 1.60 .48 .74 .47 1.70 .38
.65 .59
.96 .47 .91 .68 1.80 . 3.4 . .73 ..61 .72 .60 1.90 .54 1.04 2 .85 .90 .86 2.00 .61 .64 .78 2.10 .54
- 1.09 178
.57 .65 . 9.4 .68 2.20 *.60 .77 .61 *
.76 2.30 .. 70
.71 1.00 .95 2.40 .90
.66 .83
.73 .84 1.10 .89 2.50 .85 .57 .99 1.10 2.60 .88
.69 .61 1.06 1.09 2.70 .86 1.04 .96 .82 1.09 2.80 .98 1.40 1.01 1.10 1.22 1.18 2.90- 1.01 1.33 1.34 1.14 1.21 3.00 1.19 1.28 1.10 1.65 1.30
, 3.15 1.41 1.01 1.24 1.20 1.21 3.30 1.20 1.27 1.64 1.19 1.33 3.45 1.56 1.91 1.42 1.77 1.66 3.60 2.51 1.53 1.74 2.55 3.80 2.08 1.49 2.97 2.04 1.88 4.00 2.09 2.31 2.88 1.73 2.15 4.20 2.27 2.78 3.44 3.17 1.95 4.40 2.84 2.21 2.58 3.20 2.94 2.73 4.60 3.40 3.91 3.58 3.14 3.51 4.80 3.92 3.96 3.42 4.16 3.86 5.00 4.44 4.05 3.82 4.07 4.09 5.25 4.S8 4.72 4.24 3.66 i 4.30 9 m
. , - - . _ - . - _ , - , _ _ - . . . _ _ . . , _ . _ - _ ~ _ _ . . , . . . , . __ _.
a
" TAP..E 6 (continued)- ,
if DAMPING'HORI2, INTAL RESPONSE-SPECTRAL VALUES
'FOR ERCW PIPES EL 681.5 FT.
SSE FREQ. ' CASE 5 = CASE 6 CASE 7 CASE 8 (cps) (g) AVERAGE (g) (g) (g) -(g) 5.50 3.99 4.24 4.92 5.75 4.56 4.43 ; 3.26 3.98 4.56 3.00 6.00 3.86 3.70 3.49 3.18 2.74' 3.31-6.25- 2.87 2.44 6.50 2.10 2.07 2.84- :2.55 1.89 2.68 2.28 2.24 6.75 2.40 2.52 2.38 1.70 7.00 1.74 2.25 1.99 2.14 . 52 1.85 7.25 1.76 2.30- A.61 7.E0' 1.70 1.84 1.64 2.23 1.42 2.07 7.75 1.84
-1.43 1.55 .97 1.19 1.28 8.00 1.11 1.77 8.50 1.26 1.06 1.34 1.32 1.26 1.38 1.36 1.32 9.00 .97 1.08 1.26 1.05 9.56 1.13 1.09 '
1.20 .97 1.22 1.13 10.00 1.20 1.13 .97 , 10.50 1.22 1.16 1.20 1.12 ; 11.00 1.18 1.08 1.16 1.13 1.44 1.21 11.50 *1719 1.-06
~
1.21 1.15-12.00 1.19 1.08
'1i38 1.56 1.53 1.26
'4.19 12.50 -1 r04 1.~56 1.3C 3 43 , . .
13.00 *1.' 4 8 1;32 1.33 1.31 r 13.50 1.33 ivi7 - 17. 3 2 1.-37 1;12 1.55 .95 14.00 1.18 1.13 1.33 1.25 1.06 1.18 14.50 1.25 1.35 1.33 1.49 15.00 1.26 1.17 1.10 1.35 16.00 1.36 1.00 1.35 1.22 i 1.22 1.44 1.26 ; 17.00 1.37 1.20 1.17 18.00 1.09 1.21 1.18 1.35 1.36 .92 i 20.00 1.65 1.20 1.58 1.50 1.21 1.51 12.00 1.72 2.04 1.43 25.00 2.10 1.71 1.56 1.69 1.63 1.56 1.75 26.00 1.05 1.06 1.28 1.00 31.00 1.10 '
.67 .56 34.00 .55
.67 .69 .65 40.00
.55 .58 57 .56
.51 .48 .50 l 50.00 .43 .50 a
.49 .46 .47 .46 I
70.00 .51 .46 .55
.47 l 100.00 .47 .50
.44 .44 .46 .46
.45 '
4 l i 5
- . I I
TABLE 7
.5% DAMPING VERTICAL RESPONSE SPECTRAL VALUES FOR ERCW PIPES -EL 681.5 FT.
SSE FREQ -CASE 5 CASE 6 CASE 7 CASE 8 (cps) AVERAGE (g) (g) (g) (g) (g)
.20 .00 .00 .00 .00 .00
.30 .00 .00 .00 .00 .00
.40 .00 .00 .00 .00 .00
.50 .00 .00 .00 .00 .00
.60 .00 .00 .00
.70 . 0 0.
.00 .00
.00 .00 .00 .00
.80 .00 .00 .00 .00 .00
.90 .00 .00 .00 .00 .00 1.00 .01 .01 .00 1.10 .01
.00 .01
.01 .00 .01 .01 1.20 .00 .01 .01 .01 .01 1.30 .01 .01 .01 .02 .01 1.40 .01 .02 .01 .01 .02 1.50 .01 .02 .01 01 1.60 .01
.01 .02 .01 .01 1.70 .01
.01 .03 .01 .01 .02 1.80 .02 .02 .01 .01 .02 --
1.90 .42 .03 . . '0 3 t . 02 '
".03 2.00 -
1- .03 .02 .02 .03 .03 1-2.10 '
.' 0 3 .03 2.20
.03 .03 ' '~.03 -
m .. 03 '
.05 .'03 .03 2.30 .03
.04 .03 .04 .02 .04 2.40 .04 .04 .05 .04 .04 2.50 .03 .06 .04 .04 .04 2.60 .03 .08 .04 .05 .05 2.70 .06 .08 .04 .05 .06 2.80 .06 .07 .06 .11 .07 i
2.90 .04 .09 .07 .07 .07 3.00 .05 .11 .08 .07 .08 3.15 .09 .12 .05 .07 .08 3.30 .07 .10 .14 .08 .10 3.45 .12 .16 3.60
.10 .13 .13
.12 .10 .13 .11 3.80 .12
.11 .26 .16 .12 4.00 .16
.15 .24 .16 .12 4.20 .17
.22 .28 .23 .15 .22 4.40 .19 .20 .27 .19 .21 4.60 .31 .23 .23 .26 .26 4.80 .21 .30 .27 .34 .28 5.00 .27 .37 .30 .24 .30 5.25 .44 .62 .35 .26 .42 l
T
)
TABLE 7 (continued) ? 5% DAMPING VERTICAL RESPONSE SPECTRAL VALUES N FOR ERCW PIPES EL 681.5 FT. SSE j FREQ CASES CASE 6 CASE 7 CASE 8 AVERAGE (cps) (g) (g) (g) (g) (g) i ll 5.50 .48 .45 .43 .33 .42 5.75 .37 .38 .44 .42 .40 r-6.00 .50 .40 .44 .52 .46 6.25 .39 .38 .44 .58 .45 6.50
.48 .48 .54 .91 6.75 .40 .64 .44 .38
.60
.47 g
7.00 .69 .54 .53 .70 .62 7.25 .71 . 4 */ .66 .77 .65 _-l 7 50 .91 .8) .99 .79 .87 7.75 .82 .55 .72 .86 .74 8.00 .91 1.33 1.19 .87 1.08
. 8.50 1.40 .2' 1.33 1.12 1.19 9.00 1.11 1.4t 1.47 1.03 1.25 9.50 1.63 1.64 1.46 .85 10.00 1.39 am 1.45 1.39 1.64 1.08 1.39 10.50 1.32 1-15 1.38 1.52 1.34 -
11.00 .1 .,47 1.26 1.01 1.26 1.25 ; 11.50 1.15 1.00 1 05 1.0S 1.07 @ 12.00 .91 1.12 1.36 .89 1.07 12.50 , . 79 .81 .84 1.05 13.00
.. 8 7 AE
.82 .90 .80 .76 .82 1E 13.50 .21 .85 .59 .85 .81 MB 14.00 .96 .66 .52 .92
.76 14.50 .99 .82 .74 .74 _-
15.00 .82 == 1.05 1.02 .99 .74 2" 16.00 .95 1.00 1. 0 ". 1.38 .83 I 17.00 1.06 1.13 3 23 1.23 1.00 -- 18.00 1.15 1.08 1.02 .80 .83 20.00 .93 JE 1.49 1.46 1.83 .91 22.00 1.42 -= 2.29 3.00 2.36 1.71 25.00 2.34 EE 2.84 2.95 3.11 3.70 28.00 3.15 j= 2.74 3.61 3.76 2.76 31.00 3.22 '= 1.89 2.80 4.34 2.69 2.93 34.00 3.45 2.49 2.09 2.21 -- 40.00 2.56 1.49 1.51 1.54 1.67 1.55 -- 50.00 1.02 .79 .76 .78 "" 70.00 .84 _ 1.01 1.05 1.49 1.11 1.16 2: 100.00 .64 .51 .49 .44 "5
.52 a
4
-(
TABLE 8 1% DAMPING VERTICAL' RESPONSE SPECTRAL VALUES FOR ERCW PIPES EL 681~.5 FT. SSE FREQ CASE 5 CASE 6 CASE 7 CASES (cps) (g) AVERAGE (g) (g) (g) (g)-
.20 .00 .00 .00 .00 .00
.30 .00 .00 .00 .00 .00
.40 .00 .00 .00 .00 50 .00
. .00 .00 .00 .00 60 .00
. .00 .00 .00 .00 70 .00
. .00 .00 .00 .00 80 .00
. .00 .00 .00 .00
. 90
.00
.00 .00 .00 .00 1.00 .00
.01 .01 .00 .00 1.10 .00
.00 .01 .00 .01 1.20 .01
.00 .01 .01 .01 1.30 .01
.01 .01 .01 .01 1.40 .01
.01 .02 .01 .01 1.50 .01
.01 .02 .01 .01 .01 1.60 .01 .02 .01 .01 .01 3 1.70 .01 .03 .01 ;02
. 0.1
, 1.80 .02 .0.1 1.90
'.^ 0~1 , ,,01 : . 01
~ ~ . ~0 2 .02 *. 02 2.00
.02 .02
.02 .02 .02 .02 . 02 2.10 1. .'03 .03 .03 .'02 ' ~.' 03 -
i 2.20 [ '. M .li5 '. 0 3 .02 .03 2.30 .04 .03 .03 .02 '- .03 2.40 .03 .04 .04 .03
- .04 2.50 .03 .06 .04 .04 .04 2.60 .03 .08 .03 2.70 .05
.04 .04
.07 .03 .04 .05 2.80 .05 .06 .05 .08 2.90 .06
.04 .08 .06 .06 .06 i 3.00 .05 .09 .07 .06 .07 3.15 .07 .11 .05 .07 .08 3.30 .06 .09 .09 .07 .08 3.45 .10 .12 .08 .11 .10 3.60 .10 .10 .11 .10
.10 3.80 .10 .20 .14 .11 .14 4.00 .13 .21 .12 .10 .14 4.20 .17 .23 .14
.20 .19 4.40 .17 .19 .21 .16 .18 4.60 .23 .22 .21 .24 .22 4.80 .18 .23 .23 .27 .23 5.00 .26 .28 .28 .23 .26 5.25 .37 .50 .33 .22 .35
_ . _ _ . _ _ _ . , , . , .. --,------'-------w-- *--~*
TABLE 8 (continued) i 1% DAMPING VERTICAL RESPONSE SPECTRAL VALUES FOR ERCW PIPES EL 681.5 FT. . SSE FREQ -CASE 5 CASE 6 CASE 7 CASE 8 (cps) (g) AVERAGE. (g) (g) (g) (g) 5.50 .37 .41 .34 .26 .34 5.75 .32 .30 .32 . 41' 6.00 .35
.34
.32 .31- .45 . 36 6.25 .36 .36- .38-6.50 .36
.46 .39
.43 .43 .70 6.75 .48 :
.37 .51 .38- .34 .40 7.00 .51 .48 .48 .58 .51 7.25~ .60 .43 .52 7.50 .78
.73 .57
.67 .75 .65 .71 7.75 - .77 .50 .63 .72 8.00 .65
.73 1.10 .93 .79-
.89 I 8.50 1.02 .82 1.02 .87 .93 9.00 1.00- 1.10 1.23 9.50 1.13
.82 1.04 i
1.23 1.12 .90 1.09 10.00 1.09 1.00 1.20 10.50 1.18 .95
.87 ~ 1.04 1.03 1.21 1.10 '
J 11.00 1.16 .96 .90 1.~ 01 11.50 1.01
.92 .82 .98 .90 '
12.00 .90
.78 .91 1.07 .74 .87 12.50 .65 .68 .78 .85 l
13.00 .74
.67 .81 . 5 5 . . .. .- . . . . . .63..
13.50 .69 .73 .62 .7T ,, ,.jy g,;77 .69 66 14.00 .85 .64 .51
.77"-~
~ l
~14.50 .86
.69
.65 .62 .66 .70 15.00 .92 .83 .86 .65 i
l i 16.00 .81
.89 .87 1.26 .82 17.00 .96
.97 1.09 1.00 18.00 .94
.84 .98
.86 .70 .65 .79 -
20.00 1.48 1.11 1.40 .91 22.00 1.22 t 1.95 2.37 2.08 1.29 25.00 2.28 1.92 2.31 2.39 2.64 2.41 28.00 2.08 2.69 3.07 ! 31.00 1.89 2.61 2.61 2.26 3.56 2.07 2.45 ! 34.00 2.73 1.96 1.70 2.05 2.11 40.00 1.43 1.36 1.36 1.35 1.38 50.00 1.01 .79 .76 .77 70.00 .83 ' 1.06 .91 1.35 .96 100.00 1.07
.64 .51 .49 .44 .52 I i
t. i , i 4 > I i
..+ , . - - , , _ , ~ - , - - - . . -,,_~-,.-----.--,..m. -- , , - , - ,, ---- ,,--_-,-.,_.,7, -, . , - - - , - . - - - -
DOCUMENT REVIEW NOT!CE
~ '/ Civil / Structural DISCIPLINE x ,,o, Civil / Structural TO CHIEF ENGINEER civil / Structural ,
(DISCIPLINE) THE FOLLOWING DCCUMENTS ARE SUBMITTED: Addendum to Task Report on "Nonlinear Time History Seismic Resoonse Analyses for ERCW Cell" - Lower-Bound Concrete Modulus, For TVA Sequoyah Nuclear Plant. QUALITY ENGINEERING REVIEW: DoES THis CH ANGE CORRECT ERRORS OR DEFICIENCIES IN THE PREVIOUSLY ESTAsLISHED DESIGN? O NO Oves aoawAmo COPY 05 TaE oaN AND ATfACHMENTS TO THE SUPERVISOR OF OVALITY ENGINEERING IN ACCORDANCE wlTH MEDIEDP - 4.34. O INITI AL SUsMITTAL O nESusuiTTAL iATTACHEo CO,Y 0, Review NOTICE ,ORu PREVIOUSLY SUBMITTEDI REVIEW MADE BY REVIEW TECHNIQUE
@ GENERA L COMPLI ANCE O cow'ARisON witw PROVEN 5tANo^Ros OP DESIGN Mb N O DETAILED CHECK O otsiGN aEviEw uEETiNG INOTES ATTACHEDI STATUS j APPROV E D O AP* roves wiTw COuMENTs isELO*> 0 Not - ^"aovEo o
L T ^ ; $ /. $ 3 5b N UN!W
- OmikdNATOR DATE GRP SbPY DATE PROJ O ENG QATE PROJ ENG DATE CHICP ENG 'DAkE 88P20222,mm 142 -
E O 20. at v 3 (1921 ^ i
-ll' ADDENDUM TO TASK REPORT ON NONLINEAR TIME HISTORY SEISHIC RESPONSE ANALYSES FOR ERCW CELL (LOWER-SOUND CONCRETE MODULUS)
Prepared for TENNESSEE VALLEY AUTHORITY Sequoyah Nuclear Plant Knoxville, Tennessee by Bechtel North American Power Corporation San Francisco, California February 26, 1988 ) 1
=TA8LE OF CONTENTS 0F.
ADDENDUM SECTION PAGE
- 1. I N TR O D U CT I O N . . . . . . .' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1
- 2. NONLINER SEISHIC AdALYSIS ridTH000 LOGY FO R d AS E OP L I F T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 - 1 i
- 3. ANALYSIS H0 DEL FOR ERCW CELL . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1
- 4. SEI5d!C GROUND MOTION INPUT . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1
- 5. ANALYSIS CASf5 ........................................ 5-1
- 6. AdAL YS I S R E S UL TS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
- 7. ASSESSMENT 0F RESPONSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-1 i
- 8. CONCLUSIONS ........................................... 8-1 '
- 9. REFERENCES ............................................ 9-1 !
P Tables - Figures I t i t StaffGrp 30(b) -1
ADDENDUM TO TASK REPORT ON NONLINEAR TIME HISTORY SEISMIC RESPONSE ANALYSIS FOR ERCW CELL
- 1. INTRODUCTION This addendum to tne suoject task report presents the additional seismic analyses performed and the analysis results obtained for the Essential Raw Cooling Water (ERCW) access roadway cell suojected to tne Safe Snutdow Eartnquake (SSE) of the Sequoyah duelear Plant. The objective of these anayses is to determine the worst case upper-bound seismic displacement _of tne cell at tne location of tne ERCd piping for use in assessing tne piping stresses, by using the worst case lower-cound concrete aodulus values for tne cell and taKing into account tne nonlinear effect resulting froa partial uplifting of base during tne seisaic response.
=
The seisaic response analysis for tne ERCW cell reported in this addenouni 7 utilizes the same two-dimensional (2-0) nonlinear tiae nistory response analysis metnodology and tne associated UPLIFT conputer program as used for analysis presented in tne main report (Reference 1). Tne aethodology is based on the Winkler foundation uodel (uniforuly-distributed discrete ~ foundation springs and dampers) which has no tension capability. Section 2 of this addendum briefly recapitulates the methodology and = couputer program for nonlinear seismic analysis of structure witn case uplift. Section 3 describes the soil-structure interaction (551) analysis model for the ERCW cell using the lower-oound concrete nodulus values. Section 4 describes the seisdic ground motion inputs. Section 5 discusses the analysis cases considered. Section 6 presents the analysis results. Section 7 presents the assessuent of response. Section 8 suuuarizes the conclusions. StaffGrp 30(b) 1-1 l
o
- 2. NONLINEAR SEISMIC ANALYSIS HETH000 LOGY FOR 6ASE UPLIFT The nonlinear seistaic analysis uetnocology and coiaputer prograra used for tne additional analyses reported in this addenduu are the same as tnose described in tne main report. As described previously, tne analysis utilizes a .aodel of an elastic structure resting on the surface of WinKler foundation which has no tension capability. In order to be consistent witn the time doaain solution procedure for the nonlinear dynauic base uplifting response analysis, the foundation impedances whicn are, in general, frequency-cepen:ent functions, are siuulated by a set of equivalent frequency-independent foundation springs and daiapers for the nonlinear analysis, dased on tne equivalent constant foundation iupedance uodel, nonlinear constitutive relations oetween tne overturning uoiaent and rocking rotation and between vertical force and displaceuent at tne structure case, are derived as functions of the partial contact area between tne Dase and the foundation as a result of case uplift.
For a surface-supported circular case, the derivation of the nonlinear constitutive relations (foundation fiapedance matrix) utilizes the WinKler founda";ica iaodel and the geoiaetry and soil pressure distrioution of a partially uplifted case as snown scheuatically in Figures 1 and 2. As a result of case uplifting, coupling occurs catween tne rocking and vertical responses of the structure due to shifting of the structural case rocking axis. Tnis coupling effe:t appears as a coupling term in the nonlinear foundation impedance uatrix and it results directly frou tne derivation of nonlinear constitutive relations. Dauping of the SSI systeia witn case uplif ting response is sinulated oy the couposite of specified uodal dauping ratios for tne fixed-base structural oudes and the set of equivalent viscous foundation damping coefficients (soil daupers) for tne WinKler foundation as snown in Figure
- 1. Tne foundation dauping coefficients associated witn the structure uase are proportional tu tne case contact area wnen uplif t occurs.
StaffGrp 30(o) 2-1 4
p Tne systeu of nonlinear equations of motion for tne SSI systen witn the nonlinear constitutive relations (iinpedance matrix) for tne foundation witn case uplif t is fonaed and solved in the tiiae douain using the deaaark constant acceleration step-by-step tiiae integration algoritna wnicn ensures unconditional stability in tne numerical integration and an equilibrium 1:eration seneue for each tioe step wnicn iaaintains system dynamic equilibrium at all time steps. The nonlinear analysis procedure as descrioed above is impleraented into the OPLIFT couputer prograta which is used for tne analysis of base uplifting responses of the ERCW cell described herein. Tnis prograu has been verified against the coaaercially availaole nonlinear analysis computer programs ANSYS and ADINA, and has been benchmarked against the analytical solutions for a rocking block studied oy Psycharis as described previously in the inain report. i t i m [ t t StaffGrp "Ib) 2-2 t I t A
4
- 3. ANALYSIS H0 DEL FOR ERCW CELL ine structural configuration of tne ERCW cell used for tne additional
-analysis is the same'as that used for tne analysis in the main report.
This is snown in Figure 3. This representative cell is a circular cylinder of concrete with a diameter of 32'-7-1/2" and a neigne of 75'. It is supported on the_ surface of the rock foundation at El. 616'. The top elevation of tne cell is at El. 691'. The cell is partially suDmerged in water reservoir with the high reservoir level at El. 683' for noraal operating condition, and a low level at EL. 636' for the loss-of-downstreau-d a condition. The cell is partially emoedded in emoanxment witn tne dinitauin euoankment neignt of 25' aoove ene rock foundation. For tne purpose of assessing the seisaic case uplifting response, tne nign reservoir level (El. 683') is used since it is tne inore critical condition for seismic uplifting response. Furthermore, tne effect of emoedaent due to tne 25' eaoanKaent is negletected for the seissaic analysis. This results in a Conservative seisdiC model for the Cell since tne emoedoent contrioutes to staolizing the rocking response of tne cell. In order to ootain tne upper-bound displaceaent response at tne ERCW piping location, lower-oound values of cell concrete modulus are used for the analysis. The properties of the lower-oound cell concrete and the properties of tne foundation rock are as follows: Cell Concrete Rock Young's Hodulus = 2.d x IJ6 psi Young's Hodulus = 3.5 x 10 6 psi Poisson's datio = 0.25 Poisson's Ratio = 0.3 Unit deight = 145 pcf Unit Weight = 170 pcf damping ratio = 5% damping ratio = 21 . StaffGrp 30(o) 3-1 e n - . -- ,,,
4 In addition to'tne lower-bound cell concrete uodulus shown aoove, the concrete modulus of tne lowest 4 ft of the cell is assuaed to be even softer with 1/4 of tne lower-oound modulus value snown aoove, i.e., a oodulus value of 0.7 x 106 psi is used as the concrete modulus for the lowest 4 ft of tne cell. For the analysis using the UPLIFT computer prograu, a 2-0 lumped mass stick uodel for tne ERCW cell is developed as shown in Fig. 4. This model includes the ERCW cell from top (El. 691') to the depth of 71 ft. (El. 620'), and the lowest 4 ft of softer cell concrete between El. 620' and El. 616' is not included in this model. The stick model consists of five lumped unsses. The luiaped masses for tne submerged portion of the cell include the tributary inasses of cell concrete and the trioutary masses of water equivalent to one-displaced-volume of.the cell for tne ' norizontal direction to account for the hydrodynamic interaction between tne cell and tne surrounding water. Added nydrodynamic water masses are L not considered for t.,e vertical direction. The fixed-oase inodal properties of tne stici sodel as descrioed are suundarized in Table 1. Since tne rock properties specified above are tne same as tnose used for tne analysis reported in tne main report, tne initial linear constant foundation springs and dampers associated with the norizontal and vertical translations, and the rocking rotation of tne circular ERCW cell base used for the current analysis are the same as those snown in the uain report. Tnese values are again shown in Table 2. The lowest 4 ft of softer cell concrete between El. 620' and El. 616' (top of rock) is uodelled using a separate structural eleinent wnicn Ifnks tne 71 ft of upper cell concrete, represented by the 6 lumped-mass stick model, with the foundation represented by a set of foundation springs and dampers shown in Taole 2. The stiffness of this 4 ft of softer cell concrete for the norizontal translation, rocking, and vertical StaffGrp 30(b) 3-2
+ Ab
s g-l translation are represented using generalized springs..'0aisping of tais portion of softer concrete is simulated by equivalent viscous damping i I coefficients derived consistent with the 5% codal dauping ratio for the cell concrete. The resulting generalized stiffness and daisping coefficients as derived are shown in Table 3. Since the 4 ft, of softer concrete links the concrete cell aoove to the ,
' rock founoation oelow, tne generalized. stiffness and dauping coefficients for tnis'4 ft. of concrete shown in Table 3-snould oe linked'in series witn tne corresponding coiaponents of foundation springs and daiapers shown in Taole 2. Tne resulting stiffness and camping coefficients ootained frod coimining the two sets of values in series .are shown in Teole 4.
Tnese values are finally used as the equivalent foundation springs-and , daupers for the base uplifting analysis of the cell. By ceaparing the , values snown in Tacles'2, 3, and 4, one can see tnat the final foundation soring and daniping coefficients are dominated by tne stiffness and daqing coefficients'of the 4 ft. softer cell concrete. In other words, , the 4 ft of softer concrete acts in a manner like a "soft cushion" for the upper cell concrete. , e I i t t i [ StaffGrp 30(b) 3-3 l
'" I
4.- SEISMIC GROUND MOTION INPUT The norizontal acceleration tiine histories for the SSE used as the control iaotion input for seisaic response analyses of tne ERC4 cell are the four'artifical earthquake acceleration tiiae histories A, d. C, and 0 t for_the ode'of tne Sequoyan Nuclear Plant scaled up of a factor of 2. The vertical acceleration tiae histories used are 2/3 of tne corresponding norizontal time histories for tne SSE. The control actions are input at the surface of the rock foundation. In order to siuulate tne realistic pnasing oetween the horizontal and tne vertical tiine nistory inputs, the horizontal tiiae nistories A, d. C, and D are input,siaultaneously with tne vertical tiene histories respectively in the order of 0, A, 6, and C. Furtherdore, in order to assess the significance of tne vertical ti.ne nistory input, analyses are also ' perforced using only the horizontal time nistory as the input alone. i I StaffGrp 30(o) 4-1 I n
e i i
- 5. ANALYSIS CASES As for the analysis _ described in the main report, tne additional idC4 cell nonlinear seismic response analyses based on tne lower-cound concrete aodulus values have also been performed using tne UPLIFT prograa for tne following eignt analysis cases, each witn a different 556 time nistory input condition:
Case 1: Artifical eartnquake time history A as the horizontal input coupled witn 2/3 of artificial earthquake tiae history 0 as the vertical input. ' Case 2: Artifical eartnquaKe tiule nistory 6 as the horizontal
- input coupled with 2/3 of artificial earthquake time nistory A as tne vertical input, t
Case 3: Artifical eartnquake tiiae history C as tne horizontal input couplea witn 2/3 of artificial eartnquake tiae , nistory d as tne vertical input. { Case 4: Artifical eartnquake time history 0 as the horizontal input coupled witn 2/3 of artificial earthquake tide history C as tne vertical input. Case 6: Artifical eartnquake time history A as tne horizontal input witnout vertical time nistory input, j t Case 6: Artifical eartnquake time history 6 as tne horizontal input witnout vertical time nistory input, t Case 7: Artifical eartnquake time history C as the horizontal input witnout vertical time history input. i i Case 8: Artifical earthquake tihe history D as the horizontal 1 input witnout vertical time nistory input. - L
- StaffGrp 30(D) 5-1 i i
f. t t 6 .' ANALYSIS RESULTS The analysis results for the eight analysis cases described previously are summarized in Table 5 in terus of the following Key' response paraneters: (1) Maximum aucunt of base uplift seasured in terms of percents of cell case dia.aeter; (2) Maxinuta horizontal and vertical displaceaents relative to the free-field rock at the ERCW pipe elevation and at the extreine edge of cell base; (3) Maximudcellbaserotationinradians; (4) Haximuin toe compressive pressure at tne base of concrete resulting from tne extreae uplifted position: The norizontal and vertical displaceinent time histories relative to the free-field rocx at tne ERCW pipe location and at the extreine edge of cell case for tne eight analysis cases are plotted and snown in Figs. 5 through 20. StaffGrp 30(o) 6-1 a
.c
~.
- 7. ASSESSMENT OF RESPONSE ine results of analysis for all 8 analysis cases sui.warized in Taole 6 snuw tnat tne maxioua aiaount of base uplift averaged for 4 tii.ie nistcry input cases is 83% of tne cell case diaiaeter. Tne maxiaum horizontal displaceaent of cell at tne ERCW pipe elevation averaged for 4 tide nistory input cases is under 0.9 inches. The maximua vertical displaceiaent at tne extreiae edge of cell case averaged for 4 tiue nistory input cases is 0.2 inenes. The maxiinuia total displaceinent ootained oy cocoining tne uaximuu norizontal and vertical displacements is less than 1.0 inch. This displaceiaent is still very small even with the lower-oound cell concrete ooculus and tne 4 ft. of even softer concrete at the cell base as used for tne analysis.
Tne maximum toe pressure at tne cell base as cotained from these worst case analyses, averaged for 4 tiine history input cases, is under 800 psi. Tnis maximum toe pressure snould, nowever, not De considered as a realistic value since tne lower-oound ERCJ cell aodel was established solely for the purpose of ootaining tne upper-cound displaceaent response of tne cell. Considering tne snort transient pnenmaenon of case uplifting dynauic response, tne realistic concrete oearing stress over tne entire response duration will oe muen lower tnan tne maxiaum value. Furtneroore, due to tne confinement of cell concrete of tne coffer dam sneet piles and. cell eacakaent at tne lower portion of tne cell, the concrete
Dearing stress at tne ce',
1 base should not ce of concern. StaffGrp 30(D) 7-1 1 I,
k 8. CONCLUSIONS ine additional seistaic response analyses for the ERCW cell cased on tne lower-bound concrete inodulus for tne cell suojected to tne SSE ground motion input for the Sequoyah Nuclear Plant have oee 1 analyzed using a nonlinear time nistory dynamic analysis procedure taking into account the nonlinear geotaetry of seisaic base uplifting. Tne oojective of the analysis was to obtain the worst case upper-bound cell seisaic response displaceiaent for checking tne ERCd piping stress. Tne analysis was cased on a conservative, seisuic aodel for the cell wnich disregards the ceneficial effect of tne cell eaoedoent. The analyses nave Deen perforaed for eight different cases of seismic tiiae nistory input to account for any significant effect on tne response due to different tioe nistory inputs, different time pnasing among norizontal and vertical inputs, and the presence and aosence of vertical input. dased on the results of analysis as presented previously, tne following conclusions can oe drawn: (1) Tne seisaic staoility of ERCW cell, even with tne lower-cound concrete iaodulus values for the cell under tne SSE ground uotion input of tne Sequoyan Nuclear Plant is clearly detionstrated froin tne still very small cell displaceaent resulting from tne oase uplift effect and the lower-bound concrete cell stiffness. (2) The magnitude of cell displaceaent at the ERCW pipa location induced by the seismic response of cell cased on the worst case concrete modulus values is limited to no more tnan 1.0 inen. StaffGrp 30(o) 6-1
- -m
_2- - ~
- 9. REFERENCES
.(1) decntel 14 orth American Power Corporation," Task Report on iionlinear Time History seissaic Response ' Analyses for ERCd Cell," Report to Tennessee Valley Authority, Sequoyah iluclear Plant, Dece.eer 2, 19d7.
StaffGrp 30(b) 9-I e VS
Table 1 FIXED-BASE H0DAL PROPERTIES H0DE FREQUENCIES H00AL HASSES (IN FRACTION) 0F TOTAL NO. (CPS) HORIZONTAL (X) VERTICAL (Y) 1 6.93 .71 - 2 30.5 .22 - 3 33. - .d8 Cenulative Total .93 .88 Total Horizontal riass of fixed-base iaodel = 327.5 k-s2/ft Total Vertical Mass of fixed-oase iaodel = 239.7 k-s2/ ft e i i StaffGrp 30(b) s.
s-J Table 2 FOUNDATION SPRINGS AND DMPERS FOR ERCW CELL dASE' STIFFNESS COEFFICIENTS DMPING COEFFICIENTS COMPONENT K C Horizontal (X) 1.495 X 107 k/ft- .383 X 105 k.s/ft Translation
' Vertical (Y) 1.844 X 107 k/ft .577 X 105 k.s/ft' Translation Rocking (t) 3.28 X'109 k.ft/ rad .328 X 107 k.ft.s./ rad Rotation I
l StaffGrp 30(b)
*e.
m
=
i Taole 3 - GENERATED STIFFNESS AND DAMPING COEFFICIENTS FOR THE 4FT _ 0F SOFTER CONCRETE ; i STIFFNESS COEFFICIENTS DAMPING COEFFICIENTS _ COMPONENT K C , Horizontal (X) .744 X 107 x/ft .052 X 105 k.s/ft i Translation Vertical (Y) 2.107 X 107 k/ft .07S X 105 k.s/ft 2 Translation . Rocking (t) 1.402 X 109 k.ft/ rad .304 X 107 k.ft.s./ rad j etotation _ m am
=
l
?
a E G a I StaffGrp 30(b) _
Table.4 COMSINED STIFFNESS AND DAMP!NG COEFFICIENTS OF THE VALUES-
'IN TABLES 2 AND 3 IN SERIES STIFFNESS COEFFICIENTS DAMPING COEFFICIENTS X C C0i4PONENT dorizontal (X) .'S X 107 K/ft .047 X 105 k.s/ft Translation Vertical (Y) .983 X 107 k/ft .066 X 100 k.s/ft Translation Rocking (t) .982 X 109 x.ft/ rad .158 X 107 x.ft.s./ rad dotation l
StaffGrp 30(0) 4 e1%4
ig . n
. Table S SUPMARY OF HAXIMUM OF RESPONSES KEY PARAMETERS-AVERAGE:0F.
ANALYSIS CASE CASE.1 CASE 2- , CASE-3 CASEL4 4 CASES-- SSE Earthquake Input A(H)+2/3 U(V) d(H)+2/3A(V)- C(H)+2/38(V) O(H)+2/3C(V) H + 2/3 Y Hax. Base Oplift Ratio (%) 76 84 81 80 80 Hax. Horizontal Displacement (in) - ERCW Pipes at El. 681.S' .54 1.16 .80, .70 .80 Base Edge at El. 620' .007 .009 .008 .006 .00d Hax. Vertical Displacement (in) ERCW Pipes at El. 6dl.S' .11 .28 .16 .14 .17 dase Edge at El. 620' .17 .43 .33 .27' .30 Max. Base Rotation (10-4 rad) 6.74 15.25 10.27 8.90 10.29 Hax. Pressure at dase Edge (psi) 638 1001 781 il2 783 Comuined Total Displacement at ERCJ Pipe Location = / (0.80")2 + (0.17")2. = 0.62" StaffGrp 30(b) o l: _
f Taple 5 (Continued)
SUMMARY
OF HAXIMUM RESPONSES OF KEY PARAMETERS .. AVERAGE OF. ANALYSIS CASE CASE S- CASE 6 CASE 7 CASE 8 4 CASES SSE Earthquake Input A(H) B(H)- 'C(H)- 0(H) H I i Hax. dase Uplift Ratio (%) 77 83 82 88 16 3 Max. Horizontal Displaceinent (in) ERCW Pipes at E1. S81.S' .54 .94 .69 .32 .87 Base Edge at El. 620' .007 .008 .007 .011 .008 Max. Vertical Displaceinent (in) ERCW Pipes at El. 681.S' .11 .23 .14 .33 .20 dase Edge at El. 620' .19 .30 .29 .62 .35 Max. Base Rotation (10-4 rad) 6.69 12.19 8.99 17.73 11.4 t Hax. Pressure at dase Edge (psi) 613 810 651 830 726 Cowbined Total Displacemer.t a* ERCd Pipe Location = s (0.87")2 + (0.20")2 = 0.89" StaffGrp 30(b) 4 y-mA L
7 , i l i f Compression-only 88 is f CONTINUOUS S p r :, a. g H and da.5per
,C.
- - .. .. .. .. ,, ,, , 3 2 1 J J J J J J u u u n n in < < in ,i t u ,, uu , ,n ,, ,u ,,,,, ,,,
L, 2R I~ r Figure 1 Winkler Foundation Model for Surface-Supported Basemat l l i p l I l *
- ^*
m 2R
.- ~
r
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' ,m s s 3 ss s3 73s g-Ta 4 , -~ ~- -.-___J - 3 1 ) 5 =l, C ** *a *--3 di- . a 4 O.. C. O.4 ; ,;u 13; 3339,,3; 3; upli'ted position Y . d
- < -n":%
s . :., :s .'l l '. ! -
..- s 0.I ;;... =.
.- s ' .
~
. Uplifted
.. .. s .
. ., . e. Area
,L,i.dx .-;_-4 ,,
g- - - .
': . . . ' ' . , ' . s , . . . .:; .' 's , '.
- .,..~. s s.. . +. .. . . , ., .-.
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... .r...: .: v s .>,s.. .. .. .. :., . ,.
.- m .. . .: : , ,. .
. ... :. sss.... :. ......e.
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'. ;**.**qs .'*.**.i.***'.,.,
. p .-
. ..-s. .., . . > .. . .. ....
m ..... v:. Q 'f. M p (x) p/ T. Figure 2 Pressure Diagran for Surface-Supported Circular Basemat at Partially Uplifted Position
s, s X Top View 32.6*c5 ft.
,L_ _
ERCW Pioes - EL. 683' g EL. 681.5' 75' 65.5 i-EL. 636' 4 ?Q a SPN W
- k.rp// Ce11
., '>l.
M a Embankment a. y.. Concrete l'- a' .s N
.) Softer .r .:
( ' Concret Min.25' 4' AMWMfM&FJ.G6M9} i y EL. 616'
//Nitt n ppigt //Mr/
Rock Foundation-Figure 3 Configuration of e Representative ERCW Cell 6~ t f e .M
- l I a M*55E5 Moment of-E;evation-
{ Hori:' Vert. AtiglAgea- .Shepxftgea (10 xft ) (10 rA
)
Inge:ia
.(10 xfts);
(ftl (k- 52 / f ) ( k- s2/f t) EL. 691 <p 1 17.88 17.88 8.36 7.38' 5.56 EL.~681.5 tp 2 55.57 44.23 8.36 7.38 ;5.56
' EL. 667.5 < >3 75.38 52.7 8.36 7.38 5.56 EL. 653.5 g p 4 88.04 61.55 8.36 7.38 5.56 EL. 634.8 < >5 90.30 63.13 8.36 7.38 5.56 EL. 620 - X
//?/// /! Mil CONCRETE PROPERTIES:
Modulus of Elasticity = 403000. k/ft2
=
Poisson's Ratio .25 Damping = 5%
- Include hydrodynamic added mass.
Figure 4 Fixed-Base Lumped-!! ass Stick Model of ERCW Cell fI N - %d
- 2. 0 --
SSE ERCW PIPES (H) s.o- . E
- f
~
^ At f 4. A.. A Af :
f In m.. A A Ann _. .I $A A AaaA A.._.. _ _ _ _mA A A A A A A.a.a _ _ c . v--- y n y yy --- -
, - y)g j ;vv vyv 3 i
[ - yyvi - vu g vi vv s y- - -- - - m E -l0-j 2.0 i , i i i i i 2.0 FRCW PIPES (V)
- 1. 0 -
3
~
- - ^ - -
. c --- -- - - - -
n m
- 1. 0 -
20 i a i , , , i . 0 4.0 6.0 s2.0 16.0 23.c 2*.0 26.0 J2.0 TIME (SEC) Figure 5 DISPLACEMENT TIME HISTORY DUE TO EDTH A (H) +2/3D (V) - CASE l-
$ s
, 2. 0 - SSE FRCW PIPES (10 I i.3-E f f I f i g ..a .A.. k f i f ! A* a ff i h a .a m .A AA _. A 4 A. A a A Aa A A __maa*...... _ __ _ 3 vg gy ; [v vvv g - y- v 1v y( y yyvy yy.A.A.A ... . - - - m i
- i; k
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- 2. 0 -- , , , , , , -__.__ _ 3 _ ,
- 2. 3 -
FRCW PIPES (V)
. ..o-E
- ^ - - ^ -
l .0 n-m O
.. g , 3 _
-2.0 , , , , , , ,
4 0 4.0 6.0 e2.0 45.0 20.0 24.0 26.0 32.0-TIME (SEC) Figure 6 Di SPL ACI Mt.NI IIME 111SIORY DUE T 0 E0111 B 01) + 2/3 A (V) --CASE 2 4
1 2.0 - SSE ERCW PIPES (H) i .0 - E e
- 7 0 i n . . n .n / A n,t A n a ... . . ..a A .. A Ada..M A A f f IA Aa.
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- 1. 0 -
2.0 i , , , , , , i 2.3 - FRCW PIPES 'V) i .0 - 3
.0
* ^ ^
Q m U
-I.0-
-2.0 , , , , i i
.0 4.0 6.0 e2.0 i6 0 23.0 24.0 26.3 J2.0 TIME (SEC)
Figure 7 D1SPLACEMENT TIME IllSTORY DUE TO EDTH C (H) +2/38 (V) CASE 3 v __ W
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