ML20106C507

Draft Program to Perform Confirmatory Analyses,Nuclear Plant Island Structure Basemat at Waterford Steam Electric Station Unit 3

ML20106C507
Person / Time
Site:	Waterford
Issue date:	02/08/1985
From:	LOUISIANA POWER & LIGHT CO.
To:
Shared Package
ML20106C493	List: ML20106C507 W3P85-0362, Forwards Draft Program to Perform Confirmatory Analyses, Nuclear Plant Island Structure Basemat at Waterford Steam Electric Station Unit 3. Proposed Program Plan Provided for NRC & BNL Review & Discussion at 850213 Meeting
References
PROC-850208, NUDOCS 8502120287
Download: ML20106C507 (45)

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PROGRAM TO PERFORM CONFIRMATORY ANALYSES NUCLEAR PLANT ISLAND STRUCTURE B ASEMAT AT WATERFORD STEAM ELECTRIC STATION-UNIT NO 3

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LOUISIANA POWER AND LIGHT COMPANY 8502120287 850208 PDR ADOCK 05000382 P PDR 2658M

, February 8,1985

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PROGRAM i:

TO -

PERFORM CONFIRMATORY ANALYSES NUCLEAR PLANT 5 LAND STRUCTURE BASEMAT AT WATERFORD STEAM ELECTRIC STATION-UNIT NO 3

_ LOUISIANA POWER AND LIGHT COMPANY TABLE OF CONTENTS

- Subject Page L- INTRODUCTION 1 IL. PURPOSE OF THE CONFIRM ATORY ANALYSES 1 IIL ANALYSIS METHODOLOGY A. Dynamic Coupling of the Reactor Building and Basemat 2

-1. General Description of Analysis

2. Analysis Extension -If Warranted B. Dynamic Effects of Lateral Soil / Water Loadings 4

l. General Desription of the Analysis

2. Seismic Soil Structure Interaction Analyses

3. Material Properties

4. Parametric Studies

5. Dynamic Lateral Water Pressures

6. Finite Element Static Analyses

7. Results to be Obtained from Computer Runs

8. Application of Results to the Concerns Raised C. Artifical Boundary Constraints in Finite Element Model 7

1. General Description of the Analysis

2. Description of the Model

3. Computer Programs to be Used

4. Material Properties

5. Parametric Studies

6. Results to be Obtained from Computer Runs

7. Application of Results to the Concerns Raised forinformation on) i

1 PROGRAM TO -

PERFORM CONFIRMATORY ANALYSES NUCLEAR PLANT ISLAND STRUCTURE BASEMAT AT WATERFORD STEAM ELECTRIC STATION-UNIT NO 3 LOUISIANA POWER AND LIGHT COMPANY TABLE OF CONTENTS (Cont'd)

Subject Page D. Fineness of Basemat Finite Element Mesh 9

1. General Description of the Analysis

2. Description of the Model

3. Computer Programs to be Used

4. - Material Properties

5. - Parametric Studies

6. 'Results to be Obtained_from Computer Runs

7. Application of Results to the Concerns Raised IV.

SUMMARY

OF COMPUTER RUNS 11 A. FLUSH / SUPER-FLUSH '

B. -STARDYNE V. SCHEDULE 11 forinformation only 11

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. PROGRAM TO PERFORM CONFIRMATORY ANALYSES NUCLEAR PLANT ISLAND STRUCTURE BASEMAT AT WATERFORD STEAM ELECTRIC STATION-UNIT NO 3 LOUISIANA POWEIL AND LIGHT COMPANY L INTRODUCTION A This describes the program which Louisiana Power and & Light Company proposes 3 to . undertake to resolve the concerns raised by the Nuclear Regulatory Commission concerning the analysis of the basemat for the Nuclear Plant Island Structure (NPIS) at Waterford SES-Unit 3. The- methods to be used, the computer programs which will be utilized and the sources of data regarding the material properties which will be used are y

all included.

11. PURPOSE OF THE CONFIRM ATORY ANALYSES The staff'of the Nuclear Regulatory Commission, in their review of the basemat cracks recommended that a more detailed, confirmatory analysis be . performed for portions of the basemat structural analysis for the Waterford 3 plant. The staff requested .

that confirmatory analyses be performed that will address:

1. dynamic coupling between the reactor building and the basemat for seismic stresses resulting from the vertical earthquake input 2.- dynamic effects of lateral soll/ water loading:

3. artificial boundary constraints in finite element model 4.- fineness of basemat finite element mesh

3. origin of cracks in vertical walls.

The fifth analysis requested by the NRC staff has been adequately answered by the .

NDT studies performed on the walls. These cracks have been identified as being shallow and probably resulting from shrinkage. They are not related to the cracks in the basemat.

m Brookhaven National Laboratory, in Attachment F to the December affidavit agreed

~that.."(cracks in the vertical walls are no longer considered a problem)." Therefore the concerns which led to the request for the.fifth analysis will be considered as adequately answered and the analysis will not be pursued any further.

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+. WATERFORD-CONFIRMATORY ANALYSES IIL ANALYSIS METHODOLOGY A. DYNAMIC COUPLING OF THE REACTOR BUILDING AND BASEM AT

1. GENERAL DESCRIPTION OF ANALYSIS The subject of dynamic coupling between the reactor building and the basemat for stresses resulting from the vertical earthquake input is Interpreted by LP&L to mean the possible effect of the mat flexibility on vertical seismic responses and the sensitivity of the mat stresses to vertical seismic accelerations which reflect the mat behavior.

To address this subject, LP&L proposes to undertake an analysis which will confirm that the vertical seismic accelerations obtained under the rigid mat assumption, as described in FSAR Section 3.7.2.1 (Appendix A),

are conservative and form an acceptable design basis. The study will show that the stresses in the mat are not significantly affected and are within the Code allowables when the vertical accelerations are factored into the design.

Specifically- the proposed confirmatory analysis will consist of the following:

a. Performance of a static analysis of the mat and superstructure complex which incorporates the maximum vertical acceleration obtained from the seismic analyses cescribed in FSAR Section 3.7.2.1

. (Appendix A). The 0.175g maximum vertical acceleration indicated in Table 3.7-9 of the FSAR (Appendix B) will be applied to all the structural masses and the forces will be combined with other concurrent loads. The static analysis will be performed with the STARDYNE Computer code and the finite element model as used for the original analysis modified by the use of the Martin element in place of the original element used. This analysis is identified in the table in IV. B as Old Loads /Old Model.

b. Establish, using state-of-the-art techniques, a conservative estimate

.of material and non-hysteretic damping which are reasonable for use in the vertical seismic analyses described in FSAR Section 3.7.2.1 (Appendix A). Experts in the field of soll dynamics will be consulted.

The soll damping will be limited to 20 percent.

c. Perform vertical seismic dynamic analyses using the model shown in FSAR Figure 3.7-10 (Appendix C), incorporating soll damping which reflects material and non-hysteretic (radiation) damping, and utilizing the DYN 2037 Computer Code, as described in FSAR Section 3.8.3.4.1.1 (Appendix E).

forinformation only

• WATERFORD-CONFIRMATORY ANALYSES The maximuTi vertical acceleration will be compared to the previous maximum of 0.175g to estab!!sh the reduction in the predicted

. responses associated with the use of more realistic soll damping.

d. Perform a literature search to confirm that the maximum variation of vertical seismic responses due to assumptions related to . mat flexibility (le; mat is rigid vs mat is flexible) for nuclear structures is 120%.

2. ANALYSIS EXTENSION -IF W ARR ANTED It is believed that the above exercises in stress analysis will be# sufficient to confirm the validity and conservatism of the design of the basemat.

However, in the event that the results of the vertical seismic analyses using the more realistic soll damping do not indicate a decrease in the maximum responses that is sufficient to cover possible response variations associated with mat flexibility, LP&L will perform more extensive analyses. These would include finite element soil-structure interaction analyses using the FLUSH or SUPER-FLUSH Computer code to establish more precise values of vertical seismic accelerations.

Two dimensional analyses utilizing the existing lumped mass structural models (as shown in FSAR Figure 3.7-10 Appendix C) with modifications made to include a finite element representation of the mat and the soll beneath and surrounding the Nuclear Plant Island Structure will be performed.

Material properties will be derived as defined in Ill.B.3.

Parametric studies will be performed to determine the sensitivity of the model chosen to the various assumptions required for the performance of the analysis.

The results to be obtained from these analyses will be a listing of the amplified accelerations at each level in the various huildings supported on the basemat.

The accelerations obtained will be used to recompute the basemat internal forces caused by the vertical earthquake. This will require a

-rerun of the STARDYNE model used to evaluate the basemat internal forces. These runs will be for the DBE case for N-S and E-W earthquake directions only and will include the other loads normally included in such loadcases.

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WATERFORD-CONFIRMATORY ANALYSES 1

B. DYNAMIC EFFECTS OJ LATER AL SOIL / WATER LOADINGS

1. GENERAL DESCRIPTION OF THE ANALYSIS This analysis will oe performed to evaluate the maximum and minimum membrane forces and bending moments exerted on the basemat by the

- lateral soil and water pressures on the end walls of the NPIS during a

. seismic event. The original calculation of these forces was a static approximation utilizing a knowledge of the deformations of the soil and building during earthquake and applying these deformations to known soil properties.

LP&L proposes to perform the following confirmatory work:

a. finite element; soil-structure interaction seismic analyses under DBE horizontal earthquake input in order to establish dynamic soil pressures.

b. establish dynamic water pressures using classical (closed form) solutions.

c. finite element static analysis of the NPIS complex incorporating the dynamic soil and water pressures and appropriate concurrent loads.

2. SEISMIC SOIL STRUCTURE INTERACTION ANALYSES These analyses will be performed usirjg the FLUSH computer code or the SUPER-FLUSH code. Specific features of both programs are:

. they are imp!! cit finite element codes using the frequency domain approach.

. the non-linear soil behavior is approximated by an equivalent linear approach by iterating the stiffness and damping values for each element consistent with average values of strain occuring during the analysis.

. the only form of sex.mic input allowed is that of rigid " bedrock" shaking.

. the codes have both continuum and plain strain elements. ,

. deconvolution analyses are incorporated directly into the programs.

. the codes incorporate viscous dashpot boundaries used to simulate 3-D effects, and energy transmitting boundaries which can be used to minimize the number of finite elements required.

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• - WATERFORD-CONFIRMATORY ANALYSES In conjunction with these programs two-dimensional models utilizing the existing lumped mass structural models and augmented with a finite ,

element representation of the soll beneath and alo..; side the lateral walls, I will be developed.

Specifics regarding the FLUSH or SUPER-FLUSH analyses under horizontal DBE effects are as follows:

. two dimensional models representing the mat and side walls as rigid elements and incorporating the lumped-mass models shown in FSAR Fig. 3.7-9 (Appendix D) and a soll element mesh will be used.

. Input motion will be specified as applicable at the bottom of the mat level (El.-47.0 ft). Only DBE analyses will be performed.

North-south and east-west motion will be considered separately.

. the horizontal time history for analyses will be applied at the lower rigid boundary, the location of which will be established by performing parametric studies. This driving time history will be established using deconvolution techniques. If the location of the lower boundary is such that the size of the soll finite element model becomes too large, the compliant base available in SUPER-FLUSH, consisting of viscous dashpots at the base of the model to absorb reflected waves from the surface, will be used.

.. vertically propagating shear waves will be assumed.

. a finer soll mesh will be used against the vertical strue aral walls and 4- around the basemat edges, where the rocking effects are most pronounced, in order to account for the weakening of the soll locally due to large strains. The soil finite element mesh will extend to

- about the edge of the backfill where energy transmitting boundaries will be used.

. lateral out-of-plane viscous boundaries will be used to simulate out-of-plane radiation effects.

the vertical dimension of the soll elements will be kept smaller than one-fif th of the smallest wavelength (associated with the highest frequency) of interest. For this soft site, a cutoff frequency of 12Hz will be used.

. the computation of the Fourier transform of the input motion will be performed using a number of time and frequency increments which will allow for frequency components of the input motion up to 12Hz t- to be accurately reproduced.

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'V WATERFORD-CONFIRMATORY ANALYSES

.. the effective embeddment depth (i.e. the area over which connectivity between lateral walls and soll is assumed) will be varied.' Soil-structure 'connectivity will be assumed on both sides of the 2-D models.

-. the analyses will consider a range of shear modulus vs strain curves including average, average x 1.5 and average /1.5.

.. time history of lateral soil forces at all points of connectivity will be obtained.

3. MATERIAL PROPERTIES The material properties for the soll will be derived from material presented in Section 2.5 of the FSAR. Concrete and steel material

- properties will be normally accepted values. The structural properties of the structural spring / lumped mass model, as described in FSAR Section

3.7.2 (Appendix A) will be used.

The material soll damping and the non-hysteretic (radiation) soll damping values will be established by utilization of known site soll properties, literature values, state of the art analytical techniques and consultation with experts in the field. The ranges of shear strain vs modulus will be

. derived from literature and consultation with experts in the field.

4.- PARAMETRIC STUDIES Parametric studies will be performed to determine the sensitivity to various assumptions required in the performance of the analysis. The parametric studies will consist of:

.. a range of shear modulus vs strain curves as described above.

. . studies to establish the location of the lower rigid boundary.

studies to estab!!sh the adequacy of the soll finite element mesh.

. studies to establish the effect of the assumed effective embeddment 4 depth.

Ref. (1) .Westergaard, N. M. (1933), " Water Pressures on Dams During Earthquakes,"

Transactions of the American Society of Civil engineers, Volume 98. ,

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, WATERFORD-CONFIRMATORY ANALYSES

5. DYNAMIC LATERAL WATER PRESSURES The dynamic water pressure will be established using the Westergaard

, theory as described in Ref.1. The soll porosity will be used to establish if lower ' dynamic ' water pressures, reflecting the fact that water is entrapped in the soil, may be used.

6. FINITE ELEMENT STATIC ANALYSES The dynamic lateral soil and water pres::ures will be incorparated in static finite element analyses using the STARD 'NE compute code and the mat-superstructure representation used in the original basemat analyses.

7. RESULT 5'TO BE OBTAINED FROM COMPUTER RUNS The results to be obtained from this analysis will be a definition of the maximum and minimum membrane forces in the basemat and the maximum and minimum bending moments applied to the basemat by the lateral soll forces.

8. APPLICATION OF RESULTS TO 1HE CONCERNS RAISED The forces and bending moments will be compared to the forces and bending moments from these sources in the original basemat STARDYNE analysis to provide assurance that the basemat stresses are within code allowables under seismic loading. In particular, attention will be paid to areas where the bending moments due to the lateral forces diminish the gravity load bending moments causing tension at the top surface of the basemat.

C. ARTIFICIAL BOUNDARY CONSTRAINTS IN FINITE ELEMENT MODEL

1. GENER AL DESCRIPTION OF THE ANALYSIS This analyNs will be perforraed to demonstrate the effect on basemat

. stresses when the artificial boundary constraints used in the STARDYNE analysis are altered to more closely match physical conditions.

2. DESCRIPTION OF THE MOD'EL The STARDYNE model used for the basemat analysis will be altered so that each node point will be restrained by two horizontal springs, along with the vertical springs already used, connected to the node point by a

. stiff stick. This stick will extend from the middle of the mat (the plane of the finite element representation of the mat) to the bottom of the mat (6'). The horizontal and vertical springs will be placed at the base of the sticks. The horizontal springs will represent a distributed frictional resistance due to contact with the soll.

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WATERFORD-CONFIRMATORY ANALYSES

3. COMPUTER PROGRAMS TO BE USED The STARDYNE program used in the original basemat analysis will be used modified by the use of the Martin element in place of the original element used. ,

4. MATERIAL PROPERTIES The properties of the springs will be based upon the soll properties obtained from soil testing at the time of the PSAR along with textbook interpretations of soil stiffness. The vertical springs of the old model will be used for the new model. The horizontal springs will represent the basemat base friction and subsoil deformation characteristics under unbalanced horizontal seismic loads. The base friction is assumed to be equal to.the subsoll cohesion,1500 psf or 10.4 psi, since it is a cohesive soll. The amount of subsoil deformation is assumed to be equal to the relative -displacement between the basemat and subsoil, which ranges from 0.5 to 3.0 inches. Therefore, the horizontal spring constant can range from 20.8 to 3.5 lb/ inch per square inch of basemat area. These values will be confirmed.

5, , PAR AMETRIC STUDIES The STARDYNE runs will be made utilizing all of the loads as originally used for the basemat analysis and the modified constraints as defined above. This will define the effect of the modification of the boundary constraints on the basemat loads.

Prior to the STARDYNE runs, a sensitivity study will be made for the effect of the spring coefficient of the horizontal springs. The modified constraint model w.ill be analyzed using one load combination, DBE with east-west earthquake, with both the 3.5 and the 20.8 lb/ cubic inch spring constant. The horizontal reactions at the springs along with the flexural moments within the basemat will be evaluated for these two conditions.

The spring constant which yields the greater moments within the mat or the greater peak reaction will be selected for the STARDYNE runs. If the differences caused by varying the spring constant are small and negligible, a spring constant of 20.8 lb/ cubic inch will be used for the computer runs.

The STARDYNE runs will be made for the DBE load combination with both east-west and north-south earthquakes used. The loads as originally defined will be applied to the modified artificial boundaries models.

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l WATERFORD-CONFIRMATORY ANALYSES 6.- RESULTS TO BE OBTAINED FROM COMPUTER RUNS The results to be obtained from this analysis will be a complete listing of basemat internal forces with the old loads and with the new boundary

' constraints.

7. APPLICATION OF RESULTS TO THE CONCERNS RAISED

. The basemat stresses with the new boundary constraints will be computed from the internal forces and will be compared to code allowable stresses to assure compliance with the code under seismic loading conditions. An illustration will be prepared to demonstrate the effect of distributing the boundary constraints on the internal forces.

D. FINENESS OF B ASEMAT FINITE ELEMENT MESH

1. GENERAL DESCRIPTION OF THE ANALYSIS The existing STARDYNE finite element model will be altered by reducing the element size to provide additional elements between supports. In general, at least four elements between supports will be provided, except where supports have formed a corner. The element size of superstructures affected will be modified accordingly.

2. DESCRIPTION OF THE MODEL The existing STARDYNE model of the basemat will be modified as necessary to incorporate the finer element sizes. The areas which will be modified are areas in the vicinity of the Reactor. Shield Building wall and areas forming the junction between the exterior walls of the NPIS and the basemat. Figure i shows the proposed modifications to the basemat finite element model mesh.

3. COMPUTER PROGRAMS TO BE USED

.The STARDYNE computer program used in the original basemat analysis will be utilized modified by the use of the Martin element in place of the original element used.

4. MATERIAL PROPERTIES Material properties as utilized for the original analysis will be used.

. . _ . _ _ 3. PARAMETRIC STUDIES STARDYNE runs with the finer mesh will be made for the loads and support conditions as originally used.

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WATERFORD-CONFIRMATORY ANALYSES Prior to the STARDYNE runs, a mesh evaluation will be made using only the normal operation load combination. Typical moment and shear diagrams in the modified areas will be studied for a reasonable presentation of stress gradient and the mesh will be modified to assure a fineness sufficient to allow a reasonable definition of the stress gradient.

6. RESULTS TO BE OBTAINED FROM COMPUTER RUNS The results to be obtained from this analysis will be a listing of internal forces (shears and moments) for each element for the old and new element sizes for the old applied loads. The results obtained in this study will be those of load combinations cases:

Normal Operation DBE east to west motion DBE north to south motion.

7. APPLICATION OF RESULTS TO THE CONCERNS RAISED The internal forces will be translated into basemat unit stresses and compared to code allowable stresses to verify that they are within the allowable limits. An illustration will be assembled to demonstrate the effect that making a finer finite element mesh had on the internal forces.

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W A.iERFORD-CONFIRMATORY ANALYSES IV.

SUMMARY

OF COMPUTER RUNS A. FLUSH /5UPER-FLUSH

1. Lateral Soll Pressure (North-South and East-West)

2. - Vertical acceleration only if warranted.

B. _ STARDYNE(Each run comprises a north-south and an east-west run when lateral loads are involved). Load conditions: Normal Operation and DBE.

l----- --- M O D E L ----------------------

LOADS l OLD l NEW CONSTRAINTS l NEW MESH OLD l X l X l X NEW VERTICAL l X l l NEW LATdRAL l X l l V. SCHEDUL_E The schedule corhmitment is to have the work completed and submitted to the NRC staff prior to start-up following the first refueling.

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WSES-FSAR-UNIT-3 Frequency Range (hertz) Increment (hertz) No. of Frequencies Used l

'{ , 0.2 - 3.0 0.10 -

37  !

~3.0 - 3.6 0.15 7 3.6 - 5.0 0.20 10

'!.0 - 8.0 0.25 14 8.0 - 15.0 0.50 16 15.0 - 18.0 1.00 3 18.0 - 22.0 2.00 4 1

22.0 - 34.0 3.00 9 100 Similar. design response spectra and time history spectra uere made utilizing 200 computed period ' points within the above frequency range ,

~ which verified the above results.

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3.7.1.3 Critical Dampina values The ' damping ratios, ~ expressed as percent of critical damping, which are

- used in the analysis of eef amic Category I systems and components are

'O A- presented in Table 3.7-1. These damping values both for the SSE and OBE

..are equal to or more conservative than the values recommended by NRC

- Regulatory Guide 1.61. Damping values utilised by the -NSSS are given in Subsection 3.7.3.1.2.

- The damping-value for the soils at the ' site are selected on a conservative basis fram the strains induced by the earthquakes. Individual damping versus strain' eurves are presented in Subsection 2.5.4. -

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_ Since damping values are strain-dependent, the single values used in design were; compatible with the actual strains developed during earthquakes. An

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equivalent linear variable-dygping lumped-mass solution, similar to that developed by Idriss and Seed , was utilized. In this ' analysis , damping and shear moduli values were assumed and were.a portion of the input to the camputer. The output included a profile of calculated shear strain versus

. depth. On the first run, the calculated shear strain value did not corres-

. pond to the initially assumed value. The shear modulus was a3 justed accord-

?ingly using Figures.2.5-77 and 2.5-78 and successive iterations made until

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the- calculated shear strain and the assumed strain converged. The. point of convergence. occuired at 0.04 percent strain for the. Recent alluvium and -

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. 0.08 percent strain for the upper Pleistocene sediments. Therefore , the _

.following design' values were utilized:

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4 WSES-FSAR-UNIT-3 DAMPING percent Recent A11uvius (+13 to -40 ft. MSL) 8

. Pleistocene sediments (-40 to -317 f t. MSL) 7.5

~ 3.7.1.4 Supporting Media For Seismic Category I Structures All seismic Category I structures are founded at elevation - 47 ft. MSL on a one it. -thick compacted shell filter blanket on top of the Pleistocene clay.

The Reactor Building, Reactor Auxiliary Building, Fuel Handling Building and

- the Component Cooling Water System structures are supported on a common foundation mat, 267 ft. wide and 380 ft. long, which is embedded 64.5'ft.

below finished plant grade, in the stiff gray and tan clays.

Table 3.7-2 provides a tabulation of the foundation elevation and total structural height of the seismic Category I structures supported on common foundation mat. The plant grade elevation is +17.5 ft. MSL.

. The soil layering characteristics and soil properties are discussed in Subsection 2.5.4.

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3.7-4

WSES-FSAR-UNIT-3

( 3.7.2 SEISMIC SYSTEM ANALYSIS Thl' subsection includes discussion of seismic analysis of all seismic Lategory I structures. Seismic analysis of seismic Category I piping systems and components including the Reactor Coolant System is discussed in Sub-section 3.7.3.

3.7.2.1 Seismic Analysis Methods The seismic analyses of all seismic Category I structures were performed i using either the normal mode time history technique or the response spectrum technique. ,

In the case of seismic Category I structures, the seismic response was deter-mined by the response spectra developed for the OBE (0.05 g) and the SSE (0.10 g), as described in Subsection 3.7.1.1.

t 3.7.2.1.1 Seismic Category 1 Structures 3.7.2.1.1.1' Mathematical Model As all seismic Category I structures are founded on a common foundation mat, described in Section 3.8, the mathematica1' modeling involies construction of a single composite model for s'ach directional seismic analysis.

The model ensprises five individual cantilevers, representing the Reactor 14 ,, '. . Building, the containment vessel, the reactor internal structure. -the Reactor Auxiliary Building and the Fuel Handling Building. The Component Cooling Water System is not separately identified and is included in the Reactor Auxiliary Building and Fuel Randling Building cantilevers. The five cantilevers are founded on the same base, which is in turn supported by afoundatios springs. For each cantilever, the distributed masses of the structure are lumped at' certain select points and connected by weightless elastic bars representing the stiffness of the structure between the lumped masses. In determining the .stiffnesses, the deformation due to bending,

(. __ . shear and joint rotation are considered throughout.

Typical mathematical models for horizontal and vertical excitation analysis

! are shown on Figures 3.7-9 and 3.7-10, respectively. The input data used for.these models for seismic analyses are summarized in Tables 3.7-3 and I. 3.7-4.

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Equivalent soil springs,. as described in Subsection 3.7.2.4, and damping .

values, as described in Subsection 3.7.1.3, are. used in the analysis.

'Every mass point of the two dimensional; horizontal model is allowed two

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i degrees of freedom, namely, translation and rotation. For the vertical model, only one translational degree of freedom is considered. A mathe-L matical model for torsional effects is described in Subsection 3.7.2.11.

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WSES-FSAR-UNIT-3 3.7.2.1.1.2 Equations of Motion Once the mathematical model is established , the motio'n of each lumped mass

- under any' external excitation may be written in the matrix form as follows:

[M] A + [c] 1 + [K] A = F (1) where: [M] = square mass matrix i [K] = square matrix of stiffness coefficients including '

the shear and bending deformations

. f'Af = column matrix of acceleration vectors 1 = column matrix of velocity vectors A = column matrix of lateral displacement and joint rotation vectors

- F = column matrix of external load vectors  !

[c] = damping matrix The stiffness matrix [K] is formulated by computing the stiffness coef-ficients for each joint of the original structure and assembling them in the proper sequence to form the complete square matrix. In the computation of the stiffness matrix, it is assumed that all joints at the same level have a the ~ sase displacements (i.e., translations and rotations). '

The cantilever connecting two 1tesped masses is considered as a beam element and the effects of bending and shear deformation are included in computing the stiffness. coefficients. The effects of equivalent soil springs are also included in the formation of the' stiffness matrix K . As shown in Figure I 3.7-9, there are three s, oil springs, two translatio[n]al and one rocking being i considered for horizontal excitations. The first translational spring Ex .

' represents the shear effect between the cosmon foundation mat and the soil and it is applied at the bottom of the mat, while the second translational spring Kxx represents the bearing effect1 between the mat and the soil and it is applied at the mid height of the sat side surface. The rocking

. spring K$is considered acting at the rotation center of the mat. The l2 method used to account for torsional response is discussed-in Subsection 3.7.2.11.

e

. The effect due to relative displacement between interconnected mass points i

- are . 'also considered. The-connecting members > .sen mass points are modeled as' beams and springs and their effects to the cuctural response are incor-poratedin the stiffness matrix.

~

In the desit ' seismic Category I systems and components, the maxista relative displaces,_. histories of supports obtained from structural responses are utilised.

3.7.2.1.1.3 Natural Frequencies and Mode Shaps In' calculating the natural frequencies and the mode shapes, the damping term . -g

[c] i - is, ignored and the external load vector in equation _(1) is set to 3.7-6 Amendment No. 2, (3/79) 1

' . - WSES-FSAR-UNIT-3 h sero, the . displacement vector A is assumed to take the form of simple harmonic motion: j

& $ . Sin wt (2) dere: Relative amplitude of mode shape vector f ,

= = Natural frequency of vibration After substituting into equation (1) and simplifying, the equations of motion are reduced to the following form:

[K]~1 [M] 4 = (3) 1 . ff e2 Solution to this eigenvalue problem exists only for particular values sich correspond to the natural frequencies of vibration o~ the sesucture.

. Equation (3) is solved by the Jacobi method to obtain vat.ues of natural frequency of vibration (=) and their corresponding mode shape vectors ( ,

I.

W i

t y

0 4

k 3.7-6a knenhent No.1, (1/79) ,

L i

WSES- FSAR-UNIT-3 3.7.2.1.1.4 Modal Analysis

.[-

After all natural frequencies and their mode shapes are determined, the method of modal analysis is employed to calculate the structural responses.

This method actually simplifies the analysis of a multidegree of freedom

, system into an analysis of several equivalent single degree systems, one corresponding to each normal mode. The governing equation of motion is shown in the following:

a

~

2 sofa It) EI x xn A

a + 2#n u + = a n A A = x=1 (4)

N

+

n x=1 where: A'

= displacement of any one arbitrarily selected mass (usually the topmost mass) for the nth mode

1. , = ' damping coefficient = A,=,

A, = . percentage of critical damping of the nth mode I.

"n = natural frequency of the nth mode g Y,, = -maximum ground acceleration f,(t) = time function of ground motion

= mass at the xth level M,

a =

' number of masses subjected to inertia M,Y',,f(t) 4xn ~=

normalised displacement of the mass M,of the nth mode.

N. = total number of degrees of freedon '-

If the -two summations on the right-hand side of the equation (4) are denoted i

- by Pthen,, which is defined as the modal participation factor of the nth mode, t

u A ,+ 4 ,A, + a, = 4, y,, f,( t) *

(5)

Since the values of 4 "a and P

_ equation (5), which II,actually a "are already known n independent for eachcan equations, normal be mode, ved Loeparately using the method developed by NC Nigen and PC Jennings

~

The total displacement is the summation of the displacement of each normal mode, that is: ,

N

~] .

^

Y,(t),,, ~=

P,f ,A n (6) 3.7-7

WSES-FSAR-UNIT-3 In spectral analysis, A,'s are spectral values from the design spectral curves. The algebraic sua of equation (6) gives the upper limit of the dis-placement of any mass. However, all the maximum displacements of all normal modes do not necessarily occur at the same *ime. For the purpose of design, the root-mean-square method is adopted fro 6 the statistical point of view:

i Y ,

x max

=

N I

,g A)2' (Pn 4xn n 1/2 (7) ,

3.7.2.2 Natural Frequencies and Response Loads A suasary of natural frequencies for significant modes is presented in Table 3.7-5. ' A summary of structural responses determined by the seismic analysis for major seismic Category I structures is presented in Tables 3.7-6 through 3.7-9.

, 3.7.2.3 Procedure Used for Modeling 1

l Major seismic Category I structures that are considered in conjunction with 4

foundation media in forming a soil-structure interaction model are defined as .

" seismic systems." Other seismic Category I structures, systems, and com-ponents that are not designated as " seismic systems" are considered as  !

" seismic subsystems."

The procedure used to calculate the lumped masses at designated floor levels I consisted of combining the floor weights, . equipment weights and one-half of the wall and c'olumn weights from the adjacent upper and lover' floors. In

. solving the mathematical model for vertical, excitation, similar lumping of masses was used.

l 3.7.2.4 Soil-Structure Interaction -

The free-field motion of the site, during a seismic event, is locally affected by the presence of the buildings. The effects _ of dynamic inter-action between soil and buildings can be such that the free-field response of the soil is either amplified or attenuated in some portions of the frequency range of interest. To evaluate. the modifying effect of soil-structure inter-action on the free-field motion (at the foundation . level), a simplified .

- lumped-mass soil spring analysis has been performed. The rationale'of using lumped-mass spring method instead of finite element method for the inter-action study is as follows:

a.) The soil conditions, immediately underneath the pisnt foundations are fairly uniform and a hard rock boundary is not present in_the _.

immediate vicinity. Both these conditions dictate the use of a simplified approach for conservatism, b) The effects of. variations in soil shear modulus with strain have been considered and effective values were established from strains induced by both the static and dynamic considerstics. Statistical methods of analysis were utilized _to determine the participation of shear modulus

}

,. throughout the time history analysis. A range of soil moduli was 3.7-8

4 '-

WSES-PSAR-UNIT-3 studied to establish the responses of soil-structure system (see Appendix 3.7-A).

(

i.

4 c) All seismic Category I structures are located on a single common mat foundation. By virtue of this arrangement, the ef fects of adjacent structures on the soil-structure interaction response are auto-natically eliminated, leading to a simplified analysis.

The soil-structure interaction model for vertical and horizontal excitations consisted of a two dimensional lumped-mass spring system, representing the seismic Category I Nuclear Plant Island Structure and typical site geology. 1 A three dimensional lumped-mass spring system was used for torsional response analysis. The basis for selection of a simplified soil spring approach is discussed in. Appendix 3.7A. The foundation springs for horizontal excita-tion consisted of one rotational spring and two translational spring's as shown on Figure 3.7-9. The foundation springs for vertical excitation are shown in Figure 3.7-10. Therotationalandtranslationalspringcogants

, and were cgulated using the following formulae by Whitman and Richart Barkan  :

Rotation (or rocking) K=

4 G p BL 2 lI 1-# o Sliding (or shear) K, = 2 (1 + s) G $[

Bearing (or compression) =G 1-# 0s' [

K l,

. %sr where: G = shear modulus of soil M.= Poisson's ratio of soil

> B = width of rectangular foundation L = length of rectangular foundation A = bearing ea So, 4x and 4 = site constants dependent on B/L ratio The values of shear modulus and Poisson's ratio were obtaf ned from laboratory testing and field geophysical analysis (see Subsection 2.5.4.2).

Since shear moduli are strain-dependent, the single values used in design-were compatible with the actual strains developed during earthquakes. An .

equivalent linear variable-dgping lumped-mass solution, similar to that developed by Idriss and Seed , was utilized. In this analysis, damping

~ ~

'~and shear moduli values were assumed and were a portion of the input to the computer. The output included a profile of calculated shear strain versus depth. - On the first run, the calculated shear strain value did not corres-pond to the initially assumed value. The shear modulus was adjusted accor-dingly using Figure 2.5-77 and 2.5-78 and successive iterations made until the calculated shear strain and the assumed strain converged. The point of

' I- . convergence occurred at 0.04 percent strain for the Recent alluvium and 3.7-9 Amendment No. 1,"(1/79)

WSES-FSAR-UNIT-3 0.08 percent strain for the upper Pleistocene sediments. herefore the following design conservative values were utilized:

• SHEAR MODULUS psi Recent A11uvitan (+13 to -40 ft. MSL) 3400 (490 KSF)

Pleistocene Sediments (-40 to -317 ft. MSL) 5800 (830 KSF)

Refer to Appendix 3.7A for the results of a parametric study of shear modulus where it was varied from 5800 psi to 16,050 psi.

! 3.7.2.5 Development of Floor Response Spectra A ' time history method of analysis is used to develop floor response spectra, as described in detail in Subsection 3.7.2.1.

3.7.2.6' Three Components of Earthquake Motion

~ The seismic analysis of seismic Category I structures, systems or components does not consider simultaneous action of three components of design earth-quake nor the calculation of responses by square root of the sum of the l square of corresponding maximum values of the response as recommended in Regulatory Guide 1.92, Combination of Modes and Spatial Components in Seismic _

Response Analysis, December 1974. Instemi the maximum value of response in t, s'ach element is determined by considering each horizontal and vertical com-ponent of an earthquake separately.

For each structural element, the two responses related to one horizontal .

and one vertical earthquake' components are combined using the absolute sum

, -method. He comparisons of the maximum response used in the_ plant structural I design and that obtained using square root of the stan of the squares (SRSS) .

are provided in Tables 3.7-18 to 20. May are made for three randomly

' selected elements of the Reactor Shield Building at. elevations +184.0, +61.0 and 0.0 ft. MSL, respectively, hey-indicate that the maximum response-used is ' larger than the maximum response obtained using SRSS. Mus, the design approach in obtaining the, maximum earthquake is equivalent to that.

cbtained in accordance with Regulatory Guide 1.92.

3.7.2.7 Combination of Modal Responses men the spectrum method of modal analysis is used, the modes are combined by the square root of the sum of the squares (SRSS), without taking into consideration the effect of spacing of modes, as recommended by Regulatory Guide 1.92 (refer to Subsection 3.7.2.6) .

3.7.2.8 Interaction of Noncategory I Structures With Seismic Category I Structures

The structural frames of nonseismic structures are d' esigned to withstand seismic motion such .that nonseismic structures will not collapse and impair .I

~~~ the; integrity ~of seismic Category I structures or components.

~

~

3.7-10 Amenenent Mo,1, (1/79)

__ __. _ . _ _ _ . _ _ ._...~..._ __ _ ._ _ _ _ . - _ . . . _ _ . _ . _

1

. WSES-PSAR-UNIT-3 1.7.2.9 Effects of Parametric Variation on Floor Response Spectra

(

l The. following conservative assumptions are included in the calculation of the 1 floor response spectra:

J a) The expected actual earthquake time histories are enveloped by a ~

1 naooth ,1round response spectrum for design use. This has conservative l

< effect* on modal analysis because it treats the modes in the maximum  ;

accelesation range as though they all had the same amplification  :

' factor as the most strongly amplified mode. )

4 i

?

3. - Os knendment No. 1, (1/79)

,,+-e,. . . - .s,-..--w- ..7,,wm,,,,,,% ,3- ,v.-e.,_,,yw.~ .-_.,,,,,..,.~,--..,n--,. -

.._.v ..- ..,m-~v. -_m-~..---, ,-,,,....., .

- - ~ . . - - . . . . ~ .

2 USES-PSAR-UNIT-3 s .-.

.b) Tne time history used .to calculate the floor response spectra produces

)- a ground response spectrum which envelopes' the design ground response spectra. In order to do this, it has spectral peaks which are sub-stantially-higher than the deeign spectra.

c) The building and soil damping values used in the analysis are near the lower bound of the 'available damping data. The actual values of  ;

< damping are expected to be much higher than the values used in the analysis.

d) -The yield strengths used in the analysis are based on the minimum values and are' considerably lower than expected values, e) The additional strength and damping that are available when materials are stressed beyond yield are neglected when using linear elastic analytical sethods.

In order to maintain the consistent conservative design objective, parametric 2 studies of foundation stiffness were also performed using a range of shear modulus from 5,800 psi to 16,050 psi. As a result of these studies, con-

-servative design envelopes for all mass points and levels within the seismic Category I structures were developed for the design floor responses.

Figures 3.7-11 through 3.7-20 show the variation in floor responses (SSE with

-cne percent damping) for shear modulus values of 5,800, 8,000 and 16,050 psi and the design envelope for related mass points and levels. Each design

~

envelope encompasses all the spectral peaks occurring within the above range of soil' shear modules and results in extremely conservative equipment and paping-design at respective floor levels.

3.7.2.10 Use of Constant Vertical Load Factors A vertical seismic system multi-mass dynamic analysis is used to account for i vertical-response loads (refer to Subsection 3.7.2.1.1.1).

~3.7.2.11 -Method Used to Account for Torsional Effects The effects of torsional modes.of vibration are analyzed by a three-dimensional lumped-mass system using the.MRI/Stardyne computer program (refer to Subsection 3.8.3.4),i Each mass point of the system is given two ortho-

... gonal horizontal degrees of freedom and a thir,t rotational degree of freedon j in the same plane, as shown in. Figure 3.7-21. I'e mass points are then-

' idealized as a rigid diaphragm with three degrees of freedom, two transla -

tional and one rotational. In this analysis, torsional effect results from l- the translational seismic inputs because of the eccentricity between the l ,

1, mass center and the shear center of each floor (mass polar moment of inertia).

Soil structure interaction is considered by including translational and

!: . rotational springs at the base of the lumped-mass mathematical model as-

discussed in Subsection-3.7.2.4. In addition, a torsional spring is also

! considered.

.*-- ~ ~The maximum increase in acceleration due to torsional modes of vibration is I

3.7-11

..,w....--.-.-.--.--.-- -

i t.

WSES-FSAR-UNIT-3 l found to be less than five percent from a case without torsional mode of vibration, as shown in Table 3.7-10. The structural design takes into account the torsional effect. An additional 5 percent to or a subtraca 79

. tion of 5 percent from actual eccentricity has been found to have a nega

.ligible additional ef fect on structural acceleration responses.

3.7.2.12 Comparison of Responses In order to provide a check on the seismic analysis of seismic Category I structures, an analysis using both the moda! analysis response spectrum method and time history method has been conducted. Tables 3.7-6 through 3.7-9 give the response at selected points for major seismic Category I structures using both.these methods. These responses illustrate approximate

. equivalency between the two methods.

3.7.2.13 Methods for Seismic Analysis of Dans There are no seismic Category I dans associated with Waterford-3.

3.7.2.14 Methods to Determine Category I Structure Overturning Moments The seismically induced overturning moments in the seismic Category 1 structures are obtained from the seismic dynamic analysis discussed in Subsection 3.7.2.1.

The bearing pressures arising from two horizontal orthogonal components of seismic. motion, are combined algebraically and further combined with buoyancy and other applicable loads in accordance with the load combinations y discussed in Subsection 3.8.4.3.

In calculating factors of safety against overturning, the moments due to two horisontal orthogonal components of seismic motion are combined by the SRSS method. The factor of safety against overturning for the Nuclear Plant Island Structure is 2.77 as shown in Figure 3.7-22.

3.7.2.15 Analysis Procedures'for Damping

The structural and foundation material damping ratios considered in the seismic analyses are those specified in Subsection 3.7.1.3.

Composite damping in the mathematical models is determined by first evaluaa

(, ting the mode shapes of the system and identifying the relative participation

[

of all portions of the system for each of these modes. Were the response participation is primarily from a single material type, the assumed damping is appropriate to that material. Were no single sarerial can be identified i' as primary to the response, the damping is computed as a weighted average of; the different material damping ratios based on the relative participation of l each material in the mode shape. Using this procedure, modal damping ratios representing the composite damping characteristics are determined for each i: mode of response for use in the normal mode time history technique.

l l The procedure used to find the equivalent modal desping ratios for the natural modes of a structure having composite materials or substructures

__ with different damping ratios is as follows: )

l' j . 3.7-12 Amendment No.19, (6/81) t

WSES-FSAR-UNIT-3 a

[

I d.S D,= i=1 1 ni S,

th mde where: D, a percentage of critical damping ratio for the n th t,tructural di =' percentage of material damping ratio for the i component th th S,g=strainenergyofgei structural component in the n mode =I I p K p. where 1 and j are limited to the 1-3 In 13 Jn component only.

th

-S,= total strain energy of structure in the n mode =

g g,- pin lj Njn *** "" *** # **#* # *

• stducture.

m = number of structural components I

o (

u 3.7

. k  :<- I. '

.2_

. ~

I-i WSES-FSAR-UNIT- 3 3

TABLE 3.7-3 INPUT DATA POR SEISMIC ANALYSIS

HORIZONTAL EXCITATIONS

! Mase 1.ength Area Moment of Inertla (ftI ) Ef feetIve Area (ft ) Weight Point Q.1 N-S E-W N-S E-W (Kip)

[ShieldBuilding. I 27.73 2,554,000 401 7,010 2 21.7 4,058,000 711 4.959 3 19.7 4,058,000 711 4,318 4 20.0 4,058,000 711 4,104 5 25.0 4,058,000 711 4,446 6 25.0 4,058,000 711 6,242 7 20.0 4,058,000 711 4,446

-8 22.0- 4,058,000. 711, 4,104-9 19.0 4,058,000 711. 5,301 10 18.0 4.058,000 711 2,822

, 11 17.0 -11,782,470 2,262 10,173 Containment Vessel 12 21.5 257,500 98 354 j 13 22 527,500 129 376

14 22- 1,031,000 213 376 15 22 1,420,000 287 668 16 22 1,723,000 416 1,735 j 17 22 1,420,000 287 755 P  ; 18 22 1,420,000 287 755 7 19 22 1,420,000 287 755 g 20 22 1,420,000 287 755

?

21 11 1,420,000

• 287 755 Reactor stdg. 22 7.3 540,000 190,600 962 494 1,795 eInternal structure , 23 7 540,000 190.600 962 4% 2,167 24 11 1,770,000 1,317,000 - 1,519 670 8,060 25 12 1,770,000 1,317,000 1,519 670 5,782 26 14.5 1,876,000 1.353,000. 1,737 1,105 9,538 27 12.5 2,095,820 1,364.900 2,102 2,070 8,855 28 7 2,080,000 1,607,000 2,096 2,580 7,802 Fuel Handling alds. 29 44.5 764,130 1.561,810 292 524 6,853 1 30' 24.5 1,118,940 2,512,750 725 1,373 10,240 31 -20.0 12,545,150 45,558,660 2,110 2,160 25,010 32 36.0 15,630,050 53,700,752 2,262 2,676 - 33,670 Reactor Auxiliary . 33 15.5 42,650 10,400 .164 68 428 Building 34 15.5 . 158,800 16,050 270 68 1,029 35 23.0 4,009,200 10,607,934 531 660 17,637 36 25.0 14,056,450 24.867,658 1,0 17 1,472 34,965 37 25.0 27,605,870 50,543,260 3,177 3,055 49,093 38 .31.0 38,109,290 71,336,276 3,832 3,973 59,499

e -

WSES-FSAu-UNIT-3

)

TABLE 3.7-3 (Cont'd) i Foundation Mat Length Width . Thickness Weight Mass Moment of inertia (K-ft2)

Shape (ft.) (ft.) (ft.) (Kips) N-S E-W Rectangular 380 267 12 293.100 3.4440 x 10 9 1.6244 x 10' Soil Spring Constante K Bearing Spring Const (K/ft.) K g Sliding Spring Const (K/ft.) Rocking Spring Const (ft.-K/ radian) (Kfft. )

H2 g-W M-S E-W p N-S N-S E-W 127,500 156,500 865,000 881,000 38.4 x 109 24 x 10 9 2764.8 0.5 E: Young's Modulus of Soil Poisson's Ratio of Soil b1: Horizontal or translational spring constant for soils below base set _

K H2:

H riE0nt81 or tr8n818 tion 81 8Pring constant for soils against side faces of base mat **

h '** By including KH2, the natural period of the structure decreased approximately 7.51, thereby moving toward the peak response region of the response spectrue. Therefore, it is conservative to include this spring constant in the analysis.

Physical Properties for Structural Materials A. Concrete B. Soil e

Modulus of Elasticity: Modulus of Elssticity:

= WI *' 3 E

e 5.11 x 10 5KSF Pleistocene sediments:

where W = 140 lb./ft.3, f',= 4,000 poi #= 0.5, C g

= 6,W pel = 921.6 m

' C, = Ec / 2(1+ # ) = 2.16 x 10' KSF Eg = 1.5 x 2 x 921.6 = 2,764.8 m where f Recent Alluvium

= [ /350 = g4,000/350 = 0.18

1. = 0.5. C2 = 2,300 poi = 331.2 KSF D

t n

.F

^

O 3

. t g WSES-FSAR-UNIT-3 TA81.E 3.7-4 INPUT DATA FOR SF.ISMIC ANALYSIS

,! VERTICAL EXCITATIONS Weight- Member Length Floor Stiffness- Floor Mass Mass No. Cross-Sectlp)al Area (ft. (Kips) (ft.) (k/ft.) Point No.

Shield ^

Building  ! 802 7,010 27.'73 2 1,423 4,959- 21.7 3 1,423 4,319 19.7 4 1,423 4,104 20.0 5 ,

1,423 - 4.446 25.0.

6 1,423 6,242 25.0 7 1,423 4,446 20.0 8 1,423 4.1% 22.0 9 1,423 5,301 19.0 10 1,423 2,822 18.0 11 4,524 10,173 .17.0 containment Vessel 12 195 354 21.5 13 259 376 22.0 14 426 376 22.0 15 575 668 22.0

'." 16 832 .1,735 22.0 i

7 17 575 755 22.0 o , 19 575 755 22.0

19 575 755 22.0 20 575 755 22.0 21 575 755 11.0 Reactor Building 22 1,250 1,295 7.3 Interal Structures 23 1,250 2,167 ' 7.0 -

24 .

2.111 7,973 11.0

, 25 2,111 5,6 82 12.0 26 2,623 20.6 x 10 6 i

' 9.439 14.5 29 27 3,945 8.855 12.5 '

28 3.353 7.802 7.0 i Fuel Handling Building 30 840 6,853 44.5 31 2,357 10,240 24.5 a

32 2,441 25,010 20.0

, 33~ 2,408 33,670 36.0 Reactor Auxiliary Building 34 232 428 15.5 35 338 1 ,0 29 15.5 36 1,191 17,637 23.0 37 2,489 34,%5 ; 25.0 38 4.247 49,093 25.0

^ x ^

USES-FSAR-UNIT-3 table 3.7-4 (Cont'd) :

Welsht Vertical 6pring &

Foundation hat' Mass No. (Kips) a 40 (K/FT) ,

291,110 1.5076 x 10" Soil Spring Coastsats The vertical spring constant considered-in the present waterford - 3 studies consists of two parts: one due to normal stress over the mas,e area; another due to sheer stress around the side areas.

e

, a) 8 earing Spring Constant: K (Vertical spring constant for 1

soils below base mat)

K 8

= C $s g 1 1- p I G = 6,400 pei - 921.6 KSF Sheer modulus and Poisson's ratio a = 0.5 for pleistocess sediments L = 380', & =267

L/d = 380/267 = 1.43

p,= 2.15 (Neference

" Design Procedures for K Dynamically M ed Foundations,"

!- I

=

921 6 x 2.15 x v3so a zei a V Whitman and F E Richart, Jr 0.5 Journal of the Soil Mechanica and F Foundetion Division, 1967)

? = 1,260,988 0

= 1.260988 x 10 K/ft. '

I

~ b) Sliding Spring Constants K (Vertical spring coastsat for soils against side faces of base set)**

K = 2(1 ep ) C g d G = 2,300 poi = 331.2 Esr for recent alluvium g a = 0.5 il I L is the length of rectannuter foundation la the direction of acting force; i g for side effects L is equal to the thickness of the mat.

[ .L

= 12', Bg = 380', 52 = 267' u

L/s3 = 12'/380' = 0.0316 #eg = 1.0

, 2 .

O l

• • See Table 3.7-3 for the sisitar reasons to loclude K, in the analysis, i

l -

r,, , _

. y r _ ,- ..

, _ , . . -~ .

9 x - ,

j.

- WSES-FSAR-UNIT-3 TABLE 1. 7-4 (Cont' d) '

L/B2 = 12'/267' = 0.045 #= g = .I.0

, K, ' = 2 2(1 + 0.5) x 331.2 xs/12 a 180 + 2(I + 0.5) x 311.2 as/12 x 257.

= 6(331.2 x 67.5 + 311.2 x 56.6)

. = 6 x 'el.100 = 246,610 K/ft.

Vertical Soil Spring Constant:

.K, = 1,261,000 + 246,600

=.1.507,600

= 1.5076 x 10 6 t/ft.

Lumped Hass Weight of Foundation Mat W = 297.110E Consider Mat as a one degree of freedos structure, the natural period is:

, f = 2r 297,110

= 0.492 sec.

id y 32.2 x 1.5076 x.106 Y

ll d * **'"**"

Consider the naturalthe uhole period for mathematical modelx as W = 645.930 = 200.60 to ak.-

one sec.degree

. is:of fr!*/ft .

f= 2r 200.60

= 0. 724 sec. 100 1.5076 If the shear modulus G increases to 30, 50,'then- becomes f= 0.722 = 0.418 sec. (for 1G) 6 f= 0.722 = 0.324 sec. ( for 5G)

E

---

_______A

.I

^ ,

WSES-FSAR-UNIT TABLE 3.7-4 (Cont'd)

Pressuriser:

Floor Stiffness:

i K = 870 E I,/a2 a/h =

1_ pg. 167, Norris.

I, is the moment of inertia per unit. width.

I

'h 3

-'5 3 = 125 , a = 15

. T ,Ti 12 K =

870 x 511,000 x 125 x g = 2.06 x 10 7 K/ft.

. 12 15 K

W = 287 Re ference: Structure Design for Dynamic Loads, Charles H Norris P

Y .

12 I

4 I

n

. / , .

k

.10,000 8,000 S,000 _

g 4,000 es E FIELD SEISMIC I MEASUREMENT p

1200

$ KSF j

$ 1,000 '

g800 - ~

. m I 400 Dem k '*mg 200 100 10-8 10-5 10 4 10-3 10-2 SHEAR STRAIN AMPLITUDE 17- (INCHES / INCH) 30 7

I

,< 20 #

O /

l 5 a f V

l z p/

l J

~ 10 maa, 7 l'

i 0

.10-5 104 10-3 10-2 SHEAR STRAIN AMPLITUDE 17- (INCHES / INCH)

- -- TAKEN FROM SEED, H. BOLTON AND IDRISS 1.M. (1969)

"THE INFLUENCE OF SOIL CONDITIONS ON GROUND I

MOTIONS DURING EARTHOUAKES" t

AMENOMENT NO. 33 (9/831 LOUISIANA Figure POWER & LIGHT CO. SHEAR MODULUS & DAMPlNG VS STRAIN-Waterford Stearr, RECENT MATERIAL (GRADE TO -40 FT. MSL) 2.5-77 Electric Station

4 e

I i

10,000 , ,, , , , ,,,,,,

8,000 RANGE OF FIELD 6,000 -5100 KSF / SEISMIC MEASUREMENTS u es gr g 12ng % m 5 2800 KSF * "

I 2,000  % '

o 0  ;

O o N

E .-

d 1,000 e "

o '

. A 300 k g00 n

%0

%.Q w 400 e INDICATES TEST RESULTS r ---

e INDICATES RESULTS CALCULATED BY 200 HARDIN DRNEVICH EQUATIONS 100 10 4 10-5 104 10 4 10-2 SHEAR STRAIN AMPLITUDE 1 7 - (INCHES / INCH)

+ .

7 30 I

E I

x 30 O /

E ##

I p#

E 10 "

E -., 7 8

0 10-5 10 4 10-3 10-2 SHEAR STRAIN AMPLITUDE i 7 (INCHES / INCH)

TAKEN FROM SEED, H. BOLTON AND IDRISS, l.M. (1967)

"THE INFLUENCE OF SOIL CONDITIONS ON GROUND MOTIONS DURING EARTHOUAKES"

.%. .-m .* -

LOUISIANA .

Figure POWER & LIGHT CO. SHEAR MODULUS & DAMPING VS. STRAIN -

Waterford Steam UPPER PLEISTOCENE (-40 FT.MSL TO -317 FT.MSL) 2.5-78 Electric Station

4 4

4 APPENDIX B P

O n , n.~ -

~ l' s 1

, 6 ,-

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'i TASLE 3.7-9 COMPARISON OF ACCELERATION FOR SEtSMIC CATECORY I STRUCTURES USINC RESPONSE SPECTRA AND TIME HISTORY METH00S SSE.

Soll SHEAR MODULUS =.16050 psi Response Spectrum Method (51) Time History Method Mass Elevation E-W N-S Ve rt E-W N-S Vert No. ( Ft ) Accel (C) Accel (C) Accel (C) ' Accel (C) Accel (C) Accel (C)

Shield Bldg. ,1 200.13 0.498 0.432 0.180 0.546 0.448 0.175 4 Containment 12 197.50 0.36 2 0.314 Vessel 0.173 0.38 7 0.320 0.168 Reactor 514g, 22 60.3 0.256 0.245 Internale 0.172 0.235 0.217 0.168 FHS 29 90.0 0.276 0.247 0.176 0 .26 2 0.245 0.167 RAB 33 100.0 0.291 0.2I4 0.177 0.244 0.254 0.170 Mat. 39 -37.24, 0.200- 0.210 0.171 0.197 0.197 0.167 I'

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' - - s LOUISIANA Figure POWER & LIGHT CO. MATHEMATICAL MODEL FOR SEISMIC ANALYSIS Waterford Steam 3 *'/ 1()

(VERTICAL EXCITATION) l Electrie St0 tion

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Electric Station

APPENDIX E l

v.

LI '

WSES-FSAR-UNIT-3

-s Structural stest is designed in accordance with basic working stress 9; design methods. Increased allowable stresses are used for the accident

.- condition.-

f The final designs of the interior structures and equipment supports are reviewed to assure that they can withstand applicable design pressure i/ ~ . loads,' jet forces , pipe reactions, and earthquake loads without loss of function. The deflections or deformations of the structutes and supports are checked to ensure that the functions of the containment and safety

~

feature systems are not impaired.

3.8.3.4.1.1 Comput'er Programs Utilized for Structural and Seismic Analyses i

The following computer programs have been used in structural and seismic analyses to determine stress and-deformation responses of seismic Category 1 structures. A brief description of-each program and the extent of its use are given below: <

9

FIXMAT 2037 FIXMAT 2037 is an Ebasco in-house computer program which operates on

~

BURR 00GHS'6700 and handles the ' dynamic analysis of lump-mass-spring type'models. It provides results of natural periods of vibration, mode

_ shipes participation factors and structural responses.. Both methods of

' time history and response spectrue can be specified. The program also

. generates floor response spectra.

i' This program was used for all seismic analysis of seismic Category I structures and - to calculate all floor responses and their spectra curves.

$TARDYNE 2 AND NASTRAN 22

.STARDYNE 2 AND NASTRAN are public domain computer programs designed to analyze static and dynamic problems of linear elastic structural systems using finite ' element techniques.

The programs are capable of a) computing structural deformations and l22 aumber loads and stresses caused by an arbitrary set of thermal and aschanical applied loads and/or prescribed displacements, and b) dynamic response, analyses for transient, steady state, . harmonic, random and shock

~

i spectra excitation type loading conditions. The results are presented as t.isplacements, accelerations or velocities and/or as internal member loads / stresses.

.EAC/ EASE ,

'r The EAC/ EASE (Elastic Analysis for ' Structural Engineering) is a public domain computer program developed by Engineering / Analysis ' Corporation (Redondo Beach, California) which provides static structural analyses

"' of Llinear, three-dimensional. systems, subjected to sets of arbitrarily 7

prescribed mechanical and thermal loads and displacement boundary L. . conditions. The,, program is capable of modelling with three distinct 3.8-49 Amendment No. 22.-(9/81)

F

1 WSES-FSAR-trNIT-3 i ' types of structural elements, beams, membranes, and plates, which can be used separately or together in assembling a three-dimensional

' array . The program camputes joint displacements, r,eactive forces, --

- beas forces moments and stresses.

Rigid Frame 2117 ]

Rigid Frame 2117 is an Ebasco in-house camputer program which analyzes a two dimensional single or multi-story rigid frame under vertical '

• or horizontal ~ 1oads. This is accomplished by using a stiffness matrix approach with a Gaussian elimination method. This program was used l for frame analysis of all seismic Category I structures.; l FIXMAT 2037 program was developed by Ebasco. Since this program is-not a recognized program in public dnsain, a crusparison with STARDYhE Tversion 4/1/72) and NASTRAN, both proven programs in public domain,

'is made in Tables 3.8-23 to 3.8-30 to demonstrate its validity and

- applicability.

o Rigid Frame 2117 is also an Ebasco program and operates on a Burroughs 6600 machine. . Due to the relatively simple nature of the program, com-parison of results were made by solving several sample problems with

^ known solutions to demonstrate its validity and applicability.

As. discussed above, CDC/STARDYNE and EAC/ EASE programs are proven pro--

grams existing in the public domain and therefore no comparison of '

results with other programs is presented.

3.8.3.4.1.2 Analysis and Design Procedures a) Dynamic Analysis Analytical techniques for the seismic dynamic analysis are de scribed in - Section . 3.7.

i Analytical techniques for the protection against dynamic.

. effects associated with the postulated pipe rupture are

' described in Section 3.6.

f

' Analytical technique for the protection against missiles is ,

described in Section 3.5.

b)- Design Procedures.

All the structural element s of ' the -internal structures are analyzed statica11y' base? an a LOCA loading combination described

~in; Subsection 3.8.3.-3. The equivalent static load 'resulting from the -application of the accelerations at various levels obtained from the above mentioned dynamic analysis are

-includ ed .

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