ML20010J169
| ML20010J169 | |
| Person / Time | |
|---|---|
| Site: | Byron  |
| Issue date: | 05/09/1973 |
| From: | Brinnvasarr R, Lung Chen S, Shah I SARGENT & LUNDY, INC. |
| To: | |
| Shared Package | |
| ML20010J163 | List: |
| References | |
| SL-3026, NUDOCS 8109290661 | |
| Download: ML20010J169 (30) | |
Text
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i fj SEISMIC SOIL-STRUCTURE INTERACTION
{ ANALYSIS OF NUCLEAR POWER PLANTS C
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REPORT PREPARED FOR UNITED STATES ATOMIC ENERGY
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REPORT SL-3026 M AY 9.1973
! S ARGENT & LUNDY
'b ENGlNEER5 81099.90661 010916 CHICAGO
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, l LIST OF EXHlBlTS PAGE I INTRODU CTION 1 II SOIL-STRUCTURE INTERACTION ANALYSIS 1 i
$ III UNCOUPLED BUILDING hiODEL ANALYSIS 4 IV RECOhihiL'NDED PROCEDURE FOR ANALYSIS 5 REFERENCES 7 APPENDIX A - DYNAhiIC ANALYSIS BY COhfPONENT hiODE SYNTHESIS EXHIBITS 1- Building Aiodel 2 - Finite Element Soil hiodel f 3 - Time History hiot:ons 4 - Comparison of Foundation Level Spectra f 5 - Effect of Interaction on Base Slab hiotion 6 - Interaction Spectra at Slab #5 - Effect of Rocking P 7 -
Interaction Spectra at Slab #6 - Effect of Rocking 8 -
Coupled and Uncoupled Analyses Spectra at Slab #3 f 9- Coupled anc Uncoupled Analyses Spectra at Slab #5 l 10 - Couplcd and Uncoupled Analyses Spectra at Slab #6 i
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ac NEER5 CHICAc0 i o .
I SEISMIC SOIL-STRUCTURE INTERACTION ANALYSIS ,
OF NUCLEAR POWER PLANTS UNITED STATES ATOMIC ENERGY COMMISSION I INTRODUCTION The foundation level response spectra corresponding to the Operating Basis Earthquake (O. B. E. ) and the Safe Shutdown Earthquake (S. S. E. )
conditions prescribed for use in the seismic analysis of a nuclear power station do not include the effect of soil-structure interaction. The intent of this report is to present the soil-structure interaction study made for a nuclear power station by analyzing a coupled three-dimensional soil-structure interaction model subjected to a compatible rock motion. Based on this study a general procedure has been presented for the use in future nuclear units.
The modal synthesis technique as applied in this study analyzes soil-structure interaction along each direction separately. However, because of the coupling between the translational and torsional modes of vibration in a typical nuclear plant structure it is essential to excite the three-di-mensional structure model simultaneously along two major orthogonal directions, while generating various floor response spectra. For this reason, the response of the 3D structure model alone (uncoupled), when subjected to the modified base slab motion obtained from the interaction study, was compared with that of the coupled model. Response spectra at important locations in the structure were compared for Safe Shutdown Earthquake excitation along one direction only. It has been concluded that by properly restraining the rocking degree of freedom of the base slab, the structure model can be uncoupled from the soil model and subsequently can be analyzed for two simultaneous excitations with the base slab trans-lational motions obtained from interaction study. ,
il SOIL-STRUCTURE INTERACTION ANALYSIS In the interaction analysis the soil-structure system was divided into two subsystems, one corresponding to the soil model and the other correspond-ing to the structure model. Various modes of the soil and structure sub-systems were obtained independently and were later combined using a modal synthesis technique so as to satisfy geometrical compatibility at the common node between the soil and the structure. A brief description of the modal synthesis technique used in this study has been presented in Appendix A.
The following paragraphs describe the structure and soil models used in the PROJECT 0023 SL-3026
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, SARGENT a LUNDY ENCINEERS CHICAco interacti'on analysis, the generation of compatible rock motion, and the interaction floor response spectra.
A. STRUCTURE MODEL The building was modeled as a 3D lumped mass discrete system with shear springs and flexural members connecting the lumped masses.
The massive stiff slab-shear wall cor: figuration of the building was medeled as a slab-spring system in which the mass of the structure wai considered concentrated at the floor elevations. The slabs, treated as infinitely rigid, were interconnected by weightless linear elastic springs to simulate the stiffness of shear walls within the structural complex. The three degrees of freedom allowed for the slabs were two horizontal translations parallel to the principal axes <
of the structure and the rotation about the vertical axis. The reactor '.
containment structure was modeled with lumped masses having all the six degrees of freedom. These masses were interconnected by flex-ural members. Exhibit 1 shows the details of the building model used ir the study. In the interaction study eleven building modes were con-sidered. A constant structural damping of 5 percent of critical damp- l ing was used for all the building modes, t B. SOIL MODEL t
i The soil profile at the site was modeled as two dimensional plane strain l rectangular finite elements. The finite element model (Exhibit 2) used in the study had a total of 26 layers, the thickness of each layer varying from 3 ft to 5 ft. Such a large number of layers was used so that enough soil modes could be extracted accurately. The width of the model was made large enough to assure free field conditions at the boundary far re-moved from the structure. The nodes along this vertical boundary were
! restrained against vertical displacement to simulate free field conditions.
The strain dependent soil modulus and damping for each layer corre- l*
sponding to ie Safe Shutdown Earthquake condition at the foundatiory level f
were detet mined using the ' SHAKE' program (Ref.1). These soil prop-l erties are listed in Table 1. However, in the modal analysis of the l finite element soil model a weighted constant damping of 17 percent for all the modes was used. Eighty modes from the finite element model of the soil, shown in Exhibit 2, were extracted using 'DAPS' (Ref. 2) computer program. Soil modes were alno extracted from a similar finite eli. ment soil model made in the other orthogonal direction. The torsional effect is accounted for by including a discrete torsional mode.
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SARGENT A LUNDY ENGINEERS cmcaco TABLE I SOIL LAYER PROPERTIES Layer Unit Shear Modulus Poisson's Damping No. Weight (k/so fe) Rat 10 Ratio (k/ft3) 1 0.12 291 0.37 0.094 2 0.12 347 0.37 0.137 3 0.12 349 0.37 0.159 4 0.12 359 0.37 0.172 5 0.12 371 0.37 0.178 6 0.12 38S 0.37 0.183 7 0.12 419 0.37 0.182 8 0.12 447 0.37 0.182 9 0.12 501 0.37 0.178 10 0.12 575 0.37 0.173 11 0.12 633 . 0.37 0.169 12 0.12 660 0.37 0.168 13 0.12 698 0.37 0.165 14 0.12 742 0.37 0.162 15 0.12 440 0.37 0.183 16 0.12 493 0.37 0.178 17 0.12 553 0.37 0.171 18 0.12 604 0.37 0.166 19 0.12 636 0.37 0.163 20 0.12 603 0.37 0.168 21 0.12 535 0.37 0.178 22 0.12 480 0.37 0.186 23 0.12 437 0.37 0.193 24 0.12 412 0.37 0.197 25 0.12 403 0.37 0.199 26 0.12 411 0.37 0.200 Weighted average damping = 0.170 Average shear wave velocity = 364 ft/sec First soil period = 1.32 see Second soil period = 0.40 see
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- %.s SARGENT & LUNDY E NGIN E E R5 CHICACO C. COUPLED SOIL-STRUCTURE MODEL The building modes and soil modes obtained as described in the pre-ceding paragraphs were combined using a modal synthesis technique.
A brief description of the principle of the modal synthesis is given in Appendix A. This coupled soil-structure system was then sub-o sected to a compatible rock motion applied at the base of the soil model.
D. COMPATIBLE ROCK MOTION The compatible rock motion applied as input motion to the base of the soil-structure model was obtained using the same discrete model of the soil as described in Section IIB. A modified El Centro time-history motion (Exhibit 3), the response spectrum (5 percent spectral damping) of which envelops the specified design response spectrum for the S.S.E.
condition (Exh oit 4), was input to the free field boundary of the soil model at the base slab elevation. The frequency-dependent transfer function X(a) between the free-field boundary and the base of the soil model was determined ba_ed on the modal properties of the discrete soil model. Applying the transfer function to the Fourier Spectrum of foundation motion G(2), the Fourier Spectrum of the trotion at top of the bedrock I(w) can be obtained. The rock motion time history can then be generated by obtaining Inverse Fourier Transform of I(2). See Exhibit 3.
E. FLOOR RESPONSE SPECTRA The coupled soil-structure model was subjected to the ccmpatible S. S. E.
rock motion in the plane of the model as shown in Exhibit 2. The modal synthesis was performed using 'DYNAS' (Ref. 3) computer program develpoed by Sargent L Lundy Engineers. Fesponse spectra were gen-erated at the base slab, slab #3, Slab #5, and slab #6. These spectra are presented in Exhibits 5 through 10.
A comparison of response spectrum generated at the free field founda-tion level (at node FF, Exhibit 2) and the design spectrum is presented i in Exhibit 4. From Exhibit 4 it is also observed that the motion inpu,t I at the foundation Icvel to obtain rock motion is in very clo'se agreement with the free field motion at the foundation level. This indicates the adequacy of the finite-element model. Exhibit 5 presents the effect of soil-structure interaction on the base slab motion.
III UNCOUPLED BUILDING MODEL ANALYSIS Because of the coupling between the translational and torsional modes of vibration, it is essential to excite the 3D structure model simultaneously .
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l ENCINEERS c m c a.o y along two major horizontal directions, while generating the floor response spectra. Since the soil-structure interaction effect can only be obtained along each direction separately, an uncoupled building model with proper rocking springs and interaction time history motion at the base slab needs to be analyzed.
To determine the effect of rocking on the floor response spectra, and hence
- to determine the proper rocking springs, as a first step the coupled model was analyzed with restrained rocking degrees of freedom of the base slab.
The spectra obtained for the coupled model with and without the rocking re-straints have been compared in Exhibits 6 and 7. A fixed base structure model was excited using the translational base slab motion obtained from the interaction analysis. The results of the fixed base analysis have been compared with those obtained from the coupled interaction analysis in Exhibits 8, 9 and 10.
IV RECOMMENDED PROC.EDURE FOR ANALYSIS Based on the results of the present study the following general procedure has been recommended to account for soil-structure interaction effects in the horizontal directions.
- 1. Generate synthetic time history motions to satisfy the design site spectra for the O. B. E. and the S. S. E. in two orthogonal directions "x" and "y ".
- 2. Obtain strain de3.endent soil properties (shear modulus and damping) for each layer and compatible rock motions corresponding to the input motions described in Step 1 at the foundation level.
- 3. Using the coupled 3D soil-structure interaction model and the modal synthesis technique, obtain the L se slab motions Bxx(t) and Byy(t) and the corresponding response s ctra Bxx(2) and Byy(2), whe re the first subscript represents the dirt . tion of excitation and the second subscript refers to the direction of base slab motion. The effect of Bxy(t) and Byx(t) has been found to be insignificant. Obtain the re-sponse spectra at important floors in the structure.
- 4. Study the effect of rocking of the base slab on the floor response spectra by restraining the rocking degree of freedom of the base slab.
- 5. If Step (4) indicates insignificant rocking effect, analyze a 3D fixed base structure mod < 1. If on the other hand Step (4) indicates aignificant rocking effect (+ 10 percent or more), analyze the 3D structure model with appropriate rocking springs.
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SARGENT & LUNDY ENCINEERS CHICACO i
- 6. Using the i=teraction time history motions Bxx(t) and Byy(t), simul-taneous!r at the base slab analyze the 3D uncoupled structure model to obtai . f oor response spectra.
- 7. Envelope _he floor response spectra by widening the peaks, on either side, by 1~Eo on the period scale to account for variations in soil propertie s.
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SARGENT & LUNDY ENCINEER5 cmcaco REFERENCES
- 1. d' SHAKE ' Computer Program developed by J. Lysmer and P. B. Schnabel of the University of California, Berkeley and maintained by Sargent & Lundy Engineers.
- 2. ' DAPS ' Computer Prograrr. de- eloped by E. L. Wilson of University of California, Berkeley and maintained by Sargent &
Lundy Engineers.
- 3. ' DYNAS ' Computer Program developed and maintained by
{- Sargent & Lundy Engineers.
- 4. Hurty, W. C. , " Vibrations of Structural Systems by Component Mode Synthesis," Proceeding of American Society of Civil Engineers, Vol. 85, No. EM4, August, 1960.
- 5. Hurty, W. C. , " Dynamic Analysis of Structural Systems Using Component Modes, " AIAA Journal, Vol. 3, No. 4, April,1965.
- 6. Craig, R. R. , and Bampton, M. C. C. , " Coupling of Substruc-tures for Dynamic Analysis," AIAA Journal, Vol. 6, No. 7, July, 1968.
- 7. Goldma n, R. L. , " Vibration Analysis by Dynamic Partif'oning "
AIAA 'ournal, Vol. 7, No. 6, June,1969.
?
- 8. Benfield, W. A. , and Hruda, R. F. , " Vibration Analysis of ~
Structures by Component Mode Substitution," AIAA Journal '
( Vol. 9, No. 7, July, 1971.
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COUPLED AND UNCOUPLED ANALYSES SPECTRA AT SLAB #5 i
I
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L
SARGENT Ot. UNDY EXHIBIT 10 twoiwasms CHICAGO SL-3026 ACCELER ATION, i
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68
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- 5 PER CENT SPECTRAL DAMPING
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I APPENDIX A a
f O
e e
SARGCNT & LUNDY ENG4NEERs APPENDIX A SL-3026 DY!IAMIC Al,'t LYSIS BY COMPO!!E!!T MODE Pil,' THESIS I. INTRODUCTIU:'.
Modal synthesis techniques have been used extensively by aircraft industries for dynamic analysis of large struc-tural systems. In those techniques, the complete structure is assumed to be composed of a number of subsystems that are connected with each other. The vibration modes for each component are determined separately and then matht '-
matically combined to synthesize the system nodes. Different techniques have been used by a number of workers (Refs. 4,5,6,7,6) in this field, but the basic concept is the same. The techniques may be divided into the followin; three basic categories.
- 1. Fixed-Fixed Component Modes (Refs. 4,5,6): The natural modes of vibration for cach component are determined by fixing all interface coordinates of the subsystem and the motion of each component is written with -
reference to constraint modes and fixed constrained natural vibration modos.
- 2. Free-Free Component itodes (Ref. 7): The natural modes cf vibration for cach component are determined by frecinq ;
all interface coordinates of the subsystem and com-ponent rigid-body and clastic vibration modes' arc l used for compatibility equation.
A-1
SARGENT & LUNDY ENGINEERS c uca o APPENDIX A SL-3026 B
- 3. Fixed-Frco Co;aponent Ilodes (Ref. 8): In this method, the interface of one component is assumed to be fixed and the corresponding interface of the connecting com-ponent is frec.
All the above methods have their own advantages and disadvantages with respect to accuracy and computer core size requirements.
The method used to study the soil interaction effect L
is based on the method given'by Denfield and Hruda (Ref. 8).
The c .plete soil and structure system has been divided into twc subsystems. The basement slab has been used as the interfacc between the superstructure and the soil media. The soil media has been selected as the main body and the building part as a branch component.
The vibration modes of the soil part are detcrmined with its interface coordinates free and the vibra-tion modes of the superstructure arc determined with its interface coordinates fixed.
A-2
SARGENT a: LUNDY ENGINccas APPENDIX A SL-3026 1
II. l>ERIVATION OF BASIC EOUATIONS Let xi and xb, respectively be the relative displacements
, of interior and boundary coordinates of the branch (super-p structurc)* substructure with respect to the base (rock) motion. The equation of motion for the superstructurc is given by
' !!ii 0 'si xi kii kib xi N
- r + [c]< t + , 3 O
I*bb . .Eb. ,Ab.
kbi kbb-Xb
. s Mii 0. ,,
= -
N' {c rl Y, (t) (1)
_0 11bb.
M = the mass matrix partitioned as above c = the damping matrix
, k = the stiffncss matrix er = the vector with unity in the direction of motion and =cro otherwisc
/g(t) = the base motion Let us define the interior moQcs [cc] as the static mode shapes of the interior degree of freedo.s due to succes-
{
sive unit displacement of boundary coordinates with all other boundary coordinates constrained. Then ($c) is given by lec ) = -k ii kib , (2) ,
I The equation of motion for free vibration of the super-structure with its boundary node fixed is given by:
A-3
7
~
SARGENT & LUNDY ENGINEEns APPENDIX A SL-3026
+c Mii xi + kii x'ci=0 (3) where xC are the relative displacements of interior nodes with respect to the boundary node.
Let $1 be the normalized (with respect to mass) mode shape of Eq. (3) and El the vector of generalized coor-dinates, then, x[=elC1 (4)
Then xi=x[+$c xb (5) or ,
Cl xi = [$1 &c] > (6)
.xb,
. Tnc transformation matrix A which transforms the coor-
, dinate system xi to generalized coordinate C1 and xb is given by
~
'* 1 +c 0 I-or , , ,
xi ,C1
=A (8) a Substituting D{uation (8) into (1) and premu!tiplying by At one obtains a
a -
A4 p.
t
.. _.. _ -. . g
( SAMGENT & LUNDY
[ , ENGINEERS APPENDIX A saicano SL-3026 1
(
l _ _ _ ... ,
4 -
., ~
fili Mib <
c
+
281y w s
0 g
y
, +
Eii 0 (i
,Mbi !!bb ,Xb 0 0, i O Eib.
- b. . Xb)
T -
$1 0 Mii 0
] ,,
T \ *
Y9 (9)
,$c I- -
0 Mbb , ,
where Nii " $1 Mii el " I IIib " Nbi * 'l Mii e c
_ T -
Mbb " $c Mii ec+Mbb
) Eii = $1 kii el " I"i l Ebb = kbi ec + kbb =o 81 = critical modal damping for sunerstructure The equation of motion for soil part is given by
(
[Ms] (xs) + [cs) (As) + [ks) (xsl = -lMsl (0Rs} g(t) (10) l Let $s be the normalized mode shape with respect to mass
(
i matrix, then, the displacement vectors are given by f
xs * *s C2 (11) where C2 = vector of gr.ncralized coordinates.
Substituting for xs ira Equation (10) and prcmultiplying by 's i one gets I
g A-5 i
. i
- , . , , . - - , . -n- , . - . . . . - . .. , , - . . - - , . - -
,1 _ - . _ _ _ _
l SARGENT & LUNDY -
EN GlN E E R 5 APPENDIX A l
- c'*
- SL-3026 l T
C2 + [ 28 2 *s I C2+ IWs 3 C2 " - e s I!!sl($Rs} g (t) (12)
Let x be the portion of x 3 on the boundary node, then sb Iqua'. ion (11) may be written as f
xss 9 ss
, " . (13)
,Xsb, (4sbf (2 wherc (sb is the modal vector at the boundary coordinate.
Using compatibility equation at the boundarf coordinates, one has Xb = xsb " $sb C2 (14) and C' 1 I O .
e (1 ,(15) g txb , = 0 tsb >
io (
, 2, ,0 I.
i b
i o or ,
- m -
F IC1 ,,
- = (13] , (16)
<xb .
N -
C2 '
C
- 2, .
Cor.dsining Equations (12) and (9) one gets 281wy 0 0 flii riib 0 (1 (1 fibi !!bb 0 <
xb > + 0 0 0 <
x3, - (continued on next page) 0 0 I, , t 2, 0 C2.
28 2 "s.
. A-6
SARGENT O LUNDY
- EsciNrcas APPENDIX A caucaso SL-3026 Eli 0 8 0" '(1 " -
r < ' -
T 0 'i
+ 0 Ebb l0
, xb =-
+1 0 ttl i ,
l i 0
,_*T l 2 c1 I O Mbb
~ ~ - - - -- -
,0 0 ,ws, C2, --
f-le( T {g),
~
r 4
, 59 (t) (17) l tE s*lt .
- i using Equation (16) and prcmultiplying by [B}7 onc gets I-lii Il_.ib ,
,0 '
C1 01--
" l' - - - - El
>+[BT]
[BT) g.;bi Mbb 'O*
[D] <. [B)< -,
:.- ( 2,
. O l282us. $2 .
0 0 'I -
't1'
'E..11 0
I 0'
[BT) -
o gbb 0 [D'] < -
C2 0 0 :w s ~
f$ 1T 0],'O 01 , 'Mig
- -[B]' :, ,
., r yg(t) (18)
Cel I. ,
O Mbb l' i O i *s IMslj * -
Equation (18) could be solved using any suitable numerical
- integration routine. Finally, El and C2 and Equation (8) are used to compute the response xi of the superstructures.
A-7
I..' -
C ARGENT O LUNDY APPENDIX A
- ENOlNEERO
- "" SL-3026 III. 3-D SOIL MODE The soil modes corresponding to 3-D are obtained using 2-D
. To extract soil modes using
. finito element soil model.
3-D model for a large system (3-D soil finite cic=ent model) is very costly and there is no surcty that the final results will be reasonably correct.
Two 2-D finite element models of soil are made for two orthogonal horizontal directions and mode shdpes and frc-quencies are extracted. These modal characteristics are
~
used for translational modes.
The effect of torsional mode is taken into account by .a discrete torsional spring.
' The following assumptions have been made for the above procedure which arc justified.
O 1.
The modes in two orthogonal horicontal directions are not coupled.
2.
The torsional mode is not coupled with the trans-( lational modes.
" The above assumptions are valid if the soil m'odel is In our case, symmetrical about the two horizontal axes.
s this is reasonably true.
characteristics arc conputed
. The discreto torsional nodal as given below: ,
Let 11 = torsional soil mass A-8
CARGENT 6: LUNDY auonwccas AP"ENDIX A concaso
- SL-3026 k = torsional soil stiffness .
the torsional frequency is given by k
f" 8
[i The torsional mode shape normalized to mass is given by 1
U= --
1 #1 I
~.
- j. .
e
=
1-I-
U
)~ -
r e
3 d
, A-9 l
_ . . _ . _ _ _ . _ . . . , _ . . - . _ . . _ _ . . . . _ _ _ . _ . _ . - _ . _ _ _ _ _ . . _ . . . . . _ _ _ . _ . _ _ _ _ . _ . . _ . _ . _ _ . - . . _ _ - _ . - - . _ _