development of criteria for seismic review of selected nuclear power
TRANSCRIPT
N UR EG/C R-0098
DEVELOPMENT OF CRITERIA FOR SEISMIC REVIEW OF
SELECTED NUCLEAR POWER PLANTS
N . M. Newmark W. J. Hall
Manuscript Completed: May 1978 Date Published: May 1978
N . M. Newmark Consulting Engineering Services 121 1 Civil Engineering Building
Urbana, IL 61801
This document is PUBLICLY RELEASABLE
Authorizing ~ l d i i d
Division of Operating Reactor Off ice of Nuclear Reactor Regulation U. S. Nuclear Regulatory Commission Under Contract No. AT(49-24)-0116
Dae 7-306.7. mTRIBUTION OF THIS DOCUMENT Is_ U N L ~ T E Q
DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.
ii
TABLE OF CONTENTS
Page
I . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 . 1 General Phi losophy P e r t a i n i n g t o Review Process . . . . . . 1
1.2 General Design and A n a l y s i s Concepts . . . . . . . . . . . 3
1.3 S c o p e o f Report . . . . . . . . . . . . . . . . . . . . . . 4
I I . SELECTION OF EARTHQUAKE HAZARD FOR R E V I E W AND DESIGN . . . . . . 5
2.1 General Concepts . . . . . . . . . . . . . . . . . . . . . 5
2.2 Regional Mot ions. I n c l u d i n g Propagat ion and A t t e n u a t i o n . . 6
2.3 S i t e A m p l i f i c a t i o n and M o d i f i c a t i o n . . . . . . . . . . . . 9
2.4 V e r t i c a l Mot ions . . . . . . . . . . . . . . . . . . . . . 1 1
I l l . DESIGN S E I S M I C LOADINGS . . . . . . . . . . . . . . . . . . . . 12
3 .1 Actual versus E f f e c t i v e Earthquake Mot ions . . . . . . . . 12
3.2 Design Seismic Mot ion . . . . . . . . . . . . . . . . . . . 13
I V . SOIL-STRUCTURE INTERACTION . . . . . . . . . . . . . . . . . . . 15
V . DAMPING AND ENERGY ABSORPTION . . . . . . . . . . . . . . . . . 17
5.1 I m p l i c a t i o n s of Damage or Col lapse . . . . . . . . . . . . 17
5.2 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.3 D u c t i l i t y . . . . . . . . . . . . . . . . . . . . . . . . . 18
VI . METHODS OF DYNAMIC ANALYSIS . . . . . . . . . . . . . . . . . . 20
6.1 Response Spectrum . . . . . . . . . . . . . . . . . . . . . 20
6.2 Use o f Response Spectra for Mult i-Degree-of-Freedom Systems .. Modal A n a l y s i s . . . . . . . . . . . . . . . . . 21
6.3 Time H i s t o r y A n a l y s i s . . . . . . . . . . . . . . . . . . . 22
.... . . ..- ........ \< . . . . . i . . . . . . . . . . .
. . . . - . . . . . . . . . . . . . . . .
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V I 1 . REVIEW ANALYSIS AND DESIGN PROCEDURES . . . . . . . . . . . . . 7 . 1 General Cons idera t ions . . . . . . . . . . . . . . . . . . 7.2 M o d i f i e d Response Spectra . . . . . . . . . . . . . . . . 7.3 E f f e c t s o f S ize and Weight of S t r u c t u r e . . . . . . . . . 7.4 E f f e c t s o f I n e l a s t i c A c t i o n . . . . . . . . . . . . . . . 7.5 Seismic Design C l a s s i f i c a t i o n . . . . . . . . . . . . . . 7.6 Design Spectra . . . . . . . . . . . . . . . . . . . . . . 7.7 Combined E f f e c t s o f H o r i z o n t a l and V e r t i c a l E x c i t a t i o n . . 7.8 Unsymmetrical S t r u c t u r e s . Tors ion. Over tu rn ing and U p l i f t
7.9 Response o f Equipment and Attachments . . . . . . . . . . V I I I . SPECIAL TOPICS . . . . . . . . . . . . . . . . . . . . . . . .
8.1 F a u l t Mot ions . . . . . . . . . . . . . . . . . . . . . . 8.2 R e l a t i v e Mot ions . . . . . . . . . . . . . . . . . . . . . 8.3, Underground Conduits and P i p i n g . . . . . . . . . . . . . 8.4 Tanks and Vaults . . . . . . . . . . . . . . . . . . . . . 8.5 Equipment Q u a l i f i c a t i o n . . . . . . . . . . . . . . . . .
. 24
. 24
. 24
. 25
. 27
. 27
. 28
. 29
. 30
. 31
. 34
. 34
. 34
. 35
. 36
. 37
8.6 Q u a l i t y Cont ro l and D e t a i l s o f C o n s t r u c t i o n . . . . . . . . . 38
8.7 P r o b a b i l i t y Concepts . . . . . . . . . . . . . . . . . . . . 38
I X . SUMMARY REVIEW AND REPORTING . . . . . . . . . . . . . . . . . . 40
9.1 A u d i t Procedure and Systems Summary . . . . . . . . . . . . 40
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
I V
L I S T OF TABLES
T a b 1 e P a g e
1 RECOMMENDED DAMPING VALUES . . , . , , . . . . . . . . . . . . . 44
2 EQUATIONS FOR SPECTRUM A M P L I F I C A T I O N FACTORS FOR HORIZONTAL MOTION . . . . . . , . . . . . . . . , . . 45
3 SPECTRUM A M P L I F I C A T I O N FACTORS FOR HORIZONTAL E L A S T I C RESPONSE . . . . . . . . . . . . . . . . . 45
4 PROPOSED S E I S M I C DESIGN C L A S S I F I C A T I O N . . . , . . . . . . . . . 46
L I S T OF FIGURES
F i g u r e P a g e
1 S I M P L E UNDAMPED MASS-SPRING SYSTEM . . . . . . . . . . . . . . . 47
2 RESISTANCE-DISPLACEMENT R E L A T I O N S H I P . . . . . . . . . . . . . . 47
3 E L A S T I C DESIGN SPECTRUM, H O R I Z . MOTION, (0.5 g MAX. ACCEL., 5% DAMPING, ONE SIGMA CUM. P R O B A B I L I T Y ) . . . . . . . . . . . . . 48
4 DESIGN SPECTRA FOR EARTHQUAKES . . . . . . . . . . . . . . . . . 48
5 E L A S T I C AND I N E L A S T I C DESIGN SPECTRA . . . . . . . . . . . . . . 49
1
1. INTRODUCTION
1 . 1 General Phi losophy P e r t a i n i n g t o Review Process
Many o f t h e e a r l y nuc lea r f a c i l i t i e s were designed and cons t ruc ted
d u r i n g the t ime when se ismic design procedures f o r such s p e c i a l i z e d systems
were beg inn ing t o be developed. I t i s recognized t h a t i n many cases these
p l a n t s were designed t o c r i t e r i a t h a t a r e l ess r i go rous than those used f o r
recen t p l a n t s . I n view o f the r a p i d development o f t he s t a t e - o f - t h e - a r t
o f se ismic design d u r i n g the pas t two decades even some o f t h e more modern
p l a n t s , designed as r e c e n t l y as ten years ago, may need rev iew i n t h e l i g h t
o f c u r r e n t c r i t e r i a and p resen t knowledge.
The purpose o f t h i s r e p o r t i s t o s e t f o r t h se ismic c r i t e r i a and
design concepts a p p l i c a b l e t o rev iew analyses and upgrading f o r se lec ted
l y t o nuc lea r power p l a n t s , a l t hough t h e p r i n c i p l e s a r e a p p l i c a b l e genera
o l d e r o p e r a t i n g p l a n t s .
A t t h e o u t s e t , i t i s expected t h a t t h e rev iew process wou d
c o n s i s t o f two general tasks, one p e r t a i n i n g t o d e t a i l e d rev iew o f the
e x i s t i n g p l a n t i n the 1 i g h t of appl i c a b l e rev iew c r i t e r i a and the second
i n v o l v i n g d e t a i l e d design and a n a l y s i s s t u d i e s t o develop the des i red
(and p o s s i b l e ) upgrading o f the se ismic res i s tance .
I t i s env is ioned t h a t t h e d e t a i l e d rev iew would encompass
i n s p e c t i o n o f t h e p l a n t , rev iew o f e x i s t i n g documentation ( repo r t s , p lans ,
and c a l c u l a t i o n s ) as a p p r o p r i a t e w i t h i d e n t i f i c a t i o n o f those systems which
r e a l i s t i c a l l y and economica l l y a r e amenable t o upgrading.
t h i s rev iew i t may be d e s i r a b l e t o c a r r y o u t a r i s k a n a l y s i s t o h e l p p r o v i d e
a b a s i s f o r t h e dec i s ions t h a t must be made as t o the d e s i r a b i l i t y and
As a p a r t o f
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advantages of carrying out the upgrading.
helpful in deciding on the timing of the upgrading program since in many
cases it may not be possible to carry out the entire retrofit construction
program during one time period.
Such studies also could be
It is well known that upgrading and retrofitting constitute
expensive operations when they can be accomplished at all.
it is economically, if not physically, impossible to carry out significant
seismic upgrading improvements. In those cases where it is possible
economically it is desirable t o take advantage of the latest concepts
pertaining to development of seismic resistance. Thus in the evaluation
of the existing facility, and in the subsequent detailed design studies
for physical upgrading of structural or mechanical systems, the authors
believe it is possible (and desirable) to take into account the modest
amount of nonlinear behavior that can be permitted in many portions of
such systems without significant decrease in the margin of safety against
safe shutdown or containment.
applications to nuclear facilities) are identified herein as well, including
spectrum concepts for handling close-in versus distant earthquakes, and
bounding of forces likely to be felt by equipment.
In many cases
\
A number of other concepts (in the sense of
Last, but by no means least, is the observation that the inherent
seismic resistance of well designed and constructed systems is usually much
greater than that commonly assumed, largely because nonlinear behavior is
mobilized to limit the imposed forces and accompanying deformations. For
such systems where the resistance is nondegrading for reasonable deformations
the requirements for retrofitting may be nonex stent or at most minimal.
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1.2 General Design and Analysis Concepts
When a structure or a piece of equipment or instrumentation is
subjected to earthquake motions, its base or support tends to move with the
ground on which it is supported or with the element on which it rests.
Since this motion is relatively rapid, it causes stresses and deformations
in the item considered. I f this component is rigid, it moves with the
motion of its base, and the dynamic forces acting on it are very nearly
equal to those associated with the base accelerations. However, if the
component is quite flexible, large relative motions or strains can be
induced in the component because of the differential motions between the
masses of the component and its base. In order to survive the dynamic
motions, the element must be strong enough as well as ductile enough to
resist the forces and deformations imposed on it. The required strength
and ductility are functions of stiffness or flexibility, among other things.
In assessing seismic effects it should be remembered that the seismic
actions generally are in addition to those already existing, i.e., arising
from dead load, live load, thermal effects, etc.
Unfortunately, the earthquake hazard for which an element or
component should be designed is subject to a high degree of uncertainty.
In only a few areas of the world are there relatively long periods of
observations of strong earthquake motions. The effects on a structure,
component, or element, depend not only on the earthquake motion to which
it is subjected, but on the properties of the element itself. Among these
properties, the most important are the energy absorption within it or at
interfaces between the element and its support, either due to damping or
inelastic behavior, its period of vibration, and its strength or resistance.
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I
1.3 Scope of Report
The r e p o r t t h a t f o l l o w s conta ins a d i s c u s s i o n o f those c r i t e r i a
and p r i n c i p l e s which i t i s be l ieved would be o f p r imary concern i n a rev iew
of an e x i s t i n g nuc lear f a c i l i t y . The aim i n p repar ing t h i s summary has
n o t been to d iscuss each t o p i c i n g r e a t depth b u t ins tead t o p lace i n
p e r s p e c t i v e t h e p o i n t s of engineer ing concern and to d e l inea te the major
i tems t h a t should be considered i n t h e review.
The t e x t t h a t f o l l o w s begins w i t h a general d i s c u s s i o n o f t h e
earthquake hazard which should be used f o r the rev iew. I t i s our b e l i e f
t h a t t h e se ismic hazard should i n general be re-evaluated for each e x i s t i n g
p l a n t w i t h c o n s i d e r a t i o n o f c u r r e n t NRC procedures. T h i s s e c t i o n i s f o l l o w e d
by a s e c t i o n on se ismic mot ions to be used i n upgrading, damping and energy
absorp t ion , s o i l - s t r u c t u r e i n t e r a c t i o n , and a b r i e f d i s c u s s i o n o f methods
o f dynamic a n a l y s i s . T h e r e a f t e r f o l l o w s a d i s c u s s i o n o f s p e c i f i c t o p i c s
which must be considered i n d e t a i l i n t h e rev iew process i n c l u d i n g such
i tems as t h e m a t e r i a l p r o p e r t i e s , load combinations, response spect ra,
up1 i f t , and response o f equipment.
The n e x t s e c t i o n l i s t s and d iscusses b r i e f l y a number o f s p e c i a l
t o p i c s which may need c o n s i d e r a t i o n as a p a r t o f t h e review, i n c l u d i n g
f a u l t mot ions, condu i ts , v a u l t s and tanks, q u a l i t y c o n t r o l and r i s k
assessment. The r e p o r t concludes w i t h some observa t ions on a u d i t s and
systems summaries, s p e c i f i c a l l y w i t h re fe rence to t o p i c s which should be
examined as a p a r t o f t h e se ismic review.
The m a t e r i a l i n t h e r e p o r t i s drawn i n p a r t f rom m a t e r i a l
p r e v i o u s l y prepared by t h e authors, b u t has been supplemented w i t h much
a d d i t i o n a l m a t e r i a l r e f l e c t i n g our l a t e s t s tud ies , understanding, and
views p a r t i c u l a r l y as they r e l a t e t o rev iew and upgrading.
~- -_
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I I . SELECTION OF EARTHQUAKE HAZARD FOR R E V I E W AND DESIGN
2.1 General ConceDts
The process o f earthquake r e s i s t a n t rev iew and des ign r e q u i r e s
s e l e c t i o n o f earthquake hazards as w e l l as es t imates o f s t r u c t u r a l s t reng ths ,
e i t h e r i m p l i c i t l y o r e x p l i c i t l y , as an i n t e g r a l p a r t o f t h e review procedure.
Unless these de te rm ina t ions a r e made i n a c o n s i s t e n t manner, the f i n a l design
may be e i t h e r g r o s s l y uneconomical o r dangerously unsafe.
parameters a r e p r o b a b i l i s t i c i n n a t u r e al though, f o r convenience, many o f
the aspects o f t h e de te rm ina t ion o f s t r u c t u r a l s t r e n g t h may reasonably be
approximated as d e t e r m i n i s t i c . However, t he earthquake motions themselves
f o r wh ich t h e des ign review i s t o be accomplished, o r even the occurrence
Both se ts o f
i t s e l f o f an earthquake a f f e c t i n g t h e s i t e
I n the des ign of nuc lea r power p
i s customary t o p rov ide r e s i s t a n c e a g a i n s t
c r e d i b l e earthquake", which has o n l y a sma
must be considered as probabi 1 i s t i c .
a n t s under c u r r e n t c r i t e r i a i t
two earthquakes: ( 1 ) a ''maximum
1 p r o b a b i l i t y o f occurrence d u r i n g
the l i f e t i m e o f t h e p l a n t , w i t h a long r e t u r n p e r i o d f o r which the des ign
i s made a t y i e l d l e v e l s o r 1 i m i t s t r e n g t h c o n d i t i o n s ; and (2) an earthquake
hav ing a much h ighe r p r o b a b i l i t y o f occurrence, w i t h a r e t u r n p e r i o d s h o r t e r
than t h a t a p p l i c a b l e i n (11, o f t e n taken as h a l f o f t h e earthquake e x c i t a t i o n
d e f i n e d i n (l), f o r which t h e des ign i s made a t somewhat. lower a l l o w a b l e
s t resses and f o r somewhat d i f f e r e n t combinat ions o f c o n d i t i o n s . A t p resen t
the Nuclear Regulatory Commission d e f i n e s these earthquakes as t h e Safe
Shutdown Earthquake (SSE) and the Opera t ing Basis Earthquake (OBE) r e s p e c t i v e l y .
As p a r t o f t h e review process f o r e x i s t i n g p l a n t s i t i s recommended
t h a t a thorough i n v e s t i g a t i o n o f t h e se ismic hazard be made i n accordance w i t h
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c r , t e r i a and Standard Review Plans c u r r e n t l y employed by t h e NRC. I n t u r n
t h i s hazard should be used c o n s i s t e n t l y i n t h e rev iew e v a l u a t i o n i n o r d e r
t o p e r m i t v a l i d comparison a g a i n s t c r i t e r i a and des ign as migh t be found
i n newly designed p l a n t s . Such comparisons w i l l be r e q u i r e d as p a r t o f
the d e c i s i o n process concern ing upgrading.
2.2 Regional Mot ions, I n c l u d i n g Propagat ion and A t t e n u a t i o n
I n genera l , t w o procedures a r e a v a i l a b l e t o d e f i n e the earthquake
hazard. I n t h e f i r s t where t h e r e i s an e x t e n s i v e h i s t o r y o f earthquake
a c t i v i t y and g e o l o g i c and tec ton i c i n v e s t i g a t i o n s a re f e a s i b l e , e s t i m a t e s
can be made of t h e p o s s i b l e magnitude and t h e l o c a t i o n of f u t u r e earthquakes
a f f e c t i n g a s i t e . I n many instances, such earthquakes w i l l occur a long w e l l
d e f i n e d f a u l t s . One can then make es t imates o f t h e earthquake mot ion
i n t e n s i t y propagated t o t h e s i t e , t a k i n g i n t o account the exper imenta l and
o b s e r v a t i o n a l da ta a v a i l a b l e for t h i s purpose as descr ibed f o r example i n
d e t a i l i n Refs. 1 and 2.
Donovan (Ref. 1 ) p l o t t e d d a t a a t v a r i o u s d i s t a n c e s f o r a c c e l e r a t i o n s
from 678 w o r l d earthquake records ranging i n magnitude f rom l e s s than 5 t o
g r e a t e r than 8.
reduce somewhat by n o r m a l i z i n g the data t o t h e exponent ia l o f one-ha l f t h e
magnitude.
t h e da ta i s l o g a r i t h m i c normal. For the median o f the a c c e l e r a t i o n , a,
measured i n g r a v i t y u n i t s , g, Donovan d e r i v e d a r e l a t i o n i n v o l v i n g t h e
hyper foca l range R, i n km, measured f rom t h e earthquake focus to t h e p o i n t
on t h e ground s u r f a c e where t h e record was taken i n terms of t h e R i c h t e r
magnitude M, as g i v e n by t h e f o l l o w i n g equat ion:
He found a g r e a t deal o f s c a t t e r , which he was a b l e t o
He was a b l e t o show a l s o t h a t the p r o b a b i l i t y d i s t r i b u t i o n o f
( 1 ) -1.32 a = 1.10 ( R + 25)
7
The geometr ic standard d e v i a t i o n , 0 , designed as the r a t i o f o r t he median
p l u s one standard d e v i a t i o n va lue t o the median va lue , was ve ry n e a r l y 2.0,
i n d i c a t i n g t h a t t h e spread i n the data was q u i t e l a r g e .
For data f rom 214 San Fernando records, Donovan ob ta ined a
l a r g e r a t t e n u a t i o n and a smal le r spread i n the data, corresponding t o the
r e l a t i o n s h i p (app ly ing t o t h e magnitude f o r t h i s earthquake o f 6 . 4 ) :
-2.04 a = 21.5 g e 6.4'2 ( R + 25)
where t h e geometr ic standard d e v i a t i o n was determined t o be 1.6. Th is more
r a p i d a t t e n u a t i o n has been noted by o thers , and is c o n s i s t e n t w i t h the da ta
repo r ted i n Ref. 2.
I n a l l cases, re fe rence t o the f i g u r e s w i l l show t h a t o n l y
ve ry l i m i t e d da ta e x i s t e d f o r earthquakes c l o s e r than about 20 km t o the
hypocenter. The o n l y d e f i n i t i v e s tudy o f c l o s e - i n earthquake mot ion i s
t h a t con ta ined i n Ref. 3 , and the most recent i n t e r p r e t a t i o n p e r t a i n i n g
to c l o s e - i n e f f e c t s on nuc lear p, lants i s con ta ined i n Amendment 50 and
companion NRC s t u d i e s f o r t he D i a b l o Canyon P l a n t .
The second procedure f o r deve lop ing the earthquake hazard i n a
reg ion i s used when occurrence o f earthquake i s no t g e n e r a l l y a'ssociated
w i t h su r face f a u l t i n g , o r when i n s u f f i c i e n t da ta a r e a v a i l a b l e from records
and observa t ions . Under these c o n d i t i o n s , r e l a t i o n s h i p s have been developed
f o r c o r r e l a t i n g ground mot ions, g e n e r a l l y maximum v e l o c i t i e s o r maximum
acce le ra t i ons , t o a q u a . l i t a t i v e measure o f t h e i n t e n s i t y o f mot ion, as f o r
example t h a t o f t h e "Mod i f ied M e r c a l l i I n t e n s i t y " . Al though these r e l a t i o n s
a r e n o t as r e a d i l y sub jec t t o mathematical de te rm ina t ion as t h e r e l a t i o n s
f o r earthquake shock propagat ion, t he re a r e s u f f i c i e n t obse rva t i ons t o
8
permi t use fu l p r o b a b i l i s t i c da ta t o be obta ined. Such da ta a r e summarized
i n Refs. 4 and 5.
These da ta show even more s c a t t e r than those f rom a c c e l e r a t i o n s
and d i s t a n c e from t h e focus. They a r e compl icated by t h e f a c t t h a t t h e
MM I n t e n s i t y i s a s u b j e c t i v e measure i n l a r g e p a r t , and f o r h igher l e v e l s
o f damage i t depends t o a g r e a t e x t e n t on type o f b u i l d i n g , p r o p e r t i e s o f
b u i l d i n g m a t e r i a l s , foundat ion c o n d i t i o n s and the l i k e ; f o r these reasons,
f o r example, one would expect some changes i n damage assessment over scores
o f years as t h e q u a l i t y o f c o n s t r u c t i o n m a t e r i a l s improved. Data from
quar ry b l a s t i n g i n d i c a t e s t h a t p l a s t e r c r a c k i n g r a r e l y begins a t l e s s than
0.5 in /sec maximum ground v e l o c i t y and g e n e r a l l y i s q u i t e p r e v a l e n t f o r
v e l o c i t i e s g r e a t e r than 2 in /sec. F i n a l l y , t h e o b s e r v a t i o n i s made t h a t
i n t h e E l Centro earthquake o f 1940, t h e maximum ground v e l o c i t y was about
14 in/sec, and t h e M o d i f i e d M e r c a l l i I n t e n s i t y was r e p o r t e d as I X .
These and o t h e r da ta suggest t h a t t h e median v a l u e of the maximum
ground v e l o c i t y can be i n f e r r e d from t h e M o d i f i e d M e r c a l l i I n t e n s i t y by
u s i n g t h e r e l a t i o n s h i p t h a t t h e maximum ground v e l o c i t y i s approx imate ly
8 in /sec f o r MM VIII and changes by a f a c t o r o f 2 f o r each u n i t change i n
MM I N t e n s i t y below MM V I I I , b u t increases above t h i s l e v e l more s l o w l y .
I t i s b e l i e v e d t h a t t h i s r e l a t i o n s h i p c o r r e l a t e s w e l l w i t h observa t ions
from a l l dynamic sources. By comparison o f the a c c e l e r a t i o n and v e l o c i t y
w i t h the r e l a t i o n s h i p t h a t a v e l o c i t y o f 48 in /sec corresponds t o a 1 g
maximum a c c e l e r a t i o n i n competent s o i l s , one o b t a i n s t h e r e s u l t t h a t f o r
M o d i f i e d M e r c a l l i I n t e n s i t y V I I I , t h e a c c e l e r a t i o n i s 0.167 g and changes
by a f a c t o r of 2 w i t h each u n i t drop i n MM I n t e n s i t y . These r e l a t i o n s h i p s
should drop o f f somewhat f rom the f a c t o r of 2 increase as the i n t e n s i t y
i nc
9
2ases above V I I I , however.
I t i s be l i eved t h a t t he r e l a t i o n s h i p between maximum ground
v e l o c i t y and MM I n t e n s i t y i s n e a r l y independent o f the p r o p e r t i e s o f the
s o i l , bu t t h e r e l a t i o n s h i p between v e l o c i t y and a c c e l e r a t i o n i s s l i g h t l y
s o i l dependent and t h e r e may be some dependence o f s o i l p r o p e r t i e s on the
r e l a t i o n s h i p f o r a c c e l e r a t i o n s t a t e d above. Nevertheless, t he observa t ions
o f MM I n t e n s i t y a r e most s t r o n g l y i n f l uenced by b u i l d i n g t ype r a t h e r than
by s o i l p r o p e r t i e s when i n t e n s i t y i s assoc ia ted w i t h b u i l d i n g damage.
I n o t h e r words, t he s o i l type has i m p l i c i t l y been taken i n t o account i n
the obse rva t i on o f damage o r i n the obse rva t i ona l da ta l ead ing t o the
MM I n t e n s i t y repo r ted .
2.3 S i t e A m p l i f i c a t i o n and M o d i f i c a t i o n
The r e g i o n a l mot ions t h a t one de r i ves f rom t h e methods descr ibed
i n t h e above must be mod i f i ed t o take account o f the geo log ic and s t r a t o -
g raph ic c o n d i t i o n s p e r t a i n i n g t o the s i t e . Al though t h e r e has been a g r e a t
deal o f s tudy and research i nvo l ved i n t h i s t o p i c i t must be considered
low ( p o s s i b l y maximum a c c e l e r a t i o n l e s s than 0
t ion o f g r a v i t y ) t h e measured acce le ra t ions a r e
tt ian on rock.
then the a c c e l e r a t i o n s measured on rock appear
However, when t h e a c c e l e r a t i o n
s t i l l a c o n t r o v e r s i a l ma t te r . Nevertheless, i t i s c l e a r from observa t i ons
t h a t the t ype o f s o i l o r subso i l has a major i n f l u e n c e on the mot ions t h a t
a r e recorded. I n general , f o r t he same earthquake, where the i n t e n s i t y i s
2 g, where g i s t he acce le ra -
g e n e r a l l y h i g h e r on sediments
s h i g h ( g r e a t e r than 0.2 g ) ,
t o be h igher than those on
s o i l . I n most instances t h e measured v e l o c i t i e s a r e n e a r l y the same.
S tud ies o f the n a t u r e o f the mot ions on s i t e s o f d i f f e r e n t s t i f f n e s s e s a r e
IO
summarized i n Refs. 6 and 7 i n terms o f t he so -ca l l ed "response spectra"
a p p l i c a b l e t o t h e measured records a t v a r i o u s s i t e s .
Al though a n a l y t i c a l methods have been proposed p u r p o r t i n g t o
e x p l a i n phenomena such as those descr ibed i n the re fe rences p r e v i o u s l y
c i t e d , i n most cases these analyses cons ider a c o n d i t i o n n o t r e p r e s e n t a t i v e
o f a c t u a l c o n d i t i o n s . The p r i n c i p a l assumption ( t h a t t he earthquake mot ions
c o n s i s t o f h o r i z o n t a l shear waves propagated v e r t i c a l l y upward from some
base l a y e r where t h e mot ions a r e de f ined) i s c o n t r a r y t o obse rva t i ons .
For example, i t i s shown i n Ref. 8, and i t has long beenconsidered,
t h a t f o r longer p e r i o d mot ions, p o s s i b l y where the pe r iods a r e one second
o r longer, t h e mot ions a r e p r i m a r i l y due t o su r face waves such as Ray le igh
waves or Love waves. I t i s q u i t e l i k e l y , however, t h a t f o r moderate
d is tances , beyond those cor respond ing to the depth of focus, su r face waves
have an impor tan t e f f e c t even f o r h ighe r f requenc ies o r s h o r t e r p e r i o d
mot ions, and more complex mot ions must be considered o t h e r than those due
t o h o r i z o n t a l shears propagated v e r t i c a l l y upward. Moreover, the f a c t
t h a t v e r t i c a l mot ions occur cannot be accounted f o r by the s imple h o r i z o n t a l
shear wave model.
Cons idera t ions l ead ing t o v a r i a t i o n i n i n t e n s i t y o f mot ion w i t h
depth beneath t h e su r face a r e ve ry complex.
r e l a t e su r face mot ions t o mot ions beneath the sur face. The obse rva t i ona l
da ta f o r mot ions beneath t h e sur face , compared w i t h su r face mot ions, inc ludes
two o r t h r e e smal l earthquakes i n Japan. These and o t h e r l i m i t e d da ta
i n d i c a t e some r e d u c t i o n w i t h depth o f su r face mot ion i n t e n s i t y , bu t f o r
l a r g e mot ions o r h i g h i n t e n s i t i e s , they do no t support the c o n t e n t i o n t h a t
one can compute a c c u r a t e l y v a r i a t i o n s i n i n t e n s i t i e s o f mot ion w i t h depth
There a r e few data t h a t d i r e c t l y
1 1
by methods i n v o
wave.
I t i s
methods t o mod
t h e sur face.
i n t e n s i t y modi
v i n g on
n o t e n t
y the v e r t i c a l p ropagat ion of a h o r i z o n t a l shear
r e l y r a t i o n a l t o depend o n l y on c a l c u l a t i o n a l
f y earthquake mot ions from some deep l a y e r o r bedrock t o
t would seem d e s i r a b l e t o base in fe rences about s i t e
i c a t i o n on a c t u a l observa t ions o f sur face mot ions as w e l l as
on c a l c u l a t i o n s u n t i l such a t ime as measurements o f mot ion become a v a i l a b l e
f rom a c t u a l earthquakes a t v a r i o u s depths beneath the s u r f a c e f o r a number
o f d i f f e r e n t foundat ion c o n d i t i o n s .
I n s p i t e o f the f a c t t h a t t h e r e i s such u n c e r t a i n t y , i t i s
p o s s i b l e t o a s s i g n va lues t o t h e parameters o f importance i n assessing s i t e
e f f e c t s based on t h e genera l n a t u r e o f d i f f e r e n c e s i n mot ions t h a t appear
reasonable, however.
2.4 V e r t i c a l Mot ions
Several recent s t a t i s t i c a l s t u d i e s have been made o f v e r t i c a l and
h o r i z o n t a l earthquake mot ions (Refs. 9 and 10). A l though the s c a t t e r i n
r e s u l t s i s q u i t e g r e a t , i t i s our recommendation t h a t t h e des ign mot.ions
i n t h e v e r t i c a l d i r e c t i o n be taken as 2/3 o f t h e v a l u e i n the h o r i z o n t a l
d i r e c t i o n across t h e e n t i r e f requency range.
12
I l l . DESIGN S E I S M I C LOADINGS
3 . 1 Actual versus E f f e c t i v e Earthquake Motions
Al though peak va lues o f ground mot ion may be assigned t o the
v a r i o u s magnitudes o f earthquake, e s p e c i a l l y i n the v i c i n i t y o f the su r face
expression o f a f a u l t o r a t t h e ep icen te r , these mot ions a r e i n general
cons ide rab ly g r e a t e r than sma l le r mot ions which occur many more t imes i n
an earthquake. Design earthquake response spec t ra a r e based on " e f f e c t i v e "
values o f t he a c c e l e r a t i o n , v e l o c i t y and displacement, which occur several
t imes d u r i n g t h e earthquake, r a t h e r than i s o l a t e d peak va lues of ins t rumenta l
reading. The e f f e c t i v e earthquake hazards se lec ted f o r de termin ing des ign
spec t ra may be as l i t t l e as one-ha l f t he expected i s o l a t e d peak instrument
readings f o r near earthquakes, ranging up t o the l a t t e r values f o r d i s t a n t
earthquakes.
Design response spec t ra determined from these parameters can
take i n t o account the v a r i o u s energy abso rp t i on mechanisms, both i n the
ground and i n t h e element, i n c l u d i n g r a d i a t i o n of energy i n t o the ground
from t h e responding system.
I n t h e des ign o f any system t o r e s i s t seismic e x c i t a t i o n , as
discussed e a r l i e r here in , t he re a r e a number o f parameters and des ign '
cons ide ra t i ons t h a t must be taken i n t o account. Among these a r e the
magnitude o f t he earthquake f o r which the des ign i s t o be made, the
d i s t a n c e o f t he f a c i l i t y f rom t h e focus o r f a u l t , t he parameters governing
a t t e n u a t i o n o f mot ions w i t h d i s t a n c e from the focus o r e p i c e n t e r t h e s o i l
o r r o c k c o n d i t i o n s as w e l l as t h e general geo log i c c o n d i t i o n s i n the
v i c i n i t y , and t h e parameters governing t h e response o f t he f a c i l t y o r
13
--
the s t r u c t u r e i t s e l f . Most , i f n o t a l l , of these parameters a r e s u b j e c t
t o c o n s i d e r a b l e u n c e r t a i n t y i n t h e i r value, Because so many of t h e para-
meters invo lved have probabi 1 i s t i c ( r a t h e r than d e t e r m i n i s t i c ) d i s t r i b u t i o n s ,
i t i s n o t p roper t o take each o f them w i t h a h i g h degree o f conservat ism
because t h e r e s u l t i n g combined degree o f conservat ism would then be
unreasonable. A t the same t ime i t i s d e s i r a b l e t o have an assured margin
of s a f e t y i n t h e combined des ign c o n d i t i o n s . Hence, a cho ice must be made
as t o t h e parameters which w i l l be taken w i t h l a r g e margins of s a f e t y and
those which w i l l be taken w i t h more reasonable va lues c l o s e r t o the mean
or expected va lues of t h e parameters.
The r e l a t i o n between magnitude o f energy re lease i n an earthquake
and t h e maximum ground mot ion i s very complex. There a r e some reasons
for i n f e r r i n g t h a t t h e maximum a c c e l e r a t i o n s are, f o r example, n e a r l y
t h e same for a l l magnitudes o f r e l a t i v e l y sha l low earthquakes f o r p o i n t s
near t h e focus or e p i c e n t e r . However, f o r l a r g e r magnitudes, the va lues
do not drop o f f so r a p i d l y w i t h d i s t a n c e f r o m t h e e p i c e n t e r , and the
d u r a t i o n o f shaking i s l onger . Consequently, t h e s t a t i s t i c a l mean or
expected va lues of ground mot ions show a r e l a t i o n s h i p inc reas ing w i t h
magnitude, a l though n o t i n a l i n e a r manner.
3.2 Design Seismic Mot ion
I n s e l e c t i n g t h e earthquake hazards fo r use i n des ign o r review,
the general concept used for t h e DBE, as discussed e a r l i e r , i s t h a t the
earthquake magnitude se lec ted should be a t l e a s t as l a r g e as those t h a t
these earthquakes a r e g e n e r a l l y cons idered
t h i n reg ions of
c u l a r , t h e
t o have equal probabi
s i m i l a r or c l o s e l y r e
have occur red i n t h e past, and
i t i e s o f
a ted geo
o c c u r r i n g a t any p o i n t w
o g i c charac ter . I n p a r t
14
es t imates of mot ion considered a r e those a p p r o p r i a t e f o r competent
m a t e r i a l s a t o r near the ground sur face, i n c l u d i n g rock or competent
conso l ida ted sediments a t or near t h e sur face. I t i s f a i r l y w e l l recognized
now t h a t t h e predominant p a r t o f s t r o n g earthquake ground mot ion generated
by a near sha l low earthquake energy re lease, i s represented by sur face
waves. I n genera l , these a r e propagated i n a manner c o n s i s t e n t w i t h the
p r o p e r t i e s o f t h e m a t e r i a l a t a depth c o n s i d e r a b l y beneath t h e sur face and
a r e n o t a f f e c t e d t o a l a r g e e x t e n t by t h e s u r f a c e p r o p e r t i e s themselves.
The des ign va lues o f mot ion normal ly a r e based on the assumption t h a t the
same va lues a r e a p p l i c a b l e i n a p a r t i c u l a r zone f o r a l l competent s o i l s ,
I n summary, t h e maximum ground mot ion va lues t o be used for rev iew and
upgrading may be c o n s i d e r a b l y l e s s than the i s o l a t e d peak va lues o f mot ion
(as measured by inst ruments) t h a t correspond t o the magnitudes o f e a r t h -
quakes t h a t migh t be assigned t o t h e zones.
I V . SOIL-STRUCTURE INTERACTION
When a s t r u c t u r e i s founded w i t h i n o r on a base of s o i l and/or
rock, i t i n t e r a c t s w i t h i t s foundat ion . The f o r c e s t r a n s m i t t e d t o t h e
s t r u c t u r e and t h e feedback t o the foundat ion a r e comp
modify t h e f r e e - f i e l d mot ions. Methods f o r d e a l i n g w
i n t e r a c t i o n have been proposed by a number o f w r i t e r s
ex i n nature, and
t h s o i l - s t r u c t u r e
These methods
i n v o l v e : (1) procedures s i m i l a r t o those a p p l i c a b l e t o a r i g i d b lock
on an e l a s t i c h a l f space; (2) f i n i t e element o r f i n i t e d i f f e r e n c e procedures
corresponding t o va r ious f o r c i n g func t i ons a c t i n g on the combined s t r u c t u r e -
so! 1 complex; ( 3 ) s u b s t r u c t u r e model 1 i n g techniques which may or may no t
i n c l u d e use o f t he d i r e c t f i n i t e element method. Sumnaries o f some o f t he
f a c t o r s and u n c e r t a i n t i e s a f f e c t i n g these c a l c u l a t i o n s a r e g iven i n Refs.
1 1 th rough 15. More advanced techniques a r e under development a t a number
o f i n s t i t u t i o n s , b u t a l l methods have y e t t o be t e s t e d and t h e r e f o r e
conserva t i ve i n t e r p r e t a t i o n o f t h e r e s u l t s o f a n a l y s i s i s r e q u i r e d .
However one makes the c a l c u l a t i o n , one determines a fundamental
frequency and h ighe r f requenc ies o f t h e s o i l system which i n t e r a c t s w i t h
the s t r u c t u r e , a n d . e f f e c t i v e damping parameters f o r t h e s o i l system t a k i n g
i n t o account rad . i a t i on and m a t e r i a l damping. Both o f these q u a n t i t i e s a r e
necessary i n o r d e r t o o b t a i n r a t i o n a l r e s u l t s . Procedures t h a t emphasize
one bu t n o t t h e o t h e r cannot g i v e a proper type o f i n t e r a c t i o n .
I n genera l , c o n s i d e r a t i o n must be g i ven t o the i n f l u e n c e o f
l o c a l s o i l and geo log ic c o n d i t i o n s as a f f e c t i n g the s i t e ground mot ions,
bo th i n terms of i n t e n s i t y and frequency con ten t . S o f t s o i l c o n d i t i o n s ,
f o r example, may prec lude t h e development o f h i g h a c c e l e r a t i o n s o r
v e l o c i t i e s w
g i ven t o t h e
s lope i n s t a b
o f f o rma t ion
16
t h i n t h e founda t ion m a t e r i a l s . Cons ide ra t i on must a l s o be
development o f uns tab le c o n d i t i o n s such as s o i l l i q u e f a c t i o n ,
l i t y , o r excess ive se t t l emen ts . Fu r the r , because o f the na tu re
o f s o i l depos i t s and t h e i r l a c k of u n i f o r m i t y i n some s i t u a t i o n s ,
i n o rde r t o c a r r y o u t meaningful c a l c u l a t i o n s i t may be d e s i r a b l e t o cons ide r
t h e de te rm ina t ion o f i n - s i t u p r o p e r t i e s ; i n such cases the methods o f sampling
and t e s t i n g used t o i n f e r these p r o p e r t i e s need c a r e f u l cons ide ra t i on .
Because o f t he v a r i a t i o n s i n p r o p e r t i e s and t h e d i f f i c u l t y o f de termin ing
them a c c u r a t e l y , some degree of v a r i a t i o n i n t h e b a s i c parameters used in t he
c a l c u l a t i o n s should be taken i n t o account.
F i n a l l y , t h e method o f c a l c u l a t i o n used should a v o i d as much as
p o s s i b l e the i n t r o d u c t i o n o f spur ious r e s u l t s a r i s i n g from the c a l c u l a t i o n a l
technique. For example, i t i s o f t e n necessary t o a v o i d " r e f l e c t i n g " o r
"hard" boundaries where these do n o t a c t u a l l y e x i s t .
Th i s e n t i r e t o p i c i s one t h a t r e q u i r e s the most c a r e f u l cons idera-
t i o n , and a d d i t i o n a l research and s tudy over the nex t decade probab ly w i l l
be necessary b e f o r e d e f i n i t i v e recommendations on s o i l - s t r u c t u r e i n t e r a c t i o n
can be developed. I n the i n t e r i m f o r rev iew and upgrading, i t i s recommended
t h a t g r e a t ca re be taken i n assessing the need f o r such analyses. Care fu l
judgment as t o t h e meaning o f t he r e s u l t s , i n the l i g h t o f t h e comments
g i ven he re in , i s requ i red . Re l iance on any s i n g l e method i s t o be avoided.
17
V . DAMPING AND ENERGY ABSORPTION
5.1 I m p l i c a t i o n s of Damage or Col lapse
I n c o n s i d e r i n g t h e response o f a s t r u c t u r e t o se ismic mot ions,
one must take account o f t h e i m p l i c a t i o n s o f v a r i o u s l e v e l s o f damage,
s h o r t o f c o l l a p s e , o f t h e s t r u c t u r e . Some elements of nuc lear power p l a n t s
must remain e l a s t i c or n e a r l y e l a s t i c i n o rder to per form t h e i r a l l o c a t e d
s a f e t y f u n c t i o n . I n many instances, however, a p u r e l y l i n e a r e l a s t i c
a n a l y s i s may be unreasonably c o n s e r v a t i v e when one cons iders t h a t , even up
t o t h e near y i e l d p o i n t range, t h e r e a r e n o n l i n e a r i t i e s of s u f f i c i e n t amount
t o reduce r e q u i r e d des ign f o r c e l e v e l s cons iderab ly . T h i s i s discussed i n
more d e t a i l l a t e r h e r e i n i n Sec t ion 7 d e a l i n g w i t h rev iew and r e t r o f i t
des
nuc
Ref
gn procedures.
A d i s c u s s i o n of the des ign requirements fo r v a r i o u s i tems of
ear power p l a n t s wherein n o n l i n e a r behavior i s permi t ted , i s g iven i n
1.6, i n t h e t a b u l a t i o n o f des ign c lasses i n t h a t re fe rence. S i m i l a r
c o n s i d e r a t i o n s a r e g i v e n i n Ref. 17, p e r t a i n i n g t o t h e Trans-Alaska O i l
P i p e l i n e , where se ismic des ign c lasses a r e used i n d e f i n i n g t h e requirements
t o r e s i s t damage f o r t h e v a r i o u s elements o f t h a t system. An a p p l i c a t i o n
o f these concepts t o nuc lear r e a c t o r des ign i s g i v e n i n d e t a i l l a t e r i n
t h i s r e p o r t .
5.2 Damping
Energy a b s o r p t i o n i n t h e l i n e a r range o f response o f s t r u c t u r e s
t o dynamic l o a d i n g i s due p r i m a r i l y t o damping. For convenience i n a n a l y s i s ,
t h e damping i s g e n e r a l l y assumed t o be v iscous i n n a t u r e ( v e l o c i t y dependent)
and i s so approximated. Damping l e v e l s have been determined from o b s e r v a t i o n
18
and measurement b u t show a f a i r l y wide spread. For conservat ism, damping
\'slues f o r use i n des ign o f nuc lear p l a n t systems a r e g e n e r a l l y taken a t
lower l e v e l s than t h e mean or average est imated va lues.
Damping i s u s u a l l y considered as a p r o p o r t i o n o r percentage o f
the c r i t i c a l damping value, which i s d e f i n e d as t h a t damping i n a system
h h i c h would p revent o s c i l l a t i o n for an i n i t i a l d i s t u r b a n c e n o t c o n t i n u i n g
through the mot ion. Levels of damping, as summarized from a v a r i e t y o f
sources, a r e g i v e n i n Refs. 18-20. For convenience, t h e damping assoc ia ted
w i t h p a r t i c u l a r s t r u c t u r a l types and m a t e r i a l s as mod i f ied s l i g h t l y from
k e f . 21 i s g i v e n h e r e i n i n Table 1 . The lower levels o f the p a i r o f va lues
g i v e n f o r each i tem a r e considered t o be n e a r l y lower bounds, and a r e
t h e r e f o r e h i g h l y conserva t ive ; t h e upper l e v e l s a r e considered t o be average
o r s l i g h t l y above average va lues, and probab ly a r e the values t h a t should
be used i n des ign when moderate ly c o n s e r v a t i v e es t imates a r e made o f the
o t h e r parameters e n t e r i n g i n t o the des ign c r i t e r i a . A recent d e t a i l e d
s tudy o f damping has been completed as a p a r t o f t h e D i a b l o Canyon U n i t s
1 and 2 Review (Amendment 50) and should be considered a long w i t h o t h e r da ta
when s e t t i n g up rev iew c r i t e r i a .
5 .3 D u c t i l i t y
Energy a b s o r p t i o n i n t h e
through use of t h e s o - c a l l e d " d u c t i
the r a t i p o f t h e maximum u s e f u l ( o r
n e l a s t i c range i s commonly handled
i t y fac to r " . The d u c t i l i t y f a c t o r i s
design) displacement o f a s t r u c t u r e t o
the ' ' e f f e c t i v e " e l a s t i c l i m i t d isplacement, t h e l a t t e r be ing determined no t
from t h e a c t u a l res is tance-d isp lacement curve b u t from an e q u i v a l e n t e l a s t o -
p l a s t i c f u n c t i o n . T h i s equiva lence r e q u i r e s t h a t the energy absorbed i n
same
d i s p
duc t
D u c t i l i t y l e v e l s
as 1.0 t o 1.3, or n e a r l y e
energy can be absorbed i n
s i n i i
Refs
the s t r u c t u r e ( o r area under t h e res is tance-d isp lacement curve) a t the
e f f e c t i v e e l a s t i c l i m i t and a t t h e maximum u s e f u l d isplacement must be t h e
f o r t h e e f f e c t i v e curve as f o r t h e a c t u a l r e l a t i o n s h i p a t these two
acements. For t h e system shown i n F ig . 1 , t h e d e f i n i t i o n o f the
l i t y f a c t o r , v , i s shown i n F i g . 2 .
f o r use i n normal des ign may range from as l o w
a s t i c , t o more than 5, when a g r e a t deal o f
n e l a s t i c deformat ion. I t i s expected t h a t
a r va lues should be a p p l i c a b l e i n t h e rev iew design process.
D u c t i l i t y l e v e l s for use i n des ign a r e discussed i n d e t a i l i n
16 and 17, and i n c o s i d e r a b l e d e t a i l i n Sec t ion 7 of t h i s r e p o r t .
20
V I . METHODS OF DYNAMIC ANALYSIS
ana 1 ys
Refs.
graphi
6.1 Response Spectrum
The concepts o f t h e response spectrum and i t s use i n dynamic
s a r e discussed i n d e t a i l i n many books and a r t i c l e s , i n c l u d i n g
7 through 20, and 22. The response spectrumsis d e f i n e d as a
a1 r e l a t i o n s h i p o f maximum response o f a s ingle-degree-of- f reedom
e l a s t i c system w i t h damping t o dynamic mot ion (or f o r c e s ) .
measures o f response a r e maximum displacement, D, which i s a measure o f t h e
s t r a i n i n t h e s p r i n g element o f t h e system, maximum pseudo r e l a t i v e v e l o c i t y ,
V, which i s a measure o f t h e energy a b s o r p t i o n i n t h e s p r i n g o f t h e system,
and maximum pseudo a c c e l e r a t i o n , A, which i s a measure o f t h e maximum f o r c e
The most usual
e a r t h -
a t r a p e z o i d
o g a r i thmic
spectrum
i n t h e s p r i n g o f t h e system. Al though a c t u a l response spec t ra fo
quake mot ions a r e q u i t e i r r e g u l a r , they have t h e genera l shape of
o r t e n t : a s i m p l i f i e d spectrum i s shown i n F ig . 3 , p l o t t e d on a
t r i p a r t i t e graph, and m o d i f i e d so t h a t t h e v a r i o u s reg ions of t h e
a r e smoothed to s t r a i g h t l i n e p o r t i o n s . On t h e same graph a r e shown t h e
maximum ground mot ion components, and t h e f i g u r e t h e r e f o r e i n d i c a t e s the
a m p l i f i c a t i o n s o f maximum ground mot ions fo r t h e v a r i o u s p a r t s o f the
spectrum.
A t any f requency, f , t h e r e l a t i o n s between the va lues o f D f , V f ,
and Af a r e d e f i n e d as f o l l o w s :
( 3 )
(4 )
V f = w D f
2 Af = w V f = w Df
where w i s t h e c i r c u l a r n a t u r a l f requency, 21'rf.
21
Let us now consider the case in which the simple oscillator of
Fig. 1 deforms inelastically as in Fig. 2. It is convenient to use an
elasto-plastic resistance displacement relation because one can draw
response spectra for such a relation in generally the same way as spectra
are drawn for elastic conditions.
of spectra corresponding to the elastic spectrum of Fig. 3 . Here the
symbols D, V, A refer to the bounds of the elastic spectrum, the symbols
D ' , V I , A' to the bounds of the elasto-plastic spectrum for acceleration,
and the symbols D, V, A", A: to the bounds for the elasto-plastic spectrum
for displacement.
The method of constructing the inelastic spectra is described later in
this report.
In Fig. 4 there are shown the two types
The symbol A. refers to the maximum ground acceleration.
- 6.2 Use of Response Spectra for Multi-Degree-of-Freedom Systems -- Model Analysis
For multi-degree-of-freedom systems, the concept of the response
spectrum can also be used in most cases, although the use o f the inelastic
response spectrum is only approximately valid as a design procedure. For
a system with a number of masses at nodes in a flexible framework, the
equation of motion can be written in matrix form as follows:
MU + CG + KU = -M(Y){lI ( 5 )
where the quality in brackets represents a unit vector. The mass matrix M
is usually diagonal, but in all cases both M and the stiffness matrix K
are symmetrical. When the damping matrix C satisfies certain conditions,
the simplest of which
the systems has norma
u . n
is when it is a linear combination of M and K, then
modes of vibration, with modal displacement vectors
22
When t h e modes and f requencies o f t h e system a r e obta ined, t h e
modal responses a r e determined f o r each mode c o n s i d e r i n g t h e " p a r t i c i p a t i o n "
f a c t o r s , c f o r each mode t o be d e f i n e d as f o l l o w s : n '
u ' n M(1 ) c = n T
n u M un
I f t h e p a r t i c u l a r q u a n t i t y d e s i r e d -- say t h e s t r e s s a t a p a r t i c u l a r
p o i n t , t h e r e l a t i v e displacement between t w o re fe rence p o i n t s , o r any o t h e r
e f f e c t -- i s des ignated by a , then t h e modal va lues o f an a r e determined f o r
each mode and combined by use o f the r e l a t i o n s :
< C cnanDn amax - n I 1
a prob
(7)
For i n e l a s t i c response, t h e q u a n t i t i e s t o be used a r e DA, V A , o r
A ' f rom c a l c u l a t i o n s such as those lead ing t o F i g . 4 . Equat ion (7 ) g i v e s
an upper bound t o t h e v a l u e o f a , and Eq. (8) t h e most p robab le o r expected
value.
n
6.3 Time H i s t o r y A n a l y s i s
A l t e r n a t i v e l y one may make a c a l c u l a t i o n of response by c o n s i d e r i n g
t h e mot ions t o be a p p l i e d and t h e responses computed us ing a s tep-by-step
numer ica l dynamic a n a l y s i s . T h i s i m p l i e s a d e t e r m i n i s t i c approach s i n c e a
d e t e r m i n i s t i c t ime h i s t o r y i s invo lved. By use o f severa l t ime h i s t o r i e s
independent ly considered, one can a r r i v e a t average or c o n s e r v a t i v e upper
bounds o f response, a t t h e expense o f a cons iderab ly increased amount o f
23
c a l c u l a t i o n . I n genera l , however, t h e r e i s no r e a l advantage i n us ing a
t ime h i s t o r y as compared w i t h a response spectrum approach f o r mu l t i -degree-
o f - f reedom systems, un less one i s faced w i t h an a c t u a l d e t e r m i n i s t i c i n p u t .
Another form o f t i m e h i s t o r y a n a l y s i s sometimes employed i n v o l v e s
modal a n a l y s i s concepts i n t h e sense o f i d e n t i f y i n g the e igenvec tors and
e igenvalues, e x c i t i n g each o f t h e s i g n i f i c a n t modes by t h e t i m e h i s t o r y and
summing t h e weighted modal va lues o f s t r e s s , d isplacement, e t c . as a f u n c t i o n
o f t ime. T h i s method i s cumbersome, o b v i o u s l y must make use o f a computer
because o f t h e e x t e n s i v e c a l c u l a t i o n s requ i red , and i s n o t used w i d e l y .
I t has been common t o use t ime h i s t o r y a n a l y s i s techniques t o
generate f l o o r response spec t ra , e s p e c i a l l y a t upper f l o o r l o c a t i o n s i n
n u c l e a r power p l a n t s . Techniques c u r r e n t l y e x i s t f o r e s t i m a t i n g the peak
va lues o f response a t such l o c a t i o n s (Ref. 23) and a d d i t i o n a l research
s t u d i e s c u r r e n t l y underway a t t h e U n i v e r s i t y o f I l l i n o i s a r e intended t o
lead t o improved techniques f o r e s t i m a t i n g f l o o r response spec t ra by
employing modal a n a l y s i s w i t h response spectrum techniques. I n any case
t h e hand l ing o f f l o o r response a t m u l t i p l e at tachment l o c a t i o n s , by whatever
technique, i s ext remely d i f f i c u l t and r e q u i r e s e x e r c i s e o f .judgment; i n such
cases one p r i n c i p a l concern i s t h a t o f adequate ly p r o v i d i n g for r e l a t i v e
displacement.
V
24
V I E W ANALYSIS AN
7 .1 General Considerat ions
D E S I G N PROCEDURES
I n under tak ing rev iew se ismic analyses o f an e x i s t i n g nuc lear
p l a n t , p repara tory t o c a r r y i n g o u t upgrade des ign s t u d i e s , i t i s assumed
t h a t t h e general approach o u t l i n e d i n Sec t ion 1 o f t h i s r e p o r t would be
fo l lowed. As a p a r t o f t h e rev iew process i t i s impor tant t o a s c e r t a i n t h e
nominal p r o p e r t i e s o f t h e m a t e r i a l s i n t h e elements under c o n s i d e r a t i o n ; i n
some cases i t may be necessary t o c a r r y o u t t e s t s to determine these proper-
t i e s , e s p e c i a l l y i f aging, c o r r o s i o n o r o t h e r e f f e c t s cou ld have a f f e c t e d
t h e p r o p e r t i e s .
The load combinat ions t h a t should be considered i n the rev iew
should be those for which t h e upgrade i s to be made, and should i n c l u d e
c o n s i d e r a t i o n of c u r r e n t Nuclear Regulatory Commission g u i d e l i n e s .
I n o t h e r respects i t i s assumed t h a t t h e general load ings and s a f e t y
p r o v i s i o n s o f t h e c u r r e n t NRC standards would app ly w i t h i n t h e framework
o f t h e procedures and c r i t e r i a g i v e n i n t h i s r e p o r t .
7.2 M o d i f i e d Response Spectra
M o d i f i e d response spec t ra represent ing average ( o r some probabi 1 i t y
above the mean) c o n d i t i o n s f o r earthquake mot ions a r e discussed i n v a r i o u s
books and papers, i n c l u d i n g Refs. 16-23. I n genera l i t . h a s been shown t h a t
a response spectrum for a p a r t i c u l a r cumula t ive p r o b a b i l i t y l e v e l can be
d e r i v e d from s t a t i s t i c a l s t u d i e s o f a c t u a l earthquakes, most c o n v e n i e n t l y
as a s e t o f a m p l i f i c a t i o n f a c t o r s a p p l i e d t o the maximum components o f
ground mot ion, as i m p l i e d i n F i g . 3. The p r o b a b i l i t y f u n c t i o n which bes t
descr ibes t h e range o f va lues i s one t h a t corresponds t o a l o g a r i t h m i c
25
for
one
Tab
0.5
a r e
normal d i s t r i b u t i o n . The a m p l i f i c a t i o n f a c t o r s a r e f u n c t i o n s o f
Equat ions f o r t h e a m p l i f i c a t i o n f a c t o r s fo ' r t h e l o g normal d i s t r
b o t h t h e median o r 50 p e r c e n t i l e cumula t ive p r o b a b i l i t y l e v e
Sigma o r 84. percent cumula t ive p r o b a b i l i t y l e v e l , a r e shown i n
e 2. S p e c i f c numerical va lues f o r a range o f damping va lues from
percent c r i t c a l t o 20 percent c r i t i c a l f o r t h e t w o p r o b a b i l i t y l e v e
t a b u l a t e d s e p a r a t e l y i n Tab le 3 f o r a c c e l e r a t i o n , v e l o c i t y , and
displacement s e n s i t i v e reg ions o f t h e response spectrum as shown i n
F i g . 3 .
damping . b u t ion,
and t h e
S
I n de termin ing the ground mot ions fo r use w i t h F i g . 3, i t i s
recommended t h a t , l a c k i n g o t h e r i n f o r m a t i o n , for competent s o i l c o n d i t i o n s
a v/a r a t i o o f 48 in /sec/g be used and f o r rock a v/a r a t i o o f 36 in /sec/g
be used. Also t o ensure t h a t the spectrum represents an adequate band
( f requency) w i d t h to accommodate a p o s s i b l e range o f earthquakes i t i s
recommended t h a t ad/v be taken equal t o about 6.0. I n t h e above a, v and
d a r e t h e m a x i m u m va lues of ground mot ion ( a c c e l e r a t i o n ( i n / s e c ) , v e l o c i t y
( i n / s e c ) , and displacement ( i n ) , r e s p e c t i v e l y ) .
2
2
With
smoothed e l a s t
a g i v e n probab
these va lues one can.de termine f o r a g i v e n earthquake the
c response spectrum fo r a p a r t i c u l a r va lue o f damping and
I i t y l e v e l .
7 . 3 E f f e c t s o f S i z e and Weight o f S t r u c t u r e
There i s a good b a s i s for r e c o g n i z i n g t h a t a l a r g e and heavy
s t r u c t u r e responds t o mot ions i n t h e s o i l o r rock s u p p o r t i n g i t i n a
manner d i f f e r e n t f rom t h a t o f a l i g h t and smal l suppor t f o r a r e c o r d i n g
accelerometer . Crude a n a l y t i c a l s t u d i e s suggest t h a t h i g h f requency
26
mot ions a r e n o t t r a n s m i t t e d as e f f e c t i v e l y t o t h e f o u n d a t i o n o f a s t r u c t u r e ,
and t h e r e f o r e to the s t r u c t u r e i t s e l f , as lower f requency mot ions. Th is may
be ascr ibed t o severa l f a c t o r s , t h e most impor tant o f which a r e probably t h e
f a c t s t h a t : (1) t h e earthquake mot ion i s a wave mot ion, t h e h igher f requency
components o f which may be s h o r t e r than t h e l e n g t h o r w i d t h o f the responding
s t r u c t u r e ; and ( 2 ) t h e r e i s a l o s s o f energy i n t h e h i g h frequency range, n o t
accounted f o r i n t h e a n a l y s i s , t h a t comes from p o s s i b l e r e l a t i v e mot ions
between t h e base and t h e foundat ion. These observa t ions a r e cor robora ted
by the response o f t h e Hollywood Park ing L o t and t h e Hollywood Storage
B u i l d i n g i n Los Angeles, which a r e ad jacent t o one another , i n which i n the
f i r s t case t h e inst rument i s mounted i n the s o - c a l l e d " f r e e f i e l d " and t h e
o t h e r i n t h e basement o f t h e s t r u c t u r e . The Response Spectra and t h e
F o u r i e r Spectra a r e p r a c t i c a l l y i d e n t i c a l for f requencies lower than about
1 t o 2 h e r t z , bu t d i f f e r markedly, by as much as a f a c t o r o f 2 t o 3, f o r
f requenc ies h i g h e r than about 3 t o 4 h e r t z .
For these reasons, i t i s cons idered t h a t h i g h i n t e n s i t y earthquake
mot ions, and e s p e c i a l l y those a r i s i n g f rom near f i e l d sources, have much
l e s s i n f l u e n c e on s t r u c t u r a l response and damage produced by t h i s response
than do earthquakes hav ing a more d i s t a n t source, where t h e major mot ions
a r e i n f requency ranges t o which t h e s t r u c t u r e can respond e f f e c t i v e l y as
a u n i t . T h i s i s a j u s t i f i c a t i o n t h a t i s o f t e n used f o r d i s c o u n t i n g h i g h
i n t e n s i t i e s o f a c c e l e r a t i o n t h a t a r e measured o r i n f e r r e d , as compared
w i t h those used i n the development o f des ign spect ra. I t i s our b e l i e f
t h a t t h i s type o f s o i l - s t r u c t u r e i n t e r a c t i o n should be taken i n t o account
i n a r r i v i n g a t des ign spec t ra for f a c i l i t i e s w i t h l a r g e foundat ions, as
for example nuc lear p l a n t s . Procedures f o r making such m o d i f i c a t i o n s a r e
27
a v a i l a b l e i n the l i t e r a t u r e ( f o r example, Refs. 24 and 25) .
7 .4 E f f e c t s o f I n e l a s t i c A c t i o n
The e f f e c t s on the response o f a s t r u c t u r e deforming i n t o t h e
i n e l a s t i c range have been descr ibed and/or summarized i n Refs. 16 through 22.
I n genera l , f o r smal l excurs ions i n t o t h e i n e l a s t i c range, when the l a t t e r
i s cons idered t o be approximated by an e l a s t o - p l a s t i c r e s i s t a n c e curve,
t h e response spectrum i s decreased g e n e r a l l y by a f a c t o r which i s one over
t h e d u c t i l i t y f a c t o r . I f t h e d u c t i l i t y f a c t o r i s d e f i n e d by t h e symbol 1-1
then the r e d u c t i o n f o r t h e two l e f t - h a n d p o r t i o n s o f t h e e l a s t i c response
spectrum shown i n F igs . 3 and 4 ( t o t h e l e f t o f t h e frequency o f about 2
h e r t z ) i s reduced by the f a c t o r 1/11 f o r a c c e l e r a t i o n , and by the f a c t o r o f
l/m i n the cons tan t a c c e l e r a t i o n p o r t i o n t o t h e r i g h t , rough ly between
f requencies o f 2 and 8 hertz.. There i s no r e d u c t i o n beyond about 33 h e r t z .
Wi th t h i s concept, one can a r r i v e a t des ign spec t ra t h a t take account o f
ine1as. t ic a c t i o n even i n t h e smal l range o f i n e l a s t i c behav io r .
7 .5 Seismic Design C l a s s i f i c a t i o n
Because o f the major i n f l u e n c e t h a t the d u c t i l i t y f a c t o r has on
t h e des ign spectrum, some guidance i s needed w i t h regard t o t h e a p p r o p r i a t e
cho ice o f d u c t i l i t y f a c t o r s t o be used even f o r v i t a l elements and components
i n a nuc lear r e a c t o r f a c i l i t y . Observat ions o f t h e performance o f s t r u c t u r e s
i n earthquakes, i n t e r p r e t a t i o n o f l a b o r a t o r y t e s t s , i n c l u d i n g those on
earthquake s i m u l a t o r s and shake t a b l e s , observa t ions o f damage t o s t r u c t u r e s
28
and s t r u c
one may
I , and
r e a c t 0 r
cons i de
J r a l models i n nuc lear s, i n c l u d i n g damage b o t h from a i r b l a s t
and ground shock, as w e l l as system s a f e t y , a l l a r e p e r t i n e n t f a c t o r s i n
a r r i v i n g a t a judgment as t o t h e a p p r o p r i a t e d u c t i l i t y f a c t o r t o be used
i n rev iew analyses and upgrade design.
I n o r d e r to p r o v i d e guidance, t a k i n g i n t o account the f a c t o r s
descr ibed above, a se ismic des ign c l a s s i f i c a t i o n i s suggested i n Table 4.
I t invo lves a d e s i g n a t i o n o f t h e se ismic des ign c l a s s and a d e s c r i p t i o n o f
those i tems t h a t should be assigned t o t h a t c l a s s . For each c l a s s , a range
o f d u c t i l i t y f a c t o r s i s g iven . Obvious ly a p p r o p r i a t e damping va lues a l s o
must be chosen f o r use i n e v a l u a t i n g t h e se ismic adequacy o f t h e systems
under s tudy. I t i s b e l i e v e d t h a t even t h e upper l i m i t o f t h e range shown
i n Table 4 would be adequate ly c o n s e r v a t i v e f o r a l l i tems i n t h e c l a s s , b u t
choose, f o r g r e a t e r conservat ism, t o use a lower va lue. Classes I - S ,
I might be considered as a p p l i c a b l e t o v a r i o u s types o f nuc lear
elements, components, o r f a c i l i t i e s ; Class I l l would g e n e r a l l y be
ed t o f a l l i n t o t h e range o f o r d i n a r y s t r u c t u r e s which can be
designed by c u r r e n t o r proposed somewhat m o d i f i e d se ismic des ign s p e c i f i -
c a t i o n s and codes used f o r b u i l d i n g s .
7.6 Design Spectra
Using the concepts descr ibed above, t h e des ign spectrum for
earthquake mot ions can be drawn as shown h e r e i n i n F ig . 4 g e n e r a l l y . The
response spectrum i n d i c a t e d by the l i n e DVAA i n F ig . 4 i s t h e e l a s t i c
response spectrum obta ined from F ig . 3 , us ing t h e p r o b a b i l i t y l e v e l s ,
0
damp i ng
e x c i t a t
va lues and ampl i
on and s t r u c t u r a
i c a t i o n f a c t o r s , a p p r o p r i a t e t o t h e p a r t i c u l a r
component. From t h i s , by use o f t h e d u c t i l i t y
29
reduc t ions descr ibed i n Sec t ion 7.5, one o b t a i n s t h e des ign spectrum f o r
a c c e l e r a t i o n o r f o r c e by the curve D ' V ' A ' A and f o r displacement by t h e
curve DVAI'A;, which represents t h e t o t a l d isplacement and n o t the e l a s t i c
0 '
component o f d isplacement, f o r t h e e l a s t o -
s p e c i f i c example o f the des ign spectrum wh
descr ibed i n t h e r e p o r t , f o r a peak ground
5 percent o f c r i t i c a l damping and a d u c t i l
F ig . 5.
l a s t i c r e s i s t a n c e curve. A
ch inc ludes a l l of the quant
a c c e l e r a t i o n o f about 0.16 g
t y f a c t o r o f 3 i s presented
t i e s
n
7.7 Combined E f f e c t s o f H o r i z o n t a l and V e r t i c a l E x c i t a t i o n
I n t h e r e a l w o r l d , earthquake mot ions occur as random mot ions i n
h o r i z o n t a l and v e r t i c a l d i r e c t i o n s . I n o t h e r words, a s t r u c t u r e i s sub jec ted
t o components o f mot ion i n each o f two perpend icu la r h o r i z o n t a l d i r e c t i o n s
and t h e v e r t i c a l d i r e c t i o n , and one might a l s o cons ider t h r e e components o f
r o t a t i o n a l mot ion corresponding t o a foundat ion t w i s t about a v e r t i c a l a x i s
and t w o r o c k i n g mot ions about the h o r i z o n t a l axes. These ground mot ions
have, apparent ly , s t a t i s t i c a l independence. Consequently, i f one uses t ime
h i s t o r i e s o f mot ion one must e i t h e r use a c t u a l earthquake records o r mod i fy
them i n such a way as t o m a i n t a i n t h e same degree o f n e a r l y s t a t i s t i c a l
independence as i n a c t u a l records. Consequently, for t ime h i s t o r i e s t h a t
i n v o l v e i n e l a s t i c behavior , i t i s an o v e r s i m p l i f i c a t i o n t o consider each o f
t h e components o f mot ion independent ly s i n c e they a l l occur a t t h e same t ime
i n genera l . However, t h e r e i s o n l y a smal l p r o b a b i l i t y of t h e maximum
responses o c c u r r i n g s imu l taneous ly and methods have been d e r i v e d f o r h a n d l i n g
problems such as t h i s as descr ibed
For des ign one must cons
v a r i o u s d i r e c t i o n s . A l though t h i s
n e x t . d e r t h e combined e f f e c t s of mot ion i n
can be done i n v a r i o u s ways depending 4
30
the squares o f t h e i n d i v i d u a l e f f e c t s f o r s t r e s s o r mot ion a t
p o i n t i n a p a r t i c u l a r d i r e c t i o n f o r the v a r i o u s components o f
considered. I t i s conserva t ive , s imp ler , and much more read i
and c a l c u l a t e d t o take t h e combined e f f e c t s as 100 percent o f
upon the method o f a n a l y s i s used, i t i s reasonable t o use t h e response
spectrum approach even f o r the mul t i -degree-of - f reedom systems, t o a r r i v e
s e p a r a t e l y a t t h e responses i n t h e i n d i v i d u a l d i r e c t i o n s , and then t o
combine t h e e f f e c t s i n genera l by t a k i n g t h e square r o o t o f the sums o f
a p a r t i c u l a r
mot i o n
y de f ined
the e f f e c t s
on and 40 percent o f the e f f e c t s
mot ion a t r i g h t angles t o the
s combinat ion t h a t i s recommended
power p l a n t des ign.
due t o mot ion i n one p a r t i c u l a r d i r e c t
corresponding t o t h e two d i r e c t i o n s o f
p r i n c i p a l mot ion considered. I t i s t h
for genera l use, e s p e c i a l l y i n nuc lear
7.8 Unsymmetrical S t r u c t u r e s , Tors ion , Over tu rn ing and U p l i f t
Cons idera t ion should be g i v e n t o the e f f e c t s o f t o r s i o n on
unsymmetrical s t r u c t u r e s , and even on symmetr ical s t r u c t u r e s where t o r s i o n
may a r i s e a c c i d e n t a l l y , because o f v a r i o u s reasons, i n c l u d i n g l a c k o f
homogeneity o f t h e s t r u c t u r e s , o r t h e wave mot ions developed i n earthquakes.
So-ca l led " c a l c u l a t e d " t o r s i o n i n the s t r u c t u r e proper a r i s i n g
f r o m noncoinc ident centers o f mass and r i g i d i t y should be handled i n t h e
customary manner. The a c c i d e n t a l e c c e n t r i c i t i e s o f t h e h o r i z o n t a l f o r c e s
p r e s c r i b e d by c u r r e n t codes r e q u i r e t h a t 5 percent of t h e w i d t h o f the
s t r u c t u r e i n t h e d i r e c t i o n o f the earthquake mot ion considered be used
as an a c c i d e n t a l e c c e n t r i c i t y . The s t resses a r i s i n g from the a c t u a l
e c c e n t r i c i t y should be combined w i t h those a r i s i n g f rom t h e a c c i d e n t a l
e c c e n t r i c i t y i n a l l cases. The e f f e c t of e c c e n t r i c i t y i s t o produce
31
a g r e a t e r s t r e s s on one s i d e of t h e s t r u c t u r e than on t h e o t h e r , and t h e
o u t e r w a l l s and columns w i l l i n genera l be sub jec ted t o l a r g e r deformat ions
and f o r c e s than would be t h e case i f the s t r u c t u r e were considered to
deform u n i f o r m l y
Recent
mot ion have been
n o t c l e a r a t t h i s
wave i s j u s t i f i a b
t o values which a
y new techniques f o r e s t i m a t i n g t o r s i o n a r i s i n g f rom ground
s t u d i e d and repor ted i n t h e l i t e r a t u r e (Ref. 25) b u t i t i s
moment t h a t such t reatment i n v o l v i n g a sys temat ic p lane
e; i n some cases, e s p e c i a l l y i n l a r g e b u i l d i n g s , i t leads
e h i g h e r than appear reasonable. I n the i n t e r i m i t i s our
recommendation t h a t c u r r e n t code p r o v i s i o n s f o r "accidenta1" t o r s i o n be
emp 1 oyed . I n e s t i m a t i n g o v e r t u r n i n g e f f e c t s one commonly computes the shears
and moments throughout the s t r u c t u r e and computes the " o v e r t u r n i n g 1 ' moment
a t each e l e v a t i o n and a t t h e base. These moment fo rces g i v e r i s e t o tens ions
and compressions i n t h e columns and w a l l s o f the s t r u c t u r e , and cause t i l t i n g
o f the base c o n s i s t e n t w i t h t h e foundat ion compliance. I n some cases t h i s
t i l t i n g can lead t o p a r t i a l u p l i f t on one edge o f the base and can lead t o
o v e r l o a d i n g o f t h e foundat ion m a t e r i a l s .
7.9 Response o f Equipment and Attachments
Many impor tant p a r t s o f a nuc lear power p l a n t f a c i l i t y a r e a t tached
t o t h e p r i n c i p a l p a r t s o f t h e s t r u c t u r e and respond i n a manner determined
by t h e s t r u c t u r a l response r a t h e r than by t h e genera l ground mot ion t o which
t h e s t r u c t u r e i s subjected. T h i s m a t t e r i n v o l v e s a good deal o f d i f f i c u l t y
i n a n a l y s i s , b u t a p p r o p r i a t e c a l c u l a t i o n a l techniques a r e a v a i l a b l e . Some o f
32
these a r e descr ibed i n Ref. 23, where a s u i t a b l e des ign s i m p l i f i c a t i o n i s
invo lved i n which t h e response o f t h e at tachment i s r e l a t e d t o t h e modal
response o f t h e s t r u c t u r e . T h i s response i s a f f e c t e d by t h e r e l a t i v e mass
of t h e at tachment and t h e s t r u c t u r e . Where t h i s r e l a t i v e mass i s i n f i n i -
t e s i m a l , t h e response i s a f f e c t e d p r i m a r i l y by t h e damping o f the s t r u c t u r e
and t h e equipment, b u t as t h e r e l a t i v e mass becomes f i n i t e , even though
smal l , an e f f e c t i v e r e l a t i v e damping i s invo lved which i s r e l a t e d t o the
square r o o t o f t h e equipment t o s t r u c t u r e e f f e c t i v e mass r a t i o .
The s t u d i e s r e p o r t e d i n Ref. 23, and more recent unpubl ished
research, i n d i c a t e t h a t i n general t h e maximum response o f a l i g h t equipment
mass a t tached to a s t r u c t u r e , even when the equipment mass i s tuned t o the
same frequency as t h e s t r u c t u r e , w i l l n o t exceed t h e b a s i c response spectrum
to which t h e s t r u c t u r e responds m u l t i p l i e d by an a m p l i f i c a t i o n f a c t o r , AF,
d e f i n e d c o n s e r v a t i v e l y as f o l l o w s :
1 AF = (9) 8, + Bs + s;
i n which
8 = p r o p o r t i o n o f c r i t i c a l damping for equipment
= p r o p o r t i o n o f c r i t i c a l damping f o r s t r u c t u r e
e
8, y = r a t i o o f genera l i zed mass of equipment t o genera l i zed mass o f
s t r u c t u r e , when t h e mode displacement vec tors for bo th the
equipment and s t r u c t u r e a r e taken so as t o have u n i t p a r t i c i p a -
t i o n f a c t o r s , d e f i n e d by use of Eq. (6)
- The g e n e r a l i z e d mass f o r t h e n t h mode, Mn, i s d e f i n e d f o r e i t h e r
t h e equipment or t h e s t r u c t u r e as:
33
T n n -
'n M = u
i n which M i s t h e mass m a t r i x and u the modal displacement v e c t o r ( f o r n
e i t h e r t h e equipment or t h e s t r u c t u r e ) normal ized t o a u n i t p a r t i c i p a t i o n
f a c t o r f o r e i t h e r system a lone.
I t i s t o be noted t h a t even a mass r a t i o f o r equipment t o s t r u c t u r e
o f 0.0001 corresponds t o an e q u i v a l e n t added damping f a c t o r o f 0.01 o r 1
percent and a mass r a t i o o f 0.001 to an added f a c t o r o f about 3.2 percent .
As descr ibed e a r l i e r i n t h i s r e p o r t , a commonly employed technique
f o r hand l ing equipment response i s t h a t o f t h e s o - c a l l e d f loor - response o r
i n - s t r u c t u r e response spectrum. The use o f t h i s technique invo lves cons iderab le
judgment i n assess ing the reasonableness o f t h e peak response va lues and t h e
frequency bandwidth o f a p p l i c a b i l i t y .
troublesome t o handle, i r r e s p e c t i v e o f t h e technique employed.
M u l t i p l e connect ions a r e even more
I n any event , however t h e mot ions a r e est imated, t h e a n a l y s t o r
des igner must pay p a r t i c u l a r a t t e n t i o n t o t ie-down d e t a i l s and t o connect ing
elements which can undergo or must s u s t a i n r e l a t i v e mot ion.
34
V I I I . SPECIAL TOPICS
8.1 F a u l t Mot ions
Major f a u l t mot ions may occur i n l a r g e magnitude earthquakes o f
t h e o r d e r o f as much a s 6 t o 8 meters i n r e l a t i v e mot ion between the two
s ides o f t h e f a u l t . Such mot ions a r e v i r t u a l l y imposs ib le t o design a g a i n s t .
However, smal l f a u l t mot ions o r mot ions across s u b s i d i a r y f a u l t s , o r f a u l t
mot ions f o r smal l magnitude earthquakes, may range f rom a few cent imeters
t o a meter o r so. For these i t i s p o s s i b l e t o p r o v i d e r e s i s t a n c e t o the
r e l a t i v e mot ions by some means o f i s o l a t i o n o f t h e s t r u c t u r e . Some methods
o f do ing t h i s were descr ibed i n Ref. 18. More recent s t u d i e s and recommenda-
t i o n s p e r t a i n i n g t o p i p e l i n e s and o t h e r b u r i e d f a c i l i t i e s a r e g i v e n i n
Refs. 26 and 27.
8.2 R e l a t i v e Mot ions
R e l a t i v e mot ions between d i f f e r e n t p a r t s o f a f a c i l i t y o r between
d i f f e r e n t elements i n a s t r u c r u r e o f t e n have t o be considered i n des ign .
Because o f t h e f a c t t h a t elements and separate i tems may respond i n such a
way t h a t , even though they have t h e same p e r i o d o f v i b r a t i o n and the same
general response c h a r a c t e r i s t i c s , they may become o u t o f phase i n t h e i r
mot ions, t h e des ign r e l a t i v e mot ion g e n e r a l l y has t o be taken as the sum o f
the a b s o l u t e values o f t h e maximum mot ions o f the two components invo lved.
More d e t a i l s on t h i s t o p i c a r e conta ined i n Ref. 23.
Another o b s e r v a t i o n o f i n t e r e s t i n t h i s connect ion i s t h a t for
some elements undergoing r e s t r i c t e d mot ion, as f o r example
i t i s p o s s i b l e under c e r t a i n c i rcumstances t h a t t h e r e l a t
s t r e s s i n g may be "secondary" i n charac ter as opposed t o a
b u r i e d p i p i n g ,
ve se ismic mot ion
"primary", w i t h
35
t h e terms "secondary" and "pr imary1' r e f e r r i n g to d e f i n i t i o n s as g iven i n
c u r r e n t codes. T h i s m a t t e r deserves f u r t h e r s tudy.
8.3 Underground Conduits and P i p i n g
Impor tant components o f nuc lear r e a c t o r s o f t e n i n v o l v e underground
tunne ls o r o t h e r c o n d u i t s and p i p i n g . I n genera l these may have t o deform
i n a manner c o n s i s t e n t w i t h t h e de format ion o r s t r a i n s i n t h e s o i l o r rock
medium i t s e l f , and do n o t respond i n a way a n t i c i p a t e d by t h e s o - c a l l e d
response spectrum approach o r o t h e r s t r u c t u r a l a n a l y s i s approach. Methods
o f hand l ing t h i s problem a r e descr ibed i n some d e t a i l i n Refs. 23, 26 and
27 and have been used as des ign c r i t e r i a f o r underground p i p i n g systems.
I n t h a t re fe rence, based on the assumption t h a t over s h o r t
d is tances t h e earthquake mot ions propagate as a wave w i t h a v e l o c i t y o f
t ransmiss ion c, i t was shown t t i a t t h e maximum l o n g i t u d i n a l s t r a i n E i n a
b u r i e d c o n d u i t o r p ipe , except near a s u r f a c e break o r f a u l t , i s g i v e n by
m
t h e r e l a t i o n s :
For "compression waves" i n t h e ground
Em = vm/c P
and f o r "shear, waves"
E = Vm/2Cs rn
i n wh i c h
= maximum ground v e l o c i t y "m
c = compression wave t ransmiss ion v e l o c i t y i n medium
c = shear wave t ransmiss ion v e l o c i t y i n medium
However, t h e va lues o f c and c should n o t be taken as t h e very sma
P
S
P S 1 va lues
36
t h a t might occur near t h e sur face i n s o f t s o i l , because t h e wave t ransmiss ion
v e l o c i t y i s a f f e c t e d p r i m a r i l y by the s t i f f e r deep s t r a t a .
The s t r a i n s i n a p i p e due t o changes i n c u r v a t u r e i n the ground
a r e discussed i n Refs. 23, 26 and 27. They a r e g e n e r a l l y smal l enough t o be
neg 1 ec ted .
8.4 Tanks and V a u l t s
Ana lys is and des ign procedures f o r aboveground tanks and vau
have been based over t h e years p r i m a r i l y on t h e work by Housner, espec
as summarized i n Ref. 28. These procedures have prov ided a reasonably
t s
a1 l y
s a t i s f a c t o r y b a s i s f o r des ign over t h e years. More r e c e n t l y severa l major
s t u d i e s have been underway, p a r t i c u l a r l y w i t h re fe rence t o pet ro leum s torage
f a c i l i t i e s ; t h e s t u d i e s noted a r e those i n v o l v i n g exper imenta l t e s t i n g as
w e l l as a n a l y s i s under t h e d i r e c t i o n of R. Clough a t t h e U n i v e r s i t y o f
C a l i f o r n i a a t Berke ley and t h e o r e t i c a l s t u d i e s by A . S . Ve letsos a t R ice
U n i v e r s i t y i n Houston. I t i s expected t h a t these s t u d i e s w i l l lead t o new
g u i d e l i n e s f o r tank des ign i n the near f u t u r e .
f o r tanks a r e now f a i r l y standard and would need rev iew as would connect ing
p i p i n g .
The anchorage requirements
I n t h e case o f b u r i e d tanks o r v a u l t s t h e problems a r e s l i g h t l y
d i f f e r e n t i n t h a t t h e tanks w i l l move and deform w i t h t h e ground as a
f u n c t i o n o f t h e compl iance between t h e tank and ground. Again i t i s an
i n t e r a c t i o n problem. To some degree bu t n o t e n t i r e l y , the s t r a i n i n a tank
o r v a u l t can be i n f e r r e d f rom the s t r a i n s i n t h e ground (See Sect ion 8 . 3 ) .
O f p a r t i c u l a r concern i n rev iew o f e x i s t i n g p l a n t s would be tanks b u r i e d
f o r some p e r i o d o f t i m e where c o r r o s i o n or o t h e r ag ing e f f e c t s cou ld degrade
37
the p r o p e r t i e s o f the tank m a t e r i a l s w i t h respec t t o t h e i r a b i l i t y
w i ths tand se ismic mot ion w i t h o u t leak ing .
8 .5 Equipment Q u a l i f i c a t i o n
0
An impor tan t element o f t he rev iew o f e x i s t i n g nuclear f a c i l i t i e s
invo lve[ , the se ismic adequacy o f t he c r i t i c a l c o n t r o l s and equipment. Th i s
i s art area i n which improved techniques and p r a c t i c e s have been developed
w i t h r e g u l a r i t y . I t i s conce ivab le t h a t some o f the items o f equipment i n
the e x i h t i n g f a c i 1 ; t y which were no t evaluated d u r i n g an e a r l i e r des ign e ra
may indeed be o f a type which has been evaluated
i n f o m a t i o n should be ob ta ined i f a t a l l p o s s i b l e
receq; It:s t i ng and ana l ys i s exper ience i t i s poss
abouE t i le adequacy o f c e r t a i n types and c lasses o
n ensuing years and t h i s
I n many cases based on
b l e t o make judgments
equipment. I n s o f a r a s
possi51e i t i s recommended t h a t t he equipment q u a l i f i c a t i o n be c a r r i e d o u t
i n accordance w i t h Standard 344-75 o f I E E E and the accompanying standards
whicb r e l a t e t o genera l q u a l i f i c a t i o n requi rements. I n many cases i t i s
concervable t h a t t h e equipment i t s e l f w i l l have adequate r e s i s t a n c e f o r t h e
se ismic hazard invo lved and t h a t a d d i t i o n a l r e s i s t a n c e of the system can be
developed through the adding o f a d d i t i o n a l anchorage, b rac ing o r o t h e r
remedial measures.
I n the case o f new equipment which i s i n s t a l l e d as a p a r t o f t he
redes ign and upgrading, we c a l l p a r t i c u l a r a t t e n t i o n t o a recent systemat ic
program o f equipment e v a l u a t i o n t h a t was c a r r i e d on f o r the t rans-A laskd
p i p e l i n e as descr ibed i n d e t a i l i n Ref. 31. Th i s p a r t i c u l d r program
invo lved one o f t h e most sys temat ic and w e l l documented s t u d i e s of t h i s
t ype known t o t h e au thors .
38
8.6 Q u a l i t y Cont ro l and D e t a i l s o f Const ruc t ion
Items which do n o t lend themselves r e a d i l y t o a n a l y t i c a l
c o n s i d e r a t i o n may have an impor tant e f f e c t on t h e response o f s t r u c t u r e s
and f a c i l i t i e s t o earthquake mot ions and must be considered i n t h e design.
Among these i tems a r e such mat te rs as t h e d e t a i l s and m a t e r i a l p r o p e r t i e s
o f the elements and components, and t h e i n s p e c t i o n and c o n t r o l o f q u a l i t y
i n the c o n s t r u c t i o n procedure. The d e t a i l s o f connect ions o f the s t r u c t u r e
t o i t s suppor t o r foundat ions, as w e l l as of t h e v a r i o u s elements o r i tems
w i t h i n t h e s t r u c t u r e o r component, a r e o f major importance. F a i l u r e s o f t e n
occur a t connect ions and j o i n t s because o f inadequacy o f these t o c a r r y t h e
f o r c e s t o which they a r e subjected under dynamic c o n d i t i o n s . Inadequacies
i n p r o p e r t i e s o f m a t e r i a l can o f t e n be encountered, lead ing t o b r i t t l e
f r a c t u r e where s u f f i c i e n t energy cannot be absorbed, even though energy
a b s o r p t i o n may have been counted on i n t h e des ign and may be a v a i l a b l e
under s t a t i c load ing c o n d i t i o n s . Some o f t h e aspects o f these t o p i c s a r e
considered i n d e t a i l i n Refs. 28 and 30 for r e i n f o r c e d concre te . S i m i l a r
concepts must be fo l lowed, however, f o r o t h e r c o n s t r u c t i o n m a t e r i a l s as w e l l .
The rev iew must i n c l u d e examinat ion o f d e t a i l s o f c o n s t r u c t i o n ,
fas ten ing , and a c t u a l m a t e r i a l p r o p e r t i e s t o be sure t h a t the r e s i s t a n c e
a v a i l a b l e i s adequate t o meet t h e demands of t h e upgraded des ign requi rements.
8.7 P r o b a b i l i t y Concepts
Al though p r o b a b i l i t y concepts a r e n o t g e n e r a l l y used i n the des ign
o f new r e a c t o r s , it i s l i k e l y t h a t they can be used i n c o n s i d e r i n g the
a p p r o p r i a t e l e v e l o f upgrading and r e t r o f i t t o b r i n g an o l d e r r e a c t o r t o
acceptable s a f e t y l e v e l s . However, s t u d i e s a r e r e q u i r e d t o d e f i n e acceptab e
39
l e v e l s o f r sk and s t r u c t u r a l or component r e s i s t a n c e b e f o r e r i s k a n a l y s i s
can be used as a s o l e b a s i s for d e c i s i o n as t o redesign o r upgrading
requirements.
f o r dynamic response.
Such s t u d i e s a r e underway now, bo th for se ismic hazard and
Use o f p r o b a b i l i t y concepts i s a lmost necessary, however, t o
d e f i n e a p p r o p r i a t e l e v e l s o f damping, energy a b s o r p t i o n c a p a b i l i t y o r
d u c t i l i t y , and f r a g i l i t y l e v e l s o f components and equipment, s i n c e s e l e c t i o n
o f a l l these parameters a t extreme or bounding va lues would lead t o
unreasonable, o r a lmost i r r a t i o n a l , seismic des ign requirements t h a t would
in t roduce dangers f rom o v e r s t i f f and/or b r i t t l e behavior mechanisms t h a t
would be more s e r i o u s i n terms o f s a f e t y c o n s i d e r a t i o n s .
40
an a u d i t o f t h e s t a t u s of t h e e x i s t i n g equipment s t r u c t u r e s , elements,
o t h e r c r i t i c a l i tems. The a u d i t should i n c l u d e many t h i n g s , namely a
o f those i tems and systems considered c r i t i c a l , t h e documentation t h a t
w i t h regard t o them, and t h e methods used i n the a n a l y s i s o f t h e i tems
I X . SUMMARY R E V I E W AND REPORTING
9.1 A u d i t Procedure and Systems Summag-
As descr ibed i n Sec t ion I of t h i s r e p o r t a major p o r t i o n o f t h e
rev iew and a n a l y s i s procedure f o r an o p e r a t i n g nuc lear p l a n t invo lves making
and
i s t i n g
e x i s t s
A1 so
i t should i n c l u d e any f a c t u a l d e t a i l s t h a t e x i s t w i t h regard t o the s t r e s s
a n a l y s i s , s e l e c t i o n o f suppor t and r e s i s t i n g systems, and s p e c i f i c a l l y any
i n f o r m a t i o n t h a t e x i s t s w i t h regard t o t h e amount o f t h e s t r e s s and deforma-
se ismic hazard f o r which t h e p l a n t was
de some i n s i g h t , even i n the l i g h t o f
me, of t h e probable s i g n i f i c a n c e o f
cons i d e r a t ion .
i n v o l v e s a l a r g e amount of t ime and
n e c e s s i t y i f documentat ion and
j u s t i f i c a t i o n o f t h e e x i s t i n g f a c i l i t i e s a r e r e q u i r e d as a R a r t o f t h e
upgrading procedure, which would be expected.
t i o n which cou ld be a t t r i b u t e d t o t h e
designed. T h i s l a t t e r i tem w i l l p rov
t h e methods o f a n a l y s i s used a t t h e t
t h e se ismic e f f e c t s upon t h e i tems o f
A thorough and u s e f u l a u d i t
p a i n s t a k i n g e f f o r t bu t i s an a b s o l u t e
41
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Donovan, N. C . , "A S t a t i s t i c a l E v a l u a t i o n o f St rong Mot ion Data I n c l u d i n g the February 9, 1971 San Fernando Earthquake," Proceedings F i f t h World Conference on Earthquake Engineer ing (Rome), Vol . 1, 1974, pp. 1252-1261.
Schnabel, P. B. and H. B. Seed, "Acce le ra t ions i n Rock for Earthquake i n t h e Western Un i ted States, ' ' B u l l e t i n Seismologica l Soc ie ty o f America (USA), Vol . 63, NO. 2, 1973, pp. 501-516.
Page, R. A . , D. M. Boore, W. B. Joyner and H. W. C o u l t e r , "Ground Mot ion Values for Use i n the Seismic Design o f t h e Trans-Alaskan P i p e l i n e System," U . S . G . S . Survey C i r c u l a r 672, 1972, 23 p.
Ambraseys, N. N. , "Dynamics and Response of Foundat ion M a t e r i a l s i n E p i c e n t r a l Regions of St rong Earthquakes," Proceedings F i f t h World Conference on Earthquake Engineer ing (Rome), Vol . 1 , 1974, pp. C X X V I - C X L V I I I .
T r i f u n a c , M. D. and A. G. Brady, "On the C o r r e l a t i o n o f Seismic I n t e n s i t y Scales for t h e Peaks o f Recorded Strong Ground Motion," B u l l e t i n Seismologica l Soc ie ty o f America (USA), Vol . 65, No. 1 , 1975, pp. 139-162.
Seed, H. B . , C . Ugas and J . Lysmer, " S i t e Dependent Spectra f o r Earthquake- Res i s t a n t Des ign," Earthquake Eng ineer i ng Research Center (Berke ley , C a l i f o r n i a ) , Report No. EERC74-12, 1973, 17 p .
Mohraz, B., "A Study o f Earthquake Response Spectra f o r D i f f e r e n t Geologica l Condi t ions, ' I I n s t i t u t e o f Technology, Southern Methodis t U n i v e r s i t y (Da l las , Texas), 1975, 43 p .
Hanks, T. C . , "Strong Ground Mot ion o f t h e San Fernando, C a l i f o r n i a , Earthquake: Ground Displacements, ' ' B u l l e t i n Seismologica l Soc ie ty o f America (USA), Vol. 65, No. 1 , 1975, pp. 193-226.
Newmark, N. M., W. J. H a l l and B. Mohraz, "A Study o f V e r t i c a l and H o r i z o n t a l Earthquake Spectra,". D i r e c t o r a t e o f L icens ing , U.S. Atomic Energy Commission, Report WASH-1255, A p r i l 1973, 151 p.
H a l l , W. J., B. Mohraz and N. M. Newmark, " S t a t i s t i c a l . S tud ies o f V e r t i c a l and H o r i z o n t a l Earthquake Spectra, ' ' prepared for U.S. Nuclear Regulatory Commission, Report NUREG-0003, Jan. 1976, 128 p.
I d r i s s , . I . M., Chairman, "Analyses for S o i l - S t r u c t u r e I n t e r a c t i o n E f f e c t s f o r Nuclear Power Plants , " Report by A d Hoc Group on S o i l - S t r u c t u r e I n t e r a c t i o n , S t r u c t u r a l D i v i s i o n , American Soc ie ty o f C i v i l Engineers, D r a f t , 5 December 1975.
E . D'Appolonia Consu l t ing Engineers, Inc. , " S o i l - S t r u c t u r e l n t e r a t i o n f o r Nuclear Power Plants , " Report DAP-TOP 1, May 1975.
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Newmark, N . M . , A. R. Robinson, A.H.-S. Ang, L. A. Lopez and W. J . H a l l , "Methods f o r Determin ing S i t e Character i s t ics," Proceedings I n t e r n a t i o n a l Conference on Microzonat ion, NSF-UNESCO-University of Washington-ASCE- Acad. Mechs. ( S e a t t l e , Washington), Vol . 1 , 1972, pp. 113-129.
Chopra, A. K., " I n t e r - R e l a t i o n s h i p of Methods f o r Earthquake Ana lys is o f S t r u c t u r e - S o i l I n t e r a c t i o n , " i n Advances i n C i v i l Engineer ing through Engineer ing Mechanics, ASCE, 1977, pp. 36-39.
"Recommended Comprehensive Seismic Design P r o v i s i o n s f o r Bu i ld ings , " prepared by the Appl i e d Technology Committee, 480 Cal i f . Ave., S u i t e 205, Palo A l t o , C a l i f . 94306, a v a i l a b l e i n l a t e 1977.
Newmark, N. M. , "A Response Spectrum Approach f o r I n e l a s t i c Seismic Design of Nuclear Reactor F a c i l i t i e s , " T ransac t ions T h i r d i n t e r n a t i o n a l Conference on S t r u c t u r a l Mechanics i n Reactor Technology (London), Paper K 5 / 1 , 1975.
Newmark, N . M. , "Seismic Design C r i t e r i a f o r S t r u c t u r e s and F a c i l i t i e s , Trans-Alaska P i p e l i n e System," Proceedings U.S. - -- N a t i o n a l Conference on Earthquake Engineer ing (Ann Arbor, Michigan), Earthquake Engineer ing Research I n s t i t u t e , June 1975, pp. 94-103.
Newmark, N. M . , "Design C r i t e r i a f o r Nuclear Reactors subjected t o Earthquake Hazards," Proceedings of t h e -- I A E A Panel on Aseismic Design and T e s t i n g o f Nuclear F a c i l i t i e s , t h e Japan Earthquake Promotion Soc ie ty (Tokyo), 1969, pp. 90--113.
Newmark, N. M. and W. J. H a l l , "Seismic Design C r i t e r i a f o r Nuclear Reactor F a c i l i t i e s , " Proceedings Four th World Conference on Earthquake Engineer ing (Sant i a g o x h i l e ) , Vol. I I , 1969, pp. 84-37 - B4-50.
Newmark, N. M., J. A. Blume and K. K. Kapur, "Seismic Design Spectra f o r Nuclear Power P lan ts , " Journal Power D i v i s i o n , ASCE (New York) , Proceedings, Vol . 99, NO. P02, Nov. 1973, pp. m - 3 0 3 .
Newmark, N. M. and W . J . H a l l , "Procedures and C r i t e r i a f o r Earthquake R e s i s t a n t Design," B u i l d i n g P r a c t i c e s f o r D i s a s t e r M i t i g a t i o n , N a t i o n a l Bureau o f Standards(Washington, D.C.), B u i l d i n g Science Ser ies 46, Vol. 1 , Feb. 1973, pp. 209-236.
Newmark, N. M. and E. Rosenblueth, -- Fundamentals of Earthquake Engineer ing, P r e n t i c e - H a l l , Inc. (Englewood C l i f f s , N.JJ, 1971, 640 p.
Newmark, N. M., "Earthquake Response Ana lys is o f Reactor S t ruc tures , ' ' Nuclear Engineer ing and Design (The Nether lands) , Vol . '20, No. 2, J u l y 1972, pp. 303-322.
Newmark, N. M., W . J. H a l l and J. R. Morgan, "Comparison o f B u i l d i n g Response and Free F i e l d Mot ion i n Earthquakes," Proceedings 6 t h World Conference on Earthquake Engineer ing, 1977, 6 p. ( i n press)
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Whit le: , J . R . , J . R. Morgan, W. J . H a l l and N. M. Newmark, "Base Response A r i s i n g from Free-F ie ld Motions," Transact ions 4 t h S M i R T Conference, Paper K2/15, Vol. K(a), 1977, 10 p.
---
Newmark, N. M. and W . J . H a l l , " P i p e l i n e Design t o R e s i s t Large F a u l t Displacement, ' ' Proceedings U . S . Nat iona l Conference on Earthquake Engineer ing, E E R I , 1975, pp. 416-425.
H a l l , W. J . and N. M. Newmark, "Seismic Design C r i t e r i a for P i p e l i n e s and F a c i l i t i e s , " Proceedings L i f e l i n e Earthquake Engineer ing S p e c i a l t y Conference, ASCE, 1977, pp. 18-34.
"Nuclear Reactors and Earthquakes, ' ' Report T I D 7024, prepared by Holmes and Narver f o r US AEC, 1963.
Blume, J . A. , N. M. Newmark and L . Corning, - Design o f M u l t i - S t o r y Reinforced Concrete B u i l d i n g s f o r Earthquake Mot ions, P o r t l a n d Cement A s s o c i a t i o n (Chicago), 1961, 350 p.
Newmark, N. M. and W. J . H a l l , "Dynamic Behavior o f Reinforced and Prest ressed Concrete B u i l d i n g s under H o r i z o n t a l Forces and the Design o f J o i n t s ( i n c l u d i n g Wind, Earthquake B l a s t E f f e c t s ) , I i P r e l im inary
In t .ernat iona1 A s s o c i a t i o n f o r Br idge and S t r u c t u r a l York) , September 1968, pp. 585-613; French t r a n s l a t i o n pp. 614-638: German t r a n s l a t i o n pp 639-661.
Anderson, T. L. and D. J . Nyman, " L i f e l i n e Earthquake Engineer ing f o r t h e Trans-Alaska P i p e l i n e System," Proceedings L i f e l i n e Earthquake Engineer ing S p e c i a l t y Conference, A S C E , 1977, pp. 35-49.
44
TABLE 1. RECOHHEWED DAMPING VALUES
St ress Level Type and C o n d i t i o n Percentage of S t r u c t u r e C r i t i c a l Damplng
Work1 ng s t r e s s , a. V i t a l p i p i n g no more than about 3 y i e l d p o i n t b. Welded s t e e l , prest ressed
concrete , we 1 1 r e 1 n f orced conc re te (on l y s 11 gh t c rack ing)
c. Relnforced concrete w i t h cons l d e r a b l e c r a c k i n g
d. B o l t e d and/or r i v e t e d s t e e l , wood s t r u c t u r e s w i t h n a i l e d o r bo1 ted j o i n t s
A t o r j u s t below a. V i t a l p i p i n g y i e l d p o i n t b. Welded s t e e l , prest ressed concrete
c. Prestressed concrete w i t h no
( w i t h o u t complete loss I n p r e s t r e s s )
pres t ress l e f t
d . Re 1 n f orced concrete
e. Bo l ted and/or r l v e t e d s t e e l , wood s t r u c t u r e s , w i t h bo1 ted j o l n t s
f. Wood s t r u c t u r e s w l t h n a i l e d j o i n t s
1 t o 2
2 t o 3
3 t o 5
5 t o 7
2 t o 3 5 t o 7
7 t o IO
7 t o 10
10 t o 15
15 t o 20
45
TABLE 2. EQUATIONS FOR SPECTRUM AMPLIFICATION FACTORS FOR HORIZONTAL EIOTION
Quan t 1 t y Cumu 1 a t I ve Probab l l l t y , % Equa t ion
Acce le ra t ion 84.1 (One Sigma) 4.38 - 1.04 an B V e l o c i t y 3.38 - 0.67 An 8 D i sp lacemen t 2.73 - 0.45 An B
Acce 1 era t ion 50 (Median) 3.21 - 0.68 An B Ve loc i t y 2.31 - 0.41 An B Displacement 1.82 - 0.27 An 8
TABLE 3. SPECTRUM AMPLIFICATION FACTORS FOR HORIZONTAL ELASTIC RESPONSE
One Sigma (84.1%) Median (50%) Damp i ng , % C r i t i c a l A V D A V D
0.5 1 2 3 5 7 IO 20
5.10 4.38 3.66 3.24 2.71 2.36 1.99 1.26
3.84 3.38 2.92 2.64 2.30 2.08 1.84 1.37
3.04 2.73 2.42 2.24 2.01 1.85 1.69 1.38
3.68 3.21 2.74 2.46 2.12 1.89 1.64 1.17
2.59 2.31 2.03 1.86 1.65 1.51 1.37 1.08
2.01 1.82 1.63 1.52 1.39 1.29 1.20 1.01
46
TABLE 4. PROPOSED S E I S M I C DESIGN CLASSIFICATION
c U S S DESCRIPTION
I -s Equipment, inst ruments, o r components per fo rming v i t a l f unc t i ons
t h a t must remain o p e r a t i v e d u r i n g and a f t e r earthquakes;
S t r u c t u r e s t h a t must remain e l a s t i c o r n e a r l y e l a s t i c ;
Fac i 1 I t i e s per fo rming a v i t a l s a f e t y - r e l a t e d f u n c t i o n t h a t must
remain f u n c t i o n a l w i t h o u t r e p a i r . D u c t i l i t y f a c t o r = 1 t o 1.3.
I I tems t h a t must remain o p e r a t i v e a f t e r an earthquake bu t need
n o t operate d u r i n g the event; S t ruc tu res t h a t can deform
s l i g h t l y i n the i n e l a s t i c range; F a c i l i t i e s t h a t a re v i t a l b u t
whose s e r v i c e can be i n t e r r u p t e d u n t i l minor r e p a i r s a re made.
D u c t i l i t y f a c t o r = 1.3 t o 2.
I 1 F a c i l i t i e s , s t r u c t u r e s , equipment, inst ruments, or components
t h a t can deform i n e l a s t i c a i l y t o a moderate e x t e n t w i t h o u t
unacceptable l o s s o f f u n c t i o n ; S t r u c t u r e s housing i terns o f
C l a s s I o r I - S t h a t must t io t be p e r m i t t e d t o cause damage t o such
i tems by excess ive de format ion o f t he s t r u c t u r e , D u c t i l i t y
f a c t o r = 2 t o 3 .
I11 A l l o t h e r i tems which a re usual y governed by o r d i n a r y se ismic
des ign codes; S t r u c t u r e s r e q u i r ng se ismic res i s tance i n o rder t o
be r e p a i r a b l e a f t e r an earthquake.
depending on m a t e r i a l , type o f cons t ruc t i on , des ign o f d e t a i l s ,
D u c t i l i t y f a c t o r = 3 to 8 ,
and c o n t r o l o f q u a l i t y .
47
u = x - y
FIG, I SIMPLE UNDAMPED MASS-SPRING SYSTEM
Actual Yield
Effect ive Elastic Limit
Effect ive
J urn =puy
1
UY Urn - Uy Urn
Displacement
FIG. 2 RESISTANCE - DISPLACEMENT RELATIONSHIP
FIG. 3
48
Frequency, hertz ELASTIC DESIGN SPECTRUM, HORIZ. MOTION, ( 0 5 g MAX. ACCEL., 5 70 DAMPING, ONE SIGMA CUM. PROBABILITY I
FIG. 4 DESIGN SPECTRA FOR EARTHQUAKES
49
Frequency, cps
FIG. 5 ELASTIC AND INELASTIC DESIGN SPECTRA