Methods for Impact Analysis of Shipping Containers
Manuscript Complrted: October 1987 D a t e Published: November 1987
Prepared by T. A. Nelson, R. C. Chun
Lawrence Livermore National Laboratory 7000 East Avenue Livermore, CA 94550
Prepared for Division of Safeguards and Transportation Ofice of Nuclear Material Sakty and Safeguards U.S. Nuclear Regulatory Commission Washington, D.C. 20555 NRC FIN No. A0291
ABSTRACT
T h i s report rev iews methods f o r performing impact stress analyses o f sh ipp ing containers used t o t r a n s p o r t spent f u e l . Three methods are discussed: q u a s i - s t a t i c , dynamic lumped parameter and dynamic f i n i t e element. These methods are used by industry for performing impact analyses f o r Safety Analysis Repor ts .
The approach f o r each method i s described including assumptions and l i m i t a t i o n s and modeling considerat ions. The e f f e c t s o f u n c e r t a i n t i e s i n the modeling and a n a l y z i n g o f casks are i d e n t i f i e d . Each o f the methods uses 1 i n e a r e l a s t i c structural analysis principles. Methods f o r i n t e r f a c i n g impact stresses w i t h t h e design and load combinations c r i t e r i a s p e c i f i e d i n Regulatory Guides 7 . 6 and 7.8 are outlined.
I
The q u a s i - s t a t i c method i s based on D 'A lember t ' s p r i n c i p l e t o s u b s t i t u t e I e q u i v a l e n t s t a t i c forcer f o r i n e r t i a l forcer created by the impact . The ] lumped parameter method i s based on using a d iscrete number o f s t i f f n e s s
elements and masses t o represent the cask dur ing impact. The dynamic f i n i t e
1 element method uses f i n i t e element techniques combined w i t h t ime i n t e g r a t i o n t o analyze the cask impact. Each o f these methods can prov ide an acceptable means, w i t h i n c e r t a i n l i m i t a t i o n s , for a n a l y z i n g c a s k impact o n u n y i e l d i n g
1 surfaces.
l . i s t o f Figures ...................................................... v i i
Execut ive Summary ...............................,...........*........ 1
1.0 Introduction ................................................... 2 1.1 Background ................................................. 2 1.2 Objective and Scope ........................................ 2
2.0 Impact Analysis Methods ......................................... 5 2.1 Dynamic Lumped Parameter ................................... 5
2.1.1 Desc r i p t i on and Approach ............................ 5 2.1.2 Assumptions and Limitations ......................... 9 2.1.3 Modeling Considerat ions ............................. 10 2.1.4 Effects of Unbonded Lead ............................ 1 3
2.2 Q u a s i - S t a t i c Method o f Impact Analyses ..................... 16 2 .2 .1 D e s c r i p t i o n and Approach ............................ 16 2.2.2 Application o f Q u a s i - S t a t i c Methods and Modeling
Considerations ...................................... 2 5 2.2.3 Limitations o f Quasi-Static Methods ................. 28
2 . 3 Oynarnic F i n i t e Element Method o f Impact Analyses ........... 3 1 2.3.1 Introduction ........................................ 3 1 2.3.2 Analys i s and Model i ng Cons i dera t i ons ................ 3 1
............. 2.3.3 Desirable Features o f Computer Programs 35 2 . 3 . 4 Limitations and Closure ............................. 3 5
3.0 Stress E v a l u a t i o n ............................................... 38 ...................... 3.1 Design Criteria and Stress Categories 38 ..................... 3.2 Stress Recovery From Simplified Models 39
References ....................... ..... ............................... 45
..... Appendix A . Internal Force D i s t r i b u t i o n i n a Slender R i g i d Beam A - 1
FOREYORD
As part o f t h e i r charter t o l icense spent fuel sh ipp ing c a s k s , t h e U . S . Muclear Regulatory Comnission must evaluate the structural adequacy o f t h e container under a ser ies of postulated loading c o n d i t i o n s . Indus t ry has several opt ions a v a i l a b l e f o r performing analyses t o ensure s t ructural adequacy under impac t load ing . The purpose o f this report i s t o e v a l u a t e t h e available opt ions and descr ibe acceptatlle methods f o r performing impact a n a l y s i s .
1 The authors would like t o acknowledge the assistance o f L.E. Fischer, Lawrence Livermore N a t i o n a l Laboratory. for h i s a d v i c e d u r i n g the comp i l a t i on o f t h i s report.
EXECUTIVE SUWARY
To p r o t e c t t h e p u b l i c h e a l t h and s a f e t y , designs o f c a s k s used t o sh ip spen t nuc lear f u e l are r e q u i r e d t o be e v a l u a t e d f o r i m p a c t s on u n y i e l d i n g s u r f a c e s under c o n d i t i o n s o f normal t r a n s p o r t and h y p o t h e t i c a l a c c i d e n t c o n d i t i o n s . The c o n d i t i o n s under which t h e casks must p e r f o r m a r e s p e c i f i e d i n 10 CFR 7 1 . Accep tab l e means for rhowing a c c e p t a b l e per formance a r e d e l i n e a t e d i n U.S. N u c l e a r R e g u l a t o r y Comnission (USNRC) R e g u l a t o r y Guides 7.6 and 7.8.
Severa l d i f f e r e n t methods a r e used by t h e s h i p p i n g c a s k i n d u s t r y t o p e r f o r m impact analyses o f c a s k s . The purpose o f t h i s repo r t i s t o r e v i e w three comon ly used methods, e v a l u a t e t h e i r a p p l i c a b i l i t y , d i s c u s s a p p r o p r i a t e modeling techniques and d e s c r i b e assumpt ions and l i m i t a t i o n s o f each method. The resu l t s o f t h e r e v i e w a r e in tended t o a s s i s t t h e USNRC i n e v a l u a t i n g t h e a p p r o p r i a t e n e s s o f licensee s u b m i t t a l s .
The methods r e v i e w e d i n t h i s repo r t a r e : q u a s i - s t a t i c , dynamic lumped pa rame te r , and dynamic f i n i t e element. Each method can be used t o p r e d i c t the response of a cask t o impac t l o a d under c e r t a i n c o n d i t i o n s . The dynamic a n a l y s i s methods can more a c c u r a t e l y p r e d i c t cask response under impact l o a d i n g s i n c e t h i s l o a d i n g produces dynamic response i n t he cask.
The q u a s i - s t a t i c method i s based on D'Alembert's p r i n c i p l e t o s u b s t i t u t e e q u i v a l e n t s t a t i c f o r c e s f o r i n e r t i a l f o r c e s created by impact . Th i s method t r e a t s the cask as a slender r i g i d bar and c a n n o t c a p t u r e dynamic cask response. A l s o , r e s t r i c t i v e assumptions must be a p p l i e d t o cap tu re secondary impact . I t i s n o t recommended f o r a n a l y z i n g ob? i que impact cases .
T h e dynamic lumped parameter method combines simp1 i c i t y i n model i n g w i t h the a b i l i t y t o c a p t u r e d y n a m i c cask response as a r e s u l t o f t h e r a p i d impac t load. In a d d i t i o n , t he method can be formulated t o c a p t u r e t h e r i g i d - b o d y r o t a t i o n wh ich can occur a s a resul t of o b l i q u e impac t . O v e r a l l c a s k response can be de te rm ined as we1 1 as t h e r e s u l t i n g m a j o r s t r e s s e s . S t r e s s r e c o v e r y assumpt ions can s t a r t t o become r e s t r i c t i v e i f c a l c u l a t i o n o f d e t a i l e d s t ress s t a t e s i s a t tempted . A computer code employing a dynamic lumped parameter method, c a l l e d IMPASC ( Impac t A n a l y s i s o f Shipping C a s k s ) , has been developed by t h e Lawrence L i ve rmore N a t i o n a l L a b c r a t o r y as p a r t o f an i n t e g r a t e d s h i p p i n g cask a n a l y s i s system. I n I M P A S C , t h e c a s k i s modeled as a s e r i e s o f beams w i t h masses lumped a t t h e nodes. C u r r e n t l y , casks w i t h l e a d s h i e l d i n g a r e modeled w i t h compos i t e beam p r o p e r t i e s , w h i c h assumes t h a t t h e l e a d i s bonded t o t h e s t e e l she l l s .
In o r d e r t o o b t a i n d e t a i l e d s t r e s s r e c c v e r y or model n o n l i n e a r b e h a v i o r , such a s l e a d slump, a dynamic f i n i t e element a n a l y s i s shou ld be used. I n t h i s method, each component can be modeled s e p a r a t e l y and s t r e s s e s i n each element can be c a l c u l a t e d d i r e c t l y d u r i n g t h e z n a l y s i s . Whi le they can be expens ive and t i m e consuming, dynamic f i n i t e element a n a l y s i s methods can p r o v i d e the most a c c u r a t e and d e t a i l e d e s t i m a t e s o f cask response t o impact l o a d s .
R . G . 7.4
Tn p r o t e r t t he p u b l i c h e a l t h and ~ a f r t y , s h l p e n t s o f spent tuel are r e q u i ~ e d t o be I n accordance w ~ t h t he p r o v i s i o n s of 49 CFR 171-178 (Ref. 1) and 1 0 CFR 7 1 (Ref. 2). A l l a c t i v i t i e s , which a r e r e l a t e d t o t h e des ign, f ab r i 8 :a t i on and use o f spent f u e l casks a re documented i n a s a f e t y a n a l y s i s r e p o r - [ 5 A R ) and conducted under a q u a l l t v ~ s u t a o c e program, bo th oC which a r p reviewed and approved by t h e U . S . H u c l e b r Regujator) Cumnission ihki , ] . R ~ g l r T a t i n n 5 i n I0 CFR 71 , Sect.005 .71 arid .73 r e q u i r e that thp d e s i y n o f s p ~ n t f u e i cd.;k5 be evaluated f o r impacts on u n y i e l d i n g s u r f a c e s f o r nr~r rna l L r anspar t dnd h r p l t h e t ~ C Q I a c c l r l r n t condi Slons. I
Dyrlamic F i n i t e -umncd P n r a m e t P r k l m P n t Met hvd
Fegu1atr)ry Guides 7.6 (Re f . 31 and 7.R (Ref . a ) p r o v i d e acceptarc? - r i t e r i a f o r c ? d s t i c s t r e s s d ~ ~ d l y % i s i i m i t s and load c m b i n a t i o n s f o r t h e M a s s 8 s t l f t n e s s r o n t n i n m e n t c y r t e m . Scvcral d i f i r r e r ~ t r~~e!nads o f a n a l y s i s a r e c u r r e n t l y used Element Model tly the r.hlpp1ng ra;k industry t o eualuat~ spent fue l c a ~ k desiuns. P c m o l e t e l
1 . I m p a c t dnalysir methods were i d e n t i f i e d which c o ~ l d reasonably . yet ~ n n s c r * a t l v e l y , pvcdir t .,wn! f u ~ l c i r k r o n t a inmenf stvesser 'or. I
d e s c r i p t i o n o f t h e impact method used i n a n r l y z i n g a c a w des ign i s r e q u i r e d ! i n t h ~ SRR. T h i s HURFG d iscusses t h r e e c m o n l y used methuds fur pe r fo rm ing dna l y s i r f o r spent f u e l casks impac t i ng o n t o uny ie ld ing sur faces. I n Yn teg ra t i on i I 1, a f ow a i r e i n h o r e n i n earn method 1 Equiv'ent 5tatic o t t q u a t i o n s A n a l y r i s Loads of a n a 7 y c . i ~ . o f Motiiln
P survey was performed t o i d e n t i f y methods used by i n d u s t r y f o r p e r f o r n l n g impact analyses t o w a l u a t e t h e s t r u c t u r a l in tegr i ty of s h i p p i n g c d s i r . I n f o r m a t l o h and methods w e r e determined frbm tndustry r e p o r t < , SARs dnd c m u n i c a t i o n k i t h i n d u s t r y p r r sonne t . The a c c e p t a n r ~ rrrt v i a nf I I Oynami c
~ r n p l ~ r cari inn necvucr y ~ ~ : ~ ~ ! I ~ . : . , t>:+- ;.I; U O ~ L J i . 0 w r r . ~ rev ieweo Lo assu re t h i t the impact a n a l y s i s 1 1 method5 s e l e c t e d f c r d i s c u s s i o n would r e s u l t i n c m p l i a ~ c e w i t h these y u i d ~ r . A procedure was o u t l i n c d fo r combining and post processing l i n e a r 1
e l a s t i c s t r ~ s r a n a l y s i s r - esu l t s t o pe rm i t t h e c ~ a r i s t l n of those r e r u l t r w i t h t h e s t r e s s acceptance c r i t e r i a s p e c i f i e d i n ? . G . 7.6. Procedures werc a l s o
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discus?e0 i n the fo l low ing r P c t i o n 5 . I I
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F ig . I . : Impact Rnalysir Methods Flow Cha r t .
The o b j p c t i v e o f t h i s work dar t o document methods f3r a n a l y z i n g shipping c o n t a i n e r s f o r t h e impact I~ ,ndh specrf~ed xn 1U CFR 71. For each a n a l y t i c a l F a m i c a t ]on Load i nq Opera t i ovs
Strer re5 Combinations S t resses method, the r e p o r r d iscusses app-opriate t ~ t h n i q u e s f o r model ing t h e s t r u c t u r e and t h e reasonableness of va r i ous assmnptions t h a t tan be uxed t o f a c i l i t a t e t h e dndly515.
T h e s c o w n f t h c d i : cu>saur l was a5 tallows:
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I Regulatory Guides 7 . 6 and 7.8. S i n c e o n l y con ta:nmenl I r c o n s i d e r e d ,!
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2. The a n a l y s e s d i s c u s s e d he re ln presume e l a s t i c b e h a v i o r such t h a t 1 . I DEICPIPIIOY AMD RWROACH p r i n r i p l c c o f superposit ion a p p l y f o r t h e purposes of combin ing l o a d s . B u c k l i n g of t he containment vras n o t c o n s i d e r e d . 1 The d y n a m ~ c Iurnped parameter a p p ~ @ d r b , i 5 used t o p r o v i d c andly: ical
! r e s u l t s t h a t dCrnunt f a f t h e dynami r r-e<pc~n',a~ o f t h p r a s k d s w t l l as t h e r i g i d 3. M o d e l i n g techniques i n c l u d i n g assumpt ionr and a p p r o x i m a t i o n s ernplcredf body m o t i o n a s r o r i e t e d d i t h oh1 i q u e i m p a r t . lbe c a ~ k g ~ o m e t r y i s mudpled i n
f o r t h r e e basic typer o f a n a l y s e s w e r e e v a l u a t e d . ! one d i m e n x i o n , l h i s mudcl c o n s i s t s c r a s e r i e s r;f lumpe< m1h5ses connected by ! s p r i n g s , tieam ~ l ~ r n e n ! . , or o t h e r r ~ c c i a l ' z e d ~ l p m r n ! . , .
3. he spent f u e i C ~ S L t u n t e n t s were r n c l u d e a o n l y as i n e r t i a ! l o a d s and! houndary c o n d i t i o n s . ~ h o p r i m a r y a u r p o s c o f I h r l u rnp~d parameter madcl > s t o capture t h ~
o v e l . n i m ~ r e % p o n s c o f t he c d Z i . 5 7 n ~ c ' t h i ~ rnodcl i s v y e d I n n dynamic anali.:ls, 5 . Br:t : le f r a c t u r e e f f e c t s were not c o n s i d e r e d . i t I r s u p e r . ~ o r t o a q u a s i - s t a r i r approach 1.1 tha t rlynirrnlc effects n r -
a c c v u r ~ t e d fa t ' . T h e b d r i c dynamic a m f i l , i f i c a t i o r , pheriomcrion can he 1 1 1 1 ~ j t r a t e u 1. I e t h n i u r e r fop a n a l y z i n g s t r e r s ~ l i n c l o s u r e s and t h e i r a \ \ o c i a t e d j by means o f d sirnp'e, onm-degree-of- f recdom ry:Lem wh ich mmght a p p r a r ~ l n a t e an
b o l t i n g under impact were developed. 1 end-on impact of a c a s k . The dynamic arnp7,!f l c a t ion f a c t o r (OAF I 1 5 ? q ~ l a l t o , t h e dynarn~c d e f l e t i l o n divided by the d ~ f l e r t l : i l c a n e d b y d s t p t l ~ a l l j 7. Th? i n t r r a c t i o r , between s h f ~ l d i n g and c o n t a i o r n ~ n t m a t e r i a l . ; ( e . q .. ; a p p l i e d !oad o f t h e Sdmc magni tude ( R e f . !>). h~ OAF t s a f u n r ! i b n o f t h e
l e a d s lump) under impact were d iscussed f o r certain cases. j r i s e t i m e o f t h e a p p l ~ e b load. t h e d u r a t i r j n o f t h c l oad . t h e shape o f t h e load, and t h e n a t u r a l p e r i o d o f t he s t ruc tu re . To ;I l u ~ t r a l e the f f f e c t o f r i s e t i n e , F i g . 2 . 1 i h o w r thp marlmum DLF ar a f u n c t i o n o f r i 5 e t i m e f o r a ramp lqad. F o r an i n f i n i t e s i m a l r l r e t i m e , t h e maximum F.AF 1s 2 . n . Thus, t h e maximum d e f l v c t i o n , and the c u r r ~ r p o n d i n g f o r c e I n t h e s p r l o q . 1 5 t w i c e t h a t f o r a r t n t l c a l l y a p p l i e d Inad.
Thp e f f ~ r t i o ' l o a d d u r a L t o n and. t o some e r t e n t , l o a d shape a r e 5h11wn i n i ~ y . I . c . l r w LHO I O ~ L I C 5nuwrh 111 ~ 1 1 ' 1 T IyurY I I ~ V P dn In: r n l t e s l m d l r;:e t i m e . A s shown i n : h ~ f lqu i .e , l o a d d u r a t i o n , ar cornoared t o t h e n n t l ) r " l
I pct- lod o f t h e s y s t ~ r n , has a l a r g ~ e f f e c t on t h e m a g n i t l ~ d e o f t he DUF. Fo r a l o a d d u r a t i o n less t h a n anc h a l f o f the sysrem p e r l a d , t h e 3AF i s l e % s Lhan 2.0 dnd can be l e s s t h a n 1 . 0 .
!n g e n e r a l . an i m p a c t loaC r l r ~ c r l r n c e d b y a c d s k ~ 1 i 1 :how t h e e f f e t t s o f b o t h f i n l t f ri;p t i m e and d u r a t i o r , . AI ~ x a m p l p f o r d t r i , l n g t f l d r p d l s e i s shown i n Fig. : . I . For t h i s p a r t i r u ! a r . l o a d shapc, t h e m d * l m m 3AF worrld be 1.5.
When m l d t l I ny d t j r ee - d i m ~ n s i on31 s t r u r t l l r e d s s i m p l e lumped -ma:% system, k i m p l i f y i n q r l i ~ u r n p t i o n s need t o b e u r v d . For- end-on i m p a c t or.lg, mu1 t i - d i m e n s i o n a l ef fpyt ,5 may he d v o i d e d by o n l y d l lo*ring d x i a : degrccs 01 Freedom i n t he mode ls . F r ~ r t h e s p models, t h e cack I r d i s c r p t i 7 p r I i n t o n rs8Jmhel' O f elements. Each nwle i s dsqignerl a m e s r a n d each c l m p n t a s p r i n g s t ~ i f n r r s . I n some r m p u l p r programs ( e . q , Ref. 6 ) . t h r s ~ 5 t i X f n e i s e 5 a r e C d l r u i a t e d e x t e r n a l l , t o t h e code. P l a n s s e c t i o n s o f t h c cd:k a r p assumed t o remdi r l p l a n e and normal t o t h e r e n t e r l l n w o f t h e cask . T h u s , t h * l e a d s h i e l d i n g ;; arrumed t o e x p e r i e n c e the Sdmp d e f l e c t i o n a s t h e r l w l s h e l l s w h i c h sur rn l r+ ~ t . :n e f f e c t , th13 mudel d<sumps p p r f e c t 5 o n d l n g bptwppn t h e l e a d and s ' . ~ r l f o r t h e a x i a l c a s e . f o r tc ! id ing , c o m p o s i ! ~ s t l f f n e & \ o f
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