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cb u s)k ltI ) J 20 em Jk 25 em

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1S1 ~1) J-I ~ r ) )LOI (n(I)(1)

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rj ~ ~ S D H rfgt 111 ~~ JS is) r d$ ltNs --gtr)1 0Lj - )W ~

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1=5760 Will (W) r (rr)

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r= 125 em = 492 in t=2mm=0079 in W= 30 gr R 30 em P = 1025 kg I m3 = 64 pef Oy = 360 MPa 52 ksi IO = 876 Ns = 1969 Ibs

l1 IS) 142 mm 4 056 in ~

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6E P P 2 X 2l(I-x) (J= pm

a p2 C 2 (I-v)

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(rv)X= m

~~ ~I rr- m lojli 8 )1)gt lt45

fO-)gt AIl- )11 sl) 1

E = 21 e 11 Pa = 439 e 9 psf Pp= 7800 kg m3 48695 pef Pm = 5427 MPa = 11334468 psf

P = 1025 kg 1m3 = 64 pef c = 1463 mls 4800 fils V 03 8=2975ls m=3206psf x= 2851

89698 ksf )I) Cla)~ (r7) J~ jl~)1~

Ak)l lt45 )J )w ~1 s- ~ 4295 MPa ~

jI lt45 1 ltSII~ ~ ~gt )~ )~ )11 gtsshy(4176 MPa) 1 bulllo1 gt ~ sltgt ~

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~ 065 in )I) )15 ~ ~I) )11 ltJLI ) lt45

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ul) 41 t ~ sl )b w jSyo 015 ~

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214EPp Pm 2 X (I-x)

cr =0867 2 2P c

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middot4 ltsA)) 1SLs jacket ~~ jl ~

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4Ji jI s I )1 ~ 19 )) ~ ))li

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10 ) x4 Jb 1 80 cm ~ibS IO m ~

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1 163 mm )IJi IS ~

wGtA Pr Js ~ lSI) Nurick ~~

[A]I)j w) ~ ~

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1 ~ wGtA lSI) ~ ltS-I 14 lt1gt

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r~J6~~~ ba ~I))I))

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a = 15 em = 591 in b = 125 cm 492 in

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Jb- r pound ~ I) Jb- w )1 ) ~i ) ~ 21) ~Igt ~4J )) ~ rs ~ 6 x 5 cm

01 131 Ns = 2945 Ihs

Pr IS ~ 17270 )I) ltfgt r ~r~

~1 rs ) ~ 163 mm 4 064 in ~

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b ~Igt ~I) )1 jb ) 0 = 0813 in 207 mm

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bull1 0002 s y1y bull

~L st JIo ~l ~ () J~ )l

r-oL riO li 6 4 st ~ 1 0101 bull

JI~ )-I )l lil 0 s)lS Ili D li A 4~ -

~ (in (I) ~I) jl ~ ~flo

~ Jraquo 4 bull ~ ltS~ ~I) I 0lli1 4 LS

~ t ~ )i ~ ~ 4 y1y )i ~ sl o)b

12 JIgt~)i ~ ~ y1yJgtr 4 ~ Nuriek ~I)S )1 - 1 0 6 Jgtr y1y

s~ es I Sly s~ ~l ~ Ib l A Sly

(25 em) ~ st 6 )l 41 bulllAl IS l -

i l rmiddot llgt )l1 ~~~ byr ~I)

Sly l IS s)amp ~l )I 5s ~)l fmiddot li imiddot llgt ( 1 15 em) ~4 st 6 Sly

~ )) imiddot li rmiddot llgt )~ st 6 Sly ~))

bull ~ IS )1gt 100 ~ Slamp ~l I 5s R lao = 60 4 )~II 1 em 6 4~ Sly

r)Y li)b sgt~ s )lj ~~ )l IS

0101 (A8 li A5 st JIo) () J~ )) i ~l

(TNT j ~ ~ ) u19 JI)I 4~ II 1

- ~ )l lol l4 IS JI)I LS ~

li)Ili ~ 4 slj 9)tgt1 ~l bull l) )) oJ

bullIgttgt JI)I 4 IS 1 )-I ~l )tJ1 kLi ~

() st jgt )l ~l1S J-AgtIS LS ~

A st JIo sly ~ - ~ ()

)-I r)Y l) IS bull1 6 )l ~ J-li ~ S)

) - ~1 ~ 91)01 ~4 ~b 1 ~

l IS JIo 0jL ~I 22 m uli li sl oljl-I

r-oL 25 2 bull 15 bull 1 sUt6 4 t ~ IS Oly 100 kg TNT o~ DlL lil D ~lgt1

jl sr-o 20 16 12 8 JI )l ~ 6 A Sly

r l jl y1y u19 4 ~6kLA)l ~ ~

~ Sly Ut JIo )-I y ojs 1 bull bull lb 1) (i

slA- j 4 TNT bull~ OlL bull 1 em Igttgt 4 bull1 bull r)Y sr-o 20 l 8 J1)lJ

ollo tL - u19 ~ 41 olAgt sly IS sl olj -

~I ~yen kLi ( R lao = 60 ) 1 60 y1y 0~

bull ciJ )U )) 152 grem3 Ar TNT)~ bull1

~ to )-s)~)ls~)lj sgtLj ~)li

jl bulllli1 4 ~ ~ fr ~ )~I J-- ~

)~ IS JLs1 P(t) Pm - byr r~ ~I) 100

s )lj sgtLj ~)li olj~ sly (A) JS )l

1) Sr-o rmiddot A u19)l 100 kg TNT - b~r

360

~

ii ~

R=20m

20

lU

0 0 I 20

Time (IJIt)

IOOkg IJ s~)ut)IoJ

rmiddot A JgtI J~ ~)ll A~

TNT

)wgt r )lj )u )wgt loj )l IS l ~yen ~4

)l sgtloj 10 ~ IS )1 100 I)) l IS Jgt) s~ es l ~ IS J1 )~I uJ 11107 s llgt

LA r li ~ 11 ~ gtJY )U )) to -

)iu )l bull l)b 385 MPa y1y ~ IS ST 52

~ 4 S4R~J f WI nmiddotmiddot 4~ l~ IS ciJ

AC3D8R WI iiAmiddotmiddot 4JI- ~ 01 m llgt

s- ~ li~ IS slj-o 02 m llgt ~ 4 bull ~ raquo 100 4 ~ JL JiL JI- jL

~~ )l Ut u )-I ~ li~ IS ~~ -

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~I Jlgtu

0tS ~ )l ( f) l ( ) -S1As)l

0 )lI-SlI))l )~I-S) d ) uJb ~

)l (1 ~ r-- )l 0tS ~ oaC ltIS) s J -SlA l -SIr bull~ ollo )IJ JoIs

ltIS )1gt 01A lil bulll ~to pgtA 4 (t25 l tl)uJ

~15 0tS ~ l rlljl 4 l)lt5 )UI

)l ltIS s~)l 01 lt5 lA)b r1jl ~~~ lt5

l d bTr 0tS~ )~I J- )1 ulS I

bTr 0tS ~ )1 rs )l 30 lgtgt (ti) I em

-slAl -sIr 1 (tl5) 25 em l d

-st gtI~ )1gt d 0tS ~ r1 -i )l

~lt5~

A4 Jlo(d A3 Jlo(e

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1 o~ olb 0l lA uJ

~ () () -slAsI l) ~ )l

jI ~ uJ r JIraquoI bli -r )l ltIS 1

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)ts r-gtu 4 )lz9 ~)l ~t s (s

~~ r~l~ ltIS uJ b ~ d ~ )lo)

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middot~4

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)~Isr) 411 eo~ u_)~ 25 em 6 Irs 411 sIr 0002 s

00 05 10

o~----------

12 --------------

Dl Jc(a

~1ol)1) ~~~ ~

05 10 15 20

16 --__________J

r 2 5 2

I 5

II

12m from l()()kgof TNT

12 5

tl t I 5 I

8m from IOOmiddotkg of TNT

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20m from IOO-kgof TNT

loS (~ shy)j )~I JL s~~ siL ~ 4llii r1 )~

~I) ~ ol I~I jyi-o s1A OjL J~ )~ 1

~l ~ 1 ol ~lii ~ sU~ ~

~ ~ oL ~ ~ JlL ) ltcent~ 1Jlb1 ~

)~I o~ JlL kbU sl) sgt~ JIo JlS J~

jyi-o s1A 4lJ sIr 1 ~ s1A jL r i r)

4lJ -h9 ~ ~ -h9 ~ srb ~ Jgtlao I) ~i ~I

Jb 4lJ -h9 ~ ~ Jgtr ~ ~~

~ ~l Nuriek ~ J- f~ Jgtr Ir 12

r1 ~~ db ~ ~)b s~~ ~l ~ ~~~

JoIs )~ ~ )l ~~ ~lj ~I )gt IS 1 IS) ~~ 411 jL l )~I Jgt du ~ Igt ~

~ (~ Jlblgt ji ~ L tt= 411 4 I~ )l lS U Irj l Jlblgt fs)j ejL Jl1

rj eb ~)y ~ ~ ~yO 1)-0 ci~ lS

IS 1 tamp~ 41~~ J110Lj )l ~

4 ejL JlI ~~ 4bt1) ~ ~ ~ r1

~)~I Jgt )1 du

00 05 10 u o~--~----~--~----~

-8

125

12

115 It

16m from IOO-kgof TNT

l AS) As1A JIo 1 sr ji (6) Js )

uo ~ ~ ) Js r1 ) IJIl ltr)r (AS

1 em ~ ~ uJ sIr )~I s) ~ ) uJ 6

60 rlr R I ao ~ IS )~I ~ s1AJb sIr

JiI1gt yS11gt J~I ~ r1 )~ Jlb~ 0~ I) IJ)~

1 -WI) 4S ~1gt (0002 S 0Lj )~) ~ ~

0 05 15

0

-2 E R8-4shy RI2 c 0 -6 RI6

8 =

R20 ~ 0 10

-2 1-_____________---1

- )ltiil lIbSI1So ~ )I~ 0 JSj

Rlao =60

~I ~~ ~ IS ~ Jlbl ) r1 )~

1 sL )~I ~ ~b sIr ~ )l

~lj R lao ~I )~ IS R 411 4 LI (13S3 MPa)

411 r- 0~ ~ bull1 ao 41 ~ ~

~~ ~ ~~ 4 IS 1 r1 i lc IS ~~

uu 411 4 4i Lj ~lj s )l yS11gt

uu 411 ~ )l JItgtlS U rlr~ ~~ 411

) 0Lj -)l ~ rj eb ~~ JItgtlS

~ ~ ~ r1 ~I ~ ~yO Aigt

)~I Jgt )1 d13 ~ jL Jl1 ~~ bL)

~(R)

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rA~ 0 I JG

bulliJ 1oS1W ~ Jw 18ti ~ J~

Model

Charge weight

W(kg)

Distance between charge and pipe

R(m)

Max VonshyMisesstres5

(Numerical)

(MPa)

Max Von-Mises stress

(from Eq (26raquo

(circular plate)

Max Von-Mises stress

(from Eq (32raquo

(rectansular plate)

Max deflection

(Numerical)

d (mm)

Nurick

prediction

(Eq (20raquo

de (mm)

Rajendran

prediction

(Eq (24raquo

de (mm)

Jones

prediction

(Eq (25raquo

de (mm)

Nurick

p ediction

(Eq (28raquo

dr (mm)

Rajendran

prediction

(Eq (30raquo

dr (mm)

Jones

prediction

(Eq (31raquo

dr (mm)

E -

Al

A2

A3

A4 foshy

100

100

100

100

8

12

16

20

40010

33308

25492

20005 ---shy

30320

19470

14212

11131 ------~--

33596

21573

15748

12333

1839

1029

772

591

1808

1328

1079

925 -----shy

1587

975

658

462 ------shy

3044

2121

1641

1345 -____--shy

1923

1340

1038

851

2991

2307

1951

1732

2355

1453

1005

743 ___--shy-shy -

II- A 1509 8 27044 13467 14922 543 706 183 924 584 1419 403

A6 5094 12 25610 14645 16227 753 946 489 13 86 876 1762 778

A7 12074 16 27600 15376 17038 863 1186 795 1848 1168 2105 1195

AS 23581 20 28723 15884 17600 1004 1427 1101 2310 1460 2447 1635

E Bl 100 8 38561 27941 30960 1408 1387 683 2012 1272 2602 1103

B2 100 12 29289 18014 19960 1002 1069 279 1402 887 2150 612

II- B3 100 16 2181 13 186 14610 671 905 070 1085 687 1915 391

B4 100 20 17079 10348 11466 545 803 -060 889 563 1770 273

Cl 100 8 3693 26060 28876 1306 1237 126 15oJ 951 2601 557

sect C2 100 12 2569 16855 18676 889 1000 -176 1047 663 2263 288 N

II- C3 100 16 18871 12365 13701 624 877 -332 810 514 2088 177

C4 100 20 14761 9721 10771 490 8Ql -429 664 421 1979 121

E DI 100 8 33846 24578 27234 1174 1195 -276 12 II 767 2743 313

on D2 100 12 22817 15938 17660 778 1004 -519 844 536 2470 157

N II- OJ 100 16 16739 11713 12978 545 905 -645 653 415 2329 095

D4 100 20 13083 9220 10216 438 844 -723 535 341 2241 064

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I - Cole R H (1948) Underwater explosions NJ USA Princeton University Press

2 - Smith P D and Hetherington J G (1994) Blast and ballistic loading of structures Butterworthshy

Heinemann

3 - Chung M and Brett J (1997) Assessment of underwater blast effects on scaled submerged cylindrical

objects DSTO Aeronautical and Maritime Research Laboratory

4 - Huang H and Wang Y F (1970) Transient interactions of spherical acoustic waves and a cylindrical

elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 48 No1 PP 228-235

5 - Huang H and Wang Y F (1971) Early-time interaction of spherical acoustic waves and a cylindrical

elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 50 No3 PP 885-891

6 - Geers T L and Hunter K S (2002) An integrated wave-effects model for an underwater explosion

bubble Journal ofAcoustical Society ofAmerica Vol III No4 PP 1584-1601

7 - Nurick GN and Martin 1 B (1989) Defurmation of thin plates subjected to impulsive loading-a review

Part I theoritical consideration International Journal ofImpact Engineering Vol 8 No2 PP159-170

8 - Nurick G N and Martin 1 B (1989) Deformation of thin plates subjected to impulsive loading-a review

Part II experimental studies International Journal ofImpact Engineering Vol 8 No2 PP171-186

9 - Teeling-Smith RG and Nurick G N (1991) Deformation and rupture of blast loaded circular platesshy

predictions and experiments International Journal ofImpact Engineering Vol 11 No1 PP77-9

10 - Rajendran R and Narasimhan K (2006) Deformation and fracture behaviour of plate specimens

subjected to underwater explosion-a review International Journal ofImpact Engineering Vol 32 PP1945shy

1963

II - Rajendran R and Narasimhan K (2001) Linear elastic shock response of plane plates subjected to

underwater explosion International Journal ofImpact Engineering Vol 25 PP 493-506

12middot Bangash RY H (1993) Impact and explosion Oxford Blackwell scientific publications

13 bull Lam KY long l and Wang Q X (2003) Dynamic response of a laminated pipeline on the seabed

subjected to underwater shock Composites Part B Vol 34 PP 59-66

14 - Zong l Lam K Y (2000) The flexUral response of a submarine pipeline to an underwater explosion

bubble Journal ofQlJshore Mechanics and Arctic Engineering Vol 122 PP 194middot199

15 - ABAQUS Users Manual (2003) Ver 64

16 - Rajendran R and Narasimhan K (200 I) Performance evaluation of HSLA steel subjected to underwater

explosion ASM Journal ofMaterials Engineering and Performance Vol 10 PP 66-74

jiA )~ lI~liNIl ~ ~ ~11SAt IIjl

1- Explosion 2- High explosive

3- Pressure pulse 4- Shock wave

5middot Bubble pulse 6- Cavitation

7- Peak pressure 8- Coupled acoustic-structural medium analysis

9- Compressible 10- Volumetric drag

11- Inviscid 12- Bulk modulus

)3 Radiating acoustic boundary 14middot Transient analysis

15middot Weak form 16middot Traction

17- Mass proportional damping factor 18- Discretize

19- Strain interpolator 20- Explicit dynamic integration

21- Nonreflecting 22- Impulse

23middot VonmiddotMises 24- Inverse mass number

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