.

tye ey

“all,

TECHNICAL REPORT
CIVIL ENGINEERING LABORATORY

Naval Construction Battalion Center, Port Hueneme, California 93043

DESIGN FOR IMPLOSION OF CONCRETE CYLINDER
STRUCTURES UNDER HYDROSTATIC LOADING

By

Harvey H. Haynes

August 1979
a ed by
i FACILITIES ENGINEERING COMMAND

NO,

‘or public release; distribution unlimited.

Ret

Unclassified

SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

REPORT DOCUMENTATION PAGE

T. REPORT NUMBER 2, GOVT ACCESSION NO| 3. RECIPIENT'S CATALOG NUMBER
TR-874 DN04405 3
4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED
DESIGN FOR IMPLOSION OF CONCRETE CYLINDER Not final; Jul 78 - Mar 79
STRUCTURES UNDER HYDROSTATIC LOADING

6. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s)

Harvey H. Haynes

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK
CIVIL ENGINEERING LABORATORY : Hee ae hae cami
Naval Construction Battalion Center : 3.1610-1
Port Hueneme, California 93043

11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE
Naval Facilities Engineering Command August 1979

Alexandria, Virginia 22332 aoe OlF PINSIES

14. MONITORING AGENCY NAME & ADDRESS/if different from Controlling Office) 15. SECURITY CLASS. (of this report)

Unclassified

1Sa. DECL ASSIFICATION/ DOWNGRADING
SCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report)

18. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse side if necessary and identify by block number)

Concrete structures, pressure-resistant structures, concrete cylinders, implosion, submerged

concrete structures, undersea structures, unreinforced concrete, hydrostatic loading,
design guidelines, buckling.

20. ABSTRACT (Continue on reverse side if necessary and identify by block number)

This report presents updated design guides for both thick- and thin-walled concrete
cylinder structures under hydrostatic loading. The design approach for thick-walled cylinders
has been changed from that described in previous work to a semi-empirical basis; improve-
ments in implosion strength on the order of 10% are found. A test ona thick-walled 10-ft-diam
(3.05-m) structure loaded to failure in the ocean is reported. A major change in the guides is

continued

FORM ps
DD , jan 73 1473 = EDITION OF 1 Nov 65 1S OBSOLETE Unclassified

Ww neu nA

0 0301 0

SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

Unclassified
SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered)

20. Continued

for thin-walled cylinders, where new data on 15 relatively large-scale specimens are
reported. Design guides for thin-walled cylinders show an increase in implosion strength
ranging from 0% to 35%, depending on the structures’ t/Dg and L/D, ratios, from that
reported previously.

Civil Engineering Laboratory

DESIGN FOR IMPLOSION OF CONCRETE CYLINDER
STRUCTURES UNDER HYDROSTATIC LOADING,

by Harvey H. Haynes

TR-874 85 pp illus Aug 1979 Unclassified

1. Concrete cylinders 2. Hydrostatic loadings I. 3.1610-1

This report presents updated design guides for both thick- and thin-walled concrete
cylinder structures under hydrostatic loading. The design approach for thick-walled cylinders
has been changed from that described in previous work to a semi-empirical basis; improve-
ments in implosion strength on the order of 10% are found. A test on a thick-walled 10-ft-
diam (3.05-m) structure loaded to failure in the ocean is reported. A major change in the
guides is for thin-walled cylinders, where new data on 15 relatively large-scale specimens are
reported. Design guides for thin-walled cylinders show an increase in implosion strength rang-
ing from 0% to 35%, depending on the structures’ t/D, and L/D, ratios, from that reported
previously.

Unclassified
SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered)

INTRODUCTION .

Background
O\SNCEDE 3 o o o a
Description of Tests

DESIGN FOR IMPLOSION
Thick-Walled Cylinders

Thin-Walled Cylinders
Factor of Safety
SUMMARY .
CONCLUSIONS
ACKNOWLEDGMENTS
REFERENCES

APPENDICES

CONTENTS

A - Thick-Walled Cylinder Tests .
B - Thin-Walled Cylinder Tests

LIST OF SYMBOLS

24

29
39

81

b

INTRODUCTION

Background

In the mid-1960's ocean engineering attracted considerable interest
in research and development on providing man with the technology to
work in the deep ocean. Research on undersea concrete structures was
initiated at this time, and exploratory test results showed much promise
(Ref 1) for concrete structures at depths to 3,000 feet (1,000 meters).
The economic payoff of the research was that massive undersea concrete
structures would cost about one-tenth that of metallic structures.

For the first several years, research was directed solely to con-
crete spheres, but tests on cylinders started about 1970. The early
cylinder models had an outside diameter of 16 inches (406 mm). Param-
eters such as cylinder length, wall thickness, end closure conditions,
and concrete compressive strength (Ref 2 to 4) were investigated and
studied.

The North Sea oil boom occurred in the early 1970's, and the first
offshore concrete platform, called Ekofisk, was built. With the success-
ful installation of Ekofisk in a water depth of 270 feet (90 meters),
industry ordered additional concrete structures for oil drilling and
production. A dynamic development period ensued during which it
became apparent that knowledge on the behavior of pressure-resistant
concrete structures was substantially lacking.

In an attempt to make existing data known, Civil Engineering
Laboratory (CEL) test results were distributed widely (Ref 5 to 8).
However, the early work on cylinder structures was quite tentative

because of limited data on thin-walled cylinders.

A major oil company proposed a test program on large-scale,
thin-walled concrete models. This proposal eventually led to a joint
industry-Navy test program carried out at CEL.

During this period another important test was conducted at CEL on
a large thick-walled concrete cylinder structure. The structure, called
SEACON I, was part of an integrated seafloor engineering experiment to
demonstrate capability in constructing operational facilities in the ocean
(Ref 9). The structure was built in 1972, placed in the ocean at 600
feet (180 meters) for 10 months, and then retrieved. After being on
"display" for several years, it was tested to failure in the ocean in 1976

to determine its implosion strength.

Objective

This report presents updated design guides for implosion of con-
crete cylinders. The guides are based on the test results from the
thick-walled, SEACON I, cylinder test (Appendix A) and from the
thin-walled cylinder tests (Appendix B). The approach to design is
similar to that already presented in Reference 8. However, the new
data are superior to that presented previously, especially for the thin-
walled models. The updated guides for thin-walled cylinders allow such
structures to operate at considerably deeper depths than indicated in

the past guides.

Description of Tests

Thick-Walled Structures. The SEACON I structure was a rein-
forced concrete cylindrical hull having hemispherical end closures. The
overall structure length was 20 feet (6.1 meters); outside diameter,
10.1 feet (3.08 meters); and wall thickness, 9.5 inches (241 mm).
Steel reinforcement of 0.7% by area was used in both the hoop and axial
directions. At the time of the implosion test the concrete compressive

strength was 10,470 psi.

During the long-term loading test of the structure at 600 feet,
results were obtained on the structure's response from initial loading
and creep. Although the data are interesting, the pressure load was
relatively low, only 14% of its ultimate strength. Of more significance
was the implosicn test where the structure was lowered into the ocean
until failure. Complications occurred during this test which precluded
obtaining structural response data, but the implosion pressure was
successfully obtained. This test with its results is presented in Appen-
dix A.

Thin-Walled Structures. The thin-walled cylinder test program

encompassed 15 unreinforced concrete specimens, whose dimensions
were: 134 inches (3.4 meters) length, 54 inches (1372 mm) OD, and
1.31, 1.97, or 3.39 inches (33, 50, or 86 mm, respectively) wall thick-
ness. Two different boundary conditions were modeled, a free and a
simple support, in order that cylinders of two effective lengths could
be studied. The concrete compressive strength ranged between a
nominal 7,000 to 8,000 psi (48 to 55 MPa).

Structural deformations were monitored by recording radial dis-
placements around the circumference of the cylinder. Accurate initial
and deflected cross-sectional shapes were obtained which showed the
progressive development of out-of-roundness.

An analytical study using actual material properties and geometric
conditions was conducted. A finite-element analysis with an advanced
constitutive material model was used.

This test program on thin-walled cylinders is presented in Appen-
dix B.

DESIGN FOR IMPLOSION

Thick-Walled Cylinders

The design approach for unreinforced, thick-walled cylinders is

based on an average stress distribution across the wall of the cylinder

at implosion. Near implosion, the inelastic behavior of concrete along
with plasticity and creep impart a stress distribution across the wall
that is more closely modeled by a uniform stress distribution than by an
elastic (Lamé) stress distribution. A uniform stress at implosion is

expressed by

Zo)

Gill ee = (1)

where OF = wall stress at implosion
Me implosion pressure
Ro = outside radius
t = average wall thickness

The wall stress at implosion, OF can be expressed as the ultimate

compressive strength of concrete multiplied by a strength factor.
oO. = KO f° (2)

where kK. = strength factor for cylinder structures under
hydrostatic loading

Be = uniaxial compressive strength of concrete

The term K, was determined empirically. Figure 1 shows kK, as a
function of length-to-outside-diameter ratio, L/D); for cylinders of
various wall-thickness-to-outside-diameter ratios, t/D,.

For cylinders under hydrostatic loading, the wall is stressed
biaxially in compression on the inside surface and triaxially in compres-
sion at all other locations. The two major stresses are in the hoop and
axial direction where the hoop stress is about twice the magnitude of
the axial stress. The third, and smallest, component of stress acts
radially. If the concrete is considered biaxially loaded, then the hoop-

to-axial stress ratio of 2 is known to increase the compressive strength

‘siapur[Ad payyem-yorya 10y °q/7] pue °y usamiaq drysuonejay *{ ain8iy

p—
O
(v ddy)
uodtas sraydstuayy
a ddy dad

4 asoydstuayy
HE? aroydstuay
+ asoydsiuay

Jou uonipuop
pia

>

ae

a/7 ‘sai9ueI episino/yIBuUI7T 1epul|AD

v

€

sorayds payjem-yorya
oj Sy uinururu

90

80

Ss
as

cl

VL

oi

°y ‘tose YyIBuUaI15

of concrete by a factor of about 1.25 I (Ref 10). Therefore, Kk, values
for the cylinder test specimen of this program should show a value on
the order of 1.25. As a minimum, kK, should be 1.0.

Figure 1 shows that short cylinders, those of L/D, <1, hada kK,
around 1.25. However, longer cylinders showed a K, on the order of
1.0. The decrease in kK, was probably due to specimen imperfection.
The short specimens were also imperfect, but end-closure effects
restrained the cylinder wall. At L/D, of 2.0 the end-closure effects
were diminished.

An average K, value of 0.89 was observed at L/D, = 4. It was
speculated that some unknown fabrication or testing problem existed for
the cylinders of this length in comparison to the other specimens.*

For design purposes, a K, = 1.0 was selected for cylinders of
L/D, 22. The reader is reminded that this kK. includes the effect of
out-of-roundness and experimental error. The reduction in K, from
1.25 to 1.0, a 20% change, is difficult to assign solely to out-of-
roundness effect because thick-walled structures are usually insensitive
to small geometric out-of-roundness. Hence, K, = 1.0 should be a

conservative strength factor for design purposes.

*Much attention was given to why k_ should be as low as 0.89. If
out-of-roundness was the sole causé, then the specimens showed a
decrease in strength of 29% due to out-of-roundness, which was too
large an effect for thick-walled cylinders. There appeared to be no
reason based on engineering mechanics to cause cylinders with L/D_ of
4 to fail at lower pressures than those at, say, L/D. of 8. It is be-
lieved that some problem related to specimen fabrication or test was
responsible for the low strengths. The author personally participated
in the fabrication and testing of some of the specimens under consid-
eration. He discussed this topic with others involved in the test pro-
gram, and no procedure was singled out as suspicious. One procedure
that was distinctly different for specimens of L/D_ of 4 and 8 from
that of the shorter specimens related to the interior mold. The inter-
ior mold was made in segments having a length of L/D. = 2. Cylinders
longer than L/D, of 2 used multiple segments. During mold removal
operations it was quite difficult to disassemble the multiple segments to
extract the interior mold. If harm was done to the specimens during
this operation, it was not recognized at the time.

Although the cylinders were fabricated in rigid steel molds (Ref
2), the mold segments sprang slightly after the first disassembly.
After References 2 and 4 were already published, a short cylinder
section was mounted in a lathe to determine out-of-roundness more
accurately than had been done previously. The inside and outside
radius and the wall thickness varied by +1/32 inch (1.6 mm). The
out-of-roundness parameters are summarized in Table 1.

Substituting Equation 2 into Equation 1 and using R, = D,/2 gives

the expression to predict implosion pressure for thick-walled cylinders:

Pe — ke Ee (t/D,) (3)

where k_ = 1.25 - 0.12(L/D,) for L/D <7)
aks 1.0 for L/D, 2D.
Equation 3 is shown in Figure 2,
which can be used as a design _. ‘4 Sit ae ee mae
chart. = Al Oe
A more general design chart = He
approach is shown in Figure 3. & Seah ao
The chart is entered with a cylin- 5 ei
der L/D, and t/D, to obtain the E
Ee i ratio. The implosion pres- : 0.3 |
sure can then be calculated by Z |
assuming a concrete compressive ra a)
strength, fo = 01 C\D, |
The effect of different types — |
of end-closures on the implosion oe OORe! OGL MOTELOLOMNODe
strength was judged to be small Wall Thickness/Outside Diameter, t/D,
(Ref 3) so this parameter was not Figure 2. Relationship of Equation 3 for

included in the design equation. thick: walled cylinders:

Cylinder Length/Outside Diameter, L/Do

lo)

long
cylinders
Pim/f¢ = 0.02
0.04
| 0.06
0.08
0.10
0.12
0.14
moderately / 0.16
long cylinders if | 0.18
/
i ras
i, thick
fe cylinders
Ht | | u
10) 0.02 0.04 0.06 0.08 0.10 0.12

Wall Thickness/Outside Diameter, /Do

Figure 3. Design guide for predicting implosion of concrete cylinder structures.

Thin-Walled Cylinders Table 1. Out-of-Roundness Parameters for
16-Inch OD Cylinders (Ref 2,4)

Thin-walled cylinders are
t/Do NE a I AR;/t
divided into two categories: moder-

ately long cylinders and long cylin- oe ae
ders. Moderately long cylinders es 0:08
0.03 0.03
are influenced by end-closures
0.02 0.02
which restrain the cylinder from
Pe
instability failure. Long cylinders Thin-walled cylinder.
b
: Border between thin- and thick-walled
are not influenced by end-closures eyinder
and behave as infinitely long cylin- Grpaferewalledieylinder

ders. In Reference 8, thin-walled

cylinders included another category called short cylinders, but in this
report the thick-walled cylinder category encompasses short cylinders
(Figure 3).

The same approach used in Reference 8 is used herein. Donnell's
equation is applied to moderately long cylinders and Bresse's equation
to long cylinders. An empirical plasticity reduction factor, n, is used
in both equations to account for inelastic behavior of concrete and
specimen out-of-roundness. The new data permit an n relationship to
Oe. to be determined with far greater accuracy than previously.

Empirical n values were determined by calculating the elastic stress
at buckling and dividing this stress into the experimental stress at
implosion.

The elastic buckling stresses were calculated as follows:

Donnell's Equation

0.855 E.
i

Cao = 3/4 (Ge

R
== |i (4)
(Cs v’) y

and

Bresse's Equation

18,0 2
2 i ie
EO ie # |e) i ra

Using v = 0.20 and the approximation R = D,/2, Donnell's equation

becomes
Pes)
t
1.25 Be i foal
Gen = L/D, (7)
and Bresse's Equation
fs 2
GC )en = 104 B, "(a-) (8)

The elastic condition exists when n = 1.

E; was not measured for each specimen so an empirical relationship
was developed to calculate its value. Figure 4 shows the experimental
initial elastic moduli data as a function of compressive strength. The
American Concrete Institute (ACI) expression for elastic moduli is

shown for comparison along with the empirical expression:

ES = 530 Ene (9)

10

The empirical expression has the rational basis of being derived from

the parabolic relationship for tangent modulus as follows:

2 f
bo = se LS
u c
where E. = tangent modulus
Ey = ultimate strain (experimental average was 0.0025)

and the fitted condition of o = 0.56 f when E. = EL:

6.0

57,000,/F2

5.0

4.0

Initial Elastic Modulus, E;, x 10° (psi)

3.0

© 6x12-in. control cylinder

2.0
5,000 6,000 7,000 8,000 9,000 10,000
Compressive Strength, f{ (psi)

Figure 4. Relationship between E;
and f¢.

11

aAdaJap usuTDads

daldajap uautsadg

(450)
ss'0
Sr oO
8720
150)
LS°0
(40)

060°9T
OS9'+T
OPL'8T

06 ‘9T
O8Z‘ET
OOL‘ET
aa als

OFZ 8ST
O09 LT

bot
60'T
060
LS°0
£0'T
vIT
£0T

OTE'S
OL6L
O8E'8

079'r
060°
OLL'L
Oft'L

aanodajap uaurtdads

S>HIBUIOY

9L0
860
c8'0
LOT

= F(A
( \p
R) Sut
iJ OES a q
= Es
E) UONFHBA JO IUID173209 = AOD,
vS 088 La OLS'8 cS
€or 8LO'T CT 066° T-S

07z0'8 E+
OTE'L (Ga,
OE 6 I-+
OLT'8 be
0L8°9 E-€
0£8°9 C-E
O6T'L T-€

(isd)
d(4"0)

g SS9I1S
s,JJauu0g

(isd)
a (Ulo)
p s823S
S,assolg

siopul[Ap 3u0T

Ajaieiapow

siapuljAp 3u07

UI5 j‘ssa1sg
12M edeisay

I ull
(isd) 901 Xa (asd) 'd ON
q SnInpow ainssaig marnpndls
ose[q [eu uoisojduwiy :

yazuas
dAtssaidui0sy

suauttoads GO Youy-+§ 10} s1019eY UONONpsy AidAse[q “Z IqQeL

12

Values of n are shown in Table 2. Table 3 shows the calculation
of n values for the data from Reference 4.* All the data are shown in
Figures 5 through 7. The fitted inelastic buckling curves of Figures 5
and 6 were transferred to Figure 8. From this representation of data,
a design n curve was selected, which is applicable to both moderately

long and long cylinders. The n expression is:

oO. oO.
n = 1.65 - 1.25 (G2) On5 2) ee (10)

Gerard developed expressions to predict n for metallic structures
(Ref 11), and these expressions, which can be applied to concrete, are
shown graphically in Figure 9. The n curve from Reference 8 is also
shown. Its empirical shape was defined by limited data where several
specimens had low implosion pressures which are not in agreement with
that of the new data. The new design n curve has a maximum increase
of 35% over that of Reference 8. (For a structure of given geometry,
comparative n values are obtained by a linear curve intersecting the

origin and the n curves.)

*The values will be different than those given in Reference 8 because
an assumption has been changed. Previously, the 16-inch OD speci-
mens with hemisphere end-closures were assumed to be simply sup-
ported cylinders. This assumption was made at the time because the
analysis of results would be conservative. Data were limited so con-
servatism was warranted. In this report, the 16-inch OD specimens,
which had an L/D_ = 4, were assumed to be freely supported or, in
other words, long €ylinders.

13

Table 3. Plasticity Reduction Factors for 16-Inch OD Specimens (after Ref 4)

Compressive Long Cylinders

Strength
Sane Initial Elastic Implosion Average Wall
Oe ts Modulus,? Pressure, Stress,© dim Bresse’s
oO. a 2 : . Re ed
cov’ E;x 106 (psi) Pin (psi) (psi) Stress,
(im)B

(psi)

t/Do = 0.031; Free End-Supported; L/D, = ©

1/2-10-N 4.50 376 6,020 0.56 4,570

1/2-10-G ANOS, 349 5,580 0.51 4,610 1.21
1/2-6-N 3.00 203 3,250 0.60 3,050 1.07
1/2-6-G 2.60 214 3,424 0.59 2,640 1.30

t/D, = 0.063; Free End-Supported; L/D, = ©

10,700 1.5 4.50 1,110 8,880 0.83 18,280
10,480 1.4 4.32 1,103 8,820 0.84 17,550

6,620 LO) 3.20 543 4,340 0.66 13,000
5,920 5.8 3.10 530 4,240 0.72 12,590

t/Do = 0.125; Free End-Supported; L/D, =

3.2 3.90 DOS 9,340 0.95 63,370 0.15
407 4.24 2,455 9,820 0.99 68,900 0.14
3.0 3.29 1,387 5,550 0.91 53,460 0.10
2.3 3.36 1,447 5,780 0.96 54,600 0.11

t/D, = 0.188; Free End-Supported; L/D, =

10,350 2.8 4.10 149,910
10,800 DP) 4.60 168,190
7,000 3.0 2.94 107,490
6,200 Dol 3.11 113,710
4COV = Coefficient of Variation é 0:5 Pim
Sim «eRe
D iccranell oeltn, Do
2
t
40g, Jp = 1.04 F(55)
to)

14

= 54 in. (1372 mm)
= 127 in. (3225 mm)

\ material failure

Simple Support End Condition

h eee — ip ' :
WAST ON ale Le f¢ = 8,000 psi (55 MPa)

elastic \
buckling 2) \

\
N
\

inelastic
buckling
(fitted curve)

10) 0.02 0.04 0.06 0.08 0.10

Figure 5. Implosion of moderately long cylinder specimens with D. = 54 in. (1372 mm).
I> y tong cy P Oo

\ Free End Condition
© 4 A a f{ = 8,000 psi (55 MPa)
\ a material failure
\

, when 6; = fe
elastic

buckling

inelastic JA

buckling
(fitted curve)

0 0.02 0.04 0.06 0.08 0.10
t/D,

Figure 6. Implosion of long cylinder specimens with D_ = 54 in. (1372 mm).
g Pp g cy P 0

15

1.5

1.0

1 = Gim/Gim)B

Plasticity Reduction Factor,

oe

\ Near Free End Condition
© \ @ £¢ = 6,000 psi (41.4 MPa)
elastic \ \ ® £2 = 10,000 psi (69 MPa)
buckling @) N \
\ N material failure

\ \& 10,000 psi
N 6,000 psi
eK

inelastic buckling
(curves not fitted, from
Figure 8 design 7 curve)

ite = 10,000 psi

6,000 psi

0.02 0.04 0.06 0.08 0.10

©
12 © 1 T a
©
1.0 =|
aN © moderately long
NS cylinders, from
S Figure 5

long cylinders,
0.8 QU from Figure 6

design n curve

Do, End fc, Ej,
Symbol in. Condi- psi psix 106
(mm) tion (MPa) (GPa)

0.6

54 simple, 8,000 4.24

(1372) L/Dg= (55) (29.2)

\ 5
2.35 i]
re) 54 free 8,000 4.24 & cf!

(1372 (55) (29.2) \\,

0 16 near 6,000 3.05 Oo o)

0.4 (406) free (41.4) + (21.0) |

16 near 10,000 4.25

(406) free — (69)_~— (29.3)

a
0.2
=|
“Specimens had known defects.
(0) — J
10) 0.2 0.4 0.6 0.8 1.0 1.2

Figure 8. Plasticity reduction factor as a function of stress level
in cylinder wall at implosion.

16

Gerard’s Expressions:

3/4 i

Moderately Long Cylind ae =p ie (al Slee
Moderately Long Cylinders a= | eee care

1-v2 E _E; 4 TES

2

il > p E. E
Long Cylinders n= (4-3 =|

ee iB \Oy 2 is,

Gerard, concrete
this report

Gerard, concrete
for 16-in. OD
cylinders (data
from Ref 14)

Plasticity Reduction Factor, n

0.6

0.4

0.2

0.2

\ design

nm curve

a

Ref 8

0.4 0.6 0.8 1.0

Figure 9. Comparison of various 7 versus O5n/t¢ relationships.

17

Moderately Long Cylinders. The expressions to predict implosion

pressure for moderately long cylinders are developed as follows.

Equations 9 and 10 are substituted into Equation 7 to yield:

1.5
t
Fn = (i)
(1)

The stress level at implosion, o, /fe is calculated by knowing the
geometry of the cylinder structure. The following conditions determine

the next step:

(a) If Ohl hs > 1.0, thick-wall analysis is used to predict

implosion, Equation 3

Ca) lie O.52 < Oo /to < 1.0, then n is calculated by Equa-
tion 10

(c) If Gy S 0.52, then n = 1.0

If steps (b) or (c) control, the following expression, which was
developed by substituting Equations 7 and 9 into Equation 1, predicts

the implosion pressure.

fs (A085)
1320 n fe Gy.

im L/D,

(12)

A design chart approach is given in Figure 3. Enter the chart
with the structure's L/D, and t/D, ratio to determine the Fee ratio.

The structure is assumed to have a simple-support end condition.

18

For the case of fixed-support end condition, it has been shown
analytically (Ref 12) that an increase in implosion strength on the order
of 6% can be expected. The implosion pressure can be calculated for
this case by using the equations presented herein and a reduced cylin-
der length of 0.85L.

Long Cylinders. The expressions to predict implosion pressure for
long cylinders were developed as follows.

Equations 9 and 10 are substituted into Equation 8 to yield:

(13)

Once the stress level at implosion is calculated, the same condi-

tions as for moderately long cylinders hold; that is:

(a) If Oto > 1.0, thick-wall analysis is used to predict

implosion, Equation 3

(b) If 0.52 < Op Pe < 1.0, then n is calculated by Equa-
tion 10

(e)) lit Oe 0.52, then n = 1.0

If steps (b) or (c) control, the following expression, which was
developed by substituting Equations 8 and 9 into Equation 1, predicts

the implosion pressure:

= 8
ey = nie Gy) ee (-) (14)

1m
oO

19

A design chart approach is given in Figure 3. Enter the chart

with the structure's L/D, and t/D, ratio to determine the Bitte ratio.

Factor of Safety

Overall Factor of Safety. Up to this stage, the implosion pressure
calculated by Equations 3, 12, and 14 (or from the design chart of Fig-
ure 3) is a short-term strength without any factors of safety incorpor-
ated. Different codes of practice have different approaches to assign-
ing factors of safety. Without discussing the various methods, it can
be stated that the overall factors of safety for concrete compression
members range between 2.5 and 3.0.

This report recommends the same range. A structure whose
intended purpose is to store liquid material might be designed with a
2.5 factor of safety; whereas, a structure for human occupancy should
have a 3.0 factor of safety as a minimum.

The design approach in Reference 8 included a long-term loading
factor, A. Codes of practice typically recognize the long-term loading
effect in the overall factor of safety without itemizing the effect. This
report follows that practice. Results have recently been published on
concrete spheres subjected to long-term hydrostatic loading (Ref 13)
that have shown behavior similar to the Known behavior of concrete in
on-land compression members. This represents some assurance that

following existing on-land practice is appropriate for in-ocean concrete.

Concrete Compressive Strength. The implosion pressure is directly
related to the compressive strength of concrete, fe at the time of

failure. From available data (Ref 13), it appears that the strength
development of concrete in the ocean is different than that of the
standard fog-cure condition.

The results from Reference 13 are summarized herein.

20

If saturation of concrete is assumed to occur, then the following
interim guide can be used for strength gain with age. The initial
28-day fog-cured strength should be reduced by 10% to account for
saturation effects. Subsequent increases of in-situ strength with time
may depend on the depth at which the concrete is located. Depth is
important because it can influence the degree of saturation. At pre-
sent, data are available at depths of a few thousand feet. In such
cases, the strength increase relative to the 28-day fog-cured strength
appears to be nil at 1 year, 5% at 2 years, and 15% at 5 years. These
values of strength-increase-with-age are different from those generally
accepted (Ref 14) for on-land concrete of 20% at 6 months and 24% at 12
months.

For cases where the concrete is at a depth of a few hundred feet,
it is hard to estimate the strength gain behavior. First, it is unknown
how much of the wall thickness will become saturated. It could take
months for several feet of thickness to become saturated. If the inter-
ior of the structure were to be at a relative humidity of less than 100%,
the concrete would. never become saturated. However, some of the
concrete would be saturated near the outside wall, and that portion
would exhibit a strength different from that not saturated. For the
saturated concrete the compressive strength should be reduced by 10%
to account for saturation effects; then it is probably reasonable to
permit a strength increase relative to the 28-day fog-cured strength of
nil at 6 months and 5% at 12 months.

Effect of Reinforcement. The experimental specimens were unrein-
forced concrete, whereas any full-scale structure would be reinforced
concrete. The reinforcement certainly contributes to stiffening of the
wall during bending caused by out-of-roundness. However, under
ultimate conditions the contribution of the reinforcement is not easily

assessed.

21

It is recommended that the procedures stated in various codes of
practice be adapted. For compression members the effect of reinforce-
ment is permitted to contribute to the ultimate capacity of the member
as long as the reinforcement is tied against lateral movement as in a
column. If the compression reinforcement is not tied, then the member

is designed as unreinforced concrete.

Out-of-Roundness. The design chart in Figure 3 is based on

empirical data and, therefore, contains an inherent out-of-roundness
allowance. This allowance for thick-walled cylinders is given in Table
1. The thin-walled cylinder test specimens were studied in detail for
out-of-roundness, and Table B-2 in Appendix B (pg 51) presents a
digest of their out-of-roundness. A structure having geometric toler-
ances equal to or less than the test specimens will be safely designed
using Figure 3. Conventional construction practices should encounter
few problems in matching the geometric tolerances of the test speci-
mens.

It is recommended that, once a structure is sized-out by Figure 3
and meets its other design requirements, a detailed finite element anal-
ysis be conducted. The analysis should assume a realistic out-of-round

geometry and model the inelastic behavior of concrete materials.

SUMMARY

The updated design guides represent some significant changes
compared to the guides presented in Reference 8. The design approach
for thick-walled cylinders was made comparable to that for thick-walled
spheres by using an average wall stress equation with an empirical
strength factor, K.. Thin-walled cylinders used the same design
approach as described in Reference 8; however, new experimental
results from 15 relatively large-scale specimens permitted a more accu-

rate development of an empirical plasticity reduction factor, n.

22

The effect of test specimen out-of-roundness is included in the
empirically derived portions of the guides so use of the guides implicitly
assumes out-of-roundness of similar magnitude for the new structure.
This is a safe assumption because out-of-roundness criteria as given in
Table 1 and Table B-2 are lenient for large structures (in other words,
large structures should have better geometry control than the test
specimens).

Figure 3 is a design chart to predict implosion for thick- and
thin-walled concrete cylinder structures. A feature of the chart is its
simplicity. By knowing the t/D, and L/D, ratio of the structure, the
implosion strength in terms of Bibs can be determined. Implosion
pressure, Bee is calculated by assigning an ie to the concrete. A
factor of safety is not included in the predicted implosion pressure.

The design chart has application in sizing-out a structure for a
given depth. Advanced design techniques must be used to complete a
final design, but these techniques need to start from near-final dimen-
sions. This report provides the design charts to quickly determine the

near-final dimensions.

CONCLUSIONS

1. Failure of concrete cylindrical structures under hydrostatic
loading can be described by one of three equations: an average wall
stress equation applies to thick-walled cylinders; Donnell's equation to
moderately long, thin-walled cylinders; and Bresse's equation to long
thin-walled cylinders. An empirical parameter was used in each equa-
tion to obtain agreement between the experimental results and theoreti-

cal expression.

2. The finite element analysis method with a constitutive material

model predicted the implosion strength and structural displacement

23

behavior of the test specimens with good accuracy (Appendix B). Fig-
ure 3, which is the design chart for implosion, is within 10% accuracy

of the finite element method predictions.

3. The design chart of Figure 3 can be applied for quickly deter-
mining the implosion strength for a concrete cylinder structure of given

dimensions.

ACKNOWLEDGMENTS

EXXON Production Research Company is acknowledged for their
co-sponsorship of the thin-walled cylinder test program.

At CEL, Roy S. Highberg and Philip C. Zubiate are recognized for
conducting tests on both the thin- and thick-walled cylinder specimens.
Other participants were Joseph F. Wadsworth, Joseph Graham, Gene
McMahan, and Michael Hanks.

REFERENCES

1. Civil Engineering Laboratory. Technical Report R-517: Behavior
of spherical concrete hulls under hydrostatic loading, Part I. Explora-
tory Investigation, by J. D. Stachiw and K. O. Gray. Port Hueneme,
Calif., Mar 1967. (AD 649290)

Zo ; Technical Report R-696: Influence of length-to-
diameter ratio on the behavior of concrete cylindrical hulls under hydro-
static loading, by H. H. Haynes and R. J. Ross. Port Hueneme,
Calif., Sep 1970. (AD 713088)

Be . Technical Report R-740: Influence of end-closure
stiffness on behavior of concrete cylindrical hulls subjected to hydro-
static loading, by L. F. Kahn. Port Hueneme, Calif., Oct 1971. (AD
732363)

24

4. . Technical Report R-790: Influence of compressive
strength and wall thickness on behavior of concrete cylindrical hulls
under hydrostatic loading, by N. D. Albertsen. Port Hueneme, Calif.,
Jun 1973. (AD 764054)

5. H. H. Haynes. "Research and development of deep-submergence
concrete," in Proceedings of Federation Internationale de la Precon-
trainte (FIP) Symposium on Concrete Sea Structures. Tblisi, USSR,
Sep 1972, pp 180-185.

6. H. H. Haynes and B. A. Nordby. "Concrete cylinder structures
under hydrostatic loading," in Proceedings, American Concrete Insti-
tute, vol 73, no. 2, Feb 1976, pp 87-96.

7. H. H. Haynes. "Implosion criteria and behavior considerations for
concrete deep submergence vessels," in Proceedings of Conference on
Concrete Ships and Floating Structures, University of California,
Berkeley, Calif., Sep 1975, pp 77-92.

8. Civil Engineering Laboratory. Handbook for design of undersea,
pressure-resistant concrete structures, by H. H. Haynes. Port Hue-
neme, Calif., Sep 1976, p 35.

De . Technical Report R-817: Seafloor construction experi-
ment, SEACON I - An integrated evaluation of seafloor construction
equipment and techniques, by T. Kretschmer et al. Port Hueneme,
@alif., Feb 1975.

10. H. Kupfer, H. K. Hilsdorf, and H. Rusch. "Behavior of Concrete
Under Biaxial Stresses," in Proceedings, American Concrete Institute,
vol 66, no. 8, Aug 1969, pp 656-666. ,
11. G. Gerard. "Plastic stability theory of thin shells," Journal of the

Aeronautical Sciences, vol 24, no. 4, Apr 1957, pp 269-274.

25

12. O. Olsen. "Implosion analysis of concrete cylinders under hydro-
static pressure," in Proceedings, American Concrete Institute, vol 75,
no. 3, Mar 1978, pp 82-85.

13. Civil Engineering Laboratory. Technical Report R-869: Long-term
deep-ocean test of concrete spherical structures - Results after 6

years, by H. H. Haynes. Port Hueneme, Calif., Jan 1979, p. 48.

14. A.M. Neville. Properties of concrete, 2nd Ed., New York, N.Y.,
Pitman Publishing, 1973, p. 259.

15. Civil Engineering Laboratory. Technical Report R-588: Behavior
of spherical concrete hulls under hydrostatic loading, Part III - Rela-
tionship between thickness-to-diameter ratio and critical pressures,
strains, and water permeability rates," by J. O. Stachiw and K. Mack.
Port Hueneme, Calif., Jun 1968 (AD 8354926).

16. . Technical Memorandum M-44-76-4: Results of concrete
cylinder implosion test program, by Harvey H. Haynes and Roy S.
Highberg. Port Hueneme, Calif., Apr 1976, p. 391.

ee . Technical Note N-1367: Adhesives for use under-
water, by R. W. Drisko, J. B. Crilly, and R. M. Staples. Port Hue-
neme, Calif., Dec 1974.

18. . Technical Note N-1173: Evaluation of eight epoxy
adhesives for bonding concrete and microconcrete structural components
exposed to room and hydrostatic pressure conditions, by T. Roe, A. F.
Curry, and P. C. Zubiate. Port Hueneme, Calif., Jul 1971.

19. S. P. Timoshenko and J. M. Gere. Theory of elastic stability,
2nd Ed. New York, N.Y., McGraw-Hill, 1961, p. 295.

26

20. Purdue University. CE-STR-78-2: Analysis of concrete cylinder
structures under hydrostatic loading, by W. F. Chen, H. Suzuki, and
T. Y. Chang. West Lafayette, Ind., Apr 1978, pp 157.

Dale A. C. T. Chen and W. F. Chen. "Constitutive relations for
concrete," Journal of the Engineering Mechanics Division, ASCE, vol
101, no. EM4, Aug 1975, pp 465-481.

22. W.F. Chen. Limit analysis and soil plasticity. Amsterdam, The
Netherlands, Elsevier, 1975.

23. University of Akron, Department of Civil Engineering. Report No.
SE 76-3: NFAP - A Nonlinear Finite Element Analysis Program, by
T. Y. Chang, and S. Pinchaktan. Akron, Ohio, Oct 1976.

24. Energy Research and Development Agency. Report No. C00-2682-
7: Extended NONSAP Program for OTEC Structural Systems, by T.Y.
Chang and W. F. Chen. Washington, D.C., 1976.

25. University of California, Department of Civil Engineering. SESM
Report No. 73-3: NONSAP - A structural analysis program for static
and dynamic response of nonlinear systems, by K. J. Bathe, E. L.
Wilson, and R. H. Iding. Berkeley, Calif., 1974.

26. H. H. Haynes and L. F. Kahn. "Undersea Concrete Spherical

Structures," Proceedings, American Concrete Institute, vol 70, no. 5,
May 1973, pp 337-340.

Zit

TE tion

CWrOREE dinitarind «
’ ‘.
eri ' !
. ;
¥ nc ea
z brs ee i he!
yEN aS str
;
t ie
7 T eae

Appendix A

THICK-WALLED CYLINDER TESTS

SPECIMEN DESCRIPTION

The SEACON I structure (Figures A-1 and A-2) was assembled
from three precast, reinforced concrete sections. The straight cylinder
section, 10.1-foot (3.08-m) OD by 10-foot (3.05-m) length by 9.5-inch
(241-mm) wall thickness, was fabricated by United Concrete Pipe Cor-
poration. The concrete hemisphere end-closures, 10.1-foot (3.08-m) OD
by 9.5-inch (241-mm) wall thickness, were fabricated in-house. Toler-
ances on the sections conformed to concrete pipe standards: ID not to
exceed +0.75 in. (19 mm) or wall thickness not to exceed -0.5 in. (13
mm ).

Steel reinforcement of 0.70% by area was used in both the hoop
and axial direction. Reinforcing bars of 0.50 inch (15 mm) diameter
were employed throughout the structure. A double circular reinforce-
ment cage was fabricated for each precast section; the concrete cover
on the outside and inside reinforcing cage was 1 inch (25 mm). For
the cylinder section, hoop rebars had a center-to-center spacing of 6
inches, and axial rebars had a spacing of 27.25 inches (692 mm) and
31.25 inches (794 mm) for the inside and outside cages, respectively.

The hemispherical end-closures were bonded to the cylinder section
with an epoxy adhesive; no other attachment besides the epoxy bond
was employed. The gap between the mating surfaces of the hemisphere
and the cylinder was less than 0.13 in. (3 mm) for 75% of the contact
area. Prior to epoxy bonding, the concrete surfaces were sandblasted

and washed with acetone.

29

Figure A-1. SEACON structure prepared for ocean test to implosion.

epoxy
adhesive

2" clear

sil

1” cover

epoxy
adhesive

a” 10-1

acrylic 1
window axial and hoop reinforcement

9
eee 0.7% by area

penetrator

axial bars spaced a
at 30°

oS

1 1/2” @ bars
;
5-0" -|

20'-0" overall length

Figure A-2. Details of SEACON structure.

30

A large hull penetration, major diameter of 50.25 in. (1275 mm)
and minor diameter of 42.4 in. (1075 mm), was located at the apex of
each hemisphere. This penetration size was equivalent to 40% of the
hemisphere diameter. The design philosophy for the penetrator was to
make it stiffer than the concrete material it replaced so that the hemi-
sphere was "unaware" of the large hole. The steel penetrator was
epoxy-bonded to the concrete, using the surface preparation method
described for the joint.

During the 10-month seafloor construction experiment, an acrylic
window assembly was used in one penetrator and a hatch assembly in
the other penetrator. The window and hatch were subsequently
replaced with steel plates for the implosion test.

Six penetrations, major diameter of 6 inches (152 mm) and minor
diameter of 5 inches (127 mm), were included in one of the hemi-
spheres; these penetrations were part of a seal and gasket study.

Two smaller penetrations, major diameter of 4.5 inches (114 mm)
and minor diameter of 4.0 inches (102 mm), were also included near the
center of the cylinder section to accommodate pressure relief valves.

For the implosion test, three of the small hemisphere penetrators
were modified for electrical feed-throughs and pressure ports. The two
cylinder penetrations were sealed.

Additional irregularities in the concrete wall included five feed-
through boxes for strain gages mounted on reinforcing bars. These
boxes were located on the interior wall and measured 2.5 inches (64
mm) deep by 4 inches (102 mm) in diameter. In these areas the local
wall thickness was reduced to 7 inches (178 mm).

Prior to the implosion test, fifteen 3.25-in. (83-mm) diameter cores
were drilled from the wall at various locations around the cylinder.
Steel plugs were epoxied in the core holes.

During original assembly, the exterior of the concrete structure
was coated with a phenolic waterproofing system. After lightly sand-

blasting the concrete, a primer and topcoat (Phenoline no. 300) were

31

sprayed onto the concrete. Many air pocKets were not coated; approxi-
mately one pinhole per 2 in.2 (1300 mm2) existed in the final water-
proofing coating.

The concrete structure was instrumented with a total of 40 electri-
cal resistance strain gages to monitor hull response under long-term
loading. Half of the gages were placed diametrically opposed to each
other on the structure. The data were stored on magnetic tape inside
the structure and were recovered when the structure was retrieved
after 10 months.

The concrete material for the cylinder portion of the structure
consisted of portland cement type II, sand, and coarse aggregate in the
proportions of 1.0:1.4:2.5 by weight, respectively. The water-to-
cement ratio was 0.40 by weight, and a water-reducing admixture was
used; the slump was 1.25 inch (32 mm). The average compressive
strength at 28 days of the 6-inch (152-mm) diameter by 12-inch
(305-mm) long control cylinders was 7,800 psi (53.8 MPa).

Mix designs of different proportions were used for the hemi-
spheres: cement-to-sand-to-coarse-aggregate ratio of 1.0:1.95:2.3 by
weight; water-to-cement ratio of 0.38 by weight; and a water-reducing
admixture. Slump was again 1.25 inch (32 mm). The average compres-
sive strength at 28 days was 8,170 psi (56.3 MPa).

Of the 15 cores taken from the cylinder wall just prior to the
implosion test, 7 were subsequently cut into 3.25-in. (83-mm) diameter
by 6-in. (152-mm) long cylinders, which were tested under uniaxial
compression. Compressive strengths of the cores and from a number of
6x12-inch (152x305-mm) control cylinders at various ages are presented
in Table A-1.

Three of the core specimens were instrumented with strain gages
to obtain stress-strain data for the concrete. Curves of this relation-
ship up to about 90% of the compressive strength are shown in Figure
A-3. The secant modulus of elasticity to about 40% of ie was 4.4x10®

psi (30.4 GPa), and Poisson's ratio was 0.20.

32

Table A-1. Summary of Concrete Compressive Strengths for the Seacon Structure

Specimens

Age of Compressive
. : Concrete Strength
Size Curing :
Type (in.) Conditions@ ey) (psi)

field

fog
field

fog
field

fog
fog and ocean?

field and ocean®
d

part of structure

“Curing of all cylinders for the first 28 days was 2 days steam, 7 days water tank,
and 19 days field.

> after first 28 days, curing was 270 days fog room and 302 days on seafloor at
600 feet.

“After first 28 days, curing was 270 days field and 302 days on seafloor at 600
feet.

4Structure was field-cured on land for 298 days, on the seafloor for 302 days, and
then field-cured on land for 1,528 days.

As shown in Figure A-1, the concrete cylinder structure was
mounted in a steel framework and fitted with a ballast tank. The in-air
weight of the cylinder was 85,000 pounds (38.5 Mg), and the concrete-
steel structure weighed 102,000 pounds (46.3 Mg). The positive buoy-
ancy of the concrete hull was 12,000 pounds (5.4 Mg), and when bal-
lasted the concrete-steel structure weighed 6,800 pounds (3.1 Mg)

negative in water.

33

10,000

8,000
~ 6,000 z
a a
& cS
ip)
: z
n

4,000 n

2,000

-400 -800 -1,200 -1,600 -2,000 -2,400
STRAIN (yin./in.)

Figure A-3. Stress-strain curves from 3.25-in. diam x 6-in. long cores.

TEST RESULTS

Long-Term Test at 600 Feet

Strain Behavior. The initial strain response of the structure on
being lowered to 600 feet (180 m) showed an average strain of 380
ywin./in. in the hoop direction and 170 win./in. in the axial direction
(Ref 9). From previous work (Refs 2, 3 and 4), it was anticipated
that this low level of loading should not have produced any detectable
strain variation along the length of the cylinder section due to the
discontinuity of the cylinder/end-closure joint. The actual strains

showed this to be true.

34

The concrete was under sustained stress of 1,700 psi in the hoop
direction and 920 psi in the axial direction for 302 days. The average
total creep strain in the hoop and axial direction was 130 and 80
uin./in., respectively; these values represent a 34% and 47% increase,
respectively, over the short-term strain (mot unusual for concrete).
The data gave no indication that the creep strain was nearing termina-
tion.

The large penetration had little effect on the behavior of the
hemisphere. Again, the low stress level in the concrete might not have
been sufficient to produce a noticeable strain rise at the penetration.
In any event, it was significant that the penetrator, equivalent to 40%
of the structure's diameter, did not produce a harmful effect on the

structure.

Watertightness. Upon retrieval of the cylinder from the 600-foot
(180-meter) depth after 10 months, the interior of the structure was
free from water that permeated the concrete walis. There was no
evidence of condensation, or even dampness, on the interior concrete
walls .* .

Results from long-term loading of concrete spheres in the ocean
(Ref 13) confirm this finding of watertightness. The 66-inch (1076-mm)
OD spheres had a wall thickness of 4.12 inches (105 mm) and were
located at depths that ranged from 2,000 to 5,000 feet (600 to 1500
meters). Some of the sphere exteriors were coated identical to the
SEACON structure and showed no water on the interior after 6 years in

the ocean.

Implosion Test

Depth at Implosion. The depth of implosion for the structure was
4,700 feet (1430 m).

*Three quarts of water were found inside the structure due to a leak
in a check valve in one of the small penetrators under investigation.

35

The means of determining the depth of implosion was not as
straightforward as originally planned. Pressure transducers were
installed on the hull, but these were inoperative at the time of implo-
sion. During launching of the structure, which was off the stern of an
offshore work vessel, a small hull penetration became damaged and
resulted in a leak of about 25 gallons (95 liters) of seawater per min-
ute. The weight of the structure increased until a safety link in the
lowering line parted, which occurred at a depth of 2,900 feet (884
meters), as recorded by the pressure transducers. From this depth
on, the structure free-fell through the water column until implosion
occurred.

Data from acoustic depth-recording instrumentation were continu-
ously being recorded on tape during this sequence of events. The
noise generated by the implosion of the structure was also recorded.
This signal had a rather long duration and showed that implosion could
have occurred at a depth between 4,500 feet (1370 meters) and 4,700
feet (1430 meters). Seafloor depth was 4,700 feet (1430 meters).

It was known from data on tape that the time between the start of
free-fall and implosion was 160 seconds. By analytically bracketing the
free-fall velocity of the structure between 11.2 ft/sec (3.4 m/sec) and
12.5 ft/sec (8.8 m/sec), it was calculated that the structure free-feli
between 1,790 feet (546 meters) and 2,000 feet (610 meters). Adding
these numbers to 2,900 feet (884 meters) gave the total depth range as
4,690 feet (1430 meters) to 4,900 feet (1494 meters). Hence, it was
apparent that the structure hit the seafloor at a depth of 4,700 feet
(1430 meters) before imploding.

A manned submersible inspection by the Navy's Sea Cliff was
conducted in 1978 to determine whether the structure imploded after
impacting the seafloor. The tight grouping of fragments confirmed that
the structure hit the seafloor first. If the structure had imploded
during free-fall descent, the fragments would have been scattered.

The inspection also confirmed that the cylinder section imploded rather

36

than that one of the hemispheres or a penetrator failed. The cylinder
section was heavily fragmented while the hemispheres were rather
recognizable.

There were no means of estimating whether the structure imploded
immediately upon hitting the bottom or remained on the bottom for a
time before imploding. In any event, 4,700 feet (1430 meters) is a
conservative (or minimum) implosion depth.

It should be mentioned that the structure was instrumented for
strain readings during the implosion test. The damaged penetrator,
however, was also the electrical feed-through for strain-gage wires;

therefore strain readings were not recorded during the test.

Discussion of Implosion Strength. The effect of hull stress rate,

due to free-fall velocity, was not considered a significant parameter on
implosion strength when compared to previously tested cylinder models.
For a free-fall velocity of 11.2 ft/sec (3.4 m/sec), the hoop stresses in
the hull increased at a rate of 1,900 psi/min (13.1 MPa/min). Previous
cylinder models with geometry equivalent to that of the SEACON struc-
ture had hoop stress rates about 700 psi/min (9.8 MPa/min). This
difference in stress rate would have an insignificant effect on implosion
strength.

Pressure buildup inside the structure was minimal during the
entire test. At the 2,900-foot (880-meter) depth it was known that
13,000 pounds (5.9 Mg) of seawater leaked to the interior. This filled
about one-quarter of the interior volume. By the time implosion
occurred, the interior pressure would not have exceeded 5 psi (34 KPa)
over atmospheric. The exterior pressure at implosion was 2,100 psi
(14.5 MPa).

The implosion strength of the SEACON hull was

“an 2,100 psi
Bae 02 407epsi

= 0.200

37

The compressive strength, fe was obtained from 3.25x6-inch (83x152-
mm) core specimens. The strength of the cores was assumed equal to
that of 6x12-inch (152x305-mm) cast specimens. The smaller size of the
core specimens would cause a higher strength relative to 6x12-inch
cylinders; however, this strength increase would be offset by the effect
of drilling which causes a strength decrease.

With the use of the average wall stress approach as expressed in

Equation 3, the material strength factor was calculated as:

hare ee On 200 ee
e° 240) ~ 205i ~ ™

This factor is shown in Figure 1 for the SEACON hull which had an
L/D, =llOp

The effect of steel reinforcement on the implosion strength of the
structure could not be determined from this test. If the reinforcement
was considered effective, then the total wall thickness from transformed
sections would be 10.07 inches. This represents an increase of 6% over
that of the actual wall thickness, which should cause an equivalent
increase in the implosion pressure. This single test could not deter-

mine such a small percentage difference in strength.

FINDINGS

1. The implosion depth for the SEACON structure was 4,700 feet
(1430 meters). Core specimens 3.25 inches (83 mm) in diameter by 6
inches (152 mm) long taken from the hull gave the uniaxial compressive
strength of 10,470 psi (72.2 MPa).

2. With the use of the average wall stress equation, the material

strength factor, Ko> was 1.27; the wall stress at implosion was 13,300

psi.

38

Appendix B

THIN-WALLED CYLINDER TESTS

SCOPE

A total of 15 unreinforced concrete cylinder specimens were tested
under hydrostatic loading. The dimensions of the specimens were a
constant outside diameter, D> of 54 inches (1372 mm), overall length of
134 inches (3400 mm), and wall thicknesses, t, of 1.31, 1.97, or 3.39
inches (33, 50, or 86 mm). The wall-thickness-to-outside-diameter,
t/D,; ratios were 0.024, 0.037, and 0.063, respectively. Two different
types of boundary conditions were used: a simply supported and a
free end-condition. Twelve of the specimens were tested under short-
term hydrostatic loading where the pressure was increased until implo-
sion; the remaining three specimens were subjected to long-term load-
ing.

Structural behavior was recorded by measuring radial displace-
ments around the entire circumference of the cylinder wall at various
locations along the length. Deflected cross-sectional shapes were plot-

ted from which the following data could be determined:

(a) Initial deviations from circularity

(b) Radial displacements due to membrane shell action and

bending

39

(c) Location of the worst flat-spot and determination of

maximum radial displacement

(d) The number of buckle lobes at implosion

Attempts were made to obtain strain data but difficulties were
encountered in applying gages to wet concrete.

Inspection of failed specimens and fragments of concrete from the
failure zones yielded data on the deflected shape of the structure and
size of the failure hole.

A detailed presentation of specimen geometry and test results is

given in Reference 16. This report summarizes portions of those data.

SPECIMEN FABRICATION

Casting

The specimens were cast monolithically in steel molds. The same
outer mold was used for all specimens, but different inner molds were
used to change the wall thickness. The inner molds were built to fold
inward so that the diameter became smaller for removal from inside of
the concrete cylinder. The inner and outer molds were spaced on the
bottom by a ring and on the top by a spreader bar.

Concrete was placed in the molds by free falling from a dome
distribution plate. When the form was vibrated, the concrete flowed to
the edges of the dome and fell into the mold. By this technique, the
concrete was evenly distributed around the circumference.

Approximately 20 hours after casting, the mold was removed from
the concrete (Figure B-1). All specimens were wrapped in wet burlap
and then in polyethylene film. They were subsequently moved to a

sheltered storage area where a water drip system kept the burlap wet.

40

Figure B-1. Cylinder specimen Figure B-2. Specimen partly
being removed from mold. assembled inside polyethy-
lene tent.

The specimens were moist-cured in this manner until assembled for
test. During assembly (Figure B-2) a tent of polyethylene film was
used to maintain a high relative humidity environment around the speci-
men to minimize shrinkage cracking. Keeping the cylinder in the moist
environment assured the test conductors that the concrete was in a

"wet" condition at the time of the implosion test.

Assembly

The procedure to assemble a specimen for test (Figure B-3) began
by placing the cylinder on the bottom end-closure, which was a flat
steel plate. The top end-closure was a steel ring. The top and bottom
closures were held together by eight chains, post-tensioned to precom-
press the concrete by 20 psi (0.14 MPa) when the structure was sub-

merged in water in the pressure vessel.

41

high-speed
camera

TV camera

lights (2 locations)

top, end-closure ring

bearing for ie

center shaft 7
four-arm spider A
p
| |
1 “6 Ay !
| betedh
p \
i ;
4 \
potentiometer - le 5
' i 5 is
. i !
( / —- s : |
= 4
arm ———+ ‘
{ j A. A
| ie, Lae center shaft
6 mM 9 \
. P F za| | \ concrete cylinder
Pus J i Bea test specimen
1 uss, aN
\ ' , oe
b
O ‘ \ \
“ 6 '
iG !
p = Jb
H j oP a :
' , 9
| 4 T ge
: 7 pressure vessel
6 & i} |
2b
' 1
b
\
“( = b
4“ ee : 1
e 4 iA : \
\ \ |
6 i)
' \ ‘ bo) 1 }
' ou
, ( A \
: : \ ;
De = » '
! bz = : _ post-tensioning
' “4 : eee chain (8 equally spaced)
g J »
-

stiffener

! ;
if |
/
/

bottom end-closure

\—&«—— high-pressure

ral ‘ inlet and drain

Figure B-3. Cross section of specimen, showing test setup.

42

For the simply supported end-condition (Figure B-4) epoxy adhe-
sive was placed between the concrete and steel ends to correct for
unevenness at the mating faces. Later, steel stiffeners were placed in
the interior at the top and bottom, and expansive-cement grout was
packed between the stiffeners and the concrete wall. For the free
support end-condition (Figure B-4), a 1/8-in. (3-mm) neoprene rubber
gasket was placed between the steel and concrete. A thin layer of
epoxy adhesive or quick-setting gypsum was used between the concrete
and the neoprene gasket.

When the specimen was assembled to the stage where the center
shaft was centered at the top and bottom, radius measurements were
taken using the following procedure. An arm off the center shaft had
a scribe marker mounted to it. A fixed position table was placed
beneath the arm, so when the center shaft was rotated, a circle was
scribed on the table. The radius of this circle, r', was measured after
the table was removed from the specimen. At the circumferences of 0,
90, 180, and 270 degrees, the distance from the scribe to the wall, r",
was measured using a steel rule accurate to 0.01l-inch (0.25-mm). By
adding r' and r", the inside radius of the specimen was obtained at the
circumference locations. Deviations in radius around the circumference
were obtained from deflectometer data, so by using the deflectometer
data and the measured radius data, average radius values for the

specimens were determined.
Instrumentation

Instrumentation of the specimens consisted of mounting a deflec-
tometer system to measure radial displacements, applying strain gages
(to some specimens), installing a television camera, and installing a

high-speed motion picture camera. These systems are described below.

Deflectometer. The measuring device of the deflectometer system
was a potentiometer (linear position transducer) which had a maximum

displacement of +0.650 in. (16.51 mm) and a measurement accuracy of

43

“suOTIIpuod-pua qoddns-ajduns pure -aa1j Jo sjieioq “p-q onsIy

qioddnsg ajduis

aieyd jaais

SASS

KAAAAAAAAAAMMAAS ASSAM AAMAS AAAS

qioddnsg atduts

AU (ft I aor

"Al
de oe
“Ul Z/T-
go we “Ul 8/T
aed auaidoau
Sacer
Burd [aaqs Ks —S ~ EB} |

fe } ne 2 |

“Ul T

ynois
aatsuedxa

+0.002 in. (0.05 mm). The potentiometers were mounted on arms that
extended from a center shaft. The center shaft was motor-driven at a
rate of one revolution per 90 seconds.

Radial displacement calibration was accomplished by mounting
aluminum shims of 0.125-inch (3.18-mm) thickness on, the inside wall of
the cylinder so that the steel ball passed over the shims to record
Magnitude and direction of inward displacement. These calibration
marks also determined a 360-degree rotation.

The deflectometer system was insensitive to the axial orientation or
lack of straightness of the center shaft. The top and bottom on the
center shaft were fixed in location, and the shaft was rotated. The
arms were fixed to the center shaft; and, in plan view, the end of each
arm scribed a perfect circle. The steel ball at the end of each arm
moved in and out to conform to the shape of the concrete cylinder.
This radial movement was recorded as changes from a perfect circle.

In reducing the analog deflectometer data, an analog-to-digital
converter was used along with a timing system to control the number of
samples taken and the time interval between samples. Over 900 samples
of analog data were digitized for each 360-degree rotation. This
equates to a radial displacement data point every 0.17 inch (4.3 mm)

around the inside circumference of the cylinder.

Strain Gages. Strain gaging of the specimens proved to be diffi-
cult because the concrete was in a wet condition. Various approaches
for applying gages to wet concrete were tried, but none were success-
ful. The problem was in maintaining the bond throughout the entire
test.

The procedure for strain gaging is described as follows:
(1) Electrical-resistant strain gages (type FA-06-125,

three-element rosettes) were mounted either on brass
shim stock 0.002-inch (0.05 mm) thick or on steel shim

45

(2)

(3)

stock 0.005-inch (0.13-mm) thick and waterproofed,
using standard procedures. These procedures used
normal preparation steps for applying gages to metal
and then were waterproofed using General Electric
Clear RTV 109. This waterproofing approach works
successfully under hydrostatic pressure loadings
equivalent to thousands of feet of head. A second
type of electrical resistant gage used was a self-

encapsulated, waterproof, weldable gage.

The objective was to apply these waterproof gages to
the wet concrete surface with an adhesive of sufficient
bonding strength that strain in the parent material is
transferred through the epoxy adhesive, through the
shim stock material, to the gage. To check the accu-
racy of these shim-stock mounted gages, a control test
was conducted on an aluminum tube loaded in uniaxial
compression. Seven pairs of gages were mounted on
the aluminum cylinder; each gage in a pair was diamet-
rically opposite the other gage. The test consisted of
three pair of single wire gages mounted with Eastman
9-10, two pair of foil gages on brass shim stock
mounted with EPY-150, one pair of foil gages on brass
shim stock mounted with Eastman 9-10, and one pair of
foil gages on brass shim stock mounted with Hysol EA
934. Eastman 9-10 is an excellent adhesive in a dry
environment, so it was used in this test as a control.
The results showed that gages mounted on brass shim
stock registered accurate strains. The different glue

systems did not affect the results.

In the first method of mounting foil gages on brass
shim stock to the wet-concrete specimens, an under-

water curing adhesive developed at CEL (Ref 17) was

46

used. This method did not bond the shim stock to
concrete for the duration of the test. A second
method used epoxy adhesive Hysol EA 934, which was
known to maintain a high bond strength when dry-
concrete became wet (Ref 18). The strain data still
indicated that the brass shim stock was not adhering
to the concrete at the higher pressure (or strain)
levels. The third method used Hysol adhesive again,
but this time extra attention was paid to roughening
the brass surface, deeply roughening the concrete
surface (by grinding with silicon carbide grit) and,
when applying the gage, embedding the edges of the
brass shim stock in a thick bead of epoxy around the
periphery. These additional steps also did not solve
the problem. The fourth method was to try steel shim
stock, instead of brass, and to use the procedures
mentioned previously. At the same time, weldable
gages were tried. None of these systems was success-
ful; attempts at strain gaging were terminated. The
deflectometer data were excellent, and additional

potentiometers per test were used.

Television Camera. A closed-circuit television camera was installed
at the top of each specimen. The video tape system recorded implo-
sion. Although the frames per second rate did not permit detailed
study of the failure zone, the circumferential location of failure could
usually be defined and an interesting sequence of failure was recorded,

including the sound of implosion.

High-Speed Camera. A high-speed motion picture camera was
installed at the top of the specimens. It was hoped that a failure
sequence could be filmed. The camera speed was initially set at 200

frames/sec which permitted 40 seconds of film time. The speed could

47

have been increased to 1,000 frames/sec, if desired. However, after
several tests and no coverage of failure, the film speed was reduced to
100 frames/sec to increase the film time to 80 seconds. The camera was
installed in eight specimens but failure coverage was not obtained in
any test. The techniques used to try to predict imminence of failure

are discussed in the Test Procedure section.

TEST PROCEDURE

The pressure vessel used in the tests had an inside diameter of 72
inches (1830 mm) and an operational pressure of 5,500 psi (37.9 MPa).
The pressure load was created by pumping additional water into the
vessel and thereby compressing the fluid. Freshwater was used in the
tests.

The temperature of the water typically varied between 3° and 10°C
for different tests; however, the temperature inside the specimens
typically varied between 10° and 13°C. The higher temperature inside
the specimens was due to warmer room temperature and lights for the
television.

All specimens were placed in the pressure vessel on the evening
before testing and allowed to soak in order that the degree of water
saturation of the concrete for the different specimens would be the
same. It was hoped that soaking overnight partially saturated the
concrete to equal levels.

The rate of pressure application was 10 psi/min (0.069 MPa/min)
between hold periods where data were recorded. Hold periods occurred
at 25 psi (0.172 MPa) increments and typically lasted for 2.5 minutes.
From the beginning to the end of the test, the overall pressurization
rate was about 5 psi/min (0.034 MPa/min).

The television monitor was operated throughout the test. Its use
was invaluable in operating the deflectometer system, detecting leaks,

and recording implosion on videotape.

48

Several specimens leaked during the test. Most of the leaks
occurred between the concrete and steel end-closures. However, some
of the specimens had cracks through the wall and water slowly leaked
through these cracks until the pressure load exceeded approximately
200 psi (1.4 MPa). Leaks did not affect the test results.

For the long-term loading tests, a digital comparator was used to
control the operation of an auxiliary pressure pump and maintain the
pressure load at +2 psi (0.014 MPa).

Failure of the specimens was instantaneous, with literally a fraction
of a second of advanced warning. High-speed motion picture film of
failure was not obtained during eight attempts. In several of the
eases, the film was exposed before implosion occurred. In the other
cases, implosion occurred while the operator was waiting for an indica-

tion of failure. Methods used to indicate failure are described below.

(1) Radial Displacement - A real time signal from a poten-
tiometer -was displayed on an oscilloscope. During
pressurization periods, the potentiometer was placed on
the worst flat-spot (probable failure zone), and the
rate of inward radial displacement with pressure was
monitored. It was believed that an increase in the
rate of change of radial displacements would indicate
implosion. This was the case, but warning time was
not sufficient to trigger a toggle switch to operate the

camera.

(2) Acoustic Emissions - Acoustic emission transducers
were placed on the pressure vessel head or on the top
stiffener to record cracking activity of the concrete.
It was hoped that the concrete would show consider-
ably more cracking activity just before failure. This
method was not successful because the acoustic emis-

sion activity of concrete is high and erratic in the

49

inelastic region. It was not possible to distinguish
between spurts of activity and the activity just prior

to failure.

(3) Pressure - The technician, who pressurized the speci-
men, closely watched pressure gages during the test.
A pause in the rate of movement of a pressure gage
needle would indicate imminent failure. For several of
the tests there was no pause in needle movement; and
for the tests with a pause, time was not sufficient to

relay a message.

Upon removal, the specimens from the pressure vessel were
inspected, photographed, and sketched. Fragments of concrete from
failure zone sections were salvaged and pieced together for closer
inspection of the failure zone.

It was at this stage that wall thickness measurements were made.
The specimen was broken up, and the thickness of the pieces was
measured with a micrometer. In this manner, numerous and accurate

measurements of wall thicknesses were obtained.

SPECIMEN GEOMETRY

A summary of the specimen geometry is given in Table B-1. Data
on maximum and minimum wall thicknesses are presented. Also, con-
struction out-of-roundness data at the flat-spot locations are given.
Typically, the minimum wall thickness coincided with the flat-spot
location because this occurred at the outer mold seams. Table B-2
gives a digest of the out-of-roundness parameters. This presentation
of data, however, is not truly descriptive of the out-of-round shape.
Figure B-5 shows a cross-section at an elevation of 50 inches from the
bottom, € = 0.4, of specimen 2-3. The initial out-of-round shape for

the outer and inner mold are shown, using an exaggerated displacement

50

Table B-1. Specimen Geometry

Construction Out-of-Roundness (Flat Spots)
at or Near Failure Location

Pee b || Ate
SE eh es ‘max’ | min mn Inside Wall Outside Wall
No. (in.) (in.) t

1.439 1.201 0.08
1.462 1.178 0.08

241 0.037 oo 1.975 | 2.047 | 1.874] 0.05
2-2 = (2.48) | 1.960 | 2.092 | 1.832] 0.07
23

2-4

3-1 O.037 || 2.35 1.965 | 2.064 | 1.848] 0.06
3-2 2.065 | 1.823 | 0.06
3-3 = = 1.966 | 2.069 | 1.856 | 0.06
3-4

A 0.037 | 2.35

42

4-3

5-1 0.063 co 3.392 | 3.588 | 3.255] 0.04
5-2 = (2.48)°

“Between 100 and 250 readings.
2 nevensce value from 6-in.-sq fragmented area of imploded specimen.

© Actual specimen L/D.

Table B-2. Digest of Specimen scale. In the regions of O and 180

Out-of-Roundness

degress, it is observed that the wall is
thinner than nominal and that the
Out-of-Roundness

Parameters curvature is flatter than that of the
membrane circle. The center of the
membrane circle for the outer wall is
offset from the center of the inner wall
by about 0.02 inches.

Another cross-sectional view at

elevation € = 0.4 is shown in Figure
“Radius deviations are for radii less B-6. The data are a compilation from

thanthe nominalradt several specimens of t/D, = 0.037.

51

Radius deviation scale: 0 0.2 in.

outer shape

outer membrane circle

center of inner wall

center of outer wall sale

om
oS

inner membrane circle

inner shape

Figure B-5. Initial cross-section shape (superimposed to show relative
changes in wall thickness and flat spots) for specimen 2-3,
showing radius deviations of inner and outer wall surfaces
at 0 psi and & = 0.4 (50 inches from bottom).

52

&
Sc!
Co) ot .
“ a3 &
wy
% ee %0 s
Som M oa x
3S eo = 0
. J
» ss
x e | or
Z 90 fs ‘
23 Gh Sos
a ‘
Ew 9
ive)
lon
mn
N
avg R
270° t=2.02in.9 26.10 in. @ t=1.99 in.
eee
6 »
oS
Sg
So
°
a L095 |
se 4,
x | 2
. A 10}
5 <a
x & ‘2,
y ips o-
JL ee 2
iT
|
180°

Figure B-6. Variation in wall thickness and mean radius at different
locations on circumference at & = 0.4 (50 inches from
bottom). Values are average of several specimens.

53

90°

Variations in wall thickness and mean radius, R, are shown around the
circumference. The average R was 26.03 + 0.05 inches (661 + 1 mm).
The magnitude of the standard deviation was mostly from the lack of

accuracy in measuring the radius with the steel rule.

CONCRETE MATERIALS

Mix Design

Concrete was batched and supplied by a transit mix company.
Each delivery consisted of 2.0 yd? (1.5 m3) of concrete. The mix was
designed for 6,000 psi (41 MPa) at 28 days. The proportions of cement
to sand to aggregate were 1:1.96:2.22, respectively. The cement
content was 676 lb/yd3? (401 kg/m3). Water-to-cement ratio averaged
0.55. Slump at the time of placement controlled the total water content,
and the slumps averaged 3-3/4 + 1/4 inches (95 + 6 mm).

Portland, low alkali, type II cement was used along with a water-
reducing admixture, Zeecon H, at a rate of 6 ounces (0.17 kg) per 100
pounds (45.4 kg) of cement. The sand and aggregate were from the
Santa Clara River Basin. Maximum aggregate size was 3/8 inch (9.5
mm), and the aggregate underwent heavy media separation.

A summary of the concrete properties is given in Table B-3. The
concrete compressive strengths were measured at 7 and 28 days and at
the time of testing. Stress-strain curves were obtained from numerous
specimens. Several modulus parameters are listed in Table B-3, along
with the ultimate strain and Poisson's ratio. Figure B-7 shows repre-
sentative stress-strain curves for 7,000 and 8,000 psi (48 and 55 MPa)
concrete.

Expansive-cement grout, used as a packing material between the
stiffeners and concrete wall, had mix proportions of one part portland
cement type K, one part San Gabriel River sand between sieve sizes 4

and 16, one part San Gabriel River sand between sieve sizes 16 and 30.

54

a ‘ORY

$,UOsslod

(ar7 tt)
¢-OT X oe)
“UIRIYS

o7e C113 1)

(isd)
901 X La
FOL
snjnpow
quosue |,

(isd)
901!
36°90 01
sn[npow
qURIAS

(isd)
901 Xa
‘sn[npow
jenruy

say jo ody Iv saniodorg [euoiey

SEE
S6¢
Lic

cara
8c

LSt
9S
SOL
68

el
os
98I
82

+8
S8

(skep)
* 98V

(%)
uONRLRA
jo
WUITIIIJIOD

“OZIS “UI-Z [XQ ‘suoUTIDads XIs JO a8BIDAe RaIdA ],

“OZIS “UI-Z]XQ ‘suauIdads day] JO aBRIDAY

“sABp $T 28V 3

q

D

OLS°8
0662

07Z0'8
OLEL
OFE 6

OLIT'8
0L8°9
0£8'9
O6T'L

O7SL
OrZ'9
0698
O8L°9

OTE'8
OSL

(isd) 23
‘Iso JO 98
1® YIHUIIIS

ge aissordwo)

aqoINUOD Jo sariadoig [eLawW “¢-G I[GRL

OOL'S OO +
O€E'9 Oft'+
00r'9 007s

O£T9 OOS ‘+
OLT 9 =

ore 9 OLEe's
oystsate} 000°

£79 OfL +
oce 9 -
0¢9'9 9099'S
007:9 007 +

o0r9 O88 7
O9L'9 OFL TZ

(isd)
psAtd 8Z

“ON
uowtoads

5)

—osy 18 44
‘yaBuaias aatssordwioy

55

10,000 1 4 a ss =
8,000 bee ay Ie ea =|
ee ak
-— ge x oe
2 — al
<<
2 6,000 --_ a i
2 8,000 psi concrete ~4_(@ Myo
PA ie a |
a
a
v —
LON “*—~ 7,000 psi concrete =I
2,000 =— —— experimental
computer input model
0 f | L
2,000 3,000 4,000

Strain, win./in.

Figure B-7. Uniaxial compressive stress-strain relationship for concrete.

The water-to-cement ratio was 0.37 and a retardant admixture, E42
Master Builder, was used at 4.1 ounces (0.12 kg) per 100 pounds (45.4
kg) of cement. The compressive strength of this mix was 5,520 psi
(38.1 MPa) at 7 days taken from three 3x6-inch (76x152-mm) control
cylinders.

TEST RESULTS

Implosion

Test conditions and implosion results are presented in Table B-4.
The implosion pressure, Bat and nondimensional ratio of implosion
strength, a eS are given along with data on the failure hole size and
boundary behavior.

A summary of the implosion results is given in Table B-5.

56

“OIN[IBJ [RIO]

Aqoa ‘Q40ddns 3uevaq uaaauQ colo Joys aaI4 FOL OST _ Ss
*@ dnoiy ay1] apow ain
-[fey ‘oddns Surmeaq usaouQ Seto qoys 221} aS OOI 1-S
‘isd OS} 1” say got LL0'0 Bu0| aduurs s°s SL &+
‘isd ¢Lp

I SIY pp Ney [RIUIpINIy T80°0 Bu0| ajduiis LS SL t+
sd (Z9 3B Siy ¢°Z 990'0 Buo| ajduus ss SL I+

*DojJop BuIsRd a19AIag 800 |,89°0 Z+0'0 qoys ajdurts $9 CL $-€

= 9400 yO Ys ayduuis eS SL €-€
$80'0 10ys ajduus oF SL Ge.

9400 0 ys ayduris o's SL I-€

*9UOZ DANJIVJ Ul Iodjop Buses) 1o'0 96'0 Z+0'0 qioys Reb AG ©/} $-Z
= ssoo0 Woys pe} 6+ SL €-~

9+0'0 Woys 9915 is SL GG

090°0 doys 9915 Or SL 1-Z

O+0'0 Woys ajduuis ore Sz Z-1

6£0'0 q0ys ajduns a+r Sz II

sd) Wt 5 ‘
us )ond deeming || wagner (u1uryisd) (isd)
DANSSIIA a1eyY d1NSsaid
: JOIARYyag _ ir jo addy, Aiepunog fi ‘ON
SyrB way (scraniece dUOZ dIN[Iey uolsojdury danssaid peoaig cemmede

sipnsay iso. SUONIPUOD Isa

si[nsay pur suOTIPUuOD IsdaL “p-q a]qQuL

57

Table B-5. Summary of Test Results

Coefficient
Boundary | Type of tro Dp: i of
Condition | Loading ee Variation
(%)

Remarks

0.024 | 2.3 simple short b =
0.037 free short Specimen 2-4 excluded

0.037 : simple short g Specimen 3-4 excluded

0.037 3) simple long -

0.063 free short Specimen 5-2 excluded

Post-implosion views of several specimens are shown in Figures B-8
through B-16. For those specimens having a simple-support boundary
condition, the failure holes occurred in the midlength region away from
the ends (Figures B-8 and B-13). For those specimens having a free-
support boundary condition, the failure hole typically occurred at the
top end (Figures B-11 through B-15), but the failure hole occurred in
the midlength region for specimen 2-1 (the strongest Group 2 specimen)
(see Figure B-10).

The experimental test setup was probably the cause for the failure
holes that occurred at the top. When the specimens were fabricated,
the top cylinder edge was hand-troweled and therefore uneven. On
specimen 5-1 the top end-closure ring was placed on the cylinder with-
out the gasket material to observe unevenness. A rather large portion
of the mating surface showed a gap of from 1/16 to 1/8 inch (2 to 3
mm). A filler material, such as gypsum used in specimens 2-1 and 5-1,
filled the gap adequately. However, use of the gypsum was discontin-
ued because the material is water soluble, so small leaks grew into
major leaks. Epoxy was used as its replacement, but epoxy filler
material did not appear to perform adequately. Epoxy has a modulus
about one-tenth that of concrete and probably about one-fifth that of
gypsum. It wasn't until after specimen 5-2 was tested (at the end of

the test program) that it became quite apparent that the epoxy filler

38

Figure B-9. Fragments of failure

ew of
0.024

8. Post-implosion vi

Figure B

il.

hole from specimen 1-

sim-

?

y=

1 (t/D

specimen 1
ple support).

te

NX

Bs
"

SS
a
vena

Figure B-11. Post-implosion view of

Figure B-10. Post-implosion view of

free

’

specimen 2-2 (t/D, = 0.037

support).

specimen 2-1 (t/D,, = 0.037, free

support).

59

material was not a good substitu-
tion. Figure B-16 shows that
specimen 5-2 had a very local
failure at the top edge which was a
bearing-type failure.

Boundary behavior is quanti-
fied in Table B-4. For conveni-
ence, a nondimensional value, 90,
was selected to express boundary
behavior as the ratio of radial
displacement at the end supports to
the radial displacement at midlength
of the specimen. A rigid support
would be identified by »® = 0 and a
free support by 6 = 1.

Observed boundary perfor-
mances showed a small difference
between actual and _ theoretical
behavior. For free-support speci-
mens the ideal » of 1.00 was closely
approximated. Two specimens with
t/D , = 0.037 showed free-support
behavior where was 0.90 and
0.96. Specimen 2-3 showed unusual
behavior where the bottom of the
cylinder moved radially inward the
least, » = 0.60, but the top moved
inward) the, most.) 16) =) 17s6 sane.
the top of the cylinder at the flat
spot location moved inward more
than the middle).

60

Figure B-12. Fragments of failure
hole from specimen 2-2.

es

oes:
SSS Sees
Sr

oS
ro
tees

é S=

ra

rans
ZS

Figure B-13. Post-implosion view of
specimen 3-1 (t/D,, = 0.037, sim-
ple support).

For simple-support specimens,
thenenGdealiy on tol aezeromm wash not
obtained. The radial deflection of
the steel stiffener provided some
compliance. The stiffener deflection
was calculated to be about 0.01 inch
(0.3 mm) at a pressure load of 500
psi 5 MRD, ce A o oF O.08,

Measured radial deflections showed

values about 0.02 inch (0.5 mm), a

Figure B-14. Fragments of failure hole from
specimen 3-1.

134 Yl,
y Hole y
QI

120 -

1

100

80

60

20 F =|

Cylinder Length (in.)

0
360 330 300 270 240 210 180 150 120 90 60 30

Circumference (Deg)

Figure B-15. Post-implosion view of specimen 5-1 (t/D,, = 0.063, free support).

61

» of about 0.16, at a distance of 2 inches (50 mm) away from the stif-
feners. The test specimens had a clear length between stiffeners of
127 inches (3220 mm). After accounting for the compliance of the
stiffener, the "actual" length of the cylinder appeared to be about 130

inches (3300 mm); hence, the effect of stiffener compliance was small.

AY wt
Wy
XXX

Figure B-16. Local failure of specimen 5-2 (t/D,, = 0.063, free support).

To test for possible reduction in implosion strength due to sus-
tained loading, the implosion resistance of Group 4 specimens was
assumed to be equal to that of the average value of Group 3 specimens;
i.e., Betas 0.079. Specimen 4-1 was subjected to 85% of this load.
After 2.5 hours of load exposure the specimen imploded, which implied

a strength reduction of 15% for a relatively brief period of sustained

62

loading. Subsequently, the sustained pressure for specimen 4-2 was
lowered to 80% of predicted short-term strength, while specimen 4-3 was
subjected to 70%.

Specimen 4-2 was accidently imploded after 44 hours of load expo-
sure during modification of the electronic pump control equipment; no
record of the actual implosion pressure was obtained. The implosion
value listed in Table B-4 was based on a calculated estimate of the
pressure increase in the vessel for a known duration of pump opera-
tion. Data were available on the exact time of operation of the pump
before implosion occurred. The estimated implosion pressure is pro-
bably within a 5% error limit.

Specimen 4-3 withstood a pressure load of 450 psi (3.1 MPa) for
168 hours without incident. The pressure was then reduced to zero
where it remained for 16 hours before the specimen was subjected to
85% of short-term strength. The pressure level was sustained for 2.5
hours without any signs of major structural distress, then the pressure

level was raised to 95% where implosion occurred after 3 minutes.

Radial Displacement Behavior

Radial displacement terms are defined diagrammatically in Figure
B-17. The deflectometer instrumentation method measured radial dis-
placement from initial to deflected shape, w. Membrane radial displace-
ments, wr were determined from the w data. The following method
was used. The reader should picture radial displacement data being
displayed on oscillograph paper as a potentiometer moves around the
circumference of a cylinder. A straight line would mean a perfect
circle. The specimens were not perfect; therefore, the lne moved
upward (for inward displacement) and downward (for outward displace-
ment). The wavy line on the oscillograph paper is a chart of out-of-
roundness data. The wavy line can be digitized (i.e., each point along
the line can be given a magnitude value). The average of these values
is plotted as a straight line and represents the membrane curve. The

average defines the size or radius of the membrane circle.

63

initial shape

initial membrane
circle

deflected shape

where:
w= displacement from initial
to deflected shape
W,, = displacement from mem-

brane behavior
Wp = displacement from
bending
wy = total displacement
AR; = initial deviation in
inside radius

deflected
membrane circle

Figure B-17. Definition of displacement terms.

When a deflected shape was plotted the reference point was the
location of the center shaft that held the potentiometer; however, this
location was not the "true" center of the deflected shape. The opera-
tion of finding the true center location was that of manually super-
imposing the membrane curve on the deflected shape and using judg-
ment to decide the location. Judgment was based on fitting the mem-
brane curve (perfect circle) of known size to the deflected shape such
that the area between the wavy line and the membrane curve was
divided equally.

The initial and deflected cross-sectional shapes of a free and
simply supported specimen with their corresponding membrane circles
are shown in Figures B-18 and B-19, respectively. All specimens
having a free support deflected into an elliptical shape where the num-
ber of lobes, n, was 2. All specimens having a simple support

deflected into a shape with n = 3.

64

aoddns ajduns pue 1¢0°0
= °q/a Sutavy saputyAd yea
-1d4} jo yyZuaTprw ye uOTI—as
SSOID paida|jop pue [eu] “6 ]-g onsIy

——
7 c
(dW 9'€)

isd ogg = “Ng a]o4t9
f ye sisAjeue aueiquiaut N
“p aseD [eatur My

ee
N/
((eaw 9°¢)_ | (

N isd z¢ = q) Anauioas
wd $6'0.38

punoj-jo-1no
adeys paraijap yeriur

ouPIquIoU
paisayjap

yadue[prur

Create Ome 47 uoTa8

urcgo 10 0
a[B9S uoWaoe|dsiq qioddns a;duns
S€'z = d/T

L£0°0 = °a

“q10d
-dns 9213 pue £¢0'0 = Cq/i Butaey sapunyAd jeaidAy

JO YISUSTPIU Iv WOTIDaS ssoID poIdaTJop puk [eu] “g{-q anSty

9UuOZ sIN]IeF

(dW +7)
isd ope = “Ng ae
sisA]eue ‘9 ase

ao
7
7
LY

V

y, dueIqUIduI
oO8T yetur
i_\

1
+
|

\ ((eaW 8°2)
isd 0O+ = d) Ayqawioas
\ Wy 960.38 puno1-jo-1no

adeys PEERED Sa. yerrur

a ajoata

aueiquioul
SN peqarjap

a[@9S usuaoR|dsiq

wilh ZZ oO Na yadua[prur
2® UOTID9S
ese uoloas
uIZ70 10 0
qioddns aary
2 = °q/T
££0'0 = °a/3

65

The worst flat spot on each cylinder eventually became the failure
location; this location consistently coincided with the wall sections that
were thin and somewhat flat initially.

Radial displacement data, as shown in Figures B-18 and B-19,
were plotted at various pressure levels for the test specimens. Data
obtained from these plots were used in analyzing the _ structural
behavior.

Pressure versus w and Wa relationships are shown in Figures B-20
through B-22.* The data for w are from the worst flat spot location.
The wi, curves come from w data so the maximum pressure for the Wi
curve (experimental perfect cylinder) cannot exceed oe of the experi-
mental out-of-round specimen.

Radial displacement behavior along the length of the cylinder is
shown in Figures B-23 through B-25. The influence of the boundary
condition as it is affected by the simple-support and the free-support
conditions is vividly seen.

Radial displacement data for specimens 5-1 and 5-2 were recorded,
but meaningful data were not obtained because the end-closures shifted
position as the pressure load was increased. The center of the shaft
moved, which meant that a common reference point between various
pressure levels was not available.

In Figure B-17, it is observed that the total radial displacement,

Wr» 1S equal to:
w =i Wintan NRE (B-1)
al i

and
we = wh + Wh (B-2)

*The analytical curves will be discussed later.

66

Pressure, P (psi)

Pressure, P (psi)

T T
t/Dg = 0.024

stress L/D9 = 2.35
GUD | comErol simple support
failure
500 perfect \
cylinder, Case 1 gaa

Va
400 - »

A~ strain control

WA failure
300 + /_*
(o)

200 -
Case 2

—_O-—-__ experimental (one specimen) +

instability

out-of-round cylinder, failure

100
— — —_ analytical
0 ! “ifs
(0) 0.05 0.10 0.15 0.20

Radial Displacements, w (in.)

Figure B-20. Radial displacement behavior at midlength of specimen 1-1 having

t/D,, = 0.024 and simple support.

Td u T
Rg = 27 in. -——+
700 Ale | WD» = 00387
ki L/D, = =
600 / | free support
500 ‘ t= 1.97 in
pe perfect cylinder, Case 6
w
400 Le SESS
300 | out-of-round
cylinder, Case 5
experimental range
200 ;
of two specimens
: ——O— experimental average
———-— analytical
100 oO stress control failure
& strain control failure
0 | i 1
0) 0.10 0.20 0.30 0.40

Radial Displacements, w (in.)

Figure B-21. Radial displacement behavior at midlength of Group 2 cylinders having

t/D,, = 0.037 and free support.

67

0.50

700 +

I T

perfect cylinder, Case 3

600
Y w
500
out-of-round cylinder,
Case 4
7 400 :
& Ro = 27 in.
Ou
o
5 9 -+—
yn A
o 300 experimental |
ie range of six |
specimens ec '
200 = |
t/Do = 0.037 [| t= 1.97 in.
——_©——_ experimental average
eee 8 L/D, = 2.35
FTAA Sa FCG le ae as = analytical :
(c) stress control failure simple support
a strain control failure
0 | L
0.05 0.10 0.15 0.20
Radial Displacements, w (in.)
Figure B-22. Radial displacement behavior at midlength of Group 3
cylinders having t/D, = 0.037 and simple support.
u TT ws Ur 7 1F- Vi T T T T
SL| 4
8 \
\
\ ——©— experimental
\ (one specimen)
4L —— — analytical
me | | wat Ro = 27 in. an
3 ! ee hae coal I 5
= H TN [- We 8 |
> N I |
1S) | @s | ~ !
= 3L H % 3 !
io SE ic s |
25 g qe eel t/Do = 0.037 |
= / EK © Fy L/Dp = |
> perfect 7 > — out-of-round
is cylinder, / t=alestins oO free support N ttingter,
/ a |
it Case 1 i = | Case 6
ce = = S |
; fi t/Dp = 0.024 Baul ce |
y L/D = 2.35 28 |
p= out-of-round simple support
A cylinder, |
L Case 2 perfect w
8 Al LE cylinder, \ =
———o©— experimental 8 Case 5 |
(one specimen)
—----- analytical |
4mm 6mm 2mm 4mm
0 1 i D 1 0 i | Ll it { =
0.15 0.20 0.25 10) 0.05 0.10 0.15 0.20 0.25

Radial Displacements, w (in.)

Figure B-23. Radial displacement behavior along

length of specimen 1-1 having t/D,, = 0.024 and

simple support at a pressure load of 0.89 P;_.

68

Radial Displacements, w (in.)

Figure B-24. Radial displacement behavior

along length of specimen 2-1 having
t/D,, = 0.037 and free support at a pres-

sure load of 0.78 Pian

The Known terms are w, Wp and AR.. Hence, radial displacements due

to bending can be calculated as:

m = wy ob NRG (B-3)

An estimate of the magnitude of strain on the inside and outside

wall surfaces can be made because we and Wy are now Known. Mem-

brane strain is calculated from:

WwW :
m on zm Ro = 27 in
€ Pav roe B-4 aL = pi
m Ry Ce 8 n fe Males
\\ eee
\\ = |
3L 4 | |
Sol e oye Us J
and bending strain is calculated ¢ | Ny Dae
Bl 1D = 0.037 |
from an expression developed in {4% experiments et |
aD ran f 1m r
3 3 | pentect eens
Reference 19 as: | leylinder
Case 3
Lb 4
8 | q out-of-round ———o—— experimental average
| cylinder, —— — — analytical
Case 4 |
|
“Db £ 2 0 LG L i et]
E = —— im = i) (B-5) 0 0.05 0.10 OS OO
b 2 RZ Radial Displacements, w (in.)

Figure B-25. Radial displacement behavior

Table B-6 summarizes _ the along length of Group 3 cylinders
having t/D, = 0.037 and simple

support at a pressure load of 0.95P;

ultimate radial displacements and Fe

calculated strains. It is interesting
to note that although Wy is typi-
cally several times the magnitude of

Wit the calculated strains En and €, are nearly equal. At implosion

b
the strains at the flat-spot location on the inside wall experienced slight
tension while on the outside wall strains were on the order of 4,000

uin./in. compression.

69

Table B-6. Ultimate Radial Displacements and Calculated Strains

Strains at Flat Spot on —

1
No. of { i em Eb
Specimen (win./in.) (win./in.)

Inside Wall, | Outside Wall,

€m_~ €b €m * €b
(yin./in.) (win./in.)

Group

0.050 0.043 | 0.207 1,670
0.057 0.051 0.514 2,040

0.042 0.052 | 0.175 2,080

-40
Average = a #31880
tension compression

ANALYTICAL RESULTS AND DISCUSSION

Analysis Description

A structural analysis was performed on the experimental specimens
using a finite element method called NONSAP-A that incorporated an
advanced constitutive relation subroutine for the concrete. The analy-
sis was conducted by Chen, Chang, and Suzuki (Ref 20) without the
benefit of the test results. Information on specimen geometry (includ-
ing the out-of-round geometry, boundary conditions, and material
properties) was supplied. It was desired to computationally model the
test specimens as realistically as possible and then determine the accu-

racy of the predictions.

Constitutive Model. The constitutive model was developed in three

parts - elastic, plastic and fracture - for concrete under general stress
states.

For elastic concrete, it was assumed that, initially, concrete is an
isotropic homogeneous linear elastic material and its stress-strain rela-
tions are described completely by two elastic constants, Poisson's ratio,
v, and Young's modulus, E. For the present analysis, v = 0.19 was
used, and E = 3.66x10° sand) 4) 19x10® psi (25-2) vands28h9GPa) were

70

determined from Figure B-7. The elastic limit envelope in general
stress space was obtained by scaling the fracture envelope down to a
size where uniaxial yield point corresponded to about 43% of the uniaxial
strength.

For plastic concrete, a strain-hardening plasticity model as pro-
posed previously in Reference 21 was used to describe the nonlinear
irreversible stress-strain response of concrete material. The plastic
incremental stress-strain relationship based on the normality flow rule
in the theory of plasticity are developed in detail in Reference 22.

For fracture, the concrete failed when the state of stress reached
a certain critical value. Two different types of fracture mode are

defined here.

(1) "Cracking" Type - When the principal stresses are
either in the _ tension-tension state or _ tension-
compression state and their values exceed the limit

values.

(2) "Crushing" Type - When the principal stresses are in

the compression-compression state and their values
exceed the limit values. When concrete cracks, the
material is assumed to lose only its tensile strength
normal to the crack direction but to retain its strength
parallel to the crack direction. On the other hand,
when concrete crushes, the material element loses its

strength completely.

In the present analysis, a dual representation of fracture criterion
was expressed in terms of both stresses and strain and specifies the
limit value under multiaxial state of stresses or strains in the following

forms:

Wl

(1) Stress Criterion

: La eae :
H(i a) = a a A Ital, = us (B-6)

where (ae and u, are material constants and where a is equal to zero
when the principal stresses are in the compression state and equal to
-1/6 when in the tension-compression or tension-tension state. The

first invariant, I corresponds to the mean stress component of the

1?

stress state. The term Jo is the second invariant of deviatoric
stresses.

(2) Strain Criterion

Bn en 2) 2 -
= t esiloes paseo 1 = ee ae
Baa) S dines (3 iq tn (=) a7)
Cc c
or
Maximum of the Principal Strains = E, (B-8)

in which Yh corresponds to volumetric strain and Jo is the second invari-
ant of deviatoric strains. The terms en and Et specify the maximum
ductilities of concrete under uniaxial compressive and tensile loading
conditions, respectively. Herein, the compressive cylinder strength
was assumed as 7,000 and 8,000 psi (48 and 55 MPa); and maximum
compressive strain, &,> was 3,500 pin./in. The tensile strength, fi
was assumed to be 0.09 fs and maximum tensile strain, E,> was 800
uin./in. When the stress state in the concrete satisfied either the

stress criterion (Equation B-6) or the strain criteria (Equations B-7

72

and B-8), fracture of concrete was assumed to occur. If the fracture
stress state lies in the tension-compression or tension-tension zone, a
crack was assumed to occur in a plane normal to the direction of the

offending principal tensile stress or Strain.

Finite Element Program. In the present work all the analyses were
performed using NFAP program (Ref 23) on computer system IBM model
370-158. NFAP is a modified and extended version of NONSAP-A pro-
gram (Ref 24), which is a modified version of the NONSAP program
originally developed by Bathe, Wilson, and Iding (Ref 25). The pre-
sent concrete constitutive model has been incorporated as a subroutine
in the NFAP program. The average computing time for the two-
dimensional (plane strain or axisymmetric) problems was about 5 minutes
for each case. The average computing time for each three-dimensional

analysis was about 62 minutes.

Geometry of Analysis. The eight cases as listed in Table B-7 were

analyzed using isoparametric shell elements.

(1) Cases 1 and 3 were modeled as axisymmetrical problems

with simple-support end-condition.

(2) Cases 5 and 7 were modeled as plane strain, axisym-

metrical problems.

(3) Cases 6 and 8 were modeled as plane strain, asymmet-
rical problems. Out-of-roundness in the form of n = 2

(see Table 2) was included in the analysis.

(4) Cases 2 and 4 were treated as three-dimensional pro-
blems with large displacement. Out-of-roundness in

the form of n = 3 was included in the analysis.

73

‘punoi-jo-no = YOO,

S-€ MGR L Worz 24/d g

“UIBIIS DAISSAIdUIOD JAIssadx9 Aq 1OU ‘sasRd [[R Ul UTPIIS [RIPeI JJISUDI %BO'O Aq Pauljap snyIeY ,,

. ‘ C = u
[eloyeu Selo 096 0008 curems aueyd woo
yeliaqeur SOLO 9S0'T 000‘8 ures aueyd yoayiod
ie =
[eoaeur 6700 Ive 0002 ‘ures oueyd woo
jeli91ew i 7600 8tS 000‘Z uress sued ayiad
[Pl1o7eur ae €Z0°0 80S 000°L ¢=u'd¢ bs (@X@) ajduits L€0'0 >
jeuaiew | 060'0 | 920°0 000'L | WeuTUAsIxe qoajied ajduns | 2¢€0°0 ¢
— a
Ayyrqeasut +£0'0 +200 000'8 € =u 'd-¢ ,1OO ajdurts +700 (4
[elaieul 090°0 0S0°0 dT aw AsIxe yajiad a[duuts
dInjIey am ai siskyeuy KGET yioddns
jo spow O(Uty) | 9g) jo Ala9uWI0d») 2 puq 1

synsay jeomdjeuy °2-g IqeL

74

Constant
tavg

Varying Wall

Thickness Wall thickness = tavg -0.08 in.

Figure B-26. Idealized initial out-of-round shape for cylinders
with n = 3.

AR, = 0.06 in.

ARj = 0.06 in.

450 | 459 % R.
WA ‘ Xs 7
Jo S
4 nN
Constant |
tavg \ , AR; = -0.02 in.

Varying Wall

Thickness Wall Thickness = tayg -0.08 in.

Figure B-27. Idealized initial out-of-round shape for cylinders with n = 2.

15

Cross-sectional geometry Table B-8. Cross-Sectional Geometry for Cylinders
for the cylinders, which

Numbers
includes data on _ idealized of

Lobes,
out-of-roundness, is shown in

Figures B-26 and B-27 with
geometry values given in
Table B-8.

26.345
26.345
26.015
26.015
26.015
26.015
25.305
25.305

Implosion Results. Table
B-7 summarizes the results of

1
2
3
4
5
6
7
8

the analyses in terms. of hi

n=2 Rave = Ravggo + ARcos20
implosion pressures that were
: ‘ tge OK @ < 45°
controlled by strain failure ,
e o t o-tpo
criteria, (P;)., and stress es an ELA) AD 2M < 902
failure criteria, (P._)_. The
im’o fs be
E : = n= 3 Rave = Rae AR cos 3 0
implosion strength is given by am 0
. . . te} < < oO
the nondimensional ratio of io? OE Oe
t
Paw to ohne analyticalsimplo- GO =O
a to + ap (0 - 30°) 30° < 0 < 60°

. . oO
sion strength is compared to 30

bes ee
, See Figure B-26.
the experimental strength by

“See Figure B-27.
the ratios shown in the last
two columns of Table B-7.

The experimental specimens were out-of-round cylinders so a true
comparison between analysis and experiment is only for out-of-round
cylinder cases (Cases 2, 4, 6, and 8). The average ratio of strain-
controlled implosion strength to experimental implosion strength was
0.89 and for stress-controlled implosion strength to experimental implo-
sion strength was 0.93.

The stress criterion failure mode predicted implosion with better
accuracy than the strain criterion method. Looking more closely at
individual cases, Case 2 was an instability failure mode and analysis
predicted implosion 15% lower than experimental. Cases 4, 6, and 8
were material failure modes, and analysis predicted implosion only 4%

lower than experimental.

76

Interestingly, the strain criteria that controlled in all cases,
except Case 2, was a tensile strain limit of 800 win./in., and not a
compressive strain limit. The limiting tensile strain occurred in the
radial direction of the wall (increase in wall thickness) at midlength for
the free-support specimens and at a distance of & = 0.4 from the end
for the simple-support specimens. Tensile strain had an influence on
failure because the wall thickness would laminate and facilitate a shear-
compression type of material failure of the wall. Evidence of wall
lamination has been observed in fragments of thick-walled spheres
under hydrostatic loading (Ref 26) but was not observed in the frag-
ments of cylinder specimens.

The effect of out-of-

roundness in reducing the

Table B-9. Reduction in Implosion Strength Due to
Out-of-Roundness

implosion strength of a per-
fectly circular cylinder is
shown in Table B-9. Cylin-

der t/D , influenced the out-

Percent Reduction in Implosion Strength

31

Between Case Numbers@ —

3&4 5&6 Average
a 8 9 (0)

>

Failure
Criteria

of-roundness effect con-

Strain a

Control siderably. Cases 1 and 2 are

Stress

thinner specimens than Cases
3 and 4, but all have a

Control

ee ae simple-support end-condition;
the thinner specimens showed
a 44% reduction due to out-
of-roundness, whereas the thicker specimens showed a 16% reduction.
A similar observation is made between Cases 5 and 6 which are thinner
than Cases 7 and 8, all having a free-support end-condition.

The influence of end-condition on out-of-round effect can be
observed with Cases 3 and 4 and 5 and 6, all of which have t/D, of
0.037. Cases 3 and 4 are simply supported and showed a reduction of
16%; whereas, Cases 5 and 6 are freely supported and showed a reduc-

tion of 46%.

77

The effect of cylinder length can be observed from Cases 3 and 4
and 5 and 6, all of which have the same t/D , ratio of 0.037 but differ-
ent effective lengths. Cases 3 and 4 had an L/D, ratio of 2.35, and
Cases 5 and 6 had an L/D, ratio of infinity. For the out-of-round
cylinders (Cases 4 and 6), the shorter cylinder had a _ predicted
increase in implosion strength of 53% over that of the infinitely long

cylinder. Experimentally, the increase in strength was 41%.

Displacement Behavior

The predicted deflected shapes for free-support and _ simple-
support specimens are shown in Figures B-18 and B-19. For the free-
support cylinder (Figure B-18), the predicted shape is a fair approxi-
mation of the experimental shape. It should be noted that the pressure
level for the experimental shape is near implosion at 400 psi (2.8 MPa)
where the analytical shape is at implosion at 346 psi (2.4 MPa). For
the simple-support cylinder (Figure B-19), the comparison is good.

The predicted radial displacement behavior as a function of pres-
sure is shown in Figures B-20 and B-22. Comparison of the experi-
mental to analytical behavior is quite good. For the out-of-round
cylinders, note that the predicted implosion pressures using the strain
or stress criteria are approximately the same.

A large difference in ultimate radial displacement was observed
between perfect and out-of-round specimens. For cylinders of t/D, =
0.037 (Figure B-21), the experimental out-of-round cylinder showed
w = 0.508 inch (13 mm), while the perfect cylinder had w = 0.08 inch
(2 mm) - a 6.4-fold increase. For specimens having the same t/D,
ratio of 0.037 but different end-support conditions (Figures B-21 and
B-22), the free-support cylinders showed an ultimate displacement of
w = 0.508 inch (13 mm) compared to the simple-support cylinders of

w = 0.185 inch (5 mm) - a 2.7-fold increase.

78

Radial displacement behavior along the length of the cylinder is
shown in Figures B-23 through B-25. The effect of the simple-support
is vividly shown in Figures B-23 and B-25. The compliance of the
actual ring stiffener in the experimental tests can be observed in Fig-
ure B-25 where approximately 0.02 inch (0.5 mm) of radial movement
occurred.

For the free-support cylinder (Figure B-24), the difference
between experimental and analytical behavior appears great. However,
this same difference is shown in Figure B-21, where the comparison
appears better. Experimentally, the free-support end-condition using a

rubber gasket modeled the ideal free-support quite well.

FINDINGS

1. Analytically, using the finite element program NONSAP-A with
an advanced constitutive material model, the behavior of the cylinder
specimens was predicted with good accuracy. The implosion pressures
were predicted 7% lower than actual when a stress criterion controlled
failure. It was found experimentally that specimens of L/D, of 2.35
had an implosion strength 41% greater than specimens of infinite length
(ong cylinders); analytically, the increase in strength was predicted as
BSF

2. Out-of-roundness was an important parameter in implosion
strength and radial displacement behavior. Analytically, the effect of
out-of-roundness was to reduce the implosion strength of perfect cylin-
ders by 16% to 46% depending on t/D, ratio and end-support condition.
The ultimate radial displacement for the free-support experimental
specimens of t/D, = 0.037 was 0.508 inch (13 mm), which was 6.4 times
the displacement for a perfect cylinder. The need to model out-of-

roundness to obtain accurate analytical predictions was found important.

79

3. Radial displacement data for the specimens showed that the
deflected shape for the free-support cylinders had two lobes (n = 2)
and for the simple-support cylinders had three lobes (n = 3). The
membrane and bending radial displacements were determined, and esti-
mates of strain were calculated at the failure location. It appeared that
at the worst flat spot the strain level at failure was slght tension on
the inside wall and about 4,000 win./in. compression on the outside

wall.

80

LIST OF SYMBOLS

Outside diameter

Initial elastic modulus
Secant elastic modulus
Tangent elastic modulus

Uniaxial concrete com-
pressive strength

Material strength factor
for cylinder structures

Material strength factor
for spherical structures

Cylinder length

Number of lobes

External pressure
Implosion pressure
Analytical implosion pres-
sure controlled by strain
criteria

Analytical implosion pres-
sure controlled by stress
criteria

Average radius

Outside radius

Average wall thickness

Minimum wall thickness

Radial displacement from
initial to deflected shape

Bending radial displace-
ments

Membrane radial displace-
ments

81

Total radial displacement
(see Figure B-17)

Deviation in radius

Inside deviation from
average radius

Outside deviation from
average radius

min
Ultimate strain
Bending strain
Membrane strain

Empirical plasticity reduc-
tion factor

Angular coordinate (see
Figures B-26 and B-27)

Angular coordinates of
failure zone

Angular coordinate of
center of failure zone

Poisson's ratio

Nondimensional distance
along cylinder length
(see Figure B-4)

Wall stress
Wall stress at implosion

Wall stress at implosion
predicted by Bresse's
equation (Equation 5)

Wall stress at implosion
predicted by Donnell's
equation (Equation 4)

Ratio of radial displace-
ments between end and
middle of cylinder

DISTRIBUTION LIST

ARMY CRREL Library, Hanover NH

ARMY ENG WATERWAYS EXP STA Library, Vicksburg MS

BUREAU OF RECLAMATION (J Graham), Denver. CO; G. Smoak, Denver CO

CNO Code OPNAV 22, Wash DC; Code OPNAV 23, Wash DC; OP-23 (Capt J.H. Howland) Washinton. DC

COMOCEANSYSPAC SCE, Pearl Harbor HI

COMSUBDEVGRUONE Operations Offr, San Diego, CA

DNA (LTCOL J. Galloway), Washington, DC

DNL Washington DC

DOE (D Uthus), Arlington, VA; (G. Boyer), Washington, DC; (W. Sherwood) Washington, DC: Dr. Cohen

DTNSRDC Code 172 (M. Krenzke), Bethesda MD

DTNSRDC Code 522 (Library), Annapolis MD

ENVIRONMENTAL PROTECTION AGENCY (Dr. R Dyer), Washington. DC

MARINE CORPS BASE PWO Camp Lejeune NC

MARITIME ADMIN (E. Uttridge). Washington, DC

MCAS CO. Kaneohe Bay HI

MCRD PWO. San Diego Ca

NAVCOASTSYSTCTR Code 713 (J. Quirk) Panama City. FL; Library Panama City. FL

NAVEODFAC Code 605, Indian Head MD “

NAVFACENGCOM Code 042 Alexandria, VA: Code 0453 (D. Potter) Alexandria, VA; Code 0454B Alexandria, Va:
Code 04B (M. Yachnis) Alexandria, VA; Code 04B5 Alexandna, VA

NAVFACENGCOM - CHES DIV. Code FPO-1 Wash, DC

NAVOCEANO Code 1600 Bay St. Louis. MS

NAVOCEANSYSCEN Code 5204 (J. Stachiw), San Diego, CA; Code 93, San Diego, CA

NAVPGSCOL (Dr. G. Haderlie), Monterey, CA: J. Garrison Monterey CA

NAVPHIBASE Harbor Clearance Unit Two, Little Creek. VA

NAVREGMEDCEN SCE. Guam: SCE, Philadelphia PA

NAVSEASYSCOM (R. Sea), Washington, DC; Code 0353 (J. Freund) Washington. DC; Code SEA OOC Washington,
DC

NAVSEC Code 6034, Washington DC

NAVSURFWPNCEN J. Honaker, White Oak Lab, Silver Spring, MD

NAVTECHTRACEN SCE, Pensacola FL

NAVWARCOL President, Newport, RI

NAVWPNCEN ROICC (Code 702), China Lake CA

NCBC Code 155, Port Hueneme CA

NOAA (Dr. T. Mc Guinness) Rockville, MD: (M. Ringenbach), Rockville. MD

NRL Code 8400 Washington, DC

NUCLEAR REGULATORY COMMISSION T.C. Johnson, Washington, DC

NUSC Code $332, B-80 (J. Wilcox)

OCEANAV Mangmt Info Div., Arlington VA

ONR (Dr. E.A. Silva) Arlington, VA

SUBRESUNIT OIC Seacliff, San Diego; OIC Turtle, San Diego

PETRO MARINE ENGINEERS EDI

U.S. MERCHANT MARINE ACADEMY Kings Point. NY (Reprint Custodian)

US GEOLOGICAL SURVEY (F Dyhrkopp) Metairie, LA; (R Krahl) Marine Oil & Gas Ops, Reston, VA

USAF SCHOOL OF AEROSPACE MEDICINE Hyperbaric Medicine Div, Brooks AFB, TX

USNA Ocean Sys. Eng Dept (Dr. Monney) Annapolis. MD; Oceanography Dept (Hoffman) Annapolis MD

BROOKHAVEN NATL LAB M. Steinberg, Upton NY

CALIFORNIA STATE UNIVERSITY LONG BEACH, CA (YEN): LOS ANGELES. CA (KIM); Long Beach, CA
(Kendall)

CLARKSON COLL OF TECH G. Batson, Potsdam NY

DAMES & MOORE LIBRARY LOS ANGELES, CA

DUKE UNIV MEDICAL CENTER B. Muga, Durham NC

UNIVERSITY OF DELAWARE (Dr. S. Dexter) Lewes, DE

FLORIDA ATLANTIC UNIVERSITY Boca Raton FL (Ocean Engr Dept.. C. Lin)

FLORIDA ATLANTIC UNIVERSITY Boca Raton FL (W. Tessin)

FLORIDA ATLANTIC UNIVERSITY W. Hartt, Boca Raton FL

83

FLORIDA INSTITUTE OF TECHNOLOGY (J Schwalbe) Melbourne, FL

GEORGIA INSTITUTE OF TECHNOLOGY Atlanta GA (School of Civil Engr., Kahn)

HOUSTON UNIVERSITY OF (Dr. R.H. Brown) Houston, TX

INSTITUTE OF MARINE SCIENCES Dir. Port Aransas TX

JOHNS HOPKINS UNIV Rsch Lib, Baltimore MD

LEHIGH UNIVERSITY BETHLEHEM. PA (MARINE GEOTECHNICAL LAB., RICHARDS): Bethlehem PA
(Fritz Engr. Lab No. 13, Beedle)

LIBRARY OF CONGRESS WASHINGTON, DC (SCIENCES & TECH DIV)

MAINE MARITIME ACADEMY (Wyman) Castine ME

MIT Cambridge MA

NATL ACADEMY OF ENG. ALEXANDRIA, VA (SEARLE, JR.)

NORTHWESTERN UNIV Z.P. Bazant Evanston IL

UNIV. NOTRE DAME Katona, Notre Dame, IN

OKLAHOMA STATE UNIV (J.P. Lloyd) Stillwater, OK

PURDUE UNIVERSITY W. Chen, West Lafayette, IN

MUSEUM OF NATL HISTORY San Diego, CA (Dr. E. Schulenberger)

SCRIPPS INSTITUTE OF OCEANOGRAPHY San Diego. CA (Marina Phy. Lab. Spiess)

SEATTLE U Prof Schwaegler Seattle WA

SOUTHWEST RSCH INST R. DeHart, San Antonio TX

STANFORD UNIVERSITY Stanford CA (Gene)

STATE UNIVERSITY OF NEW YORK (Dr. H. Herman) Stony Brook, NY

TEXAS A&M UNIVERSITY College Station, TX Depts of Ocean, & Meteor; W.B. Ledbetter College Station, TX

UNIV. AKRON T.Y. Change. Akron, OH

UNIVERSITY OF CALIFORNIA Berkeley CA (B. Bresler); Berkeley CA (D.Pirtz); Berkeley CA (Dept of Naval

Arch.): Engr Lib.. Berkeley CA; M. Duncan, Berkeley CA; P. Mehta, Berkeley CA

UNIVERSITY OF DELAWARE Newark. DE (Dept of Civil Engineering. Chesson)

UNIVERSITY OF HAWAII Honolulu HI (Dr. Szilard)

UNIVERSITY OF ILLINOIS Metz Ref Rm, Urbana IL: URBANA, IL (NEWMARK); Urbana IL (CE Dept, W.

Gamble)

UNIVERSITY OF MASSACHUSETTS (Heronemus), Amherst MA CE Dept

UNIVERSITY OF MICHIGAN Ann Arbor MI (G. Berg); Ann Arbor MI (Richart)

UNIVERSITY OF NEW HAMPSHIRE DURHAM, NH (LAVOIE)

UNIVERSITY OF TEXAS AT AUSTIN Austin, TX (Breen)

UNIVERSITY OF TEXAS MEDICAL BRANCH (Dr. R.L. Yuan) Arlington, TX

UNIVERSITY OF WASHINGTON (Dr. N. Hawkins) Seattle, WA: Dept of Civil Engr (Dr. Mattock), Seattle WA:
Seattle WA (E. Linger)

WOODS HOLE OCEANOGRAPHIC INST. Doc Lib LO-206, Woods Hole MA

AGBABIAN ASSOC. C. Bagge. El Segundo CA

ALFRED A. YEE & ASSOC. Honolulu HI

AMERICAN BUR OF SHIPPING (S Stiansen) New York, NY

APPLIED TECH COUNCIL R. Scholl, Palo Alto CA

ARVID GRANT OLYMPIA, WA

AUSTRALIA A. Eddie, Victoria

BECHTEL CORP. R. Leonard, San Francisco CA

BELGIUM Gent (N. De Meyer); HAECON, N.V., Gent

BRAND INDUS SERV INC. J. Buehler, Hacienda Heights CA

CANADA Library, Calgary, Alberta; Lockheed Petro. Serv. Ltd, New Westminster B.C.; M. Malhotra, Ohawa,
Canada; Surveyor, Nenninger & Chenevert Inc., Montreal; W. German, Montreal, Quebec

CF BRAUN CO Du Bouchet, Murray Hill, NJ

CHAS. TL MAIN, INC. (R.C. Goyette), Portland, OR

COLUMBIA GULF TRANSMISSION CO. HOUSTON, TX (ENG. LIB.)

CONCRETE TECHNOLOGY CORP. TACOMA, WA (ANDERSON)

CONRAD ASSOC. Van Nuys CA (W. Gates)

CONTINENTAL OIL CO O. Maxson, Ponca City, OK

DENMARK E. Wulff, Svenborg

DILLINGHAM PRECAST F. McHale, Honolulu HI

DIXIE DIVING CENTER Decatur, GA

EXXON Production Research Co. Runge, Houston, TX

EXXON PRODUCTION RESEARCH CO Houston, TX (Chao)

84

FRANCE (J. Trinh) ST-REMY-LES-CHEVREUSE; (P Ozanne). Brest: Dr. Dutertre. Boulogne; L. Pliskin, Paris: P.
Jensen, Boulogne; P. Xercavins, Europe Etudes; Roger LaCroix. Paris

GERMANY C. Finsterwalder. Sapporobogen 6-8

GLOBAL ASSOCIATES Engr Dept (Scott), Kwajalein

GULF RAD. TECH. San Diego CA (B. Williams)

INDIA Shn J. Bodhe, Fort Bombay

ITALY M. Caironi, Milan; Torino (F. Levi)

JAPAN (Dr. T. Asama), Tokyo: M. Kokubu, Tokyo: S. Inomata, Tokyo: S. Shiraishi. Tokyo

LIN OFFSHORE ENGRG P. Chow, San Francisco CA

LOCKHEED MISSILES & SPACE CO. INC. L. Trimble, Sunnyvale CA

MC CLELLAND ENGINEERS INC Houston TX (B. McClelland)

MEXICO R. Cardenas

MOBIL R & D CORP (J Hubbard), Dallas, TX

NEW ZEALAND New Zealand Concrete Research Assoc. (Librarian), Porirua

NOBLE, DENTON & ASSOC., INC. (Dr. M Sharples) Houston, TX

NORWAY E. Gjory. Trondheim; F. Manning, Stavanger: J. Creed, Ski; Norwegian Tech Univ (Brandtzaeg).
Trondheim: P.S. Hafskjold, Oslo; R. Sletten, Oslo: S. Field, Oslo; Siv Ing Knut Hove. Oslo

OFFSHORE POWER SYS (S N Pagay) Jacksonville, FL

PACIFIC MARINE TECHNOLOGY Long Beach, CA (Wagner)

PORTLAND CEMENT ASSOC. (Dr. E. Hognestad) Skokie, IL: SKOKIE, IL (CORLEY; Skokie IL (Rsch & Dev
Lab, Lib.)

PRESTRESSED CONCRETE INST C. Freyermuth, Chicago IL

SANDIA LABORATORIES (Dr. D.R. Anderson) Albuquerque, NM

SCHUPACK ASSOC SO. NORWALK, CT (SCHUPACK)

SHELL OIL CO. HOUSTON, TX (WARRINGTON); I. Boaz, Houston TX

SOUTH AMERICA B. Contarini, Rio de Janeiro, Brazil: N. Nouel. Valencia, Venezuela

SPAIN D. Alfredo Paez, Algorta

SWEDEN Cement & Concrete Research Inst., Stockholm; GeoTech Inst: K. Christenson, Stockholm; Kurt Eriksson,
Stockholm :

THE NETHERLANDS Ir Van Loenen, Beverwijk: J. Slagter, Driebergen

TRW SYSTEMS REDONDO BEACH, CA (DAI)

UNITED KINGDOM (D. Faulkner) Glasgow, Scotland; (Dr. F.K. Garas), Middlesex; (Dr. P. Montague) Manchester,
England: (H.W. Baker) Glasgow, Scotland; (M E W Jones) Glasgow, Scotland; (M J Collard), London; A. Denton,
London; Cambridge U (Dr. C. Morley) Cabridge, GB: Cement & Concrete Assoc Wexham Springs, Slough Bucks:
Cement & Concrete Assoc. (Lit. Ex), Bucks: Cement Marketing Co. Ltd. (Brittain) London; D. Lee, London: J.
Derrington, London; Library, Bristol; P. Shaw, London; R. Browne, Southall, Middlesex; Sunderland Polytechnic
(A.L. Marshall), Great Britain: T. Ridley, London; Taylor, Woodrow Constr (Stubbs), Southall, Middlesex; Univ.
of Bristol (R. Morgan). Bristol: W. Crozier, Wexham Springs: Watford (Bldg Rsch Sta, F. Grimer)

WOODWARD-CLYDE CONSULTANTS PLYMOUTH MEETING PA (CROSS. III)

BROWN, ROBERT University. AL

DOBROWOLSKI. J.A. Altadena, CA

GERWICK, BEN C. JR San Francisco, CA

LAYTON Redmond, WA

NORWAY B. Nordby, Oslo

WATT BRIAN ASSOC INC. Houston, TX

WESTCOTT WM Miami, FL

WM TALBOT Orange CA

85

e
7 i
’
}
i i
SS
,
’
‘ 4
*
+
2 ~
eye
hy

wen

DEPARTMENT OF THE NAVY

CIVIL ENGINEERING LABORATORY
NAVAL CONSTRUCTION BATTALION CENTER POSTAGE AND FEES PAID
PORT HUENEME, CALIFORNIA 93043 REEARAENIA DHE NAVY

OFFICIAL BUSINESS

PENALTY FOR PRIVATE USE,$300

Ss

(EPRI
U.S.MAIL
RE

Decument Library wWU<U6o
Woods Hole Uceanograpnic Institution
noods Hole, MA 02543