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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS -1963

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"FEB ? 6 1968
ORNU-P.3595
Conf-680203-02
MORTAR MODELS OF PRESTRESSED CONCRETE REACTOR VESSELS*
MASTER
James M. Corum, M. AS WEL
Richard N. White, M. ASCE
Jack E. Smith
Abstract
The results of the test of a small scale model of & prestressed
concrete reactor vessel are presented. Model design and fabrication
techniques are discussed, and the test results are compared to finite
element analysis predictions for both elastic and short-term creep be-
havior. The test reported is the first of a series in a model study
program being carried out to determine to what extent small mortar
models and models of elastic materials, such as epoxy, can be used to
investigate the stress distributions and the cracking and ultimate
failure mode of prestressed concrete reactor vessels or of various
components of these vessels, such as penetration and anchor regions.
OAK RIDGE NATIONAL LABORATORY
OAK RIDGE, TENNESSEE
LEGAL NOTICE
This report wao prepared as an account of Government sponsored work. Neither the United
States, oor the Commission, nor any person acting on behalf of the Commission:
A. Makes any warranty or representation, expressed or implied, with respect to the accu-
racy, completenods, or usefulness of tho information contained in this report, or that the use
of any information, apparatus, method, or procos& disclosed in this report may not iafringe
privately owned rights; or
B. Assumes any liabilities with respect to the use of, or for damages resulting from the
Use of any information, apparatus, mctbod, or process disclosed in this report.
As usod in the above, "person acting on behalf of the Commission" Includes any am-
ployee or contractor of the Commission, or employee of such contractor, to the extent that
such employee or contractor of the Cow.col.sion, or employee of such contractor prepares,
disseminatos, or provides access to any information pursuant to die employment or contract
with the Commissina, or his employmont with such contractor.
Research sponsored by the U. S. Atomic Energy Commission under
contract with the Union Carbide Corporation.
*Reactor Division, Oak Ridge National Laboratory.
2 Associate Professor of Structural Engineering, Cornell University,
...Ithaca, New York (currently on leave with Gulf General Atomic, Inc.).
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INTRODUCTION
· The study described in this paper represents a portion of
a major program of investigation into the use of prestressed
concrete reactor vessels (hereafter referred to as the PCRV).
The overall program is being directed by the Oak Ridge National
Laboratory for the United States Atomic Energy Commission and
is directed specifically at improving the level of technology
for the design, analysis, and construction of PCRV structures.
Because of the great complexity of this type of structure,
model analysis has played an important role in the design phases
for the several European PCRV's built in recent years(b). Most
of these models have been rather large structures in themselves
and have been quite expensive. Large models have also been used
in the U.s. (2) in studies preliminary to the design of the first
PCRV to be built in this country.
: The purpose of the study reported herein is to determine
the suitability and accuracy of very small scale models for de-
termining certain behavioral aspects of the PCRV. Experience
with small scale models of other types of concrete structures!"
indicates that response to elastic loadings (prestressing, working
pressure) and inelastic behavior (short-term creep, degree of
cracking at overpressures, mode of failure, and ultimate
strength) might well be investigated economically with this
technique. Thermal effects and long-time inelastic behavior
were considered to be beyond the scope of this initial study.
The role of the small mortar model in the current study is
shown in Fig. 1. The larger structure is a relatively small
11
,
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.
2.75
and simple "prototype" prestressed concrete vessel; it repre-
sents the top half of a cylindrical vessel closed with flat
heads. A full size PCRV would be on the order of 8 times
larger than this structure. The prototype will be tested to
failure under internal hydraulic pressure at a later date and
will provide experimental results for direct conparison to the
smaller mortar models, which are also shown in Fig. 1. The two
nortar models are exact replicas of the concrete models at a
geometrựcal scale .. The pneumatic pressure test of the
first mortar model is described in this paper. The second
mortar model was tested hydraulically; detailed results of this
most recent test are not yet available.
The final model shown in Fig. 1 is a 1/5 scale prestressed
epoxy model which is to be analyzed by the scattered-light three-
dimensional photoelasticity technique. It will provide an elastic
stress distribution for prestressing and pressure loadings.
DESCRIPTION OF PROTOTYPE
The design of the prototype vessel is sion in Fig. 2. The
vessel has many features similar to those found in an actual PURV,
including thick head and walls, unbonded post-teasioned prestres-
sing in three directions to counteract the effects of internal
pressure, and a pattern of penetrations through the head. The
only conventional reinforcing elegents in the structure are the
two concentric rings of steel aesh at the base, and 8:0911 pieces
of mesn under the prestressing anchor plates in the head.
The prototype was designed for 500 psi internal pressure,
which is representative of pressures act in actual gas-cooled
-2-
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.
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reactors. A concrete vith noniaal uniaxial compressive strengta
of 6000 psi was used, and ali prestressing elements were con-
ventional Stressteel bars. A fiber-glass reinforced epoxy liner
was applied to the interior cavity of the vessel to prevent
permeation of the pressurization fluid into the concrete.
A finite element analysis program developed at Gulf General
Atomic, Inc. (4) for the AEC was used in the design of the proto-
type. The axisymmetric idealization of the strucüure is shows
in Fig. 3; the concrete and steel buse plate are represented by
triangular ring elements. Linear eleaents are used for convento
ional reinforcement and prestressing loads are idealized as
externally applied point loads. The effect of head penetrations
is accounted for by reducing the stiffness of the penetration
region.
Principal stress trajectories for the case of prestressing
plus 500 psi design pressure are shown in Fig. 4. Figs. 5 and 6
give stress contour plots for circumferential (hoop) aos meridional
stresses, respectively. At the design pressure of 500 psi, the
average hoop stress is about 500 psi compression. Since each
additional 100 jsi of pressure adds a tensile stress of about
200 psi, the average hoop stress will become about 500 psi tension
at an internal pressure of 1000 psi. The imperfections of the
idealized mathematical model (in particular, the stress concen-
trations produced at the 12 axial prestressing tend on conduits)
will lead to somewhat higher local hoop stress, and the cracking
strength of the concrete should be exceede i at this pressure .
The maximum meridional stresses of Fig. 6 beco:ne more posa.
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itive with increasing internal pressure. The haunch area, where
the head and wall join together, will become critically stressed
in tension with increasing pressure. The high localized con-
pressive stresses under the hoop prestressing load points do
not exist in the true vessel because the prestressing is dis-
tributed through steel anchor blocks (Fig. 2).
In addition to the axisynmetric analysis, the stress con-
centrations around the head penetrations were assessed by a
planar finite element analysis of the head.
MORTAR MODELS
Similitude and Materials: All geometrical features of the proto-
type were reduced by a scale factor of 2.75. Model materials
were chosen to duplicate prototype material properties as closely
as possible. The resulting mortar models can thus be coneidered
a's true models of the prototype, with strains and stresses ident-
ical in model and prototype at any given internal pressure level.
The mortar mix proportions were 1:3:1 (cenent, sand, 5/16"
aggregate) with a water/cement ratio of 0.517. A typical com-
pressive stress-strain curve from a 2 in. by 4 in. cylinder is
shown in Fig. 7; average 28 day f: was 6.83 ksi.
Stressteel rods were used for prestressing the model, and
a suitably scaled mild steel mesh was used for base reinforcing
and under the prestressing anchor plates.
Fabrication and Casting of Model: The production of high quality
models of this complexity and at a very small scale requires
extremely careful planning and workuanship at all stages of
fabrication and casting.
4.
Plexiglas was chosen as the basic forming material because
of its superior qualities -- it is easily machined to close
tolerances, does not absorb .water, produces excellent surfaces,
and permits multiple re-use of forms without deterioration. Part
of the exterior base mold and a number of steel hardware items
are shown in Fig. 8.
The interior cavity mold was constructed of aluminum tubing
with a Plexiglas top plate. The entire assembly (visible in Fig.
9) was cut into three segments to enable removal from the cavity
after casting. ' This form is also re-usable.
A partial assembly of the form is showa in Fig. 9. The
steel anchor blocks were held in position by attaching them to
the exterior walls of the form, and Plexiglas filler blocks were
inserted between the steel blocks to form the required irregular
hexagonal exterior surfaces of the model wall. Caulking compound
was used extensively in building up a water-tight assemblage of
woma.
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blocks.
annis samen met klein in the upper redan har
m
A top view of the completed form is shown in Fig. 10 just
prior to model casting. The congestion of the many internal com-
ponents severely restricted placedent of the mortar.
The entire mold was vibrated intermittently during place.
ment of mortar (Fig. 11) over a 45 minute casting period. The
placing of the low-slump nortar in the congested form would have
been impossible without the vibrating table. The transparency of.
the Plexiglas forms was invaluable in assessing the adequacy of
the vibration.
Removal of interior and exterior forms was accomplished
-50
.
according to a pre-determined schedule. at an early age (22
hours or less) to prevent the possibility of restrained early
shrinkage producing cracking in the model.
The resulting models were of very high quality with neg-
ligible voids or boney-coabing. A disassembled model is shown
in Fig. 12. Typical axial, head, and circumferential prestres-
sing bars are shown in the foregrour1. The base plate is shown
on the right with tie-rods connected to the head penetration
plugs.
The models were cured in a fog room for about fc:r weeks.:
After removal a ad a brief drying period, the surfaces of the
model were sealed with several coats of shellac. The models
were kept in a controlled enviroanent (70° F, and 50% R.H.)
during the instru nentation and testing period. The first model
was instrumented with 70 strain gages, crack detecting strips,
and transducers; the second mortar model and the prototype had
about 370 separation instrumcntation points.
Model Prestressing: The models were prestressed using convent-
ional jacking equipment. Six rams (Fig. 13) connected to a common
hydraulic pressure source were used to prestress six tendons
simultaneously. The prestressing was accomplished in two phases
with all tendons stressed to half the final load level in the
first phase. No difficulties were met in achieving an accurate.
level of prestress in these very short tendons.
TEST RESULTS AND COMPARISONS
Testinz History: Following a four week creep test period after
prestressing, the first model was pressurized with nitrogen
For . ********...........
LAK
according to the schedule shown in fig. 14. After 3 pressure
cycles (to 300, 300,, and 600. psi) of elastic loading response,
the vessel was subjected to a higher pressure level which ended
with a leak in the epoxy liner at 850 psi. Tae leak was repaired
and the vessel was pressurized again, reaching 965 psi before
significant structural cracking and sudden leaking occurred.
The only apparent evidence of failure was a sudden drop in
pressure and the loud hissing of escaping gas. The vessel was
then filled with oil and pressurized to 1045 psi, which was
more than 2.5 times the working pressure of 417 psi. Oil was
observed to be leaking from at least several major vertical hoop
cracks in the cylindrical portion of the vessel.
Comparison of Results with Elastic Analysis: Measured and pre-
dicted meridional and circunfercatial stresses for a gage rosette
near the iaside center of the vessel wall are shown in Fig. 15.
"
*
.
.
Two different short-time load ings are given -- the prestressing
sequence and the pressure cycling shown in Fig. 14 up to a
pressure of 800 psi. The solid steps are finite element pre-
dictions while the points are experimental results. The agree nent
for meridional stresses is excellent at all load levels. Cir-
cumferential stresses for the pressure test agree less favor-
ably; this is most likely due to the non-axisymmetric cross section
which would have a pronounced effect on circumferential stresses.
Stress conparisons for a location in the baunch area of
the vessel are shown in Fig. 16. Notice that once again the
computed meridional stresses are very close to measured values,
while circumferential stresses show significant differences.
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Fig. 17 gives results for a rosette in the top head
penetration region. The theoretical predictions here are a
analysis of the penetration region.
The elastic response of the prestressing tendons during
vessel pressurization was measured and also computed in the
analysis of another idealization of the vessel which included
the tendons in the structural stiffness matrix. The tendon
stress increases were as follows:
Specific Stress (psi_per_psi pressure)
Tendon
Measured
Computed
1.47
5.07
Axial
2.80
3.03
Head
1.60
Circumferential
- 8.27
It is believed that the relatively poor agreement between the
values for circumferential tendons may be due to the effects
of including only the upper portion of the actual vessel in the
idealization; a roller support permitting radial displacements
was placed in the cut wall. These assumed boundary conditions
would affect circumfere
ht,
a 1
1 tendon's much more than axial or
4
head tendons.
Inelastic Behavior: Inelastic behavior may be divided into two
phases: (a) concrete creep and prestressing steel relaxation
under relatively constant loading conditions, and (b) cracking
behavior under high pressure levels.
Measured strains during the one-month creep test at three
gage locations are shown by the dashed lines in Fig. 18. The
only loading on the vessel was the prestressing. It may be
: -S-
assumed that the strain changes are due. entirely to creep.. .
since the model surfaces were sealed against.moisture exchange
with the atmosphere.
The measured change in the axial prestressing bar strain
is also shown in this Figure. Note the two strain levels cor-
responding to 60% and 70% of the minimum ultimate tendon strength.
The first value represents the design level and the second the
maximum allowable level during prestressing.
The computed response curves shown in Fig. 18 were deter-
mined with another finite element program; this linear visco-
elastic creep analysis procedure is described in Ref. 5. The
idealization used was the same as used in determining the
elastic response of the prestressing tendons during vessel pres-
surization (described above). Because the creep function used
was only approximate , the results from the analysis and the test
cannot be expected to compare directly. The analysis results
would improve with a more detailed knowledge of the mortar creep
properties available as input to the analysis.
Relaxation effects in the prestressing steel was accounted
for in the analysis by assuming that the steel stress level would
reduce by 4% (linearly with respect to logarithm of time) during
the creep period.
. The extensive cracking of the structure under high pressure
was revealed by the patterns of oil leakage. After the fina).
pressurization test the prestressing tendons were removed and
the model was pressurized with tap water at 75 psi. Fig. 19
shows the water leakage which duplicated the pattern of oil
leakage observed during the test. Note the two main vertical
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cracks, especially the one just to the ſight of the left
anchor blocks.
Following the water test, the model was sectioned just
below its midplane, and the top half of the vessel is shown in
Fig. 20. The dark traces through the wall were caused by oil
leaking through the many hoop cracks in the vessel. The stress
raising effects of the axial tendon conduits are clearly visible
from the cracking pattern which developed. .
There were also some cracks running circumferentially
around the haunch. Fig. 21 shows a vertical crack which forks
at the haunch into two circumferential cracks. There undoubtedly
were many other small interior cracks which were not detected
either by inspection or by the instrumentation.
Soue indication of the pressure level producing the init-
iation of cracks is provided by the strain plots in Figs. 22,
23, and 24. These results are from 5 in. long crack detection
strips which were actually single wire strain gages. The first
figure is for a circumferential gage which picked up indications
of hoop-type cracking. At a pressure of just over 800 psi the
strain suddenly increased rapidly, thus marking the initiation
of hoop-type cracking.
Fig. 23 presents results for a neridional gage in the ..
haunch area of the PCRV. Notice that there is no sign of cracking
on the first pressurization to 850 psi, but some cracking appar-
ently occurred at a pressure between 500 and 600 psi during the
subsequent pressurization.
The results froin a meridional gage in the cylindrical portion
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of cracking except near the ultimate pressure of 1045 psi.
DISCUSSION AND CONCLUSIONS
1. The failure of this type of vessel is gradual and is accomp-
anied by extensive cracking which in turn relieves, the internal
pressure. The integrity of the liner is an important feature
of the vessel in reaching high pressure levels. The ductility
of the structure is assured by the proper amounts and placement
of prestressing steel.
2. The final assessment of the validity of the very small scale
modeling technique will be possible only after testing of the
larger prototype vessel is completed. Preliminary comparison
of results from the two identical mortar models indicates excel-
lent reproducibility of behavior, and the final comparison of
results is being approached with considerable optimism for success.
3. Considerable thought and care are required at all stages of
construction and instrumentation of very small structures of
this complexity.
4. Considering the complexity of the PCRV, the finite element
analysis techniques provide excellent prediction of vessel be-
havior, particularly in the elastic range. Developments currently
under way will extend the analysis capability into cracking and
post-cracking behavior. Detailed comparisons of actual test
structure behavior, such as described herein, with the computer
predictions are essential in developnent of the analysis programs.
:-1l-
:
ACKNOWLEDGEMENTS
The mortar models and their forms and accessories were
designed and built at Cornell University under a sub-contract
from the Union Carbide Corporation. Structure instrumentation
and testing was done at Oak Ridge National Laboratory. Computer
time for a portion of the analysis was provided by · Gulf Gen-
eral Atomic Inc. ; most of the elastic analysis was done in the
Computer Center at ORNL.
REFERENCES
'1. Group G Papers (Models--Comparison of Theory With Experi-
mental Results), Conference on Prestressed Concrete Pressure
Vessels, London, March 1967.
2. "Pressure Test and Evaluation of a Model Pressure Vessel,"
by W. Rockenhauser, T.E. Northup, and R.O. Marsh, Paper
38, London Conference on PCRV's, March 1967.
.
"Smal) Scale Models of Reinforced and Prestressed Concrete
Structures," by H.G. Harris, G.M. Sabnis, and R.N. White,
Dept. of Structural Engineering Report No. 326, Cornell
University, Ithaca, N.Y. September 1966.
.4.
"Analysis of Axisymmetric Composite Structure by the Finite
Element Method," By Y.R. Rashid, Nuclear Engineering Design,
January 1966, pp. 164-182.
5. "Pressure Vessel Analysis by Finite Element Techniques,"
by Y.R. Rashid and W. Rockenhauser, Paper 37, London Con-
ference on PCRV'S, March 1967.
-22
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FIG. 1. PROTOTYPE AND MODEL VESSELS.

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FIG. 2. PROTOTYPE VESSEL DDEKSIORS AND DESIGN.
ORNL-DWG 67-4346

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FIG. 4. PRINCIPAL STRESS TRAJECTORIES – PRESTRESSING PLUS
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ORNL-OWO 67-4349
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FIG. 5. CIRCUMFERENTIAL STRESSES - PRESTRESSING PLUS 500 PSI
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FIG. 6. MAXIMUM STRESSES IN MERIDIONAL PLANE – PRESTRESSING
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FIG. 9. PARTIALLY ASSEMBLED FORM.
.
ار
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: لا

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..
TOP VIEW OF FORM AND COMPONENTS.
7
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FIG. 10.
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FIG. 11. FORM IN POSITION FOR CASTING MODEL.
.

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FIG. 12. MODEL WITH PRESTRESSING ELEMENTS (DISASSEMBLED).


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FIG. 13. PRESTRESSING OPERATION.
i...
2
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miesto
.
Rose AS. MAX. TEST PRESSURE
965 psic MAX. PNEUMATIC PRESSURE
850 psi - INITIAL LINGE LEAK
INTERNAL PRESSURE psi
INITIAL CYCLING
INCREASE TO
TEST PEESSIIRE
FAILURE TEST
HYDRAULIC
..

PNEWMDiv TESTING
FIG. 14. PRESSURB LBST HISTORY, MOKTAR MODEL NO. 1.
ORNL-DWG 67-8568
500
MERIDIONAL STRESSES (psi)
1000
TomTom


0
GAGE C209
500
CIRCUMFERENTIAL STRESSES (psi)
00
500
PRESTRESSING SEQUENCE
PRESSURE TESTS
FIG. 15. PREDICTED AND MEASURED STRESSES IN VESSEL WALL.




-2000
ORNL-DWG 67-8569
.-1500
-500
MERIDIONAL STRESS (psi)
1000
4500
-2500
GAGE C244
130
CIRCUMFERENTIAL STRESS (psi)
Ir. H
.
000
500
PRESTRESSING SEQUENCE
PRESSURE TESTS
FIG. 16. PREDICTED AND MEASURED STRESSES IN HAUNCH AREA.


---.....
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---
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----
--
-
--
-
-
-
-
-
-
-
-
-
-
.
.
--
-
--
-
-
ORNL-DWG 67-8570R


-2000
-1500
-1000
00
MERIDIONAL STRESS (psi)
00
500
GAGE C219
500
CIRCUMFERENTIAL STRESS (psi)
DOO
-500
500
PRESTRESSING SEQUENCE
PRESSURE TESTS
FIG. 17. PREDICTED AND MEASURED STRESSES IN VESSEL HEAD.


2.

CONCRETE GAGE..
LOCATIONS :
3600
215
2137
zanel SÝRAIN_CORRESPONDING 70 0.ZĘ
: 1. MEASURES AVER.96E OF
4 AXIAL TENDONS :
5.95"
2
COMPUTED
STRAIN CORRESPONDING TO O.GE
CONCRETE GAGE 209 (MERIDIONAL)
COMPUTED
STRAIN (MIC20-1/..)


CONCRETE GAGE 215( MERIDIONAL)
COMPLATES
"
---

1
--
CONCRETE GAGE 213 (Hoop)
.
----------------
? computed
-5001
1
60
64
82
68 72 76 80 84
AGE IN DAYS
88
.
FIG. 18. TYPICAL TIME-DEPENDENT STRAINS, PREDICTED AND MEASURED.
..::

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FIG. 19. VESSEL LEAKAGE PATTERNS AT FAILURE.
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FIG. 20. VERTICAL CRACKING IN · VESSEL WALL.
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.
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.
.
.
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CRACKING IN HAUNCH AREA.
عننمسیسی.بعدشمنا

ORAL-DWG 67-8565
.
.
*
*
.W
CRACK DETECTION
GAGE, S002 .
H
.100 pin./in. -
-
eneam-*7*thern* venins
INTERNAL PRESSURE (psi)
t
t
u
vir
I* *** ***htal 144
*044 mwah
0
0
0
STRAIN
(min./in.)
FIG. 22. RESULTS FOR CIRCUMFERENTIAL CRACK DETECTION STRIP.
.
49
VLOTI
HL

ORNL-DWG 67-8567
********** *****.
CRACK DETECTION
GAGE, S302
200
200 min./in.
..
i
....
-----..-......
INTERNAL PRESSURE (psi)
0
0
0
0
0
STRAIN (min./in.)
FIG. 23. RESULTS FOR MERIDIONAL CRACK DETECTION STRIP ACROSS HAUNCH.
:
within
f
evening to
s
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n
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istiane f cute kada se nekim Sinondationin rekisteriseret natukemiisimaison avere una sola merastamine
midis
ording
the contra intentio

L-DWG 67-8566
AVIATUL
200 min./in.
CRACK DETECTION -
GAGE, S101
INTERNAL PRESSURE (psi)
0
0 0
STRAIN (rin./in.)
..
.
.
.
.
....
FIG. 24. RESULTS FOR MERIDIONAL CRACK DETECTION STRIP ON VESSEL WALL.

wit
*
UNE
DATE FILMED
4 / 3 / 68








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