STRUCTURAL INTEGRITY ASSESSMENT OF DISPOSAL PACKAGE FOR
RADIOACTIVE WASTE
FAILURE ASSESSMENTS FOR OVERPACK USING FINITE ELEMENT ANALYSIS
Masahiro KAWAKUBO*1, Masato KOBAYASHI*1*1 Radioactive Waste Management Funding and Research Center
Nichirei Akashicho Bldg. 12F, 6-4, Akashicho, Chuo-ku, Tokyo, 104-0044, Japan
Key words: Geological disposal, Disposal package, Structural integrity, Failure mode, Failure assessment

Abstract
In Japan, it is planning for high-level radioactive wastes to undergo geological disposal after being vitrified andencapsulated into an overpack. The carbon steel overpack is required for at least 1,000 years’ isolation of thevitrified waste to prevent its coming into contact with groundwater. The overpack is a cylindrical package andmade of carbon steel as the primary candidate material. The basic specification of the overpack was proposed asa wall thickness of 190 mm, and with a corrosion allowance layer (40 mm), radiation shielding layer (150 mm),and mechanical withstanding layer (included in radiation shielding layer). In this study, to ensure the overpack’s
integrity over the period required for, failure assessments of the overpack using finite element analysis wereperformed for all failure modes assumed during operation and after emplacement. The results of the failure
assessment showed the relationship between collapse load and overpack thickness, and the relationship between
welding residual stress and critical crack size of welded parts. It was clarified that the strength of the weld joint
can be sufficiently ensured by partial welding.

1. Introduction
In Japan, it is planning for high-level radioactive
wastes to undergo geological disposal after being
vitrified and encapsulated into an overpack. The
overpack is required for 1,000 years’ isolation of thevitrified waste to prevent its coming into contact withgroundwater [1]. One candidate material for theoverpack is carbon steel. The thickness of theoverpack was proposed to 190 mm as the sum of theradiation shielding 150 mm (including the pressure
resistance 110 mm) and the corrosion allowance 40mm. The pressure resistance was calculated using theformula specified in Notification No. 501 [2] (ThisNotification is a basis for the Code for Nuclear Power
Generation Facilities: Rules of Design andConstruction for Nuclear Power Plant edited by theJapan Society of Mechanical Engineers).
In an integrity assessment for a general structure,
failure forms (positions of failure) are assumed andall failure modes (ductile failure, brittle failure, etc.)
for each failure form are assumed. When all thefailure modes are evaluated to not occur, the integrityof a structure is confirmed.
In this study, for the overpack designed usingreference [1], failure assessments used finite element
analysis and were aimed at confirming the integrityof the overpack. First, all failure modes for theoverpack were investigated. Next, failure evaluations
were performed on each failure mode and therelationships among wall thickness, welding depth,
and load applied to the overpack were obtained.
2. Failure mode of overpack
The lid types proposed for the overpack are a drop-in
lid type and a flat lid type as shown in Fig. 1. The
jointing method of the lid and the body is welding [3].
Loads applied on the overpack are lifting load during
the operation period, external pressure after
emplacement, and welding residual stress. For these(a) Drop-in lid type(b) Flat lid typeFig. 1 Two types of lid structure model for overpack

6th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, Japanloads, failure parts of the overpack are conceivable asfollow: (i) failure of the base metal part, (ii) failurefrom the tip of the welded part, and (iii) failure froma weld flaw. The failure modes for these failure parts
are conceivable as follow:(i) Plastic collapse(ii) Plastic collapse, elastic-plastic failure, brittlefailure(iii) Brittle failure
Fatigue failure is also considered as a failure mode ina general structure. However, from the analysis result
assuming the largest domestic earthquake, the cyclicload applied on the overpack is about 1.7 MPa at
maximum [4]. There is no need to consider fatigue
failure.

Table 1 Analysis conditions
Temperature
(°C)
90

t +20

In failure of the base metal part, the failure mode isplastic collapse of the body or lid. For the calculationof the collapse load, the Twice-Elastic-Slope Method[5] was applied. In the Twice-Elastic-Slope Method,collapse load is calculated using the relationshipbetween load and displacement. The applied load
used external pressure and the displacement used a
representative point (the center of lid or the center ofinternal body). As a deformation characteristic of thematerial, elastically-perfect plastic material of yieldstrength Sy was assumed.
Fig. 3 shows the relationship between wall
thickness of overpack and collapse load. The collapse
load decreased with decrease of the wall thickness,and the collapse load depended on the yield strength.
In the case of wall thickness of 50 mm and Sy = 100
MPa, the collapse load was the smallest 19.7 MPa.
Since the external pressure applied on the overpack is10.7 MPa at 1,000 m depth in hard rock [6], thecollapse strength was about 1.8 times the safetymargin, for 50 mm thickness of the overpack.
3.2.2 Failure from the tip of welded partIn the case of failure from the tip of the welded part,

wt
1350(b) Drop-in lid type

Welded part

440tw(c) Flat lid type(a) Overpack modelFig. 2 Failure analysis model of overpack
External pressure at collapse, MPa

3.2 Analysis results
3.2.1 Failure of base metal part

Poisson’s ratio(-)
0.3

Welded part

3. Failure assessments
3.1 Analysis method and Analysis model
In order to perform failure assessment for theoverpack, it is necessary to calculate stress intensity
factor K by elastic finite element analysis, and tocalculate plastic collapse load and J-integral byelastic-plastic finite element analysis. In this study,
the failure analyses used the general purpose program
ABAQUS standard. The physical properties of thematerial used for the analysis are shown in Table 1.
The analysis model for the overpack is shown in Fig.
2.

Young’s modulus
(GPa)
199

250

Sy = 300

200

Sy = 200

150
100

Sy = 100

50
10.7MPa (Hard rock 1,000 m)

050

100
150Thickness, mm

200Fig. 3 Relationship between external pressure atcollapse and thickness of overpack
the failure modes are plastic collapse andelastic-plastic failure at lifting up during operation,and plastic collapse due to external pressure after
emplacement of the overpack.
(1) Plastic collapse of welded part for lifting load
For the calculation of the collapse load, theTwice-Elastic-Slope Method [5] was applied. The
relationship between yield strength required for thewelded part and weld depth is shown in Fig. 4. When
the welding depth was 70 mm or more, the yieldstrength required for the overpack was about 1 MPa.
When the welding part was smaller than 60 mm, theyield strength increased. However, the yield strength
did not become larger than 5 MPa in either lid case.
Since 40 mm thickness of the corrosion allowance isconsidered to be welded and the yield strength of
typical carbon steel is greater than 200 MPa, it was

6th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, Japan

Flat lid type
Drop-in lid type543210050100150
Weld depth, mm200Fig. 4 Relationship between required yield strengthand weld depth
1.416014012010080

Flat lid type60

Drop-in lid type

402010.7MPa (Hard rock 1,000 m depth)

00204060
Weld depth, mm80

100

Fig. 6 Relationship between external pressure atcollapse and weld depth (yield strength 300 MPa)
(3) Plastic collapse for external pressure

Flat lid type1.2J-integral, N/mExternal pressure at collapse, MPa

Required yield strength, MPa

6Drop-in lid type1.0
0.8
0.60.40.20.0050100150
Weld depth, mm200Fig. 5 Relationship between J-integral at tip ofweld and weld depth
revealed that the collapse strength for lifting up issufficient.
(2) Elastic-plastic failure for lifting load
If the welding depth is small, there is a possibility ofelastic-plastic failure from the tip of unwelded. Thedriving force of elastic-plastic failure is J-integral.
Therefore, the J-integral of the tip of the unweldedpart for own weight was calculated by elastic-plasticanalysis. For the stress-strain curve required for theelastic-plastic analysis, the result was approximatedby the Ramberg-Osgood equation from the result of
the tensile test using the typical carbon steel SM400.
Fig. 5 shows the relationship between J-integral
and welding depth. When the welding depth became
smaller, the J-integral became larger. If the J-integral
is smaller than the fracture toughness which is thestrength of the carbon steel, failure does not occur.
The fracture toughness obtained from the SM400 was589 kN/m, J-integral was sufficiently smaller thanfracture toughness. Therefore, it is evaluated thatelastic-plastic failure from the tip of unwelded area
does not occur.

The relationship between external pressure at plastic
collapse in the welded part and welded depth isshown in Fig. 6. In the case of the flat lid type,external pressure at plastic collapse was constant withwelding depth. The length of the unwelded part did
not influence the collapse load because unweldedparts of the flat lid and the body were in close contact
with the external pressure. In the case of the drop-inlid type, when the welding part was 70 mm or more,
the collapse load equaled that of the flat lid type.
3.2.3 Failure from weld flaw
In the case of failure from a weld flaw, the failuremode assumed brittle failure, assuming irradiatedcarbon steel from vitrified waste. The weld flaw wasmodeled as a semi-circular opening crack along thewelded part, and stress intensity factor at the tip ofthe crack was calculated. The wall thickness was setat 110 mm of pressure resistance. The externalpressure and weld residual stress for the overpack
applied were 10.7 and 100 MPa, respectively.
The relationship between stress intensity factor
and crack size for the flat lid type was shown in Fig.
7. For axial stress z of 10.7 MPa, the stress intensity
factor decreased with crack size. However, for axial
stress r of 10.7 MPa, the stress intensity factor
increased with crack size. The stress intensity factors
in both cases were negative regardless of crack size.
That means failure from weld flaws by externalpressure does not occur for crack size of 55 mm. On
the other hand, when the residual stress R of 100
MPa was applied, the stress intensity factor became
larger than the stress intensity factor by externalpressure. For example, the stress intensity factor forthe crack size of 55 mm was over 50 MPa∙m0.5. The
relationship between allowable residual stress andcritical crack size for wall thickness of 110 mm isshown in Fig. 8. When fracture toughness, KIC, of

6th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, Japan60050-140-230-320-4(r, z, R)-5010(10.7,0,0)(0,10.7,0)(0,0,100)
203040
Crack size, mm

10050

Stress intensity factor, MPa m0.5

Stress intensity factor, MPa m0.5

160

Weld residual stress, MPa

Fig. 7 Relationship between stress intensity factor
and crack size in weld part for flat lid type
400
KIC=10MPam^0.5KICKIC
KIC=30MPam^0.5KIC
KIC=50MPam^0.5350
300
250200150
100
50001020304050
Critical crack size, mm60Fig. 8 Relationship between weld residual stressand critical crack size in weld part for flat lid type
carbon steel after 1,000 years is estimated, allowable
residual stress or critical crack size can be calculatedusing this figure.
4. Thickness of overpack
The thickness of the overpack was set to 190 mm as
the sum of the radiation shielding 150 mm (including
the pressure resistance 110 mm) and the corrosion
allowance 40 mm. From the results of the collapse
analysis (Fig. 3), it was found that when carbon steel
with a yield stress of 200 MPa was used, wallthickness of 110 mm of the overpack has about 8.7
times larger than the external pressure of 10.7 MPa at
1,000 m depth of hard rock.
Ohe et al., reported that for the thickness ofradiation shielding and corrosion allowance set byreference [1], when the design conditions andevaluation formulas were revised, the thickness of theoverpack became 110 mm [7]. This report has nomention of decrease in strength by reduction in
thickness of the overpack due to corrosion; however,
the result of the collapse analysis shows that thestrength of 50 mm wall thickness is about 3.6 times
the external pressure. Therefore, it is revealed that
there is a possibility of reducing the thickness of theoverpack.

Also, from the results of failure assessment ofwelded parts, it is not necessarily required to perform
a full penetration weld of 190 mm. The welded parthas enough strength even by partial welding.
Compared with full penetration welds, partial welds
have the advantage of reduction of welded residual
stress, reduction of welding time, and improvementof measurement accuracy (weld flaw size andlocation).
5. Summary
Failure assessment by the finite element method was
carried out for all failure modes assumed for theoverpack, and the relationship among the wall
thickness, the welding depth, the weld flaw size, andthe failure load was calculated. The obtained results
were as follow.
Even if the wall thickness is 50 mm, the strengthagainst external pressure applied to the overpack
after emplacement is sufficient.
It is not necessarily required to do a full
penetration weld of 190 mm. The welded parthas enough strength even by partial welding.
It was clarified that brittle failure from a weld
flaw does not occur due to external pressure. Onthe other hand, the welding residual stresscontributes to brittle failure from a weld flaw.
When fracture toughness, KIC of carbon steel
after 1,000 years is estimated, allowable residual
stress or critical crack size can be calculatedusing figure 8.
This research is a part of “Development of Advanced
Technology for Engineering Components of HLW
Disposal” under a grant from the Japanese Ministryof Economy, Trade and Industry (METI).
References
[1]

[2]

[3]

[4]

Nuclear Waste Management Organization ofJapan: “Safety of the Geological Disposal
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Ministry of International Trade and Industry,“Notification No. 501, Technical Standard forConstruction of Nuclear Power Components”,(1980), (in Japanese).
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Geological Disposal, (I) Points at Issue
Concerning
1,000Years
Containment
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Yamamoto Y., Suzuki S., Sato S. and Ito K.,
Study on Seismic Response of Engineered
Barrier System, Journal of Japan Society of

6th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, Japan

[5][6][7]Civil Engineers, Ser. A1, Vol. 71, No. 4,pp.I_963-I_973 (2015) (in Japanese).
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6th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, Japan