Stress Analysis for the Canister under Earthquake Induced Fracture Shear
Displacement considering Long-term Creep Effect of Copper Shell
Yuan-Chieh Wu, Hsi-Ting Lo, Yi-Ren Wang
Institute of Nuclear Energy Research, Atomic Energy Council
1000 Wenhua Rd. Jiaan Village, Longtan District, Taoyuan City 32546, Taiwan

Key words: Canister, Creep, Earthquake

Topics ID: 54

Abstract
The canister design for spent nuclear fuel final disposal (SNFD) should consider three containment failure modes:
rock confining pressure, rock deformation, and corrosion. For deposal concept in hard rock such as KBS-3 inSweden, Finland, and current Taiwan test sites, the rock fractures surrounding deposition hole may turn into thepermanent shear displacement during earthquake; therefore, the stress analysis should be performed to evaluate
seismic capacity for shear displacement. On the other hand, for long-term disposal environment, copper canisterneeds to consider the creep of copper shell, so the capability to perform analyses combing these two phenomena
should be established in final disposal research team. To perform the analyses, the three dimensional canister andbuffer assembly model was built, and model test was carried out by comparing the results with SKB data toachieve the model confidence. Several shear displacement scenarios including different loading position anddirection were carried out to understand the safety margin of canister design through von Mises results comparedwith allowable stress of copper material for canister shell and cast iron material of canister insert, and also thelong-term creep effect was considered in the analysis procedure. Based on the analysis models, theparameterized sensitivity studies are also performed, and the stress and safety factor data are produced. They
demonstrate the way to keep canister safe during earthquake by enlarging deposition hole or thickness of castiron, the information can be used for design modification when large accumulative shear displacements occur inthe future disposal sites.
1. Introduction
Repetitive seismic loads from earthquakes andthermal loads generated by the decay of emplaced
waste are two significant factors for near-fieldinstability in spent nuclear fuel final disposal [1].
Although regulatory standard for the high-level
radioactive waste siting in Taiwan have requirementof exclusive zone regarding fault movement by active
fault, the accumulated influences of earthquake
through wave propagation still need to evaluate due
to multiple events occurring in long-term span forsafety analysis. When the KBS-3 deposition concept
is employed, shear failure due to earthquake induced
fracture displacement intersecting deposition holes
will cut buffer and canister is one of the failuremodes; therefore, the structural capacity of canisterneeds to be calculated. In the SKB KBS-3 design,
since the canister has 95 cm diameter cast iron insert,
5 cm thickness copper shell, and 35 cm buffer ring
block, with regard to the long-term isostatic pressure
from buffer and ground water, the creep effect ofcopper shell has been discussed and particular

formula of oxygen free copper (Cu-OFP) material isadopted [2][3][4]. Because the long-term creep of fullscale copper shell could not be tested, the better way
to realize stress distribution of canister is performing
numerical analysis. Therefore, several numericalanalyses to reflect disposal scenarios have been
carried out by SKB [6]. However, for the use of
KBS-3 design as reference in Taiwan, because ofdifferent
earthquake
environment
betweenScandinavian region and Circum-Pacific seismic
region, the SKB reference is only the basis foradapting the foreign design, and the domestic seismic
analysis capability for canister-buffer assembly needs
to be established when modification of design needed.
Regarding the safety criteria of KBS-3 canister, SKB
set 5 cm displacement of fracture as the shear
capacity considering potential initial manufacture
defect in SR-Site, although the structural analysis ofcanister can withstand 10 cm shear displacement
without the scenario of fracture mechanics previously.
Hence, cumulative displacement reaching 5 cm limit
should be check under the multiple events occurring
1

6th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, Japanpossibly in Taiwan, so the development of seismic
analysis including shear and creep effect is necessary
in SNFD program. Since Taiwan SNFD program will
go into the siting stage, the evaluation of different
sites regarding the failure rate of earthquake induced
shear on canister will be important, also accompanied
validation tests using scaled down specimens will beplanned to enhance the reliability.
Fig. 2 Canister-buffer assembly model for 22.5oshear direction at middle section case

2. Structural ModelIn this study, finite element code ABAQUS was
the analysis tool to model SKB-designed buffer andcanister [3], and nonlinear analysis is performed toconsider the large displacement on the model. The
phenomenon is the same as direct shear test. Throughthe dislocation amid deposition hole, the stress
imposed by the deposition hole will be redistributed
through buffer, copper shell and cast iron insert
section. To model the stress effect, the canister andbuffer assembly model was built, and the shear
movement of model was applied by setting boundary
condition. The element for cast iron insert and copper
shell canister is C3D8I which has the capability for
nonlinear analysis, and the element for buffer isC3D8P which allows the input of groundwaterparameters. The contact behavior between canisterand buffer is employed by using tangential behavior
to allow the slip to occur on canister surface, and thecoefficient is set as 0.1 referred to SKB data [3]. To
study the effect of shear displacement angle andlocation on canister-buffer assembly, analysis cases
include shear displacements that are located at middle
section and at quarter section, and the shear angles
are 90o and 22.5o for each location. The symmetricalmodels shown in Fig. 1 and Fig. 2 were utilized tosave computer time, and fine meshes are conducted at
the section where the 5 cm shear displacement isapplied.

3. Material ModelIn this study, material test data are referred to SKB
test result, and materials are modeled aselastic-plastic behavior. For stress strain curve ofCopper, Young’s modulus is 120,000 MPa, theyielding stress is 72 MPa, Poisson's ratio is 0.308,
and the data of stress-strain test is shown in Table 1[4]. For Cast iron, Young’s modulus is 166,000 MPa,
the yielding stress is 293 MPa, Poisson's ratio is 0.32,
and the data of stress-strain test is shown in Table
2[4]. For buffer material which uses MX-80 bentonite,
the design density is 2,050 kg/m3, Young’s modulus
is 294 MPa, the yielding stress is 2.94 MPa, Poisson'sratio is 0.49, and the data of stress-strain test is shownin Table 3. Because the properties of buffer isstrain-rate dependent, the strain rate for the data inTable 3 is 1 m/sec. Also, because pore water will
influence the behavior of buffer material, the relatedmaterial data is shown in Table 4.
To understand the safety margin, the safety factor
is defined by the ratio of allowable stress tomaximum analyzed stress, and von Mises stress will
be analyzed. The cat iron stress corresponding to halfof the strain of the ultimate elongation in uniaxial
tensile test was set as the allowable stress, which is395 MPa according to SKB test and definition [4].
For long-term pressure application, creep of copper
shell will be modeled. Compared to SKB model
method, they carried out the CREEP subroutine inABAQUS for modeling the creep curve. In this study,
Power law in ABAQUS creep model as below isused.
dεc/dt =Aσn tm(1)wheredεc/dt is the uniaxial creep strain rate;
σ is the uniaxial stress;
t is the creep time.

Fig. 1 Canister-buffer assembly model for 90oshear direction at middle section case

The curve fitting result is shown in Fig. 3; theparameter A is 7.6⨯10-26, n is 10.16, and m is -0.649.
Compared to the test data, the initial range can match test
data of both 170 MPa and 175 MPa compressive tests, but
the larger strain part only can meet 175 MPa test.

26th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, Japan

Table 1 Copper stress strain curve data
0.1 0.2 0.3
Plastic Strain (%) 072 178 235 269
Stress (MPa)
Source: Hernelind (2010, p23) [6]
Table 2 Cast iron stress strain curve data
124
Plastic Strain (%) 0293 324 349 389
Stress (MPa)8910
Plastic Strain (%) 7428 438 447 456
Stress (MPa)
Source: Raiko et al. (2010, p25) [4]

0.4
288

0.5
300

5404

6418

11465

12472

Table 4 shows it will have lesser stress, and even castiron will maintain elastic state. Because thelongitudinal loading will impose on the insert column
which has higher rigidity than transverse sections andthe lesser transverse load component will produce
lesser stress.
Since rejection criteria of deposition holes
considering one earthquake event scenario have beendeveloped in SKB, the deposition hole can be
adjusted to reduce the failure rate when facing
detrimental fractures. However, to deal withaccumulative displacement for multiple earthquake
conditions, modifications of KBS-3 design maybe theuseful approach. The influence of design parameters
including geometry, buffer density, and confiningpressure are studied, and the results are shown in
Table 5 to Table 9. They mean the safety of canister
against earthquake induced shear displacement can beachieved by using larger buffer thickness, insert
diameter but keeping same fuel cassette dimension,larger copper shell thickness, and lesser density ofbuffer, so it’s possible to design a SNFD repository
with very rare earthquake failure rate even if multiple
earthquake events definitely let 5 cm limit be reached.
However, the decision of which countermeasure isused and how low failure rate is acceptable dependon cost-effective evaluation and the failure impact onradioactive safety.

Table 3 Buffer stress strain curve data
0.4
1
1.8 2.6 3.6Plastic Strain (%) 02.94 3.93 4.52 4.83 5.03 5.10
Stress (MPa)
Plastic Strain (%) 46 100
5.04 5.04
Stress (MPa)
Source: Börgesson et al. (2010, p57) [5]
Table 3 Pore water related buffer material data
Permeability Specific Bulk Modulus Bulk Modulus
weightfor skeleton
for water(mm/s)-13

1⨯10(N/mm3)

(MPa)

(MPa)

1⨯10-52,100,000

2,100

Source: Hernelind (2010, p23) [1]

Table 4 Analysis case and result(including shear andcreep effect)
Shear angle Shear location Plastic strain (%)
Cast iron insert(1) 90oMiddle section
0.0992(2) 90o
Quarter section 0.5426(3) 22.5o
Middle section
0Copper shell(1) 90o
Middle section
2.611(2) 90o
Quarter section 0.5622(3) 22.5o
Middle section
4.981

Fig. 3 Creep strain curve of copper matched byABAQUS power-law creep model (green line)
Data source: SKB (2009, p54)

von Mises (MPa)
287.5
320.3
244.9
160.9
84.09
245.9

Table 5 Safety factor for different buffer thickness
35404550
Buffer thickness 20 25(cm)330 327 319 296 240 216
von Mises stress(MPa)1.19 1.21 1.24 1.34 1.64 1.87
Safety factor

4. Results
Three analysis results consisting different shear
angle and location are shown in Table 4; themaximum von Mises stress occurs on cast iron insert,
but maximum plastic strain occurs on copper shell.
The deformation result for Case (2) and Case (3) are
shown in Fig. 4 and Fig. 5 respectively, and bothcanisters show they have no dislocation under 5 cm
displacement on the buffer surfaces. It means 5 cm
majorly influence on the stress and deformation ofbuffer, so buffer role can be played very well at thismoment.
From stress view on Fig. 7 and Fig. 8, themaximum case is 90o shear direction at quarter
section, and the behavior is similar to cantilever beam
subject to a transverse load. For the inclined loading,

Table 6 Safety factor for different insert diameter
949
969
989 1009 1049
Insert diameter
(mm)
296
217
202
198
169
von Mises stress(MPa)1.33 1.82 1.95
2.02.34
Safety factor
Table 7 Safety factor for different copper shell thickness
1050 1070 1110 1130 1150
Shell diameter
(mm)
296
214
201
193
186von Mises stress(MPa)36th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, JapanSafety factor

1.33

1.84

1.96

2.04

2.12

Table 8 Safety factor for different buffer density
1,970
2,020
2,050
2,070
Buffer density(Kg/cm3)
195212232268
von Mises stress(MPa)
2.05
1.85
1.7
1.47
Safety factor
Table 9 Safety factor for different confining pressure
25 35 45 55 65 85 95 115
Pressure(MPa)von Mises stress 91 143 195 247 291 299 330 370(MPa)
Safety factor 4.3 2.7 2.02 1.6 1.35 1.32 1.19 1.06

Fig. 8 Stress distribution of copper shell for 90o shear
direction at quarter section case
5. Conclusion and Discussion
The numerical analyses conclude modeling process
and results as follows.
[1] ABAQUS numerical model for canister underearthquake induced fracture displacement andconsidering creep of copper shell under long-term
confining pressure has been establish in Taiwan;
therefore, they can be used in future prediction onseismic capacity of canister. However, somenumerical models regarding inclined loading
condition are still investigated due to difficulty ofnumerical convergence, so that the testing
methods will need implementation in the future.
[2] The influence of design parameter on seismic
capacity for canister and buffer are studied, andthe safety factor data could be the basis for thedecision of countermeasures.
[3] The study only focuses on structural capacity fora given earthquake hazard quantity. However, theearthquake induced hazards on deposition holes
need more effort to realize how displacements
impose, so that the different loading steps ofdisplacement can be input in the models.

Fig. 4 Deformation and stress for assembly model
imposed by 5cm shear displacement for 90o shear
direction at quarter section case

6. Reference[1] Ghosh, A., S. M. Hsiung and A. H. Chowdhury(1996), Seismic response of rock joints andjointed rock mass, US. Nuclear Regulatory
Commission technical report, NUREG/CR-6388& CNNRA 95-013, June 1996.
[2] Henrik C. M., Andersson-Ö stling, and Sandström,
R. (2009), Survey of creep properties of copper
intended for nuclear waste disposal, SKB,
TR-09-32.

Fig. 6 Deformation and stress for assembly modelimposed by 5cm shear displacement for 90o shear
direction at middle section case[3] SKB (2010), Design, production and initialstate of the canister, SKB, TR-10-14.
[4] Raiko, H. and Sandström, R. (2010), Design
analysis report for the canister, SKB, TR-10-28.
[5] Börgesson, L. and Hernelind, J. (2010),
Earthquake induced rock shear through adeposition hole, SKB, TR-10-33.
[6] Hernelind, J. (2010), Modelling and analysis ofcanister and buffer for earthquake induced rockshear and glacial load, SKB, TR-10-34.

Fig. 7 Stress distribution of cast iron insert for 90o
shear direction at quarter section case46th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, Japan