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Drop Test Simulation and Analysis of Reinforced Concrete Disposal Container
Miha Kramar
Slovenian National Building and Civil Engineering Institute - ZAG
Dimičeva ulica 12
1000, Ljubljana, Slovenia
Franc Sinur
IBE, d.d.
Hajdrihova ulica 4
1000, Ljubljana, Slovenia
Matija Gams
Slovenian National Building and Civil Engineering Institute - ZAG
Dimičeva ulica 12
1000, Ljubljana, Slovenia
ABSTRACT
The paper presents numerical analyses of reinforced concrete disposal container
intended to store Low and Intermediate Level radioactive Waste (LILW). Drop test
simulations were performed with a general purpose finite element program Abaqus using
explicit dynamics. The container was modelled in detail assuming nonlinear material
properties, multiple contact surfaces and reinforcement. Different drop scenarios were
investigated including drop on the corner and overturning. The analyses have shown that
overturning of the container is more critical than drop on the corner which causes only local
damage in concrete. In case of overturning the predicted damage was substantial indicating
that the container might not meet the safety requirements. The design of the container is still
ongoing and numerical model is yet to be verified by actual drop tests. Finally, improved
solutions will be developed taking into account the experimental and numerical results.
1 INTRODUCTION
A repository for Low and Intermediate Level Waste (LILW) will be build east of the
Nuclear Power Plant Krško (NEK). The repository is designed for disposal of 9400 m3 of
LILW produced in Slovenia with a possibility of extension of the disposal capacities. The
capacity corresponds to one half of the LILW generated by NEK within the original, non-
extended operational period till 2023, and to all the remaining Slovenian LILW. Prior to
disposal into the silo, all LILW will be inserted into 999 concrete disposal containers
qualified as IP-2 package. Each container will be filled with 4 tube-type containers (TTC, the
most often type of package in NEK) or 12 standard 200 or 320-liter drums or unpacked LILW
with a volume of approx. 6.3 m3. The containers will be filled with LILW waste at the
location of NEK and delivered by the road to the repository site. Due to the road
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Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 5-8, 2016
transportation ADR (formally, the European Agreement concerning the International Carriage
of Dangerous Goods by Road) will be followed. ADR requires that containers provide
protection against the hazard (radiation) of the material under all conditions of transport,
including foreseeable accidents. There should be no more than a 20 % increase in the
maximum radiation level at any external surface of the package even in case of the accident.
To demonstrate compliance with these requirements a drop test is required: for packages IP-2
with a weight over 15 t a drop test from 0.3 m should be performed.
2 TEST SPECIMEN
The current prototype of a disposal container (type N2c) is a reinforced concrete square
box with the dimensions of 1.95 × 1.95 × 3.3 m3 (Figure 1). The thickness of the concrete
walls is 200 mm at the top and 230 mm at the bottom. The container is filled with different
type of LILW packages as described above and the empty space is grouted. The mass of the
full container varies as it depends on the stored material. The maximum total mass is
estimated at about 40 t.
The walls are reinforced with φ10 /10 cm in both, vertical and horizontal directions
(Figure 1). The corners are additionally reinforced, again with φ10/10 cm. When the lid is
placed on the container, the connection is reinforced and cast with concrete to ensure
monolithic structure of the container. In order to minimize the possibility of damage (in case
of a collision or due to corrosion), the lifting system is designed without any handles or
exposed steel parts. Instead, the notches at the bottom corners allow the container to be lifted
from the ground.
Figure 1: Disposal container N2c
A special concrete has been designed for the container, highly resistant to different
external influences (chemical, thermal, water, freeze/thaw, abrasion). The concrete
corresponds to strength class C 60/75 according to EN 12390-3 [1] and EN 206 [2]. The
reinforcing steel corresponds to class B 500 C according to EN 1992-1-1 [3].
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Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 5-8, 2016
3 NUMERICAL ANALYSIS
3.1 Model
Drop test analyses were performed with general purpose finite element code Abaqus
[4]. 3D numerical model of the container and the contents was meshed using first-order,
reduced-integration elements (C3D8R). The mesh is shown in Figure 2. A nonlinear material
model “concrete damaged plasticity” (see section 3.2) was assumed for the concrete while the
content was assumed elastic. The reinforcement was modelled with 3-node quadratic beam
elements (B32) and the classical metal plasticity material model. The lid, the container walls
and the bottom plate were tied together to form a monolithic unit. The contact between the
container and the content was modelled by standard non-penetrating frictional contact (hard
contact in normal direction combined with friction µ = 0.1 in tangential direction). The
reinforcement elements were embedded in the solid elements meaning the translational
degrees of freedom of the embedded nodes were constrained to the host element. The
container was assumed to fall to the infinitely stiff ground. As in the case of container-content
interaction, a standard non-penetrating frictional contact was assumed between the ground
and the container.
Figure 2: Finite element model of a container: solid elements (left) and reinforcement (right)
3.2 Materials
The elastic properties of concrete and content material are: initial elastic modulus
Ec = 42.3 GPa and Poisson’s ratio ν = 0.2. The non-elastic behaviour of the concrete material
was modelled using the so-called “concrete damaged plasticity” model. This is a continuum,
plasticity-based, damage model designed for monotonic, cyclic, and/or dynamic loading. The
model assumes that the uniaxial tensile and compressive response of concrete is characterized
by damaged plasticity, as demonstrated in Figure 3. In this study, the stress-strain behaviour
in compression was determined according to Kent and Park [5] assuming the peak stress
σcu = 68 MPa, the corresponding compressive strain εc1 = 0.0026, and ultimate compressive
strain εcu = 0.004. True stress versus true crushing strain in compression is shown in Fig. 3.
To avoid mesh-sensitivity, the tensile post-failure behaviour was defined in terms of a fracture
energy cracking criterion. A stress-displacement curve (Figure 3) was specified following the
relationship proposed by Li and Ansari [6]. The ultimate tensile strength was assumed equal
to mean tensile strength, i.e. 4.4 MPa while crack width wf = 0.3 mm was adopted. The
degradation of the elastic stiffness was taken into account by two damage parameters, dt and
dc, which are assumed to be functions of the plastic strains /displacements as shown in
Figure 3. The parameters assume values from zero at the ultimate (failure) stress, to 0.8 at
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Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 5-8, 2016
ultimate strain/ displacement. The model assumes nonassociated Drucker-Prager flow
potential and yield function of Lubliner et. al. [7], with the modifications proposed by Lee and
Fenves [8] to account for different response in tension and compression. The parameters used
to define the flow potential, yield surface, and viscosity are shown in Table 1.
Figure 3: Compression and tension stress behaviour of concrete
Table 1: Concrete damaged plasticity parameters
Parameter Description Value
ψ Dilatation angle 31°
ε Flow potential eccentricity 0.1
σb0/σc0 Ratio of initial equibiaxial compressive yield stress to initial uniaxial
compressive yield stress 1.16
Kc Ratio of the second stress invariant on the tensile meridian 0.666
μ Viscosity parameter 0.001
Classical metal plasticity model was used for reinforcing steel, with assumed yield
stress equal to 500 MPa and strain-hardening ratio of 5 %. The elastic modulus (Es) and
Poisson ratio (ν) of steel were 200 GPa and 0.2, respectively.
3.3 Analysis and drop scenarios
According to the ADR requirements, a drop test from 0.3 m should be performed for
packages of type IP-2 with a weight over 15 t. In this study, two different drop scenarios were
considered exceeding the requirements of ADR: The first scenario simulated a drop from
0.3 m onto the bottom corner of the container (Figure 4, left); The second scenario assumed
that the initial collision is followed by an overturning along the bottom edge of the container
and landing on the side surface (Figure 4, right). It can be assumed that the response in the
second scenario is symmetric about the midplane of the system so only one-half of the system
has to be modelled.
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Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 5-8, 2016
Figure 4: Drop scenario 1 (left) and drop scenario 2 (right)
The analyses were performed using explicit dynamics. Instead of simulating a full
dropping event from the initial position, the container was positioned close to the floor and
prescribed an initial velocity field. The velocity just before the impact was estimated by
applying the conservation of energy principle. According to the calculations, the initial
translational velocity (scenario 1) is equal to 2.43 m/s while the initial rotational velocity
(scenario 2) amounts to 1.94 rad/s. The corresponding energy of the impact is equal to 118 kJ
and 369 kJ, respectively.
4 RESULTS
Figures 5-6 show the contour plots of the compressive damage variable (dc) and tensile
damage variable (dt) at the end of the analyses. The damage parameters (briefly described in
paragraph 3.2) are non-decreasing parameters associated with the failure of the material,
suitable for the assessment of the accumulated damage. The failure criteria is set to remove
the most damaged elements from the field output. The failure is assumed when the damage
parameters reach a value of 0.8 (this value indicates ultimate strain/ displacement of concrete
– see Figure 3). Hence, elements with a value of dc or dt larger than 0.8 are not displayed in
the plot.
The results of the 1st scenario (drop on the corner) show that there is only a limited
amount of damage after the drop. The compressive damage (5, left) is concentrated mainly in
the corner while the tensile damage (5, right) indicates the development of diagonal cracks.
Nevertheless, the amount of failed concrete is relatively small and the remaining surface of
the package should still provide sufficient protection against the radiation according to ADR
regulations.
The results of the 2nd scenario (overturning), on the other hand, show extensive damage
in both compression and tension (6) - the amount of the failed concrete was estimated to be
more than 20 %. In addition, due to the reaction forces of the content, yielding of the
reinforcement occurs at the “connection” between the lid and walls of the container (Figure 7)
which may lead to an opening of the container. Hence, it can be concluded that the requests of
ADR are unlikely to be met. The numerical results are yet to be verified by the actual drop
tests. If the tests confirm the results of numerical simulations (and the extensive damage of
the container is in fact demonstrated in the case of overturning) it will be necessary to
improve the design of the container. The improvements will be developed iteratively with the
assistance of experimental and numerical analysis.
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Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 5-8, 2016
Figure 5: Compressive damage variable (left) and tensile damage variable (right) – scenario 1
Figure 6: Compressive damage variable (left) and tensile damage variable (right) – scenario 2
Figure 7: Equivalent plastic strain (PEEQ) in rebars – scenario 2
The difference in container damage caused in the scenario 1 or 2 results mainly from the
energy of the impact – the energy of the impact in case of overturning (scenario 2) is approx.
3 times bigger than the energy of the impact in case of dropping onto the corner (scenario 1).
In addition, when the container falls to the corner most of the kinetic energy is absorbed by
the plastic deformations which increase gradually and thus dissipate the force of the impact.
On the other hand, only one third of the energy is absorbed by the plastic deformations in case
of the overturning. Moreover, the duration of the collision is very short. Figure 8 shows force-
time graphs for both scenarios which clearly show the significant difference in the force and
duration of the impact.
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Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 5-8, 2016
Figure 8: Impact force vs. time for both scenarios
5 PARAMETRIC STUDIES
Several parametric studies were performed in order to determine the sensitivity to input
parameters. The parameters considered in the analyses included different types of finite
elements (C3D8, C3D8R, C3D8I), different material model of the concrete (model Wee et al.
[9]), different material properties of the content (elastic modulus of the content is 0.01 or 100
times the elastic modulus of concrete; content is modelled with the same nonlinear model as
concrete), and different friction between the content and the container (friction coefficient 0
and 0.5 was assumed). The results were compared to the basic model described in section 3.
First, the parametric analysis showed relatively small sensitivity of the results to
different types of finite elements (Figure 9; results are compared in terms of total strain
energy flow) – these results confirm the selection of elements C3D8R in the basic model. As
for the other parameters, the difference in the results is relatively small in case of 1st scenario
and slightly larger in case of 2nd scenario (Figure 9). Especially large difference in strain
energy can be observed in case of the model with a very low elastic modulus of the content.
Nevertheless, even in this case the differences in strain energy do not significantly affect the
overall performance of the container.
Figure 9: The influence of different types of finite elements (left) and other parameters (right)
on total strain energy (ALLIE)
6 CONCLUSIONS
Drop test analyses of reinforced concrete disposal container were performed to assess
the damage of the container when dropped from the height of 0.3 m (ADR requirements). The
simulations were performed using explicit dynamics in Abaqus [4]. Detailed 3D numerical
model was built assuming nonlinear material properties, multiple contact surfaces and
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Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 5-8, 2016
reinforcement. Different drop scenarios were investigated exceeding the requirements of
ADR: 1.) A drop from 0.3 m onto the most vulnerable corner; 2) Overturning of a container
which might follow the initial collision.
The results of the 1st scenario (drop on the corner) demonstrated very limited extent of
the damage of the container. The damage was concentrated mainly in the corner with few
diagonal cracks on the sides. It was concluded that such a drop is not critical and that the
container would retain sufficient radiation shielding according to ADR regulations. However,
the results of the 2nd scenario (overturning) demonstrated much greater damage. The amount
of the failed concrete was estimated to be more than 20 %. In addition, yielding of the
reinforcement between the lid and walls of the container was predicted.
In order to determine the sensitivity to input parameters, several parametric studies were
performed assuming different types of finite elements, different properties of the materials,
and different values of friction between the container and the content. The parametric
analyses showed relatively small sensitivity to different types of finite elements and only
slightly larger sensitivity to different material properties and friction. The differences in
parameters did not significantly affect the overall performance of the container.
The design of the container is still ongoing and modified designs will be tested. Finally,
an actual drop test will be performed for the validation of the numerical model and
implementation of even more robust analyses.
ACKNOWLEDGMENTS
The presented research was funded by the consulting engineering company IBE d.d. as
part of the NSRAO project. Authors gratefully acknowledge the assistance of student Marko
Lavrenčič in performing the parametric study.
REFERENCES
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compressive strength, CEN/TC 104, Brussels, 2009.
[2] CEN, EN 206:2013: Concrete – Specification, performance, production and conformity,
CEN/TC 104, Brussels, 2013.
[3] CEN, EN 1992-1-1:2004: Eurocode 2: Design of concrete structures – Part 1-1: General
rules and rules for buildings, CEN/TC 250, Brussels, 2004.
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