drop test simulation and analysis of reinforced concrete ...the paper presents numerical analyses of...

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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

[email protected]

Franc Sinur

IBE, d.d.

Hajdrihova ulica 4


[email protected]

Matija Gams

Slovenian National Building and Civil Engineering Institute - ZAG

Dimičeva ulica 12


[email protected]

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

mailto:[email protected]



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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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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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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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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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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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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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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

[1] CEN, EN 12390-3:2009: Testing hardened concrete – Part 3: Determination of

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.

[4] ABAQUS, Theory Manual, version 6.13, Dassault Systèmes, 2013

[5] D. C. Kent, R. Park, “Flexural members with confined concrete”, Journal of the

Structural Division, vol. 97, no. 7, pp. 1969-1990, 1971.

[6] Q. B. Li, F. Ansari, “High-strength concrete in uniaxial tension”. ACI Materials Journal,

vol. 97, no. 1, pp. 49-57, 2000.

[7] J. Lubliner, J. Oliver, S. Oller, and E. Oñate, “A Plastic-Damage Model for Concrete,”

International Journal of Solids and Structures, vol. 25, pp. 299–329, 1989.

[8] J. Lee, G. L. Fenves, “Plastic-Damage Model for Cyclic Loading of Concrete

Structures,” Journal of Engineering Mechanics, vol. 124, no. 8, pp. 892–900, 1998.

[9] T. H. Wee, M. S. Chin, and M. A. Mansur, “Stress-Strain Relationship of High-Strength

Concrete in Compression,” Journal of Materials in Civil Engineering, vol. 8, no. 2, pp.

70-76, 1996.

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