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1. Introduction
According to the PRIS (Power Reactor Information System) database provided by the IAEA (International Atomic Energy Agency) as of December 2021, 437 nuclear power plants are operating in 33 countries and have been operating for more than 30 years. Nuclear power plants in operation account for about 67% of the total and efforts are being made in each country to manage aging nuclear power plants. In addition, a total of 193 nuclear power plants have been permanently shut down so far, and the number of nuclear power plants permanently shut down is expected to increase in the future as their design life approaches [1]. In Korea, starting with the permanent shutdown of Kori Unit 1 in 2017, the permanent shutdown of Wolsong Unit 1 was decided in 2019, and large-scale technology development is planned to dismantle it [2]. Following this trend, various efforts are required to address the increasing demand for nuclear power plant decommissioning worldwide.
When the decommissioning of a nuclear power plant begins, high-level radioactive waste including spent fuel and a large amount of low-and intermediate-level radioactive waste from various systems and buildings are generated in a relatively short time [3]. Therefore, to efficiently package and dispose of such decommissioning radioactive waste, it is essential to develop a dedicated container considering various operating conditions. For this reason, Korea Radioactive Waste Agency (KORAD) conducted research on the development of containers for the packaging, transportation, and disposal of decommissioning radioactive waste from nuclear power plants, and developed 10 types of containers (1 for packaging, 3 for packaging/disposal, 5 for transportation, and 1 for packaging/transport/disposal). In addition, a container operation plan was derived considering the characteristics of the cave, near-surface, and landfill disposal facility.
2. Operation and Management Concept of the LILW Disposal Facility
2.1 Operation Process of the Near-surface Disposal Facility
A near-surface disposal facility is currently under construction at the Gyeongju radioactive waste disposal facility, which is the only radioactive disposal facility in Korea. Unlike the existing Gyeongju Cave Disposal Facility, the near-surface disposal facility disposes of radioactive waste in several concrete vaults and then isolates the radioactive waste from the human living area by closing it with engineering barriers (Fig. 1). In Korea, radioactive waste can be classified into high-level, intermediate-level, low-level, very-low-level, and unregulated radioactive waste according to relevant regulations (Fig. 2). Among them, the nearsurface disposal facility has the purpose of disposing of low-level radioactive waste. The surface disposal facility’s vault, which is a reinforced concrete structure, has a square shape. The process of closing the vault is completed by placing the container inside the vault, filling the space with cement mortar, and then closing the vault with a roof. After that, to prevent the inflow of water and maintain the complete isolation level of the waste, the final closure is completed by covering the upper part of several vaults with an engineering barrier consisting of several material layers such as sand and mud (Fig. 3).
2.2 Assuming an Operational Scenario of the Container Package
According to related laws, radioactive waste and the entire container containing radioactive waste are defined as a “package” [7], [8], [9]. Therefore, a packaged radioactive waste disposal container can be defined as a “package”. These packages, which are disposed of in the vault, are exposed to “Normal” and “Accidental” scenarios depending on how the near-surface disposal facility is operated. In this study, a general crash situation that may occur in the process of putting down a disposal container, which is a package, by a crane, is assumed as a “Normal” scenario. Second, a situation in which a disposal container falls from the vault height (9 m) is assumed as an “Accidental” scenario (Fig. 4).
2.3 Mechanical Strength of the Package
WAC (Waste Acceptance Process and Criteria), published in ANDRA, France, quantitatively presents the mechanical strength limits of radioactive waste packages. This presupposes that the vertical deformation of the container placed inside the vault should be less than 3% even under the condition of 0.35 MPa load [10].
In the case of Korea, there is no similar restriction, so there is a limit to setting the required mechanical strength of the package. Therefore, considering the process of deriving the package deformation limits of ANDRA and the operating concept of near-surface disposal facilities in Korea, the load condition of the container inside the vault can be derived using Equation (1). Here, ρ means the density of each material constituting the inside of the vault, and t means the thickness of each material. The load received by the package can be derived as the sum of the values multiplied by the density and thickness of the elements stacked on top of the package, and Table 1 shows the information applied to each material. The density of radioactive waste was assumed considering conditions such as solid, fragmented concrete, and soil components such as sand and mud were considered as engineering barriers. The derived load was 0.356 MPa in total, which was similar to the load level suggested by ANDRA. Therefore, it can be judged that there is no problem in applying the vertical deformation limit of the package as 3%.
Table 1
Material density
| Material | Density |
|---|---|
|
|
|
| Steel | 78 kN·m–3 |
| Radioactive waste | 20 kN·m–3 |
| Concrete | 24 kN·m–3 |
| Engineering barrier | 16 kN·m–3 |
There are no drop test requirements for packaging and disposal containers in the domestic laws and regulations related to the nuclear power industrial field. Therefore, evaluation of the structural integrity of the package requires setting a separate condition for the routine condition of the container. To set this, the maximum vertical movement speed (50 ton capacity, 32 m·min−1 level) of the crane handling the container can be considered (Fig. 4(a)). For example, if the speed at which the package collides with the floor is applied as the maximum moving speed of the crane, the value converted to the drop height is derived at almost 15 mm. However, the derived height is an assumption to consider the normal movement conditions of the container, it may not be an accurate physical quantity the structural performance of the container. In addition, when the container is moved according to the assumed height, there is a problem that the range of mm unit error is quite limited. Therefore, in this study, in order to secure the conservatism of the performance evaluation, 30 mm, which is twice the derived height and corresponds to the allowable vertical displacement of the container, was set as the free fall height [11].
Therefore, in this study, the performance target of the metal disposal container completed with radioactive waste packaging was set as less than 3% (30 mm) of vertical deformation in a 30 mm fall from a normal posture (The condition in which the bottom of the container and the ground are in parallel).
3. Parametric Study of Reinforcement Performance of Containers
3.1 Design Information of the Disposal Container
Packaging and disposal container is separated according to the disposal process. However, in some situations where only the container is considered, the concepts can be equated, causing confusion (If radioactive waste is contained inside a disposal container and sealed, it is a package). To improve understanding, the name of the target disposal container analyzed in this study was unified as “P3” container (Fig. 5). The P3 container is one of the packaging and disposal containers developed through KORAD R&D of containers for nuclear decommissioning waste. This, P3 container is used for packaging and disposal of metal, crushed concrete, and soil generated during the decommissioning of nuclear power plants. The size of the container is 1,000 mm wide, 3,000 mm long, and 1,000 mm high. The container’s self-weight is 0.83 ton, and the maximum design weight including its weight is 10 ton. The cover, which is the top plate of the container, is made of SPA-H material and is fastened to the main body with 24EA M12 bolts. Except for some square steel pipes using SS275, SPA-H steel was used to secure the durability of the container [12-13].
3.2 Information of Container Drop Simulation
In this study, the damage analysis of the container due to free fall was performed using LS-Dyna, which is a dynamic finite element analysis program. Fig. 6 shows the finite element modeling results of the P3 container, and the analysis model consists of 167,986 nodes and 123,272 elements. Of the total elements, 69,916 shell elements were composed of metal plates, 32,236 solid elements were composed of bolts, rectangular steel pipes, reinforcing grids, and corner block, and 21,120 TSHELL elements were composed of container covers. Parts with different cross-section thicknesses or large thickness-to-length ratios were modeled using the Solid element (ELFORM = 2), and other parts with a constant cross-section thickness were modeled using the Shell element (ELFORM = 16). The preload of the bolts applied to the container cover was applied at 156 MPa, the maximum stress of the bolts (Fig. 6).
LS-Dyna is a general-purpose nonlinear program that can calculate complex and various collision problems, and has various physical property models and contact algorithms [14]. Using this, *MAT PIECEWISE LINEAR PLASTICITY (MAT 24) was used for the steel parts applied to the P3 container modeling, and *MAT ELASTIC was used for the floor assumed to be a rigid body. The coupling of each part was defined using *TIED SHELL EDGE TO SURFACE and *TIED SURFACE TO SURFACE, and *CONTACT AUTOMATIC SINGLE SURFACE and *RIGIDWALL PLANAR were applied to simulate the falling situation of the container body and the floor. Material properties and stress-strain relationship information are given in Table 2 and Fig. 7. The analysis model applied gravity acceleration (9.810 mm·s−1) to simulate the free fall of P3 containers, in addition, the falling speed of the container was set to the speed at the moment when the container and the rigid floor collided.
Table 2
Steel material parameter
| Parameter | SS275 | SPA-H |
|---|---|---|
|
|
||
| Mass density | 78 kg·m–3 | kg·m–3 |
| Young’s modulus | 210 GPa | 210 GPa |
| Poisson’s radio | 0.3 | 0.3 |
| Yield stress | 275 MPa | 355 MPa |
3.3 Damage Analysis of Containers Due to Free Fall
In this section, based on the contents described in Sections 2.2 and 3.2, the structural condition analysis results of the container for impacts occurring in general operating conditions were described. The height of the free fall considered as a general operating condition was 30 mm, and the speed when the container and the ground contact was modeled as 767.2 mm·s−1. Fig. 8 shows the history of the occurrence of vertical displacement at the center and corner (4 points) of the top plate as a results of modeling with or without the application of metal ingot for simulating the design weight of the P3 container (10 tons). In addition, Fig. 9 shows the vertical displacement history and stress distribution in the rectangular steel tube at the bottom of the container, which is an element that directly receives the weight of the metal ingot.
According to the first analysis results, it was found that the amount of impact that can occur under normal operating conditions does not significantly affect the performance of the container. The maximum vertical displacement (about 7 mm) occurred in the center of the top cover plate, and this amount was less than the allowable vertical displacement (30 mm, 3% of height) under normal operating conditions. In addition, the amount of vertical deformation in other parts was all less than 3%. In the modeling considering the metal ingot, there was a concern about the over-deformation of the square steel pipe of the bottom plate under the ingot load, but the amount of deformation was about 1mm, which is not considered to affect the structural performance. In addition, the increase in vertical displacement of the four corners (Fig. 8(a)) is due to the bouncing of the container after it hits the floor, and in the analysis with the ingot, the bouncing is suppressed due to the self-weight of the ingot.
3.4 Selecting Reinforcement Elements
Among the various parts that make up the P3 container, the elements selected for reinforcement were those that are in direct contact with the drop target (floor) or are highly affected by acceleration during free fall. The first selected stiffening elements are the Bottom plate, which is the element in direct contact with the floor during free fall; the Corner post plate, which is orthogonal to the direction of fall and has high out-of-plane stiffness, causing a large reaction force; and the Corner plate, which is the stiffener inside the corner post. In addition, for elements that are highly affected by acceleration, the Lid plate support lattice was selected, which is placed on the underside of the container cover. For the cover, which is the top of the container, the lower the internal filling rate (meaning the extent to which the container is filled with waste or backfill material), the less there is anything to control the continuation of deformation on the back of the cover. Therefore, the cover of a container with a low filling rate is more susceptible to acceleration, which can cause deformation, and the container cover plate support lattice was selected as the last reinforcement element to increase the out-of-face stiffness of such a container cover (Fig. 10). Table 3 shows the classification of the 14 reinforcement methods and the degree of reinforcement. The thickness of the container bottom plate, corner post plates, corner plates, and support lattice was increased, and a 10% increase in the material strength of SS275 steel and SPA-H steel, which comprise the majority of the P3 container, was considered.
Table 3
Classification of the reinforcement case
| Original model [843.3 kg] | Reinforcement case number | Reinforcement result | Increased weight [kg] | |
|---|---|---|---|---|
|
|
||||
| Thickness of bottom plate | → | 1 | Thickness: 8 mm | 903.6 |
| [Thickness: 6 mm] | 2 | Thickness: 10 mm | 963.9 | |
| Thickness of corner post plate | → | 3 | Thickness: 8 mm | 868.2 |
| [Thickness: 6 mm) | 4 | Thickness: 10 mm | 893.0 | |
| Thickness of corner plate | → | 5 | Thickness: 10 mm | 869.3 |
| Thickness: 8 mm] | 6 | Thickness: 12 mm | 895.3 | |
| Material property, SS275 | → | 7 | Increase ratio: 5% | 843.3 |
| [Bottom plate] | 8 | Increase ratio: 10% | 843.3 | |
| Material property, SPA-H | → | 9 | Increase ratio: 5% | 843.3 |
| [Corner post] | 10 | Increase ratio: 10% | 843.3 | |
| Material property, SPA-H | → | 11 | Increase ratio: 5% | 843.3 |
| [Corner plate] | 12 | Increase ratio: 10% | 843.3 | |
| Thickness of lid plate support | → | 13 | Thickness: 15 mm | 853.1 |
| [Thickness: 10 mm] | 14 | Thickness: 20 mm | 862.8 | |
3.5 Parametric Study of Reinforcements Method
Parametric study and sensitivity analysis is a method widely used in the design process in various industrial fields, and this method can analyze the degree to which design condition variables affect the final design result [15]. This section presented the results of the 9 m drop analysis of the 14 stiffening models described in Section 4.2. P3 containers are used to package relatively low-density waste, which means that the stiffness of the waste inside has a lower impact on container breakage. Therefore, in the analysis of the reinforcement sensitivity, the model without the internal ingot was used to identify the independent phenomenon of the container reinforcement, and the physical quantity of the drop height of 9 m was simulated with the velocity of the container contacting the ground (13,288 mm·s−1). The model with increased bottom plate thickness (Case 1, 2), where the difference in container weight according to the reinforcement element is relatively large, was found to have a slightly higher reaction force level compared to the original model, and the remaining cases showed similar reaction force levels because the total weight did not fluctuate much (Fig. 11).
The most dangerous form of damage to a container during a 9 m drop impact is the leakage of internal waste to the outside. Therefore, the most dangerous damage is the breakage of parts related to the container cover and fasteners, such as the bolts. From the normal position container falling, the reaction forces transmitted to the bottom of the container are transferred to the columns and walls of the container, resulting in significant stress concentrations in the fastening bolts. For this reason, in this study, the degree of opening (gap opening) occurring at the bolted joint of the container falling in the normal position was analyzed, and the point to check the amount of opening was set to 6 positions according to the characteristics of the container having symmetry (Fig. 12), and the container cover opening history was shown in Fig. 13.
Fig. 14(a) shows the maximum displacement history at the center of the container cover, Fig. 14(b) shows the maximum stress at the bolt, and Fig. 14(c) shows the maximum stress at all parts except the bolt. By increasing the thickness of the lid plate support on the underside of the cover, the bending stiffness can be increased by increasing the moment of inertia of the support pipe. Furthermore, this method was analyzed to be the most efficient way to prevent vertical direction displacement of the cover. If the process of controlling the deformation of the container cover by increasing the filling rate inside the container is considered together, it is determined that the structural strength of the container can be greatly increased. In addition, looking at the stress concentrated on the fastening bolts, the reinforcement method of increasing the thickness of the reinforcing plate inside the corner post was found to be the most efficient way to relieve the stress concentration of the bolts. Additionally, since the increase in the thickness of the corner post plate was also found to have a reinforcing effect, it is judged that reinforcing the corner post of the container is helpful in relieving the stress concentration of the fastening bolt. Finally, looking at the parts except for the fastening bolts, it was found that increasing the thickness of the corner post plate and the thickness of the lid plate support was effective in relieving the stress concentration phenomenon of the container body. Due to the complex behavior characteristics of the structure, reinforcing a specific element increases the stiffness of the part and at the same time, concentrates a considerable amount of additional stress. The efficiency of reinforcing the strength of columns and materials was also confirmed, but it was found that the effective method of reinforcing effect was reinforcing the corner post plate and the lid plate support. In other words, it is judged that applying indiscriminate reinforcement elements to the container in a complex manner is a method with low reinforcement efficiency.
4. Conclusions
In this study, the performance analysis results for general and accident situations of nuclear power plant decommissioning radioactive waste containers are described. As a result of comprehensive analysis, to reduce the damage that may occur when the container is dropped, it was found that the method of reinforcing the container's top plate and corner posts was the most effective. However, from the design point of view of the container, there is a limit to considering all unspecified falling conditions, so it is judged that efforts to consider the operating process of the equipment used for container handling are necessary.
In addition, if indiscriminate reinforcement is applied to solve the phenomenon of damage from an unspecified load, inappropriate results such as secondary stress concentrating on the part where the stiffness is increased by the reinforcement may be expected. If the methodology analyzed in this study is used to solve this problem, it is judged that it is possible to efficiently select the reinforcement method of the radioactive waste disposal container that has been designed.
