Transient testing of oxide fuels by spark plasma sintering and finite element analysis
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Zhao, Dong (ORCID:0000000191377257)↗
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Assessment of buffer-IPyC thermomechanical debonding behavior using new experimental strength data in BISON
TRIstructural ISOtropic (TRISO) fuel is a nuclear fuel commonly used in High Temperature Gas-cooled Reactors (HTGRs). A single sub-millimeter-diameter TRISO fuel particle consists of a spherical fuel kernel surrounded by four coating layers: a low-density pyrocarbon buffer layer, an inner pyrolytic carbon (IPyC) layer, a silicon carbide (SiC) layer, and an outer pyrolytic carbon (OPyC) layer. The kernel is commonly made of UO2 or a mixture of uranium carbide and uranium oxide (UCO). During reactor operation, the TRISO coating layers are subjected to irradiation-induced dimensional changes and the associated thermomechanical behavior of each layer. One of the observed behaviors is gap formation between the buffer and IPyC layer due to the porous buffer’s irradiation-induced shrinkage exceeding that of the IPyC layer. Not all irradiated particles will experience buffer-IPyC gap formation. The debonding may be partial, or it may be nearly total. However, from post-irradiation examination of UCO TRISO fuels irradiated as part of the Advanced Gas Reactor (AGR) Fuel Development and Qualification Program, it was concluded that partial buffer-IPyC debonding was the most common type of buffer-IPyC interaction. To predict TRISO thermomechanical performance, multi-physics models have been built that are being continually updated and refined. The BISON code is a finite element-based nuclear fuel performance code that may be used for 1D, 2D, and 3D TRISO particle simulations. This code is used to calculate fuel temperature, kernel swelling, buffer densification, thermal and irradiation creep, fracture, and fission gas production and release. One of the recent additions to the BISON code is the ability to model the process of layer debonding. This paper will focus on the simulation results of the improved BISON debonding model that will utilize updated strengths measured from irradiated AGR TRISO fuel particles. The new experimental strength data from micromechanical tests of irradiated TRISO fuel samples were exercised in the BISON simulations and compared to baseline strength data to assess their applicability in the models. This also includes updated buffer-IPyC bond strengths to simulate layer delamination. Based on current experimental observations it is noted that the buffer-IPyC separation occurs not exactly at the junction of these two layers, but more on the side of the buffer layer. That observation is also implemented in the TRISO interface debonding model. This improved modeling approach using experimental strength data to characterize buffer-IPyC debonding and its potential subsequent cracking will be presented in the paper along with comparisons to available experimental observations.
11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Architecture and Component Selection for the Remote Canister-Monitoring System
This report documents the selected system architecture and components surveyed for the development of a remote, canister-monitoring system (RCMS) for determining and monitoring environmental conditions within dry fuel storage canisters containing aluminum-clad spent nuclear fuel (ASNF) at Idaho National Laboratory (INL). These efforts are in support of the Department of Energy Office of Environmental Management (DOE-EM) investigations into the technical issues associated with extended dry storage (50+ years) of ASNF. It is important to resolve questions regarding storage because the ATR is expected to continue producing approximately 100 elements of spent fuel per year for at least another twenty years. The parameters to be monitored by the RCMS include temperature, relative humidity, hydrogen gas concentration, and radiation environment (dose). Components are selected based on the expected environmental conditions within the canister and fuel storage area and the desired performance of the RCMS. Several of these components have been purchased and are currently undergoing component testing to confirm their suitability for use in delivering the RCMS. Additional components may be identified through the course of design and may be selected in the future. Furthermore, changing performance, interfacing, and compatibility requirements and the results of component testing may necessitate revisiting component selection.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Development and formulation of physics based metallic fuel models and comparison to integral irradiation data
Metallic fuel has an important historical significance in the development of nuclear reactors and continues to be relevant to the progression of advanced test and power reactors. A number of models, ranging from empirical to mechanistic, have been developed and implemented in various fuel performance codes to describe U-Zr and U-Pu-Zr fuel and typical fast reactor cladding materials. One challenge of using these models to simulate fuel performance is the inevitable tangling of coupled phenomena that can cloud proper implementation, calibration, and eventual utilization of new models. Here in an effort to provide a baseline capability that will facilitate the use of advanced models, new capabilities have been implemented into the fuel performance code BISON specific to metallic fuel simulations, ranging from materials properties, fission gas release and swelling calculations, coolant channel models, and cladding correlations. These models have been applied to the X441/X441A EBR-II experimental assembly data, a set of irradiated metallic UPuZr fuel rods of varying pin designs. The models implemented in BISON are able to capture the general trend of the expected response of the fuel and cladding to irradiation in EBR-II, especially when considering the spread in experimental measurements and the uncertainties inherited from the historical material models. Ultimately, the models outlined here provide the baseline capabilities on which new models can build upon in order to improve the prediction of metallic fuel performance simulations in off-normal designs or operations.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Assessment of Buffer-IPyC Thermomechanical Debonding Behavior Using New Experiment Strength Data in BISON
TRIstructural ISOtropic (TRISO) single sub-millimeter-diameter nuclear fuel particle consists of a spherical fuel kernel surrounded by four coating layers. During reactor operation, the TRISO coating layers are subjected to irradiation-induced dimensional changes and the associated thermomechanical behavior of each layer. One of the observed behaviors is gap formation between the buffer and IPyC layer due to the porous buffer’s irradiation-induced shrinkage exceeding that of the IPyC layer. To predict TRISO thermomechanical performance, multi-physics models have been built that are continually updated and refined. The BISON code is a finite element-based nuclear fuel performance code that may be used for TRISO particle simulations. One of the recent additions to the BISON code is the ability to model the process of layer debonding. This paper will focus on the simulation results of the improved BISON debonding model that will utilize updated strengths measured from irradiated TRISO fuel particles. The new experimental strength data from micromechanical tests of irradiated TRISO fuel samples were exercised in the BISON simulations and compared to baseline strength data to assess their applicability in the models. This also includes updated buffer-IPyC bond strengths to simulate layer delamination. Based on current experimental observations it is noted that the buffer-IPyC separation occurs not exactly at the junction of these two layers, but more on the side of the buffer layer. This improved modeling approach using experimental strength data to characterize buffer-IPyC debonding and its potential subsequent cracking will be presented in the paper along with comparisons to available experimental observations.
11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Fabrication and Characterization of MiniFuel Specimen
Burnable absorbers (BAs) are used in UO 2 fuels to tune the reactivity in a light water reactor (LWR) particularly at the beginning of life of the fuel. BAs are elements that have high neutron absorption cross sections and because of this property can prevent power peaking. The addition of BAs reduces the reactivity at the beginning of life, and this in turn allows for the increase of enrichments from > 5 % 235 U up to ~ 10 %. This also enables the increase of the burnup limit to 75 GWd/MTU and the cycle length to 24 months. The BA are eventually consumed under irradiation, and their concentration is diminished at roughly 10-20 GWd/MTU. The objective of this report is to fabricate UO 2 fuels that have been doped with BAs (Gd 2 O 3 in this case) and subsequently irradiate them in the high flux isotope reactor (HFIR) at Oak Ridge National Laboratory. The test specimen that are fabricated include 4 and 8 weight % Gd 2 O 3 doped UO 2 to investigate the influence of the BAs on the thermophysical properties and microstructure of the fresh and irradiated fuel.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Construction of a Code Verification Matrix for Heat Conduction With Finite Element Code Applications
When establishing the pedigree of a simulation tool, code verification is used to ensure that the implemented numerical algorithm is a faithful representation of its underlying mathematical model. During this process, numerical results on various meshes are systematically compared to a reference analytic solution. The selection of analytic solutions can be a laborious process, as it is difficult to establish adequate code confidence without performing redundant work. In this report we address this issue by applying a physics-based process that establishes a set of reference problems. In this process, code simulation options are categorized and systematically tested, which ensures that gaps in testing are easily identified and addressed. The resulting problems are primarily intended for code verification analysis but may also be useful for comparison to other simulation codes, troubleshooting activities, or training exercises. The process is used to select fifteen code verification problems relevant for the one-dimensional steady-state heat conduction equation. These problems are applicable to a wide variety of simulation tools, but, in this work, a demonstration is performed using the finite element-based nuclear fuel performance code BISON. Convergence to the analytic solution at the theoretical rate is quantified for a selection of the problems, which establishes a baseline pedigree for the code. Not only can this standard set of conduction solutions be used for verification of other codes, but also the physics-based process for selecting problems can be utilized to quantify and expand testing for any simulation tool.
42 ENGINEERING↗
Separation of dilute plutonium(IV) from nitric acid solutions via Reillex HPQ anion exchange resin
Anion exchange is a common method for the separation of plutonium (Pu) in aqueous systems, providing high recovery and decontamination from impurities. Reillex HPQ anion exchange resin has been used around the Department of Energy complex in this application for decades but has typically been used for Pu feed concentrations greater than 1 g/L. It is desirable to recover Pu at more dilute concentrations from a dissolved used fuel or target element, for example. In this work, the performance of Reillex HPQ anion exchange resin was characterized with feed solutions of ca. 0.24 g/L Pu. A significant reduction in the performance of the resin was realized with this dilute concentration relative to a feed solution of 2.35 g/L Pu with similar feed flow rates and the same resin column, likely due to the increased driving force for mass transfer with a higher feed concentration. The maximum capacity of Reillex HPQ resin for Pu can be improved by reducing the flow rate and increasing the feed Pu concentration. Furthermore, the breakthrough point of Pu can be improved in the same manner and by increasing the resin bed height. Diffusion of Pu into the resin was illustrated to be the rate limiting step.
Plutonium separations↗
BISON TRISO Modeling Advancements and Validation to AGR-1 Data
BISON is a finite element-based nuclear fuel performance code. Among its unique characteristics are its ability to model 1D, 2D, and 3D geometries and its applicability to a wide variety of nuclear fuels. For the last eight years, BISON has included a beginning capability to model tri-structural isotropic (TRISO) fuel. Recently, interest in TRISO fuel has grown, and a significant effort has been made to improve BISON’s capabilities in this area. Capability development has occurred for each material present in TRISO fuel particles: the buffer, inner pyrolytic carbon, silicon carbide, and outer pyrolytic carbon layers, as well as the fuel kernel. New elastic, creep, swelling, thermal expansion, thermal conductivity, and fission gas release (FGR) models are available. New models for the graphite matrix are also now available. Another important addition is the ability to perform statistical failure analysis of large samples of fuel particles. This new capability, which continues to grow, enables evaluation of failure due to pressure or crack formation by analyzing many thousands of particles. This enables realistic calculations of fission product release from the many particles in a TRISO-fueled reactor. These capabilities were checked via regression and verification tests. A large number of code benchmarking problems were also run, showing that BISON’s results closely match those of other software tools. Finally, a significant validation effort was completed in which fission product release, measured as part of the AGR-1 capsule experiments, was compared to BISON outputs. BISON outputs compared very well to the experimental data and to PARFUME results. Interest in BISON’s TRISO capabilities is growing, with the U.S. Nuclear Regulatory Commission (NRC) and Westinghouse Electric Company receiving training during the past year. Multiple other entities have expressed interest in or are actively using BISON. Kairos Power, LLC, has a strong partnership with Idaho National Laboratory (INL) regarding the use of BISON for TRISO analysis. While its capabilities still continue to grow, BISON has already become a powerful tool for TRISO analysis.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Margin to Onset of Nucleate Boiling studies for MITR and NBSR Design Demonstration Experiments
The United State High Performance Research Reactor (USHPRR) program aims to eliminate more than 200kg of High Enriched Uranium (HEU) from commerce annually by converting five U.S. high-performance research reactors and one associated critical assembly to Low Enriched Uranium (LEU) fuel using a high-density alloy of uranium-10 wt% molybdenum (U-10Mo). The Massachusetts Institute of Technology Reactor (MITR) and the National Bureau of Standards Reactor (NBSR) are two of five research reactors selected for this program. Previous studies have addressed the thermal-hydraulics performance of the fuel Design Demonstration Elements (DDE) for these reactors under conservative assumptions in the Belgian Reactor (BR)-2. This report extends these previous studies by analyzing the margins to Onset of Nucleate Boiling (ONB) for these two DDEs under the conservative conditions used in the previous thermal-hydraulics analyses
42 ENGINEERING↗
Molybdenum and Tungsten isotope compositions of UO 2 fuel pellets: Implications for isotopically enriched taggants
The addition of isotopically enriched taggants to material at the front end of the nuclear fuel cycle could be a powerful tool used to assist law enforcement authorities should material outside of regulatory control be found. Two potential candidates for this purpose are molybdenum (Mo) and tungsten (W) as both elements have five or more stable isotopes and are trace elements contained within nuclear fuel. So there is a concern that Mo and W could undergo isotope fractionation during processes like uranium enrichment and to date, it is unknown if nuclear fuels have natural Mo and W isotope compositions. If Mo and W isotopic variability is present in nuclear fuels, this would hinder the use of these elements as isotopic taggants because it would be difficult to discern the original taggant isotope composition with high confidence. Therefore, a set of 16 low enriched uranium (LEU) fuel pellets from US commercial producers was analyzed using multi collector-inductively coupled plasma mass spectrometry (MC-ICPMS) to determine Mo and W isotope compositions (i.e., 94 Mo/ 92 Mo, 95 Mo/ 92 Mo, 96 Mo/ 92 Mo, 97 Mo/ 92 Mo, 98 Mo/ 92 Mo, 183 W/ 182 W, 184 W/ 182 W, and 186 W/ 182 W). Relative to terrestrial standards, LEU fuel pellets have variable Mo and W isotope compositions, thereby complicating the use of these elements as isotopically enriched taggants. As such, this work demonstrates that the isotope composition of any potential taggant must be well characterized in the base nuclear fuel prior to any taggant addition. Furthermore, these results suggest that Mo and W are not ideal candidates for isotopically enriched taggants.
58 GEOSCIENCES↗
Simulation of the Fast Reactor Fuel Assembly Duct-Bowing Reactivity Effect Using Monte Carlo Neutron Transport and Finite Element Analysis
This paper discusses a new method of simulating the fuel assembly duct-bowing reactivity coefficient for EBR-II run 138B. Quantification of the fuel assembly duct-bowing reactivity effect in liquid metal–cooled fast reactors has been a persistent problem since they were first designed and operated. Simulation of the duct-bowing reactivity effect is difficult because the level of detail required to simulate the effect has exceeded most modeling capabilities. The new method outlined in this paper utilizes the finite element analysis code ANSYS to analyze the thermal and structural components. Here, the displacement of the fuel assembly duct due to thermal expansion and mechanical interaction was calculated by ANSYS using recorded EBR-II run 138B temperature and power boundary value data. The displacement values were incorporated into to a Monte Carlo model of EBR-II run 138B and keff was calculated. Multiple Monte Carlo calculations were performed with duct displacement values corresponding to different reactor temperatures. Using the calculated keff values associated with the different duct displacement results allowed calculation of the duct-bowing reactivity coefficient. The duct-bowing reactivity coefficient was calculated to be –14.5 × 10 –4 $/°C/ ± 4.4%.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
The Use of High-Density UN Fuel in Heat-Pipe Microreactors
Heat-pipe microreactors (HPMRs) are very small-scale nuclear reactors that employ heat pipes (HPs) for heat removal. HPMRs can be easily integrated with other forms of renewable energies, can be used for emergency responses to disaster relief zones, can be deployed in remote locations not connected to the grid, and can be removed from sites and replaced by new ones. HPMRs can also be used for space missions as HPs do not rely on gravity for heat transfer. Conventional fuel materials, such as uranium oxide (UO 2 ) and uranium oxycarbide (UCO), are currently considered in most existing HPMR designs, but ceramic uranium nitride (UN) fuel that has high uranium density, high thermal conductivity, and high melting point may become a better fuel candidate. Through neutronics calculations, this paper assesses the impact of using UN fuel in HPMRs with two different neutron spectra (fast and thermal) and two different fuel forms [traditional solid fuel pellets and TRi-structural-ISOtropic (TRISO) fuel compacts]. It was concluded that retrofitting HPMRs with UN fuel has the potential to reduce the initial 235 U enrichment requirement by ~3 wt% (to keep the same cycle length) or increase the cycle length (by keeping the same initial 235 U enrichment), which enables more compact and transportable HPMR core designs. However, using UN fuel decreases the control element worth [by up to 20% for the Special Purpose Reactor (SPR) and 5% for HP-MR] and is up to 80% more costly. Increasing 15 N enrichment can further decrease the initial 235 U enrichment requirement and increase the control element worth but is more costly. In conclusion, compared to fast-spectrum HPMRs fueled with solid pellet fuels, retrofitting UN fuel is more suitable for thermal-spectrum HPMRs fueled with TRISO fuel compacts, where the neutron spectrum hardening caused by using UN is less significant.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
High-fidelity multiscale model development for accelerated fuel qualification for high discharge burnup [Poster]
Reactor vendors seek economic benefits associated with increasing nuclear fuel service lifetime in the existing light-water reactors fleet. FFRD phenomena represent a major safety concern which still needs to be addressed. Formation of high burnup structure (HBS) in conjunction with LOCA can lead to relocating fuel to escape the fuel pin and get dispersed into the primary coolant system.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Specification of EBR-II Contact Profilometry Data
All contact profilometry data stored in FIPD was originally measured using the HFEF vertical contact profilometer, which was an electronic gauge to measure the diameter profile of an element or capsule continuously over the region of interest. The element could be rotated as it passed through the probes if the wire wrap was not to be removed and the element could be returned to reactor for further irradiation. If the wire wrap was removed, the element could be drawn vertically through the probes, rotated, and the process repeated. In this way any cladding ovality could be observed. Figure 1 shows the setup used to measure the fuel pin diameter profile. The ambient temperature during the measurement was ~21-23 ºC. The cladding temperature during the measurement is considered to be similar to the ambient temperature by assuming the fuel decay heat did not impact the cladding temperature. Two documents contain most of the important details about contact profilometry measurements. The first one is the operational manual of the contact profilometer (title: Element contact profilometer operation and maintenance, HFEF/N OMM 4326, DOC. NO. W0202-0007-SA-01). This manual provides: (1) description of the contact profilometer including the functions of each component (support stage, sensing head, control system, and calibration standards, etc.); (2) step-by-step guidance on calibrations, operations, and measurements; and (3) maintenance procedures and other details of the contact profilometer. The second document is a publicly accessible report entitled “A Fuel-element Profilometer for the HFEF.” This report describes the development of the contact profilometer, including the design requirements, features, and details of each component, as well as the acceptance tests for the built system. This document is important because it reports the uncertainties of the measurements with detailed deduction procedures. The reported uncertainties should apply to all hard-copy contact profilometry data in FIPD. Some key information about contact profilometry measurements was extracted from these two documents. Combining the information with other sources, a specification for interpretating the contact profilometry data in FIPD was established.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Non–linear bonding trends in maleonitrile-1,2–dithiolate complexes of the transuranium actinides
The trivalent actinides are produced in the nuclear fuel cycle during power production and provide the largest long-term radiation dose in used nuclear fuel. It is ideal for these elements to be removed from used nuclear fuel for disposal and a necessity for fuel recycling. A key challenge to this is the similarity of chemical behavior of the trivalent actinides to the lanthanides that are also present as fission products in used fuel. Thus far, some of the most effective separations of actinides from lanthanides utilise chelating agents containing sulfur moieties such as dithiophosphinates that selectively bind to actinide ions because of a greater bond covalency relative to lanthanide ions. Typically, greater differences between actinide and lanthanide ions are observable the more ligands and chelators bonds have a covalent character. Here, a series of complexes of the trivalent actinides Np(III) through Cf(III) (excluding Bk(III)) with maleonitrile-1,2-dithiolate (mnt 2– ) are synthesized along with their lanthanide counterparts (La(III) – Nd(III), Sm(III) – Gd(III), Dy(III)), in order to characterize the nature of chemical bonds with these metal ions and a polarizable, non-innocent, sulfur-donor ligand. The metal-sulfur bonds in these complexes trend shorter than measured for lanthanides with equivalent ionic radii. However, particularly large deviations are observed in the neptunium and plutonium complexes in both structure and bonding, resulting in a nonlinear bond length trendline for the actinide series. Density Functional Theory (DFT) calculations with Quantum Theory of Atoms in Molecules (QTAIM) and Natural Bond Order (NBO) analyses indicate that for the neptunium and plutonium complexes, the presence of increased 5f-orbital participation, energy degeneracy of the metal and ligand orbitals, and the structure packing result in shortened M–S bonds. The stabilization of the energy of the 5f-orbitals and the decrease in f-contribution to bonding orbitals in the later actinides results in structural properties more similar to the lanthanide complexes.
07 ISOTOPE AND RADIATION SOURCES↗
Impact of uranium oxide (UO 2 ) fuel with molybdenum (Mo) inserts on pressurized water reactor performance and safety
This work investigates nuclear reactor performance and safety characteristics of UO 2 with high thermal conductivity Mo insert structures by using multiphysics modeling techniques. Additionally, the purpose of this study is to use scoping analyses to quantify the impact of using Mo inserts from neutronic and heat transfer standpoints. Attention is given to reactor performance parameters, such as cycle length, maximum fuel temperature, temperature gradients in the fuel, and stored energy in the fuel. The finite-element code BISON and the Monte Carlo particle transport code Serpent were used to perform sensitivity analyses on the Mo insert geometry to optimize the insert design and inform larger scale modeling that required the homogenization of the UO 2 and Mo. Although BISON is often used as a fuel performance analysis tool, it is used in this context for heat transfer analysis only. Fuel performance optimization is outside the scope of the current study, but would be important for future work focused on this concept. The results showed that the insert had little impact on neutronic performance and that homogenizing the UO 2 and Mo was acceptable for reactor physics calculations. Reactivity temperature coefficients calculated using homogeneous UO 2 -Mo were shown to be relatively similar to UO 2 , but higher Mo content and 235 U enrichment can reduce the worth of soluble boron and control rods. The effect of insert geometry on heat transfer was much greater, and an approximately 15–20% difference in maximum fuel temperature was predicted between the best and worst performing heat transfer geometries. Furthermore, thermal conductivity calibration based on the finite element analysis results was performed to improve the accuracy of temperature predictions in reactor analysis models that homogenized the UO 2 -Mo fuel. Compared with UO 2 in a pressurized water reactor (PWR), the optimized UO 2 -Mo design increased the margin to fuel melt by 13–32% across the fuel cycle, but it requires the 235U enrichment to exceed 5% to match the cycle length of conventional UO 2 .
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Pretest Modeling A Spent Nuclear Fuel Seismic Shake Test
The U.S. Department of Energy Spent Fuel and Waste Science and Technology (SFWST) program is planning to conduct a series of full-scale shake table tests to simulate hypothetical earthquake conditions and record the response of surrogate spent nuclear fuel (SNF) assemblies in a dry canister storage system mockup. The shake table motions will represent a range of hypothetical earthquake conditions at hypothetical locations in the continental U.S. to generally define the range of mechanical loads that SNF can be expected to experience during extended dry storage periods. This paper describes the pretest predictions made with LS-DYNA models of the mockup storage systems. The test will use two dry storage system configurations, a mockup vertical concrete cask (VCC) and a mockup horizontal storage module (HSM). The test will use a production-quality canister and basket. Within the canister will be four instrumented fuel assemblies with fuel rods containing surrogate mass and 28 instrumented dummy assemblies that are intended to match the mass and outer dimension of a fuel assembly. The finite element models include models of the VCC and HSM on the shake table to calculate the system level dynamic responses and separate single fuel assembly models to calculate stress and strain in fuel assembly components. Both types of models include nonlinear behavior like rod-to-rod contact and the ability for VCC’s to rock and slide. This paper presents the expected response of the VCC, HSM, and fuel assemblies to the shake table testing that is planned to start in April of 2024. The earthquake conditions represent seismic hazards in the 2,000-to-20,000-year return period range. The test data is expected to confirm the expectation that fuel rod cladding will remain intact, fuel assembly structural components like guide tubes will remain intact, and no significant VCC sliding or tipping will occur in the range of conditions to be tested with the shake table.
Klymyshyn, Nicholas A.↗