Conference Agenda

Accurate prediction of reactor lower head ablation and remaining wall thickness is important for evaluating the effectiveness of in-vessel melt retention and characterizing subsequent ex-vessel severe accident progression. Previous studies under the IVMR project showed that reactor pressure vessel failure was unlikely at low pressure, 3 bar, but was observed at elevated pressures, 40–52 bar, for VVER-1000-class reactors. Building on these studies, the IAEA Coordinated Research Project established a benchmark problem incorporating realistic thermal boundary conditions for the VVER-1000 lower head. In finite element heat transfer analysis, the molten region is commonly represented by increasing thermal conductivity rather than removing elements, which improves numerical stability but may introduce ambiguity in heat transfer direction. In particular, isotropic enhancement of thermal conductivity can redistribute heat laterally, reducing the heat flux transferred toward the melt front and potentially overestimating the remaining wall thickness. This study systematically investigates the effect of thermal conductivity directionality in the molten region on melt-front heat flux and wall ablation prediction.

The VVER-1000 hemispherical lower head was modeled as a two-dimensional axisymmetric finite element domain using ANSYS Mechanical 2023 R1 with PLANE292 four-node thermal elements. A 5 mm mesh was used, resulting in 40,113 elements. Time-dependent heat flux was applied to the inner surface, with the maximum heat flux of approximately 803 kW/m² occurring at 7,599 s, while prescribed ex-vessel cooling-temperature boundary conditions were imposed on the outer surface. Two reactor pressure vessel steels were compared: 15X2HMΦA, representative of the VVER-1000 vessel material, and SA533B1, representative of U.S. light water reactor vessels. Although the two materials have similar thermal conductivity near the melting point, SA533B1 exhibits an abrupt specific heat variation near 750°C associated with ferrite-to-austenite phase transformation, leading to differences in thermal diffusivity at intermediate temperatures. Six analysis cases were defined by varying the material, the application of enhanced thermal conductivity in the molten region, and the directionality of the enhanced conductivity, namely isotropic or anisotropic in the wall-thickness direction.

When the thermal conductivity of the molten region was not enhanced, the molten region acted as an artificial heat sink, leading to underprediction of ablation in some lower-head regions. Applying isotropic thermal conductivity enhancement reduced this artificial heat sink effect, but introduced another numerical bias by diverting heat laterally and reducing the heat flux transferred in the wall-thickness direction at the melt front. In contrast, anisotropic enhancement, in which high thermal conductivity was applied only in the wall-thickness direction, substantially recovered the melt-front heat flux. At the location of maximum heat flux, the predicted remaining wall thickness in the anisotropic cases was approximately 4 cm thinner than that in the isotropic cases, providing a more conservative and directionally consistent estimate of ablation depth. The material type had negligible influence on the final remaining wall thickness because the identical enhanced thermal conductivity assigned above the melting point dominated the thermal response despite differences in thermal diffusivity.

These results indicate that isotropic thermal conductivity enhancement in the molten region can introduce non-conservative bias in finite element evaluations of reactor lower head integrity under in-vessel melt retention conditions. Anisotropic treatment, which confines the enhanced thermal conductivity to the wall-thickness direction, minimizes lateral heat diversion and improves the representation of melt-front heat flux. Therefore, directional thermal conductivity treatment is recommended for future finite element analyses of reactor lower head ablation during severe accidents.

A small 360 MWth European Sodium Fast Reactor design, ESFR SMR, is studied currently in the ESFR-SIMPLE project of EURATOM by a number of partners. These studies include assessment of molten core behaviour after a hypothetical severe accident.

The ESFR SMR design includes several elements, through which molten fuel discharge may occur, bringing the core to subcritical conditions. These elements include control rod followers in the central core part and dedicated corium transfer tubes at the core periphery.

The transient simulations show the key role of these elements in the considered design for facilitating molten fuel discharge. Early fuel discharge may prevent multiple re-criticality events leading to accumulation of thermal energy in the core and causing an elevated mechanical energy release.

In the basic case, simulations show that the paths for fuel discharge may open first in the central core part, after melting of can-walls of the mentioned elements, then at the core periphery, all elements contributing to the fuel discharge. In sensitivity cases, we study the effect of particular elements. These studies show that unavailability of some elements for molten fuel discharge may not reduce the thermal energy release appreciably. The obtained results may help in future ESFR SMR studies.

Reinforced concrete walls constitute essential safety-related structures in nuclear and radiological facilities. Beyond their conventional structural role, they provide confinement of radioactive materials and shielding against ionizing radiation, thereby contributing directly to radiological protection. Earthquake-induced damage may compromise these functions, particularly through the development of cracks that increase the permeability of concrete and facilitate radionuclide transport. Consequently, seismic actions can generate cascading effects in which structural damage leads to radiological consequences. Despite this clear interaction, current engineering practice generally addresses seismic design and radiological safety assessment as separate disciplines. Seismic performance is typically evaluated using structural engineering criteria, whereas radiological safety is assessed independently through dose-based regulations. As a result, there is often no explicit and consistent link between earthquake-induced structural damage and radiological performance.

This paper presents a practical seismic verification procedure that explicitly integrates radiological safety requirements into structural design. The methodology builds on the principles of Performance-Based Earthquake Engineering (PBEE), extending the framework to account for cascading seismic–radiological hazards. Within the proposed approach, seismic hazard, structural response, damage development, and radiological consequences are treated as interconnected processes. However, because direct probabilistic assessment of all these interactions is computationally demanding and unsuitable for routine design applications, the comprehensive PBEE framework is transformed into a simplified risk-targeted verification format that can be implemented using conventional engineering tools and procedures.

A key innovation of the methodology is the translation of radiological acceptance criteria into a structural limit state. Radiological safety requirements are commonly expressed through limits on radiation dose to members of the public. In the proposed framework, these dose-based requirements are converted into a critical equivalent permeability of the reinforced concrete barrier. The equivalent permeability represents the effective transport capacity of a cracked concrete wall and depends on the crack-width distribution throughout the wall thickness. Since crack widths are governed by the internal force state generated by seismic loading, the procedure establishes a physically meaningful relationship between earthquake demand, structural damage, and radiological performance.

To account for uncertainty and reliability requirements, the methodology incorporates a risk-targeted design philosophy. The probability of exceeding the permeability-based limit state is described through a fragility function, which relates the likelihood of failure to seismic intensity. A target annual frequency of limit-state exceedance is defined based on regulatory requirements, and the corresponding median seismic intensity associated with the target reliability level is determined using the seismic hazard curve and the assumed fragility dispersion. A seismic safety factor is then introduced as the ratio between this target median intensity and the design-basis earthquake intensity. Rather than requiring analyses at multiple hazard levels, the safety factor is applied to the seismic component of the internal forces obtained from standard structural analyses. In this way, probabilistic reliability requirements are incorporated into a deterministic design framework while preserving simplicity and transparency.

The resulting verification methodology is organized as a seven-step engineering procedure. The process begins with the definition of radiological acceptance criteria and determination of the critical equivalent permeability. Target reliability levels and design-basis earthquake intensities are then selected, followed by specification of fragility dispersion and calibration of the seismic safety factor. Structural response analyses are subsequently performed for the design earthquake, and the resulting internal forces are modified using the calibrated safety factor. These forces are used to determine crack-width profiles and equivalent permeability values, which are finally compared with the critical permeability threshold. If the criterion is not satisfied, the structural design is modified and the procedure is repeated until compliance is achieved.

The applicability of the proposed procedure is demonstrated through an initial design of a near-surface repository for low- and intermediate-level radioactive waste in Slovenia. The structure of the repository consists of a cylindrical reinforced concrete silo embedded in the ground and relies on reinforced concrete barriers as the primary confinement system. Two representative configuration states of the facility were considered: the filling stage and the post-closure stage. Radiological analyses established a critical equivalent permeability of 10⁻⁸ m/s, while target reliability levels were defined in accordance with nuclear-facility seismic design standards. Using the adopted hazard model and fragility assumptions, a seismic safety factor of approximately 2.2 was obtained for both configuration states. Structural analyses revealed permeability values significantly exceeding the allowable threshold in several sections of the silo wall and base slab. The results indicated that the initial design did not satisfy the required seismic–radiological safety objectives and therefore required redesign. Recommendations included increasing reinforcement, modifying wall dimensions, improving structural connections, and refining radiological analyses to better characterize acceptable permeability limits. These recommendations triggered redesign. The repository is currently under construction.

The study demonstrates that radiological safety requirements can be directly incorporated into seismic verification through permeability-based limit states and risk-targeted design principles. The proposed methodology provides a practical and physically grounded framework for addressing cascading seismic–radiological hazards, enabling designers to evaluate structural and radiological performance within a single verification process. The proposed approach can be utilized in applications dealing with multiple interacting hazards, thereby supporting the development of more resilient nuclear and radiological facilities.

Keywords: radiological safety; seismic verification; reinforced concrete walls; permeability-based limit states; performance-based earthquake engineering; risk-targeted design; nuclear facilities.