## 1 Introduction  
It is essential to ensure plant safety in a sodium-cooled fast reactor (SFR), a next-generation nuclear energy system for the future proposed by the Generation IV International Forum. When a Severe Accident (SA) occurs, the Core Disruptive Accident (CDA) is one of the significant safety concerns of SFRs. According to the progression status of the postulated CDA, the developed sequence can be categorized into four phases: the initiating phase, the Transition phase, the Material relocation phase, and the Heat removal phase [1]. During the material relocation phase, the molten core material may be discharged downward to the lower sodium plenum through the potential path (e.g., Control Rod Guide Tube, CRGT [2,3]), and the molten material can be quenched and broken into particulate fragments due to the hydrodynamic instability and the thermal interaction with the surrounding sodium coolant under Fuel-Coolant Interaction (FCI) [4; 5]. Eventually, these fragmented particles (debris particles) accumulate and are deposited on the in-vessel debris catcher in the lower plenum to form the particulate debris bed. Based on previous studies, it can be recognized that a significant power excursion due to a re-criticality accident of the degraded molten materials would damage the integrity of the Reactor Vessel (RV), and the insufficient cooling of the generated decay heat from the debris bed to the coolant would also cause the coolant to dry out and particle re-melting following further melting through the RV boundary [1; 2; 3; 6]. In order to secure the safety margin of In-Vessel Retention (IVR), ensuring the avoidance of sudden power excursions and insufficient cooling of the debris bed are the prerequisite concerns. Therefore, investigating the factors that may affect the criticality potential and the cooling characteristics of the heat-generating particulate debris bed are crucial for realizing the goal of IVR against CDA to escalate the plant safety of SFRs. Some studies regarding the debris bed's safety analysis have been conducted on the aspects of the criticality and cooling of the generated-decay heat. As for the issues of the debris bed criticality, the Japan Atomic Energy Agency (JAEA) conducted fuel debris criticality experiments by addressing the scenario of Molten-Core-Concrete-Interaction (MCCI) in the STAtic experiment Critical facility (STACY) [7]. Two configurations of simulated fuel debris (under-moderated and over-moderated) were prepared by varying the interval between fuels. The results showed that the influence of the concrete composition on the effective multiplication factor (\(k_{eff}\) [-]) was manifested more in under-moderated configuration than over-moderated ones. [PERSON] et al. [8] conducted numerical criticality studies on a virtual spherical debris bed under an oxide fuel (\(\text{UO}_{2}\))/water system. They indicated that the factors of the burnup of the fuel material, particle size, porosity, and debris bed size affect the necessary boron concentration for securing the sub-critical state. [PERSON] et al. [9] numerically investigated the criticality safety of the conical debris bed under a Mixed Oxide (MOX) fuel/liquid system. Except for the effect of the debris bed's porosity, this also demonstrated that, based on the assumption of the same volume, the lower slope angle of the conical debris bed contributed a negative effect on the \(k_{eff}\) value of the debris bed. As for the issue of the cooling characteristics of the heat-generating debris bed, a criterion of the Dryout Heat Flux (DHF), which is the maximum heat flux prior to the incipient of the possible dryout, was selected to conduct cooling capability investigations on a particular debris bed's configuration in previous studies. For a one-dimensional debris bed, early researchers attempted to numerically predict the DHF value for a specific configuration of the heat-generating particulate bed, and several models were proposed based on the analytical or empirical corrections [10; 11; 12].