## 1 Introduction
These models can describe how the debris bed's properties, such as particle size, porosity, and bed thickness, affected the DHF value of the heat-generating porous bed. For the more plausible scenario of the multi-dimensional cases, the cooling characteristics between the top-flooded cylindrical debris bed and the heap-like conical one with multi-dimensional flooding were investigated in the COOLOCE experimental facility [13]. The results demonstrated that the multi-dimensional cooling of the conical one resulted in a higher DHF value than the top-flooded cylindrical one of the same bed heights, but the top-flooded cylindrical with lower debris heights could have a higher DHF value if two debris beds are assumed to have equal volume and bottom radius. Thus far, most previous studies on the proposed empirical models for investigating the effects of the debris bed properties on the criticality potential and the cooling characteristics are still restricted to the assumption that the debris bed is composed of homogeneous solid particles. However, based on previous studies, the debris bed in the actual scenario would be composed of a mixture of heterogeneous particles with a non-uniformity of the material composition (such as fuel particles and structure material particles [14; 15; 16]), accompanying a shape and size distribution [4; 5; 17; 18; 19; 20] due to the stochastic process of the molten material's discharging and fragmentation. Hence, there would exist a debris bed with a heterogeneous configuration created by the mixture of heterogeneous solid particles in the realistic SA scenario, which would address the uncertainty source of the bed safety assessments from previous studies. In addition, during the bed formation, the heterogeneous configuration of the debris bed would process further dynamic transformation due to the particle redistribution, such as particle avalanching (when the slope angle of the debris bed exceeded the critical repose angle during bed formation [21; 22; 23]) or possible self-leveling (due to the mechanical energy of the evaporated coolant within the particulate debris bed [24; 25; 26; 27; 28]), causing the partial fluidization of the top layer and the subsequent flattening of the bed via lateral particle redistribution. For example, considering the heterogeneous debris bed composed of the fuel and structure particles (as shown in Figure 1) under the process of particle redistribution, except for the thickness of the debris bed being suppressed, the coherent phenomenon of gradual local accumulation of the heavier fuel particles due to the density difference will also occur [14; 15; 16; 29], with the accompaniment of the local higher neutron/heat flux in the debris bed. Although previous studies have implied that the suppressed bed thickness could escalate the cooling capability and be beneficial to avoid criticality accidents [9; 13], whether the dynamic transformation of the heterogeneous configuration would increase or decreases the \(k_{eff}\) value or whether it promotes or inhibits the flow within the porous bed has not been quantitatively elucidated as yet. To the authors' best knowledge, no published document that registers the compound effect of the heterogeneous configuration and dynamic particle redistribution on the bed safety assessment has been made available. Therefore, this research aims to develop a tool for investigating the effects of the different dynamic transformations of the heterogeneous configurations on both the criticality potential and cooling characteristics of the debris bed, which is beneficial for further securing the sufficient safety margin of IVR through eliminating the source of uncertainties of this compound effect from the bed safety assessment. Even for the fixed-particle condition, there are still existing complex multi-mechanisms when considering bed safety assessment.