Determining the particle size distribution (PSD) of an industrial particle stack with precision is imperative. The inherent challenge arises from the concealed distribution within the stack. In response, we introduce a comprehensive framework that extrapolates the overall PSD from the observable surface images of the particle stack. Our methodology initiates by characterizing the hierarchical structure of the particle stack, grounded in its formation mechanism, effectively demarcating between surface and internal information. Subsequently, we present the hierarchical packing model (HPM), an innovation that integrates the permeability principle, spatial structural attributes, and a stochastic resampling probability paradigm specific to particle stacks. This model crystallizes a quantitative nexus between the surface and overall PSD of the particle stack. As an integral component, we deploy a fine-tuned segmentation large model to extract particle boundaries within the surface imagery, facilitating a statistical assessment of the surface PSD. This value can then be substituted into the HPM to obtain the overall PSD. To underscore the robustness and precision of our methodology, we executed comparative and ablation studies utilizing datasets from a blast furnace (BF) ironmaking facility. The empirical outcomes unequivocally attest to the precision and effectiveness of our method.