Robust Critical Connectivity Threshold in Ranked Percolation of Granular Packings

The formation of sintering bridges in amorphous powders affects both flow behavior and perceived material quality. When sintering is driven by surface tension, bridges emerge sequentially, favoring contacts between smaller particles first. Predicting the connectivity percolation threshold is key to understanding and controlling the onset of sintering. We investigate ranked percolation in granular packings, where particles connect based on contact number. While the percolation threshold defined by the fraction of connected particles is non-universal and highly sensitive to particle size dispersion, we find that the critical number of sintered bridges per particle provides a robust estimator across different size distributions. Through numerical simulations and a mean-field approach, we link this robustness to the spatial distribution of contacts. Our results have broader implications for understanding the resilience of spatially embedded networks under targeted attacks.