A unified predictive model for limiting void ratio of calcareous sand considering particle morphology and intra-particle porosity

Calcareous sand exhibits distinctively irregular particle morphology and abundant intra-particle porosity arising from its biogenic origin and diagenetic evolution, leading to limiting void ratios markedly different from those of silica sands. In this study, a unified predictive framework for the limiting void ratios (emax and emin) of calcareous sand was developed by simultaneously incorporating particle size, external morphology, and intra-particle pore structures. High-resolution μ-CT imaging combined with ambient occlusion analysis was employed to reconstruct accurate three-dimensional particle geometries and intra-particle pores, allowing the quantification of key morphological parameters and the definition of an overall regularity index (OR). To isolate the influence of intra-particle voids, the concept of skeletal void ratio (e’) was introduced, and a morphology correction factor (r) was proposed to capture deviations from traditional particle-size-based predictions. Results reveal distinct size-dependent trends in both intra-particle porosity (P0) and morphological regularity, with larger particles exhibiting higher porosity and more irregular shapes. The newly established model, integrating median particle size (D50), OR, and P0, accurately predicts limiting void ratios for both calcareous and silica sands, with over 90% of predictions within ±20% of measurements, underscoring the essential role of particle morphology and porosity in determining packing behavior.