Unified gradation index (Sm) for shear mechanics and particle breakage at calcareous sand-structure interfaces

This study investigates the influence of particle gradation on the shear behavior and particle breakage at the interface between calcareous sand and structural materials (concrete, aluminum alloy, and steel piles) using a self-developed large-scale interface shear apparatus. An enhanced two-parameter gradation equation was proposed to unify the representation of both uniform grading curves and continuous grading curves, incorporating a novel gradation index (S_m) to quantitatively evaluate gradation effects. The results demonstrate that increasing coarse particle content reduces both peak and residual shear stresses while intensifying particle breakage, with these effects being more pronounced under higher normal stresses. Finer gradations exhibited greater softening behavior (β_s = 47.66-54.98%), and surface roughness dominated shear strength (concrete > aluminum alloy > steel piles). Friction coefficients decreased with coarser gradations due to modified particle-structure interlocking, following a power-law relationship for shear strength. The proposed S_m index effectively unified continuous and discontinuous gradation characterization, showing exponential correlation with friction coefficients and linear relationship with breakage rates. These findings provide fundamental insights into granular-structure interactions and establish a predictive framework applicable to diverse engineering scenarios, including offshore foundations and extraterrestrial soil-structure systems. The study advances interfacial mechanics through its quantitative gradation approach while offering practical tools for geotechnical design optimization in particle-sensitive environments.