Mechanical Response of Calcareous Sand under Static and Dynamic Loading: Development of a Unified Breakage Prediction Model

Calcareous sand, characterized by high porosity and fragile particle morphology, exhibits complex mechanical responses and particle breakage under multistage shear loading in coastal and seabed environments. This study systematically investigates the effects of gradation (quantified by fractal dimension D), confining pressure σ3, and loading type (static or dynamic triaxial shear) on shear strength and breakage behavior. A single particle breakage sensitivity coefficient and cumulative breakage rate (Bacc) are introduced to characterize particle size–dependent fragmentation. A unified six-parameter model integrating the fractal dimension D, confining pressure σ3, and cyclic loading cycles N is proposed to predict the particle breakage rate. The experimental results demonstrate that an increasing fractal dimension D enhances the shear strength by 15%–20%. This can be attributed to particle interlocking, which is particularly pronounced in specimens with broader gradation and higher fine particle content. Static loading induces localized breakage, which predominantly occurs in coarse particles (2–5 mm), whereas dynamic loading (100 cycles at 200 kPa) significantly elevates the cumulative breakage rate because of repeated stress cycling. The unified model exhibits exceptional predictive accuracy, with confining pressure being identified as the dominant factor (contributing 60%–75% to the breakage rate) and with cyclic loading exerting a secondary logarithmic effect. Additionally, particle breakage leads to a reduction of permeability. The phenomenon of strain softening can be observed under K0-consolidation at 300 kPa, which is attributed to the fabric anisotropy and the formation of localized shear bands. The unified model is developed by employing six parameters, which could provide a robust framework for predicting particle breakage under static and dynamic loading. The outcome of this study could offer practical insights for optimizing gradation and mitigating breakage risk in marine geotechnical engineering.