Granular materials are widely used in engineering applications

where their internal stress distribution and fracture behavior greatly influence the stability and safety of structures such as rockfill dams and roadbeds. This study investigates the internal stress distributions and crack initiation mechanisms of spherical particles under uniaxial compression based on two analytical solutions: the Hiramatsu-Oka (HO) solution

and the Dean-Sneddon-Parsons (DSP) solution. The results indicate loading range significantly influences internal stress distribution and crack initiation location. Stress distributions obtained from both solutions are highly consistent

while the DSP solution offers superior extensibility. We further extend the DSP solution to multi-point loading conditions

and develop a rapid evaluation framework for stress distribution and crack initiation in granular assemblies based on an approach of coupling the scaled boundary finite element method (SBFEM) and DSP. This framework efficiently determines contact force distributions in granular assemblies using SBFEM

and applies the stress superposition principle of the DSP solution to achieve a rapid assessment of stress fields and crack initiation zones. The findings lay a theoretical foundation for understanding stress distribution and fracture mechanism in granular materials

and they could be further applied to rapid evaluation of the deformation and potential breakage rates in granular assemblies.