The computational efficiency of the discrete element simulation process is often a limiting factor. However, the use of the coarse-grained method, which employs dimensional analysis to amplify particles, significantly improves computational efficiency. This research utilizes the coarse-grained method to amplify particles and examines the impact of linear models on the mechanical of fly ash. By examining parameters such as magnification, stiffness, sliding friction coefficient, and rolling friction coefficient, we establish the relationship between fly ash cohesion, internal friction angle, and microscopic parameters in discrete element method (DEM) simulation. The simulation results demonstrate that the shear strength of fly ash increases as magnification, stiffness, and sliding friction coefficient increase. The rolling friction coefficient, on the other hand, has minimal effect on shear strength. The elastic potential energy of the system is unaffected by magnification, with stiffness inversely proportional to adaptable potential power. However, sliding and rolling friction coefficients positively impact adaptable potential power. Furthermore, this study proposes a practical simplification method for amplification of materials with small particle sizes. The comparison between numerical simulation and experimental data yields consistent results. As a result, this study provides a foundation for the application of large-scale fly ash transportation, storage, and other engineering purposes.