The localization of deformation in shear bands is a fundamental phenomenon in granular materials like soil. In this study, we focus on the characteristics of shear bands, particularly the size effect, by implementing biaxial discrete element method (DEM) modeling. Firstly, we describe the establishment of the biaxial experimental model with dense sands. Then, we implement analyses of specimens with different sizes and find that there is a clear size effect in the stress–strain curve after the peak strength point, and there is less of a size effect in the angle of the shear band; the angle is consistent with Arthur’s theory. Finally, the reason for the size effect is analyzed using the width of the shear band and the porosity inside the shear band. As the specimen size increases, the ratio between the shear band area and the whole specimen decreases. This effect reduces as the isotropic confining stress increases. The difference in the proportion of the shear band area mainly causes the size effect that affects the specimen deformation characteristics. We also find that with the increase in isotropic confining stress, the type of shear band gradually changes from cross-type to single-type. Our study provides valuable insights into understanding the behavior of granular materials.

Coal gangue (CG) ranks among China’s most significant industrial solid by-products. In response to China’s carbon neutrality commitments and the growing emphasis on resource recycling, finding effective ways to valorize CG has emerged as a pressing concern. Based on the mineral composition and chemical composition characteristics of CG, this study systematically investigated the enhancement effects of three alkali activators (Na₂SiO₃, NaOH, and Ca(OH)₂) on the cementitious properties of CG. Through different dosage and compressive strength tests, the efficiency ranking of the three activators was determined as follows: Na₂SiO₃ > Ca(OH)₂ > NaOH. A 10% Na₂SiO₃ dosage combined with 28-day curing was identified as the optimal condition for achieving sufficient reaction and structural densification. Under these conditions, the compressive strength of CG cementitious material reached 6.4 MPa, representing an increase of 190.9% compared to the blank group (2.2 MPa), significantly superior to Ca(OH)₂ (69.55%) and NaOH (62.27%). X-ray diffraction (XRD) and scanning electron microscopy-energy dispersive spectroscopy (SEM-EDS) analyses revealed that alkali activators function primarily by disrupting the crystalline framework of CG, promoting the cross-linking polymerization of silicon–aluminum monomers to generate dense cementitious products, thereby improving material performance. The Na₂SiO₃ is attributed to its “dual activation effect”, providing OH⁻ to create an alkaline environment while supplying reactive silicate ions (SiO₃²⁻) to accelerate N-A-S-H gel and C-A-S-H gel formation. These findings offer guidance for optimizing CG-based cementitious formulations for formula optimization and large-scale utilization of CG cementitious materials.