Mechanical Responses of Sandstone Exposed to Triaxial Differential Cyclic Loading with Distinct Unloading Rates of Confining Stress: A Particle-Based Numerical Investigation

Abstract This study numerically investigated the mechanical responses and acoustic emission (AE) behaviors of sandstone subjected to triaxial differential cyclic loading with varying unloading rates of confining stress. A coupled FLAC 3D /PFC 3D model was employed to replicate stress-controlled axial cyclic loading and servo-controlled confining stress regimes. By analyzing the stress-time-dependent evolution of the bond radius multiplier, the model accurately reproduced stress–strain relationships under four specific stress paths. AE behaviors were simulated through bond breakage, with the energy released during these events quantified as numerical AE energy for calculating the b -value. The shear bands formed by microcracks in PFC simulation closely aligned with macroscopic cracks observed in laboratory tests, while the b -value evolution exhibited strong agreement with experimental results. Additionally, the study quantified the variation in the proportion of strong contact force chains at different stress levels. The evolution of microscopic principal stresses among particles corresponded well with the macroscopic principal stress observed in true triaxial tests. The primary cause of sample failure in the numerical model under these specific stress paths was identified as the rapid escalation of microscopic tensile stresses.