# Shear Mechanical Properties of Rock Joints Under Non-Uniform Load Based on DEM
## 4 Simulation Results and Analysis
### Crack Evolution  
To investigate the law of damage evolution, crack extensions for different forms of load distribution are presented in Figure 12 (\(G_{T}\) = 20 kN), at various stress levels (\(\tau\) = 50% \(\tau_{max}\); \(\tau\) = 70% \(\tau_{max}\); \(\tau\) = 90% \(\tau_{max}\); \(\tau\) = \(\tau_{max}\); \(\tau\) = \(\tau_{failure}\)). Shear cracks are represented by the red color, while the green color indicates tensile cracks. From observing crack propagation in different load distribution modes, it can be seen that the main cause of rock mass failure was micro-tensile cracking at the highest joint center. With an increase in shear stress level, cracks initiated at the highest undulation (the center of the joint surface) and gradually expanded along the lower slope to form two macro-through-cracks. It is worth noting that there was only one through-crack for NFC and FFC at the peak shear stress, while under UD and FFC conditions, the crack growth mode was essentially similar with two obvious through-cracks at the peak shear stress. The results indicate that compared to FOC and FFC, the crack growth mode was not able to explain the crack growth mode.  
Figure 11: Relationship between cohesion and internal friction angle vs. location of load concentration (standard deviations: UD = 0.118; NFC = 0.088; FOC = 0.076; FFC = 0.075).  
Figure 10: Relationship between normal stress and shear strength under different forms of load distribution (standard deviations: UD = 0.116; NFC = 0.089; FOC = 0.078; FFC = 0.076).  
UD conditions, NFC and FFC conditions required more damage for rock mass failure and made it more difficult to destroy the rock mass structure.  
Figure 13 delineates the spatial-temporal evolution of tensile versus shear fracture distribution across distinct loading phases under varying load configuration modes. During the initial loading stages (NFC, FOC, and UD conditions), tensile fractures prevailed as the principal crack type due to localized stress concentrations exceeding the material's tensile resistance. With progressive loading, a characteristic transition occurred where shear fractures gradually dominated the failure process, achieving predominance at 90% \(\tau_{max}\) under NFC conditions. This transition occurred earlier at 70% \(\tau_{max}\) for FOC and UD configurations, indicating accelerated shear localization under these boundary constraints. Contrastingly, FFC conditions exhibited sustained shear fracture dominance throughout the entire loading history, confirming shear-driven failure as the fundamental fracture propagation mechanism under fully confined conditions.  
Figure 12: Crack expansion process under different forms of load distribution (\(G_{T}\) = 20 kN).  
The observed fracture pattern transition reveals two distinct failure pathways: (1) For the NFC, FOC, and UD conditions, initial tensile-dominated damage evolved into shear-controlled failure through progressive micro-crack coalescence and stress redistribution during shear deformation. (2) FFC conditions demonstrated immediate shear fracture nucleation and propagation due to enhanced confinement restricting tensile crack development. This mechanistic difference explains the enhanced shear strength under FFC loading; the energy-intensive shear fracture process (characterized by frictional sliding and asperity degradation) requires greater energy dissipation compared to tensile fracture mechanisms (governed by bond separation with lower energy consumption). The resultant strength hierarchy (FFC > NFC \(\approx\) FOC) directly correlated with the proportion of high-energy shear fractures in the failure process.