# Shear Mechanical Properties of Rock Joints Under Non-Uniform Load Based on DEM
## 4 Simulation Results and Analysis  
### Shear Stress-Shear Displacement Curve  
Upon completing the simulation of the direct shear test, the shear stress-displacement curves for the joint surface corresponding to three distinct load distribution forms and a uniform load distribution (UD) form were obtained, as shown in Figure 7. In the initial loading phase, peak shear stresses related to various load and distribution forms closely aligned with the slope of the curve. As loading progressed, there was a deviation between the slope of the curve, peak shear displacement, and shear strength; higher normal stress combined with a load concentration location closer to the distal end resulted in increased corresponding shear strength. The closer the load concentration location was to the far end of the shearing direction, the stronger the damage resistance of the rock mass structure was.  
The relationship between normal stress and peak shear displacement is illustrated in Figure 8. Generally, peak shear displacements increased with increasing normal stress, although the average values varied across different load distribution forms. Specifically, the average peak shear displacements for the uniform distribution (UD), near-field concentration (NFC), focus-on-central (FOC), and far-field concentration (FFC) load distribution forms were 1.634 mm, 1.576 mm, 1.656 mm, and 1.728 mm, respectively. In comparison to the NFC condition, the average peak shear displacements for FOC and FFC increased by 13.72% and 18.64%, respectively. This indicates that the average peak shear displacement  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Distribution Form** & **Total Normal Load \(G_{T}\)** & **Normal Stress \(\sigma\)** \\ \hline Uniform distribution (UD) & & \\ \hline Far-field concentration (FFC) & & \\ \hline Near-field concentration (NFC) & & \\ \hline Focus on center (FOC) & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental simulation scheme.  
Figure 6: The simulation diagram depicts a non-uniform distribution of overburden load.  
increased with the location of load concentration and could be well approximated by a linear expression, as shown in Equation (5). This finding emphasizes the significant influence of load distribution form on peak shear displacement.  
\[\overline{\gamma_{\mathrm{P}}}=0.0152\gamma_{P}+1.577 \tag{5}\]  
where \(\overline{\gamma_{\mathrm{P}}}\) is the average peak shear displacement and \(\gamma_{P}\) is the peak shear displacement, both in mm.  
To further analyze the influence of load distribution form on shear stiffness, the slope (shear stiffness) of the shear stress-shear displacement curve under normal stress 2.0 MPa was calculated as a change in the form of shear displacement, as shown in Figure 9. It can be seen from the figure that the shear stiffness in all distribution forms decreased with the increase in shear displacement, but the rate of decrease was more and more slow, which corresponded to the evolution of the elastic stage-damage-softening stage of the shear stress-shear displacement curve. However, according to the slope of the rigidity-shear displacement fitting curve under different load distribution forms, the attenuation trend of shear stiffness with shear displacement was \(k_{\mathrm{NFC}}>k_{\mathrm{FOC}}>k_{\mathrm{FFC}}\). In terms of average stiffness, the average values of \(k_{\mathrm{NFC}}\), \(k_{\mathrm{FOC}}\), and \(k_{\mathrm{FFC}}\) were 2.95, 2.99, and 3.11, respectively, and \(k_{\mathrm{FFC}}\) was 4.1% larger than \(k_{\mathrm{FOC}}\). It was 5.4% larger than \(k_{\mathrm{FFC}}\), indicating that the stiffness resistance to decay under FFC conditions was stronger and less prone to damage.  
Figure 7: Shear stress–shear displacement curves under different forms of load distribution.