## 3 Analysis of Experimental Results  
### Influencing Factor of Grain Size (\(d\))  
Figure 7 shows the effect of grain size (\(d\)) on the peak shear strength (\(\tau_{p}\)), peak shear displacement (\(u_{p}\)), post-peak modulus (\(S\)), and stress drop (\(\Delta\tau\) ) of rock joints. As shown in Figure 7a, the shear mechanical properties of rock joints are mainly determined by \(JRC\)  
Figure 4: Comparison of shear stress–displacement curves under different normal loads (_CNLs_).  
Figure 5: Comparison of shear stress–displacement curves with various grain sizes (\(d\)).  
Figure 6: Model curve for shear stress vs. shear displacement.  
under low normal load (\(CNL<5\) kN), so \(\tau_{p}\) increases with the increase in d. However, when \(CNL>5\) kN, \(\tau_{p}\) increases first and then decreases with the increase in d, which is mainly determined by the microstructure and mineral composition of rock specimens. The \(\tau_{p}\) increases first, because (1) smaller \(d\) can provide a compact structure and more grain boundaries, thus effectively preventing crack propagation and improving rock strength, and (2) the dolomite with higher Mohs hardness accounts for a higher proportion. The \(\tau_{p}\) decreases subsequently, because (1) larger \(d\) results in fewer grain boundaries; thus, the shear stress cannot be effectively dispersed, and (2) the proportion of calcite with lower Mohs hardness increases.  
As shown in Figure 7b, \(u_{p}\) generally increased first and then decreased with the increase in d, which is related to the microstructure and mineral composition of rock specimens. When \(d\) is small, the rock specimen has a compact structure, fewer inherent cracks, and a higher proportion of dolomite with large Mohs hardness, which improves rock strength, so \(u_{p}\) increases first with the increase in d. As \(d\) continues to increase, the shear stress dispersion decreases, and the proportion of calcite with lower Mohs hardness increases, which reduces the rock strength, so \(u_{p}\) decreases subsequently. In addition, the higher \(u_{p}\) values of A2 and D4 are due to the slight dislocation of the upper and lower joint surfaces during installation.  
\(S\) and \(\Delta\tau\) are important parameters to characterize the shear instability intensity of rock joints. As shown in Figure 7c and d, when \(d\) is small, \(S\) and \(\Delta\tau\) increase exponentially and linearly with the increase in d, which is related to the \(JRC\) of rock joints. Thus, when \(d<0.5\) mm, \(S\) and \(\Delta\tau\) increase first with the increase in d. However, \(S\) and \(\Delta\tau\) decrease subsequently as \(d\) continues to increase, which is due to the changes in microstructure and mineral composition. As \(d\) continues to increase, the shear stress dispersion decreases, and the proportion of calcite with lower Mohs hardness increases, which reduces the shear strength of rock joints, so the shear instability intensity of rock joints decreases accordingly.  
Figure 7: Influence of grain size (\(d\)) on shear mechanical properties of rock joints. (**a**) Peak shear displacement \(\tau_{p}\), (**b**) peak shear displacement \(u_{p}\), (**c**) post-peak modulus \(S\), and (**d**) stress drop \(\Delta\tau\).