## 5 Discussion  
### Effect of Model Size on Shear Characteristics  
Figure 12 shows the failure modes and the associated shear stress-shear displacement curves for the sample group \"SS\". With the increase in the sample size, the post-peak plasticity becomes more obvious in the curves. In particular, strain softening behaviour is apparent in the curves when the sample size surpasses 200 mm, and it is difficult for the stress values to rebound after the peak stress point (as demonstrated in the 200 mm  
Figure 11: Maximum and minimum stress evolution of sample “S-2” during failure process: (**a**) Point B; (**b**) Point C; (**c**) Point D; (**d**) Point F; (**e**) Point H.  
sample). This is primarily attributed to the diminishing interlocking of particles as the sample size expands. Larger sample sizes lead to both an increase in the quantity of cracks generated during the shear process and an improvement in the degree of crack propagation. Under a normal stress of 1 MPa, large-sized samples exhibit a failure pattern similar to that of smaller-sized samples, with shear dilatancy being a common phenomenon. However, under higher normal stresses of 2 MPa and 4 MPa, the occurrence of shear dilatancy is less frequent in the failure of large-sized samples. Rather, there is more damage near the interface, especially to the steps and rock slabs.  
Figure 12: _Cont._  
Figure 12: Size effect on stress–displacement curves and failure modes: (**a**) Curve 1 MPa; (**b**) Curve 2 MPa; (**c**) Curve 4 MPa; (**d**) Failure mode 1 MPa; (**e**) Failure mode 2 MPa; (**f**) Failure mode 4 MPa.  
The shear mechanical parameters of samples varying in size under different stress conditions were calculated, with the results presented in Figure 13. Residual strength is a value that falls within a specified interval because, during the residual stage, the curves show oscillations within a set range. To determine this range value, the residual strength is calculated as the average of the maximum and minimum values within the fluctuation range, with the standard deviation used to construct the error bars for graphical representation. As can be seen in Figure 13, a distinct size effect is observable in the variation of the three shear parameters (peak shear strength, shear elastic modulus, and residual strength) as the sample size increases. When the model size expands from 100 mm to 200 mm, there is a significant decrease in the values of all three shear parameters. However, as the sample size increases from 200 mm to 400 mm, the rate of decrease for these shear parameters begins to slow down, indicating a less pronounced attenuation. This change in the shear parameters can be characterised by a negative exponential function. To describe the variation law of the shear mechanical parameters with sample size more clearly, fitting functions were employed, which are listed in Equations (1)-(3).  
\[1\;\text{MPa}\left\{\begin{array}{l}\tau_{p}=4.128 exp(-d/76.639)+1.405\\ E_{shear}=0.449 exp(-d/74.657)+0.198\\ \tau_{r}=2.114 exp(-d/175.356)+0.126\end{array}\right. \tag{1}\]  
\[2\;\text{MPa}\left\{\begin{array}{l}\tau_{p}=8.331 exp(-d/70.807)+1.857\\ E_{shear}=1.829 exp(-d/34.974)+0.220\\ \tau_{r}=3.197 exp(-d/273.597)-0.286\end{array}\right. \tag{2}\]  
\[4\;\text{MPa}\left\{\begin{array}{l}\tau_{p}=9.213 exp(-d/59.403)+2.874\\ E_{shear}=0.389 exp(-d/729.927)\\ \tau_{r}=6.377 exp(-d/544.967)-1.981\end{array}\right. \tag{3}\]  
Here, \(\tau_{p}\), \(E_{shear}\), \(\tau_{r}\), and \(d\) are the shear peak strength (MPa), shear elastic modulus (GPa), residual strength (MPa), and sample size (mm), respectively.  
As the sample size exceeds 350 mm, the variation in the shear parameter values becomes minor with further increases in sample size. Consequently, for the band-bedrock interface under investigation in this study, under the given stress conditions and step height-to-width ratio, the representative elementary volume (REV) for the shear parameters is determined as a sample with a geometry size of 350 mm.  
Figure 13: Cont.