## 5 Detailed Analysis of Rock Mass Discontinuity Distribution in Different Rock Layers  
To analyze the differences in discontinuity orientations among different rock layers, a detailed analysis was conducted on the left part of the selected layered slope surface. This analyzed surface primarily includes green mudstone, brown shale, and marlstone (as shown in Figure 9). The rock discontinuity information was identified and extracted from high-resolution images collected on-site using MATLAB (v.2020a) software, including the trace length, dip angle, and orientation of the rock discontinuities. A total of 259 rock discontinuities were obtained for the green mudstone, 237 for the brown shale and 214 for the mudstone in the studied surface.  
To avoid potential discrepancies between the collected images and the actual conditions, the rock discontinuity information identified by the MATLAB program was compared and calibrated with the field data. The distribution of the trace length, dip angle, and orientation of the calibrated discontinuities in marlstone, green mudstone, and brown shale are shown in Figure 10. As can be seen from Figure 10, the rock discontinuities within the marlstone and brown shale are smaller in scale and more densely distributed compared to those within the green mudstone. Statistical analysis reveals that the proportion of trace lengths in the marlstone and brown shale is similar. The proportion decreases as the trace length increases, and the proportion of small-scale rock discontinuities (i.e., 0-12 cm) is significantly higher in the marlstone and brown shale compared to the green mudstone, indicating a higher degree of fracturing in the marlstone and brown shale layers, which increases the possibility of small rock falls.  
Figure 8: Isodensity contour of the poles of discontinuity.  
Figure 10: Statistical results of the rock discontinuity information in different rock layers. (**a**) The distribution of the trace length. (**b**) The distribution of the dip angle. (**c**) The distribution of the orientation angle.  
Figure 9: Distribution of the rock layer on the selected slope surface [6].  
Figure 10b shows the distribution of dip angles for the rock discontinuities in marlstone, green mudstone, and brown shale. The dip angles of discontinuities in marlstone and green mudstone primarily range from 54\({}^{\circ}\) to 63\({}^{\circ}\), whereas the dip angle distribution in brown shale is more uniform. The proportion of dip angles in the marlstone and green mudstone increases with the angle, and the proportions are notably higher than that in the brown shale for the larger angles (i.e., 54-63\({}^{\circ}\)). Additionally, to analyze the distribution characteristics of rock discontinuity orientations in different rock layers, the orientation angles (defined as the angle between the structural plane trace and the \(x\)-axis in the horizontal direction, ranging from 0\({}^{\circ}\) to 180\({}^{\circ}\), distinct from the dip angle mentioned above) were statistically quantified. Figure 10c presents the distribution of orientation angles in marlstone, green mudstone, and brown shale. It was found that the orientation angles in marlstone and green mudstone are primarily concentrated between 54\({}^{\circ}\) and 90\({}^{\circ}\), with a significantly higher proportion compared to brown shale. The brown shale contains numerous smaller orientation angles.