## 5 Joint Rock Slope Stability Analysis Using the FLAC3D Model  
There is a joint plane in the analyzed rock slope. For this joint, a low-strength elastic-plastic sandwich element is used to simulate the joint structure, and the joint inclination angle is 45\({}^{\circ}\), with a thickness of 0.1 m. The rock mass outside the joints is still considered a homogeneous body. Table 3 summarizes the material properties of the joint rock slope.  
The specific dimensions parameters of the slope are shown in Figure 11. The RHINO-FLAC3D interface program was used to establish calculations based on the slope model, and this model has a total of over 4048 units. The lower part of the boundary is fixed, the left and right sides are horizontally constrained, and the upper part is a free boundary. Figures 12-14 show different modes of contour displacement--horizontal, vertical, and total--are compared across these monitored points (points 1, 2, 3, 4, and 5).  
Figure 10: Correlation coefficients for total displacement of soil slope.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **Density (\(\rho\))** & **Young’s Modulus (E)** & **Poisson’s Ratio (v)** & **Cohesion (c)** & **Friction Angle (\(\varphi\))** \\ \hline Layer & 29 kN/m3 & 12 GPa & 0.35 & 600 kPa & 37\({}^{\circ}\) \\ Joint & 21.5 kN/m3 & 12 MPa & 0.40 & 12 kPa & 20\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Material properties of the rock.  
Figure 11: The slope model of the joint rock slope.  
Figure 12: Location of monitoring points (contour of horizontal displacement) of the joint rock slope.  
Figure 13: Location of monitoring points (contour of vertical displacement) of the joint rock slope.  
While the rock and soil slopes have similar contents that are only different in numerical value, the rock has a partly jointed surface, with other parts homogeneous, while the entire soil slope is homogeneous. However, key findings from the soil analysis remain applicable to the jointed rock case. In particular, for both models, monitoring points located outside potential failure surfaces exhibit minimal displacement variations even as stability decreases. This suggests that such points cannot provide advance warning of impending failures. Therefore, the analysis focuses on locations near expected failure zones. However, the presence of joints as persistent weaknesses means that discontinuities have a dominant influence on slope stability. Therefore, the characterization of deformations requires explicit examination of measurements along joint planes, as they may activate prior to global failures. Accordingly, monitoring points were selected at upper, middle, and lower positions along the prominent joint of the slope to profile local variations. For comparison, additional points were monitored away from joints on the slope surface itself. This targeted coverage, along with expected weaknesses, aims to relate measured displacements to stability reductions, given the central role of joints in rock slope evaluation. By distinguishing the behavior of jointed rock while retaining key insights from the homogeneous case, the analysis achieves localized insights into rock mass kinematics while enabling site-specific remediation. Figures 12-14 display the horizontal, vertical, and total displacement contours.