## 4 Analysis of the Dynamic Response Law of Layered Slopes
### Dynamic Response Analysis of Slopes Characterized by Laminated Joints  
#### 4.2.1 Characterization of Blast Wave Propagation on Different Joint Dip Slopes  
Some studies suggest that peak particle velocity, acceleration, and displacement are considered reliable vibration monitoring parameters [38]. By analyzing the variation of the Peak Ground Acceleration (PGA, measured in cm/s\({}^{2}\)) at various monitoring points on the slope, we can study the characteristics of the propagation of the blasting vibration waves in rocky jointed slopes. The generalized model and layout of monitoring points for the typical profile obtained from the survey in the study area, as shown in Figure 7, are established as the research objects, with the monitoring point distribution depicted in Figure 8. The red circles in Figure 7 represent the monitoring points on the slope surface, and the blue circles represent the monitoring points inside the slope. Table 2 provides the coordinates of each monitoring point. Figures 8a and 8b, respectively, illustrate the variation of PGA at different monitoring points on slopes without joints and with joint angles of 0\({}^{\circ}\), 15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), 75\({}^{\circ}\), and 90\({}^{\circ}\), where the corresponding rock mass mechanical parameters decrease from the bottom to the top of the slope, indicating a decrease in rock hardness from the toe to the crest of the slope. As shown in Figure 8a, the overall trend of the PGA at the slope surface fluctuates with elevation, exhibiting a pattern of initial decrease, followed by increase, and then decrease again. The PGA values on slopes with joint angles of 45\({}^{\circ}\) and 60\({}^{\circ}\) are generally greater than those of 0\({}^{\circ}\) or without joints, with the maximum PGA often occurring at relative elevations between 0.5 and 0.6. As depicted in Figure 8b, the PGA within the slopes generally exhibits an initial increase followed by a decrease with elevation. The PGA values on slopes with joint angles  
Figure 8: Changes in PGA of multiple lithological models. (**a**) Slope surface; (**b**) slope interior. of 45\({}^{\circ}\) and 60\({}^{\circ}\) are generally greater than those of 0\({}^{\circ}\) or without joints, with the maximum PGA often occurring at relative elevations between 0.3 and 0.4. Figures 9a and 9b, respectively, depict the variation of PGA with elevation for the slope surface and internal monitoring points of the soft rock model (No.1) without joints and with joint angles of 0\({}^{\circ}\), 15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), 75\({}^{\circ}\), and 90\({}^{\circ}\). Figure 10a,b illustrate the variation of PGA with elevation for the hard rock model (No.12). From Figure 9a, it can be observed that for the soft rock slope surfaces, both slopes with and without joints exhibit an overall pattern of the PGA initially decreasing, then increasing, and finally decreasing with an increasing elevation. The maximum PGA values mostly occur at relative elevations ranging from 0.5 to 0.7. The maximum PGA values for slopes with different joint angles are as follows: 45\({}^{\circ}\) > 60\({}^{\circ}\) > 30\({}^{\circ}\) > 75\({}^{\circ}\) > 15\({}^{\circ}\) > 90\({}^{\circ}\) > 0\({}^{\circ}\) > without joints. Specifically, the maximum PGA value for slopes with a joint angle of 45\({}^{\circ}\) is 0.71 cm/s\({}^{2}\), while for slopes without joints, it is 0.27 cm/s\({}^{2}\). From Figure 10a, it is evident that for hard rock slope surfaces, both slopes with and without joints exhibit overall fluctuations in PGA with an increasing elevation. They demonstrate a trend of initially decreasing, then increasing, and finally decreasing PGA  
Figure 10: Changes in PGA of hard rock slope. (**a**) Slope surface; (**b**) slope interior. Figure 9: Changes in PGA of soft rock slope. (**a**) Slope surface; (**b**) slope interior. values, with the maximum PGA values mostly occurring at relative elevations ranging from 0.4 to 0.7.