## 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
The maximum PGA values for slopes with different joint angles are as follows: 60\({}^{\circ}\) \(>\) 45\({}^{\circ}\) \(>\) 75\({}^{\circ}\) \(>\) 30\({}^{\circ}\) \(>\) 15\({}^{\circ}\) \(>\) 90\({}^{\circ}\) \(>\) 0\({}^{\circ}\) \(>\) without joints. Specifically, the maximum PGA value for slopes with a joint angle of 60\({}^{\circ}\) is 0.59 cm/s\({}^{2}\), while for slopes with a joint angle of 0\({}^{\circ}\), it is 0.37 cm/s\({}^{2}\). From this, it can be inferred that for slopes composed of both soft and hard rocks with various joint angles, the PGA of blasting vibration waves fluctuates along the slope surface with elevation. Overall, the PGA of soft rocks is significantly greater than that of hard rocks. The PGA values of slopes with different rock types and joint angles, as well as those without joints, exhibit fluctuations along the elevation, showing a trend of initially decreasing, then increasing, and finally decreasing again. The maximum PGA values are typically observed at heights ranging from half to four-fifths of the slope height. This indicates that the PGA on the slope surface does not continuously increase with elevation but rather fluctuates within a certain range as elevation increases. The decrease in PGA at the slope base is due to the attenuation effect of the blasting vibration waves moving away from the blast center. The increase near the slope shoulder reflects the amplification effect of the joints and the slope surface on the PGA. The decrease at the slope crest indicates energy dissipation during wave propagation, resulting in another attenuation effect. For slopes with different joint angles, their PGA values on the slope surface are generally greater than those of slopes without joints. This is attributed to the multiple refraction and reflection effects of the blasting vibration waves within the joints, leading to a superposition effect of the blasting vibration waves. Consequently, local amplification of the blasting vibration waves occurs, resulting in the slope surface PGA of jointed slopes being greater than that of slopes without joints. Among these, slopes with joint angles such as 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\) induce more refraction and reflection of the blasting vibration waves compared to slopes with joint angles of 0\({}^{\circ}\) and 90\({}^{\circ}\), hence their higher slope surface PGA values. From Figure 9b, it is observed that within the soft rock slope, the overall trend of the PGA with an increasing elevation follows a pattern of initial increase followed by a decrease, with greater fluctuation. The maximum PGA values tend to occur at relative elevations between 0.4 and 0.6. Overall, there is a noticeable decrease in the fluctuation of the PGA. The maximum PGA values for each joint angle slope are in the order of 60\({}^{\circ}\) \(>\) 45\({}^{\circ}\) \(>\) 75\({}^{\circ}\) \(>\) 30\({}^{\circ}\) \(>\) 15\({}^{\circ}\) \(>\) 90\({}^{\circ}\) \(>\) 0\({}^{\circ}\) \(>\) without joints, with the maximum PGA value for a 60\({}^{\circ}\) joint angle being 0.45 cm/s\({}^{2}\), and for a 0\({}^{\circ}\) joint angle being 0.31 cm/s\({}^{2}\). From Figure 10b, it is evident that within the hard rock slope, the overall trend of the PGA with an increasing elevation follows a pattern of initial increase followed by a decrease, with greater fluctuation. The maximum PGA values tend to occur at relative elevations between 0.2 and 0.4. Additionally, in the hard rock slope, the decrease in PGA above relative elevation 0.5 is more pronounced compared to the soft rock slope. The maximum PGA values for each joint angle slope are in the order of 45\({}^{\circ}\) \(>\) 60\({}^{\circ}\) \(>\) 30\({}^{\circ}\) \(>\) 75\({}^{\circ}\) \(>\) 15\({}^{\circ}\) \(>\) 90\({}^{\circ}\) \(>\) 0\({}^{\circ}\) \(>\) without joints, with the maximum PGA value for a 45\({}^{\circ}\) joint angle being 0.38 cm/s\({}^{2}\), and for a 0\({}^{\circ}\) joint angle being 0.24 cm/s\({}^{2}\).