## 5 Analysis of the Dynamic Response Law of Non-Homogeneous Slopes
### Dynamic Response Analysis of Non-Homogeneous Slopes
#### 5.2.1 Variable Sensitivity Analysis  
To investigate the influence of individual variables including the elastic modulus \(E\), cohesion \(C\), and friction angle \(\phi\) under Weibull distribution conditions on the dynamic response to a blasting vibration, different scenarios were established for each parameter by varying the shape parameters \(\beta=1\) and \(\beta=9\). A control group with homogeneous slope conditions (without a random distribution) was also set up for comparison. The rock mechanics parameters used in the case of homogeneous slope conditions are shown in Table 3. Subsequently, numerical simulations of blasting dynamics were conducted. Figure 15(a),b depict the variations of PGA with elevation for the slope surface and slope interior, respectively, under a random distribution of the shape parameter \(\beta=1\) for the elastic modulus, cohesion, and friction angle. A reference condition without parameter variations is included for comparison. Figure 16(a),b show the variations of PGA with elevation for the slope surface and slope interior, respectively, under a random distribution of the shape parameter \(\beta=9\) for the elastic modulus, cohesion, and friction angle. A reference condition without parameter variations is included for comparison. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Natural Unit** & **Elastic** & **Poisson’s** & **Friction** & **Cohesion** & **Tensile** \\
**Weight** & **Modulus** & **Ratio** & **Angle** & **(MPa)** & **Strength** \\
**(kN/m3)** & **(GPa)** & **Ratio** & **(\({}^{\circ}\))** & **(MPa)** & **(MPa)** \\ \hline
2400 & 15.0 & 0.28 & 44 & 2.3 & 2.7 \\ \hline \end{tabular}
\end{table} 
Table 3: Physical and mechanical parameters of rock mass. Figure 15: Random distribution map of different parameters of \(\beta=9\). (**a**) Elastic modulus; (**b**) cohesion; (**c**) friction angle. As shown in Figures 16a and 17a, for the slope surface, when the shape parameter \(\beta=1\), the PGA under variations in elastic modulus conditions is significantly lower than the reference condition, as well as variations in cohesion and friction angle conditions, between relative elevations of 0 to 0.4. However, between relative elevations of 0.4 to 1.0, it surpasses the reference condition. Although the PGA variation range is smaller compared to other conditions, the difference in PGA values from the reference condition is greater than those under cohesion and friction angle conditions overall. Similarly, for the slope surface, when the shape parameter \(\beta=9\), the PGA under variations in elastic modulus conditions is lower near the slope toe than the reference condition, and higher near the slope crest. The PGA variation range is also smaller compared to other conditions. Between relative elevations of 0.3 to 1.0, the difference in PGA values from the reference condition increases, but the overall trend in PGA changes remains relatively consistent with the reference condition. As shown in Figures 16a and 17a, for the slope surface, when the shape parameter \(\beta=1\), the PGA values under variations in cohesion and friction angle conditions are generally greater than those under the reference condition (no variations), slightly smaller  
Figure 16: PGA variation in \(\beta=1\) slope. (**a**) Slope surface; (**b**) slope interior. Figure 17: PGA variation in \(\beta=9\) slope. (**a**) Slope surface; (**b**) slope interior. near the slope surface, and exhibit significant fluctuations compared to the reference condition between relative elevations of 0.5 to 1.0. Similarly, for the slope surface, when the shape parameter \(\beta=9\), the PGA values under variations in cohesion and friction angle conditions remain generally greater than the reference condition. However, the overall trends in PGA changes between the two conditions remain consistent with the reference condition. Significant differences in PGA values are observed near the slope toe (at a relative elevation of 0.2) and near the slope crest (at a relative elevation of 0.8) compared to the reference condition.