## 6 Conclusions  
This paper proposes a method for modeling heterogeneous layered slopes. Utilizing the ubiquitous-joint model, slopes with different joint dip angles ranging from 0\({}^{\circ}\) to 90\({}^{\circ}\) were established. The Weibull random distribution function was introduced to characterize the heterogeneity of the rock mass, enabling spatially random distributions of the elastic  
Figure 21: Variation pattern of dynamic safety factor for heterogeneous slopes. Figure 22: Variation pattern of reduction rate of safety factor for heterogeneous slopes. modulus, cohesion, and friction angle. Based on the Sijiaying Yanshan Open-Pit Iron Mine project, the following conclusions were obtained through numerical simulation research:  
(1) The PGA on the slope surface is generally greater than that inside the slope, and the PGA on soft rock slopes is generally greater than on hard rock slopes. For the 45\({}^{\circ}\) and 60\({}^{\circ}\) scenarios, the PGA is generally greater than for the 0\({}^{\circ}\) scenario. The maximum PGA on the slope surface generally decreases first, then increases with an increasing elevation, and then decreases again, reaching the maximum value at the slope crest. The maximum PGA inside the slope generally increases first and then decreases with an increasing elevation, reaching the minimum value at the slope top. Under the action of blasting vibration waves, jointed slopes exhibit elevation amplification effects, and within a certain range, blasting vibration waves attenuate with an increasing distance from the blast center. Both the slope surface and the inside of the slope experience joint amplification effects. The elevation amplification effect is greater for soft rock than for hard rock, and the joint amplification effect is greater for the 45\({}^{\circ}\) and 60\({}^{\circ}\) scenarios than for the 0\({}^{\circ}\) scenario. (2) The PGA of the slope is most sensitive to changes in the elastic modulus, followed by sensitivity to cohesion and the friction angle, with the sensitivity to both being relatively similar. As the shape parameter \(\beta\) increases, the sensitivity of the PGA to changes in all three parameters decreases. The PGA for each scenario generally decreases with an increasing heterogeneity parameter. The higher the heterogeneity of the rock mass, the more pronounced the slope surface and elevation amplification effects. Under the same physical mechanical parameters of the rock mass, the amplification coefficient of slopes with joint dip angles is generally greater than that of homogeneous slopes, indicating that structural distribution has a stronger influence on slope amplification effects than rock mass heterogeneity. (3) Under the action of blasting loads, the dynamic time-history safety coefficients of jointed slopes and heterogeneous slopes generally exhibit a trend of first decreasing and then increasing, with the safety coefficient reaching its minimum value at the peak of the 0.2 s blasting vibration wave. The dynamic safety coefficient of slopes with 0\({}^{\circ}\) joint dip angles is generally greater than that of slopes with 60\({}^{\circ}\) and 45\({}^{\circ}\) joint dip angles. For heterogeneous slopes, those with larger shape parameters generally have higher overall safety coefficients compared to those with smaller shape parameters. In numerical analysis, placing the force too close to one of the boundaries can cause interference with the propagation of the blasting vibration wave, which may result in poor or severely distorted numerical analysis results. The position of the applied force in the numerical simulation of this article is set according to the real mining situation. Since the monitoring points are not located on the side close to the boundary, current research has not considered the influence of the distance between the closer boundaries on the applied point. This issue will be the focus of our future research. Conceptualization, Y.Z. and T.Y. ; methodology, Y.L. and S.J. ; software, Y.L. and S.J. ; validation, W.D. and S.W.