## 1 Introduction
The results indicate that the enhancement of soil heterogeneity will lead to a decrease in slope stability. The discontinuity inside the rock mass makes the influencing factors of the blasting vibration more complex [20; 21], which also makes layered rock slopes [22] and jointed slopes [8] the focus of scholars' research. The layered rock mass is a common type of rock mass in the field of geotechnical engineering, and its physical and mechanical properties and mineral composition vary greatly in the direction perpendicular to the joint surface. Under the cutting of joint surfaces, the mechanical properties of rocks and rock masses in slopes are significantly weakened, making them more susceptible to tensile, shear, tilting, and other destructive and unstable deformations under the influence of blasting vibrations [23], resulting in serious geological disasters [24]. Therefore, compared with ordinary rock slopes, layered jointed slopes have different dynamic responses under explosive loads due to their special geological structure [25]. [PERSON] and [PERSON] [26]conducted laboratory tests on intact and discontinuous rock samples to study the strength degradation of discontinuous rock masses and believed that this is the main reason why jointed rock masses are more susceptible to damage under blasting. [PERSON] et al. [27] studied the frequency band characteristics of blasting vibrations in jointed rock masses and high slopes using wavelet transform and response spectrum methods to control and predict particle vibrations in rock masses with joints and high slopes. In recent years, computer technology has developed rapidly, and numerical simulation technology has gradually been widely applied to the stability analysis of rock slopes under blasting vibration. Existing research typically uses methods such as the finite element method, discrete element method, and analysis to simulate the dynamic behavior of slopes [28; 29; 30]. With the emergence of artificial intelligence and machine learning, these advanced computing technologies, hybrid artificial intelligence models, big data methods, and simulation software have provided a new approach for intelligent research on slope stability, and significant progress has been made in slope stability analysis [31; 32]. The above studies have made many contributions to the propagation law of blasting vibration waves and blasting vibration control methods in jointed rock masses, but there is still insufficient research on the wave propagation mechanism and dynamic response analysis of heterogeneous layered rock slopes with different joint angles under a blasting vibration. In view of this, this article introduces the Weibull random distribution method of the heterogeneous slope model, establishes a joint based layered rock slope model, and studies the propagation characteristics and dynamic response laws of blasting vibration waves on slopes with different joint angles and inhomogeneity based on the investigation of the Sijiaying Yanshan Open-Pit Iron Mine project. This provides a basis for solving the formation mechanism and evolution process of blasting-vibration-type geological disasters and provides theoretical reference for the prevention of dynamic instability disasters of heterogeneous layered slopes under blasting operation conditions, as well as the stability and instability mechanism analysis of slopes during blasting excavation construction.