## 1 Introduction  
With the rapid development of mining technology, blasting operations have gradually been widely applied in the development of different types of mineral resources, especially in open-pit mining projects [1]. With the continuous increase of mining output of open-pit mines, the mining area has gradually formed deep pits, and the exposed final slope is also getting higher and steeper, bringing more and more safety problems [2, 3], which makes the safety of rock slopes a topic of great concern in the field of geotechnical engineering. The vibration effects generated by blasting loads can seriously affect the stability of rock slopes [4; 5; 6], leading to local cracking and landslides [7]. In order to achieve reasonable and controllable engineering blasting, studying the dynamic response law of slope blasting is of great value in promoting and guiding engineering safety production [8]. Domestic and foreign scholars have conducted extensive research on the dynamic response laws of rock slopes under blasting loads, and one important research method is to study their propagation laws in rock masses through blasting vibration data obtained from on-site monitoring [9; 10]. Under the action of blasting vibrations or other dynamic loads, when the vibration wave propagates to the slope, due to the combined effect of slope geometry, material properties, and structural characteristics, the vibration intensity in the slope area is significantly increased compared to flat or other areas, which is called the slope amplification effect. This effect significantly increases the instability and risk of slope failure. The dynamic amplification effect of slopes is influenced by various factors. [PERSON] et al. [11] explored the dynamic response law of rock slopes by analyzing the changes in peak acceleration, and believed that the joints, lithology, and seismic parameters of slopes can cause slope amplification effects. [PERSON] et al. [12] summarized a large amount of blasting monitoring data and concluded that the attenuation law of high slope vibration velocity and the elevation amplification effect exist. [PERSON] et al. [13] analyzed the influence of wave incidence direction on slope motion and found that soft materials strongly enhance the amplification of acceleration. [PERSON] et al. [14] analyzed the influence of frequency and joint density on the dynamic amplification effect of jointed rock slopes and believed that the propagation of high-frequency waves in slopes would be more significantly affected by joints, making the peak acceleration changes on the slope surface more chaotic. [PERSON] et al. [15] studied the dynamic response characteristics and cumulative damage evolution of jointed slopes under continuous seismic action and analyzed the influence of different joint types on the dynamic amplification effect and failure mode of slopes. [PERSON] et al. [16] proposed a model to verify that the amplification and attenuation of earthquake motion are influenced by the terrain and water depth, and slope height also amplifies the intensity of the blasting vibration. The vibration intensity caused by blasting is closely related to the lithology and structural characteristics of the rock mass [17]. The development and heterogeneity of rock joints are important factors for predicting and controlling blasting vibrations in open-pit mining. Due to the long-term effects of natural accumulation and artificial excavation and filling, the rock and soil types and properties of slopes may undergo significant changes in a short distance, and their soil strength parameters may exhibit a certain heterogeneity. Therefore, considering the heterogeneous characteristics of layered rock masses has important theoretical and practical significance for studying slope stability [18]. In 1975, [PERSON] [19] assumed a linear distribution of soil cohesion along the depth direction and used limit analysis methods to study the stability of two-dimensional heterogeneous slopes.