## 1 Introduction  
With the increasing occurrence of rock slopes in blasting projects across fields such as transportation, mining, and hydraulic engineering, incidents of instability--such as collapse and sliding--under blasting vibrations have become more frequent. Ensuring the safety and stability of rock slopes subjected to blasting vibrations has become critical for the safe and efficient progress of these projects. Previous studies have shown that when the dip angle of the bedding plane aligns with the slope angle, the stability of rock slopes is generally poor, especially under the disturbance of blasting vibrations [1]. To ensure the stability and safety of rock slopes with weak interlayers under blasting vibrations, it is essential to understand the attenuation patterns of blasting vibrations within these slopes. Currently, the attenuation pattern of blasting vibrations is commonly described by the peak particle velocity (PPV). As early as the 1940s, Soviet blasting expert [PERSON] derived the traditional Sadowsky formula through extensive monitoring data while studying the seismic effects of concentrated explosives [2]. Subsequently, various countries adapted the traditional Sadowsky formula with different parameters [3; 4; 5]. This is a semi-empirical formula that calculates the decay law of blast vibration velocity, describing the relationship between peak mass vibration velocity, blast charge and distance from the blast center [6; 7]. With continued application of these equations, an increasing number of scholars have recognized the need to modify and improve them to account for different engineering geological conditions. For instance, in tunnel engineering, the area of the tunnel's free face has a significant effect on blasting vibrations. Therefore, incorporating the influence of the free face area into the blasting vibration attenuation prediction model and modifying the prediction formula for vibration velocity can greatly improve prediction accuracy [8]. [PERSON] proposed a blasting vibration attenuation prediction model that considers delay time, among other improvements [9]. In slope engineering, the traditional Sadowsky formula can produce significant errors due to the effects of elevation and terrain, necessitating parameter adjustments [10; 11]. Additionally, most researchers study the propagation patterns of blasting vibrations by combining field monitoring data with numerical simulations [12; 13; 14; 15]. Based on the slope's dynamic response features, as observed in the field monitoring data, a logarithmic functional relationship was discovered between the number of loading times and the slope's safety factor under various loading amplitudes [16; 17]. Using LS-DYNA(R9,2,0) numerical simulation software, [PERSON] examined the effects of various blasting techniques on the stability of rock slopes and optimized the blasting and excavation procedures' parameters [18]. [PERSON] found during on-site monitoring that as the degree of jointing increased, the attenuation rate of both vibration velocity and the energy of blasting vibrations also increased. This indicates that rock mass structural parameters (such as discontinuities) significantly influence the attenuation laws of blasting vibrations [19]. [PERSON] monitored the blasting vibrations at the Manaoke open-pit gold mine slope, and conducted regression analysis of the monitoring results using the Sadowsky formula. The study examined the attenuation law of slope-blasting vibrations. Additionally, the relationship between rock mass damage depth and peak particle velocity was analyzed using ultrasonic velocity measurement, and the stability of the slope under blasting vibration conditions was assessed with finite element numerical software [20]. [PERSON] analyzed the open-pit slope of Daye Iron Mine and used the dynamic finite element method in conjunction with on-site monitoring data to establish a PPV prediction model that took into account the mining depth and the elevation difference between the explosion source and the monitoring point [21].