## 5 Conclusions  
(1) The error range between the simulated and measured values of blasting vibration velocity is 0.59 to 0.86 cm/s, with a relative error range of 7.75% to 9.85%. The relative error of the vibration velocity is less than 10%, validating the feasibility and accuracy of using the FEM-SPH algorithm for simulating blasting vibration velocity in engineering projects.  
(2) The vibration velocity generated by the blasting is significantly influenced by the ground stress, particularly in areas that are farther from the blast center, where the effect  
Figure 11: Displacement history curve of various measurement points under in situ stress of 1 MPa and 5 MPa.  
of ground stress on the vibration velocity becomes more pronounced. Under the 5 MPa ground stress condition, the maximum vibration velocity at each measurement point is noticeably higher compared to the 1 MPa condition. When the measurement points are located within 10 to 20 m of the blast center, the vibration velocity exhibits noticeable fluctuations due to the blast impact. Beyond a distance of 25 m from the blast center, the attenuation of the vibration velocity becomes more gradual.  
(3) For the vibration velocities obtained from numerical simulations at various measurement points, we employed the [PERSON]'s formula for fitting, yielding correlation coefficients ranging from 0.92 to 0.97. These relatively high correlation coefficients confirm the feasibility of using the FEM-SPH algorithm for numerical simulations of blasting models and studying the propagation patterns of blasting-induced vibration velocities. Consequently, it is possible to quickly predict on-site blasting vibration velocities based on simulation results.  
(4) The intensity of stress waves is influenced by the in situ stress, with higher in situ stress conditions resulting in greater stress wave intensities than lower in situ stress conditions. Within a range of 0 to 25 m from the explosion center, the stress waves exhibit significant variations, but beyond 25 m, the rate of intensity decay of the stress waves slows down. The stress waves do not exhibit a single decay trend as the propagation distance increases, and when the propagation path changes, the numerical values of stress waves may increase.  
Z.L.: Provision of ideas and methods. Z.C.: Editing and modification. Y.S.: Data processing. Y.L.: Investigation. Y.H.: Project administration. Z.Z.: Optimization of image tables and Supervision. All authors have read and agreed to the published version of the manuscript.  
The research received financial support from the National Natural Science Foundation of China (Grant No. 52164009 and 52164010), as well as from the Major Science and Technology Special Project of Yunnan Province (Grant No. 202202 AG050014).  
Not applicable.  
Some or all data that support the findings of this study are available from the corresponding author upon reasonable request.  
Author [PERSON] was employed by the company Yunnan Diqing Nonferrous Metals Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.