Modified Sadowski formula-based model for the slope shape amplification effect under multistage slope blasting vibration

Blasting operations, which are crucial to open-pit mine production due to their simplicity and efficiency, require precise control through accurate vibration velocity calculations. The conventional Sadowski formula mainly focuses on blast center distance but neglects the amplification effect of blasting vibration waves by terraced terrain, from which the calculated blasting vibration velocities are smaller than the actual values, affecting the safety of the project. To address this issue, our model introduces the influences of slope and time into Sadowski formula to measure safety through blast vibration displacement. In the northern section of the open-pit quartz mine in Jinchang City, Gansu Province, China, the data of a continuous blasting slope project are referred to. Our findings reveal a noticeable vibration amplification effect during blasting when a multi-stage slope platform undergoes a sudden cross-sectional change near the upper overhanging surface. The amplification vibration coefficient increases with height, while vibration waves within rocks decrease from bottom to top. Conversely, platforms without distinct cross-sectional changes exhibit no pronounced amplification during blasting. In addition, the vibration intensity decreases with distance as the rock height difference change propagates. The results obtained by the proposed blast vibration displacement equation incorporating slope shape influence closely agree with real-world scenarios. According to Pearson correlation coefficient (PPMCC) analysis, the average accuracy rate of our model is 88.84%, which exceeds the conventional Sadowski formula (46.92%).