Abstract:
In the excavation of high-steep slopes, deep-hole bench blasting is a widely adopted technique. To mitigate the hazards of blasting vibration on slope stability and the surrounding environment, the use of electronic detonators for hole-by-hole millisecond initiation has become a critical process. However, under this initiation mode, stress waves generated from sequentially detonated blast holes, due to millisecond delays, undergo complex temporal and spatial superposition and interference. This complexity makes it difficult to define the maximum charge per delay—a core parameter in the traditional Sadovsky formula for blasting vibration prediction—thereby severely compromising the accuracy of peak particle velocity (PPV) forecasting and attenuation law analysis. To address this challenge, this paper proposes a systematic method for calculating the equivalent charge per delay and an analytical framework for vibration attenuation specifically tailored to electronic detonator hole-by-hole millisecond blasting conditions. The methodology begins with specialized single-hole blasting tests at the target site to accurately collect vibration waveform data. This data is used for regression analysis to calibrate the fundamental attenuation parameters of the Sadovsky formula, which reflect the local lithology and topographic characteristics. Subsequently, the overall vibration effect of a multi-hole, hole-by-hole blast is conceptually transformed into a virtual single-hole blasting problem. This virtual blast originates from a weighted average blast center and is characterized by a specific charge. Through nonlinear fitting algorithms, the global site coefficient and the unique equivalent charge per delay for that specific blast event are simultaneously derived. To verify the physical rationality of this equivalent charge, this study further introduces the Hilbert-Huang Transform (HHT) time-frequency analysis method. By calculating the instantaneous energy distribution of the vibration waveform, the method identifies the actual number of blast holes contributing to energy superposition during the main vibration period. This yields an energy-peak-based equivalent charge, enabling mutual verification from both waveform fitting and energy mechanism perspectives. To validate the reliability and universality of the proposed method, field tests were conducted on the high-steep slope excavation project at the Chongqing Wujiang Baima Navigation-Power Junction. Blasting schemes with varying hole numbers and scales were designed. The results demonstrate that the vibration attenuation model, fitted based on the equivalent blast source and fixed attenuation parameters, shows good applicability for hole-by-hole millisecond blasts of different scales, ranging from as small as 7 holes to as large as 152 holes. The goodness-of-fit (R2) between predicted curves and measured data exceeded 0.85, and the average prediction error was controlled within 20%, meeting engineering accuracy requirements. Verification via the energy peak method showed a high degree of agreement between its calculated equivalent charge and the model-fitted value, physically confirming the model's validity. Furthermore, comparative analysis of blasting effects under different inter-hole delays (10 ms, 15 ms, 20 ms, 35 ms) clearly revealed the significant influence of delay parameters on the equivalent charge and vibration reduction effectiveness. Under the specific geological conditions of this project, an inter-hole delay of 20 ms resulted in the minimum equivalent charge and the optimal vibration reduction effect. This study provides a theoretical basis and practical reference for vibration law analysis and delay parameter optimization in electronic detonator hole-by-hole millisecond blasting.