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<p>To create effective free surfaces and throw space for subsequent blast holes, achieve adequate rock fragmentation, ensure vibration safety, and reduce overall engineering costs in multi-hole blasting, it is essential to understand the throwing dynamics of deep-hole bench blasting. Based on this, the present study is conducted following the technical route outlined below: First, based on the geometric position of the muckpile and ballistic equations, analytical expressions for the throwing velocity and trajectory during the inertial motion phase of the rock mass were derived through inverse deduction. Second, the variable-speed phase was simplified as uniform acceleration motion, and based on kinematic equations, a velocity gradient function and a displacement analytical model for this stage were established. Third, by combining the equivalent charge principle and the blasting crater theory, a prismatic throwing volume model with a top surface area greater than the bottom area was constructed, and the energy analytical expression was derived using the velocity formula. To validate the theoretical results, a single-hole bench blasting numerical model was established using the SPH-FEM coupling algorithm. Meanwhile, high-speed photography and unmanned air vehicle(UAV) photogrammetry technologies were applied to obtain field test data on the rock throwing motion. The theoretical formulas were jointly validated in terms of their accuracy, robustness, and engineering applicability. The research results show that: (1) The proposed frustum-shaped volume model agrees well with numerical simulations and field test results. (2) The motion trajectory during the initial acceleration phase is relatively straight and can be approximated as a uniformly accelerated process; when the rock throwing velocity reaches its first peak, the initial acceleration phase ends, and inertial throwing begins. (3) During the inertial throwing phase, the throwing height of rock fragments decreases progressively from top to bottom, while the throwing distance shows the opposite trend; fluctuations in throwing trajectory and velocity are caused by secondary fragmentation and inter-particle collisions, but the overall results are consistent with the theoretical model. (4) By comparing the average initial throw velocities from numerical simulation, the theoretical model, the traditional empirical formula, and field experiments, the corresponding mean errors were 3.81%, 9.27%, and 51.23%, respectively; (5)The throwing energy accounts for 5.07% of the total explosion energy.</p>

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Analysis of Rock Mass Throwing Behavior and Energy Characteristics in Open-pit Deep-hole Bench Blasting

  • 期刊论文

  • 发表日期：

    2025年11月12日

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  • Xiaoming Lou,
  • Wei Liang,
  • Xiaofeng Huo,
  • Shuyi Xiao,
  • Wang Guodin

摘要

To create effective free surfaces and throw space for subsequent blast holes, achieve adequate rock fragmentation, ensure vibration safety, and reduce overall engineering costs in multi-hole blasting, it is essential to understand the throwing dynamics of deep-hole bench blasting. Based on this, the present study is conducted following the technical route outlined below: First, based on the geometric position of the muckpile and ballistic equations, analytical expressions for the throwing velocity and trajectory during the inertial motion phase of the rock mass were derived through inverse deduction. Second, the variable-speed phase was simplified as uniform acceleration motion, and based on kinematic equations, a velocity gradient function and a displacement analytical model for this stage were established. Third, by combining the equivalent charge principle and the blasting crater theory, a prismatic throwing volume model with a top surface area greater than the bottom area was constructed, and the energy analytical expression was derived using the velocity formula. To validate the theoretical results, a single-hole bench blasting numerical model was established using the SPH-FEM coupling algorithm. Meanwhile, high-speed photography and unmanned air vehicle(UAV) photogrammetry technologies were applied to obtain field test data on the rock throwing motion. The theoretical formulas were jointly validated in terms of their accuracy, robustness, and engineering applicability. The research results show that: (1) The proposed frustum-shaped volume model agrees well with numerical simulations and field test results. (2) The motion trajectory during the initial acceleration phase is relatively straight and can be approximated as a uniformly accelerated process; when the rock throwing velocity reaches its first peak, the initial acceleration phase ends, and inertial throwing begins. (3) During the inertial throwing phase, the throwing height of rock fragments decreases progressively from top to bottom, while the throwing distance shows the opposite trend; fluctuations in throwing trajectory and velocity are caused by secondary fragmentation and inter-particle collisions, but the overall results are consistent with the theoretical model. (4) By comparing the average initial throw velocities from numerical simulation, the theoretical model, the traditional empirical formula, and field experiments, the corresponding mean errors were 3.81%, 9.27%, and 51.23%, respectively; (5)The throwing energy accounts for 5.07% of the total explosion energy.