# Characteristics and Energy Distribution of Blast-Induced Ground Vibration in Deep-Hole Blasting

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Increasing Extreme Value of Blast-Induced Ground Vibration Signal

#### 2.1. Incremental Extremum Extraction

#### 2.1.1. Threshold Function

_{i}represents the time corresponding to ${\overrightarrow{v}}_{\mathrm{p}i}$, s; and t

_{b}is the total delay time of blasting, s.

#### 2.1.2. Incremental Extremum Extraction Algorithm

## 3. Analysis of Particle Velocity Extremum

#### 3.1. Site Conditions and Blasting Parameters

#### 3.2. Ground Vibration Monitoring

_{u}is the distance between the monitoring point and the initiation point; L

_{s}is the distance between the monitoring point and the nearest point; L

_{d}is the distance between the monitoring point and the end point.

_{1}≈ L

_{2}. The two fitting lines are approximately parallel, but the fitting line of the increasing segment is slightly higher than that of the weakening segment. When the initiation hole gets gradually closer to the monitoring site, a growing signal is produced, and when it is farther away from the monitoring point, a weakening signal is observed. The corresponding monitoring point of the increasing signal is in the isochron propagation direction, and the particle velocity is high. The angle between the two lines decreases initially before growing as the slope of the increasing segment gradually decreases and the slope of the fitting line of the weakening segment increases.

#### 3.3. Surface Particle Velocity Vector Analysis

## 4. Analysis of Cumulative Energy of Blast-Induced Ground Vibration

_{k}of the unit mass rock mass at the measurement point position, and the cumulative kinetic energy $\Sigma {E}_{\mathrm{k}}$ represents the total energy passing through the measurement point position in the blasting process, and the value function is:

_{k}

_{0}(assuming no surface vibration before blasting, i.e., E

_{k0}= 0) and the maximum value of accumulated kinetic energy ($\Sigma {E}_{\mathrm{k}}$) in the three directions are mapped with the interval of [0,1], and the time history curve of normalized accumulated kinetic energy is obtained, as shown in Figure 12.

## 5. Conclusions

- (1)
- Based on the characteristics of open-pit deep-hole blasting and vibration signals of the same horizontal step, an increasing extremum extraction method was proposed which can obtain multiple particle velocity extrema corresponding to different blast center distances from a set of signals. This method forms the basis for statistics and analysis of the vibration signal.
- (2)
- The particle velocity was linearly proportional to the distance from the blasting center to the monitoring point when multiple rows of explosives in deep holes were detonated under the condition of a certain mass of charge in a single hole. Furthermore, the linear law of increasing and decreasing velocity was inconsistent, and particle velocity in the increasing stage was higher than that in the decreasing stage.
- (3)
- The method for assessing the vector of extreme particle velocity was proposed to study the relationship between the distance from the blast center to the monitoring site and particle velocity. The numerical value and vector relationship were combined for analysis based on the characteristics of the vector describing the spatial position relationship of physical quantities. The extreme particle velocity and the angle with the ground plane were expressed and statistically analyzed, which was distinct from the traditional digital signal processing method to explain the spatial dynamic problem. The kinetic energy in the vertical direction accumulates at a greater rate in positions closer to the epicenter, and the increase in kinetic energy at more distant positions is very similar to that in the horizontal (X and Y) direction.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Test | Monitoring Point | Distance/m | ||
---|---|---|---|---|

L_{u} | L_{s} | L_{d} | ||

1 | 1# | 193.4 | 48.9 | 354.8 |

2# | 301.8 | 54.0 | 256.8 | |

3# | 415.3 | 56.6 | 158.4 | |

4# | 506.0 | 71.5 | 111.8 | |

2 | 1# | 74.1 | 38.9 | 209.8 |

2# | 152.1 | 49.7 | 138.8 | |

3# | 234.1 | 43.9 | 55.5 | |

4# | 249.7 | 49.5 | 57.0 |

Velocity Direction | Measurement Point 1# | Measurement Point 2# | Measurement Point 3# | Measurement Point 4# | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a | b | R^{2} | a | b | R^{2} | a | b | R^{2} | a | b | R^{2} | ||

Test 1 | X (↗) | −0.007 | 3.911 | 0.444 | −0.015 | 5.841 | 0.846 | −0.012 | 6.081 | 0.875 | −0.019 | 10.743 | 0.937 |

X (↘) | −0.010 | 3.977 | 0.893 | −0.013 | 4.616 | 0.829 | −0.040 | 7.491 | 0.853 | −0.199 | 23.169 | 0.912 | |

Y (↗) | −0.036 | 7.831 | 0.863 | −0.022 | 7.895 | 0.909 | −0.009 | 5.613 | 0.791 | −0.014 | 8.954 | 0.865 | |

Y (↘) | −0.013 | 5.102 | 0.826 | −0.019 | 5.770 | 0.673 | −0.034 | 7.278 | 0.711 | −0.167 | 19.621 | 0.917 | |

Z (↗) | −0.089 | 19.050 | 0.904 | −0.044 | 14.473 | 0.961 | −0.024 | 10.910 | 0.952 | −0.024 | 12.779 | 0.965 | |

Z (↘) | −0.035 | 10.546 | 0.779 | −0.056 | 13.480 | 0.893 | −0.077 | 14.289 | 0.804 | −0.272 | 31.797 | 0.942 | |

Test 2 | X (↗) | −0.210 | 16.455 | 0.733 | −0.105 | 16.341 | 0.927 | −0.043 | 10.652 | 0.935 | −0.041 | 10.464 | 0.862 |

X (↘) | −0.050 | 10.049 | 0.756 | −0.109 | 14.836 | 0.905 | −0.763 | 41.881 | 0.884 | −1.221 | 70.427 | 0.690 | |

Y (↗) | −0.233 | 19.695 | 0.450 | −0.074 | 12.661 | 0.757 | −0.035 | 7.604 | 0.655 | −0.037 | 8.784 | 0.762 | |

Y (↘) | −0.066 | 13.378 | 0.889 | −0.080 | 12.114 | 0.889 | −0.717 | 40.681 | 0.831 | −0.759 | 45.487 | 0.733 | |

Z (↗) | −0.320 | 27.525 | 0.856 | −0.168 | 26.339 | 0.908 | −0.074 | 17.067 | 0.757 | −0.062 | 15.124 | 0.938 | |

Z (↘) | −0.086 | 16.885 | 0.888 | −0.183 | 25.146 | 0.796 | −1.735 | 96.905 | 0.786 | −2.097 | 117.475 | 0.844 |

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**MDPI and ACS Style**

Bao, S.; Fei, H.; Hu, G. Characteristics and Energy Distribution of Blast-Induced Ground Vibration in Deep-Hole Blasting. *Buildings* **2023**, *13*, 899.
https://doi.org/10.3390/buildings13040899

**AMA Style**

Bao S, Fei H, Hu G. Characteristics and Energy Distribution of Blast-Induced Ground Vibration in Deep-Hole Blasting. *Buildings*. 2023; 13(4):899.
https://doi.org/10.3390/buildings13040899

**Chicago/Turabian Style**

Bao, Shijie, Honglu Fei, and Gang Hu. 2023. "Characteristics and Energy Distribution of Blast-Induced Ground Vibration in Deep-Hole Blasting" *Buildings* 13, no. 4: 899.
https://doi.org/10.3390/buildings13040899