# Multifractal Characteristics of Smooth Blasting Overbreak in Extra-Long Hard Rock Tunnel

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Overview of the Tunnel Project

#### 2.1.1. Tunnel Project Introduction

#### 2.1.2. Original Tunnel Excavation Design

#### 2.2. Optimization of Tunnel Smooth Blasting

#### 2.2.1. Spaced Decoupled Charge Blasting

- Blasting equipment

- 2.
- Parameters of hole arrangement

- 3.
- Charge structure

#### 2.2.2. Bidirectional Shaped Charge Blasting

- 1.
- Peripheral hole parameters

- 2.
- Charge structure

#### 2.3. Tunnel Profile Measurement

#### 2.4. Multifractal Detrended Fluctuation Analysis Methodology

## 3. Results and Discussion

#### 3.1. Analysis of the Optimized Effect of Tunnel Smooth Blasting

#### 3.1.1. Smooth Blasting with Spaced Decoupled Charge

#### 3.1.2. Smooth Blasting with Bidirectional Shaped Charge

#### 3.1.3. Overbreak and Underbreak of Tunnel Profile of Smooth Blasting

^{2}, while the bidirectional shaped charge blasting only resulted in an overbreak and underbreak area of 4.61 m

^{2}. This indicates that the bidirectional shaped charge blasting has a significantly better smooth blasting effect compared to the interval decoupled charge blasting. As depicted in Figure 12, the average overbreak value for each measurement point in the interval decoupled charge blasting is 4.21 cm, with a maximum overbreak value of 7.91 cm occurring at the right arch shoulder. The overbreak at the right arch shoulder and arch waist is more pronounced in the interval decoupled charge blasting. On the other hand, for the bidirectional shaped charge blasting, the average overbreak value at each measurement point is 1.99 cm, with a maximum overbreak value of 4.58 cm occurring at the left arch shoulder. The overbreak values of each area of the tunnel section after bidirectional shaped charge blasting are not significantly different, indicating that the smooth blasting effect is better than that of the interval decoupled charge blasting.

^{3}of concrete cubic meters for each meter of advance. As a result, the optimized smooth blasting scheme ensured the safe and efficient completion of the extra-long hard rock tunnel.

#### 3.2. Multifractal Characteristics of Tunnel Profile Overbreak

#### 3.2.1. MF-DFA Key Parameters Determination

#### 3.2.2. Multifractal Characterization of Overbreak Section Profile

## 4. Conclusions

- The peripheral hole charging structure and blasting parameters are improved and optimized to enhance the effect of tunnel smooth blasting. The implementation of the bidirectional shaped charge significantly improves the smooth blasting effect. After blasting, the tunnel excavation contour line becomes flat, and the half-hole trace marks on the tunnel wall become more distinct. In comparison to spaced decoupled charging blasting, the smooth blasting effect with a bidirectional shaped charge is notably superior.
- The laser profiler is utilized to measure the actual excavation contour line of the tunnel section, obtaining specific data on overbreak and underbreak. A further quantitative comparison of the optimization effect of smooth blasting parameters is conducted. It is observed that the overbreak and underbreak value of each area of the tunnel section after bidirectional shaped charge blasting does not differ significantly, and the smooth blasting effect is evidently better than that of spaced decoupled charge blasting.
- MF-DFA is employed to analyze the multifractal features of the overbreak point sequences of the tunnel profile under different smooth blasting plans. It is concluded that both spaced decoupled charge and bidirectional shaped charge blasting result in measurement point sequences with multifractal features in the overbreak area. The statistical calculation results of the multifractal features of the tunnel profile under different smooth blasting plans align more closely with the actual situation.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 6.**Bidirectional shaped charge structure (physical drawing of shaped charge tube and water bag).

**Figure 7.**Measurement of overbreak and underbreak of the tunnel section: (

**a**) measurement design drawing; and (

**b**) field implementation drawing.

**Figure 9.**The effect of spaced decoupled charge of smooth blasting: (

**a**) overall diagram of half-hole trace; and (

**b**) detail diagram of half-hole trace.

**Figure 10.**Bidirectional shaped charge blasting effect of smooth blasting diagram: (

**a**) overall diagram of half-hole trace; and (

**b**) detail diagram of half-hole trace.

**Figure 11.**Scanning results of tunnel profile after blasting with two charge methods: (

**a**) spaced decoupled charge, and (

**b**) bidirectional shaped charge.

**Figure 12.**Distribution curve of overbreak and underbreak of the profile of the blasting tunnel section for two charge methods: (

**a**) spaced decoupled charge, and (

**b**) bidirectional shaped charge.

**Figure 13.**q-order wave function ${F}_{q}\left(s\right)-s$ double logarithmic fitting trend image: (

**a**) spaced decoupled charge, and (

**b**) bidirectional shaped charge.

**Figure 14.**Variation of the generalized Hurst index: (

**a**) spaced decoupled charge, and (

**b**) bidirectional shaped charge.

**Figure 15.**Variation of the scalar function $\tau \left(q\right)$: (

**a**) spaced decoupled charge, and (

**b**) bidirectional shaped charge.

Specimen Number | Specimen 1 | Specimen 2 | Specimen 3 | Specimen 4 | Average Value |
---|---|---|---|---|---|

Compressive strength | 106.0 MPa | 119.1 MPa | 129.1 MPa | 120.3 MPa | 118.6 MPa |

Event | Blasthole Depth (m) | Number of Holes | Number of Rolls per Hole (Rolls/Hole) | Charge of Single Hole (kg/Hole) | Subtotal Dosage (kg) | Total Number of Holes | Total Amount of Explosives (kg) |
---|---|---|---|---|---|---|---|

Cut hole | 4.4 | 34 | 14.5 | 2.9 | 98.6 | 252 | 437.1 |

Auxiliary hole | 4.2 | 139 | 10 | 2 | 278 | ||

Peripheral hole | 4.2 | 65 | 2.5 | 0.5 | 32.5 | ||

Floor hole | 4.2 | 14 | 10 | 2 | 28 |

**Table 3.**Comparison of the effects of spaced decoupled faceted blasting and bidirectional shaped charge blasting technology.

Sports Event | Spaced Decoupled Charge Smooth Blasting | Bidirectional Shaped Charge BSmooth Blasting | Efficiencies |
---|---|---|---|

Number of smooth holes | 65 | 51 | Decrease 21.5% |

Semi-porous trace rate/% | 56 | 89 | Increase 59.9% |

Peripheral hole explosives/kg | 32.5 | 30.6 | Decrease 5.8% |

Maximum unevenness/cm | 30 | 10 | Decrease 66.7% |

Amount of concrete m^{3}/m | 13.01 | 4.61 | Decrease 64.6% |

Cross-Section | Cross-Section 1 | Cross-Section 2 | Cross-Section 3 | Cross-Section 4 | Cross-Section 5 | Cross-Section 6 | |
---|---|---|---|---|---|---|---|

Index | |||||||

$\Delta \alpha $ | 0.559 | 0.695 | 0.746 | 0.734 | 0.737 | 0.818 | |

$\Delta f\left(\alpha \right)$ | 0.133 | 0.196 | 0.137 | 0.222 | 0.292 | 0.644 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, W.; Liu, D.; Tang, Y.; Qiu, W.; Zhang, R.
Multifractal Characteristics of Smooth Blasting Overbreak in Extra-Long Hard Rock Tunnel. *Fractal Fract.* **2023**, *7*, 842.
https://doi.org/10.3390/fractalfract7120842

**AMA Style**

Zhang W, Liu D, Tang Y, Qiu W, Zhang R.
Multifractal Characteristics of Smooth Blasting Overbreak in Extra-Long Hard Rock Tunnel. *Fractal and Fractional*. 2023; 7(12):842.
https://doi.org/10.3390/fractalfract7120842

**Chicago/Turabian Style**

Zhang, Wanmao, Dunwen Liu, Yu Tang, Weichao Qiu, and Ruiping Zhang.
2023. "Multifractal Characteristics of Smooth Blasting Overbreak in Extra-Long Hard Rock Tunnel" *Fractal and Fractional* 7, no. 12: 842.
https://doi.org/10.3390/fractalfract7120842