# Estimation of Damage Induced by Single-Hole Rock Blasting: A Review on Analytical, Numerical, and Experimental Solutions

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## Abstract

**:**

## 1. Introduction

## 2. A Review on Explosion Mechanism

## 3. Damage Pattern

- The blast hole is expanded.
- A crushed zone is formed surrounding the blast hole.
- Radial cracks penetrate through the rock, causing a cracked zone.
- Explosion-induced waves affect the surrounding environment, producing some ground vibrations.

## 4. Estimation of Induced Damage

#### 4.1. Analytical Approach

#### 4.1.1. Damage Prediction Using PPV

- Only the magnitude of the PPV is considered and the direction of the PPV is neglected.
- Only the explosive weight is taken into account, and other characteristics are ignored.
- To determine the parameters K, $\alpha $, and $\beta $, further laboratory or in-situ tests are required, which are difficult to conduct.

#### 4.1.2. Damage Prediction Using Borehole Pressure

#### Mosinets’ Model

#### Drukovanyi’ Model

#### Senuk’s Model

#### Szuladzinski’s Model

#### SveBeFo Model

#### Quasi-Static Model

**Step 1**- Calculate $q/E$ from Equation (20)
**Step 2**- Approximate a value for ${r}_{d}/{r}_{h}$ (this value is approximated in this step and later modified in a cyclic process)
**Step 3****Step 4****Step 5****Step 6**- Substitute ${P}_{h}/E$ in Equation (19) to assess if equality is achieved (if so, ${r}_{d}/{r}_{h}$ is the final answer. Otherwise, the steps 2–6 should be repeated until the final answer is reached).

#### Djordjevic’s Model

#### Kanchibotla Model

#### Johnson’s Model

#### Modified Ash’s Model

#### 4.2. Numerical Approach

#### 4.3. Experimental Approach

- Primary cracks due to the high amplitude of stress waves
- Further development of cracks due to gas penetration

^{3}), ${D}_{CJ}$ represents the ideal detonation velocity (m/s), ${E}_{d}$ denotes the dynamic Young’s modulus of rock (Pa), and ${\nu}_{d}$ refers to the dynamic Poisson’s ratio of rock. These relationships are also used to approximate blast hole pressure and rock stiffness. Where more accurate values of these parameters are available through direct measurement or numerical modeling, they can be used instead of the presented equations [118]. After calculating $CZI$, Essen et al. [2] found a power relationship between this factor and the crushed zone radius as follows:

## 5. Discussion

#### 5.1. Comparison of Different Models

#### 5.2. Probabilistic Approaches

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**Coupled method illustrating the (

**a**) physical model of explosion in jointed rock mass, (

**b**) explosion history obtained via LS-DYNA, and (

**c**) input of converted explosion history for UDEC simulation.

**Figure 6.**Single hole blasting model illustrating the model parameters including joints, the length of joints (L), distance from joints to blasting hole (${d}_{i}$), and joint angle ($\alpha $).

**Figure 7.**Comparison of different models in estimating damage radius obtained from the 13 studied samples.

No. | Sources | Parameters | Description |
---|---|---|---|

1 | Rock characteristics | ${E}_{d}$ | Young’s modulus of rock |

2 | ${\nu}_{d}$ | Poisson’s ratio of rock | |

3 | ${\sigma}_{c}$ | Uniaxial compressive strength of rock | |

4 | ${F}_{c}$ | Confined compressive strength of rock | |

5 | T | Tensile strength of rock | |

6 | Explosive characteristics | ${\rho}_{0}$ | Unexploded explosive density |

7 | ${D}_{CJ}$ | Ideal detonation velocity | |

8 | ${r}_{0}$ | Blast hole radius | |

9 | ${Q}_{ef}$ | Effective energy of explosive |

**Table 2.**PPV-based criteria for blast-induced damage in rock (adopted from Bauer and Calder [52]).

PPV (mm/s) | Effects of Damage |
---|---|

<250 | No fracture of intact rock |

250–635 | Occurrence of minor tensile slabbing |

635–2540 | Strong tensile and some radial cracking |

>2540 | Complete break-up of rock mass |

**Table 3.**PPV-based criteria for blast-induced damage in rock (adopted from Mojtabai and Beattie [53]).

Rock Type | Uniaxial Strength (MPa) | RQD (%) | PPV (mm/s) | ||
---|---|---|---|---|---|

Minor Damage | Medium Damage | Heavy Damage | |||

Soft schist | 14–30 | 20 | 130–155 | 155–355 | >355 |

Hard schist | 49 | 50 | 230–350 | 305–600 | >600 |

Shultze granite | 30–55 | 40 | 310–470 | 470–1700 | >1700 |

Granite porphyry | 30–80 | 40 | 440–775 | 775–1240 | >1240 |

PPV (m/s) | Tensile Stress (MPa) | Strain Energy (J/kg) | Typical Effect in Hard Scandinavian Bedrock |
---|---|---|---|

0.7 | 8.7 | 0.25 | Incipient swelling |

0.1 | 12.5 | 0.5 | Incipient damage |

2.5 | 31.2 | 3.1 | Fragmentation |

5 | 62.4 | 12.5 | Good fragmentation |

15 | 187 | 112.5 | Crushing |

Case No. | Rock | Explosive | P (g/cm^{3}) | q (MJ/kg) | ${\mathit{D}}_{\mathit{CJ}}$ (km/s) | ${\mathit{r}}_{0}$ (mm) | ${\mathit{r}}_{\mathit{c}}$ (mm) | ${\mathit{P}}_{\mathit{b}}$ (GPa) |
---|---|---|---|---|---|---|---|---|

1 | CL | ANFO | 0.803 | 3.812 | 5.016 | 165 | 82.5 | 3.045 |

2 | CL | ANFO | 0.803 | 3.812 | 5.016 | 229 | 114.5 | 3.477 |

3 | B | ANFO | 0.803 | 3.812 | 5.016 | 102 | 51 | 2.061 |

4 | B | ANFO | 0.803 | 3.812 | 5.016 | 165 | 82.5 | 3.148 |

5 | B | ANFO | 0.803 | 3.812 | 5.016 | 229 | 114.5 | 3.595 |

6 | CL | WR ANFO | 0.994 | 3.918 | 5.829 | 51 | 25.5 | 2.016 |

7 | CL | WR ANFO | 0.994 | 3.918 | 5.829 | 102 | 51 | 4.033 |

8 | CL | WR ANFO | 0.994 | 3.918 | 5.829 | 165 | 82.5 | 4.974 |

9 | CL | WR ANFO | 0.994 | 3.918 | 5.829 | 229 | 114.5 | 5.44 |

10 | B | WR ANFO | 0.994 | 3.918 | 5.829 | 51 | 25.5 | 2.085 |

11 | B | WR ANFO | 0.994 | 3.918 | 5.829 | 102 | 51 | 4.169 |

12 | B | WR ANFO | 0.994 | 3.918 | 5.829 | 165 | 82.5 | 5.141 |

13 | B | WR ANFO | 0.994 | 3.918 | 5.829 | 229 | 114.5 | 5.623 |

Case No. | Esen et al. [2] | Il’yushin [59] | Szuladzinski [62] | Djordjevic [72] | Kanchibotla [73] |
---|---|---|---|---|---|

1 | 372 | 1269 | 379 | 466 | 1192 |

2 | 564 | 1761 | 526 | 647 | 1654 |

3 | 67 | 402 | 108 | 139 | 339 |

4 | 143 | 651 | 175 | 225 | 549 |

5 | 217 | 903 | 242 | 312 | 762 |

6 | 88 | 441 | 132 | 186 | 476 |

7 | 277 | 881 | 264 | 372 | 953 |

8 | 513 | 1426 | 427 | 602 | 1541 |

9 | 756 | 1979 | 593 | 836 | 2139 |

10 | 34 | 239 | 61 | 90 | 219 |

11 | 107 | 478 | 122 | 179 | 439 |

12 | 198 | 774 | 197 | 290 | 710 |

13 | 291 | 1074 | 273 | 403 | 985 |

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**MDPI and ACS Style**

Shadabfar, M.; Gokdemir, C.; Zhou, M.; Kordestani, H.; Muho, E.V.
Estimation of Damage Induced by Single-Hole Rock Blasting: A Review on Analytical, Numerical, and Experimental Solutions. *Energies* **2021**, *14*, 29.
https://doi.org/10.3390/en14010029

**AMA Style**

Shadabfar M, Gokdemir C, Zhou M, Kordestani H, Muho EV.
Estimation of Damage Induced by Single-Hole Rock Blasting: A Review on Analytical, Numerical, and Experimental Solutions. *Energies*. 2021; 14(1):29.
https://doi.org/10.3390/en14010029

**Chicago/Turabian Style**

Shadabfar, Mahdi, Cagri Gokdemir, Mingliang Zhou, Hadi Kordestani, and Edmond V. Muho.
2021. "Estimation of Damage Induced by Single-Hole Rock Blasting: A Review on Analytical, Numerical, and Experimental Solutions" *Energies* 14, no. 1: 29.
https://doi.org/10.3390/en14010029