# Numerical Modelling of Blasting Fragmentation Optimization in a Copper Mine

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## Abstract

**:**

_{80}size of the blasting fragmentation, the results indicate an optimized calibrated model with an overall error equal to 4.0% using a Swebrec distribution fitted to the model data. The optimal P

_{80}size of the resulting muckpile was equivalent to ~0.53 m for the hard rock copper fragments, which was close to the desired P

_{80}size.

## 1. Introduction

#### 1.1. Particle Size Distribution Models

_{50}), when the breakage model is known. Although, different model distributions have been used to determine the PSD curve using the 80% passing size (X

_{80}) [10,16].

_{c}as the characteristic size, and X

_{80}the 80% passing size. According to Ouchterlony and Sanchidrián [10], through a series expansion of Equation (1), when $\mathrm{X}\ll {\mathrm{X}}_{50}$, then ${\mathrm{P}}_{\mathrm{RR}}\approx \mathrm{ln}2\ast {\left(\mathrm{X}/{\mathrm{X}}_{50}\right)}^{\mathrm{n}}$, and that in a log-log diagram, this reduces to a straight line of slope n. In this way, X

_{c}might be written as:

_{max}is the maximum size of particles (mm); X is the particle size (mm); X

_{50}is the sieve size that retains 50% of the material (mm); and b is the shape parameter, called the undulation exponent or sometimes the natural breakage characteristics (NBC) exponent [17]. This parameter might be between 1 and 2, where the inflection point tends towards X = X

_{max}and X = X

_{50}, respectively [11].

#### 1.2. Blo-Up Software

#### 1.2.1. Explosive Model

#### 1.2.2. Main Rock Body Representation

#### 1.2.3. Fracture Mechanics in Blo-Up

#### 1.2.4. Fragment Size Calculation

## 2. Background Review

## 3. Materials and Methods

#### 3.1. Drilling and Blasting Design

^{2}, blasthole diameter of 12 ¼, drill length of 16.1 m, subdrill length of 1.0 m and dip angle of 90°.

#### 3.2. Historical Database Analysis

_{80}) was filtered to select the data of the predominant lithology as a case study. Finally, the historical database analysis included 284 blasting designs with fragmentation sizes between 2015 and 2019. The P

_{80}data were considered in a descriptive statistics analysis.

#### 3.3. Calibration

#### 3.4. Optimization

_{80}of 0.55 m. To determine the optimal blasting, a total of 6 cases were tested (Table 5).

## 4. Results and Discussions

#### 4.1. Historical Database Analysis

_{80}size are consolidated in the histogram of P

_{80}frequency in Figure 8.

_{80}was equal to 0.25 m with a standard variation of 0.07 m and a median of 0.22 m in the BDX. These rock fragmentation results are due to different magnitudes of different drilling patterns, blasthole charges, and other parameters. The analysis of Figure 8 allows us to infer that the historical database has 95% designs with a P

_{80}≤ 0.32 m, even though there were cases with P

_{80}≥ 0.55 m, but those were a minority in the data analysed.

#### 4.2. Model for Fragmentation Analysis

_{80}close to 0.80 m, and the reports from mine operations related to boulders from the run of mine (ROM) with oversize > 1.0 m were investigated. As mentioned before, this work aimed to optimize mine blast design with an optimum size of P

_{80}equal to 0.55 m using Blo-Up software. Figure 9 shows the PSD of the L3_127_005 blast and the old model for fragmentation provided by the mine company.

_{80}size of 0.55 m, it can be observed that the L3_127_005 blasting had a smaller P

_{80}and P

_{100}smaller than 0.40 m. Analyzing these two PSD, the L3_127_005 presents a finer size, considering the size results of the muckpile. The blasting pattern used in this blast was equal to 5.0 m × 5.6 m and was considered regular blasting because it has similar results in terms of P

_{80}and the same pattern.

_{80}from ~0.21 m of the L3_127_005 blasting to achieve the desired P

_{80}of 0.55 m [9].

#### 4.3. Calibration Results

_{80}variability related to their scale and compared to the observed PSD, which could be explained by data unavailability from particle sizes larger than 0.2 m. The large models had coarser fragment sizes than the small models, and we noticed more conservative values in the range of sizes between 0.2 and 0.4 m, but a reasonable representation for the rest of the fine curves. The Swebrec distribution models the whole range of sizes, with an error of 4.0% compared to the observed P

_{80}of L3_127_005_R00 blasting. As was found by Coello-Velázquez et al. (2019), the Swebrec distribution provides the best fit compared to the observed values.

#### 4.4. Optimization Results

_{80}of ~0.53 m, which was close to the desired P

_{80}. This result was obtained with a drilling pattern of 6.0 m of burden and 8.0 m of spacing and with the same charges per blasthole as blasting design L3_127_005.

_{80}~0.55 m, and model P3 had a coarse size distribution; on the other hand, the P4 model shows finer results than expected. This finding indicates that a burden of 6 m is enough to achieve the desired P

_{80}of 0.55 m.

_{80}~0.55 m. Compared with the other optimized models, P5 and P6 were not better in terms of performance.

_{80}of the optimized model indicates that the best case is model P2, with a P

_{80}of ~0.53 m, the closest value to the desired P

_{80}. This was optimized with a blasting design with a burden of 6.0 m and spacing of 8.0 m.

## 5. Conclusions

_{80}of 0.55 m. Through historical data, observations of a blasting example (L3_127_005), and a predictive analysis, the parameters were calibrated.

_{80}of 0.25 m, and a total error of 4% was obtained when comparing the best fitted Swebrec distribution and the Blo-Up data with the data from the L3_127_005 blasting. For the optimization process, some assumptions were made to better represent the rock mass conditions under vibration and blasting.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Representation of numerical components in Blo-Up. Adapted from [18].

**Figure 2.**Main rock body representation in Blo-Up. Adapted from [18].

**Figure 3.**Lithology of the study area. Reproduced with permission from Vale S.A. [22].

**Figure 4.**Shear zone of the hard rock of a copper mine. Reproduced with permission from Vale S.A. [22].

**Figure 10.**Particle size distribution of the calibration stage: Observed in the mine vs. predicted by Blo-Up (best case).

**Figure 11.**Fragment contour over 0.5 m: (

**a**) modelled by Blo-Up and (

**b**) cross-section of the large model in Blo-Up.

**Figure 14.**Charge length optimization results: (

**a**) Blo-Up model and (

**b**) best fitted Swebrec distribution.

Lithology | RMR Classification | Tensile Strength (Mpa) | Cohesion (kPa) | Hoek and Brown Classification | Density (t/m^{3}) | |||
---|---|---|---|---|---|---|---|---|

GSI | m_{i} | UCS (MPa) | E_{i} (GPa) | |||||

BDX | I | 9.0 | 130 | 83 | 12 | 90 | 63.4 | 3.2 |

II | 9.0 | 130 | 66.5 | 12 | 90 | 63.4 | 3.2 | |

III | 9.0 | 130 | 50 | 12 | 90 | 63.4 | 3.2 | |

IV | 2.5 | 70 | 25 | 12 | 25 | 9.4 | 2.7 | |

Average BDX | I, II and III | 9.0 | 130 | 50–83 | 12 | 90 | 63.4 | 3.2 |

_{i}); geological strength index (GSI); uniaxial compressive strength (UCS); elastic modulus (E

_{i}).

Structure | Dip (°) | Dip Direction (°) | Spacing (cm) | Persistence (m) |
---|---|---|---|---|

Foliation | 68 | 243 | 70.4 | 20 |

Fractures Set 1 | 75 | 53 | 89.4 | 12.7 |

Fractures Set 2 | 80 | 143 | 89.4 | 12.7 |

Fractures Set 3 | 87 | 297 | 89.4 | 12.7 |

Fractures Set 4 | 75 | 4 | 89.4 | 12.7 |

Primary Shear Zone (ZC1) | 75 | 219 | 135.1 | 17.8 |

Secondary Shear Zone (ZC1) | 75 | 332 | 135.1 | 17.8 |

Explosive Parameter | FDS 70 | FDS 100 |
---|---|---|

Reported Density (g/cm^{3}) | 1.15–1.25 | 1.15–1.25 |

Reported VOD (m/s) | 3500–6000 | 3500–6000 |

RWS (%) | 1.07 | 0.97 |

RBS (%) | 1.6 | 1.45 |

CO_{2} Output (kg/ton) | 159 | 201 |

Mean Density (g/cm^{3}) | 1.2 | 1.2 |

Last Measured VOD (m/s) | 5636 | 5636 |

Model | Free Face Distance (m) | Burden (m) | Spacing (m) | Bench Height (m) | Hole Depth (m) | Blasthole Diameters (inch) | Stemming (m) | Charge Length (m) | Subdrill (m) |
---|---|---|---|---|---|---|---|---|---|

Small | 2.8 | 5.6 | - | 15.0 | 16.0 | 12 ¼ | 5.5 | 10.5 | 1.0 |

Large | 2.5 | 5.0 | 5.6 | 15.0 | 16.1 | 12 ¼ | 5.5 | 10.6 | 1.1 |

Model | P1 | P2 | P3 | P4 | P5 | P6 |
---|---|---|---|---|---|---|

Number of Blastholes | 30 | 30 | 30 | 30 | 30 | 30 |

Burden(m) | 6 | 6 | 6.5 | 5.5 | 5 | 6 |

Spacing (m) | 9 | 8 | 8 | 8 | 5.6 | 8.5 |

Blasthole Length (m) | 16 | 16 | 16 | 16 | 16 | 16 |

Charge Length (m) | 10.5 | 10.5 | 10.5 | 10.5 | 11.0 | 10.5 |

Subdrill (m) | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 |

Calibrated Properties | Value |
---|---|

Density (kg/m^{3}) | 3.2 |

Young Modulus (Pa) | 1.0 × 10 ^{10} |

Poisson’s Ratio | 0.24 |

UCS (MPa) | 90 |

Tensile Strength of Rock (MPa) | 4.6 |

Tensile Strength of Damaged Rock (MPa) | 3.5 |

Tensile Strength of Joints (MPa) | 3.2 |

Friction Angle (°) | 32 |

Damping | 0.3 |

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## Share and Cite

**MDPI and ACS Style**

Torres, V.F.N.; Castro, C.; Valencia, M.E.; Figueiredo, J.R.; Silveira, L.G.C.
Numerical Modelling of Blasting Fragmentation Optimization in a Copper Mine. *Mining* **2022**, *2*, 654-669.
https://doi.org/10.3390/mining2040035

**AMA Style**

Torres VFN, Castro C, Valencia ME, Figueiredo JR, Silveira LGC.
Numerical Modelling of Blasting Fragmentation Optimization in a Copper Mine. *Mining*. 2022; 2(4):654-669.
https://doi.org/10.3390/mining2040035

**Chicago/Turabian Style**

Torres, Vidal Félix Navarro, Cristian Castro, María Elena Valencia, Janine Rodrigues Figueiredo, and Leandro Geraldo Canaan Silveira.
2022. "Numerical Modelling of Blasting Fragmentation Optimization in a Copper Mine" *Mining* 2, no. 4: 654-669.
https://doi.org/10.3390/mining2040035