# Fragmentation Characteristics of Seafloor Massive Sulfides: A Coupled Fluid-Particle Flow Simulation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mechanical Property Test

#### 2.1. Sample

#### 2.2. Mechanics Test

^{2}.

_{t}is the maximum tensile stress in the center of the specimen, MPa; P is peak tensile force at failure, N; and d and t are diameter and thickness of the pressure-bearing disc, mm.

## 3. Fluid-Structure Coupling Method

#### 3.1. Rock Model—DEM

**F**

_{i}and

**T**

_{i}are the sums of force and moment of particle $i$, respectively, $m$ and $I$ are the mass and moment of inertia, $u$ is the position vector of particle centroid in a fixed coordinate system, $\omega $ is the angular velocity. The vectors

**F**

_{i}and

**T**

_{i}are calculated by Formulas (5) and (6).

#### 3.2. Fluid Model—Smooth Particle

_{V}.

#### 3.3. Boundary Identification

#### 3.4. Implementation Method

## 4. Material Calibration and Model Establishment

#### 4.1. Material Calibration

#### 4.2. Model Establishment

^{−15}. The real-time pore liquid pressure in the numerical calculation process is transmitted to PFC2D through API to promote iterative calculation. During the simulation, the model status was saved every 0.005 s, and the contact force of particles, the information of particles, cracks, and chips were also recorded.

## 5. Intact Coupling Cutting Process

## 6. Results and Analysis

#### 6.1. Crack Evolution

#### 6.2. Load Characteristics

^{2}= 0.985. The fitting curve of the white specimens was y = 0.72x + 62.99, R

^{2}= 0.984. The correlation coefficient R

^{2}of the two models was greater than 0.98, which shows a good correlation between the ambient pressure and average peak cutting force for the two SMS specimens.

#### 6.3. Fragment Morphology

#### 6.4. Specific Energy

_{R}refers to the average horizontal cutting force, L is the cutting distance, and V denotes the total volume of chips. A large amount of powder or fine particles is produced during cutting, but some rocks are still relatively complete. Note that a large amount of powder or fine particles is produced in the cutting process, so it is inaccurate to calculate the volume directly by summing the volumes of all fragments. In fact, the calculation error can be reduced by subtracting the remaining volume from the original volume of the sample model.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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Sample Type | Pyrite (FeS _{2}) | Marcasite (FeS) | Chalcopyrite (CuFeS _{2}) | Others (Including Amorphous) |
---|---|---|---|---|

Black | 25.1% | 31.9% | 5.4% | 37.6% |

White | 46.3% | — | 4.2 | 49.5% |

Sample Type | Tensile Strength/(MPa) | Compressive Strength /(MPa) | Internal Friction Angle φ/(°) | Cohesion c/MPa | Elastic Modulus/(GPa) |
---|---|---|---|---|---|

Black | 3.84 | 33.73 | 32.19 | 9.31 | 9.85 |

White | 2.25 | 20.57 | 29.67 | 5.98 | 1.98 |

Meso Parameters | Value | |
---|---|---|

Black | White | |

ρ/kg/m³ | 3050 | 3150 |

Kn | 1 | 0.8 |

Ks | 1 | 0.8 |

Tn/Pa | 13.4 × 10^{6} | 7.8 × 10^{6} |

Ts/Pa | 9.8 × 10^{6} | 6.8 × 10^{6} |

Emod/Pa | 3.5 × 10^{9} | 1.2 × 10^{9} |

Pb_emod/Pa | 34 × 10^{9} | 5 × 10^{9} |

Fluid parameters (SP) | ||

Permeability coefficient | 1 × 10^{−15} | 1 × 10^{−15} |

Biot modulus M/GPa | 2 | 2 |

Dynamic viscosity/Pa s | 0.001 | 0.001 |

Macro parameters | ||

Tensile strength/MPa | 4.01 | 2.32 |

Compressive strength/MPa | 38.6 | 20.1 |

Poisson’s ratio | 0.14 | 0.17 |

Modulus of elasticity/GPa | 9.45 | 2.13 |

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**MDPI and ACS Style**

Dai, H.; Li, H.; Li, Y.
Fragmentation Characteristics of Seafloor Massive Sulfides: A Coupled Fluid-Particle Flow Simulation. *J. Mar. Sci. Eng.* **2022**, *10*, 1306.
https://doi.org/10.3390/jmse10091306

**AMA Style**

Dai H, Li H, Li Y.
Fragmentation Characteristics of Seafloor Massive Sulfides: A Coupled Fluid-Particle Flow Simulation. *Journal of Marine Science and Engineering*. 2022; 10(9):1306.
https://doi.org/10.3390/jmse10091306

**Chicago/Turabian Style**

Dai, Huan, Hao Li, and Yan Li.
2022. "Fragmentation Characteristics of Seafloor Massive Sulfides: A Coupled Fluid-Particle Flow Simulation" *Journal of Marine Science and Engineering* 10, no. 9: 1306.
https://doi.org/10.3390/jmse10091306