# Dynamic Characteristics of Rock Holes with Gravel Sediment Drilled by Bit Anchor Cable Drilling

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Research Method

#### 2.1. Contact Model

_{n}is the standard overlap.

^{*}and equivalent radius R* are given by Equations (2) and (3), respectively:

_{i}, v

_{i}, and R

_{i}, E

_{j}, v

_{j}and R

_{j}are Young’s modulus, and Poisson’s ratio and radius of particles i and j are in contact with each other, respectively.

#### 2.2. DEM Particle Parameters

#### 2.3. Construction Model

#### 2.3.1. Build A Test-Bed

#### 2.3.2. Simulation Model

#### 2.4. Feasibility Analysis of Bit Anchor Cable Installation Method

#### 2.5. Research Program

## 3. Results and Discussion

#### 3.1. Axial Speed

#### 3.2. Feed Rate

^{2}is greater than 0.95. The slope is counted, as shown in Table 3, and the data in the Table is plotted as a curve, as shown in Figure 10. It can be considered from the discern that, at the identical speed, the slope of the geared-up straight line of the drilling resistance of the bit anchor cable is positively correlated with the feed charge of the bit anchor cable. The smaller the rotation speed of the drill anchor cable, the stronger the positive correlation between the slope of the fitting line and the feed rate of the bit anchor cable. When the feed charge of the bit anchor cable is 0.12 m/s and the rotation velocity is zero rpm, the slope of the becoming line of the drilling resistance of the bit anchor cable is 715 greater than that at the identical rotation velocity when the feed fee is 0.03 m/s. When the feed charge of the bit anchor cable is 0.12 m/s and the rotation velocity is 360 rpm, the slope of the becoming line of the drilling resistance of the bit anchor cable is solely 183 greater than that at the identical rotation pace when the feed charge is 0.03 m/s.

#### 3.3. Anchor Cable Pitch

^{2}is greater than 0.95. Figure 13 is the slope diagram of the provided straight line of the drilling resistance of the bit anchor cable at the feed rate of 0.06 m/s, and the feed rate of 0.12 m/s under different pitches.

#### 3.4. Working Aperture

## 4. Conclusions

- (1)
- Affected by using the spiral shape of the drill anchor rod, the axial velocity is negatively correlated with the drilling resistance of the bit anchor cable, and the effects are compared to confirm the correctness of the simulation. The pitch of the bit anchor thread has a hump-shaped relationship with drilling resistance. When the slope is much less than 450 mm, the drilling resistance can be decreased with the aid of appropriately lowering the pitch of the bit anchor cable;
- (2)
- The feed speed is positively correlated with the resistance encountered during drilling; the degree of influence of the anchor cable on the particles in the hole is inversely correlated with the feed rate during drilling. The slope of the drilling resistance fitting line is positively correlated with the feed velocity, and the smaller the axial speed, the stronger the positive correlation between the slope and the feed speed;
- (3)
- As the aperture increases, the drilling resistance and the hindering torque of the drill anchor cable gradually decrease. When the bit is 0.2 m away from the bottom of the hole, the particle velocity vector at the lower end of the bit shows an evident conical distribution, and the particles diffuse horizontally. When the bit is 0.05 m from the bottom of the hole, the number of particles that diffuse laterally decreases sharply.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Calibration experiment of DEM particle parameters: (

**a**) cylinder pulling experiment, (

**b**) slope experiment, (

**c**) rolling experiment, (

**d**) drop experiment.

**Figure 3.**Test-bed structure diagram; (

**a**) Mechanical module; (

**b**) Control and data acquisition module.

**Figure 6.**Drilling resistance curves of drill anchor cable under different axial speeds; (

**a**) v = 0.03 m/s; (

**b**) v = 0.06 m/s; (

**c**) v = 0.09 m/s; (

**d**) v = 0.12 m/s.

**Figure 7.**Vector diagram of particle motion around bit anchor cable at different rotation speeds; (

**a**) n = 0 rpm; (

**b**) n = 120 rpm; (

**c**) n = 240 rpm; (

**d**) n = 360 rpm.

**Figure 9.**Resistance curve of bit anchor cable drilling below exclusive feeding rates: (

**a**) n = 0 rpm; (

**b**) n = 120 rpm; (

**c**) n = 240 rpm; (

**d**) n = 360 rpm.

**Figure 10.**Comparison diagram of fitting straight line slope of bit anchor cable drilling resistance under different feeding rates.

**Figure 11.**Vector diagram of particle motion state in the hole at different feeding rates: (

**a**) v = 0.03 m/s; (

**b**) v = 0.06 m/s; (

**c**) v = 0.09 m/s; (

**d**) v = 0.12 m/s.

**Figure 13.**Fitting straight line slope diagram of drilling resistance of bit anchor cable under different pitches: (

**a**) v = 0.06 m/s; (

**b**) v = 0.12 m/s.

**Figure 15.**Dynamic features curve of bit anchor cable below amazing apertures: (

**a**) n = 240 rpm Drilling resistance; (

**b**) n = 240 rpm Hinder torque; (

**c**) n = 300 rpm Drilling resistance; (

**d**) n = 300 rpm Hinder torque.

**Figure 16.**The average value of particle obstruction at different apertures and drilling depths of 0.5–0.55 m.

**Figure 17.**Velocity vector diagram of particles at the lower end of the bit: (

**a**) Particle velocity vector diagram when the bit is 0.2 m from the bottom of the hole; (

**b**) Particle velocity vector diagram when the bit is 0.05 m from the bottom of the hole.

G (GPa) | Ρ (kg/m^{3}) | σ | μR | η | μS | ||
---|---|---|---|---|---|---|---|

Gravel | 11 | 2700 | 0.29 | Gravel—Gravel | 0.2 | 0.62 | 0.74 |

Anchor cable | 8.02 | 7801 | 0.29 | Gravel—Anchor cable | 0.25 | 0.42 | 0.49 |

Axial Speed/rpm | Feed Rate/(m/s) | Anchor Cable Pitch/mm | Working Aperture/mm |
---|---|---|---|

0, 120, 240, 360 | 0.03, 0.06, 0.09, 0.12 | 140, 240, 340, 440, 540 | 80, 120, 160, 200, 240 |

Rotating Speed (rpm) | Feeding Rate (m/s) | Fitting Straight Line Slope | Rotating Speed (rpm) | Feeding Rate (m/s) | Fitting Straight Line Slope |
---|---|---|---|---|---|

0 | 0.03 | 698 | 240 | 0.03 | 272 |

0 | 0.06 | 933 | 240 | 0.06 | 381 |

0 | 0.09 | 1153 | 240 | 0.09 | 475 |

0 | 0.12 | 1413 | 240 | 0.12 | 555 |

120 | 0.03 | 374 | 360 | 0.03 | 222 |

120 | 0.06 | 595 | 360 | 0.06 | 254 |

120 | 0.09 | 747 | 360 | 0.09 | 328 |

120 | 0.12 | 908 | 360 | 0.12 | 405 |

Feeding Rates (m/s) | Axial Speed (rpm) | Aperture (mm) | Particle Depth in the Hole (mm) |
---|---|---|---|

0.01 | 240, 300 | 80, 120, 160, 200, 240 | 800 |

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**MDPI and ACS Style**

Gao, K.; Liu, J.; Chen, H.; Li, X.; Huang, S. Dynamic Characteristics of Rock Holes with Gravel Sediment Drilled by Bit Anchor Cable Drilling. *Sustainability* **2023**, *15*, 5956.
https://doi.org/10.3390/su15075956

**AMA Style**

Gao K, Liu J, Chen H, Li X, Huang S. Dynamic Characteristics of Rock Holes with Gravel Sediment Drilled by Bit Anchor Cable Drilling. *Sustainability*. 2023; 15(7):5956.
https://doi.org/10.3390/su15075956

**Chicago/Turabian Style**

Gao, Kuidong, Jihai Liu, Hong Chen, Xu Li, and Shuan Huang. 2023. "Dynamic Characteristics of Rock Holes with Gravel Sediment Drilled by Bit Anchor Cable Drilling" *Sustainability* 15, no. 7: 5956.
https://doi.org/10.3390/su15075956