# Mechanism and Control of Grout Propagation in Horizontal Holes in Fractured Rock

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Characteristics of Macroscopic Vertical Permeability at the Top of a Middle Ordovician Limestone Layer

- (1)
- Dongpang mine: The flushing fluid leakages of a total of 88 boreholes were recorded. The end position of the No. 3 water source hole was in the upper Majiagou formation were is under the Fengfeng formation; the end positions of the others were in the Fengfeng formation. Among the 88 holes, only two holes did not leak and the other holes had various degrees of flushing fluid leakage. Within 10 m from the top of the MOL, the leakage of 90% of the boreholes was less than 1.0 m
^{3}h^{−1}, which is categorized as slight leakage and the leakage of only one hole was greater than 10 m^{3}h^{−1}. In addition, according to the statistics for every 10 m at the top of the MOL from 16 boreholes (Table 1), we found that the leakage within 40 m of the top of the MOL was minor and changed little, but the leakage of the flushing fluid increased markedly at deeper than 40 m. This indicates that the karst fracture rate in the upper 40 m of the MOL was relatively low, the water yield was weak and the water entered the strong aquifer part of the seventh section of the Fengfeng formation at a depth of 40 m. - (2)
- Wutongzhuang mine: The leakages of 11 boreholes in the MOL strata of the Wutongzhuang mine were determined. Among them, the flushing fluid leakages of two boreholes decreased within 30 m of the top of the MOL; this is for 18% of the boreholes. The leakages were 5 m
^{3}h^{−1}and 40 m^{3}h^{−1}when the lengths of the boreholes were 15 m and 24.5 m under the MOL, respectively, which indicates that the water yield property of the eighth section of the MOL was uneven but generally weak. The end positions of eight of the boreholes in the seventh section of the MOL, among which four boreholes had leakage of flushing fluid, accounted for 50% of the total boreholes. According to the analysis, there was a weathering crust at the top interface of the MOL and most of the cracks were filled with argillaceous components, so the water resistance was good. The MOL aquifer is zonal vertically. At 15 m below the top surface of the MOL, we found no leakage of flushing fluid from any boreholes; at 15 to 30 m, the water yield of the stratum was relatively weak and uneven; at more than 30 m, the water yield of the stratum was strong and uneven.

## 3. Analysis of Cement Grout Performance and Its Influencing Factors

#### 3.1. Hydro-Chemical Characteristics of a Middle Ordovician Limestone Top

#### 3.2. Test Scheme

_{16}(4

^{5}) orthogonal table, we carried out a performance test of cement grout with various contents of sodium silicate, various water–cement ratios and various groundwater hydro-chemical types of the top aquifer of the MOL in the Hanxing mining area (Table 3 and Table 4).

#### 3.3. Test Results

## 4. Grout Propagating Mechanism of Inclined Single Fracture in Horizontal Grouting Hole

#### 4.1. Basic Assumptions of Model Construction

#### 4.2. Grout Propagating Model of an Inclined Single Fracture

_{0}.

**f**is the unit mass force, the second term is the surface force generated by a pressure gradient and the third term is the friction force caused by grout viscosity.

_{1}. After the grout enters the fracture from the grouting hole, the pressure decreases due to the resistance of hydrostatic pressure, the grout viscosity and the mass gravity and finally balances with the hydrostatic pressure, grout viscosity and mass gravity. Therefore, we assume that the front pressure of grout is p

_{0}; that is to say, the hydrostatic pressure p

_{0}. When the grout propagation length along the fracture below the horizontal grouting hole reaches L

_{X}, the boundary conditions are

_{0}, the crack opening is b and the diffusion distance of the slurry in the crack below the borehole is x within duration t, the grouting amount in the fracture below is obtained by

_{1}, we can get the following result:

## 5. Grouting Control Method of Horizontal Grouting Hole at the Top of Middle Ordovician Limestone

#### 5.1. Analysis of Influencing Factors of Grout Propagation Length in a Single Fracture

_{1}, angle between fracture and grouting hole α, crack opening b and hydrostatic pressure p

_{0}were calculated and the variation characteristics were analyzed. Among them, the radius of the horizontal grouting hole r

_{0}was 0.076 m, the hydrostatic pressure p

_{0}was 10

^{7}Pa, the duration range was 0 to 6,000 s and the gravity acceleration g was 9.8 m.s

^{−2}.

#### 5.2. Numerical Calculation of Grout Propagation Based on Orthogonal Test

_{9}(3

^{4}) orthogonal table design method, we designed three levels by considering the water–cement ratio, grouting pressure, fracture width and angle between fractures and borehole. Therefore, there were nine calculation conditions. We used COMSOL numerical simulation software to analyze and calculate the influence of the grout propagation length of a single fracture in a horizontal grouting hole. The selected factors and levels are shown in Table 8 and the nine numerical simulation conditions are shown in Table 9. We obtained the grout propagation pattern and grouting pressure distribution results under various working conditions for 1 h according to the calculations, as shown in Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12.

#### 5.3. Control Method of Grout Propagation Length

## 6. Engineering Application

## 7. Discussion

- (1)
- In the numerical calculation, there was no marked difference in the grout propagation length between the upper and lower fractures of the horizontal grouting holes under various working conditions. The main reason is that the grout propagation length was always in a small range. Relative to the previous theoretical analysis, the grout propagation lengths in the upper and lower fractures of the horizontal grouting holes differed only slightly, unless the grout propagation length was hundreds of meters or more. The phenomenon of a large difference in the range of the upper kilometer was consistent.
- (2)
- Under the condition of a wide-tension-fracture opening (0.01 m), there was a large gap between the numerical calculation results and the theoretical calculation results. The main reason was that the porosity of the rock mass was set in the numerical calculation and the fracture was filled with only water in the theoretical calculation. However, the spatial and temporal distribution characteristics of various factors on the grout propagation length could be accurately given by the numerical simulation calculation. The influence factors of distance had a good qualitative analysis effect.

## 8. Conclusions

- (1)
- Based on the factors of the grouting pressure, angle between crack and grouting hole, hydrostatic pressure, grouting volume, grout viscosity, fracture width, grout gravity and grouting duration, we established a mathematical model of Newtonian fluid slurry diffusion distance in the upper and lower cracks of horizontal grouting holes.
- (2)
- As determined by theoretical analysis, the slurry in an inclined single fracture of a horizontal grouting hole increases with an increase in grouting duration under various water–solid ratios, grouting pressure, crack opening and angle between crack and grouting hole and the increase rate decreases over time. However, the slurry diffusion distance in the fracture above the horizontal grouting hole is larger than that in the lower fracture when the grout propagation length is hundreds of meters or more and the difference increases multiple times under the wide fracture scale.
- (3)
- Based on the orthogonal design and numerical calculations, we obtained a sequence of the sensitivity of the factors affecting the diffusion distance of Newtonian grout in an inclined fracture of a horizontal grouting hole: from higher to lower, they were crack opening, fracture inclination angle, water–solid ratio and grouting pressure.
- (4)
- Based on the control equation of the grout diffusion distance of an inclined fracture in a horizontal grouting hole and grouting parameters for a mine in the fourth mining area, the horizontal spacing of branch holes was not more than 65.90 m and the interface distance between the branch holes and the Ordovician limestone roof was not more than 32.95 m, which is close to the engineering practice parameters.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Variation curve of grout propagation length with duration under various influencing factors. (

**a**) Grout pressure, (

**b**) width of fracture, (

**c**) angle between fracture and horizontal hole, (

**d**) water-cement ratio.

**Figure 4.**Case 1 calculation result. (a) Grout propagation pattern. (b) Distribution of grout propagation pressure field.

**Figure 5.**Case 2 calculation result. (a) Grout propagation pattern. (b) Distribution of grout propagation pressure field.

**Figure 6.**Case 3 calculation result. (a) Grout propagation pattern. (b) Distribution of grout propagation pressure field.

**Figure 7.**Case 4 calculation result. (a) Grout propagation pattern. (b) Distribution of grout propagation pressure field.

**Figure 8.**Case 5 calculation result. (a) Grout propagation pattern. (b) Distribution of grout propagation pressure field.

**Figure 9.**Case 6 calculation result. (a) Grout propagation pattern. (b) Distribution of grout propagation pressure field.

**Figure 10.**Case 7 calculation result. (a) Grout propagation pattern. (b) Distribution of grout propagation pressure field.

**Figure 11.**Case 8 calculation result. (a) Grout propagation pattern. (b) Distribution of grout propagation pressure field.

**Figure 12.**Case 9 calculation result. (a) Grout propagation pattern. (b) Distribution of grout propagation pressure field.

**Figure 13.**Technical route of grout propagation control method for advanced regional grouting projects in coal floors.

**Figure 14.**Calculation curve of slurry diffusion distance on top of Middle Ordovician limestone in No. 4 mining area.

**Figure 15.**Design of main hole and Middle Ordovician limestone horizontal branch hole in the No. 4 mining area.

**Table 1.**Number of boreholes with different depths and drilling flushing fluid consumption at the upper layer of the MOL and the average of drilling flushing fluid consumption at corresponding depths (Dongpang mine).

Leakage/m^{3}·h^{−1} | Number of Boreholes at Different Depths | ||||
---|---|---|---|---|---|

≤10 m | 10–20 m | 20–30 m | 30–40 m | >40 m | |

≤0.1 | 5 | 5 | 7 | 7 | 3 |

0.1–1.0 | 9 | 9 | 7 | 6 | 6 |

1.0–10.0 | 2 | 2 | 2 | 3 | 5 |

>10.0 | 0 | 0 | 0 | 0 | 1 |

Average leakage | 0.5 | 0.35 | 0.38 | 0.31 | 2.12 |

**Table 2.**Hydro-chemical type and mineralization degree of an MOL aquifer in part of China’s Hanxing mining area.

Number | Mining | Borehole Number | Position | pH | Hydro-Chemical Type | Mineralization Degree/mg·L^{−1} |
---|---|---|---|---|---|---|

a | Xingmei | D3 | The eighth section of Fengfeng formation | 8.17 | HCO_{3}-Ca·Mg | 336.07 |

b | Xingdong | T3 | The seventh section of Fengfeng formation | 8.85 | SO_{4}-Ca·Mg | 1690.37 |

c | Wutongzhuang | WO3 | Fengfeng formation | 7.09 | Cl·SO_{4}-Ca·Na | 5496.47 |

d | Jiulong | / | The seventh section of Fengfeng formation | 7.75 | Cl·SO_{4}-Ca·Na | 4333.30 |

Level | Factors | ||
---|---|---|---|

Water–Cement Mass Ratio (A) | Content of Sodium Silicate/% (B) | Hydro-Chemical Type (Mining) (C) | |

1 | 0.6:1 | 0 | a (Xingmei) |

2 | 0.8:1 | 2 | b (Xingdong) |

3 | 1:1 | 5 | c (Wutongzhuang) |

4 | 2:1 | 8 | d (Jiulong) |

Test Number | Water–Cement Mass Ratio (A) | Content of Sodium Silicate/% (B) | Hydro-Chemical Type (Mining) (C) |
---|---|---|---|

1 | 0.6:1 | 0 | a |

2 | 0.6:1 | 2 | b |

3 | 0.6:1 | 5 | c |

4 | 0.6:1 | 8 | d |

5 | 0.8:1 | 0 | b |

6 | 0.8:1 | 2 | a |

7 | 0.8:1 | 5 | d |

8 | 0.8:1 | 8 | c |

9 | 1:1 | 0 | c |

10 | 1:1 | 2 | d |

11 | 1:1 | 5 | a |

12 | 1:1 | 8 | b |

13 | 2:1 | 0 | d |

14 | 2:1 | 2 | c |

15 | 2:1 | 5 | b |

16 | 2:1 | 8 | a |

Test Number | Influencing Factors | Physical and Mechanical Property Parameters | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

A | B | C | Viscosity/Pa.s | Density/g.cm^{−3} | Initial Setting Time/h | Final Setting Time/h | Stone Rate/% | Flexural Strength/MPa | Compressive Strength/MPa | |||||

3 d | 7 d | 28 d | 3 d | 7 d | 28 d | |||||||||

1 | 0.6:1 | 0 | a | 0.30 | 1.64 | 10.08 | 13.00 | 95.40 | 2.47 | 2.75 | 4.88 | 6.09 | 8.32 | 18.74 |

2 | 0.6:1 | 2 | b | 0.58 | 1.57 | 8.92 | 11.33 | 97.10 | 2.50 | 3.13 | 4.71 | 6.79 | 10.68 | 16.36 |

3 | 0.6:1 | 5 | c | 0.88 | 1.56 | 6.08 | 8.42 | 98.40 | 2.42 | 3.34 | 4.86 | 6.37 | 10.34 | 16.29 |

4 | 0.6:1 | 8 | d | 1.24 | 1.51 | 4.33 | 6.58 | 99.20 | 1.69 | 2.73 | 3.50 | 4.17 | 9.12 | 14.98 |

5 | 0.8:1 | 0 | b | 0.16 | 1.45 | 11.33 | 15.10 | 84.65 | 1.77 | 2.37 | 4.43 | 3.65 | 6.22 | 18.32 |

6 | 0.8:1 | 2 | a | 0.22 | 1.42 | 9.50 | 11.83 | 90.75 | 1.25 | 1.73 | 3.52 | 3.33 | 5.93 | 11.66 |

7 | 0.8:1 | 5 | d | 0.67 | 1.41 | 7.25 | 10.08 | 93.05 | 1.14 | 1.54 | 2.75 | 3.00 | 4.68 | 9.29 |

8 | 0.8:1 | 8 | c | 0.79 | 1.39 | 5.17 | 7.67 | 96.50 | 1.13 | 1.54 | 2.57 | 2.93 | 4.42 | 8.43 |

9 | 1:1 | 0 | c | 0.12 | 1.42 | 13.18 | 16.28 | 74.60 | 1.24 | 1.82 | 3.59 | 2.83 | 4.55 | 8.83 |

10 | 1:1 | 2 | d | 0.17 | 1.40 | 10.17 | 12.50 | 81.50 | 0.96 | 1.45 | 2.57 | 1.74 | 3.73 | 7.27 |

11 | 1:1 | 5 | a | 0.39 | 1.38 | 7.92 | 10.75 | 94.50 | 0.86 | 0.92 | 2.07 | 2.16 | 2.85 | 6.25 |

12 | 1:1 | 8 | b | 0.52 | 1.36 | 6.67 | 9.33 | 98.20 | 0.64 | 0.93 | 1.98 | 1.69 | 2.60 | 4.75 |

13 | 2:1 | 0 | d | 0.10 | 1.25 | 16.83 | 19.58 | 45.90 | 0.82 | 1.24 | 2.40 | 1.52 | 3.35 | 5.18 |

14 | 2:1 | 2 | c | 0.13 | 1.22 | 11.92 | 15.80 | 73.60 | 0.49 | 0.46 | 1.01 | 0.59 | 1.09 | 1.56 |

15 | 2:1 | 5 | b | 0.15 | 1.20 | 10.58 | 13.08 | 87.65 | 0.30 | 0.50 | 0.65 | 0.45 | 0.80 | 1.36 |

16 | 2:1 | 8 | a | 0.22 | 1.18 | 7.17 | 10.42 | 91.60 | 0.21 | 0.29 | 0.44 | 0.35 | 0.49 | 0.92 |

**Table 6.**Range of grout properties under various influence factors and their sensitivity ranking to those factors.

Physical and Mechanical Property Parameters | Water–Cement Mass Ratio (A) | Content of Sodium Silicate (B) | Hydro-Chemical Type (Mining) (C) | Sensitivity Ranking | |
---|---|---|---|---|---|

density/Kg.m^{−3} | 0.36 | 0.08 | 0.01 | A > B > C | |

viscosity/Pa.s | 0.60 | 0.52 | 0.26 | A > B > C | |

Initial setting time/h | 4.27 | 7.02 | 0.98 | B > A > C | |

Final setting time/h | 4.89 | 7.49 | 0.71 | B > A > C | |

Stone rate/% | 22.84 | 21.24 | 13.15 | A > B > C | |

Flexural strength/MPa | 3 d | 1.82 | 0.66 | 0.16 | A > B > C |

7 d | 2.36 | 0.67 | 0.36 | A > B > C | |

28 d | 3.37 | 1.70 | 0.28 | A > B > C | |

Compressive strength/MPa | 3 d | 5.13 | 1.24 | 0.57 | A > B > C |

7 d | 8.18 | 2.11 | 1.45 | A > B > C | |

28 d | 14.34 | 8.02 | 1.42 | A > B > C |

**Table 7.**Calculation parameters of grout propagation length under various factors. (a) Grout pressure. (b) Fracture width. (c) Angle between fracture and horizontal hole. (d) Water–cement ratio.

Number | Level | Water–Cement Ratio | Viscosity/Pa·s | Density/Kg.m^{−3} | Width of Fracture/m | Angle/° | Grout Pressure/Pa |
---|---|---|---|---|---|---|---|

1 | grout pressure | 2:1 | 0.0967 | 1248 | 0.0002 | 30 | 1.2 × 10^{7} |

1.5 × 10^{7} | |||||||

2.0 × 10^{7} | |||||||

2.5 × 10^{7} | |||||||

2 | width of fracture | 2:1 | 0.0967 | 1248 | 0.0002 | 30 | 2 × 10^{7} |

0.001 | |||||||

0.005 | |||||||

0.01 | |||||||

3 | angle | 2:1 | 0.0967 | 1248 | 0.0002 | 0 | 2 × 10^{7} |

30 | |||||||

60 | |||||||

90 | |||||||

4 | water–cement ratio | 3:1 | 1160 | 0.0742 | 0.0002 | 30 | 2 × 10^{7} |

2:1 | 1248 | 0.0967 | |||||

1:1 | 1424 | 0.1198 |

Factors | Levels | ||
---|---|---|---|

1 | 2 | 3 | |

water–cement ratio | 1:1 | 2:1 | 3:1 |

grouting pressure/MPa | 15 | 20 | 25 |

width of fracture/mm | 1 | 5 | 10 |

angle of fracture/° | 30 | 60 | 90 |

Number | Water–Cement Ratio | Grouting Pressure/MPa | Width of Fracture/mm | Angle of Fracture/° |
---|---|---|---|---|

1 | 1:1 | 15 | 1 | 30 |

2 | 1:1 | 20 | 5 | 60 |

3 | 1:1 | 25 | 10 | 90 |

4 | 2:1 | 15 | 5 | 90 |

5 | 2:1 | 20 | 10 | 30 |

6 | 2:1 | 25 | 1 | 60 |

7 | 3:1 | 15 | 10 | 60 |

8 | 3:1 | 20 | 1 | 90 |

9 | 3:1 | 25 | 5 | 30 |

Factor | Grout Propagation Length/m | ||||
---|---|---|---|---|---|

A | B | C | D | ||

1 | 1:1 | 15 | 1 | 30 | 46 |

2 | 1:1 | 20 | 5 | 60 | 41.57 |

3 | 1:1 | 25 | 10 | 90 | 48 |

4 | 2:1 | 15 | 5 | 90 | 43 |

5 | 2:1 | 20 | 10 | 30 | 56 |

6 | 2:1 | 25 | 1 | 60 | 27.71 |

7 | 3:1 | 15 | 10 | 60 | 42.73 |

8 | 3:1 | 20 | 1 | 90 | 24.5 |

9 | 3:1 | 25 | 5 | 30 | 53 |

mean value 1 | 45.19 | 43.91 | 32.74 | 51.67 | / |

mean value 2 | 42.24 | 40.69 | 45.86 | 37.34 | / |

mean value 3 | 40.08 | 42.90 | 48.91 | 38.50 | / |

xmax-xmin | 5.11 | 3.22 | 16.17 | 14.33 | / |

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**MDPI and ACS Style**

Liu, Z.; Dong, S.; Wang, H.; Shang, H.
Mechanism and Control of Grout Propagation in Horizontal Holes in Fractured Rock. *Water* **2022**, *14*, 4062.
https://doi.org/10.3390/w14244062

**AMA Style**

Liu Z, Dong S, Wang H, Shang H.
Mechanism and Control of Grout Propagation in Horizontal Holes in Fractured Rock. *Water*. 2022; 14(24):4062.
https://doi.org/10.3390/w14244062

**Chicago/Turabian Style**

Liu, Zhaoxing, Shuning Dong, Hao Wang, and Hongbo Shang.
2022. "Mechanism and Control of Grout Propagation in Horizontal Holes in Fractured Rock" *Water* 14, no. 24: 4062.
https://doi.org/10.3390/w14244062