# Calculation of the Height of the Water-Conducting Fracture Zone Based on the Analysis of Critical Fracturing of Overlying Strata

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mining Overburden Structure and Mechanical Analysis

#### 2.1. Determination of the Bearing Strata

^{3}.

#### 2.2. Mechanical Analysis on the Hard Rock Strata

#### 2.2.1. Analysis on the Stability of the “Masonry Beam” Structure

_{z}; h is the stratum thickness, m; L

_{z}is the length of the periodically broken block, m; $\phi $ is the friction angle between broken blocks; θ is the rotary angle between the key blocks, °.

_{c}is compressive strength of the bearing stratum, MPa;

_{p}is the dilatancy coefficient of the stratum.

#### 2.2.2. Analysis on the Bending Subsidence Deformation of the Hard Strata

^{4}; b is the width of the rectangular section of the beam, m.

#### 2.3. Mechanical Analysis on the Soft Strata

`ɛ`

_{max}is the horizontal tensile strain.

_{S}is the breaking length of the soft stratum, m; $\omega $ is its corresponding deflection of the soft stratum, m.

_{i}is the thickness of the i-th stratum, m; (K

_{p})

_{i}is the residual dilatancy coefficient of the i-th stratum.

## 3. CFSHS-Based Height Calculation Method

_{i}is the thickness of the i-th stratum, m; (K

_{p})

_{i}is the residual dilatancy coefficient of the i-th stratum.

_{max})

_{i}, which is then compared with the height of the free space below it Δ

_{i}:

## 4. Engineering Case Analysis

#### 4.1. Geological Overview

^{3/}h, and the maximum daily water inflow is 16.9 m

^{3}/h. It is the largest from June to August and the smallest from January to April, which is directly related to rainfall. The hydrogeological type is medium. Most of the surface is exposed bedrock and partially covered by Quaternary loess. The complexity of mine field structure is a simple type. In coal seam 3, there is no large geological structure and large geological events.

_{z}of the immediate roof in the goaf of working face 15,101 is 1.15; the residual dilatancy coefficient of the upper rock stratum gradually decreases in the logarithmic form. According to researches [32,33], the relationship between the average residual dilatancy coefficient K

_{p}of the stratum and the mining distance from the coal seam h is:

_{z}. Calculation reveals that the average residual dilatancy coefficient of the 16th stratum (mudstone) at a mining distance of 98.86 m from the coal seam is 1.07, so the average residual dilatancy coefficient of the 17th stratum and its upper strata shall be smaller than 1.07; hence both are set as 1.06.

#### 4.2. Engineering Case of the CFSHS-Based Height Calculation Method

_{i}under the stratum was calculated, and the results are listed in Table 1.

_{z}, θ, L

_{c}and ω

_{max}of hard strata can be obtained (Table 2).

#### 4.3. Engineering Measurement and Analysis

#### 4.3.1. Observation Scheme Design

#### 4.3.2. Observation Method

#### 4.3.3. Analysis on the Observation Results

#### 4.4. Numerical Simulation Analysis

#### 4.4.1. Model Design

#### 4.4.2. Simulation Results and Analysis

#### 4.5. Scope of Application

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Peng, S.S. Coal Mine Ground Control; Wiley: New York, NY, USA, 1978. [Google Scholar]
- Kratzsch, H. Mining Subsidence Engineering; Springer: Berlin/Heidelberg, Germany, 1983. [Google Scholar]
- Gray, R.E. Mining subsidence- past, present, future. Int. J. Min. Geol. Eng.
**1990**, 8, 400–408. [Google Scholar] [CrossRef] - Kang, Y.; Jin, R. Actuality and developing trend of long wall top coal caving mining under water. Coal Min. Technol.
**2003**, 1, 15–18. [Google Scholar] - Yan, W.; Chen, J.; Yang, W.; Liu, X.; Wang, W.; Zhang, W. On-Site Measurement on Surface Disturbance Law of Repeated Mining with High Relief Terrain. Sustainability
**2022**, 14, 3166. [Google Scholar] [CrossRef] - Fan, G.; Zhang, D.; Ma, L. Overburden movement and fracture distribution induced by longwall mining of the shallow coal seam in the Shendong coalfield. J. China Univ. Min. Technol.
**2011**, 40, 196–201. [Google Scholar] - State Administration of Safety; State Administration of Coal Mine Safety; State Energy Administration; State Railway Administration. Buildings Water, Railways and Main Well Lane of Coal Pillar and Mining Regulations; China Coal Industry Publishing House: Beijing, China, 2017. [Google Scholar]
- Sun, Y.; Xu, Z.; Dong, Q. Monitoring and simulation research on development of water flowing fractures for coal mining under Xiaolangdi reservoir. Chin. J. Rock Mech. Eng.
**2011**, 31, 3444–3451. [Google Scholar] - Cao, D.; Li, W. Estimation method for height of fratured zone with in coal mining area. Chin. J. Geol. Hazard Control
**2014**, 1, 63–69. [Google Scholar] - Vervoor, A. Various phases in surface movements linked to deep coal longwall mining: From start-up till the period after closure. Int. J. Coal Sci. Technol.
**2021**, 8, 412–426. [Google Scholar] [CrossRef] - Guo, C.; Yang, Z.; Li, S.; Lou, J. Predicting the Water-Conducting Fracture Zone (WCFZ) Height Using an MPGA-SVR Approach. Sustainability
**2020**, 12, 1809. [Google Scholar] [CrossRef] [Green Version] - Wanner, C.; Bucher, K.; von Strandmann, P.A.P.; Waber, H.N.; Pettke, T. On the use of Li isotopes as a proxy for water–rock interaction in fractured crystalline rocks: A case study from the Gotthard rail base tunnel. Geochim. Cosmochim. Acta
**2017**, 198, 396–418. [Google Scholar] [CrossRef] [Green Version] - Khanzode, V.V.; Maiti, J.; Ray, P.K. A methodology for evaluation and monitoring of recurring hazards in underground coal mining. Saf. Sci.
**2011**, 49, 1172–1179. [Google Scholar] [CrossRef] - Rezaei, M.; Hossaini, M.F.; Majdi, A. A time-independent energy model to determine the height of destressed zone above the mined panel in longwall coal mining. Tunn. Undergr. Space Technol.
**2015**, 47, 81–92. [Google Scholar] [CrossRef] - Xu, Y.; Li, J.; Liu, S.; Zhou, L. Calculation formula of “two-zone” height overlying strata and its adaptability analysis. Coal Min. Technol.
**2011**, 2, 4–7. [Google Scholar] - Xu, Y.; Liu, S. Study on method to set safety coal and rock pillar for full mechanized top coal caving mining under water body. Coal Sci. Technol.
**2011**, 11, 1–4. [Google Scholar] - Qian, M.; Miao, X. Theoretical analysis of the structural form and stability of overlying strata in Long wang mining. Chin. J. Rock Mech. Eng.
**1995**, 2, 97–106. [Google Scholar] - Guo, H.; Sun, Z.; Ji, M.; Wu, Y.; Nian, L. An Investigation on the Impact of Unloading Rate on Coal Mechanical Properties and Energy Evolution Law. Int. J. Environ. Res. Public Health
**2022**, 19, 4546. [Google Scholar] [CrossRef] [PubMed] - Wang, Y.; Wang, X.; Zhang, J.; Chen, X.; Zhu, W.; Zhang, Y. Roof Subsidence and Movement Law of Composite Strata Mining: Insights from Physical and Numerical Modeling. Minerals
**2022**, 12, 3. [Google Scholar] [CrossRef] - Zhai, W.; Li, W.; Huang, Y.; Ouyang, S.; Ma, K.; Li, J.; Gao, H.; Zhang, P. A Case Study of the Water Abundance Evaluation of Roof Aquifer Based on the Development Height of Water-Conducting Fracture Zone. Energies
**2020**, 13, 4095. [Google Scholar] [CrossRef] - Sun, Q.; Mu, Y.; Yang, X. Study on “two zones” height of overlying of fully-mechanized technology with high mining height at Hongliu Coal Mine. J. China Coal Soc.
**2013**, 38, 283–286. [Google Scholar] - Xun, Y. Research on movement and evolution law of breaking of overlying strata in shallow coal seam with a thin bedrock. Rock Soil Mech.
**2008**, 2, 512–516. [Google Scholar] - Yan, W.; Chen, J.; Tan, Y.; Zhang, W.; Cai, L. Theoretical Analysis of Mining Induced Overburden Subsidence Boundary with the Horizontal Coal Seam Mining. Adv. Civ. Eng.
**2021**, 2021, 6657738. [Google Scholar] [CrossRef] - Sun, Y.; Zuo, J.; Karakus, M.; Liu, L.; Zhou, H.; Yu, M. A New Theoretical Method to Predict Strata Movement and Surface Subsidence due to Inclined Coal Seam Mining. Rock Mech. Rock Eng.
**2021**, 54, 2723–2740. [Google Scholar] [CrossRef] - Thongprapha, T.; Fuenkajorn, K.; Daemen, J.K. Study of surface subsidence above an underground opening using a trap door apparatus. Tunn. Undergr. Space Technol.
**2015**, 46, 94–103. [Google Scholar] [CrossRef] - Vervoort, A. Surface movement above an underground coal longwall mine after closure. Nat. Hazards Earth Syst. Sci.
**2016**, 9, 2107–2121. [Google Scholar] [CrossRef] [Green Version] - Sasaoka, T.; Takamoto, H.; Shimada, H.; Oya, J.; Hamanaka, A.; Matsui, K. Surface subsidence due to underground mining operation under weak geological condition in Indonesia. J. Rock Mech. Geotech. Eng.
**2015**, 3, 337–344. [Google Scholar] [CrossRef] [Green Version] - Mokhov, A.V. A rock mass permeability model within the subsidence zone in workings of coal fields. Dokl. Earth Sci.
**2017**, 473, 390–393. [Google Scholar] [CrossRef] - Yang, W.; Guo, W.; Zhao, G.; Ma, Z.; Yang, D. Theoretical judgement method of overburden “Three-zone” based on rock strata deflection deformation and its engineering application. Coal Sci. Technol.
**2021**, 1–9. Available online: http://kns.cnki.net/kcms/detail/11.2402.TD.20211206.2350.003.html (accessed on 17 March 2022). - Hou, E.; Wen, Q.; Ye, Z.; Chen, W.; Wei, J. Height prediction of water-flowing fracture zone with a genetic-algorithm support-vector-machine method. Int. J. Coal Sci. Technol.
**2020**, 7, 740–751. [Google Scholar] [CrossRef] - Cao, Z.; Ju, J.; Xu, J. Distribution model of water-conducted fracture main channel and its flow characteristics. J. China Coal Soc.
**2019**, 12, 3719–3728. [Google Scholar] - Gao, B.; Wang, X.; Zhu, M.; Zhou, J. Dynamic development characteristics of two zones of overburden strata under conditions of compound roof highly gassy and thick coal seam in full-mechanized top cole caving faces. Chin. J. Rock Mech. Eng.
**2013**, 31, 3444–3451. [Google Scholar] - Cao, J.; Ma, Q.; Wang, Y. Study of Wide Strip Mining Based on Spatial Structure Principle of Overlying Strata. Coal Sci. Technol.
**2008**, 1, 68–72. [Google Scholar]

**Figure 1.**Schematic diagram of the “masonry beam” structure where A

_{1}, B

_{1}, C

_{1}, D

_{1}, A

_{2}, B

_{2}, C

_{2}and D

_{2}are articulated rock blocks; R is the jointing force and supporting force between rock blocks; T is the horizontal thrust for the structure; q is the load.

**Figure 5.**Relationship curve between the free space height below the stratum and the stratum height.

**Figure 8.**Photos of the overburden fractures after mining. (

**a**) 10.25 m (

**b**) 16.20 m (

**c**) 24.88 m (

**d**) 29.73 m (

**e**) 33.85 m (

**f**) 39.37 m (

**g**) 45.35 m (

**h**) 50.19 m (

**i**) 56.58 m (

**j**) 60.08 m.

**Figure 11.**Nephograms of vertical displacement of the overburden during the advancement of working face. (

**a**) Excavation to 90 m; (

**b**) Excavation to 120 m; (

**c**) Excavation to 150 m; (

**d**) Excavation to 420 m.

Number of the Stratum | Lithology | Thickness/m | Height from the Coal Seam Roof/m | ∆_{i}/m |
---|---|---|---|---|

1 | Limestone | 7.50 | 7.50 | 3.08 |

2 | Mudstone | 6.13 | 13.63 | 2.76 |

3 | Sandy mudstone | 3.17 | 16.80 | 2.49 |

4 | Limestone | 4.79 | 21.59 | 2.09 |

1st hard stratum | Mudstone | 7.49 | 29.08 | 1.50 |

(1, 1) soft stratum | Fine sandstone | 2.87 | 31.95 | 1.29 |

(1, 2) soft stratum | Limestone | 3.25 | 35.20 | 1.05 |

2nd hard stratum | Fine sandstone | 5.98 | 41.18 | 0.63 |

3rd hard stratum | Siltstone | 8.38 | 49.56 | 0.05 |

(3, 1) soft stratum | Fine sandstone | 5.77 | 55.33 | −0.32 |

(3, 2) soft stratum | Siltstone | 7.53 | 62.86 | −0.80 |

(3, 3) soft stratum | Mudstone | 4.13 | 66.99 | −1.06 |

(3, 4) soft stratum | Limestone | 5.20 | 72.19 | −1.38 |

4th hard stratum | Sandy mudstone | 9.48 | 81.67 | −1.94 |

Number of the Stratum | L_{z}/m | θ/° | L_{c}/m | ω_{max}/mm |
---|---|---|---|---|

1st hard stratum | 24.9 | 3.5 | 61.0 | 9.6 |

2nd hard stratum | 24.5 | 1.5 | 60.0 | 10.0 |

3rd hard stratum | 29.7 | 0.1 | 72.6 | 12.5 |

4th hard stratum | 22.9 | / | 56.0 | 4.3 |

Borehole Number | Diameter/mm | Elevation/(°) | Azimuth/(°) | Hole Depth/m | Vertical Depth/m |
---|---|---|---|---|---|

CH01 | Φ89 | 50 | N137 | 118 | 90 |

CH02 | Φ89 | 55 | N137 | 110 | 90 |

Lithology | Density /kg·m ^{−3} | Bulk Modulus /GPa | Shear Modulus /MPa | Cohesion /MPa | Internal Friction Angle /° | Tensile Strength /MPa | Normal Stiffness /GN*m ^{−1} | Tangential Stiffness /GN*m ^{−1} |
---|---|---|---|---|---|---|---|---|

Loess | 1832 | 0.28 | 0.093 | 0.85 | 25 | 0.35 | 0.25 | 0.25 |

Mudstone | 2540 | 1.23 | 1.06 | 2.16 | 24 | 1.26 | 0.18 | 0.18 |

Sandy mudstone | 2580 | 3.72 | 1.62 | 3.53 | 25 | 2.06 | 0.59 | 0.59 |

Medium grained sandstone | 2630 | 2.31 | 1.26 | 5.92 | 26 | 2.86 | 0.50 | 0.50 |

Siltstone | 2580 | 2.98 | 1.88 | 4.28 | 23 | 2.55 | 1.09 | 1.09 |

Fine sandstone | 2610 | 2.64 | 1.68 | 4.36 | 22 | 2.32 | 0.49 | 0.49 |

Coal | 1400 | 1.16 | 0.73 | 1.54 | 22 | 1.03 | 0.21 | 0.21 |

Limestone | 2800 | 4.45 | 8.91 | 4.20 | 39 | 3.10 | 2.60 | 2.60 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tan, Y.; Cheng, H.; Lv, W.; Yan, W.; Guo, W.; Zhang, Y.; Qi, T.; Yin, D.; Wei, S.; Ren, J.;
et al. Calculation of the Height of the Water-Conducting Fracture Zone Based on the Analysis of Critical Fracturing of Overlying Strata. *Sustainability* **2022**, *14*, 5221.
https://doi.org/10.3390/su14095221

**AMA Style**

Tan Y, Cheng H, Lv W, Yan W, Guo W, Zhang Y, Qi T, Yin D, Wei S, Ren J,
et al. Calculation of the Height of the Water-Conducting Fracture Zone Based on the Analysis of Critical Fracturing of Overlying Strata. *Sustainability*. 2022; 14(9):5221.
https://doi.org/10.3390/su14095221

**Chicago/Turabian Style**

Tan, Yi, Hao Cheng, Wenyu Lv, Weitao Yan, Wenbing Guo, Yujiang Zhang, Tingye Qi, Dawei Yin, Sijiang Wei, Jianji Ren,
and et al. 2022. "Calculation of the Height of the Water-Conducting Fracture Zone Based on the Analysis of Critical Fracturing of Overlying Strata" *Sustainability* 14, no. 9: 5221.
https://doi.org/10.3390/su14095221