# Thickness and Strength Analysis of Prestressed Anchor (Cable) Compression Arch Based on Safe Co-Mining of Deep Coal and Gas

^{*}

## Abstract

**:**

^{3D}is used to analyze the typical position of fractured mudstone, mudstone, sandy mudstone and muddy sandstone under the bolt pre-tightening force of F = 50 kN, 70 kN and 100 kN; the bolt spacing of a × b = 400 mm × 400 mm, 500 mm × 500 mm and 600 mm × 600 mm; the bolt length of L = 1500 mm, 2000 mm, 2600 mm and 3000 mm; and the distribution characteristics of additional compressive stress on the surface of the side. The influence of the different lithology and bolt parameters on the thickness and strength of the compression arch was analyzed, and on this basis, prestressed anchor cables with a pre-tightening force of F = 80 kN, 100 kN and 120 kN and length of L = 3000 mm, 4000 mm and 6000 mm were applied, and their influence on the thickness and strength of the compression arch was analyzed. The results show that the bolt pre-tightening force (F) and the bolt length (L) have a significant effect on the thickness of the compression arch, while the surrounding rock lithology, the bolt spacing (a × b), the anchor cable pre-tightening force (F) and the anchor cable length (L) have no obvious effect on the thickness of the compression arch. The surrounding rock lithology, the bolt pre-tightening force (F), the bolt length (L), the bolt spacing (a × b), the anchor cable pre-tightening force (F) and the anchor cable length (L) have a significant effect on the strength of the compression arch.

## 1. Introduction

## 2. Determination of Mechanical Parameters

## 3. Numerical Model Building

^{3D}software was used for numerical simulation. The roadway section size was taken as the roadway width × straight wall height = 4.8 m × 1.4 m. The strain-softening model was used as the constitutive model, and the Mohr–Coulomb criterion was selected as the yield criterion. The zone gridpoint fix command was used to impose constraints on the bottom and both sides of the model to limit the displacement. The calculation model is shown in Figure 1. The original mesh model radial cylinder and radial tunnel were selected, and the ratio parameter was set to 1.1. The influence range after the excavation of the roadway is generally 5–6 times the radius of the roadway. Therefore, the plane size of the mesh model is length × width = 60 m × 60 m, and the mesh model is shown in Figure 2. The lithology of surrounding rock is fractured mudstone, mudstone, sandy mudstone and muddy sandstone. Change the bolt pre-tightening force to F = 50 kN, 70 kN and 100 kN; the bolt spacing to a × b = 400 mm × 400 mm, 500 mm × 500 mm and 600 mm × 600 mm; and the bolt length to L = 1500 mm, 2000 mm, 2600 mm and 3000 mm. Then, analyze the typical position of different lithology surrounding rock side and the distribution of additional compressive stress field on the surface of side, and further analyze the influence of prestressed anchor (cable) on the thickness and strength of the compression arch.

## 4. Calculation Results and Analysis

#### 4.1. The Influence of Different Bolt Pre-Tightening Forces on the Additional Stress Distribution of Surrounding Rock

- (1)
- When the bolt pre-tightening force increases from 50 kN to 100 kN, the additional stress of the surrounding rock fluctuates within a certain range of the roadway surface. As the surface distance of the roadway side increases, the additional stress decreases rapidly.
- (2)
- The additional stress on the surface of the roadway side increases with the increase of the bolt pre-tightening force, and the additional stress distribution of different lithologies is not obvious. when the bolt pre-tightening force increases from 50 kN to 100 kN, the additional stress of fractured mudstone, mudstone, sandy mudstone and muddy sandstone increases from the ranges 0.05–0.06 MPa, 0.048–0.049 MPa, 0.049–0.05 MPa and 0.0508–0.051 MPa to the ranges 0.094–0.098 MPa, 0.095–0.098 MPa, 0.098–0.10 MPa and 0.099–0.10 MPa, respectively. The lithology of sandy mudstone and muddy sandstone is better, and the fluctuation range of additional stress on the surface of the side is smaller.
- (3)
- The additional stress at the typical position of the roadway side increases with the increase of the bolt pre-tightening force. When the bolt pre-tightening force of F = 50 kN increased to 100 kN, the average additional stress of fractured mudstone, mudstone, sandy mudstone and muddy sandstone increased from 0.062 MPa, 0.062 MPa, 0.062 MPa and 0.062 MPa to 0.12 MPa, 0.12 MPa, 0.12 MPa and 0.12 MPa, respectively. The additional stress at the place where the roadway side is close to the arch baseline is large.

#### 4.2. The Influence of Different Bolt Length on the Additional Stress Distribution of Surrounding Rock

- (1)
- When the bolt length increases from 1.5 m to 3.0 m, the additional stress of the surrounding rock fluctuates within a certain range of the roadway surface. As the surface distance of the roadway side increases, the additional stress decreases rapidly.
- (2)
- The additional stress on the surface of the roadway side increases with the increase of the bolt length, and the additional stress distribution of different lithologies is not obvious. When the length of the bolt increases from 1.5 m to 3.0 m, the additional stress of the fractured mudstone, mudstone, sandy mudstone and muddy sandstone increases from the ranges of 0.096–0.101 MPa, 0.096–0.100 MPa, 0.098–0.101 MPa and 0.099–0.101 MPa to the ranges of 0.126–0.141 MPa, 0.127–0.141 MPa, 0.128–0.140 MPa and 0.139–0.140 MPa, respectively. The lithology of sandy mudstone and muddy sandstone is better, and the fluctuation range of additional stress on the surface of the side is smaller.
- (3)
- The additional stress at the typical position of the roadway side decreases with the increase of the bolt spacing. When the bolt spacing (a × b) increases from 400 mm × 400 mm to 600 mm × 600 mm, the average additional stress of fractured mudstone, mudstone, sandy mudstone and muddy sandstone decreases from 0.17 MPa, 0.17 MPa, 0.17 MPa and 0.17 MPa to 0.14 MPa, 0.14 MPa, 0.14 MPa and 0.14 MPa, respectively. The additional stress at the place where the roadway side is close to the arch baseline is large.

#### 4.3. The Influence of Different Bolt Spacing on the Additional Stress Distribution of Surrounding Rock

- (1)
- When the bolt row spacing increases from 400 mm × 400 mm to 600 mm × 600 mm, the additional stress of the surrounding rock fluctuates within a certain range of the roadway surface. As the surface distance of the roadway side increases, the additional stress decreases rapidly.
- (2)
- The additional stress on the surface of the roadway side decreases with the increase of the bolt spacing, and the additional stress distribution of different lithologies is not obvious. When the bolt row spacing increases from 400 mm × 400 mm to 600 mm × 600 mm, the additional stress of the fractured mudstone, mudstone, sandy mudstone and muddy sandstone decreases from the ranges of 0.128–0.138 MPa, 0.124–0.139 MPa, 0.124–0.138 MPa and 0.123–0.136 MPa to the ranges of 0.098–0.105 MPa, 0.099–0.105 MPa, 0.099–0.104 MPa and 0.100–0.103 MPa, respectively. The lithology of sandy mudstone and muddy sandstone is better, and the fluctuation range of additional stress on the surface of the side is smaller.
- (3)
- When the bolt row spacing is a × b = 400 mm × 400 mm, the average additional stress of fractured mudstone, mudstone, sandy mudstone and muddy sandstone is 0.17 MPa, 0.17 MPa, 0.17 MPa and 0.17 MPa. When the bolt row spacing is a × b = 600 mm × 600 mm, the average additional stress is 0.14 MPa, 0.14 MPa, 0.14 MPa and 0.14 MPa. The additional stress at the place where the roadway side is close to the arch baseline is large.

#### 4.4. Calculation of Compression Arch Thickness of Prestressed Anchors under Different Lithologies

- (1)
- When the bolt spacing is a × b = 400 mm × 400 mm, and the bolt length is L = 1.5 m, by changing the size of the bolt pre-tightening force, when the pre-tightening force (F) increases from 50 kN to 100 kN, the thickness of the compression arch formed by the four lithologies increases from 0.73 m to 0.85 m, which is a small increase.
- (2)
- When the bolt pre-tightening force is F = 100 kN, and the bolt spacing is a × b = 400 mm × 400 mm, by changing the bolt length, when the bolt length (L) increases from 1.5 m to 3.0 m, the thickness of the compression arch formed by the four lithologies increases from 0.85 m to 1.84 m. Compared with changing the bolt pre-tightening force, changing the bolt length has a better effect on increasing the thickness of the compression arch.
- (3)
- By changing the bolt spacing, the anchor cable pre-tightening force and the anchor cable length, the changes in the thickness of the compression arch formed by the four lithologies is not obvious.

#### 4.5. Calculation of Compression Arch Strength of Prestressed Anchors under Different Lithologies

#### 4.5.1. The Percentage Increase of Compressive Arch Strength of Roadway Surrounding Rock Only under Bolt Support

- (1)
- At the arch baseline position

**Table 4.**The percentage increase in the strength of the compression arch of roadway surrounding rock at the arch baseline location under bolt support.

Bolt Support Parameters | Fractured Mudstone | Mudstone | Sandy Mudstone | Muddy Sandstone |
---|---|---|---|---|

F = 50 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 7% | 4% | 3% | 3% |

F = 70 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 9% | 7% | 5% | 4% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 12% | 9% | 7% | 5% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 2.0 m | 15% | 11% | 8% | 7% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 2.6 m | 17% | 13% | 9% | 8% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 3.0 m | 20% | 15% | 11% | 9% |

F = 100 kN, a × b = 500 mm × 500 mm and L = 2.6 m | 16% | 12% | 9% | 7% |

F = 100 kN, a × b = 600 mm × 600 mm and L = 2.6 m | 14% | 10% | 8% | 6% |

- (2)
- At 400 mm from the arch baseline location

**Table 5.**The percentage increase in the strength of the compression arch of roadway surrounding rock at 400 mm from the arch baseline location under bolt support.

Bolt Support Parameters | Fractured Mudstone | Mudstone | Sandy Mudstone | Muddy Sandstone |
---|---|---|---|---|

F = 50 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 7% | 5% | 4% | 3% |

F = 70 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 9% | 6% | 5% | 4% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 12% | 9% | 7% | 5% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 2.0 m | 15% | 11% | 8% | 7% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 2.6 m | 17% | 13% | 9% | 8% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 3.0 m | 20% | 15% | 11% | 9% |

- (3)
- At 800 mm from the arch baseline location

**Table 6.**The percentage increase in the strength of the compression arch of roadway surrounding rock at 800 mm from the arch baseline location under bolt support.

Bolt Support Parameters | Fractured Mudstone | Mudstone | Sandy Mudstone | Muddy Sandstone |
---|---|---|---|---|

F = 50 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 6% | 5% | 3% | 3% |

F = 70 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 8% | 6% | 4% | 3% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 11% | 8% | 6% | 4% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 2.0 m | 14% | 10% | 7% | 6% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 2.6 m | 16% | 12% | 8% | 7% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 3.0 m | 19% | 14% | 10% | 8% |

- (4)
- At 1200 mm from the arch baseline location

**Table 7.**The percentage increase in the strength of the compression arch of roadway surrounding rock at 1200 mm from the arch baseline location under bolt support.

Bolt Support Parameters | Fractured Mudstone | Mudstone | Sandy Mudstone | Muddy Sandstone |
---|---|---|---|---|

F = 50 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 5% | 4% | 2% | 2% |

F = 70 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 6% | 5% | 3% | 2% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 8% | 6% | 5% | 4% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 2.0 m | 11% | 8% | 6% | 5% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 2.6 m | 12% | 9% | 7% | 5% |

F = 100 kN, a × b = 400 mm × 400 mm and L = 3.0 m | 15% | 11% | 8% | 7% |

- (1)
- Under different bolt parameters’ support, the percentage increase of the strength of the compression arch formed by sandy mudstone is between 3 and 11%, and the percentage increase of the strength of the compression arch formed by muddy sandstone is between 3 and 9%, which was a small increase; the percentage increase of the strength of the compression arch formed by fractured mudstone is between 7 and 20%, and the percentage increase of strength of the compression arch formed by mudstone is between 4 and 15%, so the increase is more obvious.
- (2)
- When the bolt spacing is a × b = 400 mm × 400 mm, and the bolt length is L = 1.5 m, by changing the bolt pre-tightening force, when the bolt pre-tightening force (F) increases from 50 kN to 100 kN, the percentage increase of the strength of the compression arch formed by fractured mudstone, mudstone, sandy mudstone and muddy sandstone increases from 7%, 4%, 3% and 3% to 12%, 9%, 7% and 5%, which was a small increase.
- (3)
- When the bolt pre-tightening force is F = 100 kN, and the bolt spacing is a × b = 400 mm × 400 mm, by changing the bolt length, when the bolt length (L) increases from 1.5 m to 3.0 m, the percentage increase of the strength of the compression arch formed by fractured mudstone, mudstone, sandy mudstone and muddy sandstone increases from 12%, 9%, 7% and 5% to 20%, 15%, 11% and 9%, which was a large increase.
- (4)
- Under the same bolt parameters support, the increase of the strength of the compression arch at different positions of the same roadway side is different. The closer to the arch baseline, the more obvious the increase.

#### 4.5.2. The Percentage Increase of Compressive Arch Strength of Roadway Surrounding Rock by Adding Different Anchor Cable Parameters when the Bolt Parameters Are F = 100 kN, a × b = 400 mm × 400 mm and L = 3.0 m

- (1)
- At 400 mm from the arch baseline location

**Table 8.**The percentage increase in the strength of the compression arch of roadway surrounding rock at 400 mm from the arch baseline location under bolt and cable support.

Anchor Cable Support Parameters | Fractured Mudstone | Mudstone | Sandy Mudstone | Muddy Sandstone |
---|---|---|---|---|

F = 80 kN, a × b = 400 mm × 400 mm, L = 3.0 m | 22% | 16% | 12% | 10% |

F = 100 kN, a × b = 400 mm × 400 mm, L = 3.0 m | 23% | 17% | 13% | 11% |

F = 120 kN, a × b = 400 mm × 400 mm, L = 3.0 m | 24% | 18% | 14% | 12% |

F = 100 kN, a × b = 400 mm × 400 mm, L = 4.0 m | 26% | 19% | 15% | 13% |

F = 100 kN, a × b = 400 mm × 400 mm, L = 6.0 m | 26% | 19% | 15% | 13% |

- (2)
- At 800 mm from the arch baseline location

**Table 9.**The percentage increase in the strength of the compression arch of roadway surrounding rock at 800 mm from the arch baseline location under bolt and cable support.

Anchor Cable Support Parameters | Fractured Mudstone | Mudstone | Sandy Mudstone | Muddy Sandstone |
---|---|---|---|---|

F = 80 kN, a × b = 400 mm × 400 mm, L = 3.0 m | 25% | 19% | 14% | 11% |

F = 100 kN, a × b = 400 mm × 400 mm, L = 3.0 m | 27% | 20% | 15% | 12% |

F = 120 kN, a × b = 400 mm × 400 mm, L = 3.0 m | 28% | 21% | 16% | 13% |

F = 100 kN, a × b = 400 mm × 400 mm, L = 4.0 m | 31% | 23% | 17% | 14% |

F = 100 kN, a × b = 400 mm × 400 mm, L = 6.0 m | 32% | 24% | 18% | 14% |

- (1)
- When the bolt pre-tightening force is F = 100 kN, the bolt length is L = 3.0 m and the bolt spacing is a × b = 400 mm × 400 mm, by adding different anchor cable parameters to bolster the bolt’s support, the percentage increase of the strength of the compression arch formed by sandy mudstone is between 12 and 15%, and the percentage increase of the strength of the compression arch formed by muddy sandstone is between 10 and 13%, which is a small increase; the percentage increase of the strength of the compression arch formed by fractured mudstone is between 22 and 26%, and the percentage increase of the strength of the compression arch formed by mudstone is between 16 and19%, so the increase is more obvious.
- (2)
- Under the support of the same bolt and anchor cable parameters, the better the lithology, the smaller the percentage increase of the strength of the compression arch; the worse the lithology, the more obvious the percentage increase of the strength of the compression arch.
- (3)
- By changing the anchor cable pre-tightening force and the anchor cable length, the changes of the strength of the compression arch formed by the four lithologies become more obvious.

## 5. Engineering Verification

#### 5.1. Layout of Multi-Point Displacement Meter

#### 5.2. Field Measurement

## 6. Conclusions

- (1)
- The lithology of surrounding rock and the row spacing between bolts have no significant influence on the thickness of the compression arch, while the length of bolts and pre-tightening force have significant influence on the thickness of the compression arch, and the increase of the compression arch thickness is helpful to improve the stability of the roadway. When the bolt length is L = 1.5 m, bolt spacing is a × b = 400 mm × 400 mm and bolt pre-tightening force increased from F = 50 kN to F = 100 kN, the thickness of the compression arch formed by the four lithologies increased by 0.12 m. When the bolt pre-tightening force was F = 100 kN, the bolt spacing was a × b = 400 mm × 400 mm and the bolt length of L = 1.5 m increased to L = 3.0 m, the thickness of the compression arch formed by the four lithologies increased by 0.99 m. When the bolt pre-tightening force was F = 100 kN, the bolt length was L = 2.6 m and the bolt spacing of a × b = 400 mm × 400 mm increased to a × b = 500 mm × 500 mm and a × b = 600 mm × 600 mm, the thickness of the compression arch formed by the four lithologies was reduced by 0.01 m.
- (2)
- The influence of the surrounding rock lithology, bolt pre-tightening force, bolt length and row spacing on the strength of the compression arch is significant. At the arch baseline position, when the bolt pre-tightening force increased from F = 50 kN to F = 100 kN, the percentage increase of the compressive arch strength formed by four kinds of lithologies increased from 7%, 4%, 3% and 3% to 12%, 9%, 7% and 5%. When the bolt length increased from L = 1.5 m to L = 3.0 m, the percentage increase of the compressive arch strength formed by four kinds of lithology increased from 12%, 9%, 7% and 5% to 20%, 15%, 11% and 9%. When the bolt spacing increased from a × b = 400 mm × 400 mm to a × b = 600 mm × 600 mm, the percentage increase of compressive arch strength formed by four kinds of lithology decreased from 17%, 13%, 9% and 8% to 14%, 10%, 8% and 6%.
- (3)
- The pre-tightening force and length of the anchor cable have no obvious effect on the thickness of the compression arch but have a significant effect on the strength of the compression arch. On the basis of bolt pre-tightening force being F = 100 kN, bolt length being L = 3.0 m and bolt spacing being a × b = 400 × 400 mm, the anchor cable and bolt are added to support together. When the anchor cable pre-tightening force increased from F = 80 kN to F = 120 kN, the thickness of the compression arch formed by four kinds of lithologies increased from 1.83 m, 1.85 m, 1.83 m and 1.86 m to 1.88 m, 1.89 m, 1.89 m and 1.87 m; and the percentage increase of the strength of the compressive arch increased from 22%, 16%, 12% and 10% to 24%, 18%, 14% and 12%. When the anchor cable length increased from L = 3.0 m to L = 6.0 m, the thickness of the compression arch formed by the four kinds of lithologies changed from 1.87 m, 1.87 m,1.89 m and 1.86 m to 1.86 m, 1.87 m, 1.88 m and 1.88 m; and the percentage increase of the strength of the compression arch increased from 23%, 17%, 13% and 11% to 26%, 19%, 15% and 13%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**F = 50 kN, a × b = 400 mm × 400 mm and L = 1.5 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Typical location of fractured mudstone. (

**b**) Typical location of mudstone. (

**c**) Typical location of sandy mudstone. (

**d**) Typical location of muddy sandstone.

**Figure 4.**F = 50 kN, a × b = 400 mm × 400 mm and L = 1.5 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Roadway surface of fractured mudstone. (

**b**) Roadway surface of mudstone. (

**c**) Roadway surface of sandy mudstone. (

**d**) Roadway surface of muddy sandstone.

**Figure 5.**F = 70 kN, a × b = 400 mm × 400 mm and L = 1.5 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Typical location of fractured mudstone. (

**b**) Typical location of mudstone. (

**c**) Typical location of sandy mudstone. (

**d**) Typical location of muddy sandstone.

**Figure 6.**F = 70 kN, a × b = 400 mm × 400 mm and L = 1.5 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Roadway surface of fractured mudstone. (

**b**) Roadway surface of mudstone. (

**c**) Roadway surface of sandy mudstone. (

**d**) Roadway surface of muddy sandstone.

**Figure 7.**F = 100 kN, a × b = 400 mm × 400 mm and L = 1.5 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Typical location of fractured mudstone. (

**b**) Typical location of mudstone. (

**c**) Typical location of sandy mudstone. (

**d**) Typical location of muddy sandstone.

**Figure 8.**F = 100 kN, a × b = 400 mm × 400 mm and L = 1.5 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Roadway surface of fractured mudstone. (

**b**) Roadway surface of mudstone. (

**c**) Roadway surface of sandy mudstone. (

**d**) Roadway surface of muddy sandstone.

**Figure 9.**F = 100 kN, a × b = 400 mm × 400 mm and L = 2.0 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Typical location of fractured mudstone. (

**b**) Typical location of mudstone. (

**c**) Typical location of sandy mudstone. (

**d**) Typical location of muddy sandstone.

**Figure 10.**F = 100 kN, a × b = 400 mm × 400 mm and L = 2.0 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Roadway surface of fractured mudstone. (

**b**) Roadway surface of mudstone. (

**c**) Roadway surface of sandy mudstone. (

**d**) Roadway surface of muddy sandstone.

**Figure 11.**F = 100 kN, a × b = 400 mm × 400 mm and L = 2.6 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Typical location of fractured mudstone. (

**b**) Typical location of mudstone. (

**c**) Typical location of sandy mudstone. (

**d**) Typical location of muddy sandstone.

**Figure 12.**F = 100 kN, a × b = 400 mm × 400 mm and L = 2.6 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Roadway surface of fractured mudstone. (

**b**) Roadway surface of mudstone. (

**c**) Roadway surface of sandy mudstone. (

**d**) Roadway surface of muddy sandstone.

**Figure 13.**F = 100 kN, a × b = 400 mm × 400 mm and L = 3.0 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Typical location of fractured mudstone. (

**b**) Typical location of mudstone. (

**c**) Typical location of sandy mudstone. (

**d**) Typical location of muddy sandstone.

**Figure 14.**F = 100 kN, a × b = 400 mm × 400 mm and L = 3.0 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Roadway surface of fractured mudstone. (

**b**) Roadway surface of mudstone. (

**c**) Roadway surface of sandy mudstone. (

**d**) Roadway surface of muddy sandstone.

**Figure 15.**F = 100 kN, a × b = 500 mm × 500 mm and L = 2.6 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Typical location of fractured mudstone. (

**b**) Typical location of mudstone. (

**c**) Typical location of sandy mudstone. (

**d**) Typical location of muddy sandstone.

**Figure 16.**F = 100 kN, a × b = 500 mm × 500 mm and L = 2.6 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Roadway surface of fractured mudstone. (

**b**) Roadway surface of mudstone. (

**c**) Roadway surface of sandy mudstone. (

**d**) Roadway surface of muddy sandstone.

**Figure 17.**F = 100 kN, a × b = 600 mm × 600 mm and L = 2.6 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Typical location of fractured mudstone. (

**b**) Typical location of mudstone. (

**c**) Typical location of sandy mudstone. (

**d**) Typical location of muddy sandstone.

**Figure 18.**F = 100 kN, a × b = 600 mm × 600 mm and L = 2.6 m. Distribution diagram of additional stress in surrounding rock. (

**a**) Roadway surface of fractured mudstone. (

**b**) Roadway surface of mudstone. (

**c**) Roadway surface of sandy mudstone. (

**d**) Roadway surface of muddy sandstone.

Lithology | Cohesion, c (MPa) | Internal Friction Angle, $\mathit{\phi}$ (°) | Bulk Modulus, K (GPa) | Shear Modulus, G (GPa) | Poisson’s Ratio, $\mathit{v}$ |
---|---|---|---|---|---|

Fractured Mudstone | 0.7 | 18 | 1.42 | 0.35 | 0.36 |

Mudstone | 1.0 | 22 | 1.44 | 0.38 | 0.35 |

Sandy Mudstone | 1.5 | 28 | 1.47 | 0.45 | 0.33 |

Muddy Sandstone | 2.0 | 32 | 1.50 | 0.56 | 0.30 |

Bolt Support Parameters | Fractured Mudstone (m) | Mudstone (m) | Sandy Mudstone (m) | Muddy Sandstone (m) |
---|---|---|---|---|

F = 50 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 0.73 | 0.73 | 0.73 | 0.73 |

F = 70 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 0.80 | 0.80 | 0.80 | 0.80 |

F = 100 kN, a × b = 400 mm × 400 mm and L = 1.5 m | 0.85 | 0.85 | 0.85 | 0.85 |

F = 100 kN, a × b = 400 mm × 400 mm and L = 2.0 m | 1.22 | 1.22 | 1.22 | 1.22 |

F = 100 kN, a × b = 400 mm × 400 mm and L = 2.6 m | 1.60 | 1.60 | 1.60 | 1.60 |

F = 100 kN and a × b = 400 mm × 400 mm and L = 3.0 m | 1.84 | 1.84 | 1.84 | 1.84 |

F = 100 kN, a × b = 500 mm × 500 mm and L = 2.6 m | 1.59 | 1.59 | 1.59 | 1.59 |

F = 100 kN, a × b = 600 mm × 600 mm and L = 2.6 m | 1.59 | 1.59 | 1.59 | 1.59 |

Anchor Cable Support Parameters | Fractured Mudstone (m) | Mudstone (m) | Sandy Mudstone (m) | Muddy Sandstone (m) |
---|---|---|---|---|

F = 80 kN, a × b = 400 mm × 400 mm and L = 3.0 m | 1.83 | 1.85 | 1.83 | 1.86 |

F = 100 kN, a × b = 400 mm × 400 mm and L = 3.0 m | 1.87 | 1.87 | 1.89 | 1.86 |

F = 120 kN, a × b = 400 mm × 400 mm and L = 3.0 m | 1.88 | 1.89 | 1.89 | 1.87 |

F = 100 kN, a × b = 400 mm × 400 mm and L = 4.0 m | 1.88 | 1.89 | 1.88 | 1.87 |

F = 100 kN, a × b = 400 mm × 400 mm and L = 6.0 m | 1.86 | 1.87 | 1.88 | 1.88 |

Measuring Point | A | B | C | D | E |
---|---|---|---|---|---|

Displacement (mm) | 133 | 140 | 130 | 78 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Wu, D.; Li, N.; Zhou, S.
Thickness and Strength Analysis of Prestressed Anchor (Cable) Compression Arch Based on Safe Co-Mining of Deep Coal and Gas. *Sustainability* **2023**, *15*, 10716.
https://doi.org/10.3390/su151310716

**AMA Style**

Wu D, Li N, Zhou S.
Thickness and Strength Analysis of Prestressed Anchor (Cable) Compression Arch Based on Safe Co-Mining of Deep Coal and Gas. *Sustainability*. 2023; 15(13):10716.
https://doi.org/10.3390/su151310716

**Chicago/Turabian Style**

Wu, Deyi, Nanyu Li, and Shuang Zhou.
2023. "Thickness and Strength Analysis of Prestressed Anchor (Cable) Compression Arch Based on Safe Co-Mining of Deep Coal and Gas" *Sustainability* 15, no. 13: 10716.
https://doi.org/10.3390/su151310716