# Investigation of Deep Shaft-Surrounding Rock Support Technology Based on a Post-Peak Strain-Softening Model of Rock Mass

^{*}

## Abstract

**:**

^{3D}software. The convergence-constraint method is used to analyze the rock support structure interaction mechanism. A composiste support technique is proposed in combination with actual field breakage conditions. During the initial support stage, high-strength anchors are used to release the rock stress, and high-stiffness secondary support is provided by well rings and poured concrete. This support technology is applied in the accessory well of a coal mine in Niaoshan, Heilongjiang, China. The stability of the surrounding rock support structure is calculated and analyzed by comparing the ideal elastic-plastic model and equivalent jointed rock mass strain-softening model. The results show that a support structure designed based on the ideal elastic-plastic model cannot meet the stability requirements of the surrounding rock and that radial deformation of the surrounding rock reaches 300 mm. The support structure designed based on the equivalent joint strain-softening model has a convergence rate of surrounding rock deformation of less than 1 mm/d after 35 days of application. The surrounding rock deformation is finally controlled at 140 mm, indicating successful application of the support technology.

## 1. Introduction

## 2. Theoretical Basis

#### 2.1. Equivalent Strain-Softening Model for Jointed Rock Mass

#### 2.1.1. Quantifying the Surrounding Rock Grading System Using the GSI (Geological Strength Index) Series

#### 2.1.2. Strain-Softening Model of Equivalent Jointed Rock Mass

^{,}is the maximum principal strain of elasticity. These can be further expressed as:

#### 2.2. Principle of Convergence–Constraint Method

#### 2.3. Shaft Support Characteristic Curve

## 3. Model Validation and Analysis

#### 3.1. Triaxial Compression Tests of Surrounding Rock

#### 3.2. Parameter Determination of Equivalent Strain-Softening Model

^{3D}numerical software, the model softening parameter ${e}^{ps}$ can be calculated by:

#### 3.3. Validation and Analysis of Model Reliability

## 4. Design and Stability Analysis of Surrounding Rock-Supporting Structure of Shaft

#### 4.1. Engineering Example

_{H}is the maximum horizontal principal stress azimuth angle.

#### 4.2. Rock Mass Mechanical Properties

#### 4.3. Original Support Scheme Design

#### 4.4. Numerical Calculation Model and Model Parameters

^{3D}software is used to numerically solve the strain-softening model for equivalently jointed plutons. The structure dimensions for building the vertical well computational model are shown in Figure 10a and the model boundary conditions are shown in Figure 10b,c, where P

_{v}is the vertical principal stress, P

_{H}is the maximum horizontal principal stress, and P

_{h}is the minimum horizontal principal stress. During the excavation process, the section height was 2 m and a total of 30 excavations were cycled. The surrounding rock GRC was calculated using an equivalent two-dimensional model [39], as shown in Figure 10c. Suppose the virtual support pressure P

_{i}is gradually released, each release is 2% of the original rock stress, and the release cycle is repeated 50 times. The relationship curve between the surrounding rock pressure and rock displacement is obtained, and the model calculation parameters are listed in Table 3.

#### 4.5. Analysis of Original Supporting Structure Calculation Results

#### 4.5.1. GRC, SCC, and LDP Curves

#### 4.5.2. Damage Status and Cause Analysis of the Original Supporting Structure

#### 4.6. Support Plan Design Optimization

#### 4.7. Optimization Scheme Numerical Calculation Results Analysis

#### 4.8. Monitoring of Support Effect

## 5. Discussion

#### 5.1. Comparative Analysis of Numerical Calculation Results of Original Plan and Monitoring Data of Surrounding Rock Deformation

#### 5.2. Deviation Analysis

#### 5.3. Comparative Analysis of Calculation Results of Optimized Support Plan and Surrounding Rock Deformation Monitoring Data

## 6. Conclusions

_{1}= 1.2 m, and C35 concrete thickness t = 700 mm. The calculation results using the strain-softening model show that the surrounding rock characteristic curve and the elastic part of the supporting structure characteristic curve intersect, indicating that the surrounding rock and the supporting system are in balance. The field application results showed that 35 days after the supporting structure was constructed, the deformation rate of the surrounding rock was less than 1 mm/day and the deformation was finally controlled at 140 mm. The calculation results were in line with actual observations.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Strain-softening behavior of plutons: (

**a**) Roadway surrounding rock zoning; (

**b**) The simplified piecewise linear strain-softening model.

**Figure 8.**Model curves and test curves of tuffaceous mudstone under different confining pressures: (

**a**) σ

_{3}= 0 MPa; (

**b**) σ

_{3}= 1 MPa; (

**c**) σ

_{3}= 3 MPa; (

**d**) σ

_{3}= 7 MPa.

**Figure 9.**Vertical shaft excavation and supporting process: (

**a**) design of well circle support; (

**b**) design of support for well circle and anchor rod; (

**c**) design of well circle, anchor rod, and concrete support.

**Figure 10.**The numerical model; (

**a**) Model size picture; (

**b**) Model longitudinal section boundary conditions; (

**c**) Model transverse section boundary conditions.

**Figure 12.**Damaged support structures: (

**a**) local failure of the shaft wall; (

**b**) well wall extensibility destruction; (

**c**) systematic damage of the supporting structure.

Confining Pressureσ_{3}/MPa | σ_{3} = 0 | σ_{3} = 1 | σ_{3} = 3 | σ_{3} = 7 |
---|---|---|---|---|

Peak stress/MPa | 4.156 | 5.534 | 8.399 | 14.305 |

Peak strain/10^{−2} | 0.875 | 1.289 | 2.068 | 3.882 |

Residual stress/MPa | 0.709 | 1.787 | 3.812 | 8.051 |

residual strain/10^{−2} | 1.668 | 4.148 | 6.134 | 10.115 |

Confining Pressure σ_{3}/MPa | 0 | 1 | 3 | 7 |
---|---|---|---|---|

m_{i} | 10.00 | 9.67 | 9.08 | 8.02 |

m_{b} | 2.40 | 2.31 | 2.17 | 1.92 |

GSI^{P} | GSI^{r} | S^{P}(10 ^{−3}) | S^{r}(10 ^{−3}) | D | σ_{c}(MPa) | E (GPa) | φ (°) | v | C (MPa) | η* (10 ^{−3}) |
---|---|---|---|---|---|---|---|---|---|---|

60 | 33 | 11.74 | 0.58 | 0 | 4.156 | 4.4 | 26 | 0.25 | 2.2 | 19 |

The Depth of Measuring Point/m | σ_{H}/MPa | σ_{h}/MPa | σ_{v}/MPa | α_{H}/(°) |
---|---|---|---|---|

21 | 35.23 | 28.22 | 25.61 | 85 |

24 | 35.30 | 28.26 | 25.82 | 83 |

Peak Parameter | Residual Parameters | |
---|---|---|

σ_{c}/MPa | 4.2 | 4.2 |

GSI | 60 | 33 |

c/MPa | 2.2 | 1.4 |

φ/° | 26 | 18 |

E/GPa | 4.4 | 4.4 |

Ψ | 0 | 0 |

v | 0.25 | 0.25 |

P_{v} | 26 | 26 |

P_{H} | 36 | 36 |

P_{h} | 29 | 29 |

Well Circle | Resin Anchor Rod (End Anchor) | Concrete | |||
---|---|---|---|---|---|

Shed Distance d_{1}(m) | Diameter Φ (mm) | Length L (m) | Row Spacing d_{2} × d_{3}(m) | Thickness t (mm) | |

Original plan one | 1.5 | 22.0 | 2.5 | 1.0 × 1.2 | 600 (C30) |

Original plan two | 1.2 | 22.0 | 2.5 | 1.0 × 1.2 | 700 (C30) |

P_{max}(MPa) | K/ (MPa·m ^{−1}) | u_{max}/(mm) | E/ (GPa) | |||
---|---|---|---|---|---|---|

Well ring (No.28 A-shaped I-beam) | 0.29 | 230 | 31 | 210 | ||

Anchor rod | 0.31 | 12 | 150 | 180 | ||

High-strength anchor | 0.46 | 25 | 220 | 220 | ||

Concrete | C30 | t = 600 mm | 2.48 | 1023 | 28 | 30 |

t = 700 mm | 2.88 | 1214 | 29 | 30 | ||

C35 | t = 700 mm | 3.36 | 1275 | 26 | 31.5 |

Initial Support | Secondary Support | |||||
---|---|---|---|---|---|---|

Resin Anchor Rod (End Anchor) | Well Circle | Concrete | ||||

Diameter Φ (mm) | Row Spacing d_{2} × d_{3}(m) | Length L (m) | Shed Distance d_{1}(m) | Thickness t (mm) | ||

Original plan one | 22.0 | 1.0 × 1.2 | 2.5 | 1.5 | 600 (C30) | |

Original plan two | 22.0 | 1.0 × 1.2 | 2.5 | 1.2 | 700 (C30) | |

High-strength anchor cable (steel strand) | Well circle | Concrete | ||||

Diameter Φ (mm) | Row spacing d_{2} × d_{3} (m) | Length L _{1} (m) | Length of anchoring section L_{2} (m) | Shed distance d_{1}(m) | Thickness t (mm) | |

Optimization plan one | 22.0 | 1.0 × 1.2 | 8.0 | 3 | 1.5 | 600 (C30) |

Optimization plan two | 22.0 | 1.0 × 1.0 | 8.0 | 3 | 1.2 | 700 (C35) |

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## Share and Cite

**MDPI and ACS Style**

Zhang, J.; Wang, Y.; Yao, B.; Chen, D.; Sun, C.; Jia, B.
Investigation of Deep Shaft-Surrounding Rock Support Technology Based on a Post-Peak Strain-Softening Model of Rock Mass. *Appl. Sci.* **2022**, *12*, 253.
https://doi.org/10.3390/app12010253

**AMA Style**

Zhang J, Wang Y, Yao B, Chen D, Sun C, Jia B.
Investigation of Deep Shaft-Surrounding Rock Support Technology Based on a Post-Peak Strain-Softening Model of Rock Mass. *Applied Sciences*. 2022; 12(1):253.
https://doi.org/10.3390/app12010253

**Chicago/Turabian Style**

Zhang, Jianjun, Yang Wang, Baicong Yao, Dongxu Chen, Chuang Sun, and Baoxin Jia.
2022. "Investigation of Deep Shaft-Surrounding Rock Support Technology Based on a Post-Peak Strain-Softening Model of Rock Mass" *Applied Sciences* 12, no. 1: 253.
https://doi.org/10.3390/app12010253