# Stability Study of the Roof Plate of the Yuanjue Cave Based on the Equivalent Support Stiffness Method

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

#### 2.1. Stratigraphic Lithology

#### 2.2. Top Plate Catastrophe Mode

^{3}with a total weight of 570.88 tons. There are a large number of overhanging, broken, and fractured slates in Yuanjue Cave, which have a great impact on the stability of the roof of Yuanjue Cave. It is necessary to carry out theoretical calculations and numerical simulations on the support and the effect of vertical stress on the slates.

## 3. Analytic Methods

- (1)
- Calculation of equivalent stiffness of the sized slate

- (2)
- Determination of the contact area of the sized slates

- (3)
- Slate and joint parameter determination

Grouping | Elastic Modulus (Pa) | Poisson Ratio | Cohesion (MPa) | The Angle of Internal Friction (°) | Natural Density (kg/m^{3}) | Tensile Strength (MPa) |
---|---|---|---|---|---|---|

Group TS04 | 2.76 × 10^{10} | 0.19 | 1.38 | 38.1 | 2230 | 0.2 |

Group TS05 | 1.38 × 10^{10} | 0.25 | 1.02 | 28.2 | 2150 | 0.2 |

Group TS09 | 2.50 × 10^{10} | 0.21 | 1.1 | 30.6 | 2200 | 0.1 |

Group TS56 | 1.38 × 10^{10} | 0.25 | 1.02 | 28.2 | 2150 | 0.1 |

Group TS01 | 2.50 × 10^{10} | 0.21 | 1.1 | 30.6 | 2200 | 0.2 |

- (4)
- Equivalent support stiffness calculation

## 4. Numerical Simulation and Results

#### 4.1. Analysis of the Effect of Slate Overhang on the Force Deformation of the Roof Slab

#### 4.2. Analysis of the Effect of Slate Crushing on the Force Deformation of the Roof Slab

#### 4.3. Analysis of the Influence of the Degree of Damage to the Cracked Slates on the Force Deformation of the Top Slab

^{−6}of the original ones (where 1 × 10

^{−6}can be equated to complete damage). The overall equivalent stiffness of each group of slates was calculated, and the results are shown in Table 4 (only the slates with changed equivalent stiffness are listed).

#### 4.4. Reinforcement Measures

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Yuanjue Cave Cultural Relics Protection Zone (

**a**) outside the cave and (

**b**) inside the cave.

**Figure 2.**Detailed geological stratification of the south cliff wall on which Yuanjue Cave is located.

**Figure 5.**Schematic diagram of the grouping of supporting slates in the lower part of the roof plate.

**Figure 9.**Three-dimensional geological model. (

**a**) Schematic diagram of the development of overhanging slates. (

**b**) Location layout of the monitoring points.

**Figure 10.**Cloud diagram of vertical displacement of the top slab when the number of overhanging slates is different.

**Figure 11.**(

**a**) The variation curve of vertical displacement of each measurement point with the number of overhanging slate blocks; (

**b**) the variation curve of the increase of L6 crack width with the number of overhanging slate blocks.

**Figure 14.**(

**a**) Variation curve of vertical displacement of each measurement point with the number of broken slate blocks; (

**b**) variation curve of the increase of L6 crack width with the number of broken slate blocks.

**Figure 17.**Vertical displacement clouds of the top slab of the damage factor of different broken slates.

**Figure 18.**(

**a**) Variation curve of the vertical displacement of each measurement point with the damage factor of cracked slates; (

**b**) variation curve of the increase of the L6 crack width with the damage factor of cracked slates.

Grouping | K(N/m) | Grouping | K(N/m) |
---|---|---|---|

TS01 | 3.42 × 10^{10} | TS38 | 5.22 × 10^{9} |

TS04 | 0 | TS39 | 6.94 × 10^{9} |

TS10 | 1.55 × 10^{10} | TS40 | 5.16 × 10^{9} |

TS11 | 0 | TS41 | 5.69 × 10^{9} |

TS12 | 3.56 × 10^{10} | TS42 | 1.19 × 10^{9} |

TS13 | 9.38 × 10^{9} | TS43 | 9.10 × 10^{9} |

TS14 | 6.00 × 10^{9} | TS46 | 1.01 × 10^{7} |

TS15 | 0 | TS49 | 1.12 × 10^{10} |

TS16 | 9.99 × 10^{9} | TS51 | 1.81 × 10^{10} |

TS20 | 0 | TS52 | 2.14 × 10^{10} |

TS25 | 8.51 × 10^{9} | TS55 | 0 |

TS29 | 2.68 × 10^{10} | TS56 | 0 |

TS30 | 6.86 × 10^{9} | TS57 | 0 |

TS34 | 5.00 × 10^{9} | TS59 | 3.07 × 10^{10} |

Sequence Stratigraphy | Formation Lithology | Bulk Modulus (GPa) | Shear Modulus (GPa) | Cohesion (MPa) | Friction Angle (°) | Density (kg/m^{3}) | Tensile Strength (MPa) |
---|---|---|---|---|---|---|---|

1 | Fine sandstone | 10 | 5 | 1.38 | 38.14 | 2230 | 0.2 |

2 | Slate | 10 | 7 | 1.5 | 30 | 2300 | 0.2 |

Damage Factor | 0.5 | 0.8 | 0.9 | 0.98 | 1 |
---|---|---|---|---|---|

Grouping | K(N/m) | K(N/m) | K(N/m) | K(N/m) | K(N/m) |

TS01 | 1.71 × 10^{10} | 6.84 × 10^{9} | 3.42 × 10^{9} | 6.84 × 10^{8} | ≈0 |

TS10 | 7.77 × 10^{9} | 3.11 × 10^{9} | 1.55 × 10^{9} | 3.11 × 10^{8} | ≈0 |

TS12 | 1.78 × 10^{10} | 7.12 × 10^{9} | 3.56 × 10^{9} | 7.12 × 10^{8} | ≈0 |

TS14 | 4.71 × 10^{9} | 2.87 × 10^{9} | 1.73 × 10^{9} | 4.17 × 10^{8} | ≈0 |

TS16 | 8.91 × 10^{9} | 6.74 × 10^{9} | 4.79 × 10^{9} | 1.45 × 10^{9} | ≈0 |

TS29 | 1.89 × 10^{10} | 1.09 × 10^{10} | 6.66 × 10^{9} | 1.64 × 10^{9} | ≈0 |

TS30 | 5.23 × 10^{9} | 3.30 × 10^{9} | 2.11 × 10^{9} | 5.52 × 10^{8} | ≈0 |

TS34 | 4.00 × 10^{9} | 2.50 × 10^{9} | 1.54 × 10^{9} | 3.78 × 10^{8} | ≈0 |

TS49 | 1.04 × 10^{10} | 9.55 × 10^{9} | 9.13 × 10^{9} | 8.73 × 10^{9} | 8.61 × 10^{9} |

TS51 | 1.21 × 10^{10} | 6.05 × 10^{9} | 3.30 × 10^{9} | 7.13 × 10^{8} | ≈0 |

TS52 | 1.28 × 10^{10} | 6.43 × 10^{9} | 3.66 × 10^{9} | 8.48 × 10^{8} | ≈0 |

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## Share and Cite

**MDPI and ACS Style**

Hou, Y.; Zhang, J.; Li, B.; Gong, Y.; Xu, Y.; Wang, M.; Zhu, C. Stability Study of the Roof Plate of the Yuanjue Cave Based on the Equivalent Support Stiffness Method. *Appl. Sci.* **2023**, *13*, 4451.
https://doi.org/10.3390/app13074451

**AMA Style**

Hou Y, Zhang J, Li B, Gong Y, Xu Y, Wang M, Zhu C. Stability Study of the Roof Plate of the Yuanjue Cave Based on the Equivalent Support Stiffness Method. *Applied Sciences*. 2023; 13(7):4451.
https://doi.org/10.3390/app13074451

**Chicago/Turabian Style**

Hou, Yongli, Jiabing Zhang, Bin Li, Yifei Gong, Yingze Xu, Meng Wang, and Chun Zhu. 2023. "Stability Study of the Roof Plate of the Yuanjue Cave Based on the Equivalent Support Stiffness Method" *Applied Sciences* 13, no. 7: 4451.
https://doi.org/10.3390/app13074451