# Stability-Level Evaluation of the Construction Site above the Goaf Based on Combination Weighting and Cloud Model

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

## 3. Methodology

#### 3.1. Construction of Index System

#### 3.2. Index Weight Determination

#### 3.2.1. Improved AHP

_{ij}is the relative importance between index A

_{i}and index A

_{j}and n is the number of indexes.

_{ij}is solved by Equation (3), and then the quasi-optimal transfer matrix E

_{ij}is obtained by Equation (4).

_{i}for the data in the matrix E

_{ij}is obtained by Equation (5), and then the subjective weight B

_{i}of the index is obtained by Equation (6).

#### 3.2.2. Improved Rough Set

_{1}, D

_{2}, …, D

_{m}}) relative to C (U/C = {C

_{1}, C

_{2}, …, C

_{n}}) can be expressed by Equation (8).

_{i}) of the conditional attribute C

_{i}can be expressed by Equation (9).

_{i}) is the change degree of the attribute set after removing conditional attribute C

_{i}.

_{i}) of each condition attribute can be obtained by Equation (10).

_{i}) is the importance of the condition attribute C

_{i}itself in the decision table.

#### 3.2.3. Improved CRITIC

_{ij}is the ith evaluation object and the jth index value.

_{j}is the variation coefficient of the jth index, which can be calculated by Equation (13):

_{kj})

_{n}

_{×n}can be constructed [35]. Then, the independence coefficient η

_{j}is calculated by Equation (14).

_{j}is calculated by Equation (15).

_{j}value, the stronger the reference value of the index j, and the higher its importance, which should be given greater weight. Therefore, the weight Q

_{j}can be calculated by Equation (16).

#### 3.2.4. Game Theory

_{l}is the linear combination coefficient.

_{l}, and its objective function can be derived by Equation (19) [37].

_{1}, α

_{2}, …, α

_{L}) are obtained by solving the Equation (21). Then, the comprehensive weight W* can be obtained by Equation (22):

#### 3.3. Cloud Model

#### 3.3.1. Basic Concepts

_{min}and H

_{max}are the upper and lower boundary values of the index range, respectively. λ is a constant, and it can be changed with randomness and the actual situation of the index. In this paper, λ = 0.02 [41].

^{2}as the variance, are generated randomly by Equation (24) [42]:

_{i}, with Ex as the expectation and En′

^{2}as the variance, are generated randomly by Equation (25):

#### 3.3.2. Determination of Stability Grade

_{j}is the membership degree of the jth level, and μ

_{ij}is the membership degree of the ith index at the corresponding level j.

## 4. Results

#### 4.1. Stability Evaluation Results

_{1}is calculated according to Equation (1) to Equation (6)

_{2}are in Table 6.

_{1}= 0.6430, α

_{2}= 0.0343, α

_{3}= 0.3227, so the comprehensive weight W* can be obtained, which can reflect that the comprehensive weight not only considers the judgment of experts’ subjective factors but also takes into account the characteristics of the index itself, as shown in Table 7.

#### 4.2. Sensitivity Analysis of Subjective Weights

_{m}in the index system is selected as the target index. Under the premise of defined the RPC and IPC, its weight will generate different simulated weights after changing the percentage pc, as shown in Equation (29):

_{m}, 0) is the initial value of the weight of the index Cm, W(C

_{m}, pc) is the simulated weight of the index C

_{m}after changing the percentage pc, W(C

_{i}, 0) is the initial value of the weight of the ith index C

_{i}, and W(C

_{i}, pc) is the changed weight of other indexes.

_{m}, pc) is the evaluation score obtained as the weight of C

_{m}changes, A

_{m}is the weight ranking score of index C

_{m}, W(C

_{j}, pc) is the weight of other indexes, and A

_{j}is the ranking score value of other indexes.

_{m}, pc).

_{m}, pc) is the change rate of score after the weight of index C

_{m}changes.

_{9}(stopping time) to weight changes is the highest, and when the weight changes by 100%, the corresponding rate value is 12.44%, which is much smaller than the degree of weight change, indicating that the subjective weights determined in this paper are reasonable and effective and can objectively reflect the stability of the construction site above the goaf.

#### 4.3. Validation of Model Correctness

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Study area. (

**a**) Position in China. (

**b**) Position in Henan Province. (

**c**) Mianluan Expressway and goaf.

Group | Index | Stable (I) | Basically Stable (II) | Under Stable (III) | Unstable (IV) |
---|---|---|---|---|---|

Qualitative indexes | Score | 0–0.25 | 0.25–0.5 | 0.5–0.75 | 0.75–1 |

C_{1} | Simple structure | Simple, slightly structured | Complex structure | Extremely complex structure | |

C_{2} | Weak-weak | Hard-weak | Weak-hard | Hard-hard | |

C_{3} | No water seepage | Little water seepage | Stagnant water area | Large stagnant water area | |

C_{4} | Longwall mining | Shortwall mining | Extra-thick top caving mining | Horizontal seam mining | |

C_{5} | Slow compressive creep | Strength decay creep | Strength attenuation structural instability | Structural instability disturbed by external forces | |

C_{6} | No load disturbance | Not affected by the water-conducting fracture zone | Tangential to the height of the water-conducting fracture zone | Spread to the interior of the water-conducting fracture zone | |

Quantitative indexes | C_{7} (°) | 0–8 | 8–25 | 25–45 | 45–65 |

C_{8} | 400–600 | 200–400 | 50–200 | 0–50 | |

C_{9} (y) | 8.5–40.5 | 5.5–8.5 | 3.5–5.5 | 0.5–3.5 | |

C_{10} | 0–0.25 | 0.25–0.5 | 0.5–0.75 | 0.75–1 |

Scale | Meaning |
---|---|

1 | Equally important |

3 | Slightly more important |

5 | Obviously more important |

7 | A lot more important |

9 | Substantially more important |

2, 4, 6, 8 | Intermediate values of the scales |

Level | C_{i} | C_{7} | C_{8} | C_{9} |
---|---|---|---|---|

I | (0.125, 0.042, 0.02) | (4, 1.333, 0.02) | (500, 33.333, 0.02) | (24.5, 5.333, 0.02) |

II | (0.375, 0.042, 0.02) | (16.5, 2.833, 0.02) | (300, 33.333, 0.02) | (7, 0.5, 0.02) |

III | (0.625, 0.042, 0.02) | (35, 3.333, 0.02) | (125, 25, 0.02) | (4.5, 0.333, 0.02) |

IV | (0.875, 0.042, 0.02) | (55, 3.333, 0.02) | (25, 8.333, 0.02) | (2, 0.5, 0.02) |

Working Face | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} |
---|---|---|---|---|---|---|---|---|---|---|

Irregular goaf | 0.30 | 0.60 | 0.60 | 0.20 | 0.80 | 0.80 | 12.00 | 11.28 | 40.00 | 0.43 |

Unnamed region | 0.28 | 0.60 | 0.40 | 0.50 | 0.20 | 0.25 | 12.00 | 35.57 | 36.00 | 0.09 |

18081 | 0.30 | 0.60 | 0.35 | 0.60 | 0.20 | 0.15 | 12.00 | 51.26 | 33.00 | 0.27 |

18101 | 0.35 | 0.20 | 0.30 | 0.55 | 0.10 | 0.10 | 13.00 | 149.73 | 25.00 | 0.33 |

18121 | 0.38 | 0.60 | 0.28 | 0.65 | 0.15 | 0.10 | 13.00 | 57.55 | 30.00 | 0.29 |

18141 | 0.35 | 0.60 | 0.35 | 0.70 | 0.20 | 0.20 | 13.00 | 64.15 | 32.00 | 0.40 |

18021 | 0.30 | 0.60 | 0.30 | 0.65 | 0.28 | 0.15 | 12.00 | 53.65 | 28.00 | 0.10 |

18041 | 0.40 | 0.60 | 0.40 | 0.60 | 0.15 | 0.20 | 12.00 | 153.33 | 30.00 | 0.42 |

18061 | 0.45 | 0.40 | 0.40 | 0.55 | 0.20 | 0.15 | 12.00 | 48.90 | 19.00 | 0.30 |

21101 | 0.30 | 0.40 | 0.35 | 0.60 | 0.18 | 0.15 | 12.00 | 54.55 | 24.00 | 0.34 |

21121 | 0.35 | 0.40 | 0.28 | 0.50 | 0.25 | 0.20 | 12.00 | 56.82 | 13.00 | 0.41 |

21141 | 0.40 | 0.40 | 0.30 | 0.70 | 0.20 | 0.20 | 12.00 | 61.82 | 8.00 | 0.44 |

21181 | 0.35 | 0.60 | 0.40 | 0.60 | 0.25 | 0.10 | 11.00 | 240.00 | 15.00 | 0.73 |

21201 | 0.42 | 0.60 | 0.42 | 0.65 | 0.20 | 0.10 | 11.00 | 250.00 | 11.00 | 0.26 |

Working Face | Conditional Attributes (C) | Decision Attributes | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | ||

Irregular goaf | 2 | 3 | 3 | 1 | 4 | 4 | 2 | 4 | 1 | 2 | II |

Unnamed region | 2 | 3 | 2 | 3 | 1 | 2 | 2 | 4 | 1 | 1 | I |

18081 | 2 | 3 | 2 | 3 | 1 | 1 | 2 | 3 | 1 | 2 | II |

18101 | 2 | 1 | 2 | 3 | 1 | 1 | 2 | 3 | 1 | 2 | I |

18121 | 2 | 3 | 2 | 3 | 1 | 1 | 2 | 3 | 1 | 2 | I |

18141 | 2 | 3 | 2 | 3 | 1 | 1 | 2 | 3 | 1 | 2 | II |

18021 | 2 | 3 | 2 | 3 | 2 | 1 | 2 | 3 | 1 | 1 | I |

18041 | 2 | 3 | 2 | 3 | 1 | 1 | 2 | 3 | 1 | 2 | II |

18061 | 2 | 2 | 2 | 3 | 1 | 1 | 2 | 3 | 1 | 2 | I |

21101 | 2 | 2 | 2 | 3 | 1 | 1 | 2 | 3 | 1 | 2 | II |

21121 | 2 | 2 | 2 | 3 | 2 | 1 | 2 | 3 | 1 | 2 | II |

21141 | 2 | 2 | 2 | 3 | 1 | 1 | 2 | 3 | 2 | 2 | II |

21181 | 2 | 3 | 2 | 3 | 2 | 1 | 2 | 2 | 1 | 3 | II |

21201 | 2 | 3 | 2 | 3 | 1 | 1 | 2 | 2 | 1 | 2 | II |

Index | I(D/C_{i}) | I(D/C−C_{i}) | New Sig(C_{i}) | W_{2} |
---|---|---|---|---|

C_{1} | 0.4592 | 0.0408 | 0.0000 | 0.1360 |

C_{2} | 0.1837 | 0.0510 | 0.0102 | 0.0574 |

C_{3} | 0.4082 | 0.0408 | 0.0000 | 0.1208 |

C_{4} | 0.4082 | 0.0408 | 0.0000 | 0.1208 |

C_{5} | 0.2653 | 0.0510 | 0.0102 | 0.0816 |

C_{6} | 0.2449 | 0.0408 | 0.0000 | 0.0725 |

C_{7} | 0.4592 | 0.0408 | 0.0000 | 0.1360 |

C_{8} | 0.2551 | 0.0510 | 0.0102 | 0.0785 |

C_{9} | 0.4082 | 0.0510 | 0.0102 | 0.1239 |

C_{10} | 0.2449 | 0.0408 | 0.0000 | 0.0725 |

Weight | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} |
---|---|---|---|---|---|---|---|---|---|---|

W_{1} | 0.0340 | 0.1076 | 0.0166 | 0.0231 | 0.0508 | 0.0340 | 0.0744 | 0.2148 | 0.2912 | 0.1535 |

W_{2} | 0.1360 | 0.0574 | 0.1208 | 0.1208 | 0.0816 | 0.0725 | 0.1360 | 0.0785 | 0.1239 | 0.0725 |

W_{3} | 0.0396 | 0.0570 | 0.0484 | 0.0670 | 0.1560 | 0.1955 | 0.0143 | 0.2157 | 0.0978 | 0.1087 |

W* | 0.0399 | 0.0892 | 0.0310 | 0.0412 | 0.0861 | 0.0879 | 0.0573 | 0.2097 | 0.2219 | 0.1358 |

Number | Working Face | Membership Degree | Result | |||
---|---|---|---|---|---|---|

Stable | Basically Stable | Under Stable | Unstable | |||

1 | Irregular goaf | 0.0112 | 0.1223 | 0.0940 | 0.0032 | Basically stable |

2 | Unnamed region | 0.1984 | 0.0652 | 0.0685 | 0.0394 | Stable |

3 | 18081 | 0.1713 | 0.0809 | 0.0968 | 0.0006 | Stable |

4 | 18101 | 0.3334 | 0.1875 | 0.0632 | 0.0000 | Stable |

5 | 18121 | 0.2878 | 0.1243 | 0.0984 | 0.0001 | Stable |

6 | 18141 | 0.1010 | 0.2544 | 0.0800 | 0.0005 | Basically stable |

7 | 18021 | 0.3104 | 0.0698 | 0.0968 | 0.0004 | Stable |

8 | 18041 | 0.2212 | 0.1906 | 0.1432 | 0.0000 | Stable |

9 | 18061 | 0.1848 | 0.1802 | 0.0112 | 0.0014 | Stable |

10 | 21101 | 0.2393 | 0.2600 | 0.0320 | 0.0002 | Basically stable |

11 | 21121 | 0.0514 | 0.2715 | 0.0051 | 0.0001 | Basically stable |

12 | 21141 | 0.0807 | 0.2055 | 0.0153 | 0.0005 | Basically stable |

13 | 21181 | 0.1265 | 0.0949 | 0.1186 | 0.0065 | Stable |

14 | 21201 | 0.1629 | 0.0978 | 0.0967 | 0.0001 | Stable |

Stability Level | Surface Subsidence (mm) | Subsidence Velocity (mm/d) | |
---|---|---|---|

3 Months | 6 Months | ||

Stable | ≤15 | ≤30 | <1 |

Basically stable | 15~30 | 30~60 | |

Under stable | 30~60 | 60~120 | ≥1 |

Unstable | ≥60 | ≥120 |

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## Share and Cite

**MDPI and ACS Style**

Wang, L.; Guo, Q.; Yu, X.
Stability-Level Evaluation of the Construction Site above the Goaf Based on Combination Weighting and Cloud Model. *Sustainability* **2023**, *15*, 7222.
https://doi.org/10.3390/su15097222

**AMA Style**

Wang L, Guo Q, Yu X.
Stability-Level Evaluation of the Construction Site above the Goaf Based on Combination Weighting and Cloud Model. *Sustainability*. 2023; 15(9):7222.
https://doi.org/10.3390/su15097222

**Chicago/Turabian Style**

Wang, Liang, Qingbiao Guo, and Xuexiang Yu.
2023. "Stability-Level Evaluation of the Construction Site above the Goaf Based on Combination Weighting and Cloud Model" *Sustainability* 15, no. 9: 7222.
https://doi.org/10.3390/su15097222