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A new model is established to analyze mining stope stability, using variable weight theory to calculate the index weight for each factor in different stopes and unascertained measure evaluation technique to predict the risk grade of stope stability. In this model, an evaluation index system by virtue of the 7 most important factors is established, including rock saturated uniaxial compressive strength, rock quality designation, rock joint and fissure, stope span, condition of pillar, groundwater seepage volume, and rate of supporting pit roof. And each index is divided into 5 grades by assignment value and the classification method of standardization. Accordingly, the analysis result is also classified into 5 risk grades. This model is used for the 6 main stopes from the -270 m section in Xin-Qiao Mine, China. The results, giving risk grade for each stope and guiding the use of corresponding measures, avoided the problem of state out of balance caused by conventional invariable weight theory models and have ensured no accident occurred in mining production in recent years. This model can be used in other mines widely, by assigning values for the 7 factors on basis of current in situ cases.

During recent decades, underground space stability problems in both mining industry and underground shelter of civil defense projects have drawn enormous attention [

Stope stability is a crucial factor for selecting the mining method and ground pressure controlling method, which is closely related to the mining safety and efficiency. Many achievements of stope stability analysis have been obtained from traditional analysis methods, such as the data mining method [

In this study, a model combining variable weight theory [

The concept of unascertained information and its mathematical processing theory was first proposed by Wang [

Suppose

Denote the unascertained measurement as

Then,

The invariable weight vector that was used in the previous analysis model reflected the relative importance of each factor under ideal status. The variable weight theory which was proposed by Wang [

Invariable weight can be calculated by the AHP method before variable weight calculation [

The

Normalization:

Continuity: every variable of the vector

Monotonicity: the vector

Supposing

Suppose a mapping

Every argument of vector

To any invariable weight vector

So the mapping is a

A mapping:

Step 1. Selecting the type of balance function from sum type, product type, and exponential type.

Step 2. Relationship between weight and factor state value.

Step 3. Selecting an appropriate adjusting factor.

Based on the unascertained measurement function of a single index and weight, the unascertained measurement function of multiple indices can be worked out as follows:

In order to get the final results of the stope stability analysis, the credible degree criteria are introduced. Suppose

Then,

Stope stability is influenced not only by geological conditions but also by the mining method, ore structure, and so on. The evaluation index, which is outstanding and easy to obtain, should be taken into consideration to ensure as few indices as possible can reflect the most important and comprehensive information. The 7 most important factors, including rock saturated uniaxial compressive strength (

The unascertained measurement functions of a single index are constructed to get the value of the analysis factors, on the basis of the unascertained measurement function and the classification in Tables

Classification criterion of quantitative indices.

Classification standard | Saturated uniaxial compressive strength ( | Rock quality designation ( | Stope span ( | Groundwater seepage volume (^{-1}·(10 m)^{-1}) | The rate of supporting pit roof ( |
---|---|---|---|---|---|

>200 | ≥90 | ≤10 | ≤5 | ≥70 | |

200~100 | 90~75 | 15~10 | 10~5 | 60~70 | |

100~50 | 75~50 | 30~15 | 25~10 | 50~60 | |

50~25 | 50~25 | 50~30 | 50~25 | 35~50 | |

≤25 | <25 | >50 | >50 | <35 |

Classification criterion of qualitative indices.

Classification standard | Value | Situation of joint development ( | Situation of pillar ( |
---|---|---|---|

1 | Joint is undeveloped, joint | Rock is completed and no fracture | |

2 | Joint is undeveloped, joint spacing 1~3 m, rocks are cut into giant block rock | There are some fractures around the corner | |

3 | Joint is little developed, joint spacing 0.4~1 m, rocks are cut into block rock | There are cracks on the pillar, and the crack | |

4 | Joint is developed, joint spacing 0.2~0.4 m, rocks are cut into stone | There are cracks on the pillar, and the crack widths are 5-10 mm | |

5 | Joint is very developed, joint | The pillar is broken into bulk, the expansion of fracture through the pillar |

Unascertained measurement function of each quantitative index.

Unascertained measurement function of one certain quantitative index.

Xin-Qiao Mine is located in the special industrial area in Tongling City, Anhui Province, China. Our investigation selected the 6 main stopes from the -270 m section as research subjects. The stope of Xin-Qiao Mine is shown in Figure

The stope of Xin-Qiao Mine.

Index values.

No. | ^{-1}·(10 m)^{-1}) | ||||||
---|---|---|---|---|---|---|---|

W501 | 50.7 | 47 | 3 | 13 | 2 | 27.3 | 80 |

W507 | 94.7 | 64 | 4 | 10 | 3 | 32.7 | 30 |

E01 | 76.8 | 66 | 3 | 12 | 4 | 32.7 | 55 |

E07 | 65.3 | 38 | 4 | 14 | 4 | 53.1 | 40 |

E16 | 160 | 51 | 4 | 16 | 4 | 63.8 | 45 |

E23 | 155 | 73 | 2 | 10 | 1 | 22.6 | 75 |

Taking W501 stope as an example, the evaluation function of unascertained measurement was calculated as

Based on AHP, the decision matrix, which utilizes the ratio form to express the relative importance of two indices ([

The index weight of the 7 factors

Only data in the same dimension and unit can be compared. Normalization processing must be made for contrast in the data that has different dimensions and units. Standard decision matrix

Through normalization processing of data, a normalized index matrix is obtained in Table

Normalized index matrix.

No. | |||||||
---|---|---|---|---|---|---|---|

W501 | 0.084 | 0.139 | 0.150 | 0.173 | 0.111 | 0.118 | 0.246 |

W507 | 0.157 | 0.189 | 0.200 | 0.133 | 0.167 | 0.138 | 0.092 |

E01 | 0.127 | 0.195 | 0.150 | 0.160 | 0.222 | 0.141 | 0.169 |

E07 | 0.108 | 0.112 | 0.200 | 0.187 | 0.222 | 0.229 | 0.123 |

E16 | 0.266 | 0.150 | 0.200 | 0.213 | 0.222 | 0.276 | 0.138 |

E23 | 0.257 | 0.215 | 0.100 | 0.133 | 0.056 | 0.098 | 0.231 |

Note:

Constructing a variable weight vector is the foundation of using variable weight theory. Index variable weight vector has some advantages such as good extension ability and flexible parameter setting. Index variable weight vector was chosen in this paper. The variable weight vector,

According to the characteristics of this decision, take

The unascertained measurement function of multiple indices calculated from Equation (

The credible degree was taken as 0.5. According to the variable and invariable weight theory and credible degree identification criteria, the risk grade of stope stability could be obtained in Table

Analytically obtained risk grade of stopes’ stability.

No. | Risk grade |
---|---|

W501 | III |

W507 | III |

E01 | III |

E07 | IV |

E16 | IV |

E23 | II |

Based on the analysis, the conclusions can be drawn as follows:

E23 stope is stable, and the risk grade is allowable. Normal mining production and management are acceptable

W501, W507, and E01 stopes are generally stable. The risk grade can be accepted, but with the continual supervision and monitor during mining

E07 stope and E16 stope are unstable. The risk grade can be accepted reluctantly. Lots of measures must be taken, such as supporting stope, decreasing mining intensity, and increasing security monitoring efforts

The four indices, including rock saturated uniaxial compressive strength (

The groundwater seepage volume (

From the research, the main conclusions can be drawn as follows:

The evaluation index system is crucial in this work; the 7 most important factors mentioned above are taken into consideration in Xin-Qiao Mine, being suitable for others. Then, each index was divided into 5 grades by the means of assignment value and the classification method of standardization, and the analysis result was also denoted into 5 risk grades

The weights were calculated by variable weight theory to avoid the “state out of balance” problem caused by invariable weight theory. The model was used in Xin-Qiao Mine, and the results show that this model has been improving the precision of stope stability analysis effectively and playing a good guiding role. The corresponding measures have been taken according to the research results to ensure that no accident occurred in mining production in recent years

It is a new method to analyze stope stability, being practical and efficient, which can not only divide the stability grade of stope being produced but also reflect the risk grade about mining empty area objectively. The model can be used in other mines through assigning values for the 7 factors, and the evaluation index system and classification for each index can be improved to get better results

The table and figure data used to support the findings of this study are included within the article.

The authors declare that they have no conflict of interest.

The authors thank the financial supports from the National Natural Science Foundation program (Grant No. 51704168), the Natural Science Foundation of Hunan Province (Grant Nos. 2020JJ5494 and 2020JJ5490), the research project of the Education Department of Hunan Province (Grant Nos. 20B517 and 18C0439), and the Open Research Fund Program of State Key Laboratory of Safety and Health for Metal Mines (Grant No. 2020-JSKSSYS-04).