# Dynamic Risk Assessment of High Slope in Open-Pit Coalmines Based on Interval Trapezoidal Fuzzy Soft Set Method: A Case Study

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## Abstract

**:**

## 1. Introduction

## 2. Expansion of Interval Trapezoidal Fuzzy Soft Sets

#### 2.1. Interval Trapezoidal Fuzzy Soft Sets and Their Properties

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

#### 2.2. Correlation Theorem of Interval Trapezoidal Fuzzy Soft Sets

**Theorem**

**1.**

**Theorem**

**2.**

**Theorem**

**3.**

## 3. Establishing the Dynamic Risk Evaluation Model of High Slope in Open-Pit Mine

_{1}is hydrological-climatic conditions, and B

_{2}is internal geological structure of slope. B

_{3}and B

_{4}are slope geometry and inducing factors of landslide, respectively.

_{11}is weathering and freeze-thaw, and e

_{12}is the state of groundwater. e

_{13}is permeability of rock and soil layer, and e

_{14}is annual rainfall. e

_{21}and e

_{22}are lithology and geological structure, respectively. e

_{23}and e

_{24}are slope structure and internal friction angle, respectively. e

_{25}is cohesion of slope. e

_{31}and e

_{32}are slope angle and slope height, respectively. e

_{33}is relationship between soft surface and slope surface, and e

_{34}is slope morphology. e

_{41}and e

_{42}are human factors and impact of blasting, respectively. e

_{43}and e

_{44}are slope angle of excavation and earthquake intensity, respectively. B

_{1}~B

_{4}are primary indicators and e

_{11}~e

_{44}are secondary indicators.

#### 3.1. Determining the Weights in Different Time Range

_{1}, B

_{2}, B

_{3}using Equation (22). ${({e}_{ij}^{(k)})}_{n\times m}$ is the kth evaluation matrix. ${e}_{ij}^{(k)}(i=1,2,3\cdots n;j=1,2,3\cdots m)$ is the value of attribute c

_{j}in the form of interval trapezoidal fuzzy number about evaluation grade t

_{i}at time point of t

_{k}.

_{q}. Then, all the entropy values in the corresponding entropy matrix are added.

_{k}of B

_{q}

#### 3.2. Determining the Index Weight by FAHP Method

#### 3.3. Integration and Decision Method of Interval Trapezoidal Fuzzy Soft Sets

#### 3.4. Case Study

#### 3.4.1. Dynamic Risk Assessment Based on Trapezoidal Fuzzy Soft Set in Shengli Open-Pit Mine

- (1)
- Decision-making steps and methods

- (2)
- Determination of values for dynamic model parameter set

_{1}is 1 July 2016; t

_{2}is 1 August 2016 and t

_{3}is 1 September 2016. The three time points (July, August and September) selected are the times with strong superposition of risk factors for open-pit mine slope. In this time period, there are many unstable factors inducing landslides. On the one hand, these three months are the rainy season for the open-pit mines in northern China, with a relatively concentrated and large rainfall, and the slope stability is greatly affected by hydrogeological factors. On the other hand, the open-pit mines in northern China can only be mined but not stripped in winter due to weather reasons. In order to leave enough earthwork and coal for winter mining, the blasting frequency during the three months (July, August and September) is relatively large, and the slope stability is greatly affected by mining factors. The risk decision of high slope in open-pit mine is evaluated from four primary risk factors (S), the hydrological and climatic conditions (B

_{1}), the slope internal geological structure (B

_{2}), the slope geometric conditions (B

_{3}), and landslide risk factors (B

_{4}). The risk level may be labeled as low, general and high, which are denoted by (x

_{1}), (x

_{2}), and (x

_{3}), respectively. In addition, 17 secondary indicators are selected to carry out risk assessment in four primary indicators. This will be described in the third part later on. The risk grade is divided by considering the influence of comprehensive factors. Low and medium are classified as low decision risk, high as general decision risk, and dangerous and extremely dangerous as high decision risk. The expert evaluation method was used to evaluate the slope risk factors of open-pit mine. Data were collected mainly through questionnaires. A sample of the questionnaire is attached. The data were mainly collected from the production technicians, stripping workers and management personnel of Shengli Open-pit coal mine. It covers all positions of frontline production, management and technology in open-pit coal mines. Among them, 80 questionnaires were sent out by Shengli open-pit coal mine, and 72 questionnaires were effectively recovered. The parameters of slope risk factor B

_{1}, B

_{2}, B

_{3}and B

_{4}at time t

_{1}, t

_{2}and t

_{3}are listed in Table A2, Table A3, Table A4, Table A5, Table A6, Table A7, Table A8, Table A9, Table A10, Table A11 and Table A12 in Appendix A.

- (3)
- Calculation of weights for dynamic model

_{1}, B

_{2}, B

_{3}and B

_{4}are calculated by Equation (22), subsequently the entropy matrix of ${E}_{{B}_{q}}^{k}={(E({e}_{ij}^{(k)}))}_{m\times n}$ corresponding to t

_{k}at different moments can be obtained. For example, the calculation results of the entropy matrix of B

_{1}at different times are shown in Table 1, Table 2 and Table 3.

_{1}is calculated by Equations (23) and (24), and the result is

_{2}, B

_{3}and B

_{4}can be obtained

#### 3.4.2. Risk Evaluation

_{1}), general (x

_{2}) and high (x

_{3}). Combined with the above theory, the weights at different times are obtained and then the comprehensive interval trapezoidal fuzzy soft set evaluation information for different parameter sets in all time range can be obtained by Equation (29). That is, the comprehensive evaluation values of influencing factors B

_{1}, B

_{2}, B

_{3}and B

_{4}in the whole time range subjected to different risks can be obtained as listed in Table A14, Table A15, Table A16 and Table A17 in Appendix A.

_{1}and B

_{3}indicate a high risk level, while the values of B

_{2}and B

_{4}indicate a general risk level. Thus, among the many factors affecting the instability of the slope of Shengli #1 open-pit coal mine, hydro-climatic conditions and slope geometric conditions belong to high risk factors. Special attention should be paid to hydrology and slope geometry during slope stability maintenance. For example, slope reinforcement and radar displacement monitoring should be planned and performed during the rainy season. The stability evaluation should be performed when designing the slope angle.

## 4. Verification with Field Data

## 5. Conclusions

- (1)
- The proposed method can effectively describe dynamic evaluation information of high slope, which makes it clear for the correlation between the influence of various uncertain factors on the slope and the time dimension. Compared with the traditional probabilistic analytical method, the proposed method can integrate time points and the weights of slope risk factors, especially for complex high slopes in open-pit coalmine, which enhances the practicability of interval trapezoidal fuzzy soft set theory in slope reliability analysis;
- (2)
- The risk dynamic evaluation model of high slope in an open-pit coal mine is established based on developed interval trapezoidal fuzzy soft set. In the model, the integration operator of interval trapezoidal fuzzy soft set is calculated and the comprehensive interval trapezoidal fuzzy soft set evaluation information in all time periods for different parameter sets can be obtained. The risk assessment of different factors with time can be easily achieved with the proposed method. This is not achievable by the traditional probabilistic analyses, which greatly facilitate the application of the interval trapezoidal fuzzy soft set method in probabilistic slope stability analysis;
- (3)
- The dynamic risk assessment model established above is applied in a case study for the north end slope of Shengli #1 open-pit mine. In the application of the model, three time points are selected to calculate the parameter values required by the above method, and 17 secondary risk factors of the high slope at different time points are evaluated. The results show that, for the north end slope stability of Shengli #1open-pit coal mine, the risks of hydro-climatic conditions and slope geometric conditions are relatively high, and the risks of internal geological structure and induced factors of slope are general. Meanwhile, the field monitoring parameters of the north end slope at different time ranges are analyzed; the results show that the above-mentioned slope dynamic evaluation model and method are reasonable and effective. In the process of slope reinforcement at the later stage for Shengli #1 open-pit mine, the influence of hydrological and climatic conditions and geometric shapes should be evaluated.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Primary Indicator | Secondary Indicators | LEVEL OF RISK | ||||
---|---|---|---|---|---|---|

Low | Medium | High | Dangerous | Extremely Dangerous | ||

Hydro-climatic conditions | Weathering and freeze-thaw | Tiny | Low | Medium | large | strong |

Groundwater occurrence | Tiny | Low | Medium | large | strong | |

Water permeability | Tiny | Low | Medium | large | strong | |

Average annual rainfall | <200 | 200~400 | 400~700 | 700~1100 | >1100 | |

Geological structure inside the slope | Lithology | Wholly | Slightly weathered | Weakly weathered | Cracked | Granular structures |

Geological structure | Simple | relatively simple | Generally | Relatively complex | Complex | |

Slope structure | Overall structure | Blocky structure | Layered structure | Cataclastic structure | Granular Structures | |

Internal friction | >35 | 35~28 | 28~21 | 21~14 | <14 | |

Cohesion | >220 | 120~220 | 80~120 | 50~80 | <50 | |

Slope geometric conditions | Slope angle | <20 | 20~30 | 30~40 | 40~50 | >50 |

Slope height | <30 | 30~60 | 60~100 | 100~200 | >200 | |

Relationship between weak surface (fault) and slope | Perpendicular slope | Vertical slope | Transverse slope | Bedding slope | Parallel slope | |

Slope morphology | Concave slope | Concave and straight mixing | Straight slope | Convex and straight mixing | Convex slope | |

Induced factors | Human factors | Tiny | Low | Medium | Large | Strong |

Destructive factor | Tiny | Low | Medium | Large | Strong | |

Excavation angle | <15 | 15~30 | 30~45 | 45~60 | >60 | |

Seismic intensity | <3 | 3~5 | 5~7 | 7~8 | >8 |

**Table A2.**The different risk evaluation values subordinated by influencing factors of B

_{1}at time t

_{1}.

e_{11} | e_{12} | e_{13} | e_{14} | |
---|---|---|---|---|

x_{1} | [(0.2,0.3);0.3; 0.4;(0.5,0.6)] | [(0.2,0.3);0.3; 0.4;(0.4,0.5)] | [(0.4,0.5);0.6; 0.7;(0.7,0.8)] | [(0.5,0.6);0.6; 0.7;(0.7,0.8)] |

x_{2} | [(0.2,0.3);0.3; 0.4;(0.4,0.5)] | [(0.3,0.4);0.5; 0.6;(0.7,0.8)] | [(0.5,0.7);0.7; 0.7;(0.8,0.9)] | [(0.2,0.3);0.3; 0.4;(0.5,0.6)] |

x_{3} | [(0.3,0.5);0.5; 0.6;(0.6,0.7)] | [(0.3,0.4);0.4; 0.4;(0.5,0.6)] | [(0.3,0.5);0.5; 0.6;(0.6,0.7)] | [(0.5,0.6);0.7; 0.7;(0.8,0.9)] |

**Table A3.**The different risk evaluation values subordinated by influencing factors of B

_{2}at time t

_{1}.

e_{21} | e_{22} | e_{23} | e_{24} | e_{25} | |
---|---|---|---|---|---|

x_{1} | [(0.5,0.6);0.7; 0.7;(0.8,0.9)] | [(0.2,0.3);0.4; 0.4;(0.5,0.6)] | [(0.5,0.6);0.7; 0.7;(0.8,0.9)] | [(0.3,0.4);0.4; 0.4;(0.5,0.6)] | [(0.3,0.4);0.4; 0.4;(0.5,0.6)] |

x_{2} | [(0.1,0.3);0.3; 0.3;(0.4,0.5)] | [(0.5,0.6);0.7; 0.7;(0.8,0.9)] | [(0.6,0.7);0.7; 0.7;(0.8,0.9)] | [(0.3,0.4);0.5; 0.6;(0.7,0.8)] | [(0.2,0.3);0.3; 0.4;(0.4,0.5)] |

x_{3} | [(0.3,0.5);0.5; 0.6;(0.6,0.7)] | [(0.2,0.3);0.4; 0.4;(0.5,0.6)] | [(0.3,0.5);0.5; 0.6;(0.6,0.7)] | [(0.6,0.7);0.7; 0.7;(0.8,0.9)] | [(0.2,0.4);0.4; 0.4;(0.5,0.6)] |

**Table A4.**The different risk evaluation values subordinated by influencing factors of B

_{3}at time t

_{1}.

e_{31} | e_{32} | e_{33} | e_{34} | |
---|---|---|---|---|

x_{1} | [(0.4,0.5);0.6; 0.7;(0.7,0.8)] | [(0.5,0.6);0.7; 0.7;(0.8,0.9)] | [(0.2,0.3);0.3; 0.4;(0.4,0.5)] | [(0.1,0.2);0.2; 0.3;(0.3,0.4)] |

x_{2} | [(0.2,0.3);0.4; 0.4;(0.5,0.6)] | [(0.3,0.5);0.5; 0.6;(0.6,0.7)] | [(0.5,0.6);0.6; 0.7;(0.8,0.9)] | [(0.1,0.3);0.3; 0.4;(0.4,0.5)] |

x_{3} | [(0.1,0.3);0.3; 0.4;(0.4,0.5)] | [(0.2,0.4);0.4; 0.4;(0.5,0.6)] | [(0.4,0.5);0.6; 0.7;(0.7,0.8)] | [(0.5,0.6);0.7; 0.7;(0.8,0.9)] |

**Table A5.**The different risk evaluation values subordinated by influencing factors of B

_{4}at time t

_{1}.

e_{41} | e_{42} | e_{43} | e_{44} | |
---|---|---|---|---|

x_{1} | [(0.2,0.3);0.3; 0.4;(0.4,0.5)] | [(0.2,0.4);0.4; 0.4;(0.5,0.6)] | [(0.1,0.2);0.2; 0.3;(0.3,0.4)] | [(0.4,0.5);0.6; 0.7;(0.7,0.8)] |

x_{2} | [(0.4,0.6);0.6; 0.7;(0.7,0.8)] | [(0.2,0.3);0.3; 0.4;(0.5,0.6)] | [(0.3,0.4);0.4; 0.4;(0.5,0.6)] | [(0.6,0.7);0.7; 0.8;(0.9,1)] |

x_{3} | [(0.1,0.4);0.4; 0.4;(0.5,0.6)] | [(0.1,0.3);0.3; 0.3;(0.4,0.5) | [(0.3,0.5);0.5; 0.6;(0.6,0.7)] | [(0.5,0.7);0.7; 0.7;(0.8,0.9)] |

**Table A6.**The different risk evaluation values subordinated by influencing factors of B

_{1}at time t

_{2}.

e_{11} | e_{12} | e_{13} | e_{14} | |
---|---|---|---|---|

x_{1} | [(0.3,0.4);0.4; 0.4;(0.5,0.7)] | [(0.5,0.6);0.7; 0.7;(0.8,0.9)] | [(0.2,0.3);0.3; 0.4;(0.5,0.6)] | [(0.4,0.5);0.5; 0.6;(0.6,0.7)] |

x_{2} | [(0.1,0.2);0.2; 0.4;(0.5,0.6)] | [(0.4,0.6);0.6; 0.7;(0.7,0.8)] | [(0.1,0.2);0.2; 0.3;(0.4,0.5)] | [(0.3,0.4);0.4; 0.4;(0.5,0.6)] |

x_{3} | [(0.3,0.5);0.5; 0.6;(0.7,0.8)] | [(0.4,0.5);0.5; 0.6;(0.7,0.8)] | [(0.4,0.6);0.6; 0.7;(0.7,0.8)] | [(0.5,0.6);0.7; 0.8;(0.8,0.9)] |

**Table A7.**The different risk evaluation values subordinated by influencing factors of B

_{2}at time t

_{2}.

e_{21} | e_{22} | e_{23} | e_{24} | e_{25} | |
---|---|---|---|---|---|

x_{1} | [(0.2,0.3);0.4; 0.4;(0.5,0.6)] | [(0.1,0.2);0.2; 0.3;(0.4,0.5)] | [(0.3,0.6);0.6; 0.7;(0.8,0.9)] | [(0.4,0.6);0.6; 0.7;(0.8,0.9)] | [(0.3,0.4);0.4; 0.4;(0.6,0.7)] |

x_{2} | [(0.3,0.5);0.5; 0.6;(0.7,0.8)] | [(0.1,0.3);0.3; 0.4;(0.4,0.6)] | [(0.5,0.7);0.7; 0.7;(0.8,0.9)] | [(0.1,0.3);0.3; 0.4;(0.5,0.6)] | [(0.2,0.3);0.3; 0.4;(0.4,0.5)] |

x_{3} | [(0.4,0.5);0.6; 0.7;(0.7,0.8)] | [(0.2,0.4);0.4; 0.4;(0.5,0.7)] | [(0.3,0.5);0.5; 0.6;(0.7,0.8)] | [(0.5,0.7);0.7; 0.7;(0.8,0.9)] | [(0.4,0.5);0.5; 0.6;(0.6,0.7)] |

**Table A8.**The different risk evaluation values subordinated by influencing factors of B

_{3}at time t

_{2}.

e_{31} | e_{32} | e_{33} | e_{34} | |
---|---|---|---|---|

x_{1} | [(0.2,0.4);0.4; 0.4;(0.5,0.6)] | [(0.5,0.6);0.7; 0.7;(0.8,0.9)] | [(0.1,0.2);0.3; 0.4;(0.4,0.5)] | [(0.3,0.5);0.5; 0.6;(0.7,0.8)] |

x_{2} | [(0.2,0.3);0.3; 0.4;(0.5,0.6)] | [(0.5,0.6);0.6; 0.7;(0.7,0.8)] | [(0.1,0.2);0.2; 0.3;(0.3,0.4)] | [(0.3,0.4);0.4; 0.4;(0.5,0.6)] |

x_{3} | [(0.3,0.5);0.5; 0.6;(0.7,0.8)] | [(0.4,0.5);0.5; 0.6;(0.7,0.8)] | [(0.4,0.6);0.6; 0.7;(0.8,0.9)] | [(0.5,0.6);0.7; 0.8;(0.8,0.9)] |

**Table A9.**The different risk evaluation values subordinated by influencing factors of B

_{4}at time t

_{2}.

e_{41} | e_{42} | e_{43} | e_{44} | |
---|---|---|---|---|

x_{1} | [(0.3,0.5);0.5; 0.6;(0.7,0.8)] | [(0.3,0.5);0.6; 0.7;(0.7,0.8)] | [(0.1,0.2);0.2; 0.3;(0.3,0.4)] | [(0.4,0.5);0.5; 0.6;(0.9,1)] |

x_{2} | [(0.1,0.3);0.3; 0.4;(0.5,0.6)] | [(0.6,0.7);0.7; 0.8;(0.9,1)] | [(0.2,0.3);0.3; 0.4;(0.5,0.6)] | [(0.4,0.5);0.6; 0.7;(0.8,0.9)] |

x_{3} | [(0.2,0.4);0.4; 0.4;(0.6,0.7)] | [(0.1,0.3);0.3; 0.4;(0.4,0.6)] | [(0.1,0.2);0.2; 0.2;(0.3,0.4)] | [(0.1,0.3);0.3; 0.4;(0.5,0.6)] |

**Table A10.**The different risk evaluation values subordinated by influencing factors of B

_{1}at time t

_{3}.

e_{11} | e_{12} | e_{13} | e_{14} | |
---|---|---|---|---|

x_{1} | [(0.5,0.7);0.7; 0.7;(0.8,0.9)] | [(0.1,0.2);0.2; 0.2;(0.2,0.5)] | [(0.1,0.4);0.4; 0.4;(0.5,0.6)] | [(0.1,0.6);0.6; 0.7;(0.7,0.8)] |

x_{2} | [(0.1,0.4);0.4; 0.4;(0.5,0.6)] | [(0.1,0.6);0.6; 0.7;(0.7,0.8)] | [(0.1,0.2);0.2; 0.2;(0.2,0.4)] | [(0.1,0.3);0.3; 0.4;(0.4,0.5)] |

x_{3} | [(0.2,0.3);0.3; 0.4;(0.4,0.5)] | [(0.3,0.4);0.4; 0.4;(0.5,0.6)] | [(0.5,0.6);0.6; 0.7;(0.7,0.8)] | [(0.3,0.4);0.4; 0.4;(0.5,0.6)] |

**Table A11.**The different risk evaluation values subordinated by influencing factors of B

_{2}at time t

_{3}.

e_{21} | e_{22} | e_{23} | e_{24} | e_{25} | |
---|---|---|---|---|---|

x_{1} | [(0.1,0.7);0.7; 0.7;(0.8,0.9)] | [(0.1,0.4);0.4; 0.4;(0.5,0.6)] | [(0.1,0.2);0.2; 0.3;(0.3,0.5)] | [(0.1,0.6);0.6; 0.7;(0.7,0.8)] | [(0.1,0.3);0.3; 0.4;(0.4,0.5)] |

x_{2} | [(0.1,0.6);0.6; 0.7;(0.7,0.8)] | [(0.1,0.3);0.3; 0.4;(0.5,0.6)] | [(0.1,0.4);0.4; 0.4;(0.5,0.6)] | [(0.1,0.7);0.7; 0.8;(0.9,1)] | [(0.5,0.6);0.6; 0.7;(0.7,0.8)] |

x_{3} | [(0.3,0.4);0.4; 0.4;(0.5,0.6)] | [(0.1,0.2);0.2; 0.3;(0.3,0.4) | [(0.4,0.5);0.5; 0.6;(0.6,0.7)] | [(0.6,0.7);0.7; 0.7;(0.8,0.9)] | [(0.3,0.4);0.4; 0.4;(0.5,0.6)] |

**Table A12.**The different risk evaluation values subordinated by influencing factors of B

_{3}at time t

_{3}.

e_{31} | e_{32} | e_{33} | e_{34} | |
---|---|---|---|---|

x_{1} | [(0.1,0.2);0.2; 0.2;(0.2,0.4)] | [(0.2,0.3);0.3; 0.4;(0.4,0.6)] | [(0.2,0.3);0.3; 0.3;(0.3,0.9)] | [(0.1,0.4);0.4; 0.4;(0.5,0.6)] |

x_{2} | [(0.1,0.3);0.3; 0.3;(0.3,0.4)] | [(0.1,0.3);0.3; 0.4;(0.4,0.5)] | [(0.1,0.2);0.2; 0.2;(0.2,0.7)] | [(0.1,0.3);0.3; 0.3;(0.3,0.4)] |

x_{3} | [(0.3,0.4);0.4; 0.4;(0.5,0.6)] | [(0.1,0.2);0.2; 0.2;(0.2,0.3)] | [(0.3,0.4);0.4; 0.4;(0.5,0.6)] | [(0.2,0.3);0.3; 0.4;(0.4,0.5)] |

**Table A13.**The different risk evaluation values subordinated by influencing factors of B

_{4}at time t

_{3}.

e_{41} | e_{42} | e_{43} | e_{44} | |
---|---|---|---|---|

x_{1} | [(0.1,0.3);0.3; 0.4;(0.4,0.5)] | [(0.1,0.2);0.2; 0.2;(0.2,0.7)] | [(0.1,0.5);0.5; 0.6;(0.6,0.7)] | [(0.1,0.3);0.3; 0.3;(0.3,0.4)] |

x_{2} | [(0.1,0.2);0.2; 0.2;(0.2,0.4)] | [(0.1,0.4);0.4; 0.4;(0.5,0.6)] | [(0.1,0.3);0.3; 0.3;(0.3,0.4)] | [(0.1,0.3);0.3; 0.4;(0.4,0.5)] |

x_{3} | [(0.5,0.6);0.6; 0.7;(0.7,0.8)] | [(0.2,0.3);0.3; 0.4;(0.4,0.5)] | [(0.3,0.4);0.4; 0.4;(0.4,0.5)] | [(0.2,0.3);0.3; 0.3;(0.3,0.4)] |

**Table A14.**The influencing factors of B

_{1}in the whole time period belong to the comprehensive evaluation value of different risks.

e_{11} | e_{12} | e_{13} | e_{14} | |
---|---|---|---|---|

x_{1} | [(0.37,0.53);0.53; 0.54;(0.65,0.79)] | [(0.30,0.41);0.47; 0.49;(0.57,0.74)] | [(0.21,0.39);0.42; 0.48;(0.55,0.66)] | [(0.33,0.56);0.56; 0.66;(0.66,0.77)] |

x_{2} | [(0.12,0.30);0.30; 0.40;(0.48,0.58)] | [(0.27,0.56);0.58; 0.68;(0.70,0.80)] | [(0.21,0.35);0.35; 0.39;(0.47,0.62)] | [(0.21,0.34);0.34; 0.40;(0.46,0.56)] |

x_{3} | [(0.26,0.43);0.43; 0.53;(0.58,0.69)] | [(0.34,0.44);0.44; 0.49;(0.59,0.70)] | [(0.42,0.56);0.56; 0.65;(0.66,0.77)] | [(0.43,0.53);0.61; 0.67;(0.72,0.83)] |

**Table A15.**The influencing factors of B

_{2}in the whole time period belong to the comprehensive evaluation value of different risks.

e_{21} | e_{22} | e_{23} | e_{24} | e_{25} | |
---|---|---|---|---|---|

x_{1} | [(0.24,0.55);0.61; 0.61;(0.71,0.83)] | [(0.12,0.31);0.33; 0.36;(0.46,0.56)] | [(0.28,0.48);0.51; 0.58;(0.67,0.81)] | [(0.27,0.56);0.56; 0.65;(0.71,0.82)] | [(0.23,0.36);0.36; 0.4;(0.51,0.61)] |

x_{2} | [(0.19,0.51);0.51; 0.60;(0.65,0.76)] | [(0.21,0.38);0.42; 0.48;(0.56,0.70)] | [(0.40,0.61);0.61; 0.61;(0.71,0.83)] | [(0.15,0.51);0.53; 0.64;(0.76,1)] | [(0.33,0.44);0.44; 0.54;(0.54,0.65)] |

x_{3} | [(0.34,0.46);0.51; 0.58;(0.61,0.71)] | [(0.16,0.31);0.33; 0.36;(0.43,0.58)] | [(0.34,0.5);0.5; 0.6;(0.64,0.74)] | [(0.56,0.7);0.7; 0.7;(0.8,0.9)] | [(0.32,0.44);0.44; 0.49;(0.54,0.64)] |

**Table A16.**The influencing factors of B

_{3}in the whole time period belong to the comprehensive evaluation value of different risks.

e_{31} | e_{32} | e_{33} | e_{34} | |
---|---|---|---|---|

x_{1} | [(0.22,0.36);0.39; 0.43;(0.47,0.6)] | [(0.4,0.51);0.59; 0.61;(0.7,0.83)] | [(0.16,0.26);0.3; 0.36;(0.36,0.73)] | [(0.18,0.4);0.4; 0.47;(0.56,0.67)] |

x_{2} | [(0.16,0.3);0.32; 0.36;(0.43,0.53)] | [(0.33,0.48);0.48; 0.58;(0.58,0.69)] | [(0.21,0.32);0.32; 0.39;(0.45,0.69)] | [(0.18,0.34);0.34; 0.36;(0.41,0.51)] |

x_{3} | [(0.26,0.42);0.42; 0.49;(0.57,0.68)] | [(0.25,0.38);0.38; 0.43;(0.51,0.62)] | [(0.36,0.51);0.53; 0.61;(0.69,0.8)] | [(0.4,0.51);0.59; 0.67;(0.7,0.82)] |

**Table A17.**The influencing factors of B

_{4}in the whole time period belong to the comprehensive evaluation value of different risks.

e_{41} | e_{42} | e_{43} | e_{44} | |
---|---|---|---|---|

x_{1} | [(0.21,0.39);0.39; 0.49;(0.54,0.65)] | [(0.21,0.38);0.43; 0.49;(0.51,0.73)] | [(0.10,0.33);0.33; 0.43;(0.43,0.54)] | [(0.30,0.43);0.46; 0.54;(0.73,1.00)] |

x_{2} | [(0.18,0.35);0.35; 0.43;(0.47,0.60)] | [(0.36,0.52);0.52; 0.61;(0.73,1.00)] | [(0.19,0.32);0.32; 0.36;(0.43,0.53)] | [(0.36,0.50);0.54; 0.65;(0.74,1.00)] |

x_{3} | [(0.31,0.49);0.49; 0.54;(0.62,0.72)] | [(0.14,0.30);0.30; 0.38;(0.40,0.54)] | [(0.23,0.36);0.36; 0.39;(0.42,0.52)] | [(0.25,0.43);0.43; 0.46;(0.54,0.66)] |

B_{1} | e_{11} | e_{12} | e_{13} | e_{14} |
---|---|---|---|---|

e_{11} | 0.5 | 0.4 | 0.3 | 0.7 |

e_{12} | 0.6 | 0.5 | 0.6 | 0.3 |

e_{13} | 0.7 | 0.4 | 0.5 | 0.4 |

e_{14} | 0.3 | 0.7 | 0.6 | 0.5 |

B_{2} | e_{21} | e_{22} | e_{23} | e_{24} | e_{25} |
---|---|---|---|---|---|

e_{21} | 0.5 | 0.4 | 0.3 | 0.7 | 0.4 |

e_{22} | 0.6 | 0.5 | 0.6 | 0.3 | 0.8 |

e_{23} | 0.7 | 0.4 | 0.5 | 0.4 | 0.6 |

e_{24} | 0.3 | 0.7 | 0.6 | 0.5 | 0.3 |

e_{25} | 0.6 | 0.2 | 0.4 | 0.7 | 0.5 |

B_{3} | e_{31} | e_{32} | e_{33} | e_{34} |
---|---|---|---|---|

e_{31} | 0.5 | 0.4 | 0.3 | 0.4 |

e_{32} | 0.6 | 0.5 | 0.6 | 0.3 |

e_{33} | 0.7 | 0.4 | 0.5 | 0.4 |

e_{34} | 0.6 | 0.7 | 0.6 | 0.5 |

B_{4} | e_{41} | e_{42} | e_{43} | e_{44} |
---|---|---|---|---|

e_{41} | 0.5 | 0.4 | 0.3 | 0.7 |

e_{42} | 0.6 | 0.5 | 0.6 | 0.8 |

e_{43} | 0.7 | 0.4 | 0.5 | 0.6 |

e_{44} | 0.3 | 0.2 | 0.4 | 0.5 |

A | B_{1} | B_{2} | B_{3} | B_{4} |
---|---|---|---|---|

B_{1} | 0.5 | 0.4 | 0.3 | 0.4 |

B_{2} | 0.6 | 0.5 | 0.3 | 0.2 |

B_{3} | 0.7 | 0.7 | 0.5 | 0.4 |

B_{4} | 0.6 | 0.8 | 0.6 | 0.5 |

**Table A23.**The integrated evaluation value of different parameters belonging to open-pit slope risk.

B_{1} | B_{2} | B_{3} | B_{4} | |
---|---|---|---|---|

x_{1} | [(0.302,0.472);0.495; 0.548;(0.608,0.736)] | [(0.223,0.439);0.460; 0.509;(0.603,0.716)] | [(0.239,0.387);0.422; 0.473;(0.531,0.713)] | [(0.183,0.370);0.392; 0.476;(0.516,0.680)] |

x_{2} | [(0.205,0.392);0.396; 0.467;(0.529,0.641)] | [(0.258,0.484);0.497; 0.568;(0.641,0.783)] | [(0.224,0.364);0.367; 0.426;(0.466,0.604)] | [(0.269,0.423);0.427; 0.498;(0.584,0.771)] |

x_{3} | [(0.368,0.494);0.515; 0.588;(0.642,0.749)] | [(0.331,0.469);0.482; 0.533;(0.593,0.707)] | [(0.334,0.462);0.497; 0.567;(0.631,0.744)] | [(0.216,0.372);0.372; 0.426;(0.471,0.590)] |

A | |
---|---|

x_{1} | [(0.225,0.401);0.427;0.491;(0.548,0.704)] |

x_{2} | [(0.243,0.408);0.414;0.481;(0.546,0.699)] |

x_{3} | [(0.295,0.434);0.450;0.512;(0.567,0.681)] |

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E (e_{11}) | E (e_{12}) | E (e_{13}) | E (e_{14}) | |
---|---|---|---|---|

x_{1} | 0.13 | 0.15 | 0.13 | 0.15 |

x_{2} | 0.15 | 0.05 | 0.21 | 0.06 |

x_{3} | 0.04 | 0.08 | 0.04 | 0.20 |

E (e_{11}) | E (e_{12}) | E (e_{13}) | E (e_{14}) | |
---|---|---|---|---|

x_{1} | 0.06 | 0.20 | 0.13 | 0.05 |

x_{2} | 0.18 | 0.14 | 0.23 | 0.08 |

x_{3} | 0.06 | 0.08 | 0.14 | 0.23 |

E (e_{11}) | E (e_{12}) | E (e_{13}) | E (e_{14}) | |
---|---|---|---|---|

x_{1} | 0.21 | 0.28 | 0.10 | 0.10 |

x_{2} | 0.10 | 0.10 | 0.29 | 0.16 |

x_{3} | 0.15 | 0.08 | 0.15 | 0.08 |

Primary Indicator | Parameters | Primary Weight | Parameter Weights |
---|---|---|---|

Hydro-climatic conditions | Weathering and freeze-thaw | 0.150 | 0.225 |

Groundwater occurrence | 0.250 | ||

Water permeability | 0.250 | ||

Average annual rainfall | 0.275 | ||

Geological structure inside the slope | Lithology | 0.150 | 0.160 |

Geological structure | 0.260 | ||

Slope structure | 0.220 | ||

Internal friction | 0.180 | ||

Cohesion | 0.180 | ||

Slope geometric conditions | Slope angle | 0.325 | 0.150 |

Slope height | 0.250 | ||

Relationship between weak surface (fault) and slope | 0.250 | ||

Slope morphology | 0.350 | ||

Induced factors | Human factors | 0.375 | 0.225 |

Destructive factor | 0.375 | ||

Excavation angle | 0.300 | ||

Seismic intensity | 0.100 |

B_{1} | B_{2} | B_{3} | B_{4} | |
---|---|---|---|---|

${\eta}_{1}$ | 0.336 | −0.446 | −0.156 | −0.185 |

${\eta}_{2}$ | −1.257 | 0.397 | −1.098 | 0.88 |

${\eta}_{3}$ | 0.921 | 0.049 | 1.254 | −0.695 |

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## Share and Cite

**MDPI and ACS Style**

Wang, Z.; Hu, M.; Zhang, P.; Li, X.; Yin, S.
Dynamic Risk Assessment of High Slope in Open-Pit Coalmines Based on Interval Trapezoidal Fuzzy Soft Set Method: A Case Study. *Processes* **2022**, *10*, 2168.
https://doi.org/10.3390/pr10112168

**AMA Style**

Wang Z, Hu M, Zhang P, Li X, Yin S.
Dynamic Risk Assessment of High Slope in Open-Pit Coalmines Based on Interval Trapezoidal Fuzzy Soft Set Method: A Case Study. *Processes*. 2022; 10(11):2168.
https://doi.org/10.3390/pr10112168

**Chicago/Turabian Style**

Wang, Zhiliu, Mengxin Hu, Peng Zhang, Xinming Li, and Song Yin.
2022. "Dynamic Risk Assessment of High Slope in Open-Pit Coalmines Based on Interval Trapezoidal Fuzzy Soft Set Method: A Case Study" *Processes* 10, no. 11: 2168.
https://doi.org/10.3390/pr10112168