# Suitability Evaluation of the Lining Form Based on Combination Weighting–Set Pair Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Suitability Level of Lining Form

^{3}; ${\gamma}_{R}$ is the weight of rock mass (kN/m

^{3}); and α is the slope angle of the mountain body at the selected position of the high-pressure pipeline.

_{3}, Cr

_{10}, Cr

_{30}, Cr

_{50,}and Cr

_{100}are the core acquisition rates with lengths of 3~10, 10~30, 30~50, 50~100, and >100 cm, respectively. Furthermore, 3, 10, 30, 50, and 100 are all coefficients.

## 3. The Proposed Methodology

#### 3.1. C-OWA Operator

- (1)
- Firstly, n experts were invited to score the importance of indices at the same level (using a 10-point system) to form the initial decision data A = (x
_{1j}, x_{2j}, …, x_{mj}). Then, the initial decision data are arranged in descending order to acquire new decision data B = (y_{0j}, y_{2j}, …, y_{(m}_{−1)j}). - (2)
- The weighted vector ${u}_{i}$ of the decision data B is calculated by Equation (5).

- (3)
- The absolute weight of the assessment index P
_{j}is obtained by weighting the decision data B with the weighted vector ${u}_{i}$. The equation is as follows:

- (4)
- According to the absolute weight, the relative weight of the assessment index λ
_{j}is calculated by Equation (7).

#### 3.2. CRITIC-EWM Method

#### 3.2.1. CRITIC Method

- (1)
- The initial indicator data matrix X is defined as follows:

- (2)
- Initial data normalization

- (3)
- The standard deviation of each index is calculated by Equation (11).

_{j};$\text{}{\overline{y}}_{j}$ is the average value of the jth index.

- (4)
- Correlation coefficient of the indices is calculated by Equation (12).

_{i}and x

_{j}.

- (5)
- The objective weight of the indices is calculated by Equations (13) and (14).

#### 3.2.2. Improved EWM

#### 3.2.3. Determining the Objective Weight

#### 3.3. Combination Weighting

#### 3.4. SPA

## 4. Case Study

#### 4.1. Project Overview

#### 4.2. Calculation of Index Weight

_{i}are calculated by Equations (5)–(7):

#### 4.3. Level Determination

#### 4.4. Suitability Evaluation

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PSPS | Pumped storage power station |

OWA | Ordered weighted averaging |

C-OWA | Combination ordered eeighted averaging |

CRITIC | Criteria importance through intercriteria correlation |

EWM | Entropy eeighting model |

SPA | Set pair analysis |

IRENA | International Renewable Energy Agency |

3D-FEM | Three-dimensional finite element method |

RQD | Rock quality designation |

RBI | Rock mass block index |

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**Figure 1.**Examples of minimum and maximum values of RQD for various joint densities along drill cores (Reprinted with permission from Ref. [17]. Copyright 2022, Elsevier).

**Figure 3.**Survey and drilling schematic of hydropower station. (

**a**): topography of the project area; (

**b**): drilling of the high-pressure pipeline; (

**c**): hole-detecting of the powerhouse; (

**d**): photograph of rock cores.

Evaluation Level | Extremely Suitable (I) | More Suitable (II) | Basically Suitable (III) | Relatively Unsuitable (IV) | Extremely Unsuitable (V) |
---|---|---|---|---|---|

A | >1.5 | 1.3~1.5 | 1.2~1.3 | 1.0~1.2 | <1.0 |

B | >1.3 | 1.2~1.3 | 1.1~1.2 | 1.0~1.1 | <1.0 |

C | >1.3 | 1.2~1.3 | 1.1~1.2 | 1.0~1.1 | <1.0 |

D | <3 | 3~6 | 6~10 | 10~15 | >15 |

E | 100~50 | 50~30 | 30~10 | 10~3 | <3 |

Drilling Number | A | B | C | D | E |
---|---|---|---|---|---|

1 | 2.43 | 4.79 | 7.07 | 5.89 | 33.93 |

2 | 2.04 | 2.93 | 4.96 | 8.20 | 69.12 |

3 | 1.82 | 2.79 | 3.67 | 8.20 | 86.40 |

4 | 1.80 | 2.44 | 4.52 | 9.38 | 15.98 |

5 | 1.66 | 0.76 | 1.71 | 13.09 | 46.77 |

6 | 1.59 | 0.37 | 2.99 | 17.19 | 74.11 |

7 | 1.60 | 1.34 | 1.76 | 25.32 | 6.82 |

No. | Professional Field | Position | Educational Level |
---|---|---|---|

Expert 1 | Geological Engineering | Senior Engineer | Master |

Expert 2 | Geological Engineering | Senior Engineer | Master |

Expert 3 | Geological Engineering | Professor | Doctor |

Expert 4 | Geological Engineering | Professor | Doctor |

Expert 5 | Hydraulic Engineering | Senior Engineer | Master |

Expert 6 | Hydraulic Engineering | Senior Engineer | Master |

Expert 7 | Hydraulic Engineering | Professor | Doctor |

Expert 8 | Hydraulic Engineering | Professor | Doctor |

Index | Expert 1 | Expert 2 | Expert 3 | Expert 4 | Expert 5 | Expert 6 | Expert 7 | Expert 8 |
---|---|---|---|---|---|---|---|---|

A | 3 | 2.5 | 2 | 1 | 1.5 | 1 | 1.5 | 1.2 |

B | 1 | 2 | 1.5 | 2 | 1.5 | 2 | 1 | 1.5 |

C | 2 | 2.5 | 2.5 | 2.5 | 2.5 | 3 | 2.5 | 3 |

D | 2.5 | 2.5 | 2 | 2.5 | 1.5 | 2 | 2.5 | 1.5 |

E | 1.5 | 1 | 2 | 2 | 3 | 2.5 | 2.5 | 3 |

Suitability Level | Extremely Suitable (I) | More Suitable (II) | Basically Suitable (III) | Relatively Unsuitable (IV) | Extremely Unsuitable (V) |
---|---|---|---|---|---|

$\mu $ | [0.6, 1] | [0.2, 0.6) | [−0.2, 0.2) | [−0.6, −0.2) | [−1, −0.6) |

Working Point | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

a | 0.5243 | 0.7162 | 0.7162 | 0.5243 | 0.5222 | 0.5842 | 0.5243 |

b | 0.3051 | 0.0000 | 0.0000 | 0.0000 | 0.0620 | 0.0000 | 0.0000 |

c | 0.1706 | 0.2710 | 0.2710 | 0.3315 | 0.0000 | 0.0000 | 0.0045 |

d | 0.0000 | 0.0129 | 0.0129 | 0.1442 | 0.2168 | 0.0000 | 0.1873 |

e | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.1990 | 0.4158 | 0.2838 |

$\mu $ | 0.6769 | 0.7097 | 0.7097 | 0.4522 | 0.2457 | 0.1683 | 0.1468 |

Working Point | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

Expert subjective evaluation method | I | I | I | II | II | III | IV |

Combined objective weighting–SPA | I | I | I | II | II | III | II |

Combination weighting–SPA | I | I | I | II | II | III | III |

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**MDPI and ACS Style**

Xing, C.; Yao, L.; Wang, Y.; Hu, Z.
Suitability Evaluation of the Lining Form Based on Combination Weighting–Set Pair Analysis. *Appl. Sci.* **2022**, *12*, 4896.
https://doi.org/10.3390/app12104896

**AMA Style**

Xing C, Yao L, Wang Y, Hu Z.
Suitability Evaluation of the Lining Form Based on Combination Weighting–Set Pair Analysis. *Applied Sciences*. 2022; 12(10):4896.
https://doi.org/10.3390/app12104896

**Chicago/Turabian Style**

Xing, Chen, Leihua Yao, Yingdong Wang, and Zijuan Hu.
2022. "Suitability Evaluation of the Lining Form Based on Combination Weighting–Set Pair Analysis" *Applied Sciences* 12, no. 10: 4896.
https://doi.org/10.3390/app12104896