# 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 |

## References

- Perez-Diaz, J.I.; Chazarra, M.; Garcia-Gonzalez, J.; Cavazzini, G.; Stoppato, A. Trends and challenges in the operation of pumped-storage hydropower plants. Renew. Sustain. Energy Rev.
**2015**, 44, 767–784. [Google Scholar] [CrossRef] - Zhang, S.F.; Andrews-Speed, P.; Perera, P. The evolving policy regime for pumped storage hydroelectricity in China: A key support for low-carbon energy. Appl. Energy
**2015**, 150, 15–24. [Google Scholar] [CrossRef] - Barbour, E.; Wilson, I.A.G.; Radcliffe, J.; Ding, Y.L.; Li, Y.L. A review of pumped hydro energy storage development in significant international electricity markets. Renew. Sustain. Energy Rev.
**2016**, 61, 421–432. [Google Scholar] [CrossRef][Green Version] - Xue, F.F.; Xu, C.; Shen, W.Z.; Li, L.M. Ventilation in pumped storage power stations: Influence of dehumidifiers in an underground tunnel. Appl. Therm. Eng.
**2020**, 172, 115162. [Google Scholar] [CrossRef] - Gao, Y.; Gao, X.; Zhang, X. The 2 °C Global Temperature Target and the Evolution of the Long-Term Goal of Addressing Climate Change-From the United Nations Framework Convention on Climate Change to the Paris Agreement. Engineering
**2017**, 3, 272–278. [Google Scholar] [CrossRef] - Bao, Y.D.; Chen, J.P.; Sun, X.H.; Han, X.D.; Li, Y.C.; Zhang, Y.W.; Gu, F.F.; Wang, J.Q. Debris flow prediction and prevention in reservoir area based on finite volume type shallow-water model: A case study of pumped-storage hydroelectric power station site in Yi County, Hebei, China. Environ. Earth Sci.
**2019**, 78, 577. [Google Scholar] [CrossRef] - Dadashi, E.; Noorzad, A.; Shahriar, K.; Goshtasbi, K. Hydro-mechanical interaction analysis of reinforced concrete lining in pressure tunnels. Tunn. Undergr. Space Technol.
**2017**, 69, 125–132. [Google Scholar] [CrossRef] - Zhou, Y.F.; Su, K.; Wu, H.G. Hydro-mechanical interaction analysis of high pressure hydraulic tunnel. Tunn. Undergr. Space Technol.
**2015**, 47, 28–34. [Google Scholar] [CrossRef] - Su, K.; Wu, H.G. Analysis of Hydro-Mechanical Interaction to Pervious Pressure Tunnel. In Proceedings of the Asia-Pacific Power and Energy Engineering Conference, Chengdu, China, 28–31 March 2010. [Google Scholar]
- Zhang, C.S. Design criteria and engineering application of concrete-lined high pressure power tunnels. J. Hydroelectr. Eng.
**2009**, 28, 80–84. (In Chinese) [Google Scholar] - Bian, K.; Liu, J.; Xiao, M.; Liu, Z.P. Cause investigation and verification of lining cracking of bifurcation tunnel at Huizhou Pumped Storage Power Station. Tunn. Undergr. Space Technol.
**2016**, 54, 123–134. [Google Scholar] [CrossRef] - Schleiss, A.J. Design of reinforced concrete linings of pressure tunnels and shafts. Hydropower Dams
**1997**, 4, 88–94. [Google Scholar] - Chen, J.T.; Yang, Y.; Ye, C.; Yang, Y.; Xiao, M. Three-Dimensional Numerical Analysis of Compound Lining in Complex Underground Surge-Shaft Structure. Math. Probl. Eng.
**2015**, 2015, 387379. [Google Scholar] [CrossRef] - Gu, Z.Q. Experiences in Norwegian Hydropower Engineering; Tapir Publishers: Trondhe, Norway, 1985. [Google Scholar]
- Hu, Y.J.; Fang, J.P.; Huang, D.J.; Feng, S.N. Advances in Pressure Tunnel Design and Structure Computation. Water Power
**2011**, 37, 15–18. (In Chinese) [Google Scholar] - Du, S.G.; Xu, S.F.; Yang, S.F. Application of rock quality designation(RQD) to engineering classification of rocks. J. Eng. Geol.
**2000**, 8, 351–356. (In Chinese) [Google Scholar] - Palmstrom, A. Measurements of and correlations between block size and rock quality designation (RQD). Tunn. Undergr. Space Technol.
**2005**, 20, 362–377. [Google Scholar] [CrossRef] - Azimian, A. A New Method for Improving the RQD Determination of Rock Core in Borehole. Rock Mech. Rock Eng.
**2016**, 49, 1559–1566. [Google Scholar] [CrossRef] - Hu, X.W.; Zhong, P.L.; Ren, Z.G. Rock mass block index and its engineering practice significance. J. Hydraul. Eng.
**2002**, 33, 80–83. (In Chinese) [Google Scholar] - Huang, R.Q.; Huo, J.J. Quantitative analysis of rock mass block index for dam foundation of jinping I hydropower station. Chin. J. Rock Mech. Eng.
**2011**, 30, 449–453. (In Chinese) [Google Scholar] - Yager, R.R. On ordered weighted averaging aggregation operators in multicriteria decision-making. Ieee Trans. Syst. Man Cybern.
**1988**, 18, 183–190. [Google Scholar] [CrossRef] - Li, X.H.; Zhang, L.Y.; Zhang, R.R.; Yang, M.; Li, H. A semi-quantitative methodology for risk assessment of university chemical laboratory. J. Loss Prev. Process Ind.
**2021**, 72, 104553. [Google Scholar] [CrossRef] - Zhao, J.X.; Meng, W.; Sun, F. Construction Risk Assessment of Metro Elevated Station Based on C-OWA Operator and Improved Extenics. IOP Conf. Ser. Earth Environ. Sci.
**2020**, 525, 012012. [Google Scholar] [CrossRef] - Diakoulaki, D.; Mavrotas, G.; Papayannakis, L. determining objective weights in multiple criteria problems—The critic method. Comput. Oper. Res.
**1995**, 22, 763–770. [Google Scholar] [CrossRef] - Wang, X.G.; Zhou, Z.; Sun, L.C.; Xie, G.H.; Lou, Q.H. Research on the evaluation index system of “new energy cloud” operation mode based on CRITIC weighting method and AHP method. IOP Conf. Ser. Earth Environ. Sci.
**2021**, 831, 012017. [Google Scholar] [CrossRef] - Shi, H.T.; Li, Y.F.; Jiang, Z.N.; Zhang, J. Comprehensive power quality evaluation method of microgrid with dynamic weighting based on CRITIC. Meas. Control
**2021**, 54, 1097–1104. [Google Scholar] [CrossRef] - Wang, Z.; Xing, X.G.; Yan, F. An abnormal phenomenon in entropy weight method in the dynamic evaluation of water quality index. Ecol. Indic.
**2021**, 131, 108137. [Google Scholar] - Zou, Z.H.; Sun, J.N.; Ren, G.P. Study and Application on the Entropy method for Determination of Weight of evaluating indicators in Fuzzy Synthetic Evaluation for Water Quality Assessment. Acta Sci. Circumstantiae
**2005**, 25, 552–556. (In Chinese) [Google Scholar] - Ning, B.Q.; Liu, J.; Li, R.H.; Li, L.Y. A multi-attribute decision ranking method based on grey correlation analysis and relative entropy. Math. Pract. Theory
**2018**, 48, 2240086. [Google Scholar] - Song, D.M.; Liu, C.X.; Shen, C. Multiple Objective and Attribute Decision Making Based on the Subjective and Objective Weighting. J. Shandong Univ.
**2015**, 45, 1–9. (In Chinese) [Google Scholar] - Luo, Z.Z.; Jiang, H.F.; Fu, J.L.; Ding, G.F. Combination Weighting-based Comprehensive Evaluation for Discrete Workshop Production Plan. J. Syst. Simul.
**2021**, 33, 1856–1865. (In Chinese) [Google Scholar] - Zhao, K.Q.; Xuan, A.L. Set pair theory-a new method of non-define and its applications. Syst. Eng.
**1996**, 1, 18–23. (In Chinese) [Google Scholar] - Chen, W.; Zhang, G.H.; Jiao, Y.Y.; Wang, H. Unascertained Measure-Set Pair Analysis Model of Collapse Risk Evaluation in Mountain Tunnels and Its Engineering Application. Ksce J. Civ. Eng.
**2021**, 25, 451–467. [Google Scholar] [CrossRef] - Miao, T.S.; Lu, W.X.; Luo, J.N.; Guo, J.Y. Application of set pair analysis and uncertainty analysis in groundwater pollution assessment and prediction: A case study of a typical molybdenum mining area in central Jilin province, China. Environ. Earth Sci.
**2019**, 78, 323. [Google Scholar] [CrossRef] - Giao, N.T.; Nhien, H.T.H.; Anh, P.K.; Van Ni, D. Classification of water quality in low-lying area in Vietnamese Mekong delta using set pair analysis method and Vietnamese water quality index. Environ. Monit. Assess.
**2021**, 193, 319. [Google Scholar] [CrossRef] [PubMed] - Su, F.M.; Li, P.Y.; He, X.D.; Elumalai, V. Set Pair Analysis in Earth and Environmental Sciences: Development, Challenges, and Future Prospects. Expo. Health
**2020**, 12, 343–354. [Google Scholar] [CrossRef] - Worotnicki, G.; Denham, D. The state stress in the upper part of the Earth’s crust in Australia according to measurements in tunnels and mines and from seismic observation. In Investigation of Stress in Rock—Advances in Stress Measurement; Institution of Engineers: Sydney, Australia, 1976; pp. 71–82. [Google Scholar]
- Brown, E.T.; Hoek, E. Technical note trends in relationships between measured in-situ stress and depth. Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
**1978**, 15, 211–215. [Google Scholar] [CrossRef]

**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