Evaluation Method of Highway Plant Slope Based on Rough Set Theory and Analytic Hierarchy Process: A Case Study in Taihang Mountain, Hebei, China
Abstract
:1. Introduction
2. Study Site Description
3. Construction of Performance Evaluation Index System of the Slope
4. Construct the Evaluation Model of Highway Plant Slope
4.1. Calculation Steps of Rough Set Theory
4.2. Analytic Hierarchy Process Calculation Steps
4.3. Weight Results of First-Level Indicators
4.4. Secondary Index Weight Results
4.5. Establishment of Evaluation Model
5. A Case of Evaluation of Highway Plant Slope
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Region | Side Slope Grade | Slope Defects | Geologic Environment |
---|---|---|---|
Tuling | 1:1.5 | There are valleys on the right side of the slope, the catchment area is large, the valley mouth of the lower river is comprehensive, and there are signs of ancient debris flow | Silty clay soil, stone |
Shangjiaosi | 1:1.25 | Medium soil collapse degree | Loess-like silt, with gravel |
Lingdi | 1:1 | Strongly weathered collapsed rubble visible on both sidesRed clay deposit, poor geology. | Artificial fill, block stone, weathered marl, silt, and other combinations |
Indicators | Notations | Corresponding Grade | Discrete Values |
---|---|---|---|
Drought resistance | C1 | Excellent | 1 |
Good | 2 | ||
Average | 3 | ||
Poor | 4 | ||
Cold resistance | C2 | Excellent | 1 |
Good | 2 | ||
Average | 3 | ||
Poor | 4 | ||
Salt and alkali resistance | C3 | Excellent | 1 |
Good | 2 | ||
Average | 3 | ||
Poor | 4 | ||
Soil characteristics | C4 | Excellent | 1 |
Good | 2 | ||
Average | 3 | ||
Poor | 4 | ||
Slope height/m | C5 | 0–5 | 1 |
5–10 | 2 | ||
10–15 | 3 | ||
>15 | 4 | ||
Slope gradient/(°) | C6 | 0–20 | 1 |
20–40 | 2 | ||
40–60 | 3 | ||
>60 | 4 | ||
Precipitation intensity/mm | C7 | 0–20 | 1 |
20–60 | 2 | ||
60–120 | 3 | ||
>120 | 4 | ||
Seepage performance | C8 | Excellent | 1 |
Good | 2 | ||
Average | 3 | ||
Poor | 4 | ||
Groundwater level | C9 | Dry | 1 |
Wet | 2 | ||
Dripping | 3 | ||
Bubbling | 4 | ||
Plant type | C10 | Trees, shrubs and herbs are reasonable | 1 |
Fewer trees, reasonable shrubs and herbs | 2 | ||
Few trees, reasonable shrubs, more reasonable herbs | 3 | ||
No trees, few shrubs, more reasonable herbs | 4 | ||
Purification ability | C11 | Excellent | 1 |
Good | 2 | ||
Average | 3 | ||
Poor | 4 | ||
Vegetation cover | C12 | 85–100% | 1 |
65–85% | 2 | ||
45–65% | 3 | ||
10–45% | 4 |
Rank | Range of Values |
---|---|
1 | [90, 100] |
2 | [60, 90) |
3 | [40, 60) |
4 | [0, 40) |
Rank | Slope Stability Condition |
---|---|
One | very stable |
Two | stable |
Three | unstable |
Four | severely unstable |
U | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | C12 | D |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
U1 | 2 | 3 | 1 | 2 | 3 | 4 | 3 | 2 | 4 | 3 | 3 | 3 | Four |
U2 | 2 | 3 | 3 | 2 | 3 | 1 | 3 | 2 | 3 | 4 | 4 | 3 | Three |
U3 | 3 | 4 | 4 | 2 | 4 | 2 | 3 | 1 | 3 | 4 | 3 | 4 | Four |
U4 | 2 | 2 | 3 | 2 | 3 | 4 | 1 | 3 | 2 | 3 | 3 | 2 | Two |
U5 | 2 | 3 | 4 | 2 | 2 | 3 | 3 | 2 | 1 | 1 | 2 | 3 | Two |
U6 | 4 | 3 | 1 | 2 | 3 | 4 | 3 | 2 | 4 | 3 | 3 | 3 | One |
U7 | 2 | 2 | 3 | 2 | 3 | 1 | 3 | 2 | 3 | 4 | 4 | 3 | One |
U8 | 1 | 4 | 2 | 1 | 2 | 2 | 3 | 2 | 2 | 3 | 2 | 1 | Two |
U9 | 2 | 3 | 4 | 2 | 2 | 3 | 3 | 2 | 1 | 2 | 2 | 3 | Four |
U10 | 2 | 3 | 4 | 2 | 2 | 3 | 3 | 2 | 3 | 1 | 2 | 3 | Three |
U11 | 2 | 2 | 4 | 2 | 3 | 4 | 1 | 3 | 2 | 3 | 3 | 2 | Two |
U12 | 3 | 4 | 4 | 2 | 4 | 2 | 3 | 1 | 3 | 2 | 3 | 4 | Three |
U13 | 2 | 3 | 3 | 2 | 2 | 1 | 4 | 1 | 2 | 3 | 2 | 3 | Two |
U14 | 2 | 2 | 3 | 2 | 3 | 4 | 1 | 3 | 4 | 3 | 3 | 2 | Four |
U15 | 3 | 4 | 2 | 2 | 4 | 2 | 3 | 1 | 3 | 4 | 3 | 4 | Two |
Canonical Scale | Definition | Explanation |
---|---|---|
1 | Equally important | One factor is as important as the other |
3 | A little important | One factor is slightly more important than the other |
5 | Clearly important | The importance of one factor outweighs the other |
7 | Strongly important | One factor is significantly more important than the other |
9 | Absolutely important | One factor is more essential than the other |
A0 | A1 | A2 | A3 | A4 | Weight | Other Values |
---|---|---|---|---|---|---|
A1 | 1 | 2 | 4 | 3 | 0.4427 | CR = 0.0859 |
A2 | 1/2 | 1 | 5 | 4 | 0.3545 | |
A3 | 1/4 | 1/5 | 1 | 2 | 0.1123 | |
A4 | 1/3 | 1/4 | 1/2 | 1 | 0.0905 |
Indicator | Analytic Hierarchy Process Weight | Rough Set Weight | Coupling Weight |
---|---|---|---|
W1 | 0.3025 | 0.0503 | 0.2086 |
W2 | 0.0885 | 0.0527 | 0.0639 |
W3 | 0.0517 | 0.0959 | 0.0680 |
W4 | 0.0921 | 0.0743 | 0.0938 |
W5 | 0.1463 | 0.0767 | 0.1538 |
W6 | 0.1161 | 0.0983 | 0.1564 |
W7 | 0.0780 | 0.0792 | 0.0847 |
W8 | 0.0107 | 0.0815 | 0.0120 |
W9 | 0.0236 | 0.1007 | 0.0326 |
W10 | 0.0516 | 0.1031 | 0.0729 |
W11 | 0.0088 | 0.0818 | 0.0098 |
W12 | 0.0301 | 0.1055 | 0.0435 |
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Liu, L.; Dou, Y.; Qiao, J. Evaluation Method of Highway Plant Slope Based on Rough Set Theory and Analytic Hierarchy Process: A Case Study in Taihang Mountain, Hebei, China. Mathematics 2022, 10, 1264. https://doi.org/10.3390/math10081264
Liu L, Dou Y, Qiao J. Evaluation Method of Highway Plant Slope Based on Rough Set Theory and Analytic Hierarchy Process: A Case Study in Taihang Mountain, Hebei, China. Mathematics. 2022; 10(8):1264. https://doi.org/10.3390/math10081264
Chicago/Turabian StyleLiu, Luliang, Yuanming Dou, and Jiangang Qiao. 2022. "Evaluation Method of Highway Plant Slope Based on Rough Set Theory and Analytic Hierarchy Process: A Case Study in Taihang Mountain, Hebei, China" Mathematics 10, no. 8: 1264. https://doi.org/10.3390/math10081264