# Evaluation of the Karst Collapse Susceptibility of Subgrade Based on the AHP Method of ArcGIS and Prevention Measures: A Case Study of the Quannan Expressway, Section K1379+300-K1471+920

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## Abstract

**:**

## 1. Introduction

## 2. Overview of the Research Area

#### 2.1. Natural Geography

#### 2.2. Geological Structure

#### 2.3. Landform

#### 2.4. Overburden

#### 2.5. Hydrogeology

#### 2.6. Karst Development

_{3}l), Middle Devonian Donggangling Group (D

_{2}d), Middle Carboniferous Tai Po Group (C

_{2}d), and Lower Carboniferous Datang Group (C

_{1}d). the rock group has developed seven underground rivers. According to the field survey, there have been 45 natural collapses and 151 collapse pits. More than 90% of them are concentrated in the karst-developed section of k1380–k1410, mainly with soil collapse and no bedrock collapse. The thickness of the collapsed soil layer is about 10 m or less, the thickness of the soil layer is more than 20 m, and the scale of the collapse pits is larger, which seriously affects the engineering construction in the research area. The typical karst collapse of the study area is shown in Figure 5.

#### 2.7. Human Activities

## 3. Evaluation Index System Construction

#### 3.1. Evaluation Methodology

#### 3.2. Evaluation System Construction

_{karst}), karst landform (H

_{landform}), fault (H

_{fault}), soil thickness (H

_{soil}), karst collapse (H

_{collapse}), underground river (H

_{groundriver}), and mining well (H

_{well})).

#### 3.3. Evaluation Model Construction

_{i}is the weight of the influence factor of this layer determined by the analytical hierarchy process method (AHP); H

_{i}is the value of the impact factor of this layer. Each layer of impact factors can include multiple sub-level impact factors, and the upper-level impact factors are derived from the sub-level factors using a similar model.

## 4. Evaluation Model of the Karst Collapse Susceptibility

#### 4.1. Quantification of Evaluation Index Assignment

#### 4.2. Constructing the Judgment Matrix and Assigning Values

_{A-Bi}and K

_{Bi-Ci}were established for the association between the different layers of objective layer A and criterion layer B

_{i}, and criterion layer B

_{i}and indicator layer C

_{i}. For example, if the ratio of the importance of criterion layer B

_{1}to indicator layer C

_{3}is 3, then the ratio of the importance of indicator layer C

_{3}to criterion layer B

_{1}is 1/3; if the ratio of the importance of criterion layer B

_{1}to indicator layer C

_{2}is 2, then the ratio of the importance of indicator layer C

_{2}to criterion layer B

_{1}is 1/2. Based on this approach, the matrices were constructed, and Equations (2)–(4) are the correlation judgment matrices K

_{A-Bi}, K

_{B}

_{1-Ci}, and K

_{B}

_{2}-C

_{i}for objective layer A–criterion layer B

_{i}, criterion layer B

_{1}–criterion layer C

_{i}, and criterion layer B

_{2}–indicator layer C

_{i}

_{,}respectively.

#### 4.3. Hierarchical Single Ranking and Validation

_{1}–indicator layer C

_{i}judgment matrix (3) as an example, the weight of indicator layer C

_{i}in criterion layer B

_{1}was calculated. The square root method was used for the hierarchical analysis to calculate the following:

_{,}

_{1}= 1 × 0.4965 + 2 × 0.2668 + 3 × 0.1540 + 6 × 0.0827 = 1.9885, and (KW)

_{2}, (KW)

_{3}, and (KW)

_{4}are calculated as 1.073, 0.6184, and 0.3314, respectively.

#### 4.4. Karst Collapse Susceptibility Evaluation Model

_{karst}+ 0.1770 × H

_{landform}+ 0.1023 × H

_{fault}+ 0.0548H

_{soil}) + (0.1494 × H

_{collapse}+ 0.0830 × H

_{groundriver}) + 0.1050 × H

_{well}

## 5. Analysis of Evaluation Results

## 6. Suggestions for Prevention Measures

## 7. Conclusions

- (1)
- With the full integration of karst collapse-inducing factors, through the AHP hierarchical analysis method, it is reasonable to build a hierarchical structure evaluation system of three levels, one objective, three criteria, and seven indicators to derive the karst collapse susceptibility evaluation model.
- (2)
- Through the spatial analysis function of ArcGIS, the prediction and evaluation map of karst collapse susceptibility was obtained. According to the size of the H value, the study area was divided into five levels. There are four levels of karst collapse susceptibility, including extremely susceptible areas (2.64–2.81), susceptible areas (2.43–2.64), somewhat susceptible areas (1.88–2.43), and non-susceptible areas (1.04–1.88), and one non-karst level (0.51–1.04). The length of the extremely susceptible area is 11.9 km, accounting for about 12.85% of the total length of the line, and the remaining three susceptible areas are 23.2 km (25.05%), 36.62 km (39.54%), and 10.2 km (11.01%), respectively. The research conclusions are consistent with the geographical location of karst collapse and the susceptibility to karst collapse in recent years, and the research results are consistent with the actual situation.
- (3)
- According to the analysis results, the total length of the extremely susceptible and susceptible areas of karst collapse is 34.3 km, mainly distributed in the dissolution plain landform (88.05%). Only 4.1 km (11.95%) of the susceptible area is distributed in the erosion–dissolution landform; 99.10% of the 11.1 km of the extremely susceptible area is distributed in the strong developed karst area, 63.36% of the 23.2 km of the susceptible area is distributed in the strong developed karst area, and the rest are distributed in the moderate developed karst area. The soil thickness in the extremely susceptible area is less than 10 m or 5–10 m, and it is affected by faults, underground water, karst collapse, and mining well. Areas with soil thickness of 5–10 m have increased susceptibility. The somewhat susceptible and non-susceptible areas of karst collapse are mainly controlled by the degree of karst development, and they are located in the areas with moderate developed karst or weak developed karst. The non-karst areas are not affected by any karst collapse susceptible factors.
- (4)
- In view of the prediction and evaluation conclusions and with reference to similar engineering experience, effective karst collapse prevention measures are put forward, which can provide a reference for disaster prevention and mitigation in engineering construction.
- (5)
- The research results have played a guiding role in the safe construction and safe operation of the project after completion, which is of great practical significance and has certain academic research value, as it promotes and draws reference from the development of karst collapse research for several route projects. At the same time, the research method provides a reference for similar projects to evaluate the susceptibility of karst collapse and also provides a scientific basis for the planning and layout of route engineering and its geological disaster prevention.
- (6)
- Although the research results can provide guidance for prevention in the study area, the research results have certain limitations due to the difficulty of collecting basic research data comprehensively.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Number | Name | Characteristic | Intersection Area | Impact Degree |
---|---|---|---|---|

F1 | Bazha fault | Fracture of unknown nature | K1389+750 | High |

F2 | Yangshan fault | Normal fault | K1393+020 | High |

F3 | Bianshan fault | Normal fault | K1397+100 | High |

F4 | Yao Village fault | Fracture of unknown nature | K1398+570 | High |

F5 | Xingu Ling-Hengxian fault | Compressive fracture | K1404+340 | High |

F6 | Gaoshan fault | Normal fault | K1412+020 | Medium |

F7 | Fault of unknown nature | Fracture of unknown nature | K1415+050 | Low |

F8 | Fault of unknown nature | Fracture of unknown nature | K1416+200 | Low |

F9 | Li village fault | Normal fault | K1417+480 | Low |

F10 | Lijianpo fault | Normal fault | K1421+020 | Low |

F11 | Liantang fault | Retrograde fault | K1423+530 | Low |

F12 | Wangbuna fault | Retrograde fault | K1431+000 | Medium |

1 | Liujing-Shangzhou gentle monoclinal fault | Monoclinic structure | Liujing, Lingli, Wuhe to Shangzhou area | High |

2 | Gantang short-axis syncline | Syncline | Gantang area | Medium |

Lithological Classification | Genetic Classification | The Distribution of Section |
---|---|---|

Non-karst landforms | Erosion landforms | K1410+500~K1420+400, K1431+000~K1434+100 |

Accumulation landforms | K1420+400~K1423+600, K1425+100~K1435+900 | |

Karst landforms | Dissolution landforms | K1379+300K1410+500, K1449+500~K1456+800, K1468+300~K1471+920 |

Dissolution–erosion landforms or erosion–dissolution landforms | K1423+600~K1431+000, K1435+900~K1449+500, K1456+800~K1468+300 |

Objective Layer A | Criteria Layer B | Indicator Layer C | Impact Degree/Assignment | ||||
---|---|---|---|---|---|---|---|

Extremely High Impact/5 | High Impact/4 | Middle Impact/3 | Low Impact/2 | Extremely Low Impact/1 | |||

Evaluation of karst collapse susceptibility | Basic geological conditions B_{1} | Degree of karst development C _{1} H_{karst} | Strong | Moderate | Weak | None | |

Karst landform C _{2} H_{landform} | Plain | Erosion–karst hills valley (depression) | Dissolution–erosion low hills | Solitary and residual peak Peak clump or peak forest | Non-karst landforms | ||

FaultC_{3}H_{fault} | 0~250 m | 250~500 m | 500~750 m | 750~1000 m | >1000 m | ||

Soil thickness C_{4}H _{soil} | <5 m | 5~10 m | 10~20 m | 20~30 m | >30 m | ||

Karst risk influence B_{2} | Karst collapse C_{5}H _{collapse} | >4/km^{2} | 2~4/km^{2} | 1~2/km^{2} | 1/km^{2} | 0 | |

Underground river C_{6}H _{groundriver} | <1.5 m | 1.5~3 m | 3~6 m | 6~10 m | >10 m | ||

Human activities B_{3} | Mining well C_{7}H _{wel} | 0~250 m | 250~500 m | 500~750 m | 750~1000 m | >1000 m |

Importance Scales | Meaning |
---|---|

1 | When two elements are compared, they are of equal importance |

3 | When comparing two elements, the former is slightly more important than the latter |

5 | When comparing two elements, the former is more important than the latter |

7 | When comparing two elements, the former is significantly more important compared to the latter |

9 | When comparing two elements, the former is extremely more important compared to the latter |

2, 4, 6, 8 | The intermediate values of the above judgments |

Reciprocal | If the ratio of the importance of element I to element j is a_{ij}, then the ratio of the importance of element j to element I is a_{ji} = 1/a_{ij} |

Number of Steps n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

RI | 0 | 0 | 0.58 | 0.90 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 | 1.49 |

Objective Layer A | Evaluation of Karst Collapse Susceptibility | ||||||
---|---|---|---|---|---|---|---|

Criterion layer B | Basic geological conditions B_{1} | Karst risk influence B_{2} | Human activities B_{3} | ||||

Criterion layer weights relative to objective layer | 0.6626 | 0.2324 | 0.1050 | ||||

Indicator layer C | Degree of karst development C_{1} | Karst landform C_{2} | Fault C_{3} | Soil thickness C_{4} | Karst collapse C_{5} | Underground river C_{6} | Mining well C_{7} |

Criterion layer weights relative to indicator layer weights | 0.4965 | 0.2668 | 0.1540 | 0.0827 | 0.6429 | 0.3571 | 1.0000 |

Indicator layer weights relative to objective layer weights | 0.3285 | 0.1770 | 0.1023 | 0.0548 | 0.1494 | 0.0830 | 0.1050 |

Mileage | Susceptible Level | Length/km | Mileage | Susceptible Level | Length/km |
---|---|---|---|---|---|

k1379+300-k1381+800 | Extremely susceptible area | 2.5 | k1409+300-k1410+300 | Susceptible area | 1.0 |

k1381+800-k1388+000 | Susceptible area | 6.2 | k1410+300-k1410+600 | Somewhat susceptible area | 0.3 |

k1388+000-k1389+000 | Extremely susceptible area | 1.0 | k1410+600-k1414+500 | Non-susceptible area | 3.9 |

k1389+000-k1390+000 | Susceptible area | 1.0 | k1414+500-k1415+400 | Somewhat susceptible area | 0.9 |

k1390+000-k1391+000 | Extremely susceptible area | 1.0 | k1415+400-k1416+900 | Non-susceptible area | 1.5 |

k1391+000-k1394+000 | Susceptible area | 3.0 | k1416+900-k1417+200 | Somewhat susceptible area | 0.3 |

k1394+000-k1395+600 | Extremely susceptible area | 1.6 | k1417+200-k1418+100 | Non-karst area | 0.9 |

k1395+600-k1397+500 | Susceptible area | 1.9 | k1418+100-k1420+000 | Non-susceptible area | 1.9 |

k1397+500-k1399+700 | Extremely susceptible area | 2.2 | k1420+000-k1423+200 | Somewhat susceptible area | 3.2 |

k1399+700-k1400+500 | Susceptible area | 0.8 | k1423+200-k1425+100 | Non-susceptible area | 1.9 |

k1400+500-k1401+600 | Extremely susceptible area | 1.1 | k1425+100-k1433+000 | Non-karst area | 7.9 |

k1401+600-k1403+800 | Susceptible area | 2.2 | k1433+000-k1434+000 | Non-susceptible area | 1.0 |

k1403+800-k1405+000 | Extremely susceptible area | 1.2 | k1434+000-k1435+900 | Non-karst area | 1.9 |

k1405+000-k1408+000 | Susceptible area | 3.0 | k1435+900-k1440+000 | Susceptible area | 4.1 |

k1408+000-k1409+300 | Extremely susceptible area | 1.3 | k1440+000-k1475+000 | Somewhat susceptible area | 35.0 |

Road Section | Susceptible Level | Prevention Measures |
---|---|---|

k1379+300-k1381+800 | Extremely susceptible area | If the karst is developed in a large area and the bedrock surface is violently undulating, a large excavation program will be adopted to cut the height, fill the low level, and reinforce the substrate; on the contrary, if the solution trench and solution trough are locally developed, a local excavation and backfill or structure span program will be adopted. If the burial depth is shallow, excavation and backfill will be used to reinforce the hidden soil cave and karst cave, and if the burial depth is deep, grouting or structure can be used to span according to the specific situation. |

k1381+800-k1387+700 | Extremely susceptible area, susceptible area | |

K1387+700-K1410+500 | Extremely susceptible area | |

K1418+400-K1425+100 | Susceptible area | |

K1436+700-K1439+700 | Extremely susceptible area | |

K1439+700-K1471+920 | Susceptible area |

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**MDPI and ACS Style**

Xie, Y.-H.; Zhang, B.-H.; Liu, Y.-X.; Liu, B.-C.; Zhang, C.-F.; Lin, Y.-S. Evaluation of the Karst Collapse Susceptibility of Subgrade Based on the AHP Method of ArcGIS and Prevention Measures: A Case Study of the Quannan Expressway, Section K1379+300-K1471+920. *Water* **2022**, *14*, 1432.
https://doi.org/10.3390/w14091432

**AMA Style**

Xie Y-H, Zhang B-H, Liu Y-X, Liu B-C, Zhang C-F, Lin Y-S. Evaluation of the Karst Collapse Susceptibility of Subgrade Based on the AHP Method of ArcGIS and Prevention Measures: A Case Study of the Quannan Expressway, Section K1379+300-K1471+920. *Water*. 2022; 14(9):1432.
https://doi.org/10.3390/w14091432

**Chicago/Turabian Style**

Xie, Yan-Hua, Bing-Hui Zhang, Yu-Xin Liu, Bao-Chen Liu, Chen-Fu Zhang, and Yu-Shan Lin. 2022. "Evaluation of the Karst Collapse Susceptibility of Subgrade Based on the AHP Method of ArcGIS and Prevention Measures: A Case Study of the Quannan Expressway, Section K1379+300-K1471+920" *Water* 14, no. 9: 1432.
https://doi.org/10.3390/w14091432