# Safety Evaluation of Subway Tunnel Construction under Extreme Rainfall Weather Conditions Based on Combination Weighting–Set Pair Analysis Model

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. The SPA Theory

#### 2.2. Index Weights

#### 2.2.1. The IAHP Approach

#### 2.2.2. EWM Approach

#### 2.2.3. Comprehensive Weight

#### 2.3. Comprehensive Correlation Degree Model

#### 2.4. Set Pair Potential Analysis

#### 2.5. Procedure of Safety Evaluation Based on SPA and IAHP–EWM

## 3. Safety Evaluation Model

#### 3.1. Safety Evaluation Index System

_{1}) and Hydrogeology (B

_{2}): In the process of extreme rainfall, at the beginning of rainfall, due to the low rainfall intensity and rainfall, rainwater can infiltrate completely, and the water content (C

_{25}) of the soil increases gradually, while hydrogeological conditions such as Poisson’s ratio (C

_{22}), cohesion (C

_{23}), and internal friction angle (C

_{24}) also change accordingly. With the passage of rainfall time, the groundwater level (C

_{21}) rises gradually, which makes the subway tunnel a complex seepage field between saturated and unsaturated conditions, resulting in corresponding changes in the stress and strain of each stratum and the mechanical characteristics of the tunnel structure, so that the safety and stability of the subway tunnel structure are in a complex state that changes with time and space.

_{26}) of the soil gradually decreases until the infiltration rate of the soil is less than the rainfall intensity; then, the surface begins to accumulate water with the increase in rainfall time and rainfall (C

_{11}). The surface ponding depth (C

_{12}) increases accordingly. Under the actions of surface water’s softening and erosion, soil’s bearing capacity decreases gradually, further deteriorating the subway tunnel structure’s deformation and mechanical characteristics.

_{3}): In the tunnel structure design parameters, the tunnel burial depth (C

_{31}), tunnel diameter (C

_{32}), and lining thickness (C

_{33}) are the main parameters to ensure the safety and stability of the tunnel structure, which are determined by theoretical calculation according to the geological conditions and load pressure of the tunnel. However, in the dynamic process of extreme rainfall and saturated–unsaturated rainwater infiltration, the hydrogeological conditions and surface environment change with the gradual increase in the soil moisture content, which leads to the change in the mechanical properties of each soil layer and soil subsidence. The stress of the bearing structure, such as the lining and surrounding rock of the subway tunnel, presents varying degrees of change trend under the action of differential settlement and extrusion of the covering soil on top of the tunnel, which results in deformation and differential settlement of the tunnel.

_{4}): Based on the quality management system 4M1E standard, it is believed that incomprehensive and non-specific risk monitoring methods (C

_{41}), construction personnel irregularities (C

_{42}), and poor construction plans (C

_{43}) in underpass-tunnel construction are subjective factors in the generation of safety accidents.

#### 3.2. Grade Division Standard of Evaluation Indexes

#### 3.3. Grades of Safety Assessment

## 4. Case Study

_{1}, L

_{2}, and L

_{3}, based on the division of water-bearing layers in the foundation soil layer; these are taken as the evaluation objects for the safety evaluation of this interval tunnel.

#### 4.1. Data Acquisition

_{1}, L

_{2}, and L

_{3}are shown in Table 6.

#### 4.2. Safety Assessment

#### 4.2.1. Correlation Calculation

_{1}, L

_{2}, and L

_{3}are computed using Equations (1)–(4), and the calculation results are shown in Table 7.

#### 4.2.2. Weight Calculation

- Subjective Weight Calculation

- 2.
- Objective Weight calculation

#### 4.2.3. Combined Weight Calculation

#### 4.2.4. Calculation of Comprehensive Connection Degree

#### 4.3. Results and Discussion

#### 4.3.1. Evaluation Result Analysis

_{1}, L

_{2}, and L

_{3,}of the city rail Line 2 tunnel are 0.139, 0.168, and 0.025, respectively, all within the interval $\left(-0.2,0.2\right]$; therefore, all of them are at safety level III. Therefore, the overall safety level of the subway tunnel in this area is a medium level, which is a general risk and is consistent with the actual survey situation.

_{1}, L

_{2}, and L

_{3}are a general risk. The comprehensive connection degree of construction section L

_{1}is ${\mu}_{1}=0.193+0.312{i}_{1}+0.201{i}_{2}+0.167{i}_{3}+0.127j$, where the same degree $a=0.193$ is greater than the opposite degree, $c=0.127$, and the different degree $b=\left(0.312,0.201,0.167\right)$ is greater than the same degree, $a=0.193$. The comprehensive connection degree of construction section L

_{2}is ${\mu}_{2}=0.196+0.283{i}_{1}+0.225{i}_{2}+0.255{i}_{3}+0.041j$, where the same degree $a=0.196$ is greater than the opposite degree, $c=0.041$, and the different degree $b=\left(0.283,0.225,0.255\right)$ is greater than the same degree $a=0.174$. The comprehensive connection degree of construction section L

_{3}is ${\mu}_{3}=0.211+0.101{i}_{1}+0.333{i}_{2}+0.238{i}_{3}+0.117j$, where the same degree $a=0.211$ is greater than the opposite degree, $c=0.117$, and the different degree $b=\left(0.101,0.333,0.238\right)$ is greater than the same degree $a=0.211$. As shown in Table 2, construction sections L

_{1}, L

_{2}, and L

_{3}all belong to the micro-identity, with weak homogeneity and weak improvement trend, indicating that construction sections L

_{1}, L

_{2}, and L

_{3}are not likely to develop in the direction of “lower risk.” The evaluation results are consistent with the actual survey, which indicates that the evaluation model is feasible and universal.

#### 4.3.2. Discussion

_{11}), groundwater level (C

_{21}), water content (C

_{25}), underground permeability coefficient (C

_{26}), monitoring and detection strength (C

_{41}), and professional skills of the construction personnel (C

_{44}) are all higher than the average index weight of 0.066, showing that experts and decision makers subjectively believe that the six evaluation above indicators are the most important. From the results of the EWM model’s calculations, it is clear that the objective weights of the seven evaluation indicators, namely, rainfall (C

_{11}), groundwater level (C

_{21}), lining thickness (C

_{33}), monitoring and detection intensity (C41), construction organization design (C

_{42}), safety organization and system (C

_{43}), and professional skills of the construction personnel (C

_{44}), are all greater than the average index weight of 0.066, indicating that, from the perspective of the evaluation indicators, the design of the construction organization and from the calculation results of the linear weighting method, it can be seen that the total weights of rainfall (C

_{11}), groundwater level (C

_{21}), water content (C

_{25}), underground permeability coefficient (C

_{26}), tunnel depth (C

_{31}), monitoring and detection strength (C

_{41}), and professional skills of the construction personnel (C

_{44}) are more significant than the average index weight of 0.066, indicating that these are the main factors affecting the safety of subway tunnel construction under extreme rainfall weather conditions.

_{11}), underground water level (C

_{21}), water content (C

_{25}), under-ground permeability coefficient (C

_{26}), lining thickness (C

_{33}), monitoring and detection strength (C

_{41}), and professional skills of the construction personnel (C

_{44})) have significant weights, showing that these are the main factors that affect the safety of subway tunnel construction under extreme conditions. Although the other eight evaluation indexes have a lesser impact on the safety of subway tunnel construction than the above seven evaluation indexes, they also pose a particular threat to the safety of subway tunnels under extreme rainfall weather conditions with the changes in time and space.

## 5. Conclusions

- (1)
- We studied the safety risk of subway tunnel construction under heavy rainfall conditions. The damaging effects of heavy rainfall on the subway tunnel structural system and the influence factors of internal construction status on subway tunnel construction safety were identified.
- (2)
- Evaluating subway tunnel safety during heavy rains is a complicated, methodical, multidisciplinary issue. In this study, the central safety evaluation index system and its assessment standards were developed based on a complete investigation of the safety risk elements for subway tunnel construction during extreme rainfall, including disaster-inducing variables and disaster-nurturing environments.
- (3)
- Based on the idea of linear weighting, we optimized the combination of subjective and objective weights calculated by IAHP and EWM. More importantly, the method considers the subjective values of decision makers and the objectivity contained in the data, which makes the calculation results of the study closer to reality. Then, to address the ambiguity and uncertainty of the evaluation indexes, we introduced the SPA theory and made a quantitative judgment on the safety level and development trend of subway tunnel construction under extreme weather conditions by establishing pooled pairs.
- (4)
- Identifying the influencing factors on the safety of subway tunnel construction under extreme rainfall weather conditions in this study is not comprehensive, and there are various uncertainties. In reality, identifying such factors and the solution methods are still to be improved. In addition, sensitivity analysis of these influencing factors is needed in future studies.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Value of ${{\displaystyle \mathit{a}}}_{\mathit{i}\mathit{j}}$ | Definition |
---|---|

0 | Indicates that $j$ is more critical than $i$ |

1 | Indicates that $i$ is as crucial as $j$ |

2 | Indicates that $i$ is more critical than $j$ |

Situation | Gradation | Discriminant Condition | Coordination | Development Trend |
---|---|---|---|---|

Same potential | Quasi same potential | a > 0, b = 0 | Stronger identity | Stronger improvement trend |

Strong same potential | a > c, c > b | Strong identity | Strong improvement trend | |

Weak same potential | a > c, a > c > b | Weaker identity | Weaker improvement trend | |

Micro same potential | a = c, b > a | Weak identity | Weak improvement trend | |

Balance of power | Quasi balance of power | a = 0, b = 0 | Strong stability | Weak improvement trend |

Strong balance of power | a = c, a > b >0 | Stronger stability | Weaker improvement trend | |

Weak balance of power | a = c, b = a | Weaker stability | Stronger improvement trend | |

Micro balance of power | a = c, b > a | Weak stability | Strong improvement trend | |

Counter potential | Quasi counter potential | a < 0, b = 0 | Stronger opposition | Stronger improvement trend |

Strong counter potential | a < c, 0 < b < a | Strong opposition | Strong improvement trend | |

Weak counter potential | a < c, b > a, b < c | Weaker opposition | Weaker improvement trend | |

Micro counter potential | a < c, b > c | Weak opposition | Weak improvement trend |

Primary Indicators | Secondary Indicators | Number | Source |
---|---|---|---|

Rainfall B _{1} | Amount of Rainfall (mm/d) | C_{11} | [9,10] |

Surface water depth (mm) | C_{12} | [5] | |

Hydrogeology B _{2} | Groundwater level (m) | C_{21} | [11,52] |

Poisson’s ratio | C_{22} | [9,10] | |

Cohesion (KPa) | C_{23} | [9,10] | |

Angle of internal friction (°) | C_{24} | [10,13] | |

Water content (%) | C_{25} | [4,12] | |

Permeability coefficient (cm/s) | C_{26} | [5] | |

Construction design B _{3} | Tunnel depth (m) | C_{31} | [6,52] |

Tunnel diameter (m) | C_{32} | [4] | |

Lining thickness (mm) | C_{33} | [6,11] | |

Management B _{4} | Monitoring and testing efforts | C_{41} | —— |

Construction organization and design | C_{42} | —— | |

Safety organization and system | C_{43} | —— | |

Professional skills of construction personnel | C_{44} | —— |

Index | Grading Standard | ||||
---|---|---|---|---|---|

Extremely Safe | Safe | Basically Safe | Unsafe | Extremely Unsafe | |

C_{11} | < 25 | 25–50 | 50–100 | 100–250 | > 250 |

C_{12} | 0–400 | 400–800 | 800–1200 | 1200–1600 | 1600–2000 |

C_{21} | > 6 | 5–6 | 3–5 | 2–3 | < 2 |

C_{22} | 0–0.2 | 0.2–0.25 | 0.25–0.3 | 0.3–0.35 | 0.35–0.5 |

C_{23} | > 5.5 | 2.1–5.5 | 0.7–2.1 | 0.2–0.7 | 0–0.2 |

C_{24} | 60–90 | 50–60 | 39–50 | 27–39 | 0–27 |

C_{25} | 0–5 | 5–10 | 10–15 | 15–20 | 20–30 |

C_{26} | < 10^{−6} | 10^{−6}–10^{−4} | 10^{−4}–10^{−3} | 10^{−3}–10^{−1} | > 10^{−1} |

C_{31} | 32–40 | 24–32 | 16–24 | 8–16 | > 8 |

C_{32} | 0–6 | 6–9 | 9–12 | 12–15 | > 15 |

C_{33} | 700–800 | 600–700 | 400–600 | 200–400 | 50–200 |

C_{41} | Very high (80–100) | High (60–80) | Normal (40–60) | Low (20–40) | Very low (0–20) |

C_{42} | Perfect (80–100) | Good (60–80) | Normal (40–60) | Poor (20–40) | Worst (0–20) |

C_{43} | Perfect (80–100) | Good (60–80) | Normal (40–60) | Poor (20–40) | Worst (0–20) |

C_{44} | Very high (80–100) | High (60–80) | Normal (40–60) | Low (20–40) | Very low (0–20) |

Judgment Interval | (0.6,1] | (0.2,0.6] | (−0.2,0.2] | (−0.6,−0.2] | [−1,−0.6] |
---|---|---|---|---|---|

Safety Level | I | II | III | IV | V |

Risk Level | very low | low | medium | high | very high |

Index | Object of Evaluation | ||
---|---|---|---|

L_{1} | L_{2} | L_{3} | |

C_{11} | 45 | 45 | 45 |

C_{12} | 13 | 20 | 16 |

C_{21} | 9.1 | 8.3 | 9.0 |

C_{22} | 0.25 | 0.28 | 0.23 |

C_{23} | 12 | 25 | 10 |

C_{24} | 37 | 35 | 38 |

C_{25} | 19.7 | 16.2 | 19.7 |

C_{26} | 0.0405 | 0.0035 | 0.0347 |

C_{31} | 15 | 15.5 | 15 |

C_{32} | 6.2 | 5.5 | 6.0 |

C_{33} | 460 | 450 | 460 |

C_{41} | High (75) | High (75) | High (75) |

C_{42} | Good (75.4) | Good (74.8) | Good (75.4) |

C_{43} | Good (75) | Good (75) | Good (75) |

C_{44} | High (75.6) | High (75.4) | High (75.4) |

Index | L_{1} | L_{2} | L_{3} | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a | b_{1} | b_{2} | b_{3} | c | a | b_{1} | b_{2} | b_{3} | c | a | b_{1} | b_{2} | b_{3} | c | |

C_{11} | 0.000 | 0.200 | 0.800 | 0.000 | 0.000 | 0.000 | 0.200 | 0.800 | 0.000 | 0.000 | 0.000 | 0.200 | 0.800 | 0.000 | 0.000 |

C_{12} | 0.968 | 0.032 | 0.000 | 0.000 | 0.000 | 0.950 | 0.050 | 0.000 | 0.000 | 0.000 | 0.960 | 0.040 | 0.000 | 0.000 | 0.000 |

C_{21} | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 |

C_{22} | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.400 | 0.600 | 0.000 | 0.000 | 0.400 | 0.600 | 0.000 | 0.000 | 0.000 |

C_{23} | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 |

C_{24} | 0.000 | 0.000 | 0.000 | 0.833 | 0.167 | 0.000 | 0.000 | 0.000 | 0.670 | 0.330 | 0.000 | 0.000 | 0.000 | 0.920 | 0.080 |

C_{25} | 0.000 | 0.000 | 0.000 | 0.060 | 0.940 | 0.000 | 0.000 | 0.000 | 0.760 | 0.240 | 0.000 | 0.000 | 0.000 | 0.060 | 0.940 |

C_{26} | 0.000 | 0.000 | 0.000 | 0.600 | 0.400 | 0.000 | 0.000 | 0.000 | 0.970 | 0.030 | 0.000 | 0.000 | 0.000 | 0.660 | 0.340 |

C_{31} | 0.000 | 0.000 | 0.000 | 0.875 | 0.125 | 0.000 | 0.000 | 0.000 | 0.940 | 0.060 | 0.000 | 0.000 | 0.000 | 0.880 | 0.120 |

C_{32} | 0.000 | 0.930 | 0.070 | 0.000 | 0.000 | 0.080 | 0.920 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 |

C_{33} | 0.000 | 0.000 | 0.300 | 0.700 | 0.000 | 0.000 | 0.000 | 0.250 | 0.750 | 0.000 | 0.000 | 0.000 | 0.300 | 0.700 | 0.000 |

C_{41} | 0.000 | 0.750 | 0.250 | 0.000 | 0.000 | 0.000 | 0.750 | 0.250 | 0.000 | 0.000 | 0.000 | 0.000 | 0.750 | 0.250 | 0.000 |

C_{42} | 0.000 | 0.770 | 0.230 | 0.000 | 0.000 | 0.000 | 0.740 | 0.260 | 0.000 | 0.000 | 0.000 | 0.000 | 0.770 | 0.230 | 0.000 |

C_{43} | 0.000 | 0.750 | 0.250 | 0.000 | 0.000 | 0.000 | 0.750 | 0.250 | 0.000 | 0.000 | 0.000 | 0.000 | 0.750 | 0.250 | 0.000 |

C_{44} | 0.000 | 0.780 | 0.220 | 0.000 | 0.000 | 0.000 | 0.770 | 0.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.770 | 0.230 | 0.000 |

Index | Subjective Weight | Objective Weight | Comprehensive Weight |
---|---|---|---|

C_{11} | 0.302 | 0.077 | 0.153 |

C_{12} | 0.002 | 0.063 | 0.042 |

C_{21} | 0.178 | 0.066 | 0.104 |

C_{22} | 0.011 | 0.063 | 0.045 |

C_{23} | 0.028 | 0.059 | 0.048 |

C_{24} | 0.017 | 0.064 | 0.048 |

C_{25} | 0.137 | 0.058 | 0.085 |

C_{26} | 0.137 | 0.058 | 0.085 |

C_{31} | 0.007 | 0.058 | 0.041 |

C_{32} | 0.004 | 0.060 | 0.041 |

C_{33} | 0.017 | 0.067 | 0.050 |

C_{41} | 0.067 | 0.077 | 0.073 |

C_{42} | 0.004 | 0.077 | 0.052 |

C_{43} | 0.004 | 0.077 | 0.052 |

C_{44} | 0.085 | 0.077 | 0.079 |

Object of Evaluation | Comprehensive Connection Degree | Safety Level | Risk Level |
---|---|---|---|

L_{1} | 0.139 | III | medium level |

L_{2} | 0.168 | III | medium level |

L_{3} | 0.025 | III | medium level |

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## Share and Cite

**MDPI and ACS Style**

Liu, P.; Wang, Y.; Han, T.; Xu, J.; Li, Q.
Safety Evaluation of Subway Tunnel Construction under Extreme Rainfall Weather Conditions Based on Combination Weighting–Set Pair Analysis Model. *Sustainability* **2022**, *14*, 9886.
https://doi.org/10.3390/su14169886

**AMA Style**

Liu P, Wang Y, Han T, Xu J, Li Q.
Safety Evaluation of Subway Tunnel Construction under Extreme Rainfall Weather Conditions Based on Combination Weighting–Set Pair Analysis Model. *Sustainability*. 2022; 14(16):9886.
https://doi.org/10.3390/su14169886

**Chicago/Turabian Style**

Liu, Ping, Yu Wang, Tongze Han, Jiaming Xu, and Qiangnian Li.
2022. "Safety Evaluation of Subway Tunnel Construction under Extreme Rainfall Weather Conditions Based on Combination Weighting–Set Pair Analysis Model" *Sustainability* 14, no. 16: 9886.
https://doi.org/10.3390/su14169886