# Dynamic Evaluation Method of the EW-AHP Attribute Identification Model for the Tunnel Gushing Water Disaster under Interval Conditions and Applications

Authors: Bo Wu; Huihao Chen; Wei Huang; Guowang Meng
Journal: Mathematical Problems in Engineering
 (2021)

---

## Abstract

The gushing water disaster in tunnels is a kind of harmful and risky engineering disaster. It has become a key problem to evaluate the risk of tunnel gushing water accurately and objectively. A case study of a typical highway tunnel is performed for theory and practice analysis. For this reason, the risk identification is carried out on the assessed objects, and 10 evaluation indexes are determined. In turn, the risk evaluation index system and classification standard are established. Furthermore, the entropy weight method and the analytic hierarchy process are combined to assign the weight to each evaluation index. Therefore, a dynamic risk assessment system, including the pre-evaluation model and the postevaluation model, is constructed with the attribute identification model. As a result, the tunnel section with a high risk of water inrush is accurately assessed, which is consistent with the construction situation on site. Moreover, it is verified that the assessment results are reliable, which can provide a reference for the similar projects.


---

## Body

## 1. Introduction

China is the fastest developing country in tunneling construction [1]. However, the safety of tunneling construction is particularly prominent and has attracted much attention. In particular, the tunnel water inrush is a kind of engineering disaster which is difficult to predict. Therefore, the safety risk assessment of tunneling construction is widely practiced. By combining the interval analytic hierarchy process (I-AHP) with the technique for order preference by similarity to an ideal solution (TOPSIS), Lin et al. [2] proposed a novel fuzzy model which identified high-risk factors during excavations in urban karst geological environments. In addition, the theory of risk assessment has also developed rapidly. For example, Lin et al. [3] conducted research on the excavation system based on fuzzy set theory and machine learning methods. Furthermore, the development of assessment theory also promotes the application of safety assessment of the tunneling water inrush. For instance, Li et al. [4] established a mechanical model of the minimum safe thickness of the rock burst prevention disk and carried out a series of model tests on the rock burst prevention disk in front of the tunnel face to find out the influence rules of various factors on the tunnel gushing water disaster. Additionally, Zhu et al. [5] focused on the study of the influence of the geological influencing factors on the tunnel gushing water risk and, based on this, established the risk assessment model of tunnel gushing water based on the weighted average method, etc.At present, the lack of research on the systematic evaluation of the tunnel gushing water risk assessment theory has limited its popularization. Furthermore, many theories are static evaluation methods, which ignore that the evaluation index values are not always consistent with the previous ones during tunnel excavation. Therefore, a brand new risk assessment model is established, where the subjective and objective weighting complex method are used to calculate the indexes’ weight. Thus, the evaluation indexes can be assigned as interval or numerical values, which can change dynamically in real time according to the construction situation.A case study of a typical highway tunnel in Fujian province is performed for theory and practice analysis. Through the analysis of its engineering characteristics and special geological conditions, a dynamic evaluation model of the highway tunnel water inrush risk is proposed based on the entropy weight method.


## 2. Methods

### 2.1. Improved Theoretical Model of Attribute Interval Identification

The problem of the system comprehensive evaluation is the measurement of the qualitative description. Attribute mathematics is a new branch of mathematics which appears to solve many systematic evaluation problems. The theoretical model of the attribute interval identification is developed on the basis of attribute mathematics. Suppose that evaluation objects’ spaceX=x1,…,xi,…,xn, where all the evaluation objects could be xii=1,2,…,n. Iij is the jth evaluation index of the evaluation object xi. F is the attribute interval space of X. R1,R2,…,Rk,…,RK is an ordered partition class of F, where R1<R2<⋯<Rk [6].


#### 2.1.1. Analysis of the Single-Index Attribute Measurement

It can be supposed that the value of the evaluation objectxi of the evaluation index Iij is tij, and the attribute measure function represents the situation that the attribute measure μij changes with the value tij of the evaluation index Iij. The grading standards of the evaluation index are shown in Table 1. The main steps of the data processing are as follows:(1)bjk=ajk−1+ajk2,(2)djk=minbjk−ajk,bjk+1−ajk,where k = 1, 2, …, K and j = 1, 2, …, m in equation (1) and k = 1, 2, …, (K −1) and j = 1, 2, …, m in equation (2).Table 1
Grading standards for the evaluation index.
Evaluation indexIiEvaluation index valuetiOrder of evaluationR1R2…RkIi1ti1a10 ∼ a11a11 ∼ a12…a1 (k − 1) ∼a1kIi2ti2a20 ∼ a21a21 ∼ a22…a2 (k − 1) ∼ a2k⋮⋮⋮⋮⋱⋮Iijtijaj0 ∼ aj1aj1 ∼ aj2…aj (k − 1) ∼ ajk⋮⋮⋮⋮⋱⋮Iimtimam0 ∼ am1am1 ∼ am2…am (k − 1) ∼ amkFrom [7–9], when aj0<aj1<⋯ajk⋯ajK, the single-index attribute measure function μijkt can be expressed as follows:(3)μij1t=1,tj<aj1−dj1,aj1+dj1−tj2dj1,aj1−dj1≤tj≤aj1+dj1,0,tj>aj1+dj1,(4)μijt=0,tj<ajk1−djk−1,tj<ajk1−djk−12djk−1,ajk−1−djk−1≤tj≤ajk−1+djk−1,1,ajk−1+djk−1<tj<ajk−djk,ajk+djk−tj2djk,ajk−djk≤tj≤ajk+djk,0,tj<ajK−1−djK−1,(5)μijKt=0,tj<ajK−1−djK−1,tj−ajK−1+djK−12djK−1,ajK−1−djK−1≤tj≤ajK−1+djK−1,1,tj>ajK−1+djK−1.From [9, 10], when aj0<aj1<⋯ajk⋯<ajK, the single-index attribute measure function μijkt can be expressed as follows:(6)μij1t=1,tj<aj1−dj1,aj1+dj1+dj12dj1,aj1−dj1≤tj≤aj1+dj1,0,tj>aj1+dj1,(7)μijt=0,tj<ajk−djk,tj<ajk−1−djk−12djk−1,ajk−djk≤tj≤ajk+djk,1,ajk+djk<tj<ajk−1−djk−1,ajk+djk−tj2dj,ajk−1−djk−1≤tj≤ajk−1+djk−1,0,tj>ajk−1−djk−1,(8)μijKt=1,tj<ajK−1−djK−1,ajK−1+djK−1−tj2djK−1,ajK−1−djK−1≤tj≤ajK−1+djK−1,0,tj>ajK−1+djK−1,where i = 1, 2, …, n; j = 1, 2, …, m; and k = 1, 2, …, K.


#### 2.1.2. Multi-Index Comprehensive Attribute Measurement Analysis

(1) The evaluation index value is an interval-type index: from [9], let Sijkt be the interval metric function of the single-index attribute, and let tj+ and tj− be the upper and lower limits of the evaluation index, respectively. When αj0>αj1>⋯αjk⋯>αjK, the interval metric function Sijkt of the single-index attribute can be expressed as follows:(9)sij1t=0,tj−≥aj1+dj1,∫tj−aj1+dj1μij1tdt,tj−≤aj1+dj1≤tj+,∫tj−tj+μij1tdt,tj+≤aj1+dj1,(10)Sijkt=0,tj+≤ajk−1−djk−1,∫ajk−1−djk−1tj+μijktdt,tj−≤ajk−1−djk−1≤tj+≤ajk+djk,∫tj−tj+μijktdt,ajk−1−djk−1≤tj−≤tj+≤ajk+djk,∫tj−ajk+djkμijktdt,ajk−1−djk−1≤tj−≤ajk+djk≤tj+,0,tj−≥ajk+djk,(11)sijKt=0,tj+≤ajK−1−djK−1,∫ajk−1−djk−1tj+μijKtdt,tj−≤ajK−1−djK−1≤tj+,∫tj−tj+μijKtdt,tj−≥ajK−1−djK−1.Whenαj0>αj1>⋯αjk⋯>αjK, the interval metric function Sijkt of the single-index attribute can be expressed as follows:(12)sij1t=∫tj−tj+μij1tdt,tj−≥aj1−dj1,∫aj1−dj1tj+μij1tdt,tj−≤aj1−dj1≤tj+,0,tj+≤aj1+dj1,(13)Sijkt=0,tj+≤ajk−djk,∫ajk−djktj+μijktdt,tj−≤ajk−djk≤tj+≤ajk+djk,∫tj−tj+μijktdt,ajk−djk≤tj−≤tj+≤ajk−1+djk−1,∫tj−ajk−1+djk−1μijktdt,ajk−djk≤tj−≤ajk−1+djk−1≤tj+,0,tj−≥ajk−1+djk−1,(14)sijKt=∫tj−tj+μijKtdt,tj+≤ajK−1−djK−1,∫tj−ajk−1−djk−1μijKtdt,tj−≤ajK−1+djK−1≤tj+,0,tj−≥ajK−1+djK−1.The weight of each index can beω=ω1,ω2,…,ωm, 0≤ωj≤1, ∑i=1mωj=1. The attribute measure value μik of the evaluation index Iij belonging to the evaluation level Rk can be solved by the single-index attribute interval metric function Sijkt, which can be expressed as follows:(15)μik=∑j=1mωjSijk′,(16)Sijk′=Sijk∑k=1KSijk.(2) The evaluation index value is a noninterval-type index: as the weight of each index isω=ω1,ω2,…,ωm, 0≤ωj≤1, ∑i=1mωj=1, the attribute measure value can be expressed as follows:(17)μik=∑j=mωjμijk.


#### 2.1.3. Attribute Identification Analysis

The attribute spaceF of a class on X is set, R1,R2,…,Rk is the attribute interval set of X, and F=∪i=1kRi,Ri∩Rj=∅i≠j [6]. λ is the confidence level, and 0.5<λ≤1.WhenR1<R2<⋯<Rk<⋯Rk,(18)k=minl:∑k=llμik≥λ,1≤l≤K.WhenR1<R2<⋯<Rk<⋯Rk,(19)k=maxl:∑k=llμik≥λ,1≤l≤K,where xi belongs to risk level Rk.


### 2.2. Combination Weighting

Different evaluation indexes have different influence proportions on the risk of the highway tunnel water inrush, so the scientific index weighting method should be adopted. The common methods include the subjective weighting method and the objective weighting method [11]. In order to avoid the result deviation caused by the single weighting method, the combined weighting method is adopted, which takes the subjective and objective factors into consideration.


#### 2.2.1. Entropy Weight Method to Determine the Objective Weight

The entropy weight method [12–14] is an objective method, which can determine the weight of the evaluation index objectively. It is according to the difference degree of the evaluation index value, and it can avoid the deviation caused by the human factors. So, it has higher accuracy. However, the disadvantage is that the importance of the evaluation index itself is ignored, and its function is limited if the difference of the evaluation index value is very small. In the risk assessment of the tunnel gushing water disaster, the sensitivity of the entropy weight method to the difference of the evaluation index value can be used. Thus, the difference degree of the same evaluation index value in different tunnel sections can be used as the danger signal of the tunnel gushing water disaster to some extent. Its main steps are shown as follows:Step 1: the normalized matrix is constructed, and the normalized matrix is standardized. The normalized matrixZ=zijn×m can be obtained. Then, the proportion of the ith sample value in the jth index of the term is calculated as follows:(20)pij=zij∑i=1nzij.Step 2: the information entropy of the evaluation index is calculated as follows:(21)ej=∑i=1mpijInpijInn.Step 3: the evaluation index weight is assigned as follows:(22)αj=uj∑j=1nuj.uj is the difference coefficient of the calculated index, and uj=1−ej. The weight vector of the index is α=α1,α2,…,αn, and ∑j=1nαj=1.


#### 2.2.2. AHP Method to Determine the Subjective Weight

Analytic hierarchy process (AHP) [15–17] is a systematic analysis method, which can combine qualitative and quantitative methods organically to simplify complex system evaluation problems. It focuses on qualitative analysis and judgment. However, its shortcoming is that it is too subjective. As for too many indicators, the data statistics are large, and the weight is difficult to determine. The basic idea of the AHP is to compare the importance of multiple factors in pairs to judge each other, which improves the rationality of decision-making to some extent [18]. The main steps are as follows:Step 1: the hierarchical relationship is determined among the influencing factors, and the system hierarchy is established.Step 2: combining with the importance level (Table2), the evaluation indexes are compared in pairs, and the judgment matrix is constructed. The judgment matrix can be obtained as follows:(23)R=r11r12⋯r1Kr21r22⋯r2K⋮⋮⋱⋮rm1rm2⋯rmK.Step 3: the maximum eigenvalueλmax of the judgment matrix R is calculated, the consistency index CI and consistency ratio CR are calculated, and the consistency test is conducted.Step 4: the weightβj of each evaluation index is calculated.Table 2
Importance level table.
ValueDifference in importance1Indicatori is as important as indicator j3Indexi is slightly more important than index j5Indicatori is significantly more important than indicator j7Indicatori is strongly more important than indicator j9Indicatori is extremely important than indicator j2, 4, 6, 8Intermediate value between the above adjacent judgmentsExplanationWhen indexj is over index i, its scale value is the reciprocal of index i over index j


#### 2.2.3. Combination Weighting of the Evaluation Index

From [19], the combined weights are calculated as follows:(24)ωj=αjβj∑i=1mαjβj.


## 2.1. Improved Theoretical Model of Attribute Interval Identification

The problem of the system comprehensive evaluation is the measurement of the qualitative description. Attribute mathematics is a new branch of mathematics which appears to solve many systematic evaluation problems. The theoretical model of the attribute interval identification is developed on the basis of attribute mathematics. Suppose that evaluation objects’ spaceX=x1,…,xi,…,xn, where all the evaluation objects could be xii=1,2,…,n. Iij is the jth evaluation index of the evaluation object xi. F is the attribute interval space of X. R1,R2,…,Rk,…,RK is an ordered partition class of F, where R1<R2<⋯<Rk [6].


### 2.1.1. Analysis of the Single-Index Attribute Measurement

It can be supposed that the value of the evaluation objectxi of the evaluation index Iij is tij, and the attribute measure function represents the situation that the attribute measure μij changes with the value tij of the evaluation index Iij. The grading standards of the evaluation index are shown in Table 1. The main steps of the data processing are as follows:(1)bjk=ajk−1+ajk2,(2)djk=minbjk−ajk,bjk+1−ajk,where k = 1, 2, …, K and j = 1, 2, …, m in equation (1) and k = 1, 2, …, (K −1) and j = 1, 2, …, m in equation (2).Table 1
Grading standards for the evaluation index.
Evaluation indexIiEvaluation index valuetiOrder of evaluationR1R2…RkIi1ti1a10 ∼ a11a11 ∼ a12…a1 (k − 1) ∼a1kIi2ti2a20 ∼ a21a21 ∼ a22…a2 (k − 1) ∼ a2k⋮⋮⋮⋮⋱⋮Iijtijaj0 ∼ aj1aj1 ∼ aj2…aj (k − 1) ∼ ajk⋮⋮⋮⋮⋱⋮Iimtimam0 ∼ am1am1 ∼ am2…am (k − 1) ∼ amkFrom [7–9], when aj0<aj1<⋯ajk⋯ajK, the single-index attribute measure function μijkt can be expressed as follows:(3)μij1t=1,tj<aj1−dj1,aj1+dj1−tj2dj1,aj1−dj1≤tj≤aj1+dj1,0,tj>aj1+dj1,(4)μijt=0,tj<ajk1−djk−1,tj<ajk1−djk−12djk−1,ajk−1−djk−1≤tj≤ajk−1+djk−1,1,ajk−1+djk−1<tj<ajk−djk,ajk+djk−tj2djk,ajk−djk≤tj≤ajk+djk,0,tj<ajK−1−djK−1,(5)μijKt=0,tj<ajK−1−djK−1,tj−ajK−1+djK−12djK−1,ajK−1−djK−1≤tj≤ajK−1+djK−1,1,tj>ajK−1+djK−1.From [9, 10], when aj0<aj1<⋯ajk⋯<ajK, the single-index attribute measure function μijkt can be expressed as follows:(6)μij1t=1,tj<aj1−dj1,aj1+dj1+dj12dj1,aj1−dj1≤tj≤aj1+dj1,0,tj>aj1+dj1,(7)μijt=0,tj<ajk−djk,tj<ajk−1−djk−12djk−1,ajk−djk≤tj≤ajk+djk,1,ajk+djk<tj<ajk−1−djk−1,ajk+djk−tj2dj,ajk−1−djk−1≤tj≤ajk−1+djk−1,0,tj>ajk−1−djk−1,(8)μijKt=1,tj<ajK−1−djK−1,ajK−1+djK−1−tj2djK−1,ajK−1−djK−1≤tj≤ajK−1+djK−1,0,tj>ajK−1+djK−1,where i = 1, 2, …, n; j = 1, 2, …, m; and k = 1, 2, …, K.


### 2.1.2. Multi-Index Comprehensive Attribute Measurement Analysis

(1) The evaluation index value is an interval-type index: from [9], let Sijkt be the interval metric function of the single-index attribute, and let tj+ and tj− be the upper and lower limits of the evaluation index, respectively. When αj0>αj1>⋯αjk⋯>αjK, the interval metric function Sijkt of the single-index attribute can be expressed as follows:(9)sij1t=0,tj−≥aj1+dj1,∫tj−aj1+dj1μij1tdt,tj−≤aj1+dj1≤tj+,∫tj−tj+μij1tdt,tj+≤aj1+dj1,(10)Sijkt=0,tj+≤ajk−1−djk−1,∫ajk−1−djk−1tj+μijktdt,tj−≤ajk−1−djk−1≤tj+≤ajk+djk,∫tj−tj+μijktdt,ajk−1−djk−1≤tj−≤tj+≤ajk+djk,∫tj−ajk+djkμijktdt,ajk−1−djk−1≤tj−≤ajk+djk≤tj+,0,tj−≥ajk+djk,(11)sijKt=0,tj+≤ajK−1−djK−1,∫ajk−1−djk−1tj+μijKtdt,tj−≤ajK−1−djK−1≤tj+,∫tj−tj+μijKtdt,tj−≥ajK−1−djK−1.Whenαj0>αj1>⋯αjk⋯>αjK, the interval metric function Sijkt of the single-index attribute can be expressed as follows:(12)sij1t=∫tj−tj+μij1tdt,tj−≥aj1−dj1,∫aj1−dj1tj+μij1tdt,tj−≤aj1−dj1≤tj+,0,tj+≤aj1+dj1,(13)Sijkt=0,tj+≤ajk−djk,∫ajk−djktj+μijktdt,tj−≤ajk−djk≤tj+≤ajk+djk,∫tj−tj+μijktdt,ajk−djk≤tj−≤tj+≤ajk−1+djk−1,∫tj−ajk−1+djk−1μijktdt,ajk−djk≤tj−≤ajk−1+djk−1≤tj+,0,tj−≥ajk−1+djk−1,(14)sijKt=∫tj−tj+μijKtdt,tj+≤ajK−1−djK−1,∫tj−ajk−1−djk−1μijKtdt,tj−≤ajK−1+djK−1≤tj+,0,tj−≥ajK−1+djK−1.The weight of each index can beω=ω1,ω2,…,ωm, 0≤ωj≤1, ∑i=1mωj=1. The attribute measure value μik of the evaluation index Iij belonging to the evaluation level Rk can be solved by the single-index attribute interval metric function Sijkt, which can be expressed as follows:(15)μik=∑j=1mωjSijk′,(16)Sijk′=Sijk∑k=1KSijk.(2) The evaluation index value is a noninterval-type index: as the weight of each index isω=ω1,ω2,…,ωm, 0≤ωj≤1, ∑i=1mωj=1, the attribute measure value can be expressed as follows:(17)μik=∑j=mωjμijk.


### 2.1.3. Attribute Identification Analysis

The attribute spaceF of a class on X is set, R1,R2,…,Rk is the attribute interval set of X, and F=∪i=1kRi,Ri∩Rj=∅i≠j [6]. λ is the confidence level, and 0.5<λ≤1.WhenR1<R2<⋯<Rk<⋯Rk,(18)k=minl:∑k=llμik≥λ,1≤l≤K.WhenR1<R2<⋯<Rk<⋯Rk,(19)k=maxl:∑k=llμik≥λ,1≤l≤K,where xi belongs to risk level Rk.


## 2.1.1. Analysis of the Single-Index Attribute Measurement

It can be supposed that the value of the evaluation objectxi of the evaluation index Iij is tij, and the attribute measure function represents the situation that the attribute measure μij changes with the value tij of the evaluation index Iij. The grading standards of the evaluation index are shown in Table 1. The main steps of the data processing are as follows:(1)bjk=ajk−1+ajk2,(2)djk=minbjk−ajk,bjk+1−ajk,where k = 1, 2, …, K and j = 1, 2, …, m in equation (1) and k = 1, 2, …, (K −1) and j = 1, 2, …, m in equation (2).Table 1
Grading standards for the evaluation index.
Evaluation indexIiEvaluation index valuetiOrder of evaluationR1R2…RkIi1ti1a10 ∼ a11a11 ∼ a12…a1 (k − 1) ∼a1kIi2ti2a20 ∼ a21a21 ∼ a22…a2 (k − 1) ∼ a2k⋮⋮⋮⋮⋱⋮Iijtijaj0 ∼ aj1aj1 ∼ aj2…aj (k − 1) ∼ ajk⋮⋮⋮⋮⋱⋮Iimtimam0 ∼ am1am1 ∼ am2…am (k − 1) ∼ amkFrom [7–9], when aj0<aj1<⋯ajk⋯ajK, the single-index attribute measure function μijkt can be expressed as follows:(3)μij1t=1,tj<aj1−dj1,aj1+dj1−tj2dj1,aj1−dj1≤tj≤aj1+dj1,0,tj>aj1+dj1,(4)μijt=0,tj<ajk1−djk−1,tj<ajk1−djk−12djk−1,ajk−1−djk−1≤tj≤ajk−1+djk−1,1,ajk−1+djk−1<tj<ajk−djk,ajk+djk−tj2djk,ajk−djk≤tj≤ajk+djk,0,tj<ajK−1−djK−1,(5)μijKt=0,tj<ajK−1−djK−1,tj−ajK−1+djK−12djK−1,ajK−1−djK−1≤tj≤ajK−1+djK−1,1,tj>ajK−1+djK−1.From [9, 10], when aj0<aj1<⋯ajk⋯<ajK, the single-index attribute measure function μijkt can be expressed as follows:(6)μij1t=1,tj<aj1−dj1,aj1+dj1+dj12dj1,aj1−dj1≤tj≤aj1+dj1,0,tj>aj1+dj1,(7)μijt=0,tj<ajk−djk,tj<ajk−1−djk−12djk−1,ajk−djk≤tj≤ajk+djk,1,ajk+djk<tj<ajk−1−djk−1,ajk+djk−tj2dj,ajk−1−djk−1≤tj≤ajk−1+djk−1,0,tj>ajk−1−djk−1,(8)μijKt=1,tj<ajK−1−djK−1,ajK−1+djK−1−tj2djK−1,ajK−1−djK−1≤tj≤ajK−1+djK−1,0,tj>ajK−1+djK−1,where i = 1, 2, …, n; j = 1, 2, …, m; and k = 1, 2, …, K.


## 2.1.2. Multi-Index Comprehensive Attribute Measurement Analysis

(1) The evaluation index value is an interval-type index: from [9], let Sijkt be the interval metric function of the single-index attribute, and let tj+ and tj− be the upper and lower limits of the evaluation index, respectively. When αj0>αj1>⋯αjk⋯>αjK, the interval metric function Sijkt of the single-index attribute can be expressed as follows:(9)sij1t=0,tj−≥aj1+dj1,∫tj−aj1+dj1μij1tdt,tj−≤aj1+dj1≤tj+,∫tj−tj+μij1tdt,tj+≤aj1+dj1,(10)Sijkt=0,tj+≤ajk−1−djk−1,∫ajk−1−djk−1tj+μijktdt,tj−≤ajk−1−djk−1≤tj+≤ajk+djk,∫tj−tj+μijktdt,ajk−1−djk−1≤tj−≤tj+≤ajk+djk,∫tj−ajk+djkμijktdt,ajk−1−djk−1≤tj−≤ajk+djk≤tj+,0,tj−≥ajk+djk,(11)sijKt=0,tj+≤ajK−1−djK−1,∫ajk−1−djk−1tj+μijKtdt,tj−≤ajK−1−djK−1≤tj+,∫tj−tj+μijKtdt,tj−≥ajK−1−djK−1.Whenαj0>αj1>⋯αjk⋯>αjK, the interval metric function Sijkt of the single-index attribute can be expressed as follows:(12)sij1t=∫tj−tj+μij1tdt,tj−≥aj1−dj1,∫aj1−dj1tj+μij1tdt,tj−≤aj1−dj1≤tj+,0,tj+≤aj1+dj1,(13)Sijkt=0,tj+≤ajk−djk,∫ajk−djktj+μijktdt,tj−≤ajk−djk≤tj+≤ajk+djk,∫tj−tj+μijktdt,ajk−djk≤tj−≤tj+≤ajk−1+djk−1,∫tj−ajk−1+djk−1μijktdt,ajk−djk≤tj−≤ajk−1+djk−1≤tj+,0,tj−≥ajk−1+djk−1,(14)sijKt=∫tj−tj+μijKtdt,tj+≤ajK−1−djK−1,∫tj−ajk−1−djk−1μijKtdt,tj−≤ajK−1+djK−1≤tj+,0,tj−≥ajK−1+djK−1.The weight of each index can beω=ω1,ω2,…,ωm, 0≤ωj≤1, ∑i=1mωj=1. The attribute measure value μik of the evaluation index Iij belonging to the evaluation level Rk can be solved by the single-index attribute interval metric function Sijkt, which can be expressed as follows:(15)μik=∑j=1mωjSijk′,(16)Sijk′=Sijk∑k=1KSijk.(2) The evaluation index value is a noninterval-type index: as the weight of each index isω=ω1,ω2,…,ωm, 0≤ωj≤1, ∑i=1mωj=1, the attribute measure value can be expressed as follows:(17)μik=∑j=mωjμijk.


## 2.1.3. Attribute Identification Analysis

The attribute spaceF of a class on X is set, R1,R2,…,Rk is the attribute interval set of X, and F=∪i=1kRi,Ri∩Rj=∅i≠j [6]. λ is the confidence level, and 0.5<λ≤1.WhenR1<R2<⋯<Rk<⋯Rk,(18)k=minl:∑k=llμik≥λ,1≤l≤K.WhenR1<R2<⋯<Rk<⋯Rk,(19)k=maxl:∑k=llμik≥λ,1≤l≤K,where xi belongs to risk level Rk.


## 2.2. Combination Weighting

Different evaluation indexes have different influence proportions on the risk of the highway tunnel water inrush, so the scientific index weighting method should be adopted. The common methods include the subjective weighting method and the objective weighting method [11]. In order to avoid the result deviation caused by the single weighting method, the combined weighting method is adopted, which takes the subjective and objective factors into consideration.


### 2.2.1. Entropy Weight Method to Determine the Objective Weight

The entropy weight method [12–14] is an objective method, which can determine the weight of the evaluation index objectively. It is according to the difference degree of the evaluation index value, and it can avoid the deviation caused by the human factors. So, it has higher accuracy. However, the disadvantage is that the importance of the evaluation index itself is ignored, and its function is limited if the difference of the evaluation index value is very small. In the risk assessment of the tunnel gushing water disaster, the sensitivity of the entropy weight method to the difference of the evaluation index value can be used. Thus, the difference degree of the same evaluation index value in different tunnel sections can be used as the danger signal of the tunnel gushing water disaster to some extent. Its main steps are shown as follows:Step 1: the normalized matrix is constructed, and the normalized matrix is standardized. The normalized matrixZ=zijn×m can be obtained. Then, the proportion of the ith sample value in the jth index of the term is calculated as follows:(20)pij=zij∑i=1nzij.Step 2: the information entropy of the evaluation index is calculated as follows:(21)ej=∑i=1mpijInpijInn.Step 3: the evaluation index weight is assigned as follows:(22)αj=uj∑j=1nuj.uj is the difference coefficient of the calculated index, and uj=1−ej. The weight vector of the index is α=α1,α2,…,αn, and ∑j=1nαj=1.


### 2.2.2. AHP Method to Determine the Subjective Weight

Analytic hierarchy process (AHP) [15–17] is a systematic analysis method, which can combine qualitative and quantitative methods organically to simplify complex system evaluation problems. It focuses on qualitative analysis and judgment. However, its shortcoming is that it is too subjective. As for too many indicators, the data statistics are large, and the weight is difficult to determine. The basic idea of the AHP is to compare the importance of multiple factors in pairs to judge each other, which improves the rationality of decision-making to some extent [18]. The main steps are as follows:Step 1: the hierarchical relationship is determined among the influencing factors, and the system hierarchy is established.Step 2: combining with the importance level (Table2), the evaluation indexes are compared in pairs, and the judgment matrix is constructed. The judgment matrix can be obtained as follows:(23)R=r11r12⋯r1Kr21r22⋯r2K⋮⋮⋱⋮rm1rm2⋯rmK.Step 3: the maximum eigenvalueλmax of the judgment matrix R is calculated, the consistency index CI and consistency ratio CR are calculated, and the consistency test is conducted.Step 4: the weightβj of each evaluation index is calculated.Table 2
Importance level table.
ValueDifference in importance1Indicatori is as important as indicator j3Indexi is slightly more important than index j5Indicatori is significantly more important than indicator j7Indicatori is strongly more important than indicator j9Indicatori is extremely important than indicator j2, 4, 6, 8Intermediate value between the above adjacent judgmentsExplanationWhen indexj is over index i, its scale value is the reciprocal of index i over index j


### 2.2.3. Combination Weighting of the Evaluation Index

From [19], the combined weights are calculated as follows:(24)ωj=αjβj∑i=1mαjβj.


## 2.2.1. Entropy Weight Method to Determine the Objective Weight

The entropy weight method [12–14] is an objective method, which can determine the weight of the evaluation index objectively. It is according to the difference degree of the evaluation index value, and it can avoid the deviation caused by the human factors. So, it has higher accuracy. However, the disadvantage is that the importance of the evaluation index itself is ignored, and its function is limited if the difference of the evaluation index value is very small. In the risk assessment of the tunnel gushing water disaster, the sensitivity of the entropy weight method to the difference of the evaluation index value can be used. Thus, the difference degree of the same evaluation index value in different tunnel sections can be used as the danger signal of the tunnel gushing water disaster to some extent. Its main steps are shown as follows:Step 1: the normalized matrix is constructed, and the normalized matrix is standardized. The normalized matrixZ=zijn×m can be obtained. Then, the proportion of the ith sample value in the jth index of the term is calculated as follows:(20)pij=zij∑i=1nzij.Step 2: the information entropy of the evaluation index is calculated as follows:(21)ej=∑i=1mpijInpijInn.Step 3: the evaluation index weight is assigned as follows:(22)αj=uj∑j=1nuj.uj is the difference coefficient of the calculated index, and uj=1−ej. The weight vector of the index is α=α1,α2,…,αn, and ∑j=1nαj=1.


## 2.2.2. AHP Method to Determine the Subjective Weight

Analytic hierarchy process (AHP) [15–17] is a systematic analysis method, which can combine qualitative and quantitative methods organically to simplify complex system evaluation problems. It focuses on qualitative analysis and judgment. However, its shortcoming is that it is too subjective. As for too many indicators, the data statistics are large, and the weight is difficult to determine. The basic idea of the AHP is to compare the importance of multiple factors in pairs to judge each other, which improves the rationality of decision-making to some extent [18]. The main steps are as follows:Step 1: the hierarchical relationship is determined among the influencing factors, and the system hierarchy is established.Step 2: combining with the importance level (Table2), the evaluation indexes are compared in pairs, and the judgment matrix is constructed. The judgment matrix can be obtained as follows:(23)R=r11r12⋯r1Kr21r22⋯r2K⋮⋮⋱⋮rm1rm2⋯rmK.Step 3: the maximum eigenvalueλmax of the judgment matrix R is calculated, the consistency index CI and consistency ratio CR are calculated, and the consistency test is conducted.Step 4: the weightβj of each evaluation index is calculated.Table 2
Importance level table.
ValueDifference in importance1Indicatori is as important as indicator j3Indexi is slightly more important than index j5Indicatori is significantly more important than indicator j7Indicatori is strongly more important than indicator j9Indicatori is extremely important than indicator j2, 4, 6, 8Intermediate value between the above adjacent judgmentsExplanationWhen indexj is over index i, its scale value is the reciprocal of index i over index j


## 2.2.3. Combination Weighting of the Evaluation Index

From [19], the combined weights are calculated as follows:(24)ωj=αjβj∑i=1mαjβj.


## 3. The Dynamic Risk Assessment Model

### 3.1. The Index System and the Grading Standards

The risk factors of the gushing water disaster during highway tunneling present characteristics of fuzziness and uncertainty, which make the risk assessment become a complicated systematic evaluation problem. The adverse geological condition refers to the water-rich condition of the geological structure, which is an important influencing factor for the occurrence of tunnel water inrush. Thus, the water level refers to the elevation difference between the underground water level and tunnel floor, which represents the danger degree of water inrush in a way. Also, the length of the water-bearing layer reflects the spatial distribution of water bearing in the tunnel. Besides, the permeability coefficient of rock strata directly affects the groundwater activity. Moreover, the water inflow in the normal period reflects the water fluctuation of groundwater. Also, the negative topographic area ratio directly affects and reflects the development and occurrence characteristics of underground undesirable geology and groundwater. Except them, the dip angle of the rock stratum is an important factor affecting groundwater flow. Furthermore, the development degree of the layer and interlayer fissure affects the activity degree of groundwater, and it has an important influence on the tunnel water inrush. The situation of water dripping on the wall directly represents the current situation of water inrush after the formation of the tunnel initial support. To some extent, the buried depth of the tunnel represents the danger degree of tunnel water inrush.As for the case of the highway tunneling project in Fujian province, the evaluation indexes are divided into four levels by combining with the geological prospecting, the geological survey data, and the analysis of statistical data [7, 20–23]. Furthermore, the gushing water disaster risk evaluation index system and the gushing water risk evaluation index grading standard have been established. Some are based on the expert scoring to determine the evaluation index classification, which include the influencing factors of the adverse geological conditions I1, the level and interlayer fissure I8, and the situation of drop water on the wall I9. The index system of the highway tunnel water inrush risk assessment is shown in Figure 1. The grading standards of the highway tunnel water inrush risk assessment index are shown in Table 3.Figure 1
The index system.Table 3
The index grading standards.
Evaluation indexR1R2R3R4I135 ∼ 6060 ∼ 7070 ∼ 8585 ∼ 100I2 (m)h < 1010 ≤h < 3030 ≤h < 60h > 60I3 (m)<5050 ∼ 100100 ∼ 200200 ∼ 300I4 (10−5 cm/s)<11 ∼ 10001000 ∼ 100000>100000I5 (m3/d)<100100 ∼ 500500 ∼ 1000>1000I6 (%)<2020 ∼ 4040 ∼ 60>60I7 (°)0 ∼ 1010 ∼ 2525 ∼ 4545 ∼ 65I835 ∼ 6060 ∼ 7070 ∼ 8585 ∼ 100I935 ∼ 6060 ∼ 7070 ∼ 8585 ∼ 100I10 (m)<5050 ∼ 100100 ∼ 200>200


### 3.2. Attribute Measure Function

From equations (1)–(8), the single-index attribute measure can be calculated, and the calculation results are summarized as shown in Table 4.Table 4
The single-index attribute measure function.
R1R2R3R4μi11t=1,t≤55,65−t/10,55≤t≤65,0,t≥65,μi12t=0,t≤55,t−55/10,55≤t≤65,75−t/10,65≤t≤75,0,t≥75,μi13t=0,t≤65,t−65/10,65≤t≤75,175≤t≤77.5,92.5−t/15,77.5≤t≤92.5,0,t≥92.5,μi14t=0,t≤77.5,t−77.5/15,77.5≤t≤92.5,1,t≥92.5,μi21t=1,t≤5,15−t/10,5≤t≤15,0,t≥15,μi22t=0,t≤5,t−5/10,5≤t≤15,1,15≤t≤20,40−t/20,20≤t≤40,0,t≥40,μi23t=0,t≤20,t−20/20,20≤t≤40,1,40≤t≤45,75−t/30,40≤t≤75,0,t≥75,μi24t=0,t≤45,t−45/30,45≤t≤75,t,t≥75,μi31t=1,t≤25,75−t/50,25≤t≤75,0,t≥75,ui32t=0,t≤25,t−25/50,25≤t≤75,125−t/50,75≤t≤125,0,t≥125,μi33t=0,t≤75,t−75/50,75≤t≤125,1,125≤t≤150,250−t/100,150≤t≤250,0,t≥250,μi34t=0,t≤150,t−150/100,150≤t≤250,1,t≥250,μi41t1,t≤0.5,1.5−t,0.5≤t≤1.5,0,t≥1.5,μi42t=0,t≤0.5,t−0.5,0.5≤t≤1.5,1,1.5≤t≤500.5,1499.5−t/999,500.5≤t≤1499.5,0,t≥1499.5,μi43t=0,t≤500.5,t−500.5/999,500.5≤t≤1499.5,1,1499.5≤t≤50500,149500−t/99000,50500≤t≤149500,0,t≥149500,μi44t=0,t≤50500,t−50500/99000,50500≤t≤149500,1,t≥149500,μi51t=1,t≤50,150−t/100,50≤t≤150,0,t≥150,μi52t=0,t≤50,t−50/100,50≤t≤150,1,150≤t≤300,700−t/400300≤t≤700,0,t≥700,μi53t=0,t≤300,t−300/400,300≤t≤700,1,700≤t≤750,1250−t/500,750≤t≤1250,0,t≥1250,μi54t=0,t≤750,t−750/500,750≤t≤1250,1,t≥1250,μi61t=1,t≤10,30−t/20,10≤t≤30,0,t≥30,μi62t=0,t≤10,t−10/20,10≤t≤30,50−t/20,30≤t≤50,0,t≥50,μi63t=0,t≤30,t−30/20,50≤t≤70,70−t/20,50≤t≤70,0,t≥70,μi64t=0,t≤50,t−50/20,50≤t≤70,1,t≥70,μi71t=1,t≤5,15−t/10,5≤t≤15,0,t≥15,μi72t=0,t≤5,t−5/10,5≤t≤15,1,15≤t≤15,32.5−t/15,17.5≤t≤32.5,0,t≥32.5,μi73t=0,t≥17.5,t−17.5/15,17.5≤t≤32.5,1,32.5≤t≤35,55−t/20,35≤t≤55,0,t≥55,μi74t=0,t≤35,t−35/25,35≤t≥55,1,t≥55,μi81t=1,t≤55,65−t/10,55≤t≤65,0,t≥65,μi82t=0,t≤55,t−55/10,55≤t≤65,75−t/10,65≤t≤32.5,0,t≥75,μi83t=0,t≤65,t−65/10,65≤t≤75,1,75≤t≤77.5,92.5−t/15,77.5≤t≤92.5,0,t≥92.5,μi84t=0,t≤77.5,t−77.5/15,77.5≤t≤92.5,1,t≥92.5,μi91t=1,t≤55,65−t/10,55≤t≤65,0,t≥65,μi92t=0,t≤55,t−55/10,55≤t≤65,75−t/10,65≤t≤75,0t≥75,μti93=0,t≤65,t−65/10,65≤t≤75,1,75≤t≤77.5,92.5−t/15,77.5≤t≤92.5,0,t≥92.5,μi94t=0,t≤77.5,t−77.5/1577.5≤t≤92.5,1,t≥92.5,μi101t=1,t≤25,75−t/50,25≤t≤75,0,t≥75,μi102t=0,t≤25,t−25/50,25≤t≤75,125−t/50,75≤t≤125,0,t≥125,μi103t=0,t≤75,t−75/50,75≤t≤125,1,125≤t≤150,250−t/100,150≤t≤250,0,t≥250,μi104t=0,t≤150,t−150/100,150≤t≤250,1,t≥250,


### 3.3. Attribute Identification Analysis

Referring to the “Highway Bridge and Tunnel Engineering Construction Safety Risk Assessment System and Guide Analysis” [24], the highway tunnel gushing water risk is divided into four levels, so the evaluation set is R=R1R2R3R4. The specific levels are described as shown in Table 5.Table 5
Accident probability grading standards.
Risk levelRisk level descriptionR1Basically no riskR2Low riskR3Moderate riskR4High riskAs the confidence valueλ in attribute identification is generally 0.6 ∼ 0.7, λ = 0.65 is adopted in the calculation [10]. It can be seen from equation (18) that when R1<R2<⋯<Rk<⋯<Rk,(25)k=minl:∑k=llμik≥0.65,1≤l≤4,where xi belongs to risk level Rk.


### 3.4. Dynamic Risk Assessment

The dynamic risk assessment system based on the attribute interval identification model is composed of two parts. One is the preassessment model, and the other one is the postassessment model. The research object of the pre-evaluation model is the unexcavated tunnel section. The evaluation index and the value of the evaluation index are determined. The weight of each evaluation index combination is calculated, and the corresponding interval risk assessment is carried out by the pre-evaluation model. The assessment results can provide guidance for construction safety. The research object of the postevaluation model is the tunnel section under construction. On the basis of the pre-evaluation model, it mainly monitors the sections with high risk of water inrush. The evaluation index value can be adjusted and corrected according to the construction and excavation situation on site. The specific flowchart is shown in Figure2.Figure 2
The highway tunnel gushing water dynamic risk assessment.The specific steps are as follows:Step 1: segment the similar terrain and the geological conditions of the unexcavated tunnel section.Step 2: determine the evaluation index and its value.Step 3: the combined weighting method was used to assign weights to each evaluation index.Step 4: pre-evaluate the tunnel interval. Combined with equations (1)–(8), the single-index attribute measure analysis is carried out for each evaluation index, and the single-index attribute measure function is calculated. Determine whether the evaluation index is an interval-type index. If it is an interval-type index, the multi-index comprehensive attribute measurement analysis is conducted according to equations (9)–(16). Otherwise, the multi-index comprehensive attribute measurement analysis is conducted according to equation (17). Finally, the attribute identification analysis combined with the confidence degree is conducted to determine the hazard level of the tunnel water inrush.Step 5: dynamically revise the evaluation index value according to the construction and excavation situation, and repeat Step 4 to redetermine the hazard level of the tunnel water inrush after the evaluation of the tunnel section.Step 6: construct and excavate, and at the same time, take preventive measures for risk control, and perform a good record of emergency.


## 3.1. The Index System and the Grading Standards

The risk factors of the gushing water disaster during highway tunneling present characteristics of fuzziness and uncertainty, which make the risk assessment become a complicated systematic evaluation problem. The adverse geological condition refers to the water-rich condition of the geological structure, which is an important influencing factor for the occurrence of tunnel water inrush. Thus, the water level refers to the elevation difference between the underground water level and tunnel floor, which represents the danger degree of water inrush in a way. Also, the length of the water-bearing layer reflects the spatial distribution of water bearing in the tunnel. Besides, the permeability coefficient of rock strata directly affects the groundwater activity. Moreover, the water inflow in the normal period reflects the water fluctuation of groundwater. Also, the negative topographic area ratio directly affects and reflects the development and occurrence characteristics of underground undesirable geology and groundwater. Except them, the dip angle of the rock stratum is an important factor affecting groundwater flow. Furthermore, the development degree of the layer and interlayer fissure affects the activity degree of groundwater, and it has an important influence on the tunnel water inrush. The situation of water dripping on the wall directly represents the current situation of water inrush after the formation of the tunnel initial support. To some extent, the buried depth of the tunnel represents the danger degree of tunnel water inrush.As for the case of the highway tunneling project in Fujian province, the evaluation indexes are divided into four levels by combining with the geological prospecting, the geological survey data, and the analysis of statistical data [7, 20–23]. Furthermore, the gushing water disaster risk evaluation index system and the gushing water risk evaluation index grading standard have been established. Some are based on the expert scoring to determine the evaluation index classification, which include the influencing factors of the adverse geological conditions I1, the level and interlayer fissure I8, and the situation of drop water on the wall I9. The index system of the highway tunnel water inrush risk assessment is shown in Figure 1. The grading standards of the highway tunnel water inrush risk assessment index are shown in Table 3.Figure 1
The index system.Table 3
The index grading standards.
Evaluation indexR1R2R3R4I135 ∼ 6060 ∼ 7070 ∼ 8585 ∼ 100I2 (m)h < 1010 ≤h < 3030 ≤h < 60h > 60I3 (m)<5050 ∼ 100100 ∼ 200200 ∼ 300I4 (10−5 cm/s)<11 ∼ 10001000 ∼ 100000>100000I5 (m3/d)<100100 ∼ 500500 ∼ 1000>1000I6 (%)<2020 ∼ 4040 ∼ 60>60I7 (°)0 ∼ 1010 ∼ 2525 ∼ 4545 ∼ 65I835 ∼ 6060 ∼ 7070 ∼ 8585 ∼ 100I935 ∼ 6060 ∼ 7070 ∼ 8585 ∼ 100I10 (m)<5050 ∼ 100100 ∼ 200>200


## 3.2. Attribute Measure Function

From equations (1)–(8), the single-index attribute measure can be calculated, and the calculation results are summarized as shown in Table 4.Table 4
The single-index attribute measure function.
R1R2R3R4μi11t=1,t≤55,65−t/10,55≤t≤65,0,t≥65,μi12t=0,t≤55,t−55/10,55≤t≤65,75−t/10,65≤t≤75,0,t≥75,μi13t=0,t≤65,t−65/10,65≤t≤75,175≤t≤77.5,92.5−t/15,77.5≤t≤92.5,0,t≥92.5,μi14t=0,t≤77.5,t−77.5/15,77.5≤t≤92.5,1,t≥92.5,μi21t=1,t≤5,15−t/10,5≤t≤15,0,t≥15,μi22t=0,t≤5,t−5/10,5≤t≤15,1,15≤t≤20,40−t/20,20≤t≤40,0,t≥40,μi23t=0,t≤20,t−20/20,20≤t≤40,1,40≤t≤45,75−t/30,40≤t≤75,0,t≥75,μi24t=0,t≤45,t−45/30,45≤t≤75,t,t≥75,μi31t=1,t≤25,75−t/50,25≤t≤75,0,t≥75,ui32t=0,t≤25,t−25/50,25≤t≤75,125−t/50,75≤t≤125,0,t≥125,μi33t=0,t≤75,t−75/50,75≤t≤125,1,125≤t≤150,250−t/100,150≤t≤250,0,t≥250,μi34t=0,t≤150,t−150/100,150≤t≤250,1,t≥250,μi41t1,t≤0.5,1.5−t,0.5≤t≤1.5,0,t≥1.5,μi42t=0,t≤0.5,t−0.5,0.5≤t≤1.5,1,1.5≤t≤500.5,1499.5−t/999,500.5≤t≤1499.5,0,t≥1499.5,μi43t=0,t≤500.5,t−500.5/999,500.5≤t≤1499.5,1,1499.5≤t≤50500,149500−t/99000,50500≤t≤149500,0,t≥149500,μi44t=0,t≤50500,t−50500/99000,50500≤t≤149500,1,t≥149500,μi51t=1,t≤50,150−t/100,50≤t≤150,0,t≥150,μi52t=0,t≤50,t−50/100,50≤t≤150,1,150≤t≤300,700−t/400300≤t≤700,0,t≥700,μi53t=0,t≤300,t−300/400,300≤t≤700,1,700≤t≤750,1250−t/500,750≤t≤1250,0,t≥1250,μi54t=0,t≤750,t−750/500,750≤t≤1250,1,t≥1250,μi61t=1,t≤10,30−t/20,10≤t≤30,0,t≥30,μi62t=0,t≤10,t−10/20,10≤t≤30,50−t/20,30≤t≤50,0,t≥50,μi63t=0,t≤30,t−30/20,50≤t≤70,70−t/20,50≤t≤70,0,t≥70,μi64t=0,t≤50,t−50/20,50≤t≤70,1,t≥70,μi71t=1,t≤5,15−t/10,5≤t≤15,0,t≥15,μi72t=0,t≤5,t−5/10,5≤t≤15,1,15≤t≤15,32.5−t/15,17.5≤t≤32.5,0,t≥32.5,μi73t=0,t≥17.5,t−17.5/15,17.5≤t≤32.5,1,32.5≤t≤35,55−t/20,35≤t≤55,0,t≥55,μi74t=0,t≤35,t−35/25,35≤t≥55,1,t≥55,μi81t=1,t≤55,65−t/10,55≤t≤65,0,t≥65,μi82t=0,t≤55,t−55/10,55≤t≤65,75−t/10,65≤t≤32.5,0,t≥75,μi83t=0,t≤65,t−65/10,65≤t≤75,1,75≤t≤77.5,92.5−t/15,77.5≤t≤92.5,0,t≥92.5,μi84t=0,t≤77.5,t−77.5/15,77.5≤t≤92.5,1,t≥92.5,μi91t=1,t≤55,65−t/10,55≤t≤65,0,t≥65,μi92t=0,t≤55,t−55/10,55≤t≤65,75−t/10,65≤t≤75,0t≥75,μti93=0,t≤65,t−65/10,65≤t≤75,1,75≤t≤77.5,92.5−t/15,77.5≤t≤92.5,0,t≥92.5,μi94t=0,t≤77.5,t−77.5/1577.5≤t≤92.5,1,t≥92.5,μi101t=1,t≤25,75−t/50,25≤t≤75,0,t≥75,μi102t=0,t≤25,t−25/50,25≤t≤75,125−t/50,75≤t≤125,0,t≥125,μi103t=0,t≤75,t−75/50,75≤t≤125,1,125≤t≤150,250−t/100,150≤t≤250,0,t≥250,μi104t=0,t≤150,t−150/100,150≤t≤250,1,t≥250,


## 3.3. Attribute Identification Analysis

Referring to the “Highway Bridge and Tunnel Engineering Construction Safety Risk Assessment System and Guide Analysis” [24], the highway tunnel gushing water risk is divided into four levels, so the evaluation set is R=R1R2R3R4. The specific levels are described as shown in Table 5.Table 5
Accident probability grading standards.
Risk levelRisk level descriptionR1Basically no riskR2Low riskR3Moderate riskR4High riskAs the confidence valueλ in attribute identification is generally 0.6 ∼ 0.7, λ = 0.65 is adopted in the calculation [10]. It can be seen from equation (18) that when R1<R2<⋯<Rk<⋯<Rk,(25)k=minl:∑k=llμik≥0.65,1≤l≤4,where xi belongs to risk level Rk.


## 3.4. Dynamic Risk Assessment

The dynamic risk assessment system based on the attribute interval identification model is composed of two parts. One is the preassessment model, and the other one is the postassessment model. The research object of the pre-evaluation model is the unexcavated tunnel section. The evaluation index and the value of the evaluation index are determined. The weight of each evaluation index combination is calculated, and the corresponding interval risk assessment is carried out by the pre-evaluation model. The assessment results can provide guidance for construction safety. The research object of the postevaluation model is the tunnel section under construction. On the basis of the pre-evaluation model, it mainly monitors the sections with high risk of water inrush. The evaluation index value can be adjusted and corrected according to the construction and excavation situation on site. The specific flowchart is shown in Figure2.Figure 2
The highway tunnel gushing water dynamic risk assessment.The specific steps are as follows:Step 1: segment the similar terrain and the geological conditions of the unexcavated tunnel section.Step 2: determine the evaluation index and its value.Step 3: the combined weighting method was used to assign weights to each evaluation index.Step 4: pre-evaluate the tunnel interval. Combined with equations (1)–(8), the single-index attribute measure analysis is carried out for each evaluation index, and the single-index attribute measure function is calculated. Determine whether the evaluation index is an interval-type index. If it is an interval-type index, the multi-index comprehensive attribute measurement analysis is conducted according to equations (9)–(16). Otherwise, the multi-index comprehensive attribute measurement analysis is conducted according to equation (17). Finally, the attribute identification analysis combined with the confidence degree is conducted to determine the hazard level of the tunnel water inrush.Step 5: dynamically revise the evaluation index value according to the construction and excavation situation, and repeat Step 4 to redetermine the hazard level of the tunnel water inrush after the evaluation of the tunnel section.Step 6: construct and excavate, and at the same time, take preventive measures for risk control, and perform a good record of emergency.


## 4. Engineering Applications

### 4.1. Engineering Background

A highway tunneling case of the Puyan highway is a double-line separated tunnel in Sanming, Fujian Province. It is designed as a two-way six-lane tunnel. The main structure of the tunnel area is intrusive contact structure. The surrounding rock of the tunnel is mainly medium-weathered rock. Under the influence of the intrusive contact structure, the joints and fissures in rock mass at the tunnel site are developed, and the integrity of the rock mass is poor. The vault is prone to drop blocks, and accidents such as collapse, water gushing, and mud gushing are easy to occur in the construction. Similarly, with the influence of the stratum, lithological and geological structure, topography, and geomorphology, water in the tunnel area is mainly bedrock fissure water. Bedrock fissure water mainly occurs in strongly and moderately weathered bedrock, among which strongly weathered bedrock mass has developed joint fissure and relatively good water enrichment. According to the analysis of exploration and disclosure of the water level, groundwater in most sections of the tunnel is well developed, and the groundwater level in the tunnel area is higher than the designed elevation. The lining of the tunnel adopts the separated structure, in which the open-cut section adopts the integral lining, and the underground section adopts the composite lining. The initial support mainly consists of steel arch, steel mesh, radial anchor, and sprayed concrete. After the formation of the initial support, the water outlet of the tunnel vault at the construction site is relatively obvious, as shown in Figure3. Therefore, there is a high risk of the water inrush in this section of the tunnel, and the preventive measures should be strengthened during construction. According to the detailed geological survey reports and the design documents, the right line of the tunnel is divided into 5 sections based on the level of the surrounding rock, as shown in Table 6.Figure 3
The tunnel water inrush of the arch roof after the initial support.Table 6
Tunnel sections.
Target segmentSectional mileage rangeLength (m)X1K242 + 555 ∼ K242 + 63580X2K242 + 635 ∼ K242 + 815180X3K242 + 815 ∼ K242 + 87560X4K242 + 875 ∼ K243 + 150275X5K243 + 150 ∼ K243 + 337187


### 4.2. Risk before Assessment

#### 4.2.1. Determine the Evaluation Index and Its Value

Based on the geological exploration, the geological survey data, the advanced geological forecast, and the relevant reference, the evaluation index values of the target sectionXii=1,2,3,4,5 can be determined, which are combined with the grading standard of the highway tunnel water inrush risk assessment index in Table 2. It is shown in Table 7.Table 7
Pre-evaluation evaluation index value.
Target segmentI1I2I3I4I5I6I7I8I9I10X18316851.62[40, 50][35, 42][10, 20]8380[1, 52.13]X272251801.62[300, 330][26, 38][30, 40]8582[77.625, 340.05]X38523601.16[150, 180][41, 53][30, 45]8185[38.245, 74.16]X478352751.62[1000, 1300][55, 62][45, 55]9092[57.37, 131]X584211881.27[170, 200][32, 41][15, 25]8281[1, 131]


#### 4.2.2. Weight Calculation

The combined weighting method is used to assign weights to each evaluation index. In the middle-long highway tunnel, the difference of the same evaluation index in different sections is large due to the topographic and geological conditions and other factors, which is a danger signal for the tunnel gushing water disaster. The entropy weight method is one way to determine the index weight according to the difference between the data. Therefore, the objective weight calculation uses the entropy weight method, which takes the pre-evaluation evaluation index value as the evaluation object to study the weight of the tunnel gushing water evaluation index.The objective weight of each evaluation index can be calculated as follows:(26)α=0.0020.0340.1300.0100.4890.0240.0850.0010.0010.224.The subjective weight is calculated by the analytic hierarchy process, and the subjective weight of each evaluation index can be calculated as follows:(27)β=0.0610.1320.1210.2350.0910.0480.1110.1330.0340.035.According to the objective weight and subjective weight calculated above and equation (24), the weight of each evaluation index can be obtained as follows:(28)ω=0.0010.0520.01820.0280.5200.0140.1100.0010.0010.091.


#### 4.2.3. Preassessment

Combined with the single-index attribute measure function in Table4, the pre-evaluation evaluation index value in Table 7, and combination weight ω, the comprehensive attribute measure μik of multiple indexes can be obtained by calculating from equations (3) to (16). The calculation results are shown in Table 8. And it can be known from equation (25) as follows:(29)k=minl:∑k=1lμik≥0.Ϋ5,1≤l≤5.Table 8
Calculation table of attribute measure values.
Target segmentAttribute measure valuesRisk levelR1R2R3R4X10.61200.34050.04650.0010R2X20.00050.58690.29030.1224R3X30.09830.77070.11140.0196R3X40.00380.08950.22240.6842R4X50.04230.72640.16100.0703R2For the tunnel sectionX1, the pre-evaluation results are shown as follows:(30)∑k=11μ1k=0.6120<0.65,∑k=12μ1k=0.6120+0.3405=0.9525>0.65,∑k=13μ1k=0.6120+0.3405+0.0465=0.999>0.65,∑k=14μ1k=0.6120+0.3405+0.0465+0.0010=1>0.65.Obviously, whenk is 2, 3, or 4, all inequalities are true, so k is 2. The hazard risk level of the water inrush of the tunnel section X1 is R2. Similarly, the water gushing risks of tunnel intervals X2, X3, X4, and X5 are, respectively, R3, R3, R4, and R2. The final evaluation results are shown in Table 8.


### 4.3. Risk after Assessment

#### 4.3.1. Determine the Evaluation Index and Its Value

According to the pre-evaluation model, the highway tunnel water inrush risk in the tunnel sectionX1,X2, X3, X4, and X5 is, respectively, R2, R3, R3, R4, and R2. Tunnel sections X2 and X3 are of moderate risk in terms of water inrush, and tunnel section X4 is of high risk in terms of water inrush. Therefore, tunnel sections X2, X3, and X4 need to be segmented into smaller sections.According to the on-site construction, the evaluation index value was modified in real time, and dynamically, the tunnel gushing water risk was evaluated in a more detailed way. Tunnel intervalX4 was taken as an example. So, it takes every 10 m as the section, and 3 sections of the tunnel are selected as the research object of postevaluation, as shown in Table 9.Table 9
Tunnel sections.
Tunnel sectionX4Sectional mileage rangeX41K242 + 890 ∼ K242 + 900X42K243 + 010 ∼ K243 + 020X43K243 + 130 ∼ K243 + 140Based on the topographic and geological conditions and the grading standards in Table3, the evaluation index value of the target section of the tunnel can be determined as shown in Table 10.Table 10
Postevaluation evaluation index value.
Tunnel sectionX4I1I2I3I4I5I6I7I8I9I10X41702.085101.62[700, 800][35, 42][40, 42]8380[62.805, 65.655]X42725.205101.62[500, 600][30, 38][30, 40]8582[96.105, 101.965]X43803.625101.62[1000, 1300][55, 62][45, 55]9291[78.485, 83.18]


#### 4.3.2. Postassessment

Considering the single-index attribute measure function in Table4, the postevaluation evaluation index value in Table 10, and the combination weight, the comprehensive attribute measure of multiple indexes can be obtained by calculating from equations (3) to (16). The calculation results are shown in Table 11. And it can be known from equation (25) as follows:(31)k=minl:∑k=llμik≥0.65,1≤l≤5.Table 11
Calculation table of attribute measure values.
Tunnel sectionX4Attribute measure valuesRisk levelR1R2R3R4X410.25380.10750.59210.0466R3X420.23320.28450.47480.0075R3X430.23420.10800.15560.5022R4For tunnel sectionX41, the postevaluation results are shown:(32)∑k=11μ4k=0.2538<0.65,∑k=12μ4k=0.2538+0.1075=0.3613<0.65,∑k=13μ4k=0.2538+0.1075+05921=0.9534>0.65,∑k=4μ4k=0.2538+0.1075+0.5921+0.0466=1>0.65.Obviously, whenk is equal to 3 or 4, all inequalities are true, so k is 3. The hazard risk level of the water inrush of tunnel section X41 is R3. Similarly, the water gushing risks of tunnel intervals X42 and X43 are, respectively, R3 and R4. The water inrush hazard of tunnel intervals K242 + 890 ∼ K242 + 900 and K243 + 010 ∼ K243 + 020 is of moderate risk, while the water inrush hazard of tunnel interval K243 + 130 ∼ K243 + 140 is of high risk. The final assessment results are shown in Table 11.


## 4.1. Engineering Background

A highway tunneling case of the Puyan highway is a double-line separated tunnel in Sanming, Fujian Province. It is designed as a two-way six-lane tunnel. The main structure of the tunnel area is intrusive contact structure. The surrounding rock of the tunnel is mainly medium-weathered rock. Under the influence of the intrusive contact structure, the joints and fissures in rock mass at the tunnel site are developed, and the integrity of the rock mass is poor. The vault is prone to drop blocks, and accidents such as collapse, water gushing, and mud gushing are easy to occur in the construction. Similarly, with the influence of the stratum, lithological and geological structure, topography, and geomorphology, water in the tunnel area is mainly bedrock fissure water. Bedrock fissure water mainly occurs in strongly and moderately weathered bedrock, among which strongly weathered bedrock mass has developed joint fissure and relatively good water enrichment. According to the analysis of exploration and disclosure of the water level, groundwater in most sections of the tunnel is well developed, and the groundwater level in the tunnel area is higher than the designed elevation. The lining of the tunnel adopts the separated structure, in which the open-cut section adopts the integral lining, and the underground section adopts the composite lining. The initial support mainly consists of steel arch, steel mesh, radial anchor, and sprayed concrete. After the formation of the initial support, the water outlet of the tunnel vault at the construction site is relatively obvious, as shown in Figure3. Therefore, there is a high risk of the water inrush in this section of the tunnel, and the preventive measures should be strengthened during construction. According to the detailed geological survey reports and the design documents, the right line of the tunnel is divided into 5 sections based on the level of the surrounding rock, as shown in Table 6.Figure 3
The tunnel water inrush of the arch roof after the initial support.Table 6
Tunnel sections.
Target segmentSectional mileage rangeLength (m)X1K242 + 555 ∼ K242 + 63580X2K242 + 635 ∼ K242 + 815180X3K242 + 815 ∼ K242 + 87560X4K242 + 875 ∼ K243 + 150275X5K243 + 150 ∼ K243 + 337187


## 4.2. Risk before Assessment

### 4.2.1. Determine the Evaluation Index and Its Value

Based on the geological exploration, the geological survey data, the advanced geological forecast, and the relevant reference, the evaluation index values of the target sectionXii=1,2,3,4,5 can be determined, which are combined with the grading standard of the highway tunnel water inrush risk assessment index in Table 2. It is shown in Table 7.Table 7
Pre-evaluation evaluation index value.
Target segmentI1I2I3I4I5I6I7I8I9I10X18316851.62[40, 50][35, 42][10, 20]8380[1, 52.13]X272251801.62[300, 330][26, 38][30, 40]8582[77.625, 340.05]X38523601.16[150, 180][41, 53][30, 45]8185[38.245, 74.16]X478352751.62[1000, 1300][55, 62][45, 55]9092[57.37, 131]X584211881.27[170, 200][32, 41][15, 25]8281[1, 131]


### 4.2.2. Weight Calculation

The combined weighting method is used to assign weights to each evaluation index. In the middle-long highway tunnel, the difference of the same evaluation index in different sections is large due to the topographic and geological conditions and other factors, which is a danger signal for the tunnel gushing water disaster. The entropy weight method is one way to determine the index weight according to the difference between the data. Therefore, the objective weight calculation uses the entropy weight method, which takes the pre-evaluation evaluation index value as the evaluation object to study the weight of the tunnel gushing water evaluation index.The objective weight of each evaluation index can be calculated as follows:(26)α=0.0020.0340.1300.0100.4890.0240.0850.0010.0010.224.The subjective weight is calculated by the analytic hierarchy process, and the subjective weight of each evaluation index can be calculated as follows:(27)β=0.0610.1320.1210.2350.0910.0480.1110.1330.0340.035.According to the objective weight and subjective weight calculated above and equation (24), the weight of each evaluation index can be obtained as follows:(28)ω=0.0010.0520.01820.0280.5200.0140.1100.0010.0010.091.


### 4.2.3. Preassessment

Combined with the single-index attribute measure function in Table4, the pre-evaluation evaluation index value in Table 7, and combination weight ω, the comprehensive attribute measure μik of multiple indexes can be obtained by calculating from equations (3) to (16). The calculation results are shown in Table 8. And it can be known from equation (25) as follows:(29)k=minl:∑k=1lμik≥0.Ϋ5,1≤l≤5.Table 8
Calculation table of attribute measure values.
Target segmentAttribute measure valuesRisk levelR1R2R3R4X10.61200.34050.04650.0010R2X20.00050.58690.29030.1224R3X30.09830.77070.11140.0196R3X40.00380.08950.22240.6842R4X50.04230.72640.16100.0703R2For the tunnel sectionX1, the pre-evaluation results are shown as follows:(30)∑k=11μ1k=0.6120<0.65,∑k=12μ1k=0.6120+0.3405=0.9525>0.65,∑k=13μ1k=0.6120+0.3405+0.0465=0.999>0.65,∑k=14μ1k=0.6120+0.3405+0.0465+0.0010=1>0.65.Obviously, whenk is 2, 3, or 4, all inequalities are true, so k is 2. The hazard risk level of the water inrush of the tunnel section X1 is R2. Similarly, the water gushing risks of tunnel intervals X2, X3, X4, and X5 are, respectively, R3, R3, R4, and R2. The final evaluation results are shown in Table 8.


## 4.2.1. Determine the Evaluation Index and Its Value

Based on the geological exploration, the geological survey data, the advanced geological forecast, and the relevant reference, the evaluation index values of the target sectionXii=1,2,3,4,5 can be determined, which are combined with the grading standard of the highway tunnel water inrush risk assessment index in Table 2. It is shown in Table 7.Table 7
Pre-evaluation evaluation index value.
Target segmentI1I2I3I4I5I6I7I8I9I10X18316851.62[40, 50][35, 42][10, 20]8380[1, 52.13]X272251801.62[300, 330][26, 38][30, 40]8582[77.625, 340.05]X38523601.16[150, 180][41, 53][30, 45]8185[38.245, 74.16]X478352751.62[1000, 1300][55, 62][45, 55]9092[57.37, 131]X584211881.27[170, 200][32, 41][15, 25]8281[1, 131]


## 4.2.2. Weight Calculation

The combined weighting method is used to assign weights to each evaluation index. In the middle-long highway tunnel, the difference of the same evaluation index in different sections is large due to the topographic and geological conditions and other factors, which is a danger signal for the tunnel gushing water disaster. The entropy weight method is one way to determine the index weight according to the difference between the data. Therefore, the objective weight calculation uses the entropy weight method, which takes the pre-evaluation evaluation index value as the evaluation object to study the weight of the tunnel gushing water evaluation index.The objective weight of each evaluation index can be calculated as follows:(26)α=0.0020.0340.1300.0100.4890.0240.0850.0010.0010.224.The subjective weight is calculated by the analytic hierarchy process, and the subjective weight of each evaluation index can be calculated as follows:(27)β=0.0610.1320.1210.2350.0910.0480.1110.1330.0340.035.According to the objective weight and subjective weight calculated above and equation (24), the weight of each evaluation index can be obtained as follows:(28)ω=0.0010.0520.01820.0280.5200.0140.1100.0010.0010.091.


## 4.2.3. Preassessment

Combined with the single-index attribute measure function in Table4, the pre-evaluation evaluation index value in Table 7, and combination weight ω, the comprehensive attribute measure μik of multiple indexes can be obtained by calculating from equations (3) to (16). The calculation results are shown in Table 8. And it can be known from equation (25) as follows:(29)k=minl:∑k=1lμik≥0.Ϋ5,1≤l≤5.Table 8
Calculation table of attribute measure values.
Target segmentAttribute measure valuesRisk levelR1R2R3R4X10.61200.34050.04650.0010R2X20.00050.58690.29030.1224R3X30.09830.77070.11140.0196R3X40.00380.08950.22240.6842R4X50.04230.72640.16100.0703R2For the tunnel sectionX1, the pre-evaluation results are shown as follows:(30)∑k=11μ1k=0.6120<0.65,∑k=12μ1k=0.6120+0.3405=0.9525>0.65,∑k=13μ1k=0.6120+0.3405+0.0465=0.999>0.65,∑k=14μ1k=0.6120+0.3405+0.0465+0.0010=1>0.65.Obviously, whenk is 2, 3, or 4, all inequalities are true, so k is 2. The hazard risk level of the water inrush of the tunnel section X1 is R2. Similarly, the water gushing risks of tunnel intervals X2, X3, X4, and X5 are, respectively, R3, R3, R4, and R2. The final evaluation results are shown in Table 8.


## 4.3. Risk after Assessment

### 4.3.1. Determine the Evaluation Index and Its Value

According to the pre-evaluation model, the highway tunnel water inrush risk in the tunnel sectionX1,X2, X3, X4, and X5 is, respectively, R2, R3, R3, R4, and R2. Tunnel sections X2 and X3 are of moderate risk in terms of water inrush, and tunnel section X4 is of high risk in terms of water inrush. Therefore, tunnel sections X2, X3, and X4 need to be segmented into smaller sections.According to the on-site construction, the evaluation index value was modified in real time, and dynamically, the tunnel gushing water risk was evaluated in a more detailed way. Tunnel intervalX4 was taken as an example. So, it takes every 10 m as the section, and 3 sections of the tunnel are selected as the research object of postevaluation, as shown in Table 9.Table 9
Tunnel sections.
Tunnel sectionX4Sectional mileage rangeX41K242 + 890 ∼ K242 + 900X42K243 + 010 ∼ K243 + 020X43K243 + 130 ∼ K243 + 140Based on the topographic and geological conditions and the grading standards in Table3, the evaluation index value of the target section of the tunnel can be determined as shown in Table 10.Table 10
Postevaluation evaluation index value.
Tunnel sectionX4I1I2I3I4I5I6I7I8I9I10X41702.085101.62[700, 800][35, 42][40, 42]8380[62.805, 65.655]X42725.205101.62[500, 600][30, 38][30, 40]8582[96.105, 101.965]X43803.625101.62[1000, 1300][55, 62][45, 55]9291[78.485, 83.18]


### 4.3.2. Postassessment

Considering the single-index attribute measure function in Table4, the postevaluation evaluation index value in Table 10, and the combination weight, the comprehensive attribute measure of multiple indexes can be obtained by calculating from equations (3) to (16). The calculation results are shown in Table 11. And it can be known from equation (25) as follows:(31)k=minl:∑k=llμik≥0.65,1≤l≤5.Table 11
Calculation table of attribute measure values.
Tunnel sectionX4Attribute measure valuesRisk levelR1R2R3R4X410.25380.10750.59210.0466R3X420.23320.28450.47480.0075R3X430.23420.10800.15560.5022R4For tunnel sectionX41, the postevaluation results are shown:(32)∑k=11μ4k=0.2538<0.65,∑k=12μ4k=0.2538+0.1075=0.3613<0.65,∑k=13μ4k=0.2538+0.1075+05921=0.9534>0.65,∑k=4μ4k=0.2538+0.1075+0.5921+0.0466=1>0.65.Obviously, whenk is equal to 3 or 4, all inequalities are true, so k is 3. The hazard risk level of the water inrush of tunnel section X41 is R3. Similarly, the water gushing risks of tunnel intervals X42 and X43 are, respectively, R3 and R4. The water inrush hazard of tunnel intervals K242 + 890 ∼ K242 + 900 and K243 + 010 ∼ K243 + 020 is of moderate risk, while the water inrush hazard of tunnel interval K243 + 130 ∼ K243 + 140 is of high risk. The final assessment results are shown in Table 11.


## 4.3.1. Determine the Evaluation Index and Its Value

According to the pre-evaluation model, the highway tunnel water inrush risk in the tunnel sectionX1,X2, X3, X4, and X5 is, respectively, R2, R3, R3, R4, and R2. Tunnel sections X2 and X3 are of moderate risk in terms of water inrush, and tunnel section X4 is of high risk in terms of water inrush. Therefore, tunnel sections X2, X3, and X4 need to be segmented into smaller sections.According to the on-site construction, the evaluation index value was modified in real time, and dynamically, the tunnel gushing water risk was evaluated in a more detailed way. Tunnel intervalX4 was taken as an example. So, it takes every 10 m as the section, and 3 sections of the tunnel are selected as the research object of postevaluation, as shown in Table 9.Table 9
Tunnel sections.
Tunnel sectionX4Sectional mileage rangeX41K242 + 890 ∼ K242 + 900X42K243 + 010 ∼ K243 + 020X43K243 + 130 ∼ K243 + 140Based on the topographic and geological conditions and the grading standards in Table3, the evaluation index value of the target section of the tunnel can be determined as shown in Table 10.Table 10
Postevaluation evaluation index value.
Tunnel sectionX4I1I2I3I4I5I6I7I8I9I10X41702.085101.62[700, 800][35, 42][40, 42]8380[62.805, 65.655]X42725.205101.62[500, 600][30, 38][30, 40]8582[96.105, 101.965]X43803.625101.62[1000, 1300][55, 62][45, 55]9291[78.485, 83.18]


## 4.3.2. Postassessment

Considering the single-index attribute measure function in Table4, the postevaluation evaluation index value in Table 10, and the combination weight, the comprehensive attribute measure of multiple indexes can be obtained by calculating from equations (3) to (16). The calculation results are shown in Table 11. And it can be known from equation (25) as follows:(31)k=minl:∑k=llμik≥0.65,1≤l≤5.Table 11
Calculation table of attribute measure values.
Tunnel sectionX4Attribute measure valuesRisk levelR1R2R3R4X410.25380.10750.59210.0466R3X420.23320.28450.47480.0075R3X430.23420.10800.15560.5022R4For tunnel sectionX41, the postevaluation results are shown:(32)∑k=11μ4k=0.2538<0.65,∑k=12μ4k=0.2538+0.1075=0.3613<0.65,∑k=13μ4k=0.2538+0.1075+05921=0.9534>0.65,∑k=4μ4k=0.2538+0.1075+0.5921+0.0466=1>0.65.Obviously, whenk is equal to 3 or 4, all inequalities are true, so k is 3. The hazard risk level of the water inrush of tunnel section X41 is R3. Similarly, the water gushing risks of tunnel intervals X42 and X43 are, respectively, R3 and R4. The water inrush hazard of tunnel intervals K242 + 890 ∼ K242 + 900 and K243 + 010 ∼ K243 + 020 is of moderate risk, while the water inrush hazard of tunnel interval K243 + 130 ∼ K243 + 140 is of high risk. The final assessment results are shown in Table 11.


## 5. Verification of Evaluation Results

At about 7:20 a.m. on July 28, 2020, when the right line of the tunnel is excavated up toK243 + 132, the water inrush occurred. Gushing water appeared in the gun holes at several positions of the tunnel surface with a certain pressure, and the jetting distance was about 3–5 m. The water column on the right side of the tunnel surface was large, and some of it carried yellow mud, as shown in Figure 4.Figure 4
Verification of excavation results. (a) The lower steps were partially submerged by a surge of water. (b) Multiple jets of water spurted from the tunnel face.After the accident occurred, the evaluation index values were modified according to the site construction conditions. The tunnel water inrush risk assessment was carried out again for the same section. Thus, it was concluded that tunnel sectionK243 + 130 ∼ K243 + 140 was still of high risk. The evaluation results are in good agreement with the site construction. The comparison of risk assessment results before and after excavation is shown in Table 12.Table 12
Comparison of risk assessment results before and after excavation.
Tunnel sectionX4Attribute measure valuesRisk levelR1R2R3R4X430.23420.10800.15560.5022R4X′430.23420.10800.13850.5192R4In this risk accident, the construction company has formulated emergency risk control measures for the gushing water disaster in the tunnel in advance and convened expert meetings in time to discuss the corresponding measures after the occurrence of danger. Therefore, no casualties were caused in this risk accident, and the construction loss was reduced to the minimum.


## 6. Conclusion

In this paper, a dynamic risk assessment based on the EW-AHP attribute evaluation model is carried out for the highway tunnel water inrush under interval conditions.(1)
The index system and the index grading standards of the highway tunnel water inrush risk assessment have been established based on a highway tunnel case of the geological prospecting, geological survey data, and reference. Furthermore, a set of dynamic highway tunnel water inrush risk assessment models with preassessment model and postassessment model is established, which has combined with the combination of empowerment and the attribute identification theoretical model.(2)
The highway tunnel water gushing risk assessment model is set as a dynamic risk assessment model, which is based on the EW-AHP attribute evaluation model and composed of the pre-evaluation model and postevaluation model. The preassessment model is to control the water inrush risk of each tunnel section as a whole. Thus, the postassessment model is to carry out the risk assessment of the water inrush risk of the tunnel in time and dynamically according to the construction needs.(3)
The evaluation index values of the dynamic risk assessment model can be a certain value or range. So, it makes the evaluation index values more flexible, less restricted, and more in line with the engineering practice. Moreover, the weight calculation of each evaluation index only needs to be determined in the pre-evaluation model, and there is no need to change frequently in the postevaluation model due to the change of the evaluation index value.(4)
A case study of tunneling gushing water risk assessment was performed with the dynamic risk assessment model based on the attribute interval identification model. The water gushing risk of tunnel sectionK243 + 130 ∼ K243 + 140 is R4, which is of high risk. The evaluation results are consistent with the situation on the construction site, which verifies the rationality and feasibility of the evaluation model.



---

*Source: 6661609-2021-04-19.xml*