Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2021 / Article

Research Article | Open Access

Volume 2021 |Article ID 6661609 |

Bo Wu, Huihao Chen, Wei Huang, Guowang Meng, "Dynamic Evaluation Method of the EW-AHP Attribute Identification Model for the Tunnel Gushing Water Disaster under Interval Conditions and Applications", Mathematical Problems in Engineering, vol. 2021, Article ID 6661609, 15 pages, 2021.

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

Academic Editor: Adrian Neagu
Received11 Dec 2020
Revised31 Mar 2021
Accepted02 Apr 2021
Published19 Apr 2021


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.

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’ space , where all the evaluation objects could be . is the jth evaluation index of the evaluation object xi. F is the attribute interval space of X. is an ordered partition class of F, where [6].

2.1.1. Analysis of the Single-Index Attribute Measurement

It can be supposed that the value of the evaluation object xi 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: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).

Evaluation index IiEvaluation index value tiOrder of evaluation

Ii1ti1a10 a11a11 a12a1 (k − 1) ∼a1k
Ii2ti2a20 ∼ a21a21 ∼ a22a2 (k − 1) ∼ a2k
Iijtijaj0 ∼ aj1aj1 ∼ aj2aj (k − 1) ∼ ajk
Iimtimam0 ∼ am1am1 ∼ am2am (k − 1) ∼ amk

From [79], when , the single-index attribute measure function can be expressed as follows:

From [9, 10], when , the single-index attribute measure function can be expressed as follows: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 be the interval metric function of the single-index attribute, and let and be the upper and lower limits of the evaluation index, respectively. When , the interval metric function of the single-index attribute can be expressed as follows:

When , the interval metric function of the single-index attribute can be expressed as follows:

The weight of each index can be , , . The attribute measure value of the evaluation index Iij belonging to the evaluation level Rk can be solved by the single-index attribute interval metric function , which can be expressed as follows:

(2) The evaluation index value is a noninterval-type index: as the weight of each index is , , , the attribute measure value can be expressed as follows:

2.1.3. Attribute Identification Analysis

The attribute space F of a class on X is set, is the attribute interval set of X, and [6]. is the confidence level, and .

When ,

When ,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 [1214] 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 matrix can be obtained. Then, the proportion of the ith sample value in the jth index of the term is calculated as follows:Step 2: the information entropy of the evaluation index is calculated as follows:Step 3: the evaluation index weight is assigned as follows:

uj is the difference coefficient of the calculated index, and . The weight vector of the index is , and .

2.2.2. AHP Method to Determine the Subjective Weight

Analytic hierarchy process (AHP) [1517] 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 (Table 2), the evaluation indexes are compared in pairs, and the judgment matrix is constructed. The judgment matrix can be obtained as follows:Step 3: the maximum eigenvalue 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 weight βj of each evaluation index is calculated.

ValueDifference in importance

1Indicator i is as important as indicator j
3Index i is slightly more important than index j
5Indicator i is significantly more important than indicator j
7Indicator i is strongly more important than indicator j
9Indicator i is extremely important than indicator j
2, 4, 6, 8Intermediate value between the above adjacent judgments
ExplanationWhen index j 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:

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, 2023]. 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.

Evaluation indexR1R2R3R4

I135 ∼ 6060 ∼ 7070 ∼ 8585 ∼ 100
I2 (m)h < 1010 ≤ h < 3030 ≤ h < 60h > 60
I3 (m)<5050 ∼ 100100 ∼ 200200 ∼ 300
I4 (10−5 cm/s)<11 ∼ 10001000 ∼ 100000>100000
I5 (m3/d)<100100 ∼ 500500 ∼ 1000>1000
I6 (%)<2020 ∼ 4040 ∼ 60>60
I7 (°)0 ∼ 1010 ∼ 2525 ∼ 4545 ∼ 65
I835 ∼ 6060 ∼ 7070 ∼ 8585 ∼ 100
I935 ∼ 6060 ∼ 7070 ∼ 8585 ∼ 100
I10 (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.