Improved Attribute Interval Evaluation Theory for Risk Assessment of Geological Disasters in Underground Engineering and Its Application

Abstract

Based on the theory of attribute mathematics, this paper improves on the attribute interval evaluation theory. The main feature is that the evaluation index is an interval rather than a certain value. Using single index attribute analysis of the upper and lower limits of the interval, the paper proposes two calculation methods for the multiple index synthetic attribute measure. Based on the original AIET software, we develop a new set of software packages (NEW AIET) that can automatically complete a large number of calculations in a few seconds. Via engineering application, the accuracy and feasibility of geological disaster risk assessment are verified and can be used to better evaluate engineering disaster risk.

1 Introduction

Intrinsic risk is associated with tunnel construction because of limited a priori knowledge of the existing subsurface conditions (Sousa and Einstein 2012). Geological disasters such as landslides, water inrush, mudslides, and rock bursts often occur in underground projects, which have resulted in delays, cost overruns, and in a few cases more significant consequences such as injury and loss of life. And therefore, effective disaster prevention is an important task for geological work.

In terms of engineering risk management and evaluation research, the International Tunneling Association issued a tunnel risk management guide, which has been successfully applied in construction risk control such as landslides (Søren et al. 2004). A lot of research work has been done on domestic risk analysis and assessment. It has applied and developed in tunnel water inrush, landslide, gas outburst, etc., and prepared risk management guidelines for subway and underground construction (Ministry, 2007).

Risk assessment is the core of risk management in tunnel and underground engineering, the important link between systematic identification of engineering risks and scientific and reasonable management risks, and the basis of decision analysis. In recent years, we have researched tunnel risk assessment methods and applied the results at home and abroad, and these methods include attribute mathematics theory, analytic hierarchy process (AHP), Bayesian network (BN), fuzzy evaluation method (FMT), grey theory (GT), extension methods (EM), and others (Saaty 1980; Hwang and Lu 2007; Bukowski 2011; Song et al. 2012). In addition to the successful use of existing risk assessment methods from other engineering industries in tunnels and underground engineering, a number of risk assessment models suitable for tunnel projects have been developed based on the specific characteristics of tunnel projects.

In underground engineering, risk sources and disasters generally arise from geotechnical uncertainty (aleatory or epistemic) or error (intrinsic or implementary) (Beard 2010; Brown 2012). However, a common problem exists in the abovementioned theories and methods. In the process of geological hazard risk analysis, after establishment of the corresponding evaluation index system, the value of the index is often an exact value, which ignores the complexity of underground engineering geological conditions and the uncertainty of the risk itself. Moreover, most models can only give a risk level qualitatively or semi-quantitatively, and cannot give the probability of occurrence of the risk grade.

Therefore, based on the theory of attribute mathematics and attribute interval evaluation theory, this paper proposes an improved theory of and method for attribute interval recognition. The evaluation index is an interval rather than a certain value, and using single index attribute analysis of the upper and lower limits of the interval (with reference to the original mathematical attribute model and the idea of risk evaluation), two improved methods for comprehensive attribute measure analysis are proposed. Combined with engineering examples, we propose the adoption of the attribute recognition analysis method and demonstrate quantitative recognition of the disaster risk level (Zhou et al. 2013).

Because this paper proposes two other identification methods, an NEW AIET software package is developed to solve this problem based on the original AIET software. We verify the engineering application in different geological disasters, and the risk level obtained from the evaluation is consistent with the actual working conditions and the evaluation results of Li et al. (2013a, b), Zhou et al. (2015), Li et al. (2014), Wang et al. (2012), Chen and Li. (2008), Zhang et al. (2010) and Yang et al. (2010), thus verifying the accuracy and feasibility of the method.

2 Improved Attribute Interval Evaluation Theory

The AIET is an innovative risk assessment methodology proposed by Li et al. (2013a) based on the attribute mathematical theory (AMT). An attribute synthetic assessment system consists of three components: single index attribute measure analysis, multiple indices synthetic attribute measure analysis and attribute recognition analysis.

2.1 Single Index Attribute Measure Analysis

For a single index I_j measurement t_j, the determination of the attribute measurement μ_xjk = μ (x_ij∈C_k) with attribute C_k is intended to establish its attribute measurement function. We indicate the change of the attribute measure μ_xjk= μ (x_ij∈C_k) when the measured value t_j of I_j changes. The grading standards of evaluation indices are expressed in Table 1, where a_jk≤ b_jk should satisfy $a_{j1} < \, a_{j2} < \cdots \, < a_{jK} , \, b_{j1} < \, b_{j2} < \, \cdots \, < b_{jK} \quad or\quad a_{j1} > \, a_{j2} > \, \cdots > \, a_{jK} , \, b_{j1} > \, b_{j2} > \, \cdots > \, b_{jK} ,$If $a_{j1} > \, a_{j2} > \, \cdots > \, a_{jK} , \, b_{j1} > \, b_{j2} > \, \cdots > \, b_{jK} ,$We take the lower limit t_jx single index attribute measure calculation as an example:

$$\left\{ \begin{aligned} \mu_{jx1} = & \mu_{jx2} = \cdots = \mu_{jxK} = 0\quad t_{jx} \ge a_{j1} \\ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{jx1} = & \frac{{\left| {t_{jx} - a_{jl + 1} } \right|}}{{\left| {a_{jl} - a_{jl + 1} } \right|}},\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{jxk} = 0\quad a_{jl + 1} \le t_{jx} \le a_{jl} \\ \mu_{jxK} = & 1,\mu_{jx1} = \cdots = \mu_{jxK - 1} = 0\quad t_{jx} \le a_{jK} \\ \end{aligned} \right.$$

(1)

Table 1 Grade subdivision of a single index

Among these, k < l or k > l +1.

$$\left\{ {\begin{array}{*{20}l} {\mu _{{jxK}} = 1,\mu _{{jx1}} = \cdots = \mu _{{jxK - 1}} = 0\quad t_{{jx}} \le a_{{jK}} } \hfill \\ {\bar{\mu }_{{jxl}} = \frac{{\left| {t_{{jx}} - b_{{jl + 1}} } \right|}}{{\left| {b_{{jl}} - b_{{jl + 1}} } \right|}},\mu _{{jxl + 1}} = \frac{{\left| {t_{{jx}} - b_{{jl}} } \right|}}{{\left| {b_{{jl + 1}} - b_{{jl}} } \right|}},\bar{\mu }_{{jxk}} = 0\quad b_{{jl + 1}} \le t_{{jx}} \le b_{{jl}} } \hfill \\ {\bar{\mu }_{{jxK}} = 1,\bar{\mu }_{{jx1}} = \cdots = \bar{\mu }_{{jxK - 1}} = 0\quad t_{{jx}} \le b_{{jk}} } \hfill \\ \end{array} } \right.$$

(2)

Among these, k < l or k > l +1.

If $a_{j1} < \, a_{j2} < \cdots \, < a_{jK} , \, b_{j1} < b_{j2} < \cdots < b_{jK} ,$ the single index attribute measure function is not separately listed herein.

2.2 Synthetic Attribute Measure Analysis of Multiple Indices

We can calculate the comprehensive attribute measure μ_j′k as shown in formula (3),

$$\begin{aligned} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j\prime k}} = & \sum\limits_{j = 1}^{m} {\left( {\omega_{j} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{jk}} \right)} ,\quad \bar{\mu }_{{j^\prime k}} = \sum\limits_{j = 1}^{m} {\left( {\omega_{j} \bar{\mu }_{jk} } \right)} , \\ & \;\left( {1 \le j \le m,\quad 1 \le k \le K} \right) \\ \end{aligned}$$

(3)

Where ω_j is the weight of the jth indicator ω_j ≥ 0,

$$\sum\limits_{j = 1}^{m} {\omega_{j} { = }1}$$

(4)

We define the following vector

$$\begin{aligned} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime x}} = &\, [\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime x1}} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime x1}} , \ldots ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime x1}} ]; \\ \bar{\mu }_{{j^\prime x}} = &\, [\bar{\mu }_{{j^\prime x1}} ,\bar{\mu }_{{j^\prime x2}} , \ldots ,\bar{\mu }_{{j^\prime xK}} ]; \\ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime y}} = &\, [\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime y1}} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime y1}} , \ldots ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime y1}} ]; \\ \bar{\mu }_{{j^\prime y}} = &\, [\bar{\mu }_{{j^\prime y1}} ,\bar{\mu }_{{j^\prime y2}} , \ldots ,\bar{\mu }_{{j^\prime yK}} ] \\ \end{aligned}$$

For ease of understanding, we explain the following example.

If the evaluation object takes two evaluation indicators, we can divide it into three risk levels, namely, j = 1, 2; j′ = 1, 2; k = 1, 2, 3, and the evaluation index values are [t_1x,t_1′y],[t_2x,t_2′y].

Using formulas (1)–(2) to calculate single index attribute measure, we can obtain the vector $\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{1x}$ , $\bar{\mu }_{1x}$ , $\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{1y}$ , $\bar{\mu }_{1y}$ , $\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{2x}$ , $\bar{\mu }_{2x}$ , $\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{2y}$ , $\bar{\mu }_{2y}$, where $\mu_{1x} = \, [\mu_{1x1} \text{,}\mu_{1x2} \text{,}\mu_{1x3} ],\quad \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{1x} = \, [\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{1x1} \text{,}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{1x2} \text{,}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{1x3} ],$ etc., and eight 2 × 3 matrices U_2×3 can be generated. Using formula (3) to calculate the comprehensive attribute measure of the matrix U_2×3, we obtain $\mu_{{1^{\prime }x}} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{1^{\prime }x}} ,\mu_{{1^{\prime }y}} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{1^{\prime }y}} ,\quad \mu_{{2^{\prime }x}} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{2^{\prime }x}} ,\mu_{{2^{\prime }y}} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{2^{\prime }y}} ,$ and subsequently conduct analysis using two types of identification methods.

2.3 Attribute Recognition Analysis

The purpose of attribute recognition is to decide which of the evaluation levels x belongs to C_k using the comprehensive attribute measure μ_xk. In comprehensive evaluation of attributes, the evaluation set (C₁, C₂,…, C_K) is usually an ordered set.

When $C_{1} > C_{2} > \cdots > C_{K} ,$if:

$$k_{0} = \hbox{min} \left\{ {k:\sum\limits_{l = 1}^{k} {\mu_{xl} { \ge }\lambda \;{\kern 1pt} ,{\kern 1pt} \;1{ \le }k{ \le }K} } \right\}$$

(5)

When $C_{1} > C_{2} > \cdots > C_{K} ,$ if:

$$k_{0} = \hbox{max} \left\{ {k:\sum\limits_{l = k}^{K} {\mu_{xl} { \ge }\lambda ,\quad 1{ \le }k{ \le }K} } \right\}$$

(6)

It is considered that x_i belongs to the C_ki level.where k = 1, 2,…,K; and λ is the confidence coefficient 0.5 < λ≤1. In general, λ is found in the range 0.6–0.7.

Based on the improved attribute interval recognition theory, we propose two additional calculation methods based on the two methods proposed by Zhou et al. (2013).

(1) Recognition method one: Zhou et al. (2013) uses method one in calculation of comprehensive attribute measures. It is necessary to calculate 2^m types of comprehensive attribute measures and subsequently find the corresponding average value. This method is overly complicated. In fact, we can directly average the attribute measures corresponding to each risk level:

$$\underline{\mu }_{j^\prime xk} = \sum\limits_{j = 1}^{m} {\left( {\omega_{j} \underline{\mu }_{jxk} } \right)} ,\quad \overline{\mu }_{{j^\prime xk}} = \sum\limits_{j = 1}^{m} {\left( {\omega_{j} \overline{\mu }_{jxk} } \right)} ,$$

(7)

$$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime yk}} = \sum\limits_{j = 1}^{m} {\left( {\omega_{j} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{jyk} } \right)} ,\quad \bar{\mu }_{{j^\prime yk}} = \sum\limits_{j = 1}^{m} {\left( {\omega_{j} \bar{\mu }_{jyk} } \right)} ,$$

(8)

$$\begin{aligned} \mu_{{j^\prime k}} = & (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{j\prime xk} + \bar{\mu }_{j\prime xk} + \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime yk}} + \bar{\mu }_{{j^\prime yk}} )/4, \\ & (k = 1,\;2,\;3) \\ \end{aligned}$$

(9)

The calculation results of Eq. (9) are consistent with the calculation results of method one proposed by Zhou et al. (2013), and the calculation is simple and convenient. Therefore, we can replace the original calculation method.

(2) Recognition method two: First, we obtain the average μ_j′x and μ_j′y matrices via the comprehensive attribute measure corresponding to the risk levels of $\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime x}}$ and $\bar{\mu }_{{j^\prime x}}$, $\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime y}}$ and $\bar{\mu }_{{j^\prime y}}$ respectively.

$$\mu_{{j^\prime x}} = (\underline{\mu }_{{j^\prime x}} + \overline{\mu }_{{j^\prime x}} )/2,\quad \mu_{{j^\prime y}} = (\underline{\mu }_{{j^\prime y}} + \overline{\mu }_{{j^\prime y}} )/2$$

(10)

After orderly combination of μ_j′x and μ_j′y, we use method 2 proposed by Zhou et al. (2013) for attribute interval evaluation.

The matrix U_m×K constructed using this method contains 2^m types of combinations for each, and the attribute measurement corresponding to U_m×K can be calculated by the following formula (11):

$$\mu_{k} = \omega_{j} \mu_{kn} = \left[ {\omega_{1} ,\omega_{2} , \cdots ,\omega_{m} } \right]\left[ {\mu_{k1} ,\mu_{k2} , \cdots ,\mu_{km} } \right]^{\text{T}}$$

(11)

where ω_j is a weight vector [ω₁, ω₂, …, ω₁]_1×m; [μ_k1, μ_k2, …, μ_km]^T_m×1.

We build two sets of m × K order matrices: $\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime x}}$ and $\bar{\mu }_{{j^\prime x}}$$\bar{\mu }_{{j^\prime x}}$ is a group, $\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mu }_{{j^\prime y}}$ and $\bar{\mu }_{{j^\prime y}}$ is a group. By analysing 2^m values of k₀, we can obtain the ratios at which the risk levels can occur.

3 Development of NEW AIET Software Package

The risk assessment process of improved AIET can be considered as a series of matrix operations and requires a large number of calculations because 2^m types of combinations of measures exist for the comprehensive attributes. Different methods are applied to determine the risk level, and thus we propose two other identification methods in this paper and develop a new software package (NEW AIET) based on the original AIET software to solve this problem. The newly developed software consists of several panels, as shown in Fig. 1.

Fig. 1

Main interface of New AIET software package

The Grading Standards of Evaluation Indices panel is primarily used to obtain the single attribute measure functions based on the grading standards of the evaluation indices. We first import the threshold limits of grading standards a_ij and subsequently calculate the variables b_ij and d_ij automatically. Finally, we derive the single index attribute functions from Fig. 1 and display them in a pop-up window. We use the Evaluation Indices Values panel to import the lower and upper limit values of the evaluation indices. LLV and ULV refer to the lower and upper limit values, respectively. We use the Evaluation Weights panel to import the weights of the evaluation indices. We use the Confidence Coefficient and Recognition Method panels to assign the value of k and select the recognition method, respectively (Li et al. 2016).

We can complete all operations in a few seconds, and we display the operation results in the specific blanks in the Multiple Indices Synthetic Attribute Measure and Attribute Recognition panel. In addition, using selected important information, we can also display information such as $U_{\text{ij}}^{l}$;$U_{\text{ij}}^{\text{u}}$;$\overline{\mu }_{j}$ and N_k=j in several pop-up windows.

4 Engineering Applications in Different Geological Disasters

In recent years, many risk theories have been introduced and studied in domestic academic circles. Based on previous studies, risk assessments of several types of geological disasters, including water inrush, floor water inrush, rock burst and gas outburst, are carried out in the present study.

It should be noted that the evaluation indices for risk assessment of each geological disaster and their grading standards proposed by previous researchers and presented in the literatures are adopted and used in the present study. Analogously, the weights of evaluation indices are also obtained from the values presented in the literatures.

4.1 Risk Assessment of Water Inrush in Karst Tunnels

We often encounter karst disaster sources such as karst cavity and karst cracking in tunnel construction. The risk of water and mud inrush in a karst tunnel seriously threatens the safety and construction of the tunnel. The karst water inrush has become one of the main geological disasters for tunnel construction in karst regions. According to the karst hydrogeology and engineering geological conditions of the tunnel area, we select seven influence factors as the evaluation indices, including formation lithology, unfavourable geological conditions, groundwater level, landform and physiognomy, attitude of rock formation, contact zones of dissolvable and insoluble rock, and layer and interlayer fissures. In combination with the case of attribute recognition and analysis by Li et al. (2013a), we use the water inrush disasters at Jigongling tunnel and Xiakou tunnel for engineering applications. The grading standards and value intervals of the evaluation indices are shown in Tables 1 and 2. We take the weights of evaluation indices as 0.167, 0.349, 0.176, 0.097, 0.049, 0.114 and 0.048. The confidence coefficient value is taken as 0.65 in Table 3. According to the evaluation results shown in Table 4, we use two methods to analyse and compare case W①:

Table 2 Grading standards of water inrush evaluation indices (Li et al. 2013a, b; Zhou et al. 2015)

Table 3 ULV and LLV of water inrush evaluation indices (Li et al. 2013a)

Table 4 Evaluation results of water inrush risks (k = 0.65)

Recognition method 1: According to Sect. 2.2, we obtain the property measure from Eqs. (7) to (9):

$$\mu_{k} = \, [0.5159, 0.3161, 0.1377, 0.0303]$$

(12)

In assessing the risk level, the degree of confidence λ = 0.65 with available k₀ = 1 means that the risk of water inrush from the tunnel is C₁.

Recognition method 2: The combinatorial arrangement of μ_j′x and μ_j′y is used to analyse the comprehensive attribute measures of 128 combinations. The analysis results show that 116 cases exist for which k₀ = 1 in the combination of μ_j′x and μ_j′y, and the corresponding risk level is C₁. Additionally, we have 10 combinations for which k₀ = 2. We can conclude that the probability of water inrush at C₁ level is 91%, such that the probability of water inrush at C₂ level is 7.5% and that of 1.5% is between C₁ and C₂.

4.2 Risk Assessment of Floor Water Inrush in Coal Mines

Floor water inrush refers to the phenomenon of a sudden and exponential increase of water inrush in a short period of time. We usually divide inrush water into five categories: fault, surface, floor, collapse columns, and goaf seeper. China is a country that has experienced multiple mine water inrush accidents. According to the statistics, water inrush accidents in coal mine floors account for approximately 1/4 of the total number of various types of water inrush accidents in China, and such water inrushes often cause major catastrophic losses. Four influence factors are selected by Wang et al. (2012) and Li et al. (2014) as the evaluation indices: ① Geological structure index, including fault density, fault-water transmitting ability and fracture development degree; ② Hydrogeology index, which consists of confined water pressure, aquifer water property, karst development degree and water supply condition; ③ Floor aquifuge index, including aquifuge thickness, aquifuge strength and aquifuge integrity; and ④ Mining condition index, consisting of mining thickness, mining depth and inclined length of the mining face. As shown in Table 5, six cases introduced in Wang et al. (2012) and Li et al. (2014) are studied in this work. The value intervals of evaluation indices are shown in Table 6. We take the weights of evaluation indices as 0.109, 0.180, 0.143, 0.058, 0.042, 0.071, 0.049, 0.082, 0.059, 0.069, 0.026, 0.047 and 0.066. The confidence coefficient value is taken as 0.65. The evaluation results and comparison are shown in Table 7.

Table 5 Grading standards of floor water inrush evaluation indices (Wang et al. 2012; Li et al. 2014)

Table 6 ULV and LLV of floor water inrush evaluation indices (Wang et al. 2012; Li et al. 2014)

Table 7 Evaluation results of floor water inrush risks (k = 0.65)

The evaluation results of cases F① and F⑥ agree well with those derived from AMT (Li et al. 2014) and FMT (Wang et al. 2012), whereas the improved AIET performs conservatively again for cases F③ and F⑤. However, the cases of F① and F④ are deemed as high risk in the current study but are considered as medium risk in Wang et al. (2012) and Li et al. (2014).

4.3 Risk Assessment of Rock Burst in Deep-Buried Tunnels

Rock burst is a common dynamic failure phenomenon in construction of deeply buried underground engineering. Rock burst often causes serious damage to the excavation face as well as equipment damage and casualties and has become a worldwide problem in the field of rock underground engineering and rock mechanics. Chen and Li (2008) refer to eight influence factors as the evaluation indices for risk assessment in the current study, including brittleness coefficient, stress coefficient, liability index, linear elastic energy, surrounding rock classification, T criterion, RQD index and stress index, as shown in Table 8. This article primarily studies the engineering practice introduced in Chen and Li (2008). We take the weights of evaluation indices as 0.0774, 0.2437, 0.2322, 0.0774, 0.0808, 0.1063, 0.0892 and 0.0930. The confidence coefficient value is taken as 0.65. The value intervals of evaluation indices are shown in Table 9, and the risk results are shown in Table 10.

Table 8 Grading standards of rock burst evaluation indices (Chen and Li 2008)

Table 9 ULV and LLV of rock burst evaluation indices (Chen and Li 2008)

Table 10 Evaluation results of rock burst risks (cases S①–S⑨) (k = 0.65)

The evaluation results and comparisons shown in Table 9 indicate that the improved AIET is only successful in evaluating the risks of sections S①, S④, S⑤ and S⑨. The evaluation results of sections S②, S⑥and S⑧ derived from the improved AIET are slightly conservative, and the results of sections S③ and S⑦ are too conservative. The improved AIET performs conservatively for half of the rock burst cases in the current study. Figure 2 shows the statistical analysis chart of each evaluation result. The combinatorial arrangement of μ_j′x and μ_j′y is used to analyse the comprehensive attribute measure of 128 combinations. The analysis result of S② shows that there are 240 cases for which k₀ = 3 in the combination of μ_j′x and μ_j′y, the corresponding risk level is C₃. There are 16 combinations for which k₀ = 4, and the corresponding risk level is C₄. We can conclude that the probability of rock burst at the C₃ level is 93.75%, and the probability of rock burst at the C₄ level is 6.25%. The analysis result of S⑧ shows that there are 254 cases in which k₀ = 3 in the combination of μ_j′x and μ_j′y, and the corresponding risk level is C₃. There are 2 combinations with k₀ = 4, and the corresponding risk level is C₄. We can conclude that the probability of rock burst at the C₃ level is 99.2%, and the probability of rock burst at the C₄ level is 0.8%. For case S③, S⑥ and S⑦, the reliability index values are all 100%.

Fig. 2

Risk assessment result of rock burst in deep-buried tunnels

In addition, Zhang et al. (2010) also proposed an evaluation index system consisting of six influence factors, including uniaxial compressive strength, strength-stress ratio, brittleness coefficient, stress coefficient, liability index, and integrity index, as shown in Table 11. Combined with the case of attribute recognition analysis suggested by Zhang et al. (2010), the value intervals of the evaluation indices are shown in Table 12, and the risk results are shown in Table 13. The results are in good agreement with those derived from EM (Zhang et al. 2010).

Table 11 Grading standards of rock burst evaluation indices (Zhang et al. 2010)

Table 12 ULV and LLV of rock burst evaluation indices (Zhang et al. 2010)

Table 13 Evaluation results of rock burst risks (cases R①–R⑧) (k = 0.65)

4.4 Risk Assessment of Gas Outburst in Coal Mines

Coal and gas outburst is a powerful natural disaster in underground coal mining and is a serious threat to the safe production of coal mines. Because coal and gas outbursts can instantaneously explode large amounts of coal and gas streams into the working face of the excavation surface, these events cause severe destruction of the roadway facilities and the ventilation system. These events also fill wells in the nearby area with gas and pulverized coal, causing gas suffocation or coal flow that can bury people and might even cause coal dust and gas explosion and other serious consequences. The evaluation indices suggested by Wu and Yang (2011) and Yang et al. (2010), including mining depth, coal thickness, soft layer thickness change, coal seam inclination angle change, geological structure, sturdiness coefficient, maximum gas outburst initial velocity, dynamic phenomena and maximum gas pressure, are selected as the evaluation indices for risk assessment in the current study, as shown in Table 14. Combining the four cases introduced in Wu and Yang (2011) and Yang et al. (2010), we take the weights of evaluation indices as 0.152, 0.102, 0.081, 0.06, 0.015, 0.064, 0.247, 0.021 and 0.258. The confidence coefficient value is taken as 0.65. The value intervals of evaluation indices are shown in Table 15, and the risk results are shown in Table 16.

Table 14 Grading standards of coal and gas outburst evaluation indices (Yang et al. 2010)

Table 15 ULV and LLV of coal and gas outburst evaluation indices (Yang et al. 2010)

Table 16 Evaluation results of coal and gas outburst risks (k = 0.65)

The evaluation results and comparisons shown in Table 16 indicate that the evaluation results are generally in good agreement with those derived from the EM. For case G④, the reliability index value is 99%, and the values of the other three cases are all 100%.

5 Conclusions

• We propose a new comprehensive attribute measurement analysis method and attribute identification method. The novel characteristic of attribute interval evaluation theory is that the values of the evaluation indices are taken as intervals rather than unique values, and the single index attribute measure of the upper and lower limits is calculated separately. With further exploration and application of the evaluation method, we propose two calculation methods of the multiple index attribute measure. This method considers the complexity of underground engineering geological conditions and the uncertainty of risk and thus can better evaluate the project disaster risk.

• The risk assessment process of the improved AIET requires a large amount of calculations. Therefore, based on the original AIET software package, we develop new simple and practical NEW AIET software to overcome this shortcoming. We can complete the risk assessment process in a few seconds using the developed software.

• Engineering applications have been carried out to verify the accuracy and feasibility of the improved AIET for risk assessment of geological disasters, including water inrush, floor water inrush, rock burst and coal and gas outburst. Taking Jigongling Tunnel, Xiakou Tunnel and others as examples, the risk assessment of geological disasters in underground engineering was carried out. The evaluation results are consistent with the analysis results of other methods, which is consistent with the actual engineering excavation. Engineering application and verification show that the two multi-attribute attribute measurement analysis and identification method determination results can be analysed and evaluated for actual projects, and multiple methods can be used in comprehensive analysis in the evaluation process.