# Instability Risk Assessment for Deep Excavation of Soil-Rock Combinations Containing Groundwater
## 2 Models and Methods
### Overview of the Assessment Model  
The risk assessment model proposed in this paper comprises a risk factor selection model for identifying the most pertinent factors and an instability risk assessment model for gauging the extent of instability risk throughout a construction process. This is roughly divided into three stages when applied, namely stage 1 (factor selection), stage 2 (data handling), and stage 3 (risk assessment), and the detailed assessment process is shown in Figure 1.  
As shown in Figure 1, the potential factors affecting the stability of an excavation are first selected, based on analyzing the characteristics of a deep and large excavation with soil-rock combinations, and by combining the relevant specifications, literature research results, and the study of the risk mechanism. Then, the potential factors are screened, in order to construct an instability risk evaluate index system for deep and large excavation with soil-rock combinations, consisting of factors having a greater influence on the stability of the excavation, using a risk factor selection model. After that, we proceed to Stage 2, where the results of the data selection are verified for correctness. Data are not processed by LLE for dimensionality reduction unless the filtering is correct. Finally, in stage 3, the dimensionally reduced processed data are used as input data to the RBF neural network and are calculated to obtain the prediction results.  
In Stage 1, a factor selection model is used to filter potential risk factors. This is composed of a combination of AHP and entropy methods. The selection of factors is based on their combined weights. This combined weighting method can ameliorate the problems of missing factor selection and high subjectivity of weights [43], which was the reason for its selection. In this model, AHP is first used for initial screening of risk factors, followed by the calculation of subjective weights. Meanwhile, the objective weights of factors are obtained by combining the entropy method, in order to calculate their combined weights based on a comprehensive weighting method. The formula for calculating the combined weights weights is  
\[z_{i}=\alpha w_{i}+\gamma\beta_{i}(i=1,2,\cdots,n) \tag{1}\]  
\[\left\{\begin{aligned} &\alpha w_{i}w_{i}^{T}+\gamma w_{i}\dot{B}_{i}^{T}=w_{i}w_{ i}^{T}\\ &\alpha\beta_{i}w_{i}^{T}+\gamma\beta_{i}\dot{B}_{i}^{T}=\beta_{ i}\dot{B}_{i}^{T}\end{aligned}\right., \tag{2}\]  
where \(z_{i}\) is the combined weight, \(w_{i}\) and \(\beta_{i}\) are the subjective weight and objective weight, and \(\alpha\) and \(\gamma\) are the weighting coefficients. Indeed, calculating the combined weights is difficult when the number of risk factors is excessive. For this reason, prior to factor selection, this paper proposes pre-filtering the factors with the useful factor ratio (UR) to improve the efficiency of stage 1. The UR reflects the degree of importance of the different factors. It is introduced to quantify the survey results based on the judgment of industry experts on the reasonableness of the factor selection and to provide preliminary screening of possible factors influencing the risk. The formula for calculating UR is as follows:  
\[UR=\frac{n}{N}\cdot\lambda, \tag{3}\]  
where \(n\) is the number of group members who consider the factor essential, \(N\) is the total number of group members, and \(\lambda\) is the coefficient of variation, which takes the value of 0.9. UR values less than 0.4 indicate that the factor is unimportant and will not be involved in further calculations.  
In Stage 2 and 3, the risk assessment model is applied. It is composed of a radial basis function (RBF) network and local linear embedding (LLE) algorithm. In particular, these filtered factors are not counted unless they are confirmed as correctly selected through grey relational analysis (GRA).  
Figure 1: Evaluation process.