## 1 Introduction  
Karst is a general term for karst action and karst landforms. Karst areas are mainly concentrated in the southwest of China, such as Sichuan, Guizhou, and the Yunnan Province [1]. In recent years, with China's fast-developing transport industry, major transportation programs such as highways and railroads in China have moved to the karst area in the west with complex topographic conditions [2]. Among them, a large number of mountain-tunneling projects with deep burial and high pressure have emerged, which are accompanied by many risk factor and lead to many risk accidents (Figure 1). When a tunnel is being built, the rock properties are easily affected by high ground water pressure, high temperature, high ground stress, and so on [3]. Water inrush, as well as rock bursts, gas explosions, and other disasters inevitably occur. The types and frequency of disasters in tunneling construction are shown in Figure 2[4]. It is shown that the percentage of water inrush accounts for 45% of other disasters. It will not only cause economic losses such as machine damage but also cause significant casualties [5]. Therefore, it is essential to evaluate and control the water inrush risk in tunnel construction. Lots of researchers have conducted extensive studies in this field. [PERSON] et al. [6] study the evolution mechanism of water inrush in tunnels. [PERSON] et al. [7] used the analytic hierarchy process (AHP) for risk assessment in karst tunnels. [PERSON] et al. [8] used the fuzzy wavelet neural network for the evaluation of water inrush. [PERSON] et al. [9] used the GIS method to evaluate the tunnel water inrush of the hydropower station in the Sichuan Province. [PERSON] et al. [10] used the set pair analysis (SPA) method to construct the water inrush evaluation model. [PERSON] et al. [11] used gray theory to evaluate the water inrush risk of tunnels. [PERSON] et al. [12] applied FAHP and fuzzy set theory for water inrush assessment in the Guangdong Province. [PERSON] et al. [13] used a fuzzy Bayesian network for risk control in tunnels. [PERSON] et al. [14] applied a new cloud model in the Longinixt Tunnel. Previous research has obtained good results. However, each theory or method has its shortcomings. For example, the AHP method is susceptible to human subjectivity and the results of the fuzzy comprehensive evaluation method are fuzzy, and the neural network algorithm requires a lot of time and mass data. The GIS approach ignores the impact  
Figure 1: Total deaths and injuries of mountain tunnel construction varying from 2010–2017 in China. Figure 2: Types and percentage of disasters in tunneling construction. of the complexity of water inrush. In addition, the interaction of the indicators is not considered. In this paper, seven indicators were selected, and four risk levels were divided to establish an evaluation system for water inrush. Additionally, considering the mutual influence relationship of each factor, the index constant weights are obtained using a multi-factor interaction matrix (MFIM), and the impact factor among the evaluation indicators is determined using the C-OWA operator. The variable weight is determined using the variable weight theory. An improved non-linear attribute identification variable weight model was established for water inrush evaluation by using the nonlinear trigonometric function to optimize the traditional linear function. The model is applied to the Qiyueshan Tunnel. The results of the risk levels of six sections are II, II, II, I, II, and II. The average risk level of the tunnel is II. Additionally, the model is validated using actual engineering cases, and the results agree with engineering situation and other methods. Figure 3 expresses the risk assessment flowchart. The structure of this paper is as follows. Section 1 mainly introduces the research objectives, background, and some common evaluation methods of tunnel water inrush. Section 2 introduces the method of this paper in detail. Section 3 mainly introduces the evaluation system and risk grade classification.