# Prediction of Tunnel Face Stability Using a Naive Bayes Classifier
## 1 Introduction  
Face-stability analysis of tunnels has developed rapidly in recent years. At the construction stage, encountering face collapse is very likely for the tunnels driven in weak ground, such as clay [1], silt, and sand [2; 3], and for tunnels with large cross-sectional area [4]. The collapse of the tunnel face threatens the safety of workers, equipment, and adjacent structures, including buildings, bridges, piles [5], underground pipelines, and existing tunnels [6; 7]. Design work on the tunnel face involves the evaluation of its stability, the choice of reinforcement measures and the determination of related parameters [8; 9; 10]. The evaluation process should be conducted primarily to provide suggestions for subsequent design work. If the evaluation result indicates that the tunnel face cannot keep stable itself, it is necessary to take stabilization measures to prevent the collapse. Publications have presented various stabilization measures. For the close face tunneling method, support pressure can be applied via an earth pressure balance machine [11]. For the open face tunneling method, support pressure canbe applied by longitudinally installed face bolts [10]. Advanced reinforcement measures, such as forepooling [12] can be used to serve as a beam to reduce the vertical stress acting above the tunnel face. Ground improvement measures are also frequently used to improve the stiffness or strength of soil, aimed at improving the stability of the soil itself [13]. Beyond that, the cross-sectional area is regarded as a crucial factor that influences the stability of a tunnel face. Partial face excavation methods, such as center diaphragm (CD) method, center cross diaphragm (CRD) method, and pile-beam-arch (PBA) method [14], are more favorable than the full-face excavation method regarding the stability of a tunnel face. The existing methods that have been used for evaluations of tunnel face stability include limit equilibrium [15], limit analysis [16; 17], the displacement finite-element method [18], the discrete numerical method [19], scale model test [20; 21; 22], and centrifuge model test [23; 24; 25]. These methods have been proven to be useful in determining the limit support pressure and evaluating the effects of reinforcement measures. However, if the main concern is to figure out whether a tunnel face is stable or not, these methods are either too complicated, or too time-consuming, or both. In fact, there exists an easy-to-use indicator called the stable number, \(N~{}=~{}(\sigma_{s}+\gamma H-\sigma_{T})/c_{u}\), which can be used to estimate the stability of a tunnel face. In this equation, \(\sigma_{s}\) denotes the surcharge acting on the ground surface, \(\gamma\) is the unit weight of the soil, \(H\) is the depth to tunnel axis, \(\sigma_{T}\) is the support pressure applied at the tunnel face, \(c_{u}\) is the undrained cohesive strength of the ground prior to excavation [26; 27; 28]. Observations suggested that the tunnel face is deemed to be stable if the stable number \(N\) is less than or equal to 3 and deemed unstable if the stable number \(N\) is larger than 6. For cases where the stable number is within the range of 3 to 6, the tunnel faces can be regarded to be in a short-term stable state. Nevertheless, this method is only applicable for purely cohesive soil. As a result, an easy-to-use and more applicable method is expected to meet the demands of practical engineering, which usually requires a number of evaluations of tunnel face stability with great efficiency due to the varying values of the factors that influence tunnel face stability. Essentially, the task that aims to find out whether a tunnel face is stable or not can be treated as a classification problem, which can be solved by various machine learning algorithms like naive Bayes classifier. This algorithm greatly simplifies learning by assuming that features are independent of each other.