## 1 Introduction  
The deep foundation pit projects in the city are often surrounded by buildings, underground pipelines, subway tunnels, and others [1]. The excavation of deep foundation pits (DFPs) redistributes the groundwater level and stresses in the soil, changing the soil's original stress state, and negatively impacting the adjacent buildings, pipelines, and subway tunnels [2]. Therefore, the study of the effect of the foundation pit excavation process on the surrounding environment, especially on the adjacent existing subway tunnel, should not only consider the strength and stability of the foundation pit support itself, but also monitor and control its deformation to prevent harm to the normal use of the subway tunnel. The safety of DFP construction adjacent to existing underpass tunnels is subject to various risk factors. There is a coupling effect between risk factors, which will have a sudden, irreversible nonlinear impact on the whole DFP construction system, leading to an increase in the probability of occurrence of the risk and an increase in the severity of accident consequences, and this coupling risk will change to different degrees with the changes in coupling factors [3]. Although previous studies have analyzed the occurrence and evolution mechanism of the safety risk of construction accidents adjacent to existing underpass tunnels, the coupling mechanism within the evolution mechanism has received insufficient attention. Engineers only recognize the process and impact of a single risk in time and space, and ignoring the different kinds of safety risks in which a coupling effect can also occur increases the probability of dangerous accidents. Many scholars have carried out many related studies on similar geotechnical problems, resulting in numerous accomplishments. For instance, [PERSON] et al. [4] used machine learning models to predict the compressive strength of rocks and provide new insights into the rate-dependent strength of rocks. [PERSON] et al. [5] developed a new intelligent optimized back-analysis method, PSO-GP-FDM, to obtain the mechanical properties of the surrounding rocks of underground cavern groups. However, numerical simulation is still the most common method. In practical engineering, it is inevitable to encounter a substantial numerical simulation workload, affecting the timeliness of engineering decisions [6]. In addition, other traditional risk analysis methods have many limitations. For example, fuzzy hierarchical analysis (FAHP) is too cumbersome in the calculation process for the complex evaluation of multiple factors and levels [7]. Fault tree analysis (FTA) does not permit dynamic risk analysis [8; 9; 10]. For support vector machines (SVMs), the parameters are usually obtained by manual trials, often with a certain degree of subjectivity and blindness [11]. Neural networks (NNs) suffer from over-fitting problems [12]. Uncertainty is unavoidable when assessing and diagnosing the risk associated with deep foundation construction adjacent to existing underpass tunnels. Bayesian networks are a powerful tool for expressing uncertainty knowledge and reasoning about uncertainty, they have been widely used in reliability and risk analysis in many fields [13], and can compensate to some extent for the limitations of the above-mentioned traditional methods. For example, [PERSON] et al. [8] suggested that the relevant influencing factors are changing with the progress of shield construction. They developed a model for dynamic risk analysis using dynamic Bayesian networks (DBN) to support safety analysis in tunnel construction. Evaluating the risk of DFP construction adjacent to existing underpass tunnels also needs to consider the dynamic changes of influencing factors. However, the current dynamic Bayesian network (DBN) does not consider the coupling relationship between risk factors and cannot realize the dynamic control of coupled risks. The dynamic Bayesian network produces poor classification results when dealing with small probability risks [14].