## 1 Introduction  
The disasters that may occur during the excavation and construction of deep soft rock tunnels include the large deformation of soft rock, large collapse, sand burst collapse, high ground temperature, large water inflow, and so on. Large deformation of soft rock, high ground temperature, and large water influx are some common geological hazards encountered during the construction of deep soft rock tunnels. Large deformation of soft rock, large collapse, and sand burst collapse are often caused by improper construction methods, inadequate advance prediction and forecasting, and failure to discover adverse geological conditions. The deformation caused by the excavation of deep soft rock tunnels leads to significant unpredictability and uncertainty. Therefore, it is essential to quantitatively assess the disaster risks of deep soft rock tunnels using reliability theory. Using reliability analysis may be more reasonable to deal with the uncertainty and randomness of geotechnical parameters. Therefore, there have been many studies on the reliability of underground structure engineering in recent years [1; 2; 3; 4; 5; 6; 7]. A reliability analysis of deep circular tunnels reinforced with fully grouted bolts using a homogenization method was performed employing the first-order reliability method (FORM) and Monte Carlo simulation (MCS) [8]. The effects of the uncertainty of time-dependent mechanical properties of rock on the failure probability of a tunnel for a period of 100 years are studied by introducing the closed-form solution for a deep circular tunnel excavated within the viscoelastic Burger rock and supported by a double-layer concrete/compressible material, into the active learning reliability analysis method combining Kriging and MCS [9]. Through introducing the creep-damage theory, a time-variant reliability analysis procedure via the probability density evolution method is proposed for deep circular tunnels against delayed failure [10]. The commonly used structural reliability analysis methods include the stochastic reliability method, the response surface method, the first-order method [6; 7], and the second-order method in underground engineering [11; 12; 13; 14]. In addition, there are other innovative reliability analysis methods in tunnel engineering [15]. Surrogate numerical modelling techniques have recently been used to alleviate the computational burden and produce global response approximations. Surrogate models based on the augmented radial basis functions [16], hybrid particle swarm optimization neural network [17], XGBoost v1.4.0 [18; 19], and Bayesian entropy Gaussian process [20] have been used to evaluate the reliability of tunnels. The Kriging model is a Gaussian regression model with no parameters, which was used to calculate the reliability of tunnel engineering [3; 21; 22]. The reliability method in the framework of the Bayesian model update of the structural dynamic models using measured responses was implemented for high-dimensional model parameter spaces [23]. The system reliability of tunnels reinforced by rock bolts was analyzed through artificial neural networks and the improved hybrid method of the linear response surface method [24]. With further studies on the uncertainty in tunnel and underground engineering, reliability methods have been gradually applied. However, from the above analysis, we note that the reliability study in tunnel engineering of deep soft rock is still in the early stages, and most of the existing tunnel reliability calculation methods are proposed for circular tunnels [25]. These reliability methods make it difficult to evaluate large deformation disaster risks of non-circular deep soft rock tunnels. Using machine learning methods to establish a surrogate model of the nonlinear mapping relationship between geotechnical parameters and their responses such as displacement and support resistance of tunnels can significantly reduce the time needed for numerical calculations [26].