## 1 Introduction  
At the current rate of mine expansion, more than 30% of the metal mines in China will enter into the deep mining category (i.e., a mining depth greater than 1000 m) by the end of 2025. This indicates that the exploitation of deep mineral resources will become commonplace in China [1, 2, 3]. Under high ground stress conditions in deep metal mines, frequent and strong blast disturbances can lead to the spalling and collapse of the rock surrounding tunnels. For example, more than 20 m of the roadway in the Hongtoushan copper mine, one of the deepest nonferrous metal mines in China, was damaged by blasting disturbance at a mining depth of 1000 m [4]. In the Dongguanshan copper mine, large-scale collapses in deep tunnels were induced by high ground stress and frequent blasting. In the Jinchuan No. 2 mine, the combined effects of high geo-stress and horizontal tectonic stress resulted in the large-scale deformation and failure of the rock mass, and more than 56% of the deep tunnels have serious damage from collapse, where the maximum convergent deformation can reach 500 mm [5]. In the Ashele copper mine, tunnel collapse and the burial of drilling equipment lead to a long interruption of production. As such, a quantitative risk assessment for deep tunnel failure should be carried out to ensure the safety of workers and equipment (e.g., targeted support measures and systematic mining process optimization). The deep metal mines have many unique characteristics. First, the mining system is very complex, with the tunnel and shaft arranged in three-dimensional space that can extend thousands of meters horizontally and vertically. Second, several dozens of stopes can be actively mined at different depths, producing a complex and dynamic stress field that can ultimately lead to rock mass failure. Third, for high-production mines, especially those that use medium-length hole blasting or long-hole blasting, the explosives used can weigh several hundred kilograms or even several tons, which will cause extremely strong blast disturbance. Compared to the coal mines, which have a layered structure and use mechanized mining methods, or civil tunnel engineering, which has a linear structure and is excavated by either a smaller amount of explosive or a tunnel boring machine, the characteristics of the rock mass failure in deep metal mines are more complex and uncertain in terms of time, space, frequency, and intensity. Thus, to better assess the risk of the tunnel failure in deep metal mines, it is necessary to consider a variety of parameters and utilize a mathematical method that can evaluate both the probability and uncertainty of rock mass failure. As there are many inducing factors and evaluation indicators for tunnel failure in metal mines, a reasonable index system is necessary to ensure the accuracy of tunnel failure risk assessment. The geological condition is used to refer to the internal cause for tunnel failure (e.g., lithology and in situ stress), and thus multiple geological indicators have been commonly used to study the rock mass stability or predict rock mass hazards [6, 7, 8]. Mining disturbances are common external triggers for tunnel failure. Under high in-situ stress conditions, during the mining process, rock masses are inevitably subjected to frequent disturbances that can be classified into unloading effects (i.e., the stress change in the surrounding rock mass after the ore is mined) or dynamic disturbances (e.g., blasting). Many scholars have conducted systematic studies on the characteristics of tunnel failure due to mining disturbances and indicate that tunnel failure and mining disturbances are highly correlated [9, 10, 11, 12, 13]. Moreover, rock mass responses during tunnel failure, such as the amount of displacement, wave velocity change, microcrack generation, and propagation, are also important indexes for evaluating the stability of the tunnels.