## 1 Introduction  
With the continuous increase in traffic in China, the scale of tunnels continues to increase and a large number of technical problems have been encountered during the construction and operation of tunnels. Most tunnels have varying degrees of issues, among which tunnel leakage is one of the most common, affecting the normal service use of tunnels [1, 2]. Although railway and highway mountain tunnels use a special anti-drainage system [3], quite a few tunnels face serious leakage soon after they are built, and in China, there is even a saying: \"ten tunnels and nine leaks\". An anti-drainage system may be damaged during construction and service, in which case, when the groundwater pressure is great, the water will penetrate the waterproof layer [4]. In this case, the waterproofing of the concrete lining becomes the key to the waterproofing of the entire tunnel project. Lining joints are undoubtedly the weak link in the waterproofing of lining structures [5]. To avoid water leakage through these joints, waterstops are generally used.  
However, in actual projects, it is often difficult to achieve the desired effect through waterstop waterproofing. To meet the requirements of tunnel waterproofing, scholars at home and abroad have made a lot of optimizations. Some scholars [6, 7, 8] believe that the existing waterstop structure is not reasonable enough, based on which the structure of the waterstop has been optimized. Some studies [9, 10, 11, 12, 13] indicate that improving the adhesion of waterstops to concrete can effectively improve its waterproofing performance. On the basis of the contact between the waterstop and concrete, some scholars [14; 15; 16] have proposed inflatable waterstops, bituminous surface waterstops, and flexible waterstops as options. According to [PERSON] [17], a proper waterstop profile is critical. The above analysis of the causes of failure of a waterstop is based on engineering experience, and there is no theoretical analysis of this, which makes it difficult to explain the rationality of its optimization measures.  
Some scholars [18; 19; 20; 21] have simulated the waterstop zone through finite element analysis, analyzing its stress and deformation characteristics. [PERSON] [22] simulated the deformation of the waterstop of the deformed seam of the pipe gallery, analyzed the stress characteristics of the waterstop under different working conditions, and optimized the structure of the existing waterstop. [PERSON] and [PERSON] [23; 24] simulated the drawing of rubber strips and the deformation of the optimized waterstop, and analyzed the stress characteristics of the waterstop. They adopted the method of binding or applying tangential friction to the contact between the waterstop and the concrete, but did not consider the adhesion of the waterstop and the concrete, which is more limited. At the same time, the extrusion effect of concrete on the waterstop was considered, nor was the failure mechanism of the waterstop waterproofing studied. Only the deformation stress characteristics of the waterstop were analyzed.  
In this paper, the buried rubber waterstop commonly used in the project is the research object, and the waterproofing principle of the waterstop, the bonding of the waterstop and concrete, the extrusion effect of the concrete pouring, etc., are taken into account to carry out the finite element analysis, study the failure characteristics, and propose the relevant optimization scheme to provide a reference for the optimization of the waterproof measures of the mountain tunnel joint.