## 1 Introduction  
The environmental protection requirements of tunnels have become increasingly stringent in recent years because the amount of land resources is decreasing. Small clear-distance tunnels are widely used in highway tunnels because of their unique advantages, such as minimal environmental damage, minimal land occupation, beautiful appearance, and convenient route planning [1; 2]. During the construction of small clear-distance tunnels, the middle rock pillar must have sufficient strength and stability [3], and the independence and integrity of the surrounding rocks and lining systems must be maintained. Different from general separated tunnels, the disturbance of the two adjacent tunnels of a small clear-distance tunnel exerts a great impact during construction. After antecedent tunnel excavation, the initial stress conditions of the surrounding rock are changed, and the excavation of the rear tunnel is affected. The excavation of the rear tunnel can easily cause the deformation of the middle rock pillar, which is not conducive to the stability of tunnel construction [4; 5; 6]. Therefore, the construction safety of small clear-distance tunnels cannot be ignored. Extant research on small clear-distance tunnels at home and abroad has mainly adopted mechanical analysis, field monitoring, model testing, and numerical simulation. On the basis of complex variable theory, [PERSON] et al. [7] studied the analytical solutions of deformation, displacement, and stress of double parallel tunnels in the elastic half-plane based on the complex theory. Considering the radial stress at the tunnel boundary, [PERSON] et al. [8] proposed an analytical expression for calculating the stress and displacement around two parallel deeply buried tunnels using the Schwarz alternating method. [PERSON] et al. [9] derived the surrounding rock stress and displacement of a shallowly buried, twin-parallel tunnel in consideration of the uniform radial stress boundary condition. To study the influence of different tunnel clear distances and surface slopes on the surrounding rock pressure of complex, eccentric, shallow-buried, small, clear-distance tunnels, [PERSON] et al. [10] used the design specifications for highway tunnels, established a surrounding rock pressure calculation model, and deduced the theoretical calculation formula of tunnel surrounding rock pressure. On the basis of the actual slip surface of a tunnel, [PERSON] et al. [11] established a load calculation model for small clear-distance tunnels and proposed a calculation method for the surrounding rock pressure of small clear-distance tunnels. In terms of model tests, [PERSON] et al. [12] established a tunnel excavation simulation test system under typical asymmetric loading and applied this system to analyze the failure mechanism and load characteristics of the surrounding rock of a small, clear-distance, shallow-offset tunnel. [PERSON] et al. [13] designed a physical test model of a shallow-buried, bias-pressure, small, clear-distance tunnel with a ratio of 1:10 and conducted a large shaking table test to study the influence of seismic wave type and acceleration excitation peak value on the strain response law of the tunnel lining. In terms of field measurement, [PERSON] et al. [14] analyzed the influence of different middle rock pillar reinforcement methods on surrounding rock stability by examining the Fukuoka Metro Line 3 Project and combined on-site monitoring and measurement data. However, the field tests only focused on specific projects and lacked a systematic summary of the monitoring data. Numerical simulation has the advantages of low time consumption, low cost, and high calculation precision, and it has been widely used in the calculation of small clear-distance tunnels. [PERSON] et al. [15] studied the influence of the excavation sequence and lag distance on the load transfer mechanism and mechanical behavior of a small clear-distance tunnel. [PERSON] et al.