## 5 Guiding Significance for Engineering  
Through the above analysis, the deformation characteristics of the surrounding rock of the tunnel undercrossing multi-situational gosfs were obtained. The maximum values of horizontal convergence at the arch waist, numerical settlement at the vault, and axial force of the initial support under various goaf situations are shown in Figure 18c-e. Situations 1-4 correspond to I-1-I-4; situations 5-8 correspond to II-1-II-4; and situations 9-12 correspond to III-1-III-4, respectively. Figure 18c shows that after increasing the distance between goaf situations I-1-I-3 by 10 m, the vertical displacement difference is 0.84 mm, and after further increasing the distance by 5 m from I-3 to I-4, the vertical displacement difference is 1.36 mm. The vertical displacements for the four situations decrease by 2.6%, 6.8%, and 18.0%, respectively, indicating that as the distance increases, the impact of the goaf area on vertical displacement gradually diminishes. Figure 18d,e show that the trends of horizontal convergence and maximum axial force of the initial support are similar to the vertical displacement deformation trend. The distance in the range of 5-15 m has the greatest impact on tunnel stability. When the distance exceeds 15 m, the impact gradually decreases. Therefore, it can be inferred that in this case, the goaf area affects the deformation of the surrounding rock up to a distance of about 15 m, which is approximately 1.13 times the tunnel span. Figure 18c-e show that the impact of different diameters on the stability of the surrounding rock follows a similar increasing trend; the larger the goaf scale, the greater the impact on the stability of the surrounding rock. As shown in Figure 18c, an increase in the angle of the goaf area results in a decreasing impact on the vertical displacement of the surrounding rock, whereas the impact on the horizontal displacement and the maximum axial force of the initial support is the opposite. That is, the greater the angle, the larger the horizontal displacement and maximum axial force of the initial support, with the horizontal displacement trend increasing first and then decreasing. In this case, when the angle is less than 45\({}^{\circ}\), as shown in Figure 18c, the settlement at the tunnel crown is larger; when the angle is greater than 45\({}^{\circ}\), as shown in Figure 18d,e, the impact of the goaf area on the horizontal convergence of the surrounding rock is significantly reduced. In the tunnel line selection, the tunnel should be kept as far away from the goaf area as possible. However, if it is unavoidable for the tunnel to cross the goaf area in practical engineering, the distance should be maintained at more than 1.13 times the tunnel span, or auxiliary measures such as reinforcement should be adopted to ensure the safety and smooth progress of the project. In the design of the tunnel support scheme, different support schemes should be designed according to the location and direction of different goafs to ensure the stability of tunnel construction and operation, which means that excavation support needs to be more flexible to adapt to different conditions of the goaf tunnel surrounding rock. The above-mentioned deformation characteristics of the surrounding rock can effectively guide the safe construction of tunnels undercrossing goaf areas, as illustrated in Figure 18. Firstly, the location of the goaf area at the tunnel construction site is determined based on physical detection and drilling results, as shown in Figure 18a,b. Figure 18a presents the resistivity profile image of the Huaying Mountain High-Speed Railway Tunnel site, where the cavity shown is part of a goaf within the mountain. Figure 18b shows the drilling process of the CASAGRADNE-C\(\alpha\)xp-2 multi-functional drilling rig at the Huaying Mountain High-Speed Railway Tunnel site. After combining physical detection and drilling to determine the location of the goaf area, the corresponding reinforcement measures can be designed.