Ensuring the stability of the excavation face is essential for tunnel excavation. Existing limit equilibrium models mainly adopt two-dimensional wedge mechanisms to estimate the minimum support force for tunnels, which cannot accurately represent the failure characteristics of practical tunnels. To address this limitation, a three-dimensional logarithmic spiral sliding model is developed based on the limit equilibrium method and strength reduction technique. The model introduces an equivalent area approach to represent heterologous sections and establishes the global moment equilibrium equation using the slice method. Taking the Huashansong tunnel as a case study, a parametric analysis is conducted on the reinforcement performance of end-anchored and fully bonded rock bolts. The results indicate that the diameter, strength, and density of bolts affect the stability of the excavation face, and the No. 11 end-anchored bolt and No. 37 fully bonded bolt are recommended. Furthermore, numerical simulation shows that the maximum extrusion deformation of the excavation face decreases from 11.57 mm without bolts to 9.13 mm and 8.46 mm for the No. 11 end-anchored bolt and No.37 fully bonded bolt, while tunnel convergence deformation decreases from 4.06 mm to 3.42 mm and 3.23 mm, respectively. The application of the No. 37 fully bonded bolt in the Huashansong tunnel controls the extrusion deformation and convergence deformation within 9.25 mm and 4.47 mm, ensuring the stability and economy of the tunnel excavation.