Reliability analysis of horseshoe tunnels by radial-based importance sampling method based on complex function displacement solution

Tunnel reliability analysis is an important analytical method to ensure tunnel safety. In this paper, the plane elastic complex variable function theory is adopted, and the explicit displacement function of the horseshoe-shaped tunnel vault is derived through conformal mapping. This function is verified by ABAQUS numerical analysis, and the correctness of the derivation is further confirmed by degenerating it to a circular tunnel. Subsequently, based on this explicit displacement function, a comparative analysis is conducted on four methods: the advanced first-order second moment (AFORM) method, Monte Carlo sampling (MCS) method, importance sampling (IS) method, and radial-based importance sampling (RBIS) method. The results show that the RBIS method has higher calculation accuracy and better efficiency. Finally, considering the influences of the mean value of load, load variation coefficient, and surrounding rock parameters, the reliability of the horseshoe-shaped tunnel and the circular tunnel is compared and analyzed based on the derived explicit function. It is found that except for the lateral pressure coefficient, the two types of tunnels are similar in terms of the sensitivity of other parameters and the influence laws of parameters on reliability. The research results can provide a reference for the analogical design and analysis of horseshoe-shaped tunnels and circular tunnels.