A Method for Calculating the Instability Probability in a Deeply Buried Tunnel Construction with a Hidden Karst Cave at the Bottom

In order to quantitatively assess the risk of deeply buried tunnel construction in the case of a hidden karst cave at the bottom of the tunnel, the first deeply buried tunnel construction failure model (PH−1) is firstly proposed based on the upper bound theorem of limit analysis and Protodyakonov’s theory. Thereafter, based on the upper bound theorem of limit analysis and the energy dissipation theory, the second deeply buried tunnel construction failure model (PH−2) is proposed. Furthermore, on the basis of the reliability theory, the dimensionless performance functions of each damage region under these two deeply buried tunnel construction damage modes are constructed. Finally, the instability probability of each damage region under the two damage modes is calculated using the Monte Carlo sampling method. This study suggests that the PH−1 failure model is not suitable for analysing the probability of instability in tunnel construction in hard plastic red clay strata, while the PH−2 failure model is appropriate for analysing the probability of instability in tunnel construction in hard plastic red clay strata. The worse the geological conditions, the larger the diameter of the cavern, the smaller the clearance between the cavern and the tunnel, and the greater the threat to safe tunnel construction.