Reliability assessment on stability of tunnelling perpendicularly beneath an existing tunnel considering spatial variabilities of rock mass properties

This paper presents a simplified procedure to evaluate the failure probability of crossing tunnels considering the spatial variabilities of rock mass properties. Numerical package FLAC(3D) (Itasca, 2017) was adopted to carry out extensive parameter studies for crossing tunnels. Subsequently, two limit state functions have been developed via the logarithmic regression to estimate the global factor of safety as well as the induced maximum settlement of the existing tunnel. The developed surrogate models were implemented into the Excel First-Order Reliability Method (FORM) spreadsheet to calculate the ultimate limit state failure and the probability that the threshold maximum settlement value is exceeded. The variance reduction technique is incorporated into the FORM analysis for considering the spatial variabilities of rock mass properties. Based on the reliability results, a sensitivity analysis was carried out to determine the critical design factor in construction of crossing tunnel. The proposed method provides an effective way to evaluate the safety and serviceability of tunnelling perpendicularly beneath an existing tunnel in spatial variable rock mass.