Modified AK-MCS method and its application on the reliability analysis of underground structures in the rock mass

This work aims at proposing the methodology on the basis of the extension of the famous reliability analysis, joining the Kriging and Monte Carlo Simulation (AK-MCS) metamodeling technique for analyzing the long-term stability of deep tunnel support constituted by two layers (a concrete liner covered with a compressible layer). A novel active learning function for selecting new training points enriches the Design of Experiment (DoE) of the built surrogate. This novel learning function, combined with an appropriate stopping criterion, improves the original AK-MCS method and significantly reduces the number of calls to the performance function. The efficiency of this modified AK-MCS method is demonstrated through two examples (a well-known academic problem and the case of a deep tunnel dug in the rock working viscoelastic Burgers model). In these examples, we illustrate the accuracy and performance of our method by comparing it with direct MCS and well-known Kriging metamodels (i.e., the classical AK-MCS and EGRA methods).