Efficient and accurate methodologies for MCS-based probabilistic analysis of tunnel face stability

Abstract

This paper proposes two strategies to perform efficient and accurate MCS-based probabilistic analysis of tunnel face stability. The first strategy takes the samples that have been evaluated by three-dimensional (3D) numerical simulations as classifiers to evaluate the MCS samples generated from the statistical parameters of uncertain variables. The number of 3D simulations can be significantly reduced to only 1 % or even 1‰ because most MCS samples are evaluated by the classifiers. This method is accurate because no approximation has been made in the evaluation process. The second strategy uses a previously established training dataset to construct an ensemble of metamodels to classify the MCS samples. Backpropagation Neural Network (BP) is utilized to construct a regression metamodel to predict the safety factors of each sample; the samples that are predicted to be near the limit state will be further evaluated by an adaptive classification metamodel constructed by the combination of K-Nearest Neighbor (KNN) and Support Vector Machine (SVM). KNN is used to search k training samples that have the smallest distances with the unknown sample, whereas SVM is used to construct a classification model to classify this sample using the k training samples. This strategy is much more efficient since a probabilistic analysis can be completed within a few seconds. Several illustrative examples are used to demonstrate the applications. Results show that the failure probabilities predicted by the ensemble of metamodels compare well with those determined according to direct MCS-based 3D numerical simulations, implying that the ensemble of metamodels is also accurate.