Uncertainty analysis of rock tunnel based on fractional moment and dimensional reduction method

Abstract

In this study, fractional moment was adopted to estimate the uncertainty in a tunnel excavated in rock. The multiplicative dimensional reduction method (M-DRM) was adopted to approximate the relationship between random variables and response of the tunnel and to predict its behavior. Integer and non-integer (fractional) moments were estimated by Gaussian quadrature based on M-DRM. The maximum entropy principle was also used to estimate the probability distribution of the tunnel response using the optimization technology of Excel Solver based on fractional moment. The example of a circular tunnel in a rock mass subjected to hydrostatic stress is given. This demonstrates the uncertainty analysis procedure applied to the displacements and plastic zone induced by the excavation, for different rock-support pressures and far-field stresses. Statistical moment, standard deviation and probability distribution of the tunnel response all agree well with Monte Carlo simulation (MCS). M-DRM closely approximates the tunnel response, and improves the efficiency of the uncertainty analysis. The proposed method estimates the probability distribution based on frictional moment without any prior knowledge. The results show that the proposed uncertainty analysis method is robust, efficient and precise, and is suitable for a complex practical engineering system as encountered in rock engineering.