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Mathematical Problems in Engineering
Volume 2018, Article ID 1450683, 8 pages
Research Article

Probabilistic Analysis of Tunnel Face Stability below River Using Bayesian Framework

1School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China
2Jiangxi Science and Technology Normal University, Nanchang 330013, China
3ARC Centre of Excellence for Geotechnical Science and Engineering, University of Newcastle, Callaghan, NSW 2308, Australia
4School of Civil Engineering and Architecture, Nanchang Institute of Technology, Nanchang 330099, China

Correspondence should be addressed to Lina Hu; nc.ude.ucn@aniluh

Received 28 February 2018; Accepted 10 May 2018; Published 6 June 2018

Academic Editor: Eric Feulvarch

Copyright © 2018 Weiping Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A key issue in assessment on tunnel face stability is a reliable evaluation of required support pressure on the tunnel face and its variations during tunnel excavation. In this paper, a Bayesian framework involving Markov Chain Monte Carlo (MCMC) simulation is implemented to estimate the uncertainties of limit support pressure. The probabilistic analysis for the three-dimensional face stability of tunnel below river is presented. The friction angle and cohesion are considered as random variables. The uncertainties of friction angle and cohesion and their effects on tunnel face stability prediction are evaluated using the Bayesian method. The three-dimensional model of tunnel face stability below river is based on the limit equilibrium theory and is adopted for the probabilistic analysis. The results show that the posterior uncertainty bounds of friction angle and cohesion are much narrower than the prior ones, implying that the reduction of uncertainty in cohesion and friction significantly reduces the uncertainty of limit support pressure. The uncertainty encompassed in strength parameters are greatly reduced by the MCMC simulation. By conducting uncertainty analysis, MCMC simulation exhibits powerful capability for improving the reliability and accuracy of computational time and calculations.