Stochastic analysis of uncertainty mechanical characteristics for surrounding rock and lining in cold region tunnels

The mechanical characteristics of tunnels in cold regions are uncertain because of the randomness of temperature field and mechanical parameters. Conventional forecast analysis is always deterministic, rather than taking stochastic temperature and parameters into account. This paper aims to investigate the stochastic mechanical characteristics of tunnel in cold regions on the basis of a stochastic analysis model and stochastic finite element method. A series of computer codes is compiled by Matrix Laboratory (MATLAB) software, and the stochastic mechanical characteristics for a tunnel in a cold region are obtained and analyzed by Neumann stochastic finite element method (NSFEM). The results provide a new method to predict the uncertain mechanical characteristics of tunnel in cold regions, and it shows that the stochastic temperature has an effect on stochastic stress for surrounding rock, and the major principle stress and minor principle stress are changeable in different times. The frost heave of surrounding rock leads to the increase of mean stress and mean displacement for lining while the thawing process leads to the decline of mean stress and mean displacement for lining. With the passage of time, the stress standard deviation and displacement standard deviation for lining show an upward trend, which imply that the results of conventional deterministic analysis for mechanical characteristic of tunnel lining may be farther from the true value. These results can improve our understanding of the uncertainty mechanical characteristics for tunnel and provide a theoretical basis for engineering reliability analysis and design in cold regions.