Stochastic analysis for the uncertain temperature field of tunnel in cold regions

In cold regions, the temperature is important to determine the stability of tunnel construction. However, the conventional finite element methods for stability analysis are always deterministic, rather than taking stochastic parameters and conditions into account. In this paper, the boundary conditions are considered as stochastic processes and the rock properties are considered as random fields. A stochastic analysis for the uncertain temperature characteristics of tunnel is presented. The stochastic finite element formulae are obtained by Neumann stochastic finite element method (NSFEM), and the stochastic finite element program is compiled by Matrix Laboratory (MATLAB) software. Using our program, the random temperature fields of a tunnel in a cold region are obtained and analyzed. The results show that the temperature of a large quantity of frozen surrounding rock is stochastic, and it is bad for the thermal stability of actual tunnel engineering in cold regions. The distributions of mean temperature are the same and the distributions of standard deviation are similar for the two cases in this paper. The average standard deviation increases with time, which implies that the results of conventional deterministic analysis may be far from the true value. These results can improve our understanding of the random temperature field of tunnel and provide a theoretical basis for actual engineering design in cold regions.