Neumann stochastic finite element method for calculating temperature field of frozen soil based on random field theory

Abstract

To study the effect of uncertain factors on the temperature field of frozen soil, we propose a method to calculate the spatial average variance from just the point variance based on the local average theory of random fields. We model the heat transfer coefficient and specific heat capacity as spatially random fields instead of traditional random variables. An analysis for calculating the random temperature field of seasonal frozen soil is suggested by the Neumann stochastic finite element method, and here we provide the computational formulae of mathematical expectation, variance and variable coefficient. As shown in the calculation flow chart, the stochastic finite element calculation program for solving the random temperature field, as compiled by Matrix Laboratory (MATLAB) software, can directly output the statistical results of the temperature field of frozen soil. An example is presented to demonstrate the random effects from random field parameters, and the feasibility of the proposed approach is proven by comparing these results with the results derived when the random parameters are only modeled as random variables. The results show that the Neumann stochastic finite element method can efficiently solve the problem of random temperature fields of frozen soil based on random field theory, and it can reduce the variability of calculation results when the random parameters are modeled as spatially random fields.