Abstract: In order to further investigate the effect of spatial variability of soil parameters on the temperature field of multi-circle-pipe freezing, this paper has proposed a method to calculate the plane average variance from just the point variance by simulating heat transfer coefficient, specific heat capacity and latent heat of phase transition as spatially random fields, and by means of the local average theory of random field. Based on Neumann stochastic finite element method, the stochastic finite element calculation program has been independently developed to figure out the distribution law of temperature field of multi-circle-pipe freezing. The results have shown that the random field and the local average theory can consider the variability of soil parameters reasonably. The two-dimensional triangular local average method can perfectly be combined with triangular finite element method, and the corresponding relation is clearer, and the program is simpler to compile. The randomness of soil parameters results in the randomness of temperature field. In this paper, the mean temperature and the average thickness of stable frozen wall are -22.6 ℃ and 10.5 m. Both of their variable coefficients are 0.224. The mean temperature of shaft-lining is -12.8 ℃ and its standard deviation is 2.4 ℃.

Key words: variability of parameters, multi-circle-freezing pipe, temperature field, stochastic finite element method