关键词: 随机场, Monte-Carlo法, 立井井壁, 随机温度场

Abstract: To study the effect of uncertain factors on the temperature field of shaft wall, by modeling the parameters such as heat transfer coefficient, heat intensity, specific heat capacity and medium density as spatially random fields, an analysis of calculating the temperature field of vertical shaft wall adopting Monte-Carlo stochastic finite element method has been proposed based on the local average theory of random field. The mean of temperature response of finite element node, computational formulas of mathematical expectation, variance and variable coefficient have been given. According to the calculation steps, the stochastic finite element calculation program for solving the temperature field of vertical shaft wall has been compiled by the MATLAB software. An engineering example has been presented in order to demonstrate the effects of random field parameters on the temperature field of vertical shaft wall. These results have been compared with the results derived when the random parameters was only dealt with random variable. The results show that Monte-Carlo stochastic finite element method based on random field theory can consider the uncertainty of thermal parameters for shaft wall reasonably. Stochastic finite element calculation program compiled by MATLAB software can directly output the statistical results of the temperature field for shaft wall. The traditional certainty analysis about the temperature field of shaft wall has some defects. It will overestimate the variability when thermal parameters of shaft wall is simulated as single random variables. Therefore, the method based on random field theory is more scientific and reasonable.

Key words: random field, Monte-Carlo method, shaft wall, random temperature field