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为了深入研究土性参数空间变异性对环形多圈管冻结温度场的影响规律,将土体传热区域的导热系数、体积比热容及相变潜热模拟为随机场,基于随机场局部平均理论,建立了土性参数由点特性过渡到平面平均特性的方差计算方法。采用Neumann随机有限元法,自行研制了随机有限元程序,计算得到多圈管冻结温度场统计分布规律。结果表明:随机场及其局部平均理论能合理考虑土性参数空间上的不确定性;二维随机场三角形单元局部平均法能与三角形单元有限元法完美结合,随机场单元与有限元单元对应关系清晰,易于程序的编制;土性参数的随机性导致了冻结温度场分布的随机性;在本文条件下,形成的稳定冻结壁平均温度为-22.6℃,平均厚度为10.5 m,相应的变异系数均为0.224,井帮平均温度为-12.8℃,相应的标准差为2.4℃。
In order to study the effect of spatial variability of soil parameters on the freezing temperature field of annular multi-ring tube, the thermal conductivity, volume specific heat capacity and latent heat of the soil heat transfer zone are modeled as random fields. Based on the local average theory of random fields, The variance calculation method of the transition from the point characteristic to the plane average characteristic of the soil parameter is given. Neumann stochastic finite element method was used to develop a random finite element program to calculate the statistical distribution law of the temperature field of the multi-ring freezing tube. The results show that the stochastic field and its local average theory can reasonably consider the uncertainty of the spatial parameters; the local averaging method of triangles of two-dimensional random fields can be perfectly combined with the finite element method of triangular elements, The randomness of the soil temperature distribution leads to the randomness of the distribution of the freezing temperature. Under this condition, the average temperature of the stable frozen wall is -22.6 ℃ and the average thickness is 10.5 m. The corresponding variation The coefficients are 0.224, the average well temperature is -12.8 ℃, the corresponding standard deviation is 2.4 ℃.