This paper deals with a finite element analysis of heat transfer with phase change in frozen soil in terms of the transient temperature field and the thermally induced solid-solid phase transformations. By analyzing the shortcomings of the traditional finite element method in solving the phase change problem and the characteristics of the freezing process in frozen soil, the extended finite element method was proposed to solve the heat transfer problem with phase change for permafrost engineering. Taking a quadrilateral element as an example, the extended finite element method interpolating function and solution format of the temperature field with phase change was derived. According to studies on constructing and solving the level set function, building of the stiffness matrix, and the subdivision of the elements, a program for heat transfer with phase change was proposed. The numerical solution is in good agreement with the measured value.

本文根据瞬态温度场和热致固-固相变，对冻土中具有相变的传热进行了有限元分析。通过分析传统有限元法在解决冻土中相变问题和冻结过程特性方面的不足，提出了扩展有限元法来解决冻土工程中相变传热问题。以一个四边形单元为例，导出了扩展有限元方法的内插函数和相变温度场的求解格式。根据有关构建和求解水平集函数，建立刚度矩阵以及元素细分的研究，提出了一种具有相变的传热程序。数值解与测量值非常吻合。