一种冻土温度场方程的解析解

Analytical solution for the temperature field equation of frozen soil

摘要:

冻土在我国分布十分广泛,冻胀现象是冻土区经常出现的问题,其导致的工程病害屡见不鲜。冻胀主要是由土体内部温度变化及水分迁移造成的,是一类极其复杂的温度、渗流及应力多场耦合问题。通过对冻土中的温度场进行分析,求解含冰量及孔隙率随温度变化条件下的冻土一般性瞬态热传导方程,获得其近似解析解并应用于冻土热传导过程的预测。通过与有限元计算所得精确解对比,验证其有效性。研究成果对冻土冻胀问题的深入研究具有一定的理论和实践意义。

Abstract:

Frozen soil is widely distributed in China. As a common problem in frozen soil areas, frost heave frequently causes engineering diseases. Frost heave, which is mainly formed by the temperature change and water migration in the soil during freezing and thawing, is an extremely complex multifield coupling problem of temperature, seepage, and stress. In this paper, the general transient heat conduction equation of frozen soil under the changes of ice content and porosity with temperature was solved by analyzing the temperature field in frozen soil, and its approximate analytical solution was obtained and applied to predict the heat conduction process of frozen soil. Compared with the exact solution obtained from finite element calculation, the effectiveness of the analytical solution was verified. The research results show certain theoretical and practical significance for the intensive study of the problem of frost heave in frozen soil.