ANALYTICAL SOLUTION OF ONE-DIMENSIONAL TRANSIENT HEAT CONDUCTION EQUATION AND ITS APPLICATION

Exploring the temperature distribution characteristics of embankment and soil in shallow depth is of great significance to the rational design of embankment in permafrost areas. A one-dimensional transient heat conduction model is first established based on the actual temperature boundary conditions of shallow soil, and then the analytical solution is derived, which is verified through comparisons between numerical simulations and field test results. Careful inspection of the heat conduction process in multi-layered media found that the heat conduction problem resembled, to a certain extent, the wave problem in the reflection and transmission of heat conduction at the interface. This “temperature wave” phenomenon is explored through examining the formula as well as the calculated results of the analytical solution. It is found that this wave is always accompanied by obvious attenuation. In addition, further discussions are given with regard to the application of this analytical solution in the estimation of frost heave depth, determination of geometric similarities in related model tests and numerical simulation of "canopy effects".