A Multifront Problem of Freezing-Thawing Moist Soil

Abstract

Construction activities in the North of Western Siberia is carried out in specific conditions of the cryolithozone. The study of heat transfer processes in freezing soils near buildings is necessary to ensure their successful operation. Heat exchange with phase transition is traditionally described by Stefan problem, which is a system of differential equations of parabolic type with standard boundary conditions and a subsidiary condition on the phase transition boundary. It is possible to formally pass on to one equation of the conductivity type, but in that case the delta function appears in one of the coefficients. The delta function reflects the Joule heat release at the phase transition temperature. A widespread “pass-through counting” method reduces the Stefan problem to a boundary problem for a nonlinear heat conductivity equation. With this approach, the calculation results in a temperature field. But it is difficult to identify the position of the phase transition boundary on the temperature field. A large number of methods for solving the Stefan problem are developed, in which the required value is the phase transition front coordinate. The common disadvantage of these methods is their unsuitability for situations with several fronts, when these fronts appear and disappear, change the movement direction, merge with each other. The article presents a method for solving the Stefan problem, which allows to obtain the front coordinate as a zero isotherm. As an example this method is used to solve the problem of freezing-thawing of moist soil under the influence of seasonal surface temperature fluctuations. The method eliminates the need to control the evolution of each front. The Stefan problem is considered as a limiting case of the general phase transition problem in a certain temperature range. Standard transformations and application of Green’s function allow to write down a problem in the form of an integral equation. The approximate solution is obtained in the form of a recurrent formula.