A temperature behavior of frozen soils: Field experiments and numerical solution

On the basis of the field (natural) measurements, which were carried out by the authors in cold regions such as Siberia in The Russian Federation, the temperature distributions and the phase front propagation are analyzed during thawing process in frozen soils (permafrost).The treatment of the experimental data was carried out on the basis of the likeness and dimensionality theory. In this way the temperature distribution as a function of the dimensionless values (criteria), characterizing the geometry of the calculation domain, thermo-physical properties of the soils and also level of the phase transitions — a criterion of Stefan was to be obtained in general form. The treatment of the experimental measurements in obtained general dimensionless form shows that the natural measurements for a wide range of both the soil surface temperature variation and thawing depth group near certain universal curves for the loamy and sandy soils, respectively. These curves may be approximated by the dimensionless self-similar function with a parameter which depends on the thermal and physical properties of the soil massif. By the method of linear regression the dependence of the front penetration coordinate on time is obtained and discussed in detail. It is shown that this dependence is different from the self-similar solution. The phase front propagation described by generalized approximation function obtained in this study is in good agreement with experimental data.On the basis of the nonlinear system of equations (general Boundary Value Problem) corresponding to the considered problem, the numerical solution for the temperature distribution in the soil is presented. For the temperature distribution the good agreement between experimental measurements and numerical solution is observed.

► The field measurements on the temperature behavior of frozen soil are presented. ► General dimensionless form for the treatment of experimental data is obtained. ► It is shown that the temperature distribution is approximated by self-similar function. ► It is proved that the law of front movement is different from self-similar solution. ► The obtained generalized numerical solution is close to the experimental data.