Abstract: The subject of this research is automobile roads in permafrost zones, which are subject to the negative effects of cryogenesis. The focus of the study is on thermal insulation coatings based on mixtures of insulating and heat-accumulating construction materials. The work aimed to determine the area of economic efficiency of using mixtures of construction thermal insulation materials in road pavement structures for the cryolithozone. One possible option for reducing the construction costs of roads in the cryolithozone is the use of thermal insulation layers in road pavements made from thermal protection mixtures, which consist of a heat-accumulating binder (such as sand or gravel) and a heat-insulating filler (expanded clay, azurite, polystyrene granules, or glass debris). The influence of the thermal-physical characteristics of the binder and filler on the economic viability of using thermal insulation mixtures in road pavements has been investigated. To facilitate the analysis, two new dimensionless simplexes have been introduced. The thermal-physical simplex characterizes the ratio of the thermal conductivity coefficients of the filler and binder. The economic simplex characterizes the ratio of the cost per unit volume of the filler to the cost per unit volume of the binder. A target function has been constructed, allowing for the calculation of the conditions under which the ratio of the cost of filler to the cost of binder makes the use of material mixtures (compared to a homogeneous equivalent layer of binder with respect to thermal resistance) economically efficient. Basic quantitative patterns have been obtained, characterizing the relationship between the concentration of the filler and the dimensionless simplexes: thermal-physical and economic. A dependency has been derived for determining the limiting value of the dimensionless cost simplex, enabling the identification of the boundary of economic efficiency when using thermal insulation mixtures with varied thermal and physical properties. It has been shown that thermal insulation material mixtures can be recommended as an economically efficient alternative to homogeneous construction materials when designing road pavements. A 3D graph has been constructed to quickly assess the conditions under which the specific cost simplex value makes it advisable to apply a particular thermal insulation binary mixture in road pavements.

Abstract: The subject of the research was the functional dependence of the thermal conductivity coefficient of snow on density at various temperatures. The goal of the research was to establish a connection between the dimensionless value of the thermal conductivity coefficient (the thermal conductivity simplex) and the dimensionless value of density (the density simplex) of snow. To obtain dimensionless parametric criteria (simplexes), the thermal conductivity coefficient and the density of ice were used as scale units, which are generally a function of temperature. The dependence of the thermal conductivity coefficient and the density of ice on temperature was examined in detail, represented as linear functional relationships. Special attention was given to the assessment of errors that arise from linearizing functional dependencies and averaging the original data. The classic formula of G.P. Abels was used as the basic functional dependence of the thermal conductivity coefficient of snow on density. The method of natural scales was used to obtain parametric criteria (simplexes) of the thermal conductivity coefficient and the density of snow, allowing the conversion of dimensional physical quantities to dimensionless parameters. The average values of the thermal conductivity coefficient and the density of ice within a specified temperature range were used as scale units. Using the method of natural scales, parametric criteria (simplexes) of the thermal conductivity coefficient and density of snow were obtained. Based on the classic formula of G.P. Abels, a functional relationship was established between the found parametric criteria, which can be formulated as follows: "The simplex of the thermal conductivity of snow is equal to the square of the simplex of its density." This regularity has been obtained for the first time and defines the scientific novelty of the theoretical research conducted. Using the dependence of the thermal conductivity coefficient and the density of ice on temperature, it is easy to determine the influence of temperature on the change of the thermal conductivity coefficient of snow concerning density with known values of the simplexes. An assessment was made of the errors that arise when averaged scale units are used in calculations. It was shown that averaging the original quantities does not lead to errors larger than the acceptable values adopted in engineering practice. For example, the error in determining the proportionality coefficient between the simplexes of thermal conductivity and density varies from ±9.0% in the temperature range from 0 to -40°C. In the most realistic range of temperature change for snow (from -5 to -20°C), the average error does not exceed 3.0%.

Abstract: The subject of the study is the snow cover, which determines the formation of the thermal regime of soils in winter. The purpose of the work is to determine the depth of the zone of thermal influence of the surface in the snow cover. That is, the determination of the zone of temperature fluctuations (daily, decadal) in the snow cover when the temperature of the atmospheric air changes. Determining the depth of this zone is important both for taking into account the formation of the properties of the snow cover itself, and for choosing a method for modeling the process of thermal interaction of the atmosphere with the ground in the presence of snow cover. In particular, the possibility of taking into account snow cover as thermal resistance in modeling thermal processes. To assess the depth of thermal influence, the well-known Goodman formula was used, obtained by solving the corresponding problem of thermal conductivity by the integral method and representing the dependence of the depth of the zone of temperature change in a solid with an abrupt change in surface temperature on time and thermal conductivity of the material (in this case, snow of a certain density). To determine the thermal conductivity, the formulas of Abels and Osokin were used to determine the thermal conductivity coefficient of snow depending on density. At the same time, it was taken into account that the density of snow cover is a variable in depth, determined by the linearized Abe formula. Alternatively, a snow cover with a density equal to the average integral density in depth is considered. Dependences are obtained to determine the duration of the attenuation period of surface temperature fluctuations at a certain depth of snow cover. An indicator of the change in the depth of vibration attenuation (the depth of thermal influence) is proposed. To assess the effect of snow reclamation, a formula is proposed that allows us to determine the degree of change in the duration of the period of complete attenuation of temperature in depth during compaction of snow cover, depending on the compaction coefficient. A dependence has been obtained linking the depth of the zone of thermal influence with the duration of the period of daily temperature fluctuations on the surface of the snow cover and its density. Comparison of the calculated data according to the obtained formulas with the data on the depth of attenuation of daily temperature fluctuations in snow cover with different snow densities, given in the literature, showed good convergence. This allows us to recommend the obtained formulas for practical use in assessing the process of formation of the thermal regime of snow cover.

Abstract: The aim of the work is to obtain generalized simple formulas for calculating the coefficient of thermal conductivity of snow cover when calculating its thermal resistance. To achieve the goal, a comparison was made of the parabolic formula of N.I. Osokin, obtained on the basis of generalization and correlation analysis of existing dependencies for calculating the coefficient of thermal conductivity having fractional coefficients, with its simplified version with integer coefficients. Based on the linearization of the base Simple linear formulas for determining the coefficient of thermal conductivity depending on the density of snow for two characteristic density ranges (200-300) and (300-400) kg/m3 were also obtained. The percentage errors in the calculations of the coefficient of thermal conductivity of snow, which are possible with the simplification of the coefficients and linearization of the basic parabolic dependence of the coefficient of thermal conductivity on the density of the snow cover, are determined. It is established that the errors arising from the linearization of the basic function do not exceed 5%, which is quite acceptable in engineering calculations. The discrepancy between the results of calculations according to the basic and simplified formula (with coefficients rounded to integer values of the first order) does not exceed 1.5% in the entire considered range of changes in snow density. The results of numerical calculations are presented in the form of graphs that allow you to visually assess the impact of simplifying the calculation formula and its linearization on the accuracy of determining the coefficient of thermal conductivity of snow cover.