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%.