Thermal resistance of the structural layers of a road is one of the important parameters that determine the choice of technical solutions of road design in the permafrost area. The purpose of this research is a quantitative assessment of the influence of the extent to which the pores in a gravel bedding are filled with ice or sand on the thermal conductivity of an ice-gravel or sand-gravel mixture. Lichtenecker formula was used to calculate the thermal conductivity coefficient of a three-component mixture. Different levels of ice content and moisture levels ofthe sand in the pores were considered. It was shown that the thermal resistance of the road structure can change significantly depending on the choice of the filler material. This allows to regulate the thermal regime of the road without adding new structural layers. The results of the calculations are presented as 2D and 3D charts to assess the influence of the filler material and the extent to which the pores are filled on the thermal conductivity coefficient of the mixture. The charts allow to see the possible changes in thermal conductivity coefficient of the structure and make a correct decision regarding the technologies to be used in construction. For example, to decide on the necessity to use a special thermal protection layer in the road structure.

The subject of the research is the functional dependence of the thermal conductivity coefficient of snow on its density. The object of the research was the linearization of the function expressed by a polynomial of arbitrary degree, characteristic of the quantitative dependence of the thermal conductivity coefficient on the density of snow. Special attention is paid to the analysis of errors arising from replacing a polynomial function with a linear one. Particular attention is also given to the analysis of existing functional dependencies of the thermal conductivity coefficient on snow density, which is an integral indicator of complex heat and mass transfer processes occurring during the metamorphism of the snow cover. The main formulas for predicting the thermal conductivity coefficient based on snow density have been analyzed. All dependencies are conditionally divided into two groups: linear and nonlinear (expressed by polynomials of the second, third, and fourth degrees). To find the point corresponding to the maximum value of the linearization error of the second group of methods, an appropriate target function has been constructed and studied in its most general form. When constructing the function defining the absolute error that arises from linearization, a generalized polynomial of derivative degree, which describes known experimental and theoretical dependencies of the thermal conductivity coefficient of snow on its density, was taken as the original formulas. The resulting function was analyzed for its maximum using the classical method of differentiating the original dependence with respect to the argument. The scientific novelty lies in the fact that for the first time a dependence has been obtained between the error arising from the linear and nonlinear representations of the experimental approximating dependencies of the thermal conductivity coefficient of snow and its density. It has been shown that when linearizing a quadratic dependence (Abel's, Kondratyeva's, Brecht's, Sturm's formulas, etc.), the maximum absolute error is found in the middle of the averaging interval. At this point, its value equals the value of the original function. As the degree of the polynomial increases, the maximum error shifts toward the upper boundary of the linearization interval and changes, for example, for the cubic polynomial (Van Dussen's formula) to a value equal to 0.58 of the linearization range. For the fourth-degree polynomial (Jansen's formula), it reaches 0.63 of the range. When the degree is reduced to less than two (Yen's, Schwander's formula), on the contrary, the maximum linearization error shifts from the middle of the interval to the lower boundary.

A correct consideration of the thermal factors during the design phase of civil engineering structures in the permafrost area determines their reliable and safe exploitation. Among the important indicators in selection of design solutions is the thermal conductivity coefficient of the construction materials used. The thermal conductivity coefficient is usually chosen from reference tables, but when using mixtures, the thermal conductivity coefficient is determined through a calculation. The aim of the present research was to compare the calculated values of thermal conductivity coefficient of binary mixtures (a mixture of a binding material and a filler) obtained using Lichtenecker and Schwerdtfeger formulas. The comparison was conducted in the range of properties of materials used for thermal accumulation and thermal insulation mixtures. It was determined that for thermal accumilation binary mixtures the calculation results are quite similar within a wide range of initial values. For thermal insulation binary mixtures, the calculation results are significantly different. The divergencies are by hundreds of percents. At the current stage of research it is impossible to make a conclusion about suitability of either calculation method to determine the thermal conductivity of a thermal insulation binary mixture.

A brief review of research on variation of thermal resistance of snow cover and formulas to determine the thermal conductivity coefficient of snow are presented. This article aims to establish the regularities of variation in thermal resistance of snow when compressive melioration is applied to the snow cover. A criterion consisting of ratio of initial thermal resistance to the thermal resistance after compression is introduced. Two practically relevant cases, a full and partial compression, whereby the snow density after compression is a constant and a variable respectively, are considered. It is demonstrated that the area where it can be assumed that the snow density after compression is a constant has a low confidence interval and in practical applications it needs to be accounted for that the snow cover is not fully compressed under load. The calculation results are presented in a generalized dimensionless form that includes an indicator of arbitrary exponent in an approximated formula to determine the thermal conductivity coefficient from snow density. It has been established that the type of functional dependence of thermal conductivity coefficient on snow density has a significant influence on the calculation results of the thermal resistance of snow cover. The boundary values of snow compression coefficient within the permissible error level (10 %) were found. For example, for a linear dependence of the thermal conductivity coefficient on density the permissible compression coefficient is no higher than 1.25. For a quadratic dependence, it is 1.11. The results of variant calculations are presented as 2D and 3D charts, which allow quickly assessing the assumptions and conclusions.