Abstract: The subject of research is the underground structures of the cryolithozone (permafrost zones). The design of such structures, in particular the choice of space-planning solutions, methods and means of fastening rocks, unlike structures located not in frozen rocks, has a number of features and is associated with the need to take into account the zone of thermal influence of chambers operated with different thermal conditions constantly or periodically. For example, when changing the type of thermal regime in the chambers in cases of natural or man-made accidents and catastrophes. The purpose of the research was to determine the zone of thermal influence of a single chamber of an underground cryolithozone structure, depending on the type of fastening used (in the presence and absence of a thermal protective layer) and the duration of the operational period, using various calculation formulas. To achieve this goal, three types of formulas were studied that determine the dependence of the dimensionless radius of thermal influence of chambers on Fourier and Bio criteria. Multivariate calculations were performed using the formulas, which are presented in the form of 3D graphs. The analysis of the performed calculations showed that the calculations for all three formulas give similar results in a fairly wide range of changes in the initial parameters. Moreover, the formula, which does not take into account the influence of the Bio number on the radius of thermal influence, gives a certain calculated margin. In general, it is shown that the higher the value of the Bio number, the less its effect on the depth of the thermal influence zone of the underground chamber. Small values of the Bio number (up to 5-6) are typical for cameras that are fixed with sprayed concrete or have special heat-protective coatings.It is established that when choosing space-planning solutions for underground structures to assess the influence of the thermal factor, it is quite acceptable to use an approximate formula to estimate the radius of the thermal influence of a single chamber. The scientific novelty lies in establishing the scope of the studied formulas for predicting the radius of the zone of thermal influence of cameras with various types of fastening and thermal protection.

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.

Abstract: The thermal regime of road surface and basements is an important factor determining their reliable and safe operation in the cryolithozone. The aim of the research was to quantify the possibility of replacing the layered environment of the road's soil base with an equivalent homogeneous soil with an average coefficient of thermal conductivity when calculating the depth of the road's thermal influence zone. Two methods of averaging the thermophysical properties of a layered medium are considered: weighted average and arithmetic average. Dependences are obtained for determining the degree of deviation of the properties and thicknesses of the layers of the soil base, in which both methods are acceptable for engineering calculations. As an example, the two-layer medium of the road base is considered. For the analysis, the classical formula of the depth of thermal influence was used, obtained from the solution by the integral method of the one-dimensional equation of unsteady thermal conductivity. Simple engineering formulas are given for the relative error in determining the values of the depth of thermal influence when using an equivalent layer of pavement in calculations. A concrete example of calculating the depth of the zone of thermal influence in the two-layer soil of the road base is considered. The equation of the functional relationship between the parameters characterizing the degree of deviation of the thickness and thermophysical properties of individual layers from each other is obtained, which provides an error in the calculations of the depth of the zone of thermal influence less than the permissible value. The results of numerical calculations are presented in the form of 2D and 2D graphs, which allow us to visually assess the influence of the range of changes in the values of the thermal conductivity coefficients of individual soil layers on the legality of using various methods of constructing an equivalent single-layer road foundation structure.

Abstract: The thermal regime of underground cryolithozone structures for various purposes, both related and not related to mining production, is an important factor determining their reliable and safe operation. In this regard, the forecast of the thermal regime in mine workings is a mandatory and important element in the justification of design solutions for the construction and reconstruction of underground structures in the areas of distribution of continuous and island permafrost. One of the main sources of heat generation in the workings is the work of diesel equipment, which is widely used, both in the development of mineral deposits by the underground method, and to ensure technological processes in underground structures of non-mining profile. The purpose of the research was to quantitatively assess the effect of diesel installations on the thermal regime in the underground structures of the cryolithozone. The results of numerical calculations are presented in the form of 2D and 3D graphs, which allow you to visually assess the effect of diesel equipment on the increment of air temperature in the underground structure, depending on the time of year and the efficiency of the diesel installation. It is shown, in particular, that in the most probable range of changes in the efficiency of a diesel installation, the air temperature can vary from 3.2 to 6.3 °C, depending on the standard values of the ventilation air flow. It is established that the temperature increment does not depend on the number of simultaneously operating diesel units and is determined only by the specific standard air flow (m3 / s per 1 kW of installation power).

Abstract: When designing cryolithozone engineering structures, proper consideration of the thermal factor largely determines their subsequent reliable and safe operation. One of the important indicators when choosing design solutions is the coefficient of thermal conductivity of materials used in the construction of objects. The accuracy of determining the thermal conductivity coefficient also depends on the accuracy of determining the thermal resistance of heat-protective structures. The coefficient of thermal conductivity of materials is usually selected from the reference tables. When using mixtures of materials, the coefficient of thermal conductivity is determined by calculation. The purpose of this work was to compare the calculated values of the thermal conductivity coefficient of binary mixtures (a mixture of binder and filler) determined by the formulas of K. Lichtenecker and P. Schwerdtfeger. The comparison was carried out in the range of changes in the properties of materials characteristic of heat-accumulating and heat-insulating mixtures. It is established that for heat-accumulating mixtures, both calculation formulas give similar results. For thermal insulation mixtures, the results differ significantly. Moreover, the discrepancy for some ranges of changes in filler concentrations is hundreds and thousands of percent, which indicates a complete disagreement of the results obtained. The validity of applying one or another formula in different ranges of changes in the initial parameters for thermal insulation binary mixtures needs separate special studies.
Note that the results obtained and the conclusions drawn can be extended to compare the formulas of K.Lichteneker and V.I.Odelevsky.
At the same time, at this stage of research, it is not possible to reliably determine which of the two formulas should be used when calculating the thermal conductivity coefficient of thermal insulation mixtures.

Abstract: The purpose of this work was to determine the range of changes in the Fourier criterion (number) when predicting the thermal regime of dispersed rocks in thawed and frozen state. And, also an assessment of the possibility of averaging the thermophysical characteristics of rocks to obtain universal values of Fourier numbers. To achieve this goal, an assessment of the influence of the thermophysical properties of dispersed rocks on the range of changes in the values of the Fourier number used in thermal calculations of technical objects of the cryolithozone is made. The calculation formulas took into account the functional dependence of the coefficient of thermal conductivity, density and specific heat capacity of rocks on humidity (iciness) in the thawed and frozen state. As an example, a mixture of quartz sandstone with water in a thawed and frozen state is considered when the ice content changes from zero (dry quartz sandstone) to full moisture saturation. It is established that the range and nature of the change in Fourier numbers for thawed and frozen dispersed rocks, depending on their humidity (iciness), differs significantly, not only quantitatively, but also qualitatively: for thawed dispersed rocks, the Fourier number decreases with increasing humidity, and for frozen rocks increases. The possibility of averaging the thermophysical characteristics of rocks to obtain universal values of Fourier numbers has been evaluated. It is shown that the use of universal Fourier numbers leads to a significant error for both thawed and frozen rocks and their use in thermal calculations with annual temperature fluctuations is impractical.

Abstract: The design and construction of highways in the cryolithozone is associated with a number of difficulties, which are determined not only by geocryological and climatic operating conditions, but also by the complexity of the actual forecast of the thermal regime of road coverings and foundations. Many thermal calculations to substantiate technical solutions for the protection of highways in the cryolithozone from negative cryogenic phenomena are based on the determination and selection of a given thermal resistance of the structural layers of the pavement. The purpose of these studies was to assess the feasibility of using equivalent thermal resistance in modeling thermal processes and to determine the error in calculations that we make by replacing the layered pavement structure with an equivalent one.     Simple engineering dependences are obtained that allow us to determine the error in calculations when using equivalent thermal resistance. The calculation of the thermal resistance of the three-layer construction of the pavement is made. It is established that for a three-layer pavement structure, the error value in the calculation of thermal resistance is directly related to the degree of deviation of the values of the thermal conductivity coefficient of the materials of individual layers from each other. Moreover, the parameters of the inequality of thermal conductivity coefficients for individual structural layers when determining the minimum calculation error are functionally related to each other. The results of variant numerical calculations are presented in the form of 3D and 2D graphs, which allow us to visually assess the influence of the studied parameters on the relative error of calculating the thermal resistance of the pavement.

Abstract: One of the important parameters determining technical solutions in the design of highways in the cryolithozone is the depth of thawing of the soils of the road base. The aim of the work was to quantify the degree of influence of the iciness of the soil foundations of roads in the cryolithozone on the depth of their seasonal thawing. For the analysis, the classical formula for calculating the thawing depth for bodies of plane symmetry, obtained by solving the single-phase Stefan problem, was used. The results of calculations are presented in the form of 2D and 3D graphs, which allow us to visually assess the effect of the iciness of the soil and the degree of its change during the operation of the road on the depth of thawing of the road base. It was found, in particular, that the degree of change in the depth of thawing at the same value of the increase in ice content in different ranges (for example, from 10 to 20% and from 30 to 40%) for the considered typical case of the ground base of the cryolithozone decreases by almost 1.3 times. It is shown that the greater the initial iciness of the soil, the degree of decrease in the depth of thawing when the iciness changes by a constant value will be less. A 3D graph was built to determine the depth of thawing of the soils of the active layer of the road base in a wide range of possible changes in ice content during the construction and use of the highway. The availability of a schedule allows to quickly assess possible options for changing the depth of thawing and make a correct, informed technical decision when designing the road. For example, when assessing the need to use a special heat-protective layer in road clothing. Further directions of research in this area should be aimed at studying the effect of humidity (iciness) of dispersed soils on the depth of thawing of road foundations, taking into account the dependence of the density and thermal conductivity of the soil on the iciness.