Modern studies of heat losses of a building basement through a soil mass

. This study aims at considering the methods of calculating heat losses to the soil through the floor structures of the basement. Classical methods of calculating heat losses through the soil according to the updated set of rules are presented. Modern methods of calculation based on mathematical modeling have been studied. A full-scale experiment of one of the developed methods that proves the possibility of its application and the need for further enhancement has been considered. Methods for estimating the resistance to the heat transfer through the soil are introduced. The method of "concentric circles" is presented in comparison with the given values in Set of Rules 50.13330.2012. A comparative analysis of new methods with standard methods for calculating heat losses to the soil through the basement floor structures was carried out. Such methods as calculation "by zones" based on the principle of dividing the basement floor into strips have been studied. Various options for the building basement insulation that can affect the heat losses of the building have been considered. An analysis of the factors influencing heat loss such as the type of soil, the geometric dimensions of the building, the actual heat transfer resistance of the insulation, the temperature regime of the room and the presence of insulation has been presented. The formulas for calculating the complex heat-shielding characteristic in accordance with modern changes in the regulatory documentation are given.


Introduction
A number of heat losses occur in any building through a variety of structural elements such as roof, exterior walls, windows, ventilation and basement floors.

Classic method of calculating heat losses through the soil
Calculation of heat losses is carried out in accordance with Set of Rules 60.13330.2020 Heating, ventilation and air conditioning, Appendix A. Heating and ventilation consumption for adverse conditions is determined taking into consideration paragraph 5 In her manual, the researcher Malyavina E.G. describes a simplified method of calculating the resistance to a heat transfer of a structure based on dividing the surface of the floor and walls that are in contact with the ground into strips 2 meters wide. Zones are numbered along the wall from ground level. If there is no such wall, the floor strip closest to the outer wall is taken. The next strips will be zones 2 and 3, whereas the rest of the floor will be zone 4. Figure 1 shows the layout of the building basement [2].
where if R -resistance to heat transfer of the considered zone of an uninsulated floor, / ( ) W m С ) [2].
If the floor is on floor joists, the resistance to the heat transfer should be calculated using the following formula [2]: Thus, not only the described method can significantly simplify the calculations of heat losses to the soil, but also allow us to take into account the insulating material of the structure [2].

Modern changes of regulatory documents in the calculation of a complex heat-shielding characteristic through the soil
The specific heat-shielding characteristic of a building is the amount of heat equal to the loss of thermal energy through the heat-shielding shell of the building of a unit of heated volume per unit of time with a temperature drop of 1 С С .
In accordance with Set of Rules 50.13330.2012 Thermal protection of buildings, Appendix G, the specific heat-shielding characteristic is calculated using the formula: where , r sh i R -reduced resistance to heat transfer of the i-th fragment of the heat-shielding shell of the building, -overall building heat transfer coefficient, It is important to take into account that the specific heat-shielding characteristic should not exceed the normalized value.
Also, the specific heat-shielding characteristic can be found by means of characteristics of the elements that make up all the structures of the building shell according to the formula: where j L -total length of linear inhomogeneity of the j-th type throughout the building shell, м; k N -the total number of point inhomogeneities of the k-th type throughout the building shell, pcs;

Scientific methods of assessing the resistance to heat transfer through the soil
In his study, O.D. Samarin considered a simplified method of calculating a stationary twodimensional temperature field of the soil mass, the key point of which is to select a quarter of an infinite array enclosed between the ground surface plane and the outer wall surface plane. The calculation scheme of heat transfer through the soil mass is demonstrated in Figure  2   temperature at the boundaries of the auxiliary layers is taken. As a solution to the problem, the author proposes the method of sources and sinks. A point vortex acts as a source [3][4].
The total linear heat flux is found by the formula [3-4]: where -average thermal conductivity of soil, W/(m К), 1 r -radius of the first concentric circle, м; 2 r -radius of the second concentric circle, м; in t -indoor air temperature in the basement, К; out t -design outdoor temperature, К [3-4].
Next, we can calculate the average value of the resistance to heat transfer for a section of the wall surface with a width of according to the formula [3-4]: where in t -indoor air temperature in the basement, К; out t -design outdoor temperature, К; 1 2 А -surface area of a wall between two concentric circles 1 r and 2 r , 2 м [3][4].
The author conducts a comparative analysis of the calculation results according to the formula and the values given in Set of Rules 50.13330.2012 (Fig. 3).

Mathematical modeling of heat transfer through the soil mass of the building basement
The researcher Gnezdilova E.A. has considered a mathematical model of non-stationary thermal soil and adjacent structures. Her study is based on the differential equation of thermal conductivity in the soil [5]: where c -specific heat capacity of soil, / ( ) J kg С ) ; -specific heat capacity of soil 3 / kg m ; -soil thermal conductivity, / ( ) W m С ) ; z -time with origin, с; ( , ) t x ztemperature at any point x along the depth of the soil and at any time z from the origin, С С [5].
A method of calculating the heat equation in finite differences was considered. A calculation of one-dimensional soil field has been performed. The boundary conditions on the earth surface that describe the solar radiation absorbed by the soil, heat exchange with the atmosphere, and long-wave radiation were taken into account. Moreover, in order to solve the problem, the author introduced a non-uniform difference grid for compiling difference equations for elementary layers, which made it possible to compose implicit difference schemes for heat equation and soil boundary conditions. After calculating the sweep coefficients, the author determined the temperature values at the lowest point of the soil area under consideration, as well as at all nodes up to the day surface of the soil [5].
During the study, the influence of freezing and thawing of moisture in the pores of the soil was taken into account by the method of smoothing of the coefficients [5].
When passing to a plane problem, the soil boundaries were chosen by the locally onedimensional method in order to maximally reduce the artificial limitation of the heat flux from the building due to a small volume of soil. This will allow us not to distort the temperature field [5].
A program for performing calculations using technical support was compiled based on above mentioned method [5].
A full-scale experiment was set up to apply this method in real conditions. The aim was to measure the heat loss of the floor over the ground in real conditions and compare them to the calculated data. During the experiment, heat flux density and temperature sensors were installed. The results obtained formed the basis of a comparative analysis, as a result of which it was possible to provide confirmation of the suitability of this development for identifying the thermal regime of enclosing structures that have direct contact with the ground surface [5].  [5].
The discrepancy between the results was not more than 10 %, which also indicates the suitability and reliability of the developed method [5].
Gnezdilova E.A. also gives a method of mathematical modeling of the thermal regime of floors on the ground with indirect insulation to determine the factors that most affect the amount of heat loss [5].
The technique is based on the temperature field of the soil mass, which is formed together with the floor structure adjacent to the soil [5].  [5].
For the convenience and the possibility of comparing the results to the classical methods, the author proposes to move on to the zonal calculation method [5].
Having considered the options for different types of insulation of the building basement (floors, walls, blind areas), Gnezdilova E.A. comes to the conclusion that the geometric parameters of the structure, the type of soil, the actual resistance to the heat transfer of the insulation and the temperature regime of the room have the greatest influence on heat losses. The researcher also notes a tendency to reduce the resistance to the heat transfer of the structures that are built on sandy soils [5].
Insulation of the attached floor area is an effective measure for any building and structure. Moreover, an important aspect is also the prevention of soil heating from a warm room, which increases heat losses in the closest calculation zone [5].

Conclusion
As a result of considering a great variety of methods for calculating heat losses through floor structures into the soil, two main simplified methods that are classic and popular can be distinguished, namely the method of partitioning into zones and the method of concentric circles. The partitioning method is also specified in Set of Rules 50.13330.2012 Thermal protection of buildings. When using it, inaccuracies in the calculations do not have critical values. Nevertheless, the method of concentric circles appeared to be more extensive in order to take into account numerous heterogeneous factors in the interaction of soil and floor structures [1][2][3][4][5].
Thus, E.A. Gnezdilova's study has a great perspective. Due to the fact, that the results of the methodology developed by her are close to the results of classical methods, they are of great interest. However, the method still requires further improvement in terms of correction factors, as well as tests [1][2][3][4][5].