The effect of the iciness of the soil on the depth of thawing of the road base

Introduction

The operation of highways in the cryolithozone is complicated by many objective reasons, including the dependence of the strength properties of the foundation soils on the temperature factor and on the natural or man-made humidity (iciness) of the soils of the active layer of the road ^[1,2,3]. Moreover, as noted in ^[4,5], it is the technogenic moistening of the soils of the active layer that plays the greatest role. Therefore, when designing highways, it is important to know not only the natural humidity (iciness) of the soils of the road base, but also the degree of their change during the operation of the highway. One of the main parameters of the design of technical objects interacting with the soils (rocks) of the cryolithozone is the depth of thawing ^[6,7,8]. This also applies to the design of highways in the cryolithozone ^{[9, 10]}.

The purpose of the research is to quantify the degree of influence of the iciness of the ground foundations of roads in the cryolithozone on the depth of their seasonal thawing.

Methods

To achieve this goal, we will use the well-known formula for determining the depth of thawing of soils ^[10,11,12] at their initial temperature equal to the melting temperature of ice.

 (1)

Where: ? is the duration of the warm period of the year, s; ? is the thermal conductivity coefficient of thawed soil, W/m· K; t is the average air temperature during the thawing period, 0C; ? is the density of the soil, kg/m3; L is the latent heat of melting ice, J/ kg; ? is humidity (iciness) of soil, D.E.

 This formula does not take into account the amount of heat that goes to heat the frozen ground from the natural negative temperature to the melting point of ice. In this regard, in ^[11] we evaluated the correctness of this assumption when predicting the depth of thawing of rocks in underground structures of the cryolithozone. It is shown that for the majority of practically interesting cases, the application of formula (1) does not lead to an error greater than the error allowed in engineering practice (usually equal to 10%). Therefore, the use of this formula for the purpose pursued in this work will be considered quite acceptable.

For the convenience of analysis, we additionally introduce the parameter "?", which characterizes the degree of change in the depth of thawing of the soils of the active layer of the road base with changes in humidity (ice content) during the operation of the automobile road.

(2)

Where:? i is the humidity (iciness) of the soil, natural (i=1) and man–made (i=2), i.e.

Formula (1) includes time in seconds, which is not very convenient when calculating seasonal soil thawing. Therefore, considering that the latent heat of melting of ice for the case under consideration is a constant value equal to 335.0 kJ/kg, we convert formula (1) to the form

(3)

Where: N is the number of months in the warm period of the year, units.

Results and discussion

To achieve the goal, variant calculations were carried out according to the above formulas, the results of which are presented in the form of 2D and 3D graphs in Fig. 1-3. Figure 1 shows the dependence of the thawing depth of a typical cryolithozone soil with a density of 1600 kg/^m3 and a thermal conductivity coefficient of 1.4 W/m·K depending on the iciness for different climatic zones, characterized, in this case, by the product of the duration of the warm period by the average air temperature – "Nt", month · ^o C.

Fig. 1. The depth of thawing of the soil of the road base, depending on the ice content W, (ie) for different values of the complex "Nt" (month ·^oWith): 1- 25,0; 2 - 35,0; 3 – 50,0.

It can be seen from the graphs in the figure that with an increase in the iciness of the soil (the degree of filling of the pores with ice), the depth of thawing increases throughout the considered range of changes in iciness, regardless of the climatic zone of the road location.  Moreover, the smaller the range of change in iciness, the stronger the dependence of the depth of thawing on the iciness. This is evidenced by both the nature of the curves in Figure 1 and the quantitative analysis. For example, for the case (Nt) = 25 (curve 1 in the figure), when the iciness changes from 0.1 to 0.2 (an increase of 0.1), the depth of the thawing halo increases by 1.4 times. And, when the iciness changes from 0.3 to 0.4 (an increase of 0.1), the depth of the thawing halo increases by 1.15 times. Which is almost 1.3 times less.

Figure 2 shows 3D graphs that clearly demonstrate this pattern (see the blue and brown area in Figure 2).

Fig. 2. The depth of thawing of the soil of the road base depending on the ice content W, (ie) and climatic characteristics of the warm period of the year (values of the complex "Nt", month · ^o S)

The conclusion is also confirmed by a simple quantitative analysis of the calculation formula. The results of the analysis are presented in the table.

Table.

The degree of change in the depth of thawing of the soil in a different range

increasing its iciness

From the data given in the table, it follows 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 amount (in this case, an increase of 0.1) will be less.

Figure 3 shows a 3D graph of the dependence of the parameter "?", which characterizes the degree of change in the depth of thawing of the soils of the active layer of the road base when the ice content changes during the operation of the automobile road.

Fig.3.The degree of change in the depth of thawing of the soils of the active layer of the road base when the ice content changes from the value of W1 to the value of W2 during the operation of the motor road.

The graph clearly demonstrates not only the previously described patterns, but also allows you to assess the degree of change in the depth of thawing, both with a possible increase in iciness during the operation of the highway, and with a decrease in iciness (for example, due to soil drying). The availability of a schedule allows you to quickly evaluate possible options and make a correct, reasonable technical decision when designing a highway in the cryolithozone. For example, to justify the need to use a special heat-protective layer in road clothing ^[13,14,15].

Conclusion

The influence of humidity (iciness) of the soil bases of highways in various climatic zones on the change in the depth of thawing in the warm season is investigated. The results of numerical calculations are presented in the form of graphs and tables that 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 has been constructed 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 operation of the highway. The availability of a schedule allows you to quickly assess possible options for changing the depth of thawing and make a correct, informed technical decision when designing. For example, to justify 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.