V ERIFICATION OF BOUNDARY CONDITIONS OF NUMERICAL MODELING OF THE TRACK SUBSTRUCTURE THERMAL REGIME – INFLUENCE OF THE SNOW COVER

The initial part of the paper briefly characterizes a long-term experimental activity at the Department of Railway Engineering and Track Management (DRETM). The research of the DRETM focuses, besides other research activities and specific problems in the field of railway engineering (application of new structures and construction materials in conventional and modernized railway tracks, modernisation and rehabilitation of existing railway tracks for higher speeds, track diagnostics, influence of track operation on noise emissions and design of structural measures, possibility of application of recycled ballast bed material in the track substructure, ballast recycling technologies, ecological assessment of recycled material of the track substructure), on various factors affecting track substructure freezing. In 2012-2017, in the campus of the University of Žilina (UNIZA), an Experimental stand DRETM was built for the research purposes. The experimental stand DRETM consists of 6 types of track substructure placed in an embankment or a cut, in the 1:1 scale. Besides conventional building materials (crushed aggregate), these structures also include various thermal insulation materials (Liapor concrete, Styrodur, foam concrete). A significant part of the paper deals with numerical modeling of the freezing process of track substructure (an embankment with the embedded protective layer of crushed aggregate, fr. 0/31.5 mm) for various boundary conditions (air frost index, average annual air temperature), using SoilVision software. The aim of this research is to identify the thermal insulation effects of different thicknesses of snow cover on the depth of penetration of the zero isotherm into the track substructure (railway track). The paper conclusion specifies the influence of different snow cover thicknesses, or nf factor (factor expressing the dependency between the mean daily air temperature and the temperature on the ballast bed surface) and various climatic conditions (frost indexes and average annual air temperatures), affecting the railway infrastructure, on the resulting depth of freezing of the track substructure (railway track). These outputs will be in the further research used for the design of nomogram for determining the thickness of the protective layer of the frost-susceptible subgrade surface of the track substructure.


Introduction
The research of the Department of Railway Engineering and Track Management (DRETM) focuses, besides other research activities and specific problems in the field of railway engineering, on various factors affecting track substructure freezing.In the campus of the University of Žilina (UNIZA), an Experimental stand DRETM was built for the research purposes.This experimental stand contains 6 various types of track substructure in the 1:1 scale.These models are the most frequent types of track substructure as well as newly designed track substructures.The aim of this research is to increase their deformation resistance and to improve their thermal insulation properties.Within the experimental activities, the basic physical properties of building materials, applied or planned to be applied in the track substructure after verification, are determined.The respective properties are thermal conductivity coefficients, thermal capacity, density, bulk density, temperature and moisture values of building materials.The climatic characteristics (mean daily air temperature θs, average annual air temperature θm, air frost index IF, depth of track substructure freezing DF), are essential prerequisites for a correct track substructure design of non-traffic load (effects of climatic factors, especially of water and frost).Due to this reason, they also need to be verified.The determination of all the relevant boundary conditions affecting the penetration of the zero isotherm into the track substructure for various Slovak regions is time-consuming and costly.Because of this, computing support was applied, in the form of numerical modeling of various track substructure freezing by SoilVision software, specifically SVHeat programme.To gain relevant output values of the parameter depth of track substructure freezing DF, it is necessary to enter correct input parameters in the SVHeat.Many of these parameters were collected within the extensive experimental activity, recently conducted at DRETM, in the field of non-traffic load of railway track, on railway track models in 1:1 scale.However, some input parameters must be determined on the basis of knowledge and experience and verified by numerical modeling.Such parameters include the influence of snow cover thickness as an active thermal insulation layer on the railway track surface on track substructure freezing.This paper is dedicated to the identification of influence of the snow cover thickness on the track substructure freezing.As this influence will be verified by numerical modeling of the thermal regime or track substructure freezing, it is necessary to state the method of entering the snow cover thickness.Subsequently, various methods of entering must be compared and then the design values for snow cover thickness for particular Slovak regions based on frost index IF and average annual air temperature θm must be specified.In this way, it is possible to create conditions for identification of relevant influence of the snow cover thickness tsnow on the depth of track substructure (railway track) freezing DF.Based on this influence, a design nomogram for dimensioning the structural thickness of the protective layer of the frost-susceptible subgrade surface tpl can be created.

Review of literature
In the past, the primary importance in the track design procedure was exclusively placed on the railway superstructure quality.Only later it was generally accepted that to secure quality and safe roadway, the attention also needs to be paid to the track substructure, especially the track composition and the selection of suitable materials.The problem of soil behaviour in various boundary conditions (deformation resistance, thermal insulation properties) has been studied by many experts (Vanapalli and Oh, 2010), (Sussmann and Hyslip, 2010), (Akrouch et al., 2016), (Pentland, 2000), (Farbrot et al., 2013).An important factor affecting the quality of structural layers of the track subgrade is the effects of frost (Tang et al., 2018), (Hansson et al., 2004), (Nassar et al., 2000), (Panteleev et al., 2017), (Newman, 1995), (Wang et al., 2014), (Watanabe and Wake, 2009), often reduced by the occurrence of a snow cover (Ottaviani et al., 2015).All the achieved knowledge was applied in the SoilVision software which enables numerical modelling of complex cases of soil behaviour in subgrade of the line transport structures (Fredlund et al., 2011).A prerequisite for developing a quality numerical model is the knowledge of relevant input data.This problem has been studied by the Department of Railway Engineering and Track Management since 2003 (Ižvolt et al., 2013), (Ižvolt and Dobeš, 2014), (Ižvolt et al., 2014), (Ižvolt and Dobeš, 2015), (Ižvolt et al., 2016), (Ižvolt et al., 2018a), (Ižvolt et al., 2018b).

Numerical modeling of the thermal regime
at the Experimental stand DRETM For the purposes of numerical modeling of the thermal regime of railway track and the track substructure, and verification of the influence of the snow cover thickness tsnow on the value of railway track freezing DF, a 2D railway track model (Fig. 1) was built.A mesh generation module constructs a triangular finite element mesh over an arbitrary twodimensional model domain.Finite element basis is set to quadratic (number of elements is approximately 1000).This model is identical to the measuring profile no. 1 of the Experimental stand DRETM.The input parameters, which characterize the building materials of the measuring profile no. 1, were determined on the basis of the procedure in (Ižvolt and Dobeš, 2014).Within the numerical modeling of the thermal regime of the railway track in the Experimental stand DRETM (measuring profile no.1), the frostiest period was also determined.In terms of the achieved air frost index, it was winter 1986/1987 in Poprad (IF = -741 ˚C, day over the past 50 years).Frost index IF is determined by adding up mean values of the day air temperatures θs in the winter season based on the equation: The datainput parameters (mean daily air temperatures θs) were provided by the Slovak Hydrometeorological Institute (SHMÚ).Mean daily air temperatures θs were determined based on the equation:  In the numerical model, the time units are set as TIME=1.This setting always matches the time moment of January 1.The TIME=365 is the day of December 31, (to consider the influence of average annual air temperature θm), TIME=333 -448 is used for 115-day winter period in 1986/87.The last day of the model, marked TIME=465 matches April 10, which was 3 days after the snow cover on the surface of the structure melted.
As previously mentioned, a partial aim of the research of the influence of non-traffic load on the railway track structure is the determination of the snow cover thickness tsnow.Specifically, we need to determine the effects, for which the depth of railway track freezing DF would be identical to the thermal insulation effects of snow cover entered using the nf factor.(The nf factor expresses the conversion ratio of the mean daily air temperature θs to the mean daily air temperature on the ballast bed surface θbb).

Influence of nf factor on the depth of railway track freezing
The nf factor, entered in the numerical modeling of the thermal regime of the railway track for a respective winter period, expresses the ratio of conversion of the mean daily air temperature θs to the mean daily air temperature on the ballast bed surface θbb (hereinafter surface air temperature θbb).As already mentioned, entering the nf factor is one of methods of defining the thermal insulation effects of the snow cover in the numerical modeling of the thermal regime of the railway track.The nf factor in the numerical modeling can be either entered using a single average value or tables for particular days.This was also our case, we applied TIME 333 to TIME448.The individual limit values of nf factors, applied in the numerical modeling, were determined in the following way.The first step was the nf factor determination for the meteorological station Poprad (High Tatras area) and the winter period 1986/87.With respect to the negative (positive) values of the mean daily air temperature θs and the negative (positive) surface mean daily temperatures θbb, recorded in winter 1986/87, an average nf factor value = 0.58 was stated (Fig. 2 -left).As in the winter period 1986/87 the stated air frost index value was IF = -741 ˚C, day, and for numerical modeling of the thermal regime of the track substructure the air frost index value was IF = -800 ˚C, day, the nf factor value was modified to 0.55.The highest applied factor value was nf = 0.80.It was determined by the identical method, again for the winter period 1986/87, but for the town Topoľčany (southwestern Slovakia).There the reached air frost index was IF = -300 ˚C, day, coincidentally identical to the minimum design air frost index value IFd, considered for the Slovak territory.The nf factor value nf = 0.81 (Fig. 2 -right) was determined as the average value of all ratios of negative (positive) mean daily air temperatures θs to negative (positive) surface daily temperatures θbb in the entire winter period.Tab. 3 provides a set of values of nf factors, assigned to the particular air frost index values IF and the average annual air temperatures θm, subsequently applied to the numerical modeling of the railway track.The entered nf factor values for particular days of the numerical model can be observed in Fig. 3, which demonstrates the winter time period TIME 333 -TIME 448.).The thickness of the snow cover tsnow can be defined as an average one, where the time period of its influence can be entered, or it can be entered as a table value, separately for particular model days (our case).Maintenance of the railway tracks has not been taken into account in the model.The snow cover thickness was entered as assumed and then modified with the aim of achieving values of the depth of structure freezing DF identical to the values achieved by the numerical modeling with the use of the nf factor (Fig. 5).Fig. 6 depicts a graphical output of numerical modeling of the railway track freezing for the limit (most adverse winter) boundary conditions (air frost index IF = -800 ˚C, day, average annual air temperature θm = 5 ˚C and the average snow cover thickness tsnow = 0.25 m) By numerical modeling of the railway track freezing, the differences in values of the achieved depths of structure freezing DF, up to ± 5 mm, for identical boundary climatic conditions were identified.The only variable here was the method of defining the thermal insulation function of the snow cover (nf factor vs. entering the snow cover thickness).The final snow cover thickness values, entered for numerical modeling, can be found in Fig. 7. Conclusions Partial results of scientific research of the non-traffic load of railway track (track substructure), presented in this paper, include the determination of the influence of the thermal insulation effects of snow cover on the thermal regime, (the penetration of the zero isotherm into the track substructure), and the method of its correct entering in the SoilVision software.The first method of its entering was conducted using the nf factor, (which expresses the conversion of the mean daily air temperature θs to the temperature on the ballast bed surface θbb in the considered period of their influence).The second method focuses on entering the snow cover thickness tsnow on particular days in the identical period.The snow cover thicknesses tsnow, matching the respective nf factor values, and the values of the depth of freezing of the railway track model DF for both methods can be found in Tab. 4. The determination of the snow cover influence on the track substructure model freezing is only a partial task of experimental activity at DRETM.The parameters in Tab. 4 will be applied in the further research of influence of non-traffic load on the thermal regime and the achieved depth of railway track freezing DF as entry parameters for numerical modeling.The output of this research will be a design nomogram for determination of necessary thickness of the protective layer of frostsusceptible subgrade surface tpl in the methodology of track substructure dimensioning for non-traffic load.

Notes :
values valid for positive mean daily air temperatures, ** values valid for shorter period of snow cover effects (Fig. 7 left), *** values valid for modeling with the snow cover.
Fig. 1.Model of the Experimental stand DRETMmeasuring profile No.1

Fig. 6 .Fig. 7 .
Fig. 6.Graphical output of modeling of the railway track freezing for limit (most adverse winter) boundary climatic conditions (IF = -800 ˚C, day, θm =5 ˚C, tsnow = 0.25 m) (Ižvolt and Dobeš, 2015) average annual air temperatures θm were combined to determine the maximum but real effects (in the Slovak territory) of frost on the depth of the railway track freezing DF in a particular winter period.For the purposes of creating a new design map of frost indexes IFd for the Slovak territory(Ižvolt et al., 2018a), the SHMÚ provided the Department, besides values of mean daily air temperatures θs at all meteorological stations in Slovakia in the coldest (frostiest) winter period 1986/87, also with data for the coldest year 1980.These data were requested to draw a new design map of average annual air temperatures θmd for the Slovak territory(Ižvolt et al., 2018b).Based on these inputs, combining frost indexes IF and average annual air temperatures θm was not demanding.Besides climatic characteristics, in the numerical model it was also necessary to define the physical and thermal technical parameters of particular structural layers of the track substructure.These parameters were determined on the basis of laboratory measurements(Ižvolt and Dobeš, 2014)and experimental monitoring at the Experimental stand DRETM(Ižvolt et al., 2014),(Ižvolt et al., 2016),(Ižvolt and Dobeš, 2015).All the necessary input parameters for numerical modeling of the thermal regimefreezingof the railway track model are clearly stated in Tab. 1 and Tab. 2.

Table 1 .
Input parameters for numerical modeling of the thermal regime-freezingof the railway track model(Ižvolt and Dobeš, 2014)

Table 4 .
Values of snow cover thickness matching the respective nf factor values