Numerical simulation of the stress-strain state of snow and ice layer on the road when it is destroyed under the influence of the proposed device

. In the winter season, we can observe the increased number of personal injuries and road vehicle accidents because of ice coating on paved roads. Surface refining from icing field involves two process operations: breaking it up and transporting the resulting segments. The basic process prevailing in cleaning effective output is the cutting process, i.e. the separation of icy fragments from the pavement with the cutting tools of special machines. The purpose of the research is to simulate the ice crust breaking influenced by the device designed by the authors. The modeling of ice flow failure is rather complicated and not a trivial task. An advanced Lagrangian model is applied in a modern software system. As a result, based on a computing model implemented in ANSYS software system, we have developed an algorithm for determining a mode of the ice crust deformation caused by the circular cutters put into it. The review of the stress strain behavior of ice crust shows that the biggest movement of ice crust fractions arises along the outline (perimeter) of discs and at the surface of the cover. The greatest equivalent stresses are observed along the disc outline (perimeter). The middle part of the disc (approaching to the centre) is nearly involved in equipment operation. The greatest displacement of icy particles is along the disc contour, while they are near zero along the edges. In the paper, we also determined recoverable and shearing deformations, regular and shear stresses in the ice crust at different thickness and movement speed of the device. The calculated motion rate and ice coating thickness at which the destructive effect is most distinctive, has been found out.


Introduction
For clearing snow and ice from pavements, roads and airfields, snow-removal equipment is used to sweep, rake and load snow onto trucks to take it to the collecting ground (snow dumps and snow melters followed by drainage into the sewer system): plough (side, front, speed blades, rear scraper); brush, rotary (with plough, screw and cutter-rotor working bodies), snow carriers with scraper conveyors, as well as gas-jet machines and sprayers of de-icing (technological) materials.All these machines perform 'fight' against ice crust by the destruction method, i.e. they are used when ice coating is already formed [1][2].
The common drawbacks of all the above-mentioned types of machines are: usage frequency (it is necessary to provide summer storage conditions), forced rotation of actuation devices, which inevitably results in pavement and related engineering structure damage (road kerbs, rails, etc.), and high cost (additional energy costs regarding auxiliary mechanisms operation are inevitable).
In the research [5], a device is proposed to implement the second method of packed ice removal from the hard crust road surface, which can be at work effectively in a standby mode, energy cost effectively, easy to assemble (install) and service, and does not cause damage to the asphaltic surface, maintaining the integrity of related engineering structures (kerbs, rails, ditch covers).Moreover, it is important to note that there are various solutions for removing snow and ice from road surfaces by V.M. Kozin, V.L. Zemlyak, N.V. Protasov et al. [3][4][5][6][7][8].
The article deals with the results of a numerical simulation of the packed ice breakup process by the proposed device [5].Modelling of ice flow failure is a rather challenging and uncommon task.Joint finite element procedures combine equilibrium equation and continuity equation through acting principal stresses and volume strain [9], Carter et al. [10] presented a general theory of elastic finite strain, which was later generalized to elasticplastic hardening [11].Prevost [12,13] generalized an additional form of hardening, considering finite deformations and non-linearity of the material.Zienkiewicz and Shiomi [14] and Meroi [15] studied saturated and non-saturated porous media under dynamic loads, respectively.In all these studies, basic equations typified by velocity are used to integrate stresses over calculated incremental strain.
Based on the multiplicative decomposition of deformation gradients [16][17][18], Borja and Alarcon [19] presented a mathematical formulation of elastic-plastic strains implemented by the finite element method [20].Later, the same approach using a multiplicative decomposition of strain gradients was used by Sanavia et al. [21], who presented a problem formulation on searching large deformations for saturated and partially saturated porous media.This type of problem statement outperforms in its applicability.Speed strain integration technique is also effective for the calculation of large elastic stresses.To process both types: speed and multiplicative decomposition, an advanced Lagrange method (UL) is used and adopted where the particle coordinates are regenerated according to moving after each time incrementation.In case of relatively large deformations, the UL method can cause severe mesh distortions, which can lead to spontaneous termination of calculation.
On the other hand, a certain Lagrangian-Euler method (ALE) has been developed for solving deformation calculation problems with severe mesh distortion in solid mechanics and fluid mechanics.This method, however, has attracted little attention in geomechanicsmainly because of its complexity, especially in related problems involving both deformation and flow of the material in pores.A recent study by Nazem [22] has shown that the ALE method based on the split operator [23] can provide an effective solution to the mesh distortion problem encountered in the UL method.This paper presents a formulation of ALE for compaction problems.The ALE method is based on a split operator method, in which the Lagrangian solution is convected into an Eulerian mesh.

Methods and Materials
Packed snow and ice are modeled in the ANSYS software suite using the Euler-Lagrange model [16].In the UL method, the equilibrium equation is of the form [16]: where σi,j is the stress tensor (Cauchy), bi is the body force vector and ∇ is the gradient operator.The upper right index denotes the time when the quantities are measured.The basic assumption in equation ( 1) is that all state variables and parameters are known at time t.The aim of the calculation is to find the unknowns at time t + ∆t. Figure 1 shows a discrete model of the problem.The packed snow was modelled by hexahedrons with a maximum side length of 0.1 m, the breaking device as cylindrical discs divided into tetrahedron finite elements.In numerical experiments, the thickness of naled ice was assumed to be h=25-100 mm, in increments of 25 mm.The speed of the device considering for the disc cells were introduced to the hard road crust surface was u=0.83-2.5 m/s.

Findings and Discussion
The calculations have been performed in order to determine the most efficient modes of operation of the device depending on the thickness of naled ice.The main results of numerical calculations to determine the stress-strain state of ice coating are shown in Figures 2 -4  Figure 2 shows the dependencies of shear strain wY on the speed of the device for different thickness of ice coating.It can be seen from the graphs that maximum displacements were typical of naled ice of thickness h=50 mm.The shear strain for ice coating is h=25 mm thickness was reduced to 30%.The minimum values of wY were taken at 75-100 mm thickness of the layer, and were far below the values at h=25-50 mm.The maximum shearing stress τxy (Figure 3) and direct stress Ϭx were observed for ice coating h=25 mm (Figure 4).Minimum values were also typical for the cases of h=75-100 mm.-7 show the examples of isofields of elastic, shear deformations and normal stresses.The analysis of the stress-strain behavior of the packed ice shows that the biggest movements of the icy particles occur along the contour (perimeter) of the discs and on the surface of the coating.The highest equivalent stresses are observed along the contour of disks (perimeter).The middle part of the disc (approaching to the centre) is nearly involved.The greatest displacement of naled ice particles occurs along the contour of the disc, while they are near-zero at the edges.The most important is the stress distribution pattern, where the highest stress values are evaluated.Based on the analysis of computational modelling solutions, it can be concluded that the maximum intensity of ice spalling occurs at an angle of 45°.
The key conclusions can be drawn from the findings of the numerical experiment: -The best effect has been observed for ice coating of thickness of h=25-50 mm, the destruction of ice coating of thickness over 50 mm with given physical and mechanical properties by the proposed device is very ineffective; -maximum values of shear deformation and tangential and direct stresses responsible for the destruction of icy layer and its separation from the pavement surface have been observed for the same thickness of h=25-50 mm; -optimum velocity is 1.67 m/s, at a low speed of 0.5 m/s the investigated values were much lower.Increasing the speed did not result in a significant increase in strain and stress values.

Directions for Further Research
The authors plan to further investigate the behavior of snow and ice layer on the road under the action of ice-breaking devices.
-It is necessary to carry out calculations for packed ice with different physical and mechanical properties, as well as with different surface hardness, because in real conditions, packed snow is often covered by ice crust with sharp variations in temperature; -It is necessary to determine the optimum attack angle for the cutter sections and angles of cutting edge, which for the numerical experiment was 45°; -At present, the numerical model is unbreakable and does not allow us to see a pattern of ice coating breakage.

Conclusion
During the performance, the following results have been obtained: -The developed algorithm based on a numerical model was implemented in the ANSYS software system to determine the stress-strain state of the ice coating because of circular cutters put into it; -Elastic and shear deformations, normal and shear stresses arising in the ice coating of different thickness and movement speed of the device are determined.Both maximum values of shear deformations and values of shear and normal stresses, which handle the destruction of the icy cover layer and its separation from the hard road surface, were observed for packed ice of thickness of h=25-50 mm; -Optimum running speed and thickness of the packed ice layer is discovered at which the destructive effect is the most distinctive.The best effect was observed when the ice coating thickness was h=25-50 mm.The destruction of more than 50 mm of thickness with the given physical and mechanical properties of the proposed device is very inefficient.Optimal movement speed was 1.67 m/s, the investigated values were much lower at low movement speed of 0.5 m/s.The increased movement speed did not increase strain and stress values much; -The analysis of stressed-strained behavior of packed ice shows that the biggest displacements of packed ice particles take place along the contour (perimeter) of discs and on the surface of the covering.The middle part of the disc (approaching to the centre) is out of device operation.The maximum intensity of the packed ice spalling takes place at an angle of 45°.

Fig. 2 .
Fig. 2. Dependences of shear deformations wY on the speed of movement of the device for different thicknesses of ice layer on the road: 1 -h=25 mm; 2 -h=50 mm; 3 -h=75 mm; 4 -h=100 mm