Simulation of stresses in asphalt-concrete pavement with frost heaving

The article reviews the issue of the stress-strain state of the road surface in the winter period as a result of roadbed soil heaving. The main purpose of the work is to determine the stress fields in the asphaltconcrete pavement, which is necessary for designing of frost-resistant roadbeds in the areas with seasonal freezing of roadbed soils. The following research methods were used: theoretical, laboratory, field. With consideration of different properties of materials and geometric dimensions of the road surface section, stress fields in the asphalt-concrete pavement during freezing were obtained with the use of the software product. Comparison of theoretical studies with the results of experimental and fullscale tests showed that the forms of theoretical solutions describe the stress fields in the freezing asphalt-concrete pavement quite accurately.


Introduction
Strains in the form of cracks, which are often formed during the first three years of highway operation, are widespread in northern districts [1,2]. Occurrence of cracks on the pavement in winter can be caused by low-temperature cracking [3,4] or uneven elevation of the pavement surface as a result of frost heaving of soils. In areas with deep seasonal freezing of soils, cracks formed as a result of uneven elevation of the road surface due to frost heaving of soils were most widely spread [5 -7].
To forecast the future state of highways and minimize operating costs for their maintenance, large-scale studies were performed as described in [8]. In this work, occurrence of cracks on the surface of the asphalt-concrete pavement is described by the mathematical model based on statistical study methods. This allows predicting arising of cracks on the road surface with a certain accuracy, but does not explain the process of crack formation.
It is necessary to study the stress-strain state of roadbed in winter for the purpose to increase frost resistance of road surfaces. Works in this field [9 -12] are focused on studying the impact of the automobile wheels on the road surface. At present, the topic of the stress-strain state of roadbed as a result of frost heaving remains poorly studied.
To achieve this goal, a mathematical model of stresses of asphalt-concrete pavements caused by frost heaving was built with consideration of elastoplastic strain by the Huber-Mises criterion [13].

Study methods
Soil conditions of the existing highway network were studied and monitoring of strain in asphaltconcrete pavement in winter was performed at the first stage. Observations were performed at specially prepared posts (sections) of the operated road for three calculation schemes for wetting the ground roadbed. Points for monitoring of the pavement strain were fixed with dowels and painted over (Fig. 1). Roadbed was opened at each site to determine the number of layers and their thickness. The material of each layer was also determined. Soils were sampled to determine their characteristics and heaving properties [14]. To ensure the invariability of the reference point during freezing and heaving of soils, freezing reference points were set up, which were used to measure the roadbed surface in winter [15].
Laboratory experimental studies of asphalt-concrete samples (in the form of small beams) were performed at the second stage. Bending tension tests were performed at negative temperatures. As a result, tensile strength characteristics of asphalt-concete of the A and BI type with 90/130 bitumen were obtained in the range of temperatures from -21 0 С to -35 0 С [16]. The third stage is building a mathematical model for determination of stresses in asphaltconcrete pavement as a result of freezing soils heaving in the roadbed based on the available exact solutions of the mechanics of the rigid strained body (elasticity and plasticity theory) [17]. Critical stresses for asphalt-concrete pavement were determined based on the strain strength characteristics of asphalt-concrete of the A and BI type with 90/130 bitumen obtained as a result of the experiments. Critical stresses were compared to the field measurements. Stree fields were built on the example of the 1st area type by the wettening condition of "Teguldet -B. Dorokhovo, km 19+400, in Tomsk region", where winter monitoring over the pavement strain was performed.

Results
Winter monitoring over the pavement strain as a result of roadbed soils heaving was performed during 2017 to 2018 (Table 1). Note: see distances between points in a row and in a section in Figure 1.
On the basis of these results, it is possible to determine the components of gradient tensor of characterizes rotations (deflections). The symmetric part of this  characterizes the stretching/compression and shear strain (the Cauchy strain) and can be used in case of small deflections. In case of large deflections, the use of the Cauchy strain measure becomes incorrect. It is necessary to use nonlinear Green's ratios [18] to describe the stress-strain state at large deflections: (1) then Green's strain tensor components may be expressed as follows: The stress field can be determined after determination of strains. If the strain is elastic, then Hooke's law is observed, which is as follows in the index form [19]:   where E is the pavement elasticity module (assumed to be 3000  E MPa in the calculations on the basis of design pavement temperature at section "Teguldet -B. Dorokhovo, km 19+400, in Tomsk region" of -21 0 С), is the Poison's ratio. The design pavement temperature was assumed based on the air temperature regime in the area where the monitoring of pavement strain in winter was monitored and was determined by formula [20]: where min T is the 5-day minimum air temperature, 0 С, The invariant measure of strain is intensity of shear deformations: As the stress invariant, shear stress intensity can be considered [21]: According to the Huber-Mises-Henki condition, the transition from the elastic state to the plastic state occurs when the S Y   condition is met [22]. In this case, stress tensor components may be determined from the following equations [18]:  (14)   The results of calculations of stress fields of the asphalt-concrete pavement are presented in Figures 2 to 7. In Figures 2 and 7, maximum shear displacement arise at the beginning and at the end of pavement section "Teguldet -B. Dorokhovo, km 19+400, in Tomsk region" in the xz vertical plane. The cracks that appeared on the pavement did not reach the monitoring area (Fig. 1). Perhaps, a greater increase in shear stresses caused formation of a transverse crack on the road surface.  In Figure 4, stresses in the xy plane are insignificant as compared to the obtained value of asphalt-concrete bending strength of 6.8 MPa (at the design negative temperature of -21 0 С) for this area. The adequacy of the model is confirmed by the results of field studies of pavements and laboratory experiments (Table 2). It must be noted that there are small areas in Figures 5 and 6 that exceed limit values of the bending strength. Cracks of local nature and not long cracks were not registered. It was very difficult to visually regster formation of micro cracks.

Conclusion
Development of the pavement stress prediction model allows considering material characteristics and determining the most critical conditions of the pavement during operation of roads in winter. Based on the results of the study, the model was built that adequately predicted stresses in pavement. Application of the model will ensure the quality of designing frost-resistant roadbeds in areas with deep seasonal freezing. However, the model requires further calibration and continued monitoring of strains in road pavement in winter. To ensure that the model conforms to the actual conditions of pavement operation, more initial information on the pavement material is needed. For example, the effect of aging of bitumen on the strain strength characteristics of asphalt-concrete. Development of a model for predicting behavior of materials of the underlying layers of pavement as a result of frosty soils heaving in the roadbed is not less important.