## 1 Introduction  
Asphalt concrete layers of highways during their service life are subject to complex combinations of mechanical impacts of vehicles' wheels and environmental temperature. As is known, the mechanical properties of asphalt concrete depend greatly on temperature and load characteristics, such as value, duration, and rate of loading [1; 2; 3]. Therefore, the experimental determination of asphalt concrete characteristics, as well as modeling of its mechanical behavior in conditions close to the real ones, is practically important. The mechanical failure of asphalt concrete pavement of the highway occurs gradually under impact of frequently repeated vehicle's load, i.e., the damage occurring with each passage of the vehicle's wheel is accumulated. There are several approaches to taking into account the damage accumulation in asphalt concrete pavements. For example, the four-point bending test is used [4; 5]. The vehicles running along the highways have different numbers of axles, the load on which varies within the wide range. It is natural that the axles with different values of load cause different damage levels for pavement. One of the prediction models for materials and structures damage, considering load impact of different values, is the well-known Miner's law [6]. Miner's law is also known as the principle of linear summation of damages [7] and has found wide application in engineering calculations. For example, in the US, it is used for prediction of the fatigue life for the asphalt concrete pavement of highways [8]. In this regard fatigue damage is calculated under the following equation:  
\[D=\sum\limits_{i=1}^{T}\frac{n_{i}}{N_{i}} \tag{1}\]  
where \(D\) is damage, \(T\) is total number of periods, \(n_{i}\) is actual traffic period \(i\), and \(N_{i}\) is traffic allowed under conditions prevailing in \(i\). Vehicles run along the highway with different speed, i.e., they affect the pavement structure for a different duration. As under real road conditions, the speed of the vehicles varies within wide ranges, and axle load duration differs greatly. Unfortunately, Equation (1), based on Miner's law, does not consider load duration, which can be a source of systematic large inaccuracies during determination of fatigue life for asphalt concrete pavement of the highway. At present, the so-called Bailey's criterion is well known in science and engineering practice [9], which can be described in the following form:  
\[\int\limits_{0}^{t_{p}}\frac{dt}{\tau[\sigma(t)]}=1 \tag{2}\]  
where \(t_{p}\) is failure time, \(\sigma(t)\) is stress, varied in time, and \(\tau[\sigma(t)]\) is dependence of material failure time on stress. Contrary to [PERSON]'s law (1), [PERSON]'s criterion (2) considers load duration, i.e., the speed of the vehicle along the highway. Dependence \(\tau[\sigma(t)]\) of [PERSON]'s criterion represents by itself the analytical equation for the so-called curve of long-term strength, which is constructed based on the test results of the material according to the creep scheme [10; 11; 12]. Regarding asphalt concrete, specialists know well the so-called viscoelastic continuum damage mechanics approach (VECD), which is based on the extended elastic-viscoelastic correspondence principle proposed by [PERSON] [13]. This approach, used for the first time by [PERSON] and [PERSON]. [14; 15; 16; 17], has been applied by other researchers for the characterization of asphalt concrete fatigue considering non-linear strain and healing [18; 19]. In the VECD approach, the physical strain and physical stiffness of the viscoelastic material (asphalt concrete) are replaced for their pseudo similarities, i.e., for pseudo strain and pseudo stiffness, respectively, which are varied from one loading cycle to another. Calculation of pseudo strain requires knowledge of dynamic modulus and phase angle, which can be determined experimentally by appropriate devices.