# Steady-State Creep of Asphalt Concrete
## 1 Introduction  
Asphalt concrete is one of the main materials used for highway pavements. Mechanical properties of an asphalt concrete are highly dependent on temperature and time of loading [1; 2; 3]. Therefore, the determination of the mechanical behavior of an asphalt concrete, taking into account the variation of the above-mentioned factors, has important practical value. It is known that the basic methods for evaluating the mechanical behavior of viscoelastic materials are tests on creep and relaxation [4; 5; 6]. Technically, creep test investigations are easy to conduct, and their results make it possible to construct creep and long-term strength curves. Relaxation curves can be obtained from the creep curves by using known methods [6; 7]. The long-term strength curves enable us to determine the service life of an asphalt concrete pavement. The work in Reference [8] analyzes experimentally the process of uniaxial and triaxial creep for two asphalt concrete types (dense bitumen macadam and hot rolled asphalt) at a temperature range of 10 to 40 \({}^{\circ}\)C. It was determined that the creep curve of asphalt concretes has three characteristic stages, the second of which (steady-state creep stage) has a constant strain rate. The viscosity of asphalt concretes for this stage of creep curve depends nonlinearly on the stress. As the result of experimental tests for four asphalt concrete types, [PERSON] [9] approximated the first and the second stages of the creep curve by power function. However, an attempt to establish a linear correlation relationship between an exponent of power function and an exponent of Paris law was not successful. [PERSON] et al. [10] obtained results experimentally that demonstrated the creep strain rate of recycled asphalt shingles with bottom ash (RAS-BA) increased the most with the increase of appliedstress value. The relationship of creep strain rate with stress is described by the power function and showed that the strain and the strain rate of creep increased with a temperature increase. The asphalt concrete test for uniaxial creep at four different temperatures and three levels of stress, with the purpose of permanent strain evaluation was performed by [PERSON] [11]. Test results showed that both stress and temperature impact greatly on creep strain and permanent strain. Having tested the cylindrical specimens of two asphalt concrete types for uniaxial creep during compression at the temperatures of 25, 40, and 60 \({}^{\circ}\)C and three levels of stress, [PERSON] et al. [12] also determined that the creep curve of asphalt concrete had three stages, where the second stage had a constant strain rate. The authors defined creep strain as a viscous flow deformation, and also called the gradual reduction of deformation on the first stage and maintenance of strain rate as a constant on the second stage as the \"consolidation effect\". Either temperature or stress greatly impacts creep strain. The greater the temperature, the less the asphalt concrete resists strain. The greater the stress at a similar temperature, the faster the damage occurs. The time period for the test was 5000 s. A simple model of creep with five parameters was determined from a generalized model of Kelvin, and was proposed for the same maximum duration of deformation. The work in Reference [13] used the test results of asphalt concretes based on the three point bending test at different temperatures and levels of stress to develop master curves of stiffness modulus. In this paper, test results of hot fine-grained asphalt concrete samples on creep are presented. Creep tests were carried out by a direct tensile scheme until complete fracture of the asphalt concrete samples was obtained. The test temperature was 20 \(\pm\) 2 \({}^{\circ}\)C. The applied stress was changed from 0.055 to 0.311 MPa. Creep curves under different loads of the asphalt concrete were constructed. Three characteristic stages of creep curves--the unsteady-state, the steady-state, and the accelerating creep stages--are shown.