# Determination of Nonlinear Creep Parameters for Hereditary Materials
## 5 Application of Proposed Algorithm and Methods
### Asphalt Concrete  
Hot dense asphalt concrete of type B which meets the requirements of the Kazakhstan standard ST RK 1225-2013 [32] was prepared with use of aggregate fractions of 5-10 mm (20%), 10-15 mm (13%), 15-20 mm (10%) from Novo-Alekseevsk rock pit (Almaty region), sand of fraction 0-5 mm (50%) from the plant \"Asphaltconcrete-1\" (Almaty city), and activated mineral powder (7%) from Kordai rock pit (Zhambyl region).The used crushed stone meets the requirements of the standard of Kazakhstan ST RK 1284-2004 [33]. In this paper, bitumen of grade 100-130 has been used which meets the requirements of the Kazakhstan standard ST RK 1373-2013 [34].The bitumen grade on Superpave is PG 64-40 [35]. Bitumen has been produced by Pavlodar processing plant from crude oil of Western Siberia (Russia) by the direct oxidation method. Bitumen content of grade 100-130 in the asphalt concrete is 4.8% by weight of dry mineral material. Samples of the hot asphalt concrete in the form of a rectangular prism with the length of 150 mm, width of 50 mm, and height of 50 mm were manufactured in the following way. Firstly, the asphalt concrete samples were prepared in the form of a square slab by means of the Cooper compactor (UK, model CRT-RC2S) according to the standard EN 12697-33 [36]. Then the samples were cut from the asphalt concrete slabs in the form of a prism. Deviations in sizes of the beams didn't exceed 2 mm. Tests of the asphalt concrete samples on creep at the temperature of 22 \(\pm\) 2 \({}^{\circ}\)C were carried out according to the direct tensile scheme in specially contracted equipment. The detailed information regarding characteristics of bitumen, asphalt concrete, and equipment can be found in the work [28]. The stresses were constant during the tests and equal to 0.041, 0.074, 0.111, 0.148, and 0.183 MPa. Durations for tests have been accepted as similar ones and equal to 570 s. 10 parallel asphalt concrete samples have been tested at each constant stress. Mean values of creep strain for the tested 10 asphalt concrete samples are represented in Table 4.  
Creep curves of asphalt concrete at various stresses, constructed according to data of Table 4, are represented in Figure 7. As it is seen, the creep curves represent by themselves the lines which change monotonously with the increase of stress duration. The value of instantaneous strain (at \(t=0\)) and slope of creep curves increase with the increase of stress. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Time \(t\), h**} & \multicolumn{5}{c}{**Strain \(\varepsilon_{E}\) (t), \%, at Stress \(\sigma\), MPa**} \\ \cline{2-6}  & **0.041** & **0.074** & **0.111** & **0.148** & **0.183** \\ \hline
0 & 0.0475 & 0.0543 & 0.0805 & 0.1313 & 0.1782 \\
30 & 0.0633 & 0.0728 & 0.1018 & 0.1584 & 0.2305 \\
90 & 0.0849 & 0.0932 & 0.1338 & 0.1782 & 0.2855 \\
150 & 0.0988 & 0.1102 & 0.1491 & 0.2084 & 0.3310 \\
210 & 0.1099 & 0.1232 & 0.1643 & 0.2484 & 0.3710 \\
270 & 0.1194 & 0.1346 & 0.1795 & 0.2696 & 0.4081 \\
330 & 0.1255 & 0.1457 & 0.1937 & 0.2839 & 0.4482 \\
390 & 0.1339 & 0.1546 & 0.2055 & 0.3184 & 0.4812 \\
450 & 0.1415 & 0.1627 & 0.2158 & 0.3293 & 0.5105 \\
510 & 0.1460 & 0.1713 & 0.2273 & 0.3478 & 0.5433 \\
570 & 0.1488 & 0.1759 & 0.2349 & 0.3632 & 0.5741 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Values of creep strain for asphalt concrete. Then, using the values of stresses and strains, which correspond to various load durations, one can construct the isochronous creep curves (Figure 8). As it is seen, the asphalt concrete is deformed considerably in a nonlinear way at the given temperature, and the nonlinearity degree of relationship between stress and strain has been increased with the stress and strain duration increase. Nonlinearity of strain for asphalt concrete has been noted by other researchers [37,38]. It should be also noted that the isochronous creep curves are similar ones. The property of similarity gives an opportunity to obtain all other isochronous creep curves, if any of them is known.