## 2 Laboratory Experimental Program
### Testing Conditions and Procedures
#### 2.2.2 Triaxial Test  
The triaxial test method is used to characterize the mechanical properties of asphalt mixtures under complex stress states, especially in the triaxial tensile stress state, as shown in Figure 2. In this test, a hollow cylinder specimen was placed in the test equipment while the inner and outer surfaces of the specimen were loaded by two independent flexible airbags. Hence, adjustable radial compressive stress and circumferential tensile stress can be generated. Meanwhile, the axial tensile or compressive stresses were produced by a material testing system MTS (Mechanical Testing & Simulation systems company, Minneapolis, USA). Therefore, the three-dimensional unequal stress states can be generated to simulate the complex stress states of asphalt pavement materials in the pavement structures. \begin{table}
\begin{tabular}{c c c} \hline
**Test** & **SBS Modified Bitumen** & **Technical Requirements** \\ \hline penetration (25 \({}^{\circ}\)C) (0.1 mm) & 55.9 & 30–60 \\ penetration index & 0.53 & \(>\)0 \\ ductility (5 \({}^{\circ}\)C /cm, 5 cm/min) & 34.2 & \(\geq\)20 \\ softening point (\({}^{\circ}\)C) & 79.4 & \(\geq\)60 \\ viscosity (135 \({}^{\circ}\)C, Pa\(\cdot\)s) & 2.30 & \(\leq\)3 \\ \hline \end{tabular}
\end{table} 
Table 1: Properties of SBS (Styrene Butadiene Styrene) modified bitumen. \begin{table}
\begin{tabular}{c c c} \hline
**Test** & **Lignin Fiber** & **Technical Requirements** \\ \hline fiber length (mm) & 3.5–4.8 & \(\leq\)6 \\ ash content (\%) & 15.9 & \(18\pm 5\) \\ pH value & 7.12 & 7.5 \(\pm\) 1.0 \\ oil absorption (\%) & 841 & \(\geq\)500 \\ moisture content (\%) & 1.29 & \(\leq\)5.0 \\ density (g/cm\({}^{3}\)) & 0.938 & / \\ \hline \end{tabular}
\end{table} 
Table 2: Properties of fiber. According to elastic mechanics, the principal stresses, including axial stress, \(\sigma_{z}\), radial stress, \(\sigma_{\rho}\), and circumferential stress, \(\sigma_{\varphi}\), can be sorted numerically in terms of the principal stresses \(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\), respectively [29]. In order to simulate the weather of the middle and lower reaches of the Yangtze River and some seasonally frozen areas of China in winter, as shown in Figure 3, 5 \({}^{\circ}\)C was selected as the testing temperature. Before the test, the specimens were kept in the temperature control chamber for more than 6 h. The axial loading rate was 2 mm/min, which is the same as the loading rate of the uniaxial compressive test in the current specification. Before the triaxial compressive test, some measures have been taken to reduce the friction at the end of the specimen. For example, lubricant oil was smeared on the upper and lower surfaces of the specimen. During the triaxial tensile test, it is necessary to ensure that the specimen is broken without degumming [29]. The triaxial test procedures are as follow:  
(1) Tensile meridian and compressive meridian: The tensile meridian/compressive meridian can be obtained by the triaxial tensile/compressive test. Three-direction isobaric stress condition (\(\sigma_{1}=\sigma_{2}=\sigma_{3}\)) of specimens were set at certain stress levels by applying the inner, outer airbags and loading shaft of MTS, and thereafter, the axial tensile/compressive stress \(\sigma_{1}/\sigma_{3}\) was applied until the failure of the specimen. A series of tensile tests were carried out under different three-direction isobaric stress conditions to obtain the tensile meridian. Likewise, the compressive meridian can be obtained. On the tensile meridian and compressive meridian, the lode angle was equal to 0\({}^{\circ}\)and 60\({}^{\circ}\), respectively. The stress path of the tensile meridian and compressive meridians are shown in Figure 4.  
Figure 3: Average temperature map of China in January 2018. Figure 2: Diagram of triaxial test. (2) Strength envelope curve: The strength envelope curve can be obtained by plane tensile and compressive/axial tensile tests.