## 5 Discussion  
All the curves in Figures 3-5 show that the compressive strength of AC-13 and cement-stabilized macadam in a complex stress state is very different to that from the uniaxial compression test. However, uniaxial strength theory is still the mainstream methods to design pavements structure and materials. For example, the stress at one direction of a point in pavements is always calculated to compare with its material's uniaxial strength, which is used as the failure criteria for pavement design. In fact, any point inside pavements is in a three-dimensional stress state. The stress state is different between the calculating point and uniaxial strength test, which will result in design error. Therefore, more complex strength theory should be introduced to evaluate pavement materials' performance, such as the strength theory considering all of the three-principal stress. It has been proved that intermediate principal stress has a great influence on the strength of AC-13 and cement-stabilized macadam. In this section, how to use the results will be discussed. Since the strength model had been developed for AC-13 in Reference [15], only the cement-stabilized macadam's strength model will be discussed here. Many scholars have proposed various strength models for engineering materials. Several strength models considering the effect of intermediate principal stress will be discussed on its applicability for cement stabilized macadam at following, which include a Mohr-Coulomb model, Double-Shear-Corner Model and Double-Shear Model. The coordinate system (\(\sigma_{1}\), \(\sigma_{2}\), \(\sigma_{3}\)) in principal stress space will be converted to a cylindrical coordinate system (\(\xi\), \(r\), \(\theta\)) which includes hydrostatic stress axis \(\xi\) and \(\pi\) plane. A \(\pi\) plane can be determined by \(\xi\), \(\theta\) and \(r\) represents the stress angle and radius vector on a \(\pi\) plane respectively. There is a corresponding limit curve on a \(\pi\) plane, which represents the strength boundary on that \(\pi\) plane. When the value of \(r\) calculating with test data (\(\sigma_{1}\), \(\sigma_{2}\), \(\sigma_{3}\)) is greater than the value \(r(\theta)\) on failure (\(\xi\), \(\theta\)), it means the structure or material will be in a state of failure. For comparison purposes, \(r(\theta)\) will be nondimensionalized as follows:  
\[g(\theta)=r(\theta)/r(60^{\circ}), \tag{1}\]  
where \(r(\theta)\) is the radius vector on a \(\pi\) plane when stress angle is \(\theta\), and  
\[\text{tg}\theta=\sqrt{3}(\sigma_{1}\ -\ \sigma_{2})/(\sigma_{1}\ +\sigma_{2}\ - \ 2\sigma_{3}). \tag{2}\]  
Based on the strength data of different cement content cement-stabilized macadam, its \(\theta\), \(r(\theta)\) and \(r(60^{\circ})\) can be directly calculated. Then, the limit curve \(g(\theta)\) based on measured data can be obtained. This limit curve \(g(\theta)\) will be compared with strength models. The \(g(\theta)\) of the Mohr-Coulomb model, Double-Shear-Corner Model and the Double-Shear Model will be calculated with test data \(\theta\) according to relevant equations in Reference [25]. The calculating results are shown in Tables 5-7. \begin{table}
\begin{tabular}{c c c c} \hline
**Cement Content** & \begin{tabular}{c} **Minimum Principal** \\ **Stress/MPa** \\ \end{tabular} & \
\begin{tabular}{c} **Peak Intermediate Principle** \\ **Stress Influence Factor \(b_{m}\)** \\ \end{tabular} &
\begin{tabular}{c} **Failure Stress Corresponding** \\ **to the Peak Point/MPa** \\ \end{tabular} \\ \hline \multirow{3}{*}{5.5\%} & 2 & 0.49 & 58.75 \\  & 5 & 0.44 & 61.38 \\  & 8 & 0.38 & 65.26 \\ \hline \multirow{3}{*}{4.5\%} & 2 & 0.53 & 54.97 \\  & 5 & 0.47 & 57.89 \\  & 8 & 0.43 & 60.58 \\ \hline \multirow{3}{*}{3.5\%} & 2 & 0.55 & 52.79 \\  & 5 & 0.51 & 54.32 \\ \cline{1-1}  & 8 & 0.45 & 56.95 \\ \hline \end{tabular}
\end{table} 
Table 4: Intermediate principal stress on the compressive strength of cement stabilized macadam.