## 4 Unconfined Compressive Resilient Modulus Test
### Patterns of Variation of Compressive Modulus at Different Curing Times and Loading Rates  
The modulus of the cement-treated aggregate base material with a curing time of 3 days, 7 days, 14 days, 28 days, 60 days and 90 days was determined under the loading rate of 1 mm/min. Then, modulus tests of the cement-treated aggregate base material specimens with a curing time of 28 days were conducted under the loading rates of 0.1 mm/min, 0.5 mm/min, 1 mm/min, 3 mm/min, 5 mm/min, 10 mm/min. The test results are presented in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Curing Times (\(t\)/d)**} & \multirow{2}{*}{**Loading Rates**} & \multicolumn{6}{c}{**Unconfined Compressive Modulus of Parallel**} & \multirow{2}{*}{**Average Value**} \\  & & & & & **Specimens E\({}_{c}\) (MPa)** & & & \\  & & **(r/mm/min)** & & & & & & **\(E_{c}\) (MPa)** & \\ \hline
3 & 1 & 1830 & 1515 & 1573 & 1370 & 1518 & 1578 & 1365 & 1536 & 10.20 \\
7 & 1 & 1919 & 1946 & 2294 & 2126 & 1988 & 2276 & 2179 & 2104 & 7.37 \\
14 & 1 & 2564 & 2493 & 2344 & 2397 & 2379 & 2156 & 2378 & 2387 & 5.35 \\
28 & 1 & 3004 & 3243 & 2806 & 2793 & 3286 & 3049 & 2935 & 3017 & 6.43 \\
60 & 1 & 3556 & 3974 & 40426 & 3860 & 3762 & 3869 & 4125 & 3882 & 4.82 \\
90 & 1 & 4222 & 4204 & 4107 & 4571 & 4127 & 3942 & 4150 & 4189 & 4.58 \\
28 & 0.1 & 1876 & 2163 & 1636 & 1599 & 2140 & 1784 & 1912 & 1873 & 11.86 \\
28 & 0.5 & 2424 & 2296 & 2351 & 2189 & 2634 & 2306 & 2405 & 2372 & 5.87 \\
28 & 1 & 3004 & 3243 & 2806 & 2793 & 3286 & 3049 & 2935 & 3017 & 6.43 \\
28 & 3 & 3437 & 3679 & 3523 & 3356 & 3240 & 3482 & 3176 & 3413 & 5.04 \\
28 & 5 & 3628 & 3827 & 3741 & 3976 & 3664 & 3792 & 4006 & 3805 & 3.80 \\
28 & 10 & 4040 & 3713 & 3863 & 3752 & 3941 & 4120 & 3723 & 3879 & 4.16 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Test results of the compressive resilient modulus with different curing times and loading rates.  
Figure 6: Device of compression resilience modulus test.  
From the results of the unconfined compressive strength test presented in Table 4, it can be noted that the unconfined compressive modulus of the cement-treated aggregate base material varied significantly with both curing times and loading rates. The patterns of variation might be similar to that of strength, so the average value of the modulus test results with different curing times and loading rates were fitted by Equations (5) and (6), as shown in Figure 7, where \(R^{2}\) is the correlation coefficient.  
\[E_{c}=m_{1}+n_{1}In(t+p_{1}) \tag{5}\]  
\[E_{c}=m_{2}+n_{2}In(t+p_{2}) \tag{6}\]  
where \(E_{c}\) is the compressive modulus, \(t\) is the curing time, \(v\) is the loading rate; \(m_{1}\), \(m_{2}\), \(n_{1}\), \(n_{2}\), \(p_{1}\), and \(p_{2}\) are the fitting parameters.  
Based on the fitting results, it can be observed that:  
1. The effect of the curing times on the modulus of the cement-treated aggregate base material was similar to that for the strength. The modulus varied dramatically with the curing times, especially from 3 days to 28 days, the modulus value increased by 96 % (from 1536 MPa to 3017 MPa). The modulus increased slowly with the later curing times, therefore the cement-treated aggregate base should be maintained for about 28 days after being paved, before paving the upper layer.
2. The modulus of the cement-treated aggregate base material is also affected by the loading rates. The modulus value increased by about 107% (from 1873 MPa to 3879 MPa) with the increase of the loading rates (from 0.1 mm/min to 10 mm/min). Therefore, when the compressive resilience modulus is taken as the pavement design parameter, the effect of the loading rates on it should be considered.  
Figure 7: Patterns of variation for compressive resilient modulus with curing times and loading rates.