# Resilient Modulus--Physical Parameters Relationship of Improved Red Clay by Dynamic Tri-Axial Test
## 2 Material Properties and Testing Method
### Testing Method  
In the test, the resilient modulus values were measured by the dynamic servo system UTM400. The loading waveform is half-sine waveform and the load frequency is 1 Hz. The holding time and interval time are 0.1 s, and 0.9 s, respectively. The repeated load and resilient strain were measured by load sensor and displacement sensor respectively in the dynamic tri-axial chamber. The adopted stress loading sequence of subgrade soil was obtained from the international research results [67; 68; 69; 70]. It is necessary to preload the samples before the test to simulate the history of subgrade stress during construction, eliminate the influence of load difference factors, such as initial loading and repeated loading and reduce the variability of test results. In addition, preloading can eliminate the possible bad contact between the bottom of the samples and the pressure plate to improve the accuracy of the  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Samples**} & **Grain** & **Natural Dry** & **Maximum Dry** & **Optimum** & **Liquid** & **Plastic** & **<0.075 mm** \\  & **Density** & **Density** & **Dry Density** & **Moisture Content** & **Limit** & **Limit** & **Grain Size** \\ \cline{2-7}  & **/g/cm** & **/g/cm** & **/g/cm** & **/\%** & **/\%** & **/\%** & **Soil particle** \\  & **/g/cm** & **/g/cm** & **/\%** & **/\%** & **/\%** & **content/\%** \\ \hline Red clay & 2.72 & 1.28 & 1.73 & 27.8 & 52.6 & 30.7 & 90 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Basic properties of red clay.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Mineral**} & \multicolumn{5}{c}{**Mineral Compositions/(\%)**} \\ \cline{2-7}  & **Al\({}_{2}\)Si\({}_{2}\)O\({}_{5}\)(OH)\({}_{4}\)** & **Al(OH)\({}_{3}\)** & **FeO(OH)** & **SiO\({}_{2}\)** & **Deviation** \\ \hline Content(\%) & 60.87 & 11.72 & 13.13 & 11.96 & \(-\)2.32 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Chemical compositions of red clay.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Clinical**} & \multirow{2}{*}{**Mineral**} & \multicolumn{5}{c}{**Mineral Compositions/(\%)**} \\ \cline{2-7}  & & **Al\({}_{2}\)Si\({}_{2}\)O\({}_{5}\)(OH)\({}_{4}\)** & **Al(OH)\({}_{3}\)** & **FeO(OH)** & **SiO\({}_{2}\)** & **Deviation** \\ \hline Content(\%) & 60.87 & 11.72 & 13.13 & 11.96 & \(-\)2.32 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mineral composition of red clay.  
test [70]. A dynamic resilient modulus is defined as the ratio of repeated axial deviatoric stress to the recoverable axial strain as Figure 1. The cyclic number of loading is 100, and the average resilient deformation during the last 5 cycles, for each magnitude of repeated loading, was recorded. The dynamic resilient modulus of samples was calculated according to Equation (1).  
\[M_{\mathrm{r}}=\frac{\Delta\sigma_{d}}{\Delta\varepsilon_{axial}} \tag{1}\]  
where \(\Delta\sigma_{d}\) = deviatoric stress (\(=\sigma_{1}-\sigma_{3}\)), \(\sigma_{1}\) and \(\sigma_{3}\) = major and minor principal stresses, and \(\Delta\varepsilon_{axial}\) = recoverable axial strain.