# Resilient Modulus--Physical Parameters Relationship of Improved Red Clay by Dynamic Tri-Axial Test
## 3 Analysis of Results
### Regression Analysis Results  
The fitting performance of a regression model is frequently evaluated by the determination coefficient, R\({}^{2}\), defined as the ratio of regression sum of squares (SSR) to total sum of square (SST), that is R\({}^{2}\) = SSR/SST.  
\[SSR=\sum_{i=1}^{n}\Bigl{(}y_{i}-\widehat{y}_{i}\Bigr{)}^{2} \tag{5}\]  
\[SST=\sum_{i=1}^{n}(y_{i}-\overline{y}_{i})^{2} \tag{6}\]  
In Equations (5) and (6), \(y_{i}\) is actual value, \(\widehat{y}_{i}\) is predicted value, \(\overline{y}_{i}\) is sample mean, SSR is regression sum of squares, SST is total sum of square.  
Regression analysis of the test data was conducted for various conditions, and the results are shown in Table 6. From the regression results, a high coefficient of determination between the three prediction models, and the test results, is observed. For the Uzan-Witczak model, NI model and Andrei model, the coefficient of determination \(R^{2}\) was greater than 0.80, 0.934, and 0.937, respectively. By comparing the coefficients of determination for the three prediction models, it can be concluded that the regression results, generated by the Andrei model and the NI model, are better than the regression results generated by the Uzan-Witczak model. In particular, the Andrei model can fit the test data better than the NI model does.  
In the above three prediction models of the resilient modulus, k1 is used to characterize the stiffness of the subgrade soil and is proportional to the resilient modulus. The value of k1 increases with an increase in effective stress, additive content and compactness, and decreases with an increase in moisture content. k2 reflects the influence of confining pressure (bulk stress) on resilient modulus and is positively associated with confining pressure. The value of k2 as a whole decreaseswith an increase in moisture content, and increases with an increase in additive content and compactness. The value of k3 is negative, indicating that a negative correlation between the resilient modulus and the deviatoric stress (octahedral shear stress). k3 shows that the dynamic resilient modulus of subgrade soils decreases with an increase in shear stress, and its value is not obviously related to the moisture content and the compactness.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Additive**} & \multirow{2}{*}{**Compactness/\%**} & \multirow{2}{*}{**Moisture**} & \multicolumn{4}{c}{**Uzan-Witzczak Model**} & \multicolumn{4}{c}{**NM Model**} & \multicolumn{4}{c}{**Andersi Model**} \\ \cline{3-14}  & & **Content/\  
Table 7 and Figure 3 show that predicted resilient modulus versus measured resilient modulus for the improved red clay prepared at 93% compactness and 6% additive (cement and lime). It can be seen that the maximum errors, between the measured and the predicted resilient modulus, by using the [PERSON] model, NI model and Uzan-Witczak model are, respectively, 4.533%, 3.934%, and 6.133%. In addition, the average error and variance of Andrei, NI and Uzan-Witczak models are 1.70% \(\pm\) 1.14%, 2.11% \(\pm\) 1.07%, and 2.32% \(\pm\) 1.75%, respectively. It can be concluded that the fitting performance of [PERSON] model is better than that of NI model and Uzan-Witczak model.