# Compression Law and Settlement Calculation Method of Over-Wet Soil Based on Large Samples
## 3 Results and Discussion
### Calculation Method for Settlement of Over-Wet Soil  
The sample size in conventional one-way compression tests is small. Owing to the size effects, the creep process differs from the actual situation, leading to errors in predicting foundation settlement and causing engineering problems. Therefore, if the creep law of a large sample can be used to correct foundation creep based on the water content, the accuracy of the calculation results can be improved. Equations (6) and (7) are the layered summation method calculation equations for general foundations [28; 29; 30], where the compressive modulus \(E_{s}\) is obtained from one-way compression tests, as follows:  
\[S=\sum_{i=1}^{n}S_{i}, \tag{6}\]  
\[S_{i}=\frac{1}{E_{si}}P_{i}H_{i}, \tag{7}\]  
where \(S=\) settlement of foundation (m). \(S_{i}=\) settlement of \(i\)th soil layer (m). \(E_{si}=\) compression modulus of the \(i\)th soil layer (kPa). \(P_{i}=\) average stress of the \(i\)th soil layer (kPa). \(H_{i}=\) thickness of the \(i\)th soil layer (m). According to Equations (4), (6) and (7), the settlement calculation equation for an over-wet soil foundation is expressed in the following Equation (8):  
\[S_{io}=\sum_{n=1}^{i}(\lambda_{i}w_{i}+\frac{P_{i}}{\text{E}_{i}})\cdot H_{i}, \tag{8}\]  
where \(S_{io}=\) settlement of the over-wet soil layer (m). \(\lambda_{i}=\) creep coefficient of the \(i\)th soil layer. \(w_{i}=\) water content of \(i\)th soil layer. To verify Equation (8), conventional one-way compression tests were conducted using the soil samples listed in Table 3, and the compression data are shown in Figure 17. The compressive moduli of the specimens were calculated using the data in Figure 17 and according to the guidelines given by ASTM [31], as listed in Table 8.  
Figure 16: Relationship between water and load with different binding forces. To simplify the calculation of the creep coefficient \(\lambda\) in Equation (8), based on the data in Table 6, the variation law of \(\lambda\) with load was analyzed, as shown in Figure 18. Figure 18 shows that as the load increases, \(\lambda\) exhibits a typical exponential increase. Equation (9) shows the fitting curve with a correlation coefficient of 0.989, as follows:  
\[\lambda=5.0\times 10^{-21}P^{6.57}, \tag{9}\]  
where \(P\) = load (kPa). By combining Equations (8) and (9), the calculation equation for the creep strain of over-wet soil can be obtained, as shown in Equation (10). \[S_{io}=\sum_{n=1}^{i}(5.0\times 10^{-21}P_{i}^{6.57}w_{i}+\frac{P_{i}}{\text{E}_{ i}})\cdot H_{i}. \tag{10}\]  
Based on Equation (10), the deformations of the large specimens were calculated according to the compression moduli in Table 8. The height of the sample was 320 mm, which meets the requirement of a soil layer thickness of between 0.3 m and 1 m. Figure 19a compares the calculated and measured results. Figure 19b shows the calculation results obtained using the conventional layered summation method (Equations (7) and (8)). \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Number** & **1** & **2** & **3** & **4** & **5** \\ \hline Compression modulus, \(E_{i}\)/Mpa & 110.5 & 88.2 & 62.1 & 27.0 & 18.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Compressive modulus of over-wet soil. Figure 17: Compression data of five samples. Figure 18: Variation law of \(\lambda\). Figure 19a shows that the settlement of the over-wet soil calculated using Equation (10) is consistent with the measured values, with errors within 1 mm and an average error of 0.4 mm, indicating high accuracy. The calculation results of the conventional layered summation method, shown in Figure 19b, differed significantly from the measured values, with a maximum error of 6.3 mm and an average value of 2.3 mm. However, the conventional layered summation method does not calculate creep deformation. Figure 19b shows that the conventional layered summation method is more accurate in predicting non-over-wet soil (number 1).