# Predictive Models for Correlation of Compaction Characteristics of Weakly Cohesive Soils
## 5 Results and Discussions
### The Law of the Dependence of the Specific Pressure in the Soil and Settlement
The summarized cumulative settlement variation laws, \(\Delta\text{h}_{\text{c}}=\Delta\text{h}_{\text{c}}(\text{N})\), are provided in Table 5.  
The Law of the Dependence of the Degree of Compaction on the Number of Passes of the Compactor Established for Each Type of Soil Analyzed  
In formulating these laws (Figure 13), the general trend in the evolution of material compaction was also considered. From a mathematical perspective, this trend is represented by a logarithmic function with a horizontal asymptote, reflecting the maximum compressibility limit of the material's structure. This is why, in certain cases, logarithmic functions were favored to establish approximate relationships between parameters (Table 6), even though the resulting error was higher compared to the use of linear approximations. \[\text{p}(\text{N})=4\cdot 10^{-5}\frac{\Delta\text{h}(\text{N})}{\text{h}_{\text{c }}}+1.32\left[\text{daN}/\text{cm}^{2}\right], \tag{11}\]0 Current and cumulative settlement variation for compact passes. Considering that it is recommended to perform the first three passes statically during the compaction process, followed by subsequent passes with the rollers in vibration (dynamic) mode, the authors propose a linear empirical relationship for calculating the predicted degree of compaction after each of the first three passes. This calculation is based on parameters that characterize the initial state of the soil, including initial and maximum dry density, initial moisture content, optimal moisture content (w\({}_{\text{opt}}\)), and the number of passes. The proposed relationship takes the following form:  
\[\text{p}(\text{N})=4\cdot 10^{-5}\frac{\Delta\text{h}(\text{N})}{\text{h}_{\text{c }}}+1.32\left[\text{daN}/\text{cm}^{2}\right], \tag{11}\]1 \begin{table}
\begin{tabular}{c c} \hline \hline
**Measurement Points** & **Approximative Laws** \\ \hline F & for N = 1...12: \(\text{D}_{\text{i}}(\text{N})\) = 2.9599 In(N) + 89.524; \(\text{R}^{2}\) = 0.9987 or \(\text{D}_{\text{i}}(\text{N})\) = 0.6273N + 89.80; \(\text{R}^{2}\) = 0.8753. \\ G & for N = 1...11: \(\text{D}_{\text{i}}(\text{N})\) = 1.1525N + 86.991; \(\text{R}^{2}\) = 1. \\ H & for N = 1...10: \(\text{D}_{\text{i}}(\text{N})\) = 2.152 In(N) + 93.76; \(\text{R}^{2}\) = 0.5907 or \(\text{D}_{\text{i}}(\text{N})\) = 0.5859N + 93.835; \(\text{R}^{2}\) = 0.8846. \\ I & for N = 1...10: \(\text{D}_{\text{i}}(\text{N})\) = 0.468N + 95.086; \(\text{R}^{2}\) = 0.8667. \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Centralization of variation laws \(\text{D}_{\text{i}}=\text{D}_{\text{i}}(\text{N})\). Figure 13: Compaction degree variation in function by roller passes for the soil with different initial compaction degree: (**a**) point F with \(\text{D}_{\text{i}}\) = 74.5%; (**b**) point G with \(\text{D}_{\text{i}}\) = 79.7%; (**c**) point H with \(\text{D}_{\text{i}}\) = 78.5%; (**d**) point I with \(\text{D}_{\text{i}}\) = 81.7%. where \(\alpha\) is a correction coefficient defined as follows:  
\[\alpha=\left\{ \begin{array}{c}1.135\ \mathrm{for}\ 70\%\leq\mathrm{D}_{\mathrm{i}}<75 \%\\ 1.0\ \mathrm{for}\ 75\%\leq\mathrm{D}_{\mathrm{i}}<80\%\\ 1.025\ \mathrm{for}\ 80\%\leq\mathrm{D}_{\mathrm{i}}<85\%\\ 1.1\ \mathrm{for}\ \mathrm{D}_{\mathrm{i}}\geq 85\%\end{array} \right.. \tag{17}\]  
The validity of Equation (17) must also be correlated to the machine's technological index, \(\mathrm{i}_{\mathrm{m}}\), as defined by the following relation:  
\[\mathrm{i}_{\mathrm{m}}=\beta\frac{\mathrm{m}_{\mathrm{r}}}{\mathrm{BD}_{ \mathrm{r}}}\left[\mathrm{kg}/\mathrm{m}^{2}\right] \tag{18}\]  
where \(\mathrm{m}_{\mathrm{r}}\) is the roller drum mass, \(\mathrm{B}\) is the roll width, \(\mathrm{D}_{\mathrm{r}}\) is the roller drum diameter, and \(\beta\) is the load amplification coefficient when the roller operates with vibrations, calculated as the ratio between the dynamic force and the weight of the roller. Under static working conditions with the compactor roller, this coefficient is equal to one.