# Predictive Models for Correlation of Compaction Characteristics of Weakly Cohesive Soils
## 5 Results and Discussions
### The Law of Dependence Between the Dry Density and the Moisture Content  
This section aims to identify approximate correlation laws between other parameters that influence the performance of the compaction process for the same type of weakly cohesive soil, but with different initial states, as determined by investigations and laboratory tests for the four measurement points (F, G, H, I). For these points, the focus was on establishing the variation laws between the soil's dry density and its moisture content, using polynomial function approximations (Figure 7). The expressions are presented in Table 3, as this approach resulted in the highest values for the mean square deviation. Figure 6: Representation of the law \(\mathrm{E_{st}}=\mathrm{f}(\mathrm{e_{d}})\) for the four types of soil, corresponding to the four measurement points: (**a**) F; (**b**) G; (**c**) H; (**d**) I.  
Figure 7: The law of variation of the density in the dry state as a function of the soil moisture content with the layer thickness for: (**a**) \(\mathrm{h_{c}}=26.4\) cm (point F); (**b**) \(\mathrm{h_{c}}=24.5\) cm (point G); (**c**) \(\mathrm{h_{c}}=28\) cm (point H); (**d**) \(\mathrm{h_{c}}=29.5\) cm (point I). Since substantial settlement is typically achieved during the first three passes of the machine, it is useful to have a formula for calculating the average dry density of the soil at any given moment, based on specific initial conditions. For example, using experimental data from investigations conducted at measurement point F (with moisture content ranging from 11% to 13.6%) under static compactor conditions, the authors suggest the following empirical equation for calculating dry density after each pass:  
\[\rho_{\rm d}=\rho_{\rm dmax}-\sqrt{\left(\rho_{\rm dmax}-\rho_{\rm di}\right)^{ 2}-k_{\rm\rho}\left(w_{\rm opt}-w_{\rm i}\right)\rho_{\rm dmax}^{2}\frac{\Delta h }{D_{\rm r}}\left[g/cm^{3}\right]}, \tag{8}\]  
where the \(\varrho_{\rm dmax}\) is the maximum dry density, specific to the type of soil being considered (determined by the Proctor test), \(w_{\rm opt}\) is optimal moisture content of the soil for achievement of the maximum compaction degree, \(w_{\rm i}\) is the current moisture content of the soil at a given time (must be less than the optimal moisture), \(k_{\rm\rho}\) is an index accounting for the number of compact passes (\(k_{\rm\rho}=0.7\) for the first four passes, and \(k_{\rm\rho}=0.6\) for passes 5 to 12), Ah, expressed in cm, is the cumulative settlement of the soil achieved at a given time, and \(D_{\rm r}\), expressed in cm, represents the roller diameter of the compaction machine. Moisture content will be reported as a percentage. The Law of Dependence Between the Width of the Contact Patch, Degree of Compaction, Settlement, and Number of Passes  
The contact width \(b^{*}\), measured at a given moment during the static compaction of weakly cohesive soils, can be expressed in terms of several specific parameters, as stated in bibliographic reference [22]. In the case of measurement point F, the expression is given by the following empirical equation:  
\[b^{*}=0.667D_{\rm r}\sqrt{\left(1-D_{\rm i}\right)^{2}-k_{\rm\rho}\frac{\Delta h }{D_{\rm r}}[cm]}, \tag{9}\]  
where the settlement \(\Delta h\) and the diameter \(D_{\rm r}\) of the compactor roller are given in centimeters [cm], while the degree of initial compaction \(D_{\rm i}\) is dimensionless. During the experiments conducted in the soil channel, the contact lengths of the front vibratory drum were measured during vibration compaction. The centralized data from Table 4 served as the basis for identifying the variation law shown in Figures 8 and 9.