# 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 characterization of the soil, based on its response to the load applied by the compactor roller, is derived from in situ experimental investigations. Considering the regression curve, the analytical expression for the function \(\Delta\text{h}/\text{h}_{\text{c}}-\text{p}\) (which corresponds to the variation of specific settlement \(\Delta\text{h}/\text{h}_{\text{c}}\) with the specific load p applied immediately after loading, based on the experimental results of the oedometer test conducted on Giurgiu loess at the DN 2 construction site--km 39 + 200--Movilita) is established in the form (see Figure 11). \[\frac{\Delta\text{h}}{\text{h}_{\text{c}}}=1000(25.1\text{p}-33.3), \tag{10}\]  
\[\text{p}(\text{N})=4\cdot 10^{-5}\frac{\Delta\text{h}(\text{N})}{\text{h}_{\text{c }}}+1.32\left[\text{daN}/\text{cm}^{2}\right], \tag{11}\]  
where \(\Delta\text{h}\) is the settlement achieved by the machine during the time \(\text{t}_{\text{c}}\) of applied stress under the load of the soil during a passage, and \(\text{h}_{\text{c}}\) is the thickness of the compacted layer. To simulate the compaction process, it is more convenient to derive an expression that describes the time-dependent behavior of a given parameter. This allows for an analytical approximation of the function \(\Delta\text{h}/\text{h}_{\text{c}}-\text{t}_{\text{c}}\) (which corresponds to the variation in settlement), indicating the specific \(\Delta\text{h}/\text{h}_{\text{c}}\) during the loading period \(\text{t}_{\text{c}}\). The expression takes the form:  
\[\frac{\Delta\text{h}}{\text{h}_{\text{c}}}=0.0049\text{Ln}(\text{t}_{\text{c} })+0.0529. \tag{12}\]  
The Law of the Dependence of the Stiffness and Natural Frequency of the Soil on the Density in the Dry State  
One of the main goals of the compaction process is to enhance soil stiffness to the level corresponding to the maximum degree of compaction. Therefore, it is crucial to establish a correlation between the variation in soil stiffness and other parameters specific to the compaction process, such as the static modulus (\(\text{E}_{\text{st}}\)), roller width (B), contact patch width (\(\text{b}^{\star}\)), and Poisson's ratio (\(\
u\)), after each pass (N) of the machine. To analyze the variation in compaction effect within the test area, dynamic stiffness (\(\text{k}_{\text{d}}\)) can be estimated [22] using Equation (13):  
\[\text{k}_{\text{d}}=\text{k}(\text{N})=\frac{1.13\text{E}_{\text{st}}(\text{N })\sqrt{\text{BB}^{\star}(\text{N})}}{1-\text{g}^{2}}. \tag{13}\]  
Figure 11: The regression curve and its analytical expression for the function \(\Delta\text{h}/\text{h}_{\text{c}}-\text{p}\), corresponding to the determinations on loess from Giurgiu (DN 2—km 39 + 200—Movilita site) [6]. Additionally, as the internal state of the material changes, the natural frequency of the ground adjusts accordingly, along with its stiffness. Therefore, it is essential to determine the variation law of this parameter, expressed as follows [22]:  
\[f_{0}(N)=\frac{1}{4h_{c}}\sqrt{\frac{G(N)}{\rho(N)}}, \tag{14}\]  
where  
\[G_{d}=G(N)=\frac{E_{st}(N)}{2(1+\vartheta)}, \tag{15}\]  
where \(h_{c}\) is layer thickness, in \(m\); \(G_{d}\) is shear modulus, in \(kN/m^{2}\); \(\rho\) is density, in \(g/cm^{3}\); and \(f_{0}\) is natural frequency of soil, in \(Hz\). The Law of the Dependence of Settlement on the Number of Passes of the Compactor Established for Each Type of Soil Analyzed  
During the compaction process, after each pass of the machine (without using vibrations), measurements were taken to assess the current and cumulative settlement of the analyzed soil at four measurement points (F-I). These results formed the basis for identifying approximation laws for the variation in settlement as a function of the number of compact passes, as shown in Figure 12.  
Figure 12: Cont.