# Experimental and Numerical Study in Dynamic Compaction of Weakly-Cohesive Soils
## 4 Results  
The global characterization of the material in the initial state of the soil is impetuously necessary to estimate the efficiency of the compaction process. Thus, soil samples for conducting investigations were taken from the deposited layer and sent to the authorized laboratory for testing and analysis. It should be specified that the machine maintained a constant working speed of v = 1.44 km/h and performed the first 3 passes without vibrations, then the rest up to 12 passes with vibrations (4 to 6 passes with 50 Hz frequency and 7 to 12 passes with 66.7 Hz). The results of the experimental geochemical determinations carried out by taking samples from the soil, starting from the initial state, during the compaction process (every two passes), and until reaching the required degree of compaction, are centralized in Table 1. It is observed that, as the compaction of the soil increases, the width of the contact area between the terrain and drum decreases, which is an important factor to consider in the rheological model [18; 33]. A similar observation can be made regarding the variation in soil density with the number of machine passes. In this case, establishing a parametric relationship is also highly valuable [34; 35; 36]. The authors of this paper noted that alternative relationships between the parameters involved in assessing the efficiency of the compaction process are of interest, and these are illustrated in Figure 7.  
Linear laws are often used for predicting compaction because they simplify calculations, making them suitable for numerical simulations, but they may not always capture the complexity of real compaction behavior, which can often be nonlinear. Proposed laws in the research can be used to predict the number of passes required to achieve the desired compaction degree when a similar type of weakly cohesive soil is used for construction. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Passes** & **Contact Area Width** & **Settlement** & **Dry Density** \\
**No** & **[cm]** & **[cm]** & **[kg/cm\({}^{3}\)]** \\ \hline
0-3 & 16 & 0 & 1.465 \\
4 & - & - & 1.820 \\
6 & 8 & 0.720 & 1.850 \\
8 & 7 & 0.950 & 1.873 \\
10 & 6 & 1.470 & 1.900 \\
12 & 5.5 & 1.490 & 1.953 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of experimental investigations during compaction process [23]. Figure 7: Laws approximation for contact area width vs. compaction degree (**a**) and contact area width vs. terrain settlement (**b**) [23]. For large-scale projects, it is important to develop similar kinds of equations to achieve effective quality control and optimize the process of compaction. On the other hand, dynamic response analysis was conducted on multiple samples to assess vibration levels by recording signals during each pass. The results are shown in Figure 8 in the form of diagrams of the drum vibration amplitude and the spectral analysis of the signal after 12 passes at the completion of the compaction process. The working frequency of the vibrating roller on the 12 th pass is 66.7 Hz, which means that the period is T = 0.014 s. Thus, in the interval of 1 s, we have 71.4 vibration cycles, which explains the behavior of the signal shown in Figure 8a. Predominant frequency peaks were observed in the analyzed signal, and their values have the following results:  
* The natural frequency of the roller is 0.95 Hz. * The eigenfrequency of the terrain needed to reach the maximum degree of compaction is 50 Hz. * The vibration working regime of the roller is 66-68 Hz. Based on Equations (13)-(15) and experimental results, the evaluation of the natural frequency of the terrain as its stiffness increases is highlighted in Figure 9 during the 12 passes of the compactor. To facilitate the simulation of the motion of the vibratory roller--terrain system with the rheologic model to evaluate the performance of the compaction process, the following hypotheses are formulated [13]:  
* Cohesionless soil is represented by the Voigt-Kelvin model. * The inertial properties of the soil are neglected.