# Experimental and Numerical Study in Dynamic Compaction of Weakly-Cohesive Soils
## 4 Results
* The dynamic system contains two masses that perform only movements contained in a single plane and only in the vertical direction. * The working tool has vibratory motion only in the horizontal plane. * The vibrating system is placed so that the unidirectional dynamic force (in the vertical plane) passes through the center of gravity of the working tool (on the symmetry axis). Figure 8: Curves of the drum motion amplitude in vertical plane (**a**) and signal spectrum (**b**) [23]. Figure 9: Curves of the drum motion amplitude in the vertical direction (**a**) and signal spectrum (**b**). The generalized Kelvin-Voigt model was used to simulate viscoelastic deformation of the tested terrain under subjected to the dynamic force developed by the vibratory roller drum of ABG-DD16 type (Volvo Construction Equipment), and the results were obtained for the parameters indicated in Table 2[35]. The variation of the parameter k across a broad range of values in the rheological model reflects an evolution in the degree of compaction and, consequently, an improvement in the efficiency of the technological process. The material damping at the point of drum-terrain contact is very small [17], and the variation is negligible. The simulation scenario consisted of the variation of the discrete values of the stiffness parameter k\({}_{i}\), corresponding to the first three passes, obtaining the curves represented in Figures 10 and 11 with the variation of the model-specific parameters (vibration amplitude A, force transmitted to the ground Q\({}_{0}\) and transmissibility T, damping ratio \(\zeta\)), as well as the dynamic stiffness k\({}_{d}\) and dissipated energy W\({}_{d}\) in relation to the excitation source pulsation \(\omega\) corresponding working regime, with both parameters k and c, with the pulsation ratio \(\Omega\) (between the own pulsation \(\omega_{n}\) and the excitation \(\omega\)). It is remarkable that, as a result of the nature of the soil (weakly cohesive), the value of the energy transferred to the compacted material during one work cycle is very small (until 0.35 J), and the transmissibility reaches the value of 35%. For the simulation using the advanced Kelvin-Voigt model, it is recommended to apply a computational algorithm utilizing optimized calculation routines, such as those available in Matlab(r) R2023 software. The numerical results, shown in Figure 12, are presented as graphs that depict the variation of the total deformation and its components (elastic, plastic, and viscous) within the compacted layer in response to the action of the compactor roller moving at a constant speed and under specific working parameters. In the simulated scenario, the continuous change in the contact area width was accounted for after each of the 12 passes of the roller based on the data summarized in Table 1. \begin{table}
\begin{tabular}{c c c} \hline
**Terrain** & **Vibratory Drum** & **Drum Roller–Terrain Interaction** \\ \hline cohesionless soil & \(M=830\) kg & fast working regime \\ \hline E\({}_{st}=139.4\)e\({}^{5}\) N/m\({}^{2}\) & \(M_{st}=m_{0}r=0.072\) kgm & high frequency vibration \\ \hline \(\zeta=0.283\) & \(f=48\) Hz & \(k=2\times 10^{6}\), \(4\times 10^{6}\), \(6\times 10^{6}\), \(8\times 10^{6}\), \(10\times 10^{6}\) N/m \\ \hline \(D_{i}=0.8567\) & \(F_{0}=6480\) N & \(c=1\times 10^{4}\), \(2\times 10^{4}\), \(3\times 10^{4}\), \(4\times 10^{4}\), \(5\times 10^{4}\) Ns/m \\ \hline \end{tabular}
\end{table} 
Table 2: Input data for compaction simulation process. Figure 11: Variation curves for dynamic stiffness \(\mathrm{k_{d}}\) (**a**) and dissipated energy \(\mathrm{W_{d}}\) (**b**) at excitation source frequency corresponding working regime, for the state of the terrain after successive passes of the roller, defined by the values of the parameters \(\mathrm{k}\) and \(\mathrm{c}\). Figure 10: Variation curves for vibration amplitude, terrain transmitted force, transmissibility, and damping ratio in relation to terrain stiffness and damping.