# Predictive Models for Correlation of Compaction Characteristics of Weakly Cohesive Soils
## 5 Results and Discussions
### Results of Simulations  
To simulate the behavior of the soil, a numerical application was developed in a MATLAB R2023 environment. The virtual model implemented incorporates the initial geotechnical data from measurement point F, along with the inter-parametric relationships outlined in Sections 5.1-5.7 of this paper. This application can be generalized by inputting the initial geotechnical data of the soil, supplemented with the inter-parametric laws corresponding to a different compaction scenario to be analyzed. All the results are presented in Figure 16, using a set of diagrams showing the variation of the soil's main parameters in relation to the resulting degree of compaction and the achieved settlement. Figure 15: The variation of the degree of compaction according to the initial condition of the soil, the thickness of the layer and the number of passes of the compactor, corresponding to the measurements from points F, G, H, I. The primary experimental data obtained from in situ measurements and laboratory investigations, processed and synthesized into final results, are compared with the results from the compaction process simulation based on the predictive soil behavior model, as presented in Table 7.  
Figure 16: Curves of the main parameters that characterized the overall compaction process. Based on the comparative data in Table 7, conclusions can be drawn regarding the validation of the predictive model of soil behavior for qualitative estimates. These estimates are useful both in the machine design phase and in the technological planning of compaction work (e.g., selecting the optimal type and size of the compaction machine, optimizing its operating regime, etc.). In this way, the evolution of the soil state after successive passes of the compactor was demonstrated by an increase in the natural frequency of the soil, reaching approximately 50 Hz after the 12 th pass. The example was tailored for the field measurement point F, and similarly, the compaction performance of other types of soil can be qualitatively estimated, provided that they fall within the applicability range corresponding to the initial geotechnical data determined and experimentally measured at the other three measurement points (G, H, I). The objective of numerical simulation of soil compaction using the Voigt-Kelvin model is to predict the soil's viscoelastic behavior during compaction processes. This includes understanding and quantifying how soil responds to applied stresses and strains over time, accounting for both elastic (instantaneous) and viscous (time-dependent) deformations. Using the input values from Table 8, a computational algorithm was implemented in MATLAB to assess the compaction process parameters and examine inter-parameter correlations based on the roller-soil system's equations of motion. A simulation scenario was conducted wherein stiffness \(\text{k}_{\text{i}}\) varies with discrete values, resulting in a curve (Figure 17) that illustrates changes in vibration amplitude A in relation to the excitation frequency \(\omega\) and damping coefficient c.  
For optimizing the numerical program, we chose the Runge-Kutta numerical method, as it has medium complexity, and both the accuracy and computation speed were highly satisfactory, without redundant operations or large datasets. Regarding the testing and validation of the proposed models, this was done by comparing analytical solutions and experimental test results, and the accuracy of the numerical applications was verified. Thus, the simulation predicted a settlement of 3.5 cm, compared to the experimental test result of 3.245 cm (Table 7), representing a 7.2% error, which is within an acceptable range for validating the model's accuracy. The response force from the soil to the roller action showed a significant increase during the compaction process. After the 12 th pass, the response force had increased by 21% compared to the soil's initial state, demonstrating the compaction's effectiveness in altering soil resistance.