# Predictive Models for Correlation of Compaction Characteristics of Weakly Cohesive Soils
## 4 Modeling and Simulation of the Compaction Process  
### The Overall Prediction of the Compaction Process Efficiency  
The simulation of the static and vibratory compaction process is valuable for assessing soil behavior when the initial geotechnical parameters are known. In this context, certain clarifications regarding the input data in the model's calculation algorithm are required, including:  
* geotechnical parameters for describing the soil and its initial compaction state. * characteristic parameters of the roller-soil contact. * parameters defining the operating conditions of the compactor, in line with the adopted working technology. * interdependent laws between the specific parameters of the compaction process. To accurately interpret the simulation results and those presented in the compaction sheets, the following clarifications are necessary:  
* The stress duration under load (t) and the settlements (\(\Delta\text{h}_{\text{i}}\)) refer to the current pass i. * The required number of passes is defined as the number for which the maximum soil stiffness coefficient (kmax) is exceeded. This corresponds to the maximum achievable values for the parameters \(\varrho_{\text{d}}\) (dry density), Est (static modulus of longitudinal deformation), and Di (degree of compaction). The actual values for these parameters, as determined in the field, are known through specific experimental methods. * The pressure (p) considered is the pressure at the beginning of the current passe, but in practice, it reflects the pressure developed at the end of the previous passe. * Settlement \(\Delta\text{h}\) is a cumulative value of settlements \(\Delta\text{h}_{\text{i}}\) from both previous passes and the current pass. * The parameter values of D\({}_{\text{i}}\), \(\varrho_{\text{d}}\), and Est are those obtained after completing the current pass. * The degree of compaction corresponds to conditions of the normal Proctor test, where the specific mechanical work of compaction is 6 dJ/cm\({}^{3}\). * The technological compaction load, quantified by the degree of compaction required to achieve D\({}_{\text{i,rec}}\), is considered the maximum possible value for the working technology used. This corresponds to a state of soil compaction where the maximum value of the soil stiffness coefficient kmax is reached. Developing a mathematical model of a mechanical system associated with the roller-soil system involves representing the physical behavior of the system using mathematical equations following the steps in the Figure 2.  
Figure 2: Steps for developing a mathematical model of a mechanical system. This mathematical model of the roller-soil system involves a structured process to accurately represent the system's behavior using the common next steps:  
* Defining the problem and scope:
* Objectives: To predict soil compaction and the dynamic behavior of the roller. * Boundaries condition: A single-degree-of-freedom (1 DOF) model is used to describe the roller-soil interaction. * Assumptions: The soil properties are assumed to be uniform to simplify the model. * Defining the mechanical system:
* System analysis: Focuses on the motion of the roller-soil system. * Physical properties: Mass, stiffness, and damping are used to describe the behavior of the soil and roller. * Input-output relations: System inputs include the excitation force from the roller drum, vibration amplitude, and frequency. Outputs consist of the roller's vertical displacement. * Drawing the schematic diagram:
* Simplified representation: The Voigt-Kelvin model was selected for system simulation. * Define parameters: The model is represented with 1 DOF and includes a spring element (k) to represent the soil's elasticity, accounting for its ability to recover after being compressed by the roller; a dashpot element (c) to model soil damping, representing energy dissipation during compression; and the mass of the roller drum (m) to represent the roller's weight, influencing its interaction with the soil's resistance.