## 2 Intelligent Compaction System
### Compaction Strength Measurement  
The strength of the earnthen material is named as a bearing coefficient measured in terms of the change in stress (load applied) and the material settlement. Intelligent Compaction Measurement Values (ICMV) are the most common terminology for analyzing the compaction strength. The CMV, CCV (compaction control value), stiffness \(K_{s}\), and vibration modulus \(E_{vib}\) are the most common IC compaction measurement values that interpret the data from the accelerometer for quality control (Table 2). The FHWA and several state Departments of Transportation of the US suggested that these values strongly correlate with traditional in situ strength measurement tests [30]. The CMV is used in this research for the characterization of compaction. Its calculation is based on the relationship between the acting vibrations on the roller drum and the repulsive ground force by measuring the g forces on the vibrating drum [19; 31]. During compaction vibrating, the drum exerts vibration energy on the earnthen material. The material vibration response is recorded, and the Fast Fourier Transform (FFT) spectral analysis is applied to the vibration acceleration value to calculate the CMV based on the power spectrum (amplitude). FFT is an optimized algorithm of the Fourier Transform (FT) discovered by French mathematician [PERSON]. A signal wave is repeated over a period of time and factorized in frequency components. The theory has been applied successfully in developing machine and electronic sectors based on time signals such as time or vibration \begin{table}
\begin{tabular}{c c c c} \hline
**Roller MV** & **Unit** & **Calculation Equation** & **IC System** \\ \hline Compaction Meter Value & None & CMV = C \(\frac{\lambda_{200}}{\alpha_{00}}\) &
\begin{tabular}{c} Dynamic \\ Carepillar \\ HAMM \\ Volvo \\ \end{tabular} \\ \hline Compaction Control Value & None & CCV = \(\left[\frac{\lambda_{00}\mathbf{x}-\lambda_{10}\mathbf{x}+\lambda_{200}\mathbf{x }+\lambda_{300}\mathbf{x}}{\lambda_{000}\mathbf{x}-\mathbf{100}}\right]\cdot 100\) & Sakai \\ \hline Stiffness & None & \(K_{S}=\mathbf{y}^{2}\cdot[m_{d}+\frac{\pi\omega_{0}\cos\theta}{\lambda_{d}}]\) & Ammann-Case \\ \hline Vibration Modulus \(E_{vib}\) & None & \(\frac{\frac{E_{vib}\cdot 2\pi v}{2(1-\mathbf{x}^{2})}}{2(1-\mathbf{x}^{2}) \left[\frac{\pi\omega_{0}\mathbf{x}}{(1-\mathbf{x}^{2})\ln(\mathbf{x}_{vib}+ \mathbf{x}^{2})}\right]}\) & BOMAG \\ \hline \end{tabular}
\end{table} 
Table 2: IC roller compaction measurement values. Figure 4: Entity-relation diagram of a system for compaction information. signals. Since the change in stress is directly proportional to vertical acceleration measured from the drum accelerometer, FFT can be used to measure the compaction strength of the ground indirectly in terms of CMV [12; 32]. Figure 5 represents the equilibrium diagram of the centrifugal force (F\({}_{\text{C}}\)), drum load (F\({}_{\text{D}}\)), and repulsive ground force (F\({}_{\text{R}}\)) acting on the roller drum and the ground. This can be expressed as Equation (1); the amplitude can be calculated by integrating the acceleration measured twice. \[m_{w}\cdot\ddot{x}_{w}=m\cdot e\cdot w^{2}\cos wt-\Big{(}m_{w}+m_{f}\Big{)} \cdot g-F_{\text{R}} \tag{1}\]  
Here, \(m_{w}\) is the weight of the drum, \(\ddot{x}_{w}\) is the acceleration of the drum, \(m\) is the eccentric load, \(e\) is the eccentricity, \(w\) is the angular speed, \(t\) is the time, \(m_{f}\) is the weight of the roller frame, and \(g\) is the gravitational acceleration. The vibration of the roller has certain frequencies for different compaction qualities, and FFT can be used to measure the repulsive force. The repulsive force also increases if the compaction roller is operated several times to increase the compaction. The force of the vibrating roller depends upon the vibration frequency and the repulsive force, and they have different frequency amplitudes on the power spectrum according to the compaction material stiffness.