## 1 Introduction
On the other hand, some studies [10,11,14] have highlighted the importance of Soil Behavior Type Index (I\({}_{\text{c}}\) ) as an indicator of soil compaction state with Soil Behavior Type (SBT), as shown in Table 1 and classified the soil into 9 zones based on I\({}_{\text{c}}\) values. [PERSON] et. al. [10] proposed Equations (3)-(5) relating normalized and dimensionless cone parameters; Q\({}_{\text{n}}\) and F\({}_{\text{r}}\). In addition, [PERSON] [15] proposed a correlation to calculate the percentage of fineness in the soil profile using I\({}_{\text{c}}\) values, as shown in Equation (6). \[\text{Ic }=\left[\left(3.47-\log\text{Qtn}\right)^{2}+\left(\log\text{Fr}+1.22 \right)^{2}\right]^{\frac{1}{2}} \tag{3}\]\[\text{Qtn}\;=\;\left[\frac{\text{qt}-\sigma\
u}{\text{pa}}\right]\times\left(\frac{ \text{pa}}{\sigma^{\prime}\,\
u\text{o}}\right)^{n} \tag{4}\]  
\[\text{Fr}\;=\;\frac{\text{fs}}{\text{qt}-\sigma\
u\text{o}}\times 100 \tag{5}\]  
\[\%\text{F}C=\left\{ \begin{matrix}0,\;\text{I}_{\text{c}}<1.26\\ 1.75\times\text{I}\text{c}^{3.25}-3.7,\;1.26\leq\text{I}_{\text{c}}\leq 3.5\\ 100,\;\text{I}_{\text{c}}>3.5\end{matrix} \right. \tag{6}\]  
where:  
\(\text{q}_{\text{f}}=\text{CPT}\) corrected total cone resistance  
\(\text{f}_{\text{s}}=\text{CPT}\) sleeve friction  
\(\sigma_{\text{vo}}=\text{pre-insertion}\) in-situ total vertical stress  
\(\sigma^{\prime}_{\text{vo}}=\text{pre-insertion}\) in-situ effective vertical stress  
\((\text{qt}-\sigma_{\text{vo}})/\text{p}_{\text{a}}=\text{dimensionless}\) net cone resistance, and,  
\((\text{p}_{\text{a}}/\sigma^{\prime}\,\
u_{\text{o}})n=\text{stress}\) normalization factor  
\(\text{n}=\text{stress}\) exponent that varies with SBT  
\(\text{p}_{\text{a}}=\text{atmospheric pressure}\) in same units as qt, \(\sigma\
u\)  
\(\text{Q}_{\text{m}}=\text{Normalized cone resistance}\)  
\(\text{Fr}=\text{Normalized friction ratio}\)  
However, the literature indicates that few researchers have related the cone penetration test (CPT) data with the characteristics of soil profile [10]. [PERSON] et. al. [16] introduced a correlation between cone resistance (Qc) and soil friction ratio (fr) based on Cone Penetration Testing (CPT). However, the proposed correlation assumes that the soil profile is homogeneous, which is not realistic. [PERSON] et. al. [10] linked the I\({}_{\text{c}}\) value and soil bearing-capacity improvement using CPT test data before and after the application of the DC technique in soil improvement projects. The results show that each I\({}_{\text{c}}\) value has a range of improvement with minimum and maximum load-bearing capacity values or thresholds as follows: (i) If I\({}_{\text{c}}\) is less than 2.25, then expected improvement ranges from 10 to 20 MPa; (ii) if I\({}_{\text{c}}\) ranges from 2.25 to 2.6, then the expected improvement ranges from 5 to 10 MPa; (iii) if I\({}_{\text{c}}\) ranges from 2.6 to 2.95, the expected improvement ranges from 0 to 5 MPa; and (iv) if I\({}_{\text{c}}\) is larger than 2.95, the expected improvement is 0 MPa. However, the selected ranges of I\({}_{\text{c}}\) values followed the pattern of collected data rather than soil zone categories. Furthermore, the results depend considerably on the relatively narrow CPT data in which the majority of I\({}_{\text{c}}\) values fall between 2.25 and 2.95. Recently, [PERSON] et al. [17] developed a DC technology-based model under the framework of Mohr-Coulomb criterion to study the characteristics of gravelly soils. The improvement of the saturated foundation under dynamic compaction (DC) by incorporating the soil cap yield hardening model was proposed by [PERSON] et al. [18]. [PERSON] and coworkers [5] studied the impact of dynamic compaction by multi-point tamping on the compaction of sandy soils, whereas [PERSON] et al. [19] performed an in-situ test with vibratory plates to enhance the compaction of granular soils. [PERSON] et al. [20] studied the dynamic response and strengthening mechanisms