## 4 Estimation of Improvement Depth of Dynamic Compaction  
The improvement depth of dynamic compaction is estimated from the relationship with the compaction energy. [PERSON] [6] explained the mechanism of subsurface improvement of saturated clay layers by the presence of microbubbles in soil, gradual liquefaction under repeated impacts, and fissure creation and following permeability change. [PERSON] [6] proposed an equation to estimate the improvement depth of dynamic compaction in proportion to the square root of dynamic compaction energy (WH). [PERSON] et al. [7] collected in-situ dynamic compaction test data to find the relationship between dynamic compaction energy (WH) and improvement depth (DI) and proposed Equation (1) using the coefficient of improvement depth, \(\alpha\). Table 3 summarizes the coefficient of improvement depth for various soil types. From Table 3, the sabkha deposit in this study area can be classified as fine sand or silty sand, and the coefficient of improvement depth can be evaluated as 0.60-0.65. \[DI=\ \alpha\sqrt{WH} \tag{1}\]  
where \(DI\) = improvement depth; \(W\) = weight of tamper (tons); \(H\) = drop height (m); and \(\alpha\) = coefficient of improvement depth. [PERSON] and [PERSON] [10] studied the mechanics of dynamic compaction using two-dimensional Finite Element (FE) analyses compared with the centrifuge model results. [PERSON] and [PERSON] [10] concluded that the depth of improvement depends on the momentum per blow and energy per blow. It was found that determining the parameters of the constitutive model using one-dimensional compression data provides reasonably good prediction of both experimental and field data. Figure 4: Falling head permeability test results on sabkha soil [5]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Soil Type** & \(\alpha\) & **Proposed by** & **Soil Type** & \(\alpha\) & **Proposed by** \\ \hline  & 1 & [PERSON] [6] & & 0.3–0.8 & [PERSON] et al. [7] \\  & 0.5 & [PERSON] (1980) & & 0.5–1.0 & [PERSON] [9] \\ Rockfill & 1 & [PERSON] & FINE SAND & 0.65 & \\ Soil with unstable structure & 0.5 & & soft clay & 0.66 & [PERSON] \\ SILTS and SANDS & 0.67 & [PERSON] (1983) & [PERSON] & 0.55 & \\ Purely friction sands & 1 & & SILTY SAND & 0.65 & [PERSON] \\  & 0.65–0.8 & [PERSON] [3] & clayy sand & 0.5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of empirical coefficient of improvement depth, \(\alpha\)[8]. [PERSON] and [PERSON] [4] proposed a method for estimating the ground improvement depth of dynamic compaction on sand using two-dimensional dynamic finite element analyses. The proposed method considered momentum, energy, taper area as well as the initial state of the ground, which is not considered in Equation (1). [PERSON] [8] carried out a parametric study by means of changing Cam-Clay parameters. Two-dimensional and three-dimensional numerical analyses were performed, and the correlation between soil properties and tamping energy and improvement depth of dynamic compaction was presented. However, the study did not explain clearly the problem of dissipation of excess porewater pressure when applying dynamic compaction to clay deposit. The improvement depths are estimated for various tamper drop heights in Table 4. It is suggested that a 20-ton tamper be dropped from 15 m above the ground surface in order to improve the 10-m-deep loose silty sand layer (N = 5-15). [PERSON] et al.