## 5 Parameter Analysis through Numerical Analysis
### Numerical Analysis Results  
Figure 9 is the numerical analysis results of the volumetric strain increment with depth for various tamper sizes when a 20-ton tamper was dropped 12 times at a height of 15 m. The numerical analysis results showed that both large compression and large expansion of ground tended to occur in the range of about GL-6 m depth. It is thought that this phenomenon is caused by rebound when the loading on the ground surface is removed after applying for 0.05 second to simulate the impact loading in numerical analysis by referring to the deceleration response curve (Figure 8). Therefore, it could be reasonable to consider the region where compression and expansion are mixed as the expected region where large deformation following particle rearrangement occurred due to the high stress above the yielding stress induced by dynamic compaction. As shown in Figure 9, only compressive deformation occurred below the region of large deformation, and the change of volumetric strain with depth tended to decrease linearly without showing an inflection point, which indicates linear decrease in the degree of improvement.  
Figure 8: Curve of deceleration response measured during dynamic compaction tests ([PERSON] et al., 1984).  
Figure 9: _Cont._In this study, the depth of the region where the volumetric strain increment was less than \(-0.1\%\) was considered as the improvement depth. The improvement depth was estimated to be 10.0-11.5 m from the numerical analysis when the ground was compacted 12 times by a 20-ton tamper, and the estimated improvement depth was similar to that estimated using the empirical equation (Table 4). Also, the numerical analysis results showed that the maximum improvement depth, where large deformation takes place, was located at about 1/3 to 1/2 of the improvement depth.  
Figure 10 shows the horizontal and vertical displacement distribution when a 20-ton tamper with diameter of 4 m was dropped 12 times. Numerical analysis results showed that the effects of dynamic compaction, such as settlement and rebound, were large within the 2D (D = diameter of tamper) range from the center of the tamper and showed almost no effect of dynamic compaction at distances greater than 4D. The volumetric strain increment distribution shown in Figure 11 also shows a similar tendency.  
Figure 10: Horizontal and vertical displacement due to compaction (D = 4 m, W = 20 tons, N = 12, H = 15 m): (**a**) ground settlement distribution; (**b**) horizontal displacement contour; (**c**) vertical displacement contour.  
On the other hand, the ground subsidence increased continuously as the number of compaction increased, as shown in Figure 13. It is thought that the additional compaction after shear failure of ground caused the continuous increase in ground subsidence along with heating around the crater. However, dissipation of excess porewater pressure and rearrangement of particles will occur during dynamic compaction after shear failure in actual sabkha ground, and the ground subsidence will not increase much after a certain number of drops as the improvement depth and the strength of ground gradually increase.  
Figure 12: Relationship between improvement depth and compaction energy with increase in number of drops: (**a**) H = 10 m; (**b**) H = 15 m; (**c**) H = 20 m; (**d**) N = 20.  
Figure 13: _Cont._