## 3 Test Results and Analysis  
### Relationship between Pile Head Displacement and Vertical Load  
Figure 6 shows the relationship between the vertical load (P\({}_{\rm v}\)) of each pile slope and vertical displacement (\(\rho\)) of the pile head by relative density (D\({}_{\rm r}\)). The allowable load was set at 2/3 of the loading when the displacement of pile head was 1.2 cm (Indian Standard 2911), and the increment ratio of batter angle and bearing capacity in each relative density could be set using the value of the allowable load as shown in Figure 7. The increment ratio of bearing capacity was the highest when the batter angle was 20\({}^{\circ}\) regardless of the relative density. In ground with a low relative density (D\({}_{\rm r}\) = 31%), the bearing capacity was always less than the vertical pile except when the angle was 20\({}^{\circ}\). In a medium and high density ground, the bearing capacity kept increasing when the angle of the pile moved from a vertical position to about 20\({}^{\circ}\), and then decreased gradually after 20\({}^{\circ}\). It seems that while the bearing capacity at the front end of the pile decreased as the batter angle of the pile increased, the bearing capacity was the greatest near 20\({}^{\circ}\) of the angle of the pile due to the increase in the surface friction of the pile.  
1.1 Relationship between Horizontal Displacement and Vertical Load of Each Pile Slope by Relative Density  
Figure 8 shows the relationship between the horizontal displacement (\(\delta\)) and vertical load of each slope by relative density. In the same vertical load, horizontal displacement increased as the batter angle increased, and the range of increase was more after 30\({}^{\circ}\). It seems that the horizontal displacement increased by the increase in bending moment caused by the increase in the batter angle of the pile.  
With the same horizontal displacement, the vertical load of the pile tended to decrease as the batter angle increased, which means that if the batter angle of the batter pile under the same vertical load is large, the bending moment of the pile increases gradually and as a result the horizontal displacement increases gradually.  
.1.2 Relationship between the Total Displacement and Vertical Load of Each Slope by Relative Density  
Horizontal displacement and vertical displacement occur in the slope pile under vertical load. For the two kinds of displacement, \(\delta_{t}\) was defined as the total displacement as shown in Figure 9 using Pythagorean theorem.  
Figure 6: _Cont._Figure 6: Relation of vertical load and pile head vertical displacement due to the Batter angle.  
Figure 7: Comparison of bearing capacity.  
Figure 8: Relation of load and pile head total displacement according to Batter angle.  
Figure 10 shows the relationship between the total displacement of the independent batter pile and the vertical load. The total displacement of the pile head increase with the increased in relative density, and the greatest bearing capacity occurred at 20\({}^{\circ}\) of pile slope regardless of the relative density of the ground.  
1.3 Proposal of an Experimental Formula for the Total Displacement and Vertical Load according to Relative Density  
Figure 11 is a graph that proposes an experimental formula using the vertical load according to relative density and the trend line (TL) in the total displacement.  
In Figure 11i, y = ax\({}^{2}\) + bx + c is used to represent a quadratic function, and the values of the a, b, and c coefficients in the trend lines can be represented as a linear function in the graph of Figure 11 ii. As shown in Figure 11i, the  
Figure 10: Relation of vertical load and pile head total displacement.  
Figure 11: _Cont_.  
Figure 11: Experimental formularization by total displacement.