## 4 Results and Discussions
### Effect of Pile Inclinations
#### 4.1.1 Pile Deflection  
Figure 10 illustrates the variation of non-dimensional pile deflection with depth under different pile inclinations (\(\beta\) = \(-20^{\circ}\), \(-10^{\circ}\), \(0^{\circ}\), \(+10^{\circ}\), and \(+20^{\circ}\)). All the deflection curves of the battered piles are enveloped by those of the vertical piles, indicating that all the deflections of the battered piles (\(\beta\) \(\
eq\)\(0^{\circ}\)) are less than those of the battered piles (\(\beta\) = \(0^{\circ}\)). For cases of negative pile inclinations, the variation of pile inclination from \(0^{\circ}\) to \(-10^{\circ}\) and \(-20^{\circ}\) would reduce the non-dimensional pile head deflection by 22.2% and 44.4%, respectively, when \(p\) equals 34.375 kPa, and the reductions would be 60.3% and 98.2%, respectively, when \(p\) equals 84.375 kPa. For cases of positive pile inclinations, the change of pile inclination from \(0^{\circ}\) to \(+10^{\circ}\) and \(+20^{\circ}\) would result in reductions of 3.7% and 29.6%, respectively, when \(p\) equals 34.375 kPa, and the reductions would further increase to 12.2% and 49.5%, respectively, when \(p\) equals 84.375 kPa. Note that the deflection at \(z_{\alpha}=-0.07\) in the case of \(\beta\) = \(-20^{\circ}\) and \(p\) = 84.375 kPa is abnormally less than that of greater depth and regarded as the type-I abnormal point (Figure 10b).  
These observations reveal that battered piles are significantly superior to vertical piles in resisting lateral soil movement because their axial forces can provide additional horizontal resistance components, and particularly, the negative battered piles outperform the positive ones. The positive battered pile would provide b  
Figure 10: Variations of the non-dimensional pile deflection with depth under different pile inclinations: (**a**) \(p\) = 34.375 kPa; (**b**) \(p\) = 84.375 kPa.  
vertical pile due to an increase in resisting passive wedge. In the case of the negative one, although there is a decrease in resisting passive wedge, the force that can produce the lateral displacement of interest is even smaller due to the pile inclination. The lateral thrusts on the pile should be first decomposed into the component of compression within the pile and the component normal to the pile, and only the latter can increase the lateral movements. More importantly, compared with positive battered piles, compression would be produced within the negative battered piles and surrounding soil to better mobilize lateral soil resistance [22]. The greater the magnitude of the pile inclination, the better the lateral resisting capacity. On this basis, a further field test would be carried out to improve the stability of the embankment by replacing the vertical piles in the original plan with the negative battered piles.  
In addition, it is undeniable that a rigid pile will rotate under lateral soil movement. However, it does not mean that a rotation failure would necessarily occur for a rigid pile. The rotation angle can be calculated from the displacement of the pile and the length of the pile. Only when the rotation angle or pile head deflection is greater than a certain value can it be regarded as rotation failure, and the rotation angles in most cases before the failure are relatively low.