## 5 The Distribution and Development of the Bending Moment of Symmetric Batter Pile  
Batter piles will generate additional bending moments under the action of dead weight or vertical load. This working behavior is significantly different from that of vertical piles, which is one of the main shortcomings pointed out by the community. In engineering practice, the conformation of symmetrical batter piles is widely used in whavres to bear the vertical loads of equipment and cargo. Therefore, it is necessary to explore the distribution of bending moments. The bending moment is obtained by Equation (7), where \(EI\) is the bending stiffness of the pile section, \(\Delta\epsilon\) is the difference between a pair of strain gauges, and \(d\) is the inner diameter of the pile. \[M(T)=\frac{EI\Delta\epsilon}{d}=\frac{EI(\epsilon_{1}-\epsilon_{2})}{d} \tag{7}\]  
Figure 11 is the distribution of bending moments along the depth under vertical loading, where Figure 11a shows the bending moment of all tests and Figure 11b,c show the comparison of bending moments when the pile inclination or pile spacing is the same. It can be seen that regardless of how the pile spacing or pile inclination changes, the distributions are similar. The maximum bending moment appears at the pile head, and the attenuation rate below 0.2\(L\) is the same. When the pile spacing is 7\(D\), the maximum bending moment of the pile head is largest for all tests. This is because the upper deformation of the pile is largest in all tests, thus enhancing the P-\(\Delta\) effect. The additional bending moment of batter piles is the major disadvantage when comparing with plumb piles. However, when the batter pile appears in the conformation of symmetry, this disadvantage is not that prominent. The comparison of the bending moment between the symmetrical and single batter pile will support the conclusion. The experimental results of [PERSON] et al. [17] are also analyzed. ([PERSON] et al. [17] carried out a series of tests of a single batter under vertical loading. There are two testing groups, in which the material and dimension of the pile, embedded depth, loading height, and method are the same as in this paper.) Figure 12 shows the comparison results, where Figure 12a shows the test results of  
Figure 11: The variation in bending moment of the symmetrical batter pile under vertical loading: (**a**) the bending moment of all tests, (**b**) \(\beta=10^{\circ}\) pile spacing = 3\(D\) vs. 5\(D\), (**c**) \(\beta=10^{\circ}\) pile spacing = 3\(D\) vs. 7\(d\), and (**d**) pile spacing = 5\(D\)\(\beta=10^{\circ}\) vs. 20.  
this paper with different loadings (only loads below 600 N are shown, because 600 N is close to the failure load of the single batter pile), and Figure 12b shows the comparison between [PERSON] and this paper under the load close to failure. It should be noted that in [PERSON]'s experiment, the free length is basically zero, so only the bending moment below the mud-line is analyzed. The disadvantage of an additional moment is fully displayed in the moment distribution of the single pile, namely, the large value and concentration of the bending moment. Due to the action of the free pile head and lateral load component, the P-\(\Delta\) effect is enhanced, which results in the distribution of the bending moment under vertical loading being similar to that of the plumb pile under horizontal loading. Compared with the single batter pile, the symmetrical batter pile can activate deeper pile sections to resist loads either in the working state (Figure 12a) or under ultimate load (Figure 12a). The bending moment develops along the entire pile. Moreover, the P-\(\Delta\) effect is reduced by the constraint of the pile cap and mirror-like pile. Therefore, the maximum bending moment decreases greatly. Even if the pile inclination of the symmetrical conformation is larger than that of the single pile, the maximum bending moment is reduced by 43% (\(\beta=20^{\circ}\) compared with \(\beta=15^{\circ}\)).