## 3 The Deformation Mode and Bearing Capacity of Symmetrical Batter Piles
The reasons are illustrated in Figure 5.  
Figure 5a shows the deformation mode assumed by [PERSON] et al. [29]. The author believes it has limitations. When the symmetrical batter pile is subjected to the vertical loading, the settlement difference between the cap and pile tip must be compensated by the pile deformation. Due to the fixed pile head, the displacement along the X direction is not allowed. Therefore, only two kinds of deformation modes can meet the boundary conditions of the pile and cap connection. They are shown as Figure 5b,c, called mode No. 1 and No. 2, respectively. The deformation of No. 2 is the same as the assumption of [PERSON] et al. Due to the pile inclination and dead weight of the pile, the at-rest soil pressures in the front and back areas of the batter pile are different (Figure 5d) [21]. The pile front is higher than the pile back. From the perspective of force balance, deformation mode No. 2 is less likely to occur. Second, the \"clamping\" effect makes No.2 more difficult to occur. The \"clamping\" refers to the compression of soil between the piles caused by the deformation. This phenomenon is consistent with [PERSON]'s report [30]. The symmetrical batter pile deforms in opposite directions. The greater the pile deforms, the greater the confining pressure on the trapezoidal soil (Figure 5b) between the two piles. It is widely known that the increase in confining pressure will decrease the void ratio and increase the soil stiffness. Considering the above two reasons, only deformation No. 1 could occur, and it is also the only kind of deformation mode. Moreover, the \"clamping\" effect will enhance the pile-soil interaction. The variation in axial force, pile tip resistance ratio, and skin-friction are also affected. These issues will be discussed in the next section. For very flexible piles such as micro-piles, and batter piles of the high-piled wharf and super-long batter piles, the deformation mode mentioned above should be given sufficient attention. According to the deformation value of the batter pile, the method in Figure 6 was used to correct the displacement of the cap based on Equations (4) and (5). Figure 6a,b show the correction method corresponding to deformations No.1 and No.2, respectively. Figure 7 is the corrected result. The response of the pile cap only considers the factors of skin-friction and pile tip resistance, and the influence of deformation (\(\Delta L\)) is removed. The ultimate bearing capacity is also listed in the lower left corner. \[\Delta L=L(1-\cos\theta) \tag{3}\]  
\[\Delta L=\Delta L_{1}+\Delta L_{2}=L_{1}(1-\cos\theta_{1})+L_{2}(1-\sin\theta_ {2}) \tag{4}\]  
Figure 6: Displacement correction method of batter piles (**a**) No.1 and (**b**) No.2. It can be seen from Figure 7a that when the pile inclination \(\beta\) changes from 10\({}^{\circ}\) to 20\({}^{\circ}\), the differentiation between the load-displacement curves is slight. The relative difference is less than 5%, which is quite different from the single pile test (the bearing capacity increases with the pile inclination). The author believes that this is due to the x-direction constraint weakening the influence of the pile inclination on the ultimate bearing capacity. Although the pile spacing increases with the depth, the pile group effect is still obvious from the difference in ultimate bearing capacity between different pile spacings. In this paper, the test with a pile spacing of 7\(D\) was set as the reference to investigate the influence of pile spacing and inclination on the group effect. The pile group effect is defined in Equation (5), where \(UV_{nD}\) and \(UV_{\text{single}}\) represent the loads of the symmetrical and single batter pile under the same displacement, respectively (below the failure load), and \(n\) is the number of piles in the pile group, which equals 2 in this paper. The lower the coefficient, the more significant the pile group effect. The results are shown in Figure 8b.