## 4 The Internal Force Distribution of Symmetrical Batter Piles and \"Clamping\" Effect  
The distribution and variation in axial force, pile tip resistance ratio, skin-friction, and the influence of the \"clamping\" effect on them will be analyzed in this section. Figure 8 shows the variation in axial force along the depth of the batter pile, where Figure 8a shows the axial force of all tests. Figure 8b shows the variation in axial force under the same pile inclination and different pile spacings, while Figure 8c shows the variation in axial force under the same pile spacing and different pile inclinations. It can be seen that the axial force decreases nonlinearly along the depth and presents as an inverted  
Figure 7: (**a**) Load–displacement of pile cap, and (**b**) variation in symmetric batter pile group efficiency with pile spacing. triangle, which is similar to the distribution of the plumb pile. It indicates that the activation sequence of the skin-friction is identical to the plumb pile. However, it can be seen from Figure 8a,b that in the upper pile section (the dotted circle), the attenuation rate of axial force gradually increases with the pile spacing. This tendency is more obvious when the load is greater, which is quite different from the symmetrical plumb pile. The author believes that this is caused by the \"clamping\" effect. The deformation of symmetrical batter piles leads to the compression of the soil between the piles. The pile-soil normal contact force increases and so does the friction coefficient. Moreover, the increase in confining pressure will result in the increase in the soil stiffness. All the reasons together will lead to an increase in the skin-friction attenuation rate. In terms of Figure 4, the greater the pile spacing, the larger the deformation of the upper pile part, which will further aggravate the \"clamping\" effect. This is consistent with the phenomenon that the skin-friction attenuates rapidly in the upper part of the pile with greater pile spacing. Figure 9c shows the influence of pile inclination on axial force. The influence area also appears on the upper part. The working principle is the same as the influence of the pile spacing on axial force, namely, the deformation of the upper section of the batter pile enhances the \"clamping\" effect. However, the influence of the pile inclination on the axial force is less than that of the pile spacing, and it is significant only when the load is greater. Figure 8: The variation in axial force along depth: (**a**) axial force of all tests, (**b**) axial force when \(\beta=10^{\circ}\), and (**c**) axial force \(\beta=10^{\circ}\) vs. \(\beta=20\). Figure 9: The variation in the pile tip resistance ratio of the symmetrical batter pile. The pile tip resistance ratio (the ratio between the pile head axial force and pile tip reaction force) is an important indicator for investigating the load transfer of the pile foundation [33]. It is commonly used on plumb piles subjected to vertical loading, which can directly reflect the proportion of loading borne by the pile tip and skin-friction. Figure 9 shows the variation in the pile tip resistance ratio under different loadings. The position indicated by the dashed arrow is near the ultimate bearing capacity of each test. It can be seen that when the loading is within 300-600 N, the pile tip resistance ratios are the same. This indicates that the pile skin-friction along the pile axis is not fully activated. As the load increases, the pile tip resistance shows a nonlinear increase. The ratio is negatively correlated with the pile spacing. In terms of Figures 5 and 6, the stronger the \"clamping\" effect, the earlier and more sufficient the skin-friction is mobilized. Therefore, the load transferred to the pile tip is reduced, which indirectly affects the pile tip resistance ratio. The averaged skin-friction per unit length of the batter pile can be obtained from Equation (6), where \(Q_{i}\) is the axial force and \(Z_{i}\) is the depth corresponding to \(Q_{i}\).