## 3 Results and Discussion
### The Investigation of the Relationship between Pile Bending Moment and Soil Depth  
This paper presents an analysis of the bending moments of each pile shaft, using data measured from the strain gauge during the test. The calculation of the bending moment was based on the theory of elastic foundation beams, which can be shown in Equation (1):  
\[M_{e}=\frac{EI}{D}(\varepsilon_{te}-\varepsilon_{ce}) \tag{1}\]  
where \(M_{e}\) represents the bending moment of the pile, \(D\) denotes the pile diameter, \(\varepsilon_{te}\) and \(\varepsilon_{ce}\) represent the tensile strain and compressive strain of the pile side, respectively, and \(EI\) is the bending stiffness of the pile.  
The arrangement of the pile group is shown in Figure 13. Considering the symmetry of the bearing deformation, this paper only discussed the bending moment distribution of piles 1, 2, and 3.  
Figure 14 shows the variation of the moment of the pile group along the soil depth for different piles. As shown in Figure 14, when s = 3D and CLR = 0.25, the bending moment of each pile at the mud surface increased by 60-70% after 1000 cycles, compared with that at 10 cycles, and by 5-10% at 5000 cycles compared with that at 1000 cycles, which shows a similar law to the horizontal deformation of the bearing platform. At the same time, the pile bending moment of each pile at 1000 cycles was more than 90% of that at 5000 cycles, which indicates that the effect of horizontal cyclic loading on the pile bending moment was mainly concentrated in the early stage of loading. In the whole loading cycle, the bending moment of the pile exhibited a continuous increase with the burial depth, reaching its peak at a depth of \(Z\) = 15-20 cm (approximately 6-8 times the pile diameter). Subsequently, the bending moment of the pile gradually decreased with a further increase in the burial depth, and a point of reverse bending was observed at the burial depth of \(Z\) = 30 cm. As the burial depth exceeded 30 cm, the pile bending moment gradually approached 0 N\(\cdot\)m. This indicates that the effect of horizontal cyclic loading on the pile-soil system of the pile foundation was mainly in the range of 0-30 cm (approximately 0-12 times the pile diameter) below the mud surface and was concentrated in the middle and upper parts of the foundation soil. Meanwhile, with the increase of cyclic loading, the maximum value  
Figure 13: The arrangement of the pile group (The numbers here refer to the number of piles).  
of the pile bending moment was also increased, and there was a downward trend in the location of the maximum value of the bending moment due to the development of cracks around the pile.  
It was also found from Figure 14 that the development of the bending moment for each pile was different under the same force environment due to the influence of the pile-soil-pile interaction. Moreover, the bending moment distribution of pile 1 was similar to pile 2, and they increased by 9-16% compared with pile 3. Therefore, it can be concluded that the bending moment of front-row piles was larger than the back-row piles under the horizontal cyclic loading.  
Figure 14: The variation in the bending moment of the pile group with depth is depicted when the pile spacing is set at 3 times the pile diameter and the horizontal loading ratio is 0.25. (**a**) The loading cycle is set at 10 times. (**b**) The loading cycle is set at 1000 times. (**c**) The loading cycle is set at 5000 times.