## 4 Validation of the Calculation Method
### Passive Pile Analysis Based on Staged Descriptions of Additional Loads
The extreme point of the negative bending moment is located at a depth of 6.5 m, which is close to the interface between the mixed fill soil and silt layer (depth of 4.8 m), and the extreme point of the positive bending moment is located at a depth of 14 m, which is close to the interface between the silt layer and silt clay layer (depth of 13.1 m). This experimental phenomenon is also consistent with the conclusion obtained by [PERSON] [28] from a model test where the maximum pile-bending moment occurred near the pile top or near the interface between soft and hard soil. Figure 7 shows the comparison between the calculation and measured results under working condition 1. Here, we can see that the pile displacement at the ground does not exceed 6.0 mm (the passive load was calculated using the improved Boussinesq theory), and the calculated results agree with the experimental results. The calculated value of pile-top displacement is 21.61 mm, and the corresponding test value is 4.01 mm. The calculated maximum bending moment of the pile shaft is 59.45 kN, and the corresponding test value is 107.48 kN. The difference between the calculated pile-top displacement and the measured value is only 3.1%, and the relative error of the pile maximum bending moment is 44.6%. Figure 8 shows that the pile displacement and pile-bending moment calculated under working condition 2 are basically consistent with the measured results. The calculated maximum bending moment of the pile shaft is 297.09 kN, which is 3.97 kN greater than the test value. The calculated value of pile-top displacement is 21.61 mm, which is 1.71 mm larger than the test value. The relative error between the calculated pile-top displacement and measured result is only 6.7%, and the relative error between the maximum pile-bending moment and measured result is only 0.5%. Figure 9 shows the additional load caused by the same surcharge when the surcharge distance (\(e\)) and the surcharge width (\(B\)) are different. The black curve in Figure 9 corresponds to working condition 2. Our calculation results show that the horizontal displacement of the pile within 10.5 m below the ground is greater than 6 mm, that the soil around the pile within 4 m of the buried depth is in the plastic flow state, and that the soil around the pile within the buried depth of 4 m to 10.5 m is in an elastoplastic state. The displacement of the pile body with a buried depth greater than 10.5 m is less than 6 mm, and the soil around the pile side is in the elastic state. Figure 8: The calculated and measured values in working condition 2 (\(e\) = 10 m). (**a**) Pile displacement; (**b**) pile-bending moment. Figure 9 shows that when other factors are the same, as the surcharge distant(\(\epsilon\)) changes from 5 m (0.5\(B\)) to 15 m (1.5\(B\)), the additional load gradually decreases, and the maximum additional load decreases from 99.54 kN/m to 20.40 kN/m, about 79.5%. In addition, the position of the maximum additional load gradually moves upward from a depth of about 10.5 m (0.23 L) to a depth of about 5.0 m (0.11 L). When the surcharge width (\(B\)) changes from 5 m to 15 m, the maximum additional load increases from 21.16 kN/m to 71.52 kN/m, a factor of approximately 2.4 times. The position of the maximum additional load gradually moves down with the increase in the stacking width, and its position moves down from a depth of about 7 m (0.16 L) to a depth of about 8.5 m (0.19 L). We thus consider our method to be highly applicable for calculating the passive load caused by the adjacent surcharges in nonlinear settings.