## 6 Numerical Calculation of Working Behavior of Bag-Grouting-Pile Foundation
### Parameter Analysis of the Bag Grouting Pile  
Under stable foundation conditions, we set the pile length of the bag grouting pile at different lengths: 9.5 m, 10.5 m, 11.5 m, 12.5 m, 13.5 m, and 15 m. Figure 14 shows the relationship between pile length and the final subsidence. When the minimum pile length was 9.5 m, the final subsidence was 153.69 mm. At 15 m high, the pile passes through the fine pebble soil under the silty soil with a final subsidence of 135.51 mm. The overall subsidence reduction was 11.8%. In addition, the final subsidence amount of the 11.5 m pile was 145.37 mm. After increasing the pile length, the pile passed through the gravel soil layer, and the subsidence decreased by 6.7%. The bag grouting pile is a kind of friction pile. The bottom of the pile is arranged in the thin round gravel soil with a strong bearing capacity. We found that the appropriate increase in its length was conducive to improving its ability to strengthen the foundation. However, the calculation shows that the subsidence-control effect is not obvious with the increase in designed pile length.  
Figure 14: Pile-length effect on subsidence curves.  
Figure 13: Pile bending and friction distribution.  
To analyze the influence of pile diameter on the subsidence-control effect, we set the diameter of piles as 0.30 m, 0.35 m, 0.40 m, 0.45 m, 0.50 m, and 0.60 m, respectively. The result is shown in Figure 15. When the diameter of the pile was 0.3 m, the corresponding final subsidence was 148.46 mm. When the pile diameter was 0.6 m, the corresponding final subsidence was 139.51 mm. Therefore, its subsidence decreased by 6.02%. When the diameter of the pile was 0.4 m, its final subsidence as 145.37 mm. After increasing pile diameter to 60 cm, the subsidence decreased by 2.08%. The calculation results show that pile diameter has no obvious influence on subsidence. Next, we set different pile spacing: 1.1 m, 1.3 m, 1.6 m, 1.8 m, 2.0 m, and 2.2 m, respectively. The calculation results are shown in Figure 16.  
When the pile spacing was 1.1 m, its final subsidence was 132.34 mm. When the pile spacing was increased to 2.2 m, the final subsidence was 146.85 mm. Its subsidence decreased by 9.8%. With the change in pile diameter and pile spacing, the replacement rate will also change. There is no significant difference in the subsidence-control effect. From a cost-saving perspective, we can reduce the cost by appropriately increasing the pile spacing.  
So, the change in the length of the bag grouting pile has an obvious effect on the subsidence control. However, we think that the change in the replacement rate is relatively small. This means that it can be used as a friction pile to strengthen the foundation, while changes in pile diameter or spacing have an insignificant impact on subsidence. The pile body with a pile-soil stress ratio between 1-4 was deemed a flexible pile, according to field tests. The calculation shows that the bearing capacity of the pile was not fully utilized. The layout of the square of the pile did not change. We can improve the displacement rate of  
Figure 16: Pile-spacing impact on the subsidence curve.  
Figure 15: Impact of pile diameter on the settlement curve.  
the foundation of the bag grouting pile to ensure the subsidence-control standards meet the requirements. For example, we can appropriately increase pile spacing to yield greater bearing capacity and reduce project cost.