# Influence of Deep Foundation Pit Excavation on Adjacent Pipelines: A Case Study in Nanjing, China
## 4 Numerical Simulations
### Validation of Numerical Simulation against Measured Results  
The ground movement caused by excavation has three-dimensional effects and is closely related to the distribution of the lateral deformation of the diaphragm wall. Figure 6 presents an example of the three-dimensional spatial distribution of ground settlement caused by excavation. It shows the maximum lateral displacement of the diaphragm wall and how it changes from the middle to the corner of the pit, illustrating a distinctive three-dimensional pit angle effect. This effect is critical in understanding the variation in surface settlement around the different sides of a foundation pit. The relationship between lateral wall deformation and surface settlement is also evident. The wall between the lateral displacement of the 30 mm wall was selected as the critical displacement interval. It can be seen that the critical interval of the wall is almost the same as the surface settlement interval on different sides of the pit wall. Regarding the lateral deformation of the wall, a gradual transition from the middle to the corner indicates a broader area of surface settlement, while a rapid change leads to a more localized subsidence. The figure thus provides crucial insights into the spatial dynamics of ground movement during excavation projects.  
Figure 7 depicts the settlement distribution curve of the pipeline (P1-8, P9-16) along the parallel direction of the foundation pit's retaining structure. When excavating to the bottom of the pit, the settlement curve of each pipeline shows a concave deformation mode, showing an approximately Gaussian distribution. It can be seen in the figure that the pipe settlement values obtained from numerical simulation tended to coincide with the measured values, which proves the rationality of the numerical simulation. Monitoring points P6-8 and P14-16 were close to the corner of the foundation pit, and the final settlement changes were not significant due to the influence of the pit corner effect. Monitoring points P1-5 and P9-13 are close to the middle of the pit, and the maximum settlement value of the pipeline was more than 30 mm in these locations due to the spatial effect. The settlement and curvature of pipeline in the middle of foundation pit were the largest. It is estimated that for cast iron pipes (P9-16), the maximum curvature was \(4.8\times 10^{-4}\), and the maximum tensile stress was 28.8 MPa. Although this will not damage the strength of the pipe, too large an angle poses a greater threat by weaking the connections of the pipeline.  
It can be seen that the distributions of pipeline subsidence and ground settlement are highly similar. The measured settlement values at the surface and pipeline settlement measuring points with similar plane positions were also close. This shows that the relationship between the settlement of the pipeline and the material and size of the pipeline is not strong but mainly depends on the distance between the pipeline and the foundation pit. This also shows that there is a good contrast between the pipeline and the ground settlement from another point of view. Using the spatial distribution law of the pipeline can further reveal the distribution of ground settlement over a large range, helping to overcome  
Figure 6: Spatial distribution cloud map of ground settlement.  
the shortcomings of most of the previous studies that focused on local ground settlement perpendicular to the retaining structure of the foundation pit. Combining these results with the specifics of this project, it can be found that the range of surface settlement influence caused by foundation pit excavation can extend beyond the edge of the retaining structure. Different from the concave deformation mode of pipeline settlement in the middle of the foundation pit, the pipeline settlement near the pit corner shows convex deformation.