## 3 Examples
### The Effects of Calculated Parameters on Results
#### 3.2.2 The Effects of Calculated Length \(l\) on the Pipeline Settlement  
The ranges and values of parameters involved in Case#1 and Case#2 are \(l\) = 11-15 m and \(l\) = 60-90 m, respectively. It is clearly seen from Figure 7 that the calculated length \(l\) has a significant impact on the settlement displacement of pipelines. In Case#1, the maximum settlement increases with the calculated length \(l\). When \(l\) increases from 11 m to 15 m, the maximum settlement displacement of pipelines increases by 128.04% (from 14.55 mm to 33.18 mm). In Case#2, although there is substantially no change for the peak settlement of pipelines with length \(l\) increase, there is a certain change in displacement on both sides. This is related to the calculated length \(l\) of Case#2. Figure 8 illustrates the effects of the calculated length \(l\) on the maximum settlement. The ranges and values of parameters involved in Case#1 and Case#2 are \(l\) = 5-50 m. It is clearly seen from Figure 8 that the maximum settlement displacement of pipelines first increases as the calculated length \(l\) is increased and then decreases slightly, and finally keeps a constant value as the calculated length \(l\) is further increased. It means that when the \(l\) increases to a certain level, the maximum settlement displacement is no longer changing. As compared with Figure 7, it can be concluded that even if the maximum settlement displacement is steady with the \(l\) increase, the settlement of other positions still changes conspicuously. Therefore, the calculated length \(l\) is also of great significance for predicting the settlement distribution of pipelines, and it is an important factor that cannot be ignored in the analytical calculation. Figure 8: Relationship between calculated length and maximum settlement displacement. Figure 7: Effect of calculated length on the pipeline settlement. 3.2.3. The Effects of Subgrade Modulus \(k\) on the Pipeline Settlement  
The settlement displacement of pipelines is calculated under different values of the subgrade modulus illustrated in Figure 9. As is to be expected, the settlement displacement decreases with an increase in the subgrade modulus \(k\), and the maximum settlement is also highly sensitive to the change in \(k\). As for an illustration in Case#1, when \(k\) increases from 20 \(\times\) 10 kN/m\({}^{3}\) to 40 \(\times\) 10 kN/m\({}^{3}\), the settlement decreases by 44.48% (from 33.25 mm to 18.46 mm). In Case#2, when \(k\) increases from 10 \(\times\) 10 kN/m\({}^{3}\) to 30 \(\times\) 10 kN/m\({}^{3}\), the settlement decreases by 33.28% (from 32.96 mm to 21.99 mm). That is because, the higher the subgrade modulus \(k\), the more difficult deformation is. Thus, determining the reasonable subgrade modulus parameter is a critical step during the analytical calculation. Obviously, this depends on the abundant engineering geological investigation data. The relationship between the maximum settlement and subgrade modulus is shown in Figure 10. It can be seen from Figure 10 that the maximum settlement displacement value of pipelines first decreases as the subgrade modulus \(k\) is increasing, and then the value of settlement tends towards stability. When the subgrade modulus \(k\) is small, the settlement displacement gradient has a relatively high value because the soil deformation may be great. This large change gradient is reflected mainly in the small modulus stage, especially before the subgrade modulus \(k\) = 30 \(\times\) 10 kN/m\({}^{3}\). This indicates that the deformation of pipelines in the small subgrade modulus should be the focus of attention. Figures 11 and 12 show the influence of pipeline diameter and elastic modulus on the settlement displacement, respectively. In the calculated results, the settlement displacement,  
Figure 10. Relationship between subgrade modulus and maximum settlement displacement. Figure 9. Effect of subgrade modulus on the pipeline settlement. whether in curve shape or value, shows no significant change.