## 4 An Engineering Application
### Analysis of the Pipeline Settlement Displacement
#### 4.2.2 Determination of Calculated Parameters  
(1) Length of outmost boundary of the subsidence area  
Based on the results of Table 1, the weighting method is used to calculate the average angle of the internal friction of soil, i.e., \(\varphi=17^{\circ}\). The retaining wall height is 25 m, according to Equation (1), and the length of outmost boundary of the subsidence area affected by the foundation pit excavation can be calculated as  
\[z_{0} =H_{\mathrm{g}}\tan\left(45^{\circ}-\frac{\varphi}{2}\right)=25 \times\tan\left(45^{\circ}-\frac{17}{2}\right)\] \[=18.49\ \mathrm{m}\]  
(2) Bending stiffness  
The power pipeline tunnel consists of concrete with a strength grade of C30, so its elastic modulus \(E=3.0\ \times 10^{4}\ \mathrm{MPa}\). In order to simplify the calculation, the tunnel section is transformed into a hollow rectangle plane. The relevant geometric parameters are represented as \(B=3.03\ \mathrm{m}\), \(H=3.3\ \mathrm{m}\), \(b=2\ \mathrm{m}\), and \(h=2.3\ \mathrm{m}\). \(B\) and \(H\) are the length and width of the rectangle, respectively, and \(b\) and \(h\) are the length and width of the hollow part. Therefore, the bending stiffness of the power pipeline tunnel can be calculated as  
\[EI =3\times 10^{10}\times\left(\frac{BH^{3}-BH^{3}}{12}\right)=3 \times 10^{10}\times\frac{3.03\times 3.3^{3}-2\times 2.3^{3}}{12}\] \[=2.19\times 10^{11}\mathrm{N}\cdot\mathrm{m}^{2}\]  
(3) Calculated length  
It can be seen from Figure 2 and Table 2 that most of the measuring points are in the range of the subsidence area; thus, the length of the power pipeline can be taken as the distance of GX01-GX09. It is deduced by calculation that the total length of the pipeline is 147 m, and then the round \(I=150\ \mathrm{m}\) for the sake of convenience in the calculation. (4) Subgrade modulus  
The characteristics of the soil physical parameters are statistically analyzed according to the engineering geologic investigation data and the subgrade modulus \(k=1.0\ \times 10^{7}\) N/m\({}^{3}\) is adopted. (5) Pipeline outer diameter  
It is worth noting that the power pipeline tunnel sectionis hollow rectangular, and not circle. In order to determine the outer diameter \(D\), a circle-section with equivalent stiffness is used to replace the rectangular-section under the same wall thickness conditions. According to Figure 14, the wall thickness of the pipeline is 0.515 m, so the relationship between the outer diameter \(D\) and inner diameter \(d\) can be expressed as  
\[D=d+0.515 \tag{9}\]  
Then, according to the general principle of material mechanics, we can derive the moments of inertia by  
\[I=\frac{\pi\left(D^{4}-d^{4}\right)}{64}=\frac{\left(BH^{3}-bh^{3}\right)}{12} \tag{10}\]  
Thus, the outer diameter is \(D=4.42\ \mathrm{m}\), and the inner diameter is \(d=3.91\ \mathrm{m}\). (6) Ground displacement  
In analytical calculation, an important problem is how to determine the ground settlement corresponding to the center of the pipeline \(\delta\). Although this calculation work is hard, \(\delta\) will be obtained by step-by-step calculation in this study. The basic consideration of the calculation method is to, at first, calculate the settlement of the retaining wall based on the inclinometer hole data, and then the settlement of the power pipeline, obtained with the interpolation calculation, using the distance between the pipeline and retaining wall. This study takes the measuring point GX05 as an example, and defines the position of GX05 as the coordinate origin and GX05\(\rightarrow\)GX09 as the coordinate positive direction. From Figure 13, it can be seen that there are no inclinometer holes in the middle of the powerpipeline, so \(\delta\) can be calculated by data fitting. Additionally, it can also be observed that the inclinometer hole CX4 is adjacent to the measuring point GX03, and the settlement of GX03 can be calculated.