## 5 Parametric Analysis
### The Effect of Model Parameters on Settlement and Stress  
Considering the same situation as in Section 4.1, point C, point D, point E, and point F (\(m=4\)) are used as the control points of the mapping function. The values of the stratum loss rate \(\eta\), buried depth \(d\), span \(l\), and stratum unit weight \(\gamma\) of the pipe jacking excavation are changed individually. Then, the analytical solution is used to calculate and analyze the effect of the changes in each parameter on the surface subsidence and the major principal stress (\(\sigma_{1}\)) at the excavation boundary, respectively. As shown in Figure 10(a), the surface subsidence keeps increasing with the increase in the stratum loss rate and shows an accelerating trend, but the influence range of the surface subsidence does not change much. When the stratum loss rate \(\eta=1\%\) (change in lateral convergence coefficient of both boundaries of the excavation and vertical subsidence coefficient of the top boundary \(\varepsilon=0.5\%\)), the maximum value of surface subsidence is \(21.7\) mm. As shown in Figure 10(b), with the increase in the strata loss rate, the major principal stress near the top corner and near the bottom corner have a more obvious increase, and the major principal stress in other positions has a smaller effect. As shown in Figure 11(a), with the increase in buried depth, the maximum surface subsidence gradually decreases and tends to a constant value, but the settlement range gradually increases and tends to a constant value. As shown in Figure 11(b), the major principal stress at the top boundary decreases and tends to a constant value, the major principal stress at the bottom boundary increases and tends to a constant value, and the difference between the two values gradually decreases with the increase in buried depth. The change in the major principal stress is more obvious in the position nearer to the top  
Figure 11: The effect of different stratum loss rates \(\eta\): (**a**) displacements \(\sigma\) of the surface and (**b**) major principal stress \(\sigma_{1}\) around the excavation boundary. Figure 10: The effect of the values of \(m\) on the displacements and stresses at specific points of the stratum. corner (\(\theta_{2}=26^{\circ}\)) or the bottom corner point (\(\theta_{z}=-26^{\circ}\)) and tends to be closer to 0 at the position of the two side edges. As shown in Figure 13a, the value and range of surface subsidence increase with the increase in span. When the span is 12.5 m (span-height ratio is 2.5:1), the maximum surface subsidence is 27.3 mm. As shown in Figure 13b, no matter how the span increases, the major principal stress in the vicinity of the corners is very obvious (the angle corresponding to the corner point might not be able to be), and the increase in the major principal stress at other locations is also more obvious. The major principal stresses near the top corner point and near the bottom corner point in each condition increase very obviously (the corresponding angles of the corners \(\theta_{z}\) are different). The increase in the major principal stress at the top boundary is also more obvious, and the changes in the major principal stress at other positions are very small. As shown in Figure 14a, the surface subsidence keeps increasing with the increase in the stratum unit weight and shows an accelerating trend, but the influence range of the surface subsidence does not change much. As shown in Figure 14b, with the increase in stratum unit weight, the major principal stresses near the top corner, near the bottom corner, and the top boundary have a more obvious increase, and the major principal stresses in other positions have a smaller effect. Figure 12: The effect of different buried depths \(d\): (**a**) displacements \(v\) of the surface and (**b**) major principal stress \(\sigma_{1}\) around the excavation boundary. Figure 13: The effect of different spans \(l\): (**a**) displacements \(v\) of the surface and (**b**) major principal stress \(\sigma_{1}\) around the excavation boundary.