## 5 Results and Discussion
### Parametric Study of Underground Diaphragm Wall  
The main factors that affect the ground heave induced by tunnels passing through a diaphragm wall are thickness \(b\), elasticity modulus \(E\), and depth \(H\) of diaphragm wall. However, how those factors affect the ground heave is not known, which should be studied.  
Based on the proposed method, the thickness of the diaphragm wall of 600 mm, 800 mm, 900 mm, 1000 mm, 1100 mm, and 1200 mm is used to calculate ground heave, and other parameters are the same as those in Section 5.2. Figure 15 plots the ground heave under different thicknesses of diaphragm wall at center of the twin tunnels. As the thickness of the diaphragm wall increases, the ground heave decreases gradually. The maximum deformation values are 8.1 mm, 7.64 mm, 7.26 mm, 7.03 mm, 6.88 mm, and 6.84 mm for thicknesses of 600 mm, 800 mm, 900 mm, 1000 mm, 1100 mm, and 1200 mm, respectively. Compared with the maximum deformation value of thicknesses of 600 mm, the decrements of 0.46 mm, 0.84 mm, 1.07 mm, 1.22 mm, and 1.26 mm are for the thickness of 800 mm, 900 mm, 1000 mm, 1100 mm, and 1200 mm, respectively. This indicates that the ground heave trends to stability as the thickness increases. Hence, the large thickness of the diaphragm wall can control the ground heave, but the effect of larger thicknesses is limited. Reasonable selection of thickness of diaphragm wall is significant.  
The effects of elastic modulus of diaphragm wall on ground heave is shown in Figure 16. The values of elastic modulus \(E\) are selected as 15 GPa, 20 GPa, 25 GPa, 30 GPa, and 35 GPa, and other parameters are same as those in Section 5.2. As the elastic modulus increases, the deformation gradually decreases; meanwhile, the ground heave curve is getting much narrower and shallower. Further analysis shows that compared with maximum deformation value of elastic modulus of 15 GPa, the decrements of 0.39 mm, 0.77 mm, 1.16 mm, and 1.55 mm are for the elastic modulus of 20 GPa, 25 GPa, 30 GPa, and 35 GPa, respectively. Hence, the stiff diaphragm wall facilitates the control of ground heave, and the effect is significant.  
Figure 14: 3D ground heave distribution of the proposed method.  
To discuss the effect of the embedded length of the diaphragm wall on ground heave, an embedded ratio \(r_{e}\) is defined as  
\[r_{e}=\frac{H_{e}}{H} \tag{12}\]  
where \(H_{e}\) is the length between the bottom of tunnels and the top of the diaphragm wall.  
The effect of the embedded ratio \(r_{e}\) of the diaphragm wall on ground heave is shown in Figure 17. The length of the diaphragm wall \(H\) is set as 41 m, 49.2 m, 61.5 m, 82.0 m, and 123 m and He kept a constant value of 24.6 m. It is shown that as the embedded ratio increases, the ground heave gradually increases. The increase in degrees for the \(r_{e}\) of 0.3, 0.4, 0.5, and 0.6 are 1.02%, 2.15%, 7.83%, and 13.5%, respectively. This indicates that the embedded length of the diaphragm wall is beneficial to control ground heave, but when the embedded length reaches a certain value, it has little effect on the surface deformation.  
Figure 16: The effects of elasticity modulus E of diaphragm wall on ground heave.  
Figure 15: The effects of thickness of diaphragm wall b on ground heave.  
Considering the above studies, the length of 49.2 m and thickness of 1000 mm diaphragm wall is capable to keep shield tunneling and the ground safe. This design of diaphragm wall is also economical.