## 3 Control Effect of Ground Improvement on Tunnel Displacement
### Simulation Conditions of Ground Improvement  
In this study, numerical simulations were conducted to investigate the effects of ground improvement strength (\(q_{\text{u}}\)), ground improvement depth (\(h\)), and ground improvement width (\(w\)) on the control effect on tunnel displacement.  
[PERSON] (2008) [31] pointed out, for cement-improved soil, the unconfined compressive strength \(q_{\text{u}}\) = 0.5-4 Mpa, the ratio of cohesive force to compressive strength \(c/q_{\text{u}}\) = 0.2-0.3, the internal friction angle \(\varphi\) = 20-30\({}^{\circ}\), and the deformation modulus \(E\) = (120-150) \(q_{\text{u}}\). [PERSON] and [PERSON] (2009) [32] pointed out, for cement-improved soil, when the unconfined compressive strength \(q_{\text{u}}\) = 0.5-4.0 MPa, its cohesive force \(c\) = 0.1-1.1 MPa, the internal friction angle \(\varphi\) = 20-30\({}^{\circ}\), and the deformation modulus \(E\) = (100-150) \(q_{\text{u}}\).  
Figure 9: Schematic diagram of ground improvement outside the pit.  
Referring to the above research, in numerical simulations, the unconfined compressive strengths of improved soil \(q_{\rm u}\) = 0.5 MPa, 1.0 MPa, 1.5 MPa, 2.0 MPa, 2.5 MPa, 3.0 MPa, 3.5 MPa, and 4.0 MPa are adopted, totaling eight values. The ratio of cohesive force to unconfined compressive strength \(c/q_{\rm u}\) = 0.25 is adopted; the internal friction angle \(\varphi\) is determined at equal intervals within 20\(\sim\)30\({}^{\circ}\) according to different unconfined compressive strengths; the deformation modulus \(E\) = 130 \(q_{\rm u}\) is adopted. The basic physical parameters of cement-improved soil, such as gravity \(\gamma\) and Poisson's ratio \(\
u\), are taken at equal intervals between 20\(\sim\)21.4 \(\rm{kN/m^{3}}\) and 0.20\(\sim\)0.34 according to different unconfined compressive strengths. Table 4 lists the physical and mechanical parameters of cement-improved soil, corresponding to different unconfined compressive strengths.  
To block the propagation path of lateral unloading stress induced by deep excavation, the ground improvement depth outside the pit is generally deeper than the buried depth of the tunnel. In this study, the values of \(h\) = 1.5\(H_{\rm t}\), 2.0\(H_{\rm t}\), 2.5\(H_{\rm t}\), and 3.0\(H_{\rm t}\) are adopted, totaling four values.  
The ground improvement width is determined according to the horizontal distance between the tunnel and the retaining wall, and the distance from the improved soil to the springing line of the tunnel should be less than 1 m to avoid construction disturbance to the tunnel. In this study, the values of \(w\) = \(L_{\rm t}\)/6, \(L_{\rm t}\)/3, \(L_{\rm t}\)/2, and 2\(L_{\rm t}\)/3 are adopted, totaling four values.  
After considering the three factors of ground improvement strength \(q_{\rm u}\), ground improvement depth \(h\), and ground improvement width \(w\), a total of 128 simulation conditions and numerical models are set.
It is concluded from the above analysis that there are limits to increasing the control effect on tunnel displacement by only increasing the ground improvement strength. Considering the control effect and engineering economy together, it is suggested that the ground improvement strength should be kept within 1.5\(\sim\)2 MPa.