# Ground Stability Analysis in Non-Open-Cut Tunneling Method Using Small-Diameter Steel Pipe Piles
## 5 Numerical Analysis of Pile Behavior under Conditions of Actual Tunnel Size  
### Numerical Modeling Method  
The behaviors of the piles were analyzed by numerically modeling the actual tunnel size. The weathered soil is too weak to endure the collapse of the tunnel face; thus, it can flow down. Therefore, Abaqus 2019, which enables the analysis of large deformations, was used for the numerical analysis in this study. The nonlinear geometry tool of Abaqus was used for the analysis of large deformations, and an explicit analysis was conducted to improve the convergence of the analysis. The Abaqus interaction tool allows the friction coefficient and penetration to be set under the properties of each object. In this study, for the convergence of the numerical analysis, the friction coefficient between the precast structure and the ground was set as zero. The precast structure was set as the master surface and the ground was set as the slave surface. The Mohr-Coulomb model was used for the ground of constitutive model and ground properties is shown in Table 4. Two-dimensional finite element analysis under the plane strain condition was performed using the CPE4R mesh, considering the reduced integration elements option. This option is more suitable for large deformation analysis [14]. The range of analysis is depicted in Figure 11, considering the installed pile specifications listed in Table 5.  
As mentioned above, the tunnel is constructed by repeating the processes of stages 1 and 2, and this repeated process is referred to as one cycle. The piles are installed continually between stages 1 and 2; accordingly, the stresses on the piles keep varying. The distance through which the precast structure is propelled in one cycle is 0.4 m. Therefore, the tunnel moves forward by 0.4 m at the end of each cycle. The distance between the pile and the tunnel during the progress of tunnel construction is depicted in Figure 12. The behaviors of the piles and the ground at cover depths of 1.5, 2.5, and 3.5 m were analyzed.  
In contrast to the procedure followed in static analysis, a time factor should be set for the numerical analysis conducted in explicit analysis; this time factor impacts the result of such numerical analysis. In particular, during construction Stage 1, sufficient time is required to stabilize the ground owing to the collapse of the tunnel face.  
The results of numerical analysis for the maximum stress on the pile for each period of analysis during the fifth cycle at a cover depth of 1.5 m, which constitute the most probable cases for ground failure, are presented in Figure 13. The nearest pile from the tunnel face was numbered Pile-1. The piles were named in numerical order according to the distance from the tunnel face. As depicted in Figure 14, the tunnel face starts to collapse by moving the pressure panel away from the tunnel face. From the point of 4.8 s, the ground remain separated from the pressure panel (Figure 14c), but there is still a slight settlement of the ground and variations in the stresses acting on the piles. For this reason, all analyses in this study were conducted for 12 s, which is long enough to minimize the variations in the stresses acting on the piles.  
Figure 11: Specification of modeling range.  
Figure 12: Location of piles according to progress of construction: (**a**) initial state of first cycle. (**b**) Initial state of second cycle. (**c**) Initial state of third cycle. (**d**) Initial state of fourth cycle. (**e**) Initial state of fifth cycle.  
Figure 13: Variation in stress acting on piles according to time during the fifth cycle at cover depth of 1.5 m.