# 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
### Results of Numerical Analysis for Stage 2 of Each Construction Cycle  
The displacement of the ground occurred upwards from the tunnel face during Stage 2 of each construction cycle when there was no pile. However, when the piles were installed, it prevented the heave and dispersed the displacement of the ground forward. This tendency was observed particularly at low cover depths (Figure 21).  
Figure 21: Ground displacement during Stage 2 of each construction cycle.  
Figure 20: Variation in stress acting on Pile-1 during Stage 1 of each construction cycle at cover depth of 1.5 m.  
In the presence as well as absence of piles, with a decrease in cover depth, the heave of the ground surface increased owing to the small overburden load, because the load counters the force of heave (Figure 22). The graph presented in Figure 23 depicts the heave of the ground surface according to the progress of the construction at a cover depth of 1.5 m. A heave of 94.0 mm was measured in the absence of the piles, but it was minimized to below 53.3 mm when the piles were installed. No relation was seen between heave and the progress of construction. Thus, the largest amount of heave among all the cycles of pushing the precast structure, with the consideration of overlapping length, was estimated to be 53.3 mm, which is the largest one among the results of the analysis.  
The stresses acting on the piles when the precast structure is pushed, based on each cover depth and cycle, are illustrated in Figure 24. The piles were bent upwards, which helped to restrain the heave of the ground.  
Figure 23: Surface heave trough according to progress of construction at cover depth of 1.5 m.  
Figure 22: Displacement during Stage 2 of each construction cycle based on cover depth.  
As illustrated in Figure 24, the stress acting on a pile during the third cycle at a cover depth of 3.5 m, which was a large tensile stress, was concentrated at the bottom of Pile-1. Owing to the bending of the pile, it had no connection with the stress acting on the pile. This occurred because the inserted shoe structure was close to the bottom point of the pile. Except for this case, the maximum stress acting on the piles was 85.2 MPa, which is an acceptable value for the tendency of the graph (Figure 25). As the cover depth decreased, the piles were bent more owing to the small overburden load, which counters the force of heave. Therefore, the stresses acting on the piles generally increased. However, no relation was identified between the stresses acting on the piles and the order of the cycle when the precast structure was pushed. The graph presented in Figure 26 displays the variation in stress acting on the pile at a cover depth of 1.5 m based on the progress of the construction. It was seen that, because the relative locations of the pile and shoe structure were varied based on the progress of the construction, the point of maximum stress moved to the latter part of the pile during the first to fifth cycles. Considering the overlapping length of the pile as listed in Table 5, the stress acting on Pile-1 was estimated to be between 123.4 (fourth cycle) and 132.9 MPa (fifth cycle).  
Figure 24: Stresses acting on piles during Stage 2 of each construction cycle.  
Figure 25: Maximum stress acting on pile during Stage 2 of each construction cycle based on cover depth.