# Displacement Monitoring of Subway Tracks and Tunnels According to Adjacent Construction
## 2 Displacement Monitoring of Tunnel Structures
### Gaussian Analysis Results  
In this study, a gaussian probability density function analysis was performed using data obtained after 1, 10, and 18 months of monitoring. The 1-month monitoring data were used from the beginning to the 1 st month of measurement. The 10-month data were used from the 9 th to the 10 th month. The 18-month data were used from the 17 th to the 18 th month. Figure 5 shows an example of the Gaussian probability density function analysis results for each section using the monitoring data. The Gaussian analysis for each section revealed that in Section A (TL-1), the vertical displacement increased as the adjacent excavation work progressed, as shown in Figure 5a. Compared with that during the initial stage of the adjacent excavation work, the average vertical displacement decreased by approximately 0.022 mm 18 months after construction. As shown in Figure 5b, in Section A (TL-2), the displacement increase was greater than that measured by the TL-1 sensor. Figure 4: Tunnel displacement measurements (Section C, sensor TL-2). Figure 5: Example of gaussian analysis results (1, 10, and 18 months): (**a**) Section A (TL-1); (**b**) Section A (TL-2); (**c**) Section B (TL-1); (**d**) Section B (TL-2); (**e**) Section C (TL-1); (**f**) Section C (TL-2). Compared with the initial stage of the adjacent excavation work, the average vertical displacement decreased by approximately 0.792 mm 18 months after construction. Therefore, as shown in Figure 5, tunnel deformation was affected during construction at a location adjacent to the subway. The change in the vertical displacement of Section C (TL-2) was the largest, and the vertical displacement resulting from the adjacent excavation work decreased by approximately 1.634 mm. Table 3 lists the safety evaluation results for the subway tunnel structure [14; 16; 17; 18; 19; 20; 21; 22]. The safety evaluation results of the subway tunnel structure, shown in Table 3, revealed that the minimum value considering the standard deviation for sensor TL-2 in Section A was approximately \((-)0.937\) mm. The management standard for subway tunnel structures is 3.0 mm. The vertical displacement in Section A was approximately 31.23% of the management standard value. Considering the standard deviation of sensor TL-1 in Section B, the minimum value was approximately \((-)0.354\) mm. The vertical displacement of Section B was approximately \(11.8\%\) of the management standard. Figure 6 shows the analysis results of the maximum vertical displacement according to the measurement month for each section. An analysis of the maximum vertical displacement by section revealed that in Section A, the TL-1 sensor measurement was close to 0, as shown in Figure 6a. However, the vertical displacement of sensor TL-2 increased significantly during the 2 nd to 3 rd months of measurement. In addition, the trend decreased until the 9 th to 10 th months of construction and then increased until the 18 th month. In Section B, as shown in Figure 6b, the change in vertical displacement was more significant for sensor TL-1 than for sensor TL-2. In Section C, no significant change in the displacement was observed for sensor TL-1, as shown in Figure 6c. However, the displacement continued to increase until the 6 th month of measurement with sensor TL-2; nonetheless, the change in displacement until the 18 th month of measurement was not significant. Therefore, for the tunnel structure, the deformation of Section B, the center of the excavation area, was not substantial. However, notable tunnel structure deformations were observed in Sections A and C, located near the start and end points of the excavation area. Subway tunnel structures appear to be more vulnerable as they move from the center of the excavation area to the start and end points.