## 4 Analysis of Settlement Data and Discussion
### The MDD/GNSS Settlement Prediction Model
This prediction was due to the difference in observed total settlement between Position 1 and other positions in the MDD. A 2.0 mm difference in total settlement was assured again by the prediction as shown Figure 24. This settlement difference provides insight into calculation of the void size (\(L\)) using the flexural stiffness (\(EI\)) of the slab and the equivalent design wheel load of the train (\(w\)) using Equation (13). A simple assumption applied for this calculation is that the slab is simply supported and uniformly loaded across its void space length L. In addition, the slab with the void space acts like a two-way slab that is supported on all four sides (Figure 25). Thus, by adapting this assumption, Equation (13) can be used to obtain the maximum deflection (2.0 mm) at the center of the slab. \[\delta_{v}=\frac{5 wL^{5}}{384E  
Figure 20: Comparison of vertical settlement for measured and predicted MDD data (Position #1). Figure 21: Comparison of vertical settlement for measured and predicted MDD data (Position #2). Figure 22: Comparison of vertical settlement for measured and predicted MDD data (Position #3). Figure 23: Comparison of vertical settlement for measured and predicted MDD data (Position #4). Figure 24: Comparison of vertical settlement for all MDD predicted results. For simply assumed parametric values of the flexural stiffness (_EI_) of the slab, the equivalent design wheel load of the rail car (\(w=110\) kN/m) and the generated deflection (2.0 mm) at the center of the slab due to a void space at the bottom, the void space length (_L_) of the space was computed as explained in \[y=7.42-8.38e^{-0.0075x} \tag{10}\]0 We assumed that the initial elastic modulus of 32 GPa of the slab was reduced up to 50% as shown in Table 3 by considering the observed cracks on the surface of the track slab. Then, the void space length (_L_) was calculated to investigate the influence of reduced flexural stiffness, _EI_, of the slab. As can be seen in Table 3, the void space length (_L_) was not sensitively reduced in proportion when the elastic modulus of the slab (_E_) was reduced drastically to 50% of the initial value. This means, conversely, that even though we observed many cracks on the slab that are evidence indicating reduced flexural stiffness at an amount of the surface settlement on the track slab, the slab may contact the outer rim of the track foundation soil surface due to reduced void space. Reversely, at the small amount of the measured settlement of the track slab with high flexural stiffness that is not broken thoroughly yet, it does not tell us whether it fully contacts the bottom soil; otherwise, it has a relatively wide void space at the bottom. This leads to a meaningful implication that rail authorities need to manage the track slab based not only on the measurement of the settlement of the track slab but also on the number of observed cracks and patterns on it. In addition, the lack of bearing capacity due to the existing small void space can be compensated with the flexural stiffness of the slab and is equivalent to the deflection of a 2.0 mm difference between Position 1 and other positions in the MDD (Figure 25). This means that previous repair work was not sufficient, and that new repair needs to be performed in the future even though there was no severe measured settlement using the MDD/GNSS system by the time of 18 April 2020, the end of this study's observation.