## 5 Behavior Prediction during Tunnel Excavation
### Summary of Ground Behavior When a Tunnel Is Excavated in a Ground Mixed with Gravel  
From these results, when excavating a tunnel in a gravel-mixed ground, an equivalent numerical analysis model that inputs the homogeneous physical properties considering the gravel content can express the gravel extrusion and the accompanying large deformation of the sandy ground. However, from the numerical analysis results, it was found that the engineer may make an unsafe judgment. Since these ground behaviors are directly related not only to the workability of the tunnel but also to the safety of the builder, gravel smaller than the tunnel diameter is expected to appear on or near the tunnel face surface. Thus, it is preferable to perform numerical analysis simulating the substrate part. In addition, when performing numerical analysis considering gravel and substrate, the tendency of displacement to the tunnel periphery by the gravel modeling method does not differ significantly in the ground with a gravel content of 40% or less where there is little contact between gravel. Under a gravel content of 40% or more, where gravel is in contact with one another, the rectangular division model forms a collection of rod-shaped or uneven gravel that is rarely seen in the ground where the actual tunnel is dug. It can also be seen the Voronoi division model that reproduces the gravel shape is beneficial because the tunnel displacement is constrained by their engagement. The analysis results thus far show an example for each gravel content rate; however, in many cases, the gravel arrangement of the Voronoi partition model considering the gravel shape and the equivalent physical property model not considering it are changed. Figure 13 shows the difference in displacement that occurs in the tunnel when it is excavated in the created ground. Here, the equivalent physical property model is the result of plotting the analysis results when the Young's modulus of the ground is 10 MPa to 800 MPa and the Poisson's ratio is 0.3, and the Voronoi division model has a gravel content of 40%. Below that, gravel contents of 40-60% and 60% or more cases are colored. The crown subsidence shown on the vertical axis of the graph is the vertical displacement at the tunnel top contact, which is considered + (positive) in the downward direction. However, the side wall displacement is the average of the left- and right-side wall node displacements 1 m above S.L., and the sign is positive on the air side inside the tunnel. In tunnel standard specification (Japan Society of Civil Engineers, [19]), the displacement measurements for tunnel excavation include measurements of internal space displacement, crown subsidence, and leg subsidence. Under the analytical conditions used in this study, no support was installed, and it was not necessary to consider the subsidence of the legs. Therefore, the nodal displacements corresponding to the inward displacement and crown subsidence of the tunnel were obtained. From Figure 13, it can be seen that in the case of the equivalent physical property model, the crown subsidence is directly proportional to the side-wall displacement. On the contrary, in the Voronoi partition model, there are cases where the crown subsidence and side-wall displacement are predominant, so there is a possibility that gravel may be missed in the equivalent elasticity model. Thus, it becomes difficult to predict. Furthermore, Figure 14 shows the analysis results of the Voronoi division model in relation to the gravel content rate and the maximum displacement. For the maximum displacement of the tunnel here, the maximum value of the displacement that occurs in the tunnel wall surface element is plotted. Figure 13: Displacement in the tunnel. From Figure 14, it was found that the maximum displacement of the tunnel tended to decrease as the gravel content increased. However, there are variations in the maximum displacement with respect to the gravel content.