## 4 Discussion  
### Ground Deformation Mechanism  
According to the PIV analysis mentioned before, the ground disturbance range induced by the advancement of the excavation face is approximately fishtail-shaped. The greater the burial depth, the more difficult for the ground deformation induced by excess support pressure to extend to the surface. For the case where the deformation can propagate to the surface, the surface disturbance range can extend horizontally to about twice the buried depth beyond the front of the face and the maximum heave occurred at a distance of approximately buried depth beyond the front of the excavation face. Take the buried depth of 0.5 D as an example, the surface displacement induced by excess support pressure (the support pressure ratio is approximately 4.8 which is also mentioned in Section 4.2.2) is presented in Figure 14. As it can be seen, the disturbance range extends horizontally to about 1.0 D beyond the front of the shield. The maximum heave is located at about 0.5 D ahead of the tunnel face, which equals the buried depth of the tunnel. Besides, only a little settlement occurred behind the tunnel face. In the case of excess support pressure, [PERSON] [41] proposed a three-dimensional kinematically admissible failure mechanism deduced from numerical simulations, which is an extension of the mechanism developed by [PERSON] and [PERSON] [42]. However, [PERSON] found his analytical model over-estimates the volume at failure according to numerical simulations which considered elastic-perfectly-plastic material of Coulomb type with an associated flow rule. According to the centrifuge tests in this paper, fishtail type of ground disturbance range induced by excess support pressure can be found, which consists of the upward moving rigid block, forward moving rigid block and downward moving rigid block that are above the front, right in front and below the front of the excavation face respectively, as Figure 15 illustrated. The upward and downward rigid block extends horizontally to at least 2.0 D beyond the front of the face. For points upfront of the face, they slide up and forward at an angle of about 45\({}^{\circ}\) to the ground surface. At the same time, the upward rigid body movement conduces disturbance to the area above the face, which inducing settlement within a range of approximately 1.0 D. The experimental mechanism mobilizes a smaller soil volume than that considered in the framework of theoretical analysis, which is consistent with the result obtained by [PERSON]. Figure 14: The surface displacement induced by excess support pressure (buried depth of 0.5 D). In terms of the ground deformation induced by insufficient support pressure, the chimney-shaped moving mass is characterized by the appearance of vertical displacements in the ground shortly after the continuous moving of the face once the support pressure reaches the limit pressure, as Figure 16 illustrated. These vertical movements are localized in a spatial region above the tunnel face, between the crown and the ground surface. Finally, it propagates towards the ground surface and a sinkhole appears at the ground surface, which then gradually expands  
In comparison with the ground deformation mechanism in dry sand as shown in Figure 16, it was observed by [40] in large-scale model tests that the failure zone on the ground surface was an area of 1 D width and 0.75 D length in front of the tunnel face and the middle point of the subsidence area laid in the range of (0.25-0.3) D in front of the tunnel face. However, the range of ground disturbance area in water-rich sand was observed larger in this centrifuge test, which was an area of approximately 1.5 D width and 1.0 D length in front of the tunnel face and the middle point of the subsidence area laid in the range of (0.2-0.3) D in front of the tunnel face.