# Analysis of Deformations of the Tunnel Excavation Face via Simplified Calculation Methods
## 5 The Effect of a Pressure Applied to the Excavation Face  
The study also investigated the phenomenon of face extrusion during the tunnel construction under different face pressures. The analysis focused on evaluating the extent of face extrusion for various combinations of rock type, tunnel radius, lining thickness, and in situ stress state. The findings provide valuable insights into the effects of face pressure on the stabilization of the tunnel face. Figures 12-14 depict the impact of tunnel face pressures on the extrusion behaviour of a tunnel with a radius of 2 m, for the three values of the in situ stress from 1.1 to 11 MPa. From the figures, it can be seen how as the pressure applied to the excavation face increases, the extrusion is considerably reduced following a hyperbolic trend. Furthermore, the application of the pressure at the face is able to induce an extrusion that is lower than the limit one, permitting the stabilization of the tunnel face. From a design point of view, therefore, it can be very useful to identify the pressure at the face which is able to reduce the extrusion to values lower than the limit ones, thus allowing the elimination of the risk of instability of the excavation face during the tunnel excavation.  
Figure 11: Face extrusion at the centre of the tunnel face: simplified numerical modelling and hemispherical approach (\(R=5\) m). Key: S: the concrete lining thickness; Good: rock mass type C; Intermediate: type B; Poor: type A; dashed lines: maximum admissible extrusion values for type C (green), type B (yellow), and type A (red), according to [30].  
Figures 15-17 provide a visual representation of the influence of tunnel face pressures on the extrusion behaviour of a tunnel with a larger radius of 3.5 m, and Figures 18-20 for a tunnel radius of 5 m. Furthermore, it is worth highlighting that the thickness of the lining has a minimal impact on the face extrusion, resulting in only a slight variation of its value only for the Poor type of rock. Another noteworthy outcome is that increasing the diameter of the tunnel a corresponding increase in the face extrusion can be seen.  
In Figures 14, 17 and 20, the limit extrusion \(u_{lim}\) was represented with a horizontal red dash dotted line. Through this representation, it is simple to identify the stabilization pressure to be applied to the face, in the case of Poor rock (type A), in order to obtain an extrusion lower than the limit one and, therefore, the guaranteed stability of the face during excavation. This pressure can simply be applied by the TBM head in the case of mechanized excavation; it is to be understood as an equivalent pressure that can also be provided by rock reinforcing (through longitudinal fiberglass bolts) in the case of excavation using the traditional advancing method.  
The figures that have been obtained for this section allow the evaluation of the effect of the pressure applied to the excavation face on the level of rock deformation (extrusion). They therefore represent a useful design tool that can lead to the definition of the detailed characteristics of the TBM machine to be used in a specific case or in the definition of the number and dimensions of the fiberglass bolts that can be adopted to stabilize the excavation face of a tunnel.