# Numerical Modeling for Tunnel Lining Optimization
## 7 Conclusions  
Modern tunnel lining design must include the revision of state limits of failure and service simultaneously using a performance-based design approach. In urban areas, this is a key step to effectively reduce ground movement of the tunnel's surrounding soil, which, in turn, can lead to differential settlements on adjacent structures, and potential structural damage. This paper aims to partially fill the gap in field data regarding the load distribution acting on primary linings during conventional tunneling. An extensive instrumentation of a section of a tunnel of a 4.5 km long metro currently under construction in the northwestern area of Mexico City was carried out. The instrumentation comprised load cells to measure radial and axial pressures in the primary lining, an extensometer, topographical survey points at the ground surface, and convergence and divergence readings of the tunnel cross-section. The presented results are further analyzed with three-dimensional finite difference numerical models. From both experimental and numerical data gathered, it can be clearly seen that the traditional analytical models substantially underpredict both ground deformations as well as design loads in the primary lining. This is most likely due to the hypothesis employed to derive these analytical solutions, such as circular tunnel cross-section and uniform isotropic stress field, among others. It is important to highlight that in the horseshoe tunnel geometry studied here, the displacement distribution is strongly affected by the vertical component, and not by radial deformations as assumed in the CCM approaches revised. Therefore, the lining performance design following these procedures is not optimal and can potentially lead to unsafe and costly designs, and in extreme cases, damage to surrounding structures. Special care should be exercised in brittle soils, such as cemented sandy silts and silty sands, which exhibit a strain softening behavior, and in which the failure surface is reached at relatively small ground deformations, precluding catastrophic collapses. Underprediction of the equilibrium tunnel crown vertical deformation on the order of one-third of the measured deformation was observed. Loads inferred in the secondary lining based on the back-calibrated numerical model are almost one-tenth of those taken by the primary lining. This fact can be attributed to the brittleness of the cemented silty sands, which leads to the fact that approximately 70 to 90% of the soil load is taken by the primary lining during the initial excavation advance, prior to the construction of the secondary lining. Thus, from the numerical study presented here, it can be concluded that it is more efficient in urban populated areas, when using the conventional tunneling method in stiff cemented soils, to have a robust lining that allows better control of the ground deformation, less detrimental impact in adjacent structures, and  
Figure 37: Surface vertical displacements perpendicular to the tunnel axis for each case analyzed. faster construction than a support comprising primary and secondary linings. Therefore, one robust lining can support the surrounding soil loads, redistribute the soil stresses around the tunnel during excavation, and decrease the impact on the surface. Both state limits of failure and service are to be revised during the design phase. Using empirical and analytical approaches should be restricted to preliminary estimations. Some of the limitations and uncertainties that could be considered in the present research are as follows:  
1. Instrumentation: The complexity during the installation of the instruments can affect the accuracy of the data obtained, as well as soil heterogeneities which lead to an irregular contact surface between the load cell and the adjacent soil. 2. Single control section: Only one control section was instrumented.