Robust design of shield tunnels

Differential settlements in a shield tunnel can affect the tunnel performance (in this paper, the "performance" of concern are structure safety and serviceability of tunnel cross sections). The differential settlements are often caused by the spatial variation (in the longitudinal domain) of input parameters (e.g., the stiffness of the ground under the tunnel). However, in the conventional design approach, only a few critical cross sections of a shield tunnel are identified and analyzed, and the longitudinal variation of input parameters is not considered. In this paper, the longitudinal variation of tunnel input parameters is explicitly considered using a finite element method that is based upon the theory of Winkler foundation. Further, a new design methodology, called robust geotechnical design (RGD), is integrated into the tunnel design procedure to reduce the effect of the longitudinal variation of input parameters on the tunnel performance. For robust design, the feasibility-based robustness measure is employed, in which the feasibility robustness is taken as the percentage of tunnel segment rings that meet the tunnel performance requirements. Within the framework of advanced RGD of shield tunnels, easy-to-control design parameters (e.g., segment thickness) are optimized so that the design robustness is maximized and the cost is minimized. To this end, a multi-objective optimization is performed in the robust design process and a Pareto front showing a trade-off between design robustness and cost efficiency is obtained. The Pareto front is a useful tool that can aid in making an informed design decision. Through an illustrative case, the effectiveness and significance of the advanced RGD of shield tunnels is demonstrated.