An analytical method of continuous upper bound limit analysis for the stability of shallow shield tunnels in cohesive-frictional soils

Abstract

For stability analysis of shallow shield tunnels in cohesive-frictional (clayey–sandy) soils, an analytical method of continuous upper bound limit analysis is developed to determine the most critical slip line position and the minimum required tunnel support pressure. The ground displacement field due to composite volume loss is calculated using a complex variable solution, and the optimization problem is solved by employing the particle swarm optimization technique. Energy dissipation at the potential slip boundary, which is determined through a system of tracking schemes, and in the corresponding potential plastic zone is taken into account. Example calculations are carried out to verify the proposed method via finite element simulations and comparisons with solutions from existing methods, and to study the effects of soil strength properties and tunnel size and depth. The results show that both the internal friction and the cohesion of the surrounding soil may help reduce the range of the potential collapse zone and the magnitude of the necessary support pressure. This study represents the first attempt to deal with cohesive-frictional soils via an analytical and continuous approach, and the developed method can be extended for various tunnel and other geotechnical stability problems involving cohesive-frictional soils.