Abstract
An analytical continuous upper bound limit analysis is developed to analyse the effects of seepage on the transverse stability of underwater shield tunnels. The approach is based on an analytical continuous upper bound limit analysis method for cohesive-frictional soils. It employs the complex variables solution of the displacement field due to tunnel deformation and movement, and the analytical solution of the pore water pressure field for steady state seepage due to pore water influx at the tunnel perimeter. The most critical slip line position and the minimum required tunnel support pressure are determined by using a particle swarm optimization scheme for various generic situations. The method is verified via finite element simulation and comparison with the solution from using rigid block upper bound limit analysis. The parametric analysis revealed among other things that both the infimum of the necessary tunnel support pressure and the most critical plastic zone increase when the hydraulic head at the ground surface increases, but decrease when the tunnel influx increases due to the fact that pore water pressure at the tunnel perimeter decreases with the tunnel influx.
Highlights
Shield driven tunnels are common for under crossings of surface waters, such as lakes, rivers, and seas
The method differs from the limit equilibrium method and the rigid body upper bound limit analysis method in that it may take into account of the continuities of both the ground material properties and the ground displacements, and that it does not need to prescribe any failure modes
An analytical formulation of continuous upper bound limit analysis is presented for studying the effects of seepage on the transverse stability of underwater shield tunnels
Summary
Shield driven tunnels are common for under crossings of surface waters, such as lakes, rivers, and seas. There exist publications of the analytical continuous upper bound limit analysis method for shield tunnel stability problems, such as Osman et al [1,2], Klar et al [3], Mollon et al [4], Klar and Klein [5], Xiang and Song [6], Zhang et al [7], Huang et al [8], Song and Xiang [9], Xiang and Song [10], none of them and other analytical continuous upper bound limit analysis developments in the existent literature has taken into consideration of groundwater seepage effect. In this paper, taking account of pore water effect, two types of formulations of the upper bound theorem are presented, and the necessary condition for the tail stability during construction of underwater shield tunnels is developed, in which the ground displacement velocity. Parametric analysis with regard to the soil’s friction angle, the tunnel cover to diameter ratio, the tunnel influx, and the surface water level are presented
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