Static and Dynamic Loads on a Shallow Circular Tunnel: Practical Design Considerations

Abstract

In the current study we analyze the lining forces developed on a shallow circular tunnel in medium sand under two loading conditions: (i) gravity loads, and (ii) static plus dynamic loads due to ground motions. Motivated by the field performance of actual tunnels, the purpose of this study is to explore a recurrent question regarding the safety of tunnels and other underground facilities: “does a shallow tunnel properly designed to resist static loads has enough safety margins to withstand severe ground shakings without significant damage?”. The study unit is a typical 0.3 m thick sprayed concrete tunnel, 6 m in diameter, and built in a 60 m deep deposit of Leighton Buzzard sand (Dr 75%) at a crown depth of 12 m. The soil deposit has a total width of 140 m, free field boundary conditions, and is underlain by an elastic halfspace with a shear wave velocity of 760 m/s. A 2D plain strain finite element model was implemented in OpenSees [1]. The tunnel was modeled using elastic frame elements and the soil’s stress-strain behavior was modeled using the PressureDepenMultiYield [2] constitutive relation. A quiet (absorbing) boundary was added at the model base to dissipate the rebounding shear waves [3]. After the initial gravity analysis of a uniform soil deposit, the static lining forces were obtained from a 4-staged excavation analysis, in which one quarter of the circle was removed and the corresponding lining elements were added at each stage. To characterize the dynamic loads on the tunnel, and properly account for the ground motion variability, a set of 112 records from subduction interface earthquakes [4] were used to run non-linear time history analyses. Our results suggest that tunnels designed statically can indeed undergo significant shaking without excessive damage.