Three-dimensional numerical modelling of circular tunnels under seismic actions

Dynamic effects on shallow circular tunnels in soft ground have often been neglected based on the assumption that their response to earthquakes loading is relatively safe as compared to that of surface structures. Nevertheless, several example of recorded damage to underground structures for which seismic forces were not considered in the design can be quoted. In some cases, damage was associated with strong ground shaking and site amplification, which increased the stress level in the tunnel lining. Ovaling or racking deformations are mostly due to shear waves propagating perpendicularly to the tunnel axis, resulting in a distortion of the cross-section of the structure, while axial compression and extension, or longitudinal bending are due to shear waves propagating parallel or obliquely to the tunnel axis. Pseudo-static and simplified dynamic analyses enable to assess transient changes in internal forces during shaking. In the simplified methods, a tunnel structure is generally designed by imposing a displacement field to its boundary, as obtained from a site seismic response under free field conditions, and calculating the forces in the lining in an uncoupled manner. Axial and bending deformations are generated by the components of the seismic waves producing particle motion parallel or perpendicular to the longitudinal axis of the tunnel, respectively. Nevertheless, experimental evidences of permanent changes in internal loads in the tunnel lining would suggest that a full three-dimensional dynamic analysis including plastic soil behavior should be performed when modelling the dynamic interaction between the tunnel and the ground. In the paper three-dimensional numerical analyses were performed to simulate the response of circular tunnels subjected to different seismic loads acting in the transversal and in the longitudinal direction of the tunnel axis. The main purpose of this study was to provide a three-dimensional numerical model, which would allow the tunnel lining behavior and the displacement field surrounding the tunnel to be evaluated for different directions of seismic wave propagation.