Seismic Response of Tunnels

Ulas Cilingir, Cambridge University, Geotechnical Engineering Group


Tunnels in seismically active areas are under earthquake induced risks. These risks involve damage to the tunnel structure due to slope failures, large fault displacements, liquefaction and deformation of tunnel due to seismic wave action. Although a careful site investigation and a proper mitigation method might avoid dangers of the tunnel being damaged due to above mentioned risks, some deformation of tunnels due to seismic wave action is inevitable.

Tunnels are generally considered as being resistant to strong earthquake motions. Contemporary design methods rely on solutions based on the theory of elasticity ignoring soil nonlinearity and inertial effects. More complex numerical methods exist, but there is very little experimental evidence to verify their findings.

This dissertation presents the methods and the results of an investigation aimed at discovering the soil-structure interaction of tunnels during earthquakes. The focus has been on relatively shallow and flexible tunnels in loose dry sand. Dynamic centrifuge tests have been conducted on small-scale tunnel models for this purpose. These small-scale models were constructed at different flexibilities and shapes. They were tested at two different embedment depths. Soil and lining deformations were recorded using a fast digital camera which is capable of taking 1000 high quality images per second. These deformations were measured using Particle Image Velocimetry (PIV) technique for the first time in a dynamic centrifuge test involving earthquakes. This allows the evaluation of tunnel deformations in each quarter cycle. Accelerations around the tunnel and earth pressures on the lining were also measured. In addition, complementary Finite Element (FE) analyses have been carried out using a general purpose Finite Element code. A stress-dependent stiffness formulation was embedded into the code using a user subroutine. Contact between the tunnel lining and the soil was also modelled.

Comparison of tunnels with different flexibilities showed that bedrock accelerations are amplified more as the flexibility of the tunnel decreases. Experimental results suggest that relatively flexible tunnels are able to deform and conform to the ground deformations rather than resist them and undergo rigid body translations and rotations. In case of square tunnels, PIV analyses showed that side walls of a flexible square tunnel tend to cave-in as the deformations getting larger with every cycle. All these findings suggest that the deformation of tunnels, especially square ones, cannot be simplified by using swaying type of pseudo-dynamic analysis methods.

Tests on tunnels at two different embedment depths reveal that incremental bending moments around circular tunnels decrease as the depth increases. This behaviour is more pronounced for the flexible tunnel models. It suggests that a flexible tunnel, which is able to conform the ground motions, experiences more shear strain at shallow depths compared to a similar tunnel embedded at a greater depth. Incremental compressive forces are also affected by the embedment depth.

Based on Finite Element analyses and centrifuge tests with input motions at different amplitude, duration and frequency content it was concluded that the dynamic response of a tunnel-soil system can be split into three parts defining a transient part, where the response is non-linear and the change in lining forces and earth pressures are rapid, a steady-state part, where the tunnel deforms cyclically and a post-earthquake (residual) part, where permanent earth pressures and lining forces are left on the lining. It was concluded that the location of the peak ground acceleration in time history dictates when the initial stage occurs. The amount of plastic deformation is largest in the initial stage and depends on maximum peak acceleration. This suggests that the distance of tunnel from earthquake focus (hypocentre) that affects the peak acceleration felt by the tunnel may be an important factor in the seismic design of underground structures.