Seismic distortions of a deep circular tunnel in elastic slightly anisotropic ground

Tunnels must withstand not only the demands stemming from normal working conditions but also from extreme events such as earthquakes.Indeed,there is consistent evidence in the technical literature that indicates that tunnels are vulnerable to damage and must be designed to adequately support the demand imposed by the earthquake.Such demand should be estimated using dynamic numerical methods that include soil-structure interaction and incorporate realistic models for the support and surrounding ground.For preliminary analysis,however,or when the seismic demand is insufficient to take the ground beyond its elastic regime,analytical solutions may provide a reasonable estimate of the tunnel behavior,especially if the tunnel is sufficiently far from the seismic source such that a pseudostatic analysis is acceptable.Most analytical solutions are based on the assumption that the ground is isotropic,which may not be realistic,as e.g.depositional processes may result in engineering properties that depend on the direction of deposition.The work presented in the paper builds on the results by Bobet(2011,2016)who provided closed-form solutions for deep tunnels in elastic transversely anisotropic ground;however,the paper provides much simpler solutions for those cases where the ground is slightly anisotropic.A comparison between the approximate and the exact solutions shows that the errors are negligible when the ground anisotropy is small and grow,albeit slowly,as the ground anisotropy increases.The conclusion applies to different loading conditions,drained and undrained,and to different ground-support interfaces,tied or frictionless.