Anisotropic linear elastic materials subject to undrained plane strain deformation

A previous generation seems to have ‘known’ that if a linear elastic ‘soil’ with E′ v /E′ h anisotropy is subject to undrained plane strain, the anisotropy is not detectable. This fact has significant consequences for modelling of many undrained geotechnical situations, including computed displacements caused by tunnelling. The author has often found that it is not known by numerical modellers, and he has not been able to find a proof of it in the literature. In this paper, it is proved that if a linear elastic ‘soil’ with E′ v /E′ h anisotropy is subject to undrained plane strain, the anisotropy is not detectable. This is shown mathematically and also demonstrated by finite-element analysis. Properties of linear elastic anisotropic total stress models are also investigated. The independent shear stiffness, G vh , is important to undrained deformation problems, however.