Pseudo-static Winkler springs for longitudinal underground structures subjected to shear waves

Shear waves in underground longitudinal structures impose deformations that need to be accounted for in structural design. Simplified approaches for such structures typically consider the Winkler foundation model, assuming Euler-Bernoulli beam theory, which neglects shearinginduced distortions, especially significant when shear waves are a dominant component of the seismic motion. In order to overcome these limitations, Timoshenko beam models have been proposed in the literature. These approaches however depend on an appropriate determination of the ground springs. Existing analytical formulations often assume plane-strain conditions, inadequate for representing low frequencies and thus are not directly applicable for pseudo-static interaction analyses. The present paper develops analytical solutions to determine transverse and rotation Winkler springs for structures subjected shear waves. The proposed springs overcome the drawbacks of plane-strain models and can be construed as a generalisation of them. The springs are obtained as a function of the seismic wavelength and the ground-structure stiffness contrast. Results obtained are validated against solutions from the literature and numerical results from a full 3D finite-element model. A non-dimensional parametric study is also presented, that allow an expedited evaluation of ground springs for practical applications.