Dynamic soil impedance functions for cylindrical structures buried in elastic half-space

Abstract

Spatially-distributed buried structures are highly susceptible to seismic ground motions. The macroscopic soil reactions to soil–structure relative displacements, aka. soil impedance functions (SIFs) and represented by a set of springs and dashpots, are thus very important for the assessment and design of those systems. Previous models to investigate the interaction problems between soil and horizontally buried structures (such as pipelines, tunnels) have been using spring stiffness chosen as static or frequency-independent constants, ignoring the nature of seismic loading and the energy reflected from the ground free surface. This paper presents analytical solutions for computing the frequency-domain SIFs for an infinitely-long cylindrical structure buried horizontally in homogeneous elastic half-space. The main challenge lies in mixed-boundary-value condition, where displacements are prescribed at the circular soil–structure interface and traction-free condition is satisfied along the straight-line ground surface. We used Hankel–Fourier series expansion, image technique, and Graf’s addition theorem to derive solution for axial SIFs. For a more complex in-plane SIFs problem, meanwhile, we used Hankel- and Bessel–Fourier series expansion. The in-plane solution requires numerical evaluation of contour integrals on the physical Riemann sheet, thus nested Gauss–Kronrod quadrature rule as well as Cauchy’s residue theorem are employed. We then verified our analytical solutions using results obtained from finite element simulations, in which a perfect agreement is shown between two approaches. The half-space SIFs are shown to also converge to their full-space counterparts in case of large burial depth. Additionally, parametric study was conducted to examine the variation of frequency-dependent SIFs, normalized with soil shear modulus, in response to the changes in soil Poisson’s ratio and the structure burial depth.