1D harmonic response of layered inhomogeneous soil: Exact and approximate analytical solutions

George E. Mylonakis*, Emmanouil Rovithis, Haralambos Parashakis

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

5 Citations (Scopus)


The seismic response of inhomogeneous soils is explored analytically by means of one-dimensional viscoelastic wave propagation theory. The system under investigation comprises of a continuously inhomogeneous layer over a homogeneous one of higher stiffness. The excitation is specified at the bottom of the base layer in the form of vertically propagating harmonic S waves. Shear wave propagation velocity in the inhomogeneous layer is described by a generalized parabolic function, which allows modeling of soil having vanishing shear modulus at the ground surface. The problem is treated analytically leading to an exact solution of the Bessel type for the natural frequencies, mode shapes and base-to-surface response transfer function. The model is validated using available theoretical solutions and finite-element analyses. The exact analytical solution is compared with energybased Rayleigh techniques and equivalent homogeneous soil approximations. The latter are defined by means of alternative definitions for the representative shear wave velocity in the inhomogeneous layer. Results are presented in the form of normalized graphs demonstrating the effect of salient model parameters such as layer thickness, impedance contrast between surface and base layer, surface-to-base shear wave velocity ratio in the inhomogeneous layer, rate of inhomogeneity and hysteretic damping ratio. Harmonic response of inhomogeneous soils with vanishing shear wave velocity near soil surface is explored by asymptotic analyses.

Original languageEnglish
Title of host publicationComputational Methods in Earthquake Engineering
PublisherSpringer, Dordrecht
Number of pages32
Publication statusPublished - 1 Jan 2013

Publication series

NameComputational Methods in Applied Sciences
ISSN (Print)1871-3033


  • Inhomogeneous soil
  • Rayleigh method
  • Shape functions
  • Wave propagation

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