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1D harmonic response of layered inhomogeneous soil: Analytical investigation
Authors:EN Rovithis  H Parashakis  GE Mylonakis
Institution:1. Institute of Engineering Seismology and Earthquake Engineering (ITSAK), 5 Ag. Georgiou Str., Patriarchica Pylaia, P.O. Box 53 Finikas, 55102 Thessaloniki, Greece;2. Department of Civil Works Technological Educational Institute of Crete, Heraclion, Greece;3. Department of Civil Engineering, University of Patras, 26500, Rio, Patras, Greece
Abstract:The seismic response of inhomogeneous soil deposits is explored analytically by means of one-dimensional viscoelastic wave propagation theory. The problem under investigation comprises of a continuously inhomogeneous stratum over a homogeneous layer of higher stiffness, with the excitation defined in terms of vertically propagating harmonic S waves imposed at the base of the system. A generalized parabolic function is employed to describe the variable shear wave propagation velocity in the inhomogeneous layer. 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. 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, rate of inhomogeneity and hysteretic damping ratio. Equivalent homogeneous soil approximations are examined. The effect of vanishing shear wave propagation velocity near soil surface on shear strains and displacements is explored by asymptotic analyses.
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