1D HARMONIC RESPONSE OF INHOMOGENEOUS SOIL DEPOSITS WITH EXPONENTIALLY VARYING STIFFNESS: EXACT & APPROXIMATE SOLUTIONS

The harmonic response of an inhomogeneous soil layer with exponentially varying stiffness with depth is explored by using one-dimensional viscoelastic wave propagation theory. An exact solution of the Bessel type is derived from the governing equation, which allows for: (i) a novel interpretation of the attenuation patterns with depth for soil strains, displacements and stresses without a counterpart in other relevant solutions; (ii) identification of the parameters that control soil curvatures close to soil surface and at depth. New approximate solutions are also proposed for the fundamental natural frequency of the layer and the base-to-surface transfer function at high and low frequencies, which show a good agreement with the exact solution. A full-domain approximation is finally proposed as an alternative to the complex exact solution furnishing base-to-surface transfer function over the entire frequency range which can be used in practical applications. A numerical example is presented.