1D Seismic Response of Soil: Continuously Inhomogeneous Vs Equivalent Homogeneous Soil

Abstract eng:
Equivalent homogeneous soils are investigated as simplified approximations of continuously inhomogeneous soils. The examined system comprises of an inhomogeneous surface layer over a homogeneous one of higher stiffness. Five alternative definitions are adopted for the representative shear wave velocity (Vhom) in the inhomogeneous layer: (i) Vhom1 at the base of the inhomogeneous layer (ii) Vhom2 in the middle of the inhomogeneous layer (iii) Vhom3 equal to the mean shear wave velocity within the inhomogeneous layer (iv) Vhom4 providing equal travel time from base to surface between homogeneous and inhomogeneous soil and (v) Vhom5 corresponding to an equivalent homogeneous soil having the same fundamental frequency as the inhomogeneous profile. Seismic response between inhomogeneous and equivalent homogeneous soils is compared by means of exact analytical solutions for single- and two-layer inhomogeneous soils. Fundamental frequencies and resonant peak amplitudes are examined, as affected by salient model parameters such as inhomogeneity factor, surface-to-base shear wave velocity ratio in the inhomogeneous layer, shear wave velocity contrast between the inhomogeneous and the homogeneous layer and relative layer thickness. It is observed that resonant frequencies of a smoothly-to-moderately inhomogeneous soil may be adequately captured by an equivalent homogeneous soil of either equal shear wave propagation velocity at the mid depth of the inhomogeneous layer, or of equal mean shear wave velocity within the whole layer. On the contrary, resonant amplitudes of a moderately-tostrongly inhomogeneous soil may be significantly underestimated or overestimated when an equivalent homogeneous soil is adopted, especially at higher resonances. The response of inhomogeneous soils with vanishing shear wave velocity near soil surface is explored.

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