Shear Resonance Frequencies of Alluvial Valleys by Rayleigh's Method

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Abstract
A simple approach based on Rayleigh's method has been used for the fast estimation of the shear resonance frequencies of alluvial valleys. After an example considering a 1-D non-homogeneous configuration, the method is applied to 2-D and 3-D homogeneous simple-shaped valleys, for which numerical solutions exist in the literature. The application of the proposed method to deep non-homogeneous sedimentary basins is then illustrated, showing that even in a rather complex soil configuration the prediction errors do not exceed about 20%. If one considers the uncertainties related to the determination of the mechanical properties of a real soil configuration, this prediction is quite reasonable. Furthermore, the predicted fundamental frequency always provides an upper limit of the true value. Although the predicted results are not very accurate, the proposed procedure may be helpful in several practical applications, such as in the case of complex geological configurations, where the problem exists of assessing in which frequency band 1-D resonance will differ significantly from the 2-D or 3-D one. This is important to decide whether performing more sophisticated analyses of site effects and whether the use of standard code spectral shapes is appropriate.

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