Fundamental period and mode shape of layered soil profiles

The estimation of the fundamental period of soil profiles has been the subject of numerous studies. An extensive evaluation of several procedures by Dobry et al. 1] concluded that both the Simplified Version of the Rayleigh Procedure 1] and the Successive Use of Two-Layer Solution by Madera 2] give errors of less than 10% for all of the 76 representative soil profiles considered in the evaluation. The simplified Rayleigh procedure is iterative and requires an initial estimate of the mode shape. The Madera procedure is based on the solution of a two-layer system, usually obtained from charts. In this paper the solution charts are replaced by approximate relations for implementation on a spreadsheet. Since the Madera procedure calculates only the fundamental period, mode shapes need to be calculated by other means. The Madera procedure is extended to calculate mode shapes and modal participation factors of layered soil profiles. Unlike the simplified Rayleigh procedure 1], the proposed solution incorporates the different densities of the layers and gives direct results without iterations. The proposed solution can be considered a simpler alternative to the Rayleigh method for shear beams or soil columns.