A class of inhomogeneous shear models for seismic response of dams and embankments

Results of linear and nonlinear static analyses of gravity-induced stresses in several typical dam cross-sections, in conjunction with published experimental correlations of shear modulus versus confining pressure for a large variety of soils, reveal that the average shear modulus across the width of earth/rockfill dams may be expressed as a power m of depth, with m ranging from 0.35 to 0.90 and depending on material and geometric parameters. A general inhomogeneous shear beam model is developed to account for any possible such variation of modulus with depth. Perhaps somewhat surprisingly, closed-form analytical expressions are derived for natural frequencies, modal displacements, participation factors, and steady-state response functions for all values of the inhomogeneity factor m. Parametric results are presented in tabular and graphical form and conclusions are drawn of practical significance. Finally, a comprehensive comparative study is undertaken to investigate the validity of the inhomogeneous shear beam (SB) models. For five different dam cross-sections, each excited by four recorded accelerograms, it is shown that plane-strain finite-element analyses yield fundamental periods and peak displacements within the dam which are in very good accord with the predictions of a ‘consistent’ inhomogeneous SB model. A companion paper¹ extends the present work and focuses on seismic shear strains and seismic coefficients within dams and embankments.