Natural frequency of earthen dams at different induced strain levels

Abstract

A method is proposed to estimate the degradation of the first natural frequency of vibration of earthen dams with increase in strain levels induced due to seismic events. A synthesised wave, referred to as the ‘sum of sines’, generated by the superposition of sinusoidal waves with frequencies ranging from 0.01 Hz to 25 Hz, is scaled to different peak accelerations and used to simulate seismic excitations at the base of the dam. The natural frequency is then determined by studying the response of the structure in the frequency domain. For this study, four dams with varying complexities of geometry, constituent material properties, and known natural frequencies were at first selected from previously published literature to establish the validity of the proposed method for determining natural frequencies of the dams at small strain levels. Plane strain models of these structures were constructed and analysed, using a commercially available finite element method-based software that is capable of performing time-history analyses. Results from the analyses indicate a good agreement between the natural frequencies predicted using the proposed method and the frequency values reported in the literature for the corresponding structures at small strain levels. The method was later used to determine the strain-dependent natural frequency of a hydraulic-fill dam in North Texas. Twenty-one different earthquake conditions, with different peak ground accelerations, frequency contents, and mean periods, were used to thoroughly validate the applicability of the developed methodology. Numerical analyses indicate that the strain-dependent variation of the first natural frequency follows a similar trend as that obtained using the ‘sum of sines’ excitation when the dam is subjected to widely different earthquake conditions.