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Elastic-viscoplastic response of earth structures to earthquake motion Byrne, Peter Michael

Abstract

A theory for predicting the dynamic response of earth structures subject to earthquake forces as presented herein. The proposed theory essentially introduces a stress limit into the viscoelastic shear-slice or shear-beam analogy and thus, in essence, the structure is modelled by a multidegree of freedom system which responds in an elastic-viscoplastic manner. The stress limit may be varied with both the magnitude of displacement and the number of stress cycles so that, in practice, a complex stress-strain relationship can be considered in the analysis. The method allows the dynamic displacements, velocities, and accelerations within the structure to be calculated at any time, t, when the base is subjected to a known acceleration. If magnitude of displacements is considered the criterion for earthquake design, then the proposed method of analysis gives a direct measure of these displacements. The analysis is applied to a number of earth structures using a base acceleration corresponding to the 0-10 secs. of El Centro, 1940 earthquake. Displacements, velocities and accelerations are calculated at discreet time intervals. Results are compared with those obtained from a viscoelastic dynamic analysis and it is found that plastic action causes larger displacements and smaller accelerations. The location of plastic yield is dependent on the strength properties of the material. For material of uniform strength, yield will occur essentially at the base of the structure, while for ideal frictional material, yield will take place throughout the structure but will be greatest at the top. Lateral force or seismic,coefficients from viscoelastic and elastic-viscoplastic are compared. Results suggest that the common practice of allowing for plastic-action by assuming some high viscous damping factor such as 20% of critical in a viscoelastic analysis is unlikely to give correct results.

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