Energy Dissipation of a Cohesive Soil by the Fourier Transformation of Stress Relaxation Response

Abstract

The energy dissipation of a cohesive soil is obtained by the Fourier transformation of stress relaxation test data. Energy dissipation is expressed in terms of the loss tangent. The soil response is nonlinear. Because of the difficulty in obtaining a mathematical expression to fit the relaxation data adequately over the entire time scale of interest, an approximate method of evaluating the transform is used. The relaxation response functions are approximated by straight line segments to form a piecewise continuous relation. By using a large number of straight line segments, the error between the actual and approximate transformation can be made negligible. The segment slopes with corresponding values of time are used in a digital computer program to evaluate the transform. The results clearly indicate a decrease of loss tangent with increased applied strain level. For constant strain level, the variation of loss tangent as a function of moisture content is not clearly defined. The loss tangent vs. logarithm of time relation gives a characteristic single peak bell-shaped distribution for each strain level.