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In many foundation vibration problems, such as the vibration of machine foundations, the supporting soil is first subjected to static stresses caused by the weight of the installation and then small amplitude vibratory stresses are applied. The vibratrion response depends on the stiffness of the soil. Experimental data are presented to show the effect of various static states of stress on the dynamic shear modulus of dry sand measured by vibration and on the static shear modulus measured by repeated torsion tests. The stiffness of the sand was found to be independent of the deviatoric component of the initial static state of the stress and independent of rate of loading. The effect of stress history was small. Equations for the computation of the shear modulus, for use in design, from the value of the isotropic component of static stress and the void ratio are presented.
Hardin et al. (1966) studied this question.