Axisymmetric Vibration of Disk Resting on Saturated Layered Half‐Space

Abstract

The force‐displacement relationship associated with the vertical vibration of a circular rigid disk resting on a saturated layered half‐space is derived using Biot's two‐phased linear theory. The analysis relies on the use of integral transform techniques in conjunction with axisymmetric potential theory by means of which Green's functions are derived. Using the latter, the determination of the force‐displacement relationship of the disk is reduced to the evaluation of a stress function that satisfies a Fredholm integral equation of the second kind similar to that obtained in relative studies involving uniform or layered dry media. Plots of vertical stiffness and damping coefficients in terms of frequency and saturation depth‐to‐disk radius ratio are given. Comparisons are also presented with results from the corresponding dry case. Numerical results obtained from a representative range of parameters show that the effect due to the saturation on the impedence functions is generally not significant. Specifically, at low dimensionless frequencies (i.e., less than 3), this effect is practically negligible, while at higher dimensionless frequencies (i.e., between 3 and 6), the departure from the dry case was about 30%.