On the frequencies of inhomogeneous soil strata: Dobry's paradox

Abstract

This brief article elaborates on some clearly unlikely predictions made some four decades ago by R. Dobry within the context of his doctoral dissertation, which concerns the resonant frequencies of soil strata whose stiffness starts at zero at ground level and then increases continuously as some power of the depth. Although the problem was eventually traced to subtle changes in the boundary conditions which take place when the soil parameter exceeds a threshold value, and the discrepancy was ultimately fully resolved, Dobry initially countered to the technical objections of the writer by presenting an extremely elegant counter-proof based on dimensional analysis whose strength emanated from the fact that it was free from the issue of the boundary conditions, and thus forced the writer to seek alternative explanations for the contradictory results. It is this fruitful exchange of ideas which provides the motivation for this brief technical note expounding on an apparent paradox, which may prove useful to the soil dynamics community for its potential didactical value, not to mention as an outright tool.