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Foundation Vibration Analysis Using Simple Physical Models by John P. Wolf

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Appendix A. Interaction Force-Displacement Relationship and Green’s Function of Cone Model

In Appendix A the strength-of-materials theory of the truncated semi-infinite cone [M5, M11] is derived. This one-sided cone is used directly to model a disk on the surface of a homogeneous soil halfspace, or as a double-cone model represents a disk embedded in a fullspace. The trapped mass present for incompressible material for the vertical and rocking motions (see Section 2.1.4) can be shifted to the basemat and thus to the superstructure. This “trick” enables the analysis of the cone models in the same manner for all values of Poisson’s ratio. Section A1 addresses the translational cone, whereby axial distortion (vertical motion) is examined; for the ...

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