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Lumped‐parameter model for a rigid cylindrical foundation embedded in a soil layer on rigid rock
Author(s) -
Wolf John P.,
Paronesso Antonio
Publication year - 1992
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290211201
Subject(s) - foundation (evidence) , stiffness , radiation damping , radius , hammer , mechanics , geotechnical engineering , degrees of freedom (physics and chemistry) , frequency domain , rigid body , time domain , structural engineering , engineering , geology , mathematics , mathematical analysis , physics , classical mechanics , computer science , archaeology , history , computer security , particle physics , quantum mechanics , computer vision
To represent a cylindrical rigid foundation vibrating in horizontal, vertical, rocking or torsional motions embedded in a soil layer resting on rigid rock, a lumped‐parameter model is described. The coupling between the horizontal and rocking degrees of freedom is considered. For each degree of freedom eight frequency‐independent real coefficients determine the springs, dashpots and the mass of the lumped‐parameter model with two internal degrees of freedom. These coefficients are specified for various ratios of the radius of the foundation to the depth of the layer and lateral contact ratios. To derive the mechanical properties of the lumped‐parameter model a systematic procedure of curvefitting of the dynamic‐stiffness coefficient up to, in general, twice the fundamental frequency of the layer is applied, capturing the fact that below the (horizontal) fundamental frequency (cutoff frequency) no radiation of energy occurs. The lumped‐parameter model can be used to represent the soil in a standard finite‐element program for structural dynamics working in the time domain, whereby the structure can exhibit non‐linear behaviour. Stability of the unbounded soil‐layer model and of the total system is guaranteed. A hammer foundation with partial uplift of the anvil is analysed for illustration.