Strain and strain rate effects on the rocking response of footing subjected to machine vibrations

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Footings subjected to dynamic loads are commonly designed under the simplifying assumption of linear or equivalent-linear soil behaviour. Even though this approach is simple to implement and, in some cases, could take advantage of available closed-form solutions, the outcomes remain a gross approximation. Although considerable research has been conducted for the case of high-amplitude footing vibrations, where uplift, slippage or even failure may occur, there remains a research gap for small to medium strain amplitudes, for which the behaviour is also non-linear. To address this problem, a numerical methodology is developed herein, for the analysis and design of shallow footings, while taking into consideration shear modulus degradation and hysteretic damping increase effects for the foundation subsoil. The analysis methodology is based on the implementation of the modified hyperbolic model as a user-defined formulation into the explicit finite difference code FLAC. Focus is then given on a rigid strip surface foundation subjected to a harmonic rocking motion, and results from preliminary analyses are presented in terms of the variation of the dynamic impedance with the dimensionless frequency of the
excitation. Different excitation amplitudes are examined to demonstrate the effects of soil non-linearity, while strain rate effects are also investigated.
Original languageEnglish
Title of host publicationProceedings of the 16th European Conference on Earthquake Engineering
PublisherEuropean Association for Earthquake Engineering (EAEE)
Number of pages13
Publication statusPublished - 22 Jun 2018
Event16th European Conference on Earthquake Engineering: Thessaloniki - 2018 - Thessaloniki, Greece
Duration: 18 Jun 201821 Jun 2018
Conference number: 16


Conference16th European Conference on Earthquake Engineering
Abbreviated title16ECEE
Internet address


  • shallow foundations
  • machine vibrations
  • modified hyperbolic model
  • strain rate effects


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