Variational approach for settlement analysis of circular plate on multilayered soil

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A continuum-based analysis method is developed to analyze a uniformly-loaded circular plate founded on a multilayered soil deposit. The multilayered soil deposit forms a semi-infinite half space, and the behavior of each soil layer is assumed to be linear elastic. The plate is considered to be isotropic, homogeneous, and linear elastic. We apply variational principles to obtain the governing differential equations of the plate-layered soil system and solve them semi-analytically. We then compare results from the present analyses with those from finite element analysis. Using the proposed analysis method we perform a parametric study, results from which provide important insights into the effects of soil layering – such as the thicknesses and stiffness ratios of multiple soil layers – on the flexural behavior of the circular plate. Analyses for wide ranges of plate-to-soil stiffness ratios provide further insights on plate-soil interactions.

Original languageEnglish
Pages (from-to)152-170
Number of pages19
JournalApplied Mathematical Modelling
StatePublished - Jun 2019


  • Circular plate
  • Differential settlement
  • Elastic analysis
  • Multilayered soil
  • Variational principles


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