Modified lysmer’s analog model for two dimensional mat settlements under vertically uniform load

Der Wen Chang, Ming He Hung, Sang Seom Jeong

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


A two dimensional model of linearly elastic soil spring used for the settlement analysis of the flexible mat foundation is suggested in this study. The spring constants of the soils underneath the foundation were modeled assuming uniformly vertical load applied onto the foundation. The soil spring constants were back calculated using the three-dimensional finite element analysis with Midas GTS NX program. Variation of the soil spring constants was modeled as a two-dimensional polynomial function in terms of the normalized spatial distances between the center of foundation and the analytical points. The Lysmer’s analog spring for soils underneath the rigid foundation was adopted and calibrated for the flexible foundation. For validations, the newly proposed soil spring model was incorporated into a two dimensional finite difference analysis for a square mat foundation at the surface of an elastic half-space consisting of soft clays. Comparative study was made for elastic soils where the shear wave velocity is 120~180 m/s and the Poisson’s ratio varies at 0.3~0.5. The resulting foundation settlements from the two dimensional finite difference analysis with the proposed soil springs were found in good agreement with those obtained directly from three dimensional finite element analyses. Details of the applications and limitations of the modified Lysmer’s analog springs were discussed in this study.

Original languageEnglish
Pages (from-to)221-231
Number of pages11
JournalGeomechanics and Engineering
Issue number3
Publication statusPublished - 2021 May 10

Bibliographical note

Funding Information:
The content of this paper is partial result of the research grant (MOST-106-2211-E-032-025-MY2) supported by Ministry of Science and Technology (MOST) in Taiwan. The authors express their sincere gratitude towards the funding.

Publisher Copyright:
© 2021 Techno-Press, Ltd.

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Geotechnical Engineering and Engineering Geology


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