Macro-element method with water absorption and discharge functions for vertical drains

Shotaro Yamada, Toshihiro Noda, Mutsumi Tashiro, Hong Son Nguyen

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


When simulating the vertical drain method using a soil-water coupled finite element analysis, a macro-element method can be used as a means of approximately applying the water absorption function of drains to individual elements. In this paper, the discharge function of vertical drains was added to the method by treating the water pressure in the drain as an unknown and adding a continuity equation for the drains to the governing equations. By extending the method in this way, the analytical results came to exhibit the well-resistance phenomenon automatically, depending on the analytical conditions. Numerical analyses were conducted after incorporating the proposed macro-element method into a quasi-static soil-water coupled elasto-plastic finite element method based on the finite deformation theory. The main conclusions are as follows: (1) the proposed method enables highly accurate approximations for problems involving material and/or geometrical nonlinearity and multilayered grounds; (2) the proposed macro-element method is capable of reproducing various phenomena that occur when the vacuum consolidation method is applied to a clayey ground containing a middle sand layer; (3) by following the formulation used in this paper, it is unnecessary to match the mesh division width to the drain arrangement and spacing. In addition, it is possible to obtain solutions that are minimally affected by the mesh size.

Original languageEnglish
Pages (from-to)1113-1128
Number of pages16
JournalSoils and Foundations
Issue number5
Publication statusPublished - 2015 Oct
Externally publishedYes


  • Elasto-plasticity
  • Finite deformation theory
  • Finite element method
  • Macro-element method
  • Multilayered ground
  • Soil-water coupled analysis
  • Vacuum consolidation method
  • Vertical drain method
  • Well resistance

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Geotechnical Engineering and Engineering Geology


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