Elasto-plastic Analysis of Footing Structure by the Stiffness Method with Subgrade Structure Interaction

Lam Sze Chuen, Law Chi Wai, Cheng Yung Ming

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


Analysis of footing founded on subgrade should take the compatibility of the settlements of the footing structure and that of the subgrade into account. By the conventional approach–the ‘Winkler’s spring’ method which is popularly employed in Hong Kong and other countries, the subgrade reaction is modelled by isolated springs without interaction among themselves through the subgrade. This assumption actually contradicts the theory of elasticity as well as the continuum mechanism. Various researches have therefore been conducted to establish relations among the springs so as to simulate their ‘interactions’. However, these approaches were often approximate ones and may require calibration against results of exact analysis. In this paper, a refined analysis is formulated where the relations between loads and settlements of subgrade are based on the Boussinesq or Mindlin equations for elastic subgrade which, though originally used to solve settlement of semi infinite elastic subgrade, can be extended to analyse subgrade of layered and finite depths. The approach is more reasonable than that based on the ‘Winkler’s spring’ and other refined approaches as it takes into account the ‘subgrade structure interaction’ without arbitrary assumption. By the approach, the settlements of the footing structure and the subgrade become fully compatible. In addition, the stresses at the edges of the foundation can be very high (especially when the footing structure is comparatively rigid) which turns the behavior of the subgrade from elastic to plastic, and effects on the settlements and stress distributions due to partial yielding of the subgrade are also explored. Method of analysis for the partial plastic behavior is discussed with illustration by worked examples. Finally, design based on analysis by the proposed method is compared with that of the constant ‘Winkler’s spring’ by an illustrative example, demonstrating that design by the former is also a more economical solution for design.
Original languageEnglish
Pages (from-to)15-25
Number of pages11
JournalHKIE Transactions Hong Kong Institution of Engineers
Issue number3
Publication statusPublished - 1 Jan 2009


  • Elasto-plastic Analysis
  • Subgrade Structure Interaction
  • Winkler’s Spring

ASJC Scopus subject areas

  • General Engineering


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