Elastic solutions for a transversely isotropic half-space subjected to arbitrarily shaped loads using triangulating technique

C. D. Wang*, Jyh-Jong Liao

*Corresponding author for this work

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

Elastic closed-form solutions for the displacements and stresses in a transversely isotropic half-space subjected to a buried right triangular loaded region are presented. The loading types include a uniform load, a linearly varied load in the X-direction, and a linearly varied load in the Y-direction, respectively. The planes o f transverse isotropy are assumed to be parallel to its horizontal surface. These solutions are obtained from integrating the point load solutions in a transversely isotropic half-space. The exact solutions indicate that the displacements and stresses are influenced by several factors, such as the buried depth, the loading types, the dimensions o f loaded region, and the degree and type o f material anisotropy. Two illustrative examples are presented to investigate the effect o f various parameters on the displacement and stress induced by uniform/linearly varying triangular loads. The results indicate that the displacement and stress distributions accounted for rock anisotropy are quite different fo r those calculated from isotropic solutions. Besides, an example to demonstrate the extension o f triangular loading solutions to calculate the stress due to arbitrarily shaped loads is also illustrated. It is shown that the usage o f triangulating technique fo r calculating the displacements and stresses due to any type o f loaded area is simple, efficient, as well as accurate enough. This method can be a practical alternative to the existing numerical and graphical methods.

Original languageEnglish
Pages (from-to)193-224
Number of pages32
JournalInternational Journal of Geomechanics
Volume1
Issue number2
DOIs
StatePublished - 1 Dec 2001

Keywords

  • Arbitrarily shaped load
  • Closed-form solutions
  • Rock anisotropy
  • Transversely isotropic half-space
  • Triangulating technique
  • Uniform and linearly varying triangular loads

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