Bifurcation of Cylindrical Sand Specimens

  • Kiyohiro Ikeda
  • Kazuo Murota
Part of the Applied Mathematical Sciences book series (AMS, volume 149)


A triaxial compression test is employed in soil mechanics to obtain the mechanical properties of soils and sands. A cylindrical soil or sand specimen is subjected to axial pressure (stress) σ 1 that is to be varied during the test, in addition to constant uniform circumferential pressure (stress) σ 3. See Photo 12.1 for a soil specimen during a triaxial compression test. In association with the increase in the axial strain or the axial pressure, the specimen is subjected to the shear due to the difference of the axial and circumferential pressures, and the deformation of the specimen progresses until reaching the final failure. In the course of this, the axial strain ε a, axial stress σ l, and volumetric strain ε v are measured to plot experimental curves, which are employed in an engineering judgement of the soil in question. The axial strain is to be obtained as the average of the shortening of the whole specimen, whereas the axial stress is obtained as the average on the top surface of the specimen. The deviatoric stress σ a = σ 1σ 3 is employed to characterize the shear behavior. For more issues on this test, refer, e.g., to Terzaghi and Peck, 1967 [172], Cernica, 1995 [22], and Craig, 1997 [31].


Bifurcation Point Dihedral Group Triaxial Compression Test Initial Imperfection Bifurcation Equation 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Kiyohiro Ikeda
    • 1
  • Kazuo Murota
    • 2
  1. 1.Department of Civil EngineeringTohoku UniversityAoba SendaiJapan
  2. 2.Department of Mathematical InformaticsUniversity of TokyoTokyoJapan

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