Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A mathematical treatment of one-dimensional soil consolidation

Author: A. McNabb
Journal: Quart. Appl. Math. 17 (1960), 337-347
MSC: Primary 73.00
DOI: https://doi.org/10.1090/qam/113405
MathSciNet review: 113405
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Abstract: Terzaghi's conception of the nature of one-dimensional soil consolidation [1] is shown to lead to a non-linear differential equation. A dimensional analysis of this equation and the boundary conditions of the standard consolidation test [2] gives a more general explanation of a well known linear relationship between the total consolidation $ U\left( t \right)$ after a time $ t$ and $ {t^{1/2}}$. By linearizing the equation in a general manner, an expression is obtained for $ U\left( t \right)$ which includes secondary consolidation terms. Two solutions of the linearized equation are obtained; the first for the standard consolidation test and the second for consolidation under a boundary load increasing uniformly with time.

References [Enhancements On Off] (What's this?)

  • [1] K. Terzaghi, Theoretical soil mechanics, Chapman and Hall Ltd., London, Chap. XIII
  • [2] G. Gillroy, Improved soil testing methods, Engineering Newsrecord, May 21st, 1936
  • [3] K. Terzaghi, Erdbaumechanik, F. Deutiche, Vienna
  • [4] D. W. Taylor and W. Marchant, Theory of clay compression accounting for secondary compression, J. Math. Phys. 19, 167 (1940)
  • [5] A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of integral transforms. Vol. I, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954. Based, in part, on notes left by Harry Bateman. MR 0061695
  • [6] E. Jahnke and E. Emde, Tables of functions, Dover Publications, New York, 1945, p. 2

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DOI: https://doi.org/10.1090/qam/113405
Article copyright: © Copyright 1960 American Mathematical Society

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