Exact Solution of Terzaghi’s Consolidation Equation and Extension to Two/Three-Dimensional Cases

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References

[1] K. Terzaghi, “Die Berechnung der Durchlassigkeitsziffer des Tones aus Dem Verlauf der Hidrodynamichen Span-nungserscheinungen Akademie der Wissenschaften in Wien,” Mathematish-Naturwissen-Schaftiliche Klasse, Vol. 132, 1923, pp. 125-138.

[2] K. Terzaghi and O. K. Fröhlich, “Theorie der Setzung von Tonschichte,” Franz Deuticke, Leipzig/Wien, 1936.

[3] T. W. Lambe and R. W. Whitman, “Soil Mechanics,” John Wiley & Sons, New York, 1969.

[4] K. Terzaghi, “Principles of Soil Mechanics: I—Phenomena of Cohesion of Clays,” Engineering News-Record, Vol. 95, No. 19, 1925, pp. 742-746.

[5] A. Casagrande, “Structure of Clay and Its Importance in Foundation Engineering,” Journal of Boston Society of Civil Engineers, Vol. 19, No. 14, 1932, pp. 168-209.

[6] G. Gilboy, “Improved Soil Testing Methods,” Engineering News Record, 21 May 1936.

[7] P. C. Rutledge, “Relation of Undisturbed Sampling in Laboratory Testing,” Tr. Am. Soc. C.E., No. 109, 1944.

[8] C. Viggiani, “Foundations,” Hevelius Editore, Benevento, 1999.

[9] R. Nova, “Fundamental of Soil Mechanics,” McGraw-Hill, Milano, 2002.

[10] R. Lancellotta, “Geotechnical,” 3rd Edition, Zanichelli Editore, Bologna, 2004.

[11] M. A. Biot, “General Theory of Three-Dimensional Consolidation,” Journal of Applied Physics, Vol. 12, No. 2, 1941, pp. 155-164.

[12] M. A. Biot and F. M. Clingan, “Consolidation Settlement of Soil with an Impervious to Surface,” Journal of Applied Physics, Vol. 12, No. 7, 1941, pp. 578-581.

[13] J. Mandel, “Consolidation des Couches d’Argille,” Proc. IV ICSMFE, London, 1957.

[14] J. De Jong, “Application of Stress Function to Consolidation Problems,” Proc. IV ICSMFE, London, 1957.

[15] R. E. Gibson and J. McNamee, “The Consolidation Settlement of a Load Uniformly Distributed over a Rectangular Area,” Proc. IV ICSMFE, London, 1957.

[16] J. McNamee and R. E. Gibson, “Plane Strain and Axially Symmetric Problems of the Consolidation of a Semi Infinite Clay Stratum,” Quarterly Journal of Mechanics and Applied Mathematics, Vol. 13, No. 2, 1960, pp. 210-217.

[17] J. Mandel, “Tassements Produits par la Consolidation d’une Couche d’Argille de Grande Epaisseur,” Proc. V ICSMFE, Paris, 1961.

[18] C. W. Cryer, “A Comparison of the 3-Dimensional Theories of Biot and Terzaghi,” Quarterly Journal of Mechanics and Applied Mathematics, Vol. 16, 1963, pp. 401-412.

[19] R. L. Schiffman and A. Fungaroli, “Consolidation Due to Tangential Loads,” Proc. VI ICSMFE, Montreal, 1965.

[20] R. E. Gibson, J. K. L. Schiffman and S. L. Pu, “Plain Strain and Axially Symmetric Consolidation of a Clay Layer of Limited Thickness,” University of Illinois, Mate Report, 1967, pp. 67-74.

[21] R. L. Schiffman, A. T. F. Chen and J. C. Jordan, “An Analisys of Consolidation Theories,” Proceedings of the American Society of Civil Engineers, Vol. 98, No. SM1, 1969, pp. 285-312.

[22] P. A. Vermeer and A. Verruijt, “An Accuracy Condition for Consolidation by Finite Element,” International Journal for Numerical Analytical Methods in Geomechanics, Vol. 5, No. 1, 1981, pp. 1-14.
doi:10.1002/nag.1610050103

[23] T. J. R. Hughes, “The Finite Element Method,” Prentice-Hall, Upper Saddle River, 1987.

[24] D. W. Taylor, “Fundamental of Soil Mechanics,” Jonh Wiley & Sons, New York, 1948.