Vol. 5 No. 01 (2024)
Articles

Galerkin Kantorovich Method for Solving the Terzaghi’s One-Dimensional Soil Consolidation Equation

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  • Charles IKE,
  • Benjamin Okwudili Mama,
  • Onyedikachi Aloysius Oguaghamba,
  • Michael Ebie Onyia
Charles IKE
Enugu State University of Science and Technology, Agbani, Enugu State, Nigeria.
Benjamin Okwudili Mama
2Department of Civil Engineering, University of Nigeria, Nsukka, Enugu State, Nigeria
Onyedikachi Aloysius Oguaghamba
3Department of Civil Engineering, University of Nigeria, Nsukka, Enugu State, Nigeria
Michael Ebie Onyia
Department of Civil Engineering, University of Nigeria, Nsukka, Enugu State, Nigeria
DOI: https://doi.org/10.38094/jocef50183

Published 2024-08-16

Keywords

  • Galerkin-Kantorovich Method,
  • Terzaghi’s One-Dimensional Consolidation Equation,
  • Excess Pore Water Pressure Distribution,
  • Average Degree of Consolidation

How to Cite

[1]
C. IKE, B. O. . Mama, O. A. Oguaghamba, and M. E. Onyia, “Galerkin Kantorovich Method for Solving the Terzaghi’s One-Dimensional Soil Consolidation Equation”, JoCEF, vol. 5, no. 01, pp. 29-33, Aug. 2024.

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Abstract

This paper presents the Galerkin-Kantorovich variational method for solving the Terzaghi’s one-dimensional consolidation equation for two-way drainage conditions. The solution was considered as an infinite series of known coordinate (shape) functions and unknown function  of time which we sought such that the resulting functional is minimized. The shape functions satisfied the hydraulic boundary conditions at the boundary of the consolidating soil. Galerkin-Kantorovich variational integral equation was thus formulated for the initial boundary value problem using residual minimization principles. The solution resulted in a system of first order ordinary differential equations in  which was solved for  Orthogonalization principles were used to obtain the integration constants in terms of initial pore water pressure, thus yielding the general solution. Solutions for constant initial excess pore water pressure were obtained and found to be the closed-form solution. The solutions were presented in terms of global (average) degrees of consolidation and tabulated. The results obtained were exact and identical with results previously found using separation of variables techniques.

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