Numerical Solution to One-dimensional Consolidation by the Finite Element Method
Journal of Advances in Mathematics and Computer Science,
Adequate prediction of structures settlement is of utmost importance in order to prevent future failure of civil engineering structures due to excessive settlement resulting from an inadequate settlement prediction. In this paper, laboratory consolidation test was performed on five different clay samples from different locations to determine the soil consolidation in terms of pore water pressure. A formulation of Finite Element (FE) method was also developed for solving one-dimensional consolidation problem and its validity checked out. The one-dimensional consolidation differential equation was solved using finite element analysis by Rayleigh-Ritz method to obtain an approximate solution and ten elements were used to discretize the domain. MATLAB program was used to write the finite element codes. Considering the graphs generated from the MATLAB program which compares the consolidation behavior of the soil sample from analytical and numerical point of view, it is seen that there is a good agreement between Terzaghi’s exact solution to consolidation behavior of soils and numerical solution using the finite element method.
- Terzaghi’s solution
- finite element method
How to Cite
Terzaghi K, Peck RB. Soil mechanics in engineering practice. John Wiley, New York; 1955.
Ho L, Fatahi B. Analytical solution for the two-dimensional plane strain consolidation of an unsaturated soil stratum subjected to time-dependent loading. Comput. Geotech. 2015;67:1–16.
Sun M., Zong M, Wu SW, Liang R. Analytical solution for one-dimensional consolidation of soil with exponentially time-growing drainage boundary under a ramp load. Mathematical Problems in Engineering. 2018;1-10.
Craig RF. Craig's soil mechanics (7th Ed.). New York, NY: Spon Press; 2004.
Wong LS, Somanathan S. Analytical and numerical modelling of one-dimensional consolidation of stabilized peat. Civil Engineering Journal. 2019;5(2):398-411.
Dew C, Johnson LD. Evaluation of two finite element formulations for one-dimensional consolidation. Computers & Structures. 1972;2:469-466.
Menendez C, Nieto PJG, Ortega FA, Bello A. Mathematical modelling and study of the consolidation of an elastic saturated soil with an incompressible fluid by FEM. Mathematical and Computer Modelling. 2009;49:2002-2018.
Zhou WH, Zhao LS, Li XB. A simple analytical solution to one-dimensional consolidation for unsaturated soils. Int. J. Numer. Anal. Met. Geomech. 2014;38:794–810.
Shan ZD, Ling DS, Ding HJ. Exact solutions for one-dimensional consolidation of single-layer unsaturated soil. Int. J. Numer. Anal. Met. Geomech. 2012;36:708–722.
Ho L, Fatahi B, Khabbaz H. Analytical solution for one-dimensional consolidation of unsaturated soils using eigenfunction expansion method. Int. J. Numer. Anal. Met. Geomech. 2014;38:1058–1077.
Liu JC, Griffiths DV. A general solution for 1D consolidation induced by depth- and time-dependent changes in stress. Géotechnique. 2015;65:66–72.
Xie KH, Xie XY, Li BH. Analytical theory for one-dimensional consolidation of clayey soils exhibiting rheological characteristics under time-dependent loading. Int. J. Numer. Anal. Met. Geomech. 2008;32:1833–1855.
Wang L, Sun DA, Xu YF. Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with semi-permeable drainage boundary. Appl. Math Mech. Engl. 2017;38:1439–1458.
Cai YQ, Liang X, Wu SM. One-dimensional consolidation of layered soils with impeded boundaries under time-dependent loadings. Appl. Math. Mech. Engl. 2004;25:937–944.
Abstract View: 3390 times
PDF Download: 1143 times