Alternative Solutions for Consolidation Problems in Isotropic Clay Stratum Using Laplace Heaviside’s Theorem
This study offers an alternative analytical solution, for one and two-dimensional consolidation problem, for functionally-homogenous isotropic clay layer. The fundamental analytical solution presented in this study is derived based on the Laplace transform which eliminates the time-dependent and Heaviside's inversion theorem to extract the inverse. The alternative solutions have been derived based on the governing available fundamental consolidation equations solution. The derived solutions have shown good estimation with the exact solution. The two dimensions of isotopic permeability expressed significant influence on the accumulated excess pore water pressure and approximate time for full consolidation. The analytical solution shows identical results with the numerical one.
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Biot, M.A., 1941. General theory of three‐ dimensional consolidation, Journal of applied physics, 12 (2), pp.155-164.
McNamee, J.O.H.N. and Gibson, R.E., 1960. Displacement functions and linear transforms applied to diffusion through porous elastic media. The Quarterly Journal of Mechanics and Applied Mathematics, 13 (1), pp.98-111.
Gibson, R.E., Schiffman, R.L. and Pu, S.L., 1970. Plane strain and axially symmetric consolidation of a clay layer on a smooth impervious base. The Quarterly Journal of Mechanics and Applied Mathematics, 23 (4), pp.505-520
Booker, J.R., 1974. The consolidation of a finite layer subject to surface loading. International Journal of Solids and structures, 10 (9), pp.1053-1065.
Bærland, T., Lee, J.J., Mardal, K.A. and Winther, R., 2017. Weakly imposed symmetry and robust preconditioners for Biot’s consolidation model. Computational Methods in Applied Mathematics, 17 (3), pp.377-396.
Ai, Z.Y. and Wu, C., 2009. Plane strain consolidation of soil layer with anisotropic permeability. Applied Mathematics and Mechanics, 30 (11), p.1437.
Chen, G.J., 2004. Consolidation of multilayered half space with anisotropic permeability and compressible constituents. International Journal of Solids and Structures, 41 (16-17), pp.4567-4586.
Ai, Z.Y., Cheng, Y.C., Zeng, W.Z. and Wu, C., 2013. 3-D consolidation of multilayered porous medium with anisotropic permeability and compressible pore fluid. Meccanica, 48 (2), pp.491-499.
Cheng, Y.C. and Ai, Z.Y., 2016. Consolidation analysis of transversely isotropic layered saturated soils in the Cartesian coordinate system by extended precise integration method. Applied Mathematical Modelling, 40 (4), pp.2692-2704.
Ai, Z.Y., Ye, Z., Zhao, Z., Wu, Q.L. and Wang, L.J., 2018. Time-dependent behavior of axisymmetric thermal consolidation for multilayered transversely isotropic poroelastic material. Applied Mathematical Modelling, 61, pp.216-236.
Mei, G.X., Yin, J.H., Zai, J.M., Yin, Z.Z., Ding, X.L., Zhu, G.F. and Chu, L.M., 2004. Consolidation analysis of a cross‐anisotropic homogeneous elastic soil using a finite layer numerical method. International Journal for Numerical and Analytical Methods in Geomechanics, 28 (2), pp.111-129.
Yi, S.Y., 2013. A coupling of nonconforming and mixed finite element methods for Biot's consolidation model. Numerical Methods for Partial Differential Equations, 29 (5), pp.1749-1777.
Yi, S.Y., 2014. Convergence analysis of a new mixed finite element method for Biot's consolidation model. Numerical Methods for Partial Differential Equations, 30 (4), pp.1189-1210.
Safadoust, J., Amiri, S., Esmaeily, A., Numerical Analysis of Reinforced Embankment Over Soft Foundation, (2013) International Review of Civil Engineering (IRECE), 4 (4), pp. 225-232.
Fattah, M., Mahmood, K., Al-Dosary, M., Simulation of Unsaturated Soil Behavior by the Finite Element Method, (2013) International Review of Civil Engineering (IRECE), 4 (1), pp. 34-46.
Al-Obaidy, N., Al-Shueli, A., Sattar, H., Majeed, Z., Hamid, N., An Experimental Study on Geotechnical and Electrical Properties of an Oil-Contaminated Soil at Thi-Qar Governorate/Iraq, (2019) International Review of Civil Engineering (IRECE), 10 (3), pp. 148-154.
Ito, M. and Azam, S., 2013. Large-strain consolidation modeling of mine waste tailings. Environmental Systems Research, 2 (7), pp.1-14.
Eltayeb, H. and Kılıçman, A., 2008. A note on solutions of wave, Laplace’s and heat equations with convolution terms by using a double Laplace transform, Applied Mathematics Letters, 21 (12), pp.1324-1329
Tanigawa, Y., Akai, T., Kawamura, R. and Oka, N., 1996. Transient heat conduction and thermal stress problems of a nonhomogeneous plate with temperature-dependent material properties. Journal of Thermal Stresses, 19 (1), pp.77-102.
Di Francesco, R., 2011. Exact solutions of two-dimensional and tri-dimensional consolidation equations. arXiv preprint arXiv:1103.6084, 1 (3), pp. 1–8.
Di Francesco, R., 2011. Exact Solution to Terzaghi's Consolidation Equation, arXiv preprint arXiv:1102.2060, 1 (4), pp.713–717.
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