Abstract
A new method is developed to solve Biot’s consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot’s consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface (z = 0) and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.
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References
Biot M.A. (1941). General theory of three-dimensional consolidation. J. Appl. Phys. 12: 155–164
McNamee J. and Gibson R.E. (1960). Displacement functions and linear transforms applied to diffusion through porous elastic media. Q. J. Mech. Appl. Math. 13(1): 98–111
McNamee J. and Gibson R.E. (1960). Plane strain and axially symmetric problem of the consolidation of a semi-infinite clay stratum. Q. J. Mech. Appl. Math. 13(2): 210–227
Schiffman R.L. and Fungaroli A.A. (1965). Consolidation due to tangential loads. Proc. 6th Int. Conf. Soil Found. Eng. 1: 188–192
Yue Z.Q. and Selvadurai A.P.S. (1995). Contact problem for saturated poroelastic solid. J. Eng. Mech. ASCE 121(4): 502–512
Pan E. (1999). Green’s functions in layered poroelastic half-space. Int. J. Numer. Anal. Meth. Geomech. 23: 1631–1653
Booker J.R. and Small J.C. (1982). Finite layer analysis of consolidation I. Int. J. Numer. Anal. Meth. Geomech. 6: 151–171
Booker J.R. and Small J.C. (1982). Finite layer analysis of consolidation II. Int. J. Numer. Anal. Meth. Geomech. 6: 173–194
Booker J.R. and Small J.C. (1987). A method of computing the consolidation behavior of layered soils using direct numerical inversion of Laplace transforms. Int. J. Numer. Anal. Meth. Geomech. 11: 363–380
Christian J.T. and Boehmer J.W. (1970). Plane strain consolidation by finite elements. J. Soil. Mech. Found. Div. ASCE 96(4): 1435–1457
Cheng A.H.-D. and Liggett J.A. (1984). Boundary integral equation method for linear porous-elasticity with applications to soil consolidation. Int. J. Numer. Meth. Eng.20(2): 255–278
Ai Z.Y., Yue Z.Q., Tham L.G. and Yang M. (2002). Extended Sneddon and Muki solutions for multilayered elastic materials. Int. J. Eng. Sci. 40: 1453–1483
Ai, Z.Y., Han, J.: A solution to plane strain consolidation of multi-layered soils. Soil and rock behavior and modeling. ASCE GPS06, 276–283 (2006)
Talbot A. (1979). The accurate numerical inversion of Laplace transforms. J. Inst. Math. Appl. 23: 97–120
Sneddon I.N. (1972). The Use of Integral Transform. McGraw-Hill, New York
Muki T. (1960). Asymmetric problems of the theory of elasticity for a semi-infinite solid and a thick plate. In: Sneddon, I.N. and Hill, R. (eds) Progress in Solid Mechanics, pp 399–439. North-Holland, Amsterdam
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The project supported by the National Natural Science Foundation of China (50578121).
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Ai, Z., Wang, Q. & Wu, C. A new method for solving Biot’s consolidation of a finite soil layer in the cylindrical coordinate system. Acta Mech Sin 24, 691–697 (2008). https://doi.org/10.1007/s10409-008-0187-5
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DOI: https://doi.org/10.1007/s10409-008-0187-5