Consolidation of a Finite Transversely Isotropic Soil Layer on a Rough Impervious Base
Publication: Journal of Engineering Mechanics
Volume 131, Issue 12
Abstract
A semianalytical solution to axisymmetric consolidation of a transversely isotropic soil layer resting on a rough impervious base and subjected to a uniform circular pressure at the ground surface is presented. The analysis uses Biot’s fully coupled consolidation theory for a transversely isotropic soil. The general solutions for the governing consolidation equations are derived by applying the Hankel and Laplace transform techniques. These general solutions are then used to solve the corresponding boundary value problem for the consolidation of a transversely isotropic soil layer. Once solutions in the transformed domain have been found, the actual solutions in the physical domain for displacements and stress components of the solid matrix, pore-water pressure and fluid discharge can finally be obtained by direct numerical inversions of the integral transforms. The accuracy of the present numerical solutions is confirmed by comparison with an existing exact solution for an isotropic and saturated soil that is a special case of the more general problem addressed. Further, some numerical results are presented to show the influence of the nature of material anisotropy, the surface drainage condition, and the layer thickness on the consolidation settlement and the pore pressure dissipation.
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References
Biot, M. A. (1941). “General theory of three-dimensional consolidation.” J. Appl. Phys., 12(2), 155–164.
Biot, M. A. (1962). “Mechanics of deformation and acoustic propagation in porous media.” J. Appl. Phys., 33(3), 1482–1498.
Biot, M. A. (1955). “Theory of elasticity and consolidation for a porous anisotropic solid.” J. Appl. Phys., 26(2), 182–185.
Booker, J. R. (1974). “The consolidation of a finite layer subjected to surface loading.” Int. J. Solids Struct., 10(9), 1053–1065.
Booker, J. R. (1973). “A numerical method for the solution of Biot’s consolidation theory.” Q. J. Mech. Appl. Math., 26(4), 457–470.
Booker, J. R., and Small, J. C. (1982a). “Finite layer analysis of consolidation. I.” Int. J. Numer. Analyt. Meth. Geomech., 6(2), 151–171.
Booker, J. R., and Small, J. C. (1982b). “Finite layer analysis of consolidation. II.” Int. J. Numer. Analyt. Meth. Geomech., 6(2), 173–194.
Booker, J. R., and Small, J. C. (1987). “A method of computing the consolidation behaviour of layered soils using direct numerical inversion of Laplace transforms.” Int. J. Numer. Analyt. Meth. Geomech., 11(4), 363–380.
Chen, S. L., Chen, L. Z., and Zhang, L. M. (2005). “Axisymmetric consolidation of a semi-infinite transversely isotropic saturated soil.” Int. J. Numer. Analyt. Meth. Geomech., 29(8), in press.
Cheng, A. H.-D. (1997). “Material coefficients of anisotropic poroelasticity.” Int. J. Rock Mech. Min. Sci., 34(2), 199–205.
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. Methods Eng., 20(2), 255–278.
Christian, J. T., and Boehmer, J. W. (1970). “Plane strain consolidation by finite elements.” J. Soil Mech. Found. Div., 96(4), 1435–1457.
Cryer, C. W. (1963). “A comparison of the three–dimensional consolidation theories of Biot and Terzaghi.” Q. J. Mech. Appl. Math., 16(3), 401–412.
Davies, D., and Martin, B. (1979). “Numerical inversion of the Laplace transform: A survey and comparison of Methods.” J. Comput. Phys., 33(1), 1–32.
Dubner, H., and Abate, J. (1968). “Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform.” J. Assoc. Comput. Mach., 15(1), 115–223.
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.” Q. J. Mech. Appl. Math., 23(4), 505–520.
Kazi-Aoual, M. N., Bonnet, G., and Jouanna, P. (1988). “Green’s functions in an infinite transversely isotropic saturated poroelastic medium.” J. Acoust. Soc. Am., 84(5), 1883–1890.
Liao, J. J., and Wang, C. D. (1998). “Elastic solutions for a transversely isotropic half-space subjected to a point load.” Int. J. Numer. Analyt. Meth. Geomech., 22(6), 425–447.
McNamee, J., and Gibson, R. E. (1960a). “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. (1960b). “Plane strain and axially symmetric problems of the consolidation of a semi-infinite clay stratum.” Q. J. Mech. Appl. Math., 13(2), 210–227.
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.” Int. J. Numer. Analyt. Meth. Geomech., 28(2), 111–129.
Poulos, H. G., and Davis, E. H. (1974). Elastic solutions for soil and rock mechanics, Wiley, New York.
Runessan, K., and Booker, J. R. (1982). “Exact finite layer method for the plain strain consolidation.” Proc., Int. Conf. on Finite Element Methods, Peking, China, 781–785.
Schapery, R. A. (1962). “Approximate methods of transform inversion for viscoelastic stress analysis.” Proc., 4th U.S. Nat. Congress on Applied Mechanics, ASME Publication, Berkeley, Calif., 2, 1075–1085.
Schiffman, R. L., Chen, A. T.-F., and Jordan, J. C. (1969). “An analysis of consolidation theories.” J. Soil Mech. Found. Div., 95(1), 285–312.
Schiffman, R. L., and Fungaroli, A. A. (1965). “Consolidation due to tangential loads.” Proc., 6th Int. Conf. on Soil Mechanics and Foundation Engineering, Montreal, 1, 188–192.
Schmitt, D. P. (1989). “Acoustic multipole logging in transversely isotropic poroelastic formations.” J. Acoust. Soc. Am., 86(6), 2397–2421.
Selvadurai, A. P. S., and Yue, Z. Q. (1994). “On the indentation of a poroelastic layer.” Int. J. Numer. Analyt. Meth. Geomech., 18(3), 161–175.
Senjuntichai, T. (1994). “Green’s functions for multi-layered poroelastic media and an indirect boundary element method.” PhD thesis, Univ. of Manitoba, Winnipeg, Manitoba, Canada.
Sneddon, I. N. (1951). Fourier transforms, McGraw–Hill, New York.
Wang, C. D., and Liao, J. J. (1999). “Elastic solutions for a transversely isotropic half-space subjected to a buried asymmetric-load.” Int. J. Numer. Analyt. Meth. Geomech., 23(2), 115–139.
Yue, Z. Q., and Selvadurai, A. P. S. (1995). “Contact problem for saturated poroelastic solid.” J. Eng. Mech. Div., 121(4), 502–512.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 131 • Issue 12 • December 2005
Pages: 1279 - 1290
Copyright
© 2005 ASCE.
History
Received: Jun 22, 2004
Accepted: Apr 4, 2005
Published online: Dec 1, 2005
Published in print: Dec 2005
Notes
Note. Associate Editor: Alexander H.-D. Cheng
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