Layer-element analysis of multilayered saturated soils subject to axisymmetric vertical time-harmonic excitation

doi:10.1007/s10483-017-2241-8

Abstract

Abstract:

The analytical layer-elements for a single poroelastic soil layer and the underlying half-space are established using an algebraic manipulation and Hankel transform. According to the boundary conditions and adjacent continuity conditions of general stresses and displacements, a global matrix equation in the transform domain for multilayered saturated soil media is assembled and solved. Solutions in the frequency domain can be further obtained with an inverse Hankel transform. Numerical examples are used to examine accuracy of the present method and demonstrate effects of soil parameters and load conditions on dynamic responses of the multilayered poroelastic saturated soils.

Key words: multilayered saturated soil, nonlinear waves, fKdV equation, surface tension, steady state dynamic response, analytical layer-element method, axisymmetric vertical excitation

2010 MSC Number:

Zhiyong AI, Lihua WANG. Layer-element analysis of multilayered saturated soils subject to axisymmetric vertical time-harmonic excitation. Applied Mathematics and Mechanics (English Edition), 2017, 38(9): 1295-1312.

TrendMD

References

[1] Biot, M. A. General theory of three-dimensional consolidation. Journal of Applied Physics, 12, 155-164(1941)
[2] Biot, M. A. Theory of propagation of elastic waves in a fluid-saturated porous solid I:low-frequency range. The Journal of the Acoustical Society of America, 28, 168-178(1956)
[3] Biot, M. A. Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics, 33, 1482-1498(1962)
[4] Paul, S. On the displacements produced in a porous elastic half-space by an impulsive line load. (non-dissipative case). Pure and Applied Geophysics, 114, 605-614(1976)
[5] Paul, S. On the disturbance produced in a semi-infinite poroelastic medium by a surface load. Pure and Applied Geophysics, 114, 615-627(1976)
[6] Lamb, H. On the propagation of tremors over the surface of an elastic solid. Philosophical Transactions of the Royal Society of London Series A, 203, 1-42(1904)
[7] Gakenheimer, D. C. and Miklowitz, J. Transient excitation of an elastic half space by a point load traveling on the surface. Journal of Applied Mechanics, 36, 505-515(1969)
[8] Halpern, M. R. and Christiano, P. Response of poroelastic halfspace to steady-state harmonic surface tractions. International Journal for Numerical and Analytical Methods in Geomechanics, 10, 609-632(1986)
[9] Halpern, M. R. and Christiano, P. Steady-state harmonic response of a rigid plate bearing on a liquid-saturated poroelastic halfspace. Earthquake Engineering and Structural Dynamics, 14, 439-454(1986)
[10] Philippacopoulos, A. J. Lamb's problem for fluid-saturated, porous media. Bulletin of the Seismological Society of America, 78, 908-923(1988)
[11] Philippacopoulos, A. J. Axisymmetric vibration of disk resting on saturated layered half-space. Journal of Engineering Mechanics ASCE, 115, 2301-2322(1989)
[12] Senjuntichai, T. and Rajapakse, R. Dynamic Green's functions of homogeneous poroelastic halfplane. Journal of Engineering Mechanics ASCE, 120, 2381-2404(1994)
[13] Rajapakse, R. K. N. D. and Senjuntichai, T. Dynamic response of a multi-layered poroelastic medium. Earthquake Engineering and Structural Dynamics, 24, 703-722(1995)
[14] Zhang, Y. K. and Huang, Y. The non-axisymmetrical dynamic response of transversely isotropic saturated poroelastic media. Applied Mathematics and Mechanics (English Edition), 22, 63-78(2001) DOI 10.1007/BF02437945
[15] Wang, X. G. and Huang, Y. 3-D dynamic response of transversely isotropic saturated soils. Applied Mathematics and Mechanics (English Edition), 26, 1409-1419(2005) DOI 10.1007/BF03246246
[16] Cai, Y. Q., Meng, K., and Xu, C. J. Stable response of axisymmetric two-phase water-saturated soil. Journal of Zhejiang University-Science A, 5, 1022-1027(2004)
[17] Cai, Y. Q., Xu, C. J., Zheng, Z. F., and Wu, D. Z. Vertical vibration analysis of axisymmetric saturated soil. Applied Mathematics and Mechanics (English Edition), 27, 83-89(2006) DOI 10.1007/s10483-006-0111-z
[18] Ding, B. Y., Dang, G. H., and Yuan, J. H. Lamb's integral formulas of two-phase saturated medium for soil dynamic with drainage. Applied Mathematics and Mechanics (English Edition), 31, 1113-1124(2010) DOI 10.1007/s10483-010-1347-9
[19] Zhou, S. H., He, C., and Di, H. G. Dynamic 2.5-D Green's function for a poroelastic half-space. Engineering Analysis with Boundary Elements, 67, 96-107(2016)
[20] He, C., Zhou, S. H., Guo, P. J., Di, H. G., and Xiao, J. H. Dynamic 2.5-D Green's function for a point fluid source in a layered poroelastic half-space. Engineering Analysis with Boundary Elements, 77, 123-137(2017)
[21] Zheng, P., Zhao, S. X., and Ding, D. Dynamic Green's functions for a poroelastic half-space. Acta Mechanica, 224, 17-39(2013)
[22] Zheng, P., Ding, B. Y., Zhao, S. X., and Ding, D. 3D dynamic Green's functions in a multilayered poroelastic half-space. Applied Mathematical Modelling, 37, 10203-10219(2013)
[23] Lu, J. F. and Hanyga, A. Fundamental solution for a layered porous half space subject to a vertical point force or a point fluid source. Computation Mechanics, 35, 376-391(2005)
[24] Liu, T. Y. and Zhao, C. B. Dynamic analyses of multilayered poroelastic media using the generalized transfer matrix method. Soil Dynamics and Earthquake Engineering, 48, 15-24(2013)
[25] Liu, Z. X., Liang, J. W., and Wu, C. Q. Dynamic Green's function for a three-dimensional concentrated load in the interior of a poroelastic layered half-space using a modified stiffness matrix method. Engineering Analysis with Boundary Elements, 60, 51-66(2015)
[26] Ai, Z. Y., Wang, L. J., and Zeng, K. Analytical layer-element method for 3D thermoelastic problem of layered medium around a heat source. Meccanica, 50, 49-59(2015)
[27] Ai, Z. Y., Wang, L. J., and Li, B. Analysis of axisymmetric thermo-elastic problem in multilayered material with anisotropic thermal diffusivity. Computers and Geotechnics, 65, 80-86(2015)
[28] Ai, Z. Y., Cheng, Y. C., and Zeng, W. Z. Analytical layer-element solution to axisymmetric consolidation of multilayered soils. Computers and Geotechnics, 38, 227-232(2011)
[29] Ai, Z. Y. and Zeng, W. Z. Analytical layer-element method for non-axisymmetric consolidation of multilayered soils. International Journal for Numerical and Analytical Methods in Geomechanics, 36, 533-545(2012)
[30] Ai, Z. Y. and Wang, L. J. Axisymmetric thermal consolidation of multilayered porous thermoelastic media due to a heat source. International Journal for Numerical and Analytical Methods in Geomechanics, 39, 1912-1931(2015)
[31] Ai, Z. Y. and Wang, L. J. Three-dimensional thermo-hydro-mechanical responses of stratified saturated porothermoelastic material. Applied Mathematical Modelling, 40, 8912-8933(2016)
[32] Ai, Z. Y., Li, Z. X., and Cang, N. R. Analytical layer-element solution to axisymmetric dynamic response of transversely isotropic multilayered half-space. Soil Dynamics and Earthquake Engineering, 60, 22-30(2014)
[33] Ai, Z. Y. and Li, Z. X. Time-harmonic response of transversely isotropic multilayered half-space in a cylindrical coordinate system. Soil Dynamics and Earthquake Engineering, 66, 69-77(2014)
[34] Ai, Z. Y. and Zhang, Y. F. Plane strain dynamic response of a transversely isotropic multilayered half-plane. Soil Dynamics and Earthquake Engineering, 75, 211-219(2015)
[35] Ai, Z. Y. and Ren, G. P. Dynamic analysis of a transversely isotropic multilayered half-plane subjected to a moving load. Soil Dynamics and Earthquake Engineering, 83, 162-166(2016)
[36] Timoshenko, S. P. and Goodier, J. N. Theory of Elasticity, 3rd ed., McGraw-Hill, New York (1970)
[37] Zienkiewicz, O. C. Basic Formulation of Static and Dynamic Behaviour of Soil and Other Porous Media, Springer, New York (1982)
[38] Sneddon, I. N. The Use of Integral Transform, McGraw-Hill, New York (1972)
[39] Ai, Z. Y., Yue, Z. Q., Tham, L. G., and Yang, M. Extended Sneddon and Muki solutions for multilayered elastic materials. International Journal of Engineering Science, 40, 1453-1483(2002)