Dynamic Responses of Saturated Half-Spaces under Distributed Buried Loads
Publication: Journal of Engineering Mechanics
Volume 144, Issue 6
Abstract
In this paper, three-dimensional dynamic responses of a saturated half-space under arbitrary distributed buried time-harmonic load are investigated through analytical developments. In the development, the linear porous medium model established by de Boer is employed to describe the mechanical behavior of the saturated medium. By virtue of displacement potentials, the field equations are fully decoupled into four independent wave equations, which are then treated with finite Fourier and Hankel transformations. Finally, the solutions of filed variables are obtained via the imposition of boundary as well as interfacial conditions, and thereupon presented in the form of an inverse Hankel transform that in general is evaluated with numerical methods. Examples involving surface, buried patch loads are also presented to validate the solutions and examine the effect of the saturated soil’s permeability coefficient.
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Acknowledgments
The support offered by the China Scholarship Council and the guidance offered by Professor Ronald Y. S. Pak on this work are gratefully acknowledged.
References
Biot, M. A. (1956). “Theory of propagation of elastic waves in a fluid-saturated porous solid. I: Low-frequency range.” J. Acoust. Soc. Am., 28(2), 168–178.
Boer, R. D. (2000). Theory of porous media: Highlights in the historical development and current state, Springer, Berlin.
Boer, R. D., and Liu, Z. F. (1994). “Plane waves in a semi-infinite fluid saturated porous medium.” Transp. Porous Media, 16(2), 147–173.
Chen, S. L., Chen, L. Z., and Pan, E. (2007). “Three-dimensional time-harmonic Green’s functions of saturated soil under buried loading.” Soil. Dyn. Earthquake Eng., 27(5), 448–462.
Halpern, M. R., and Christiano, P. (1986). “Response of poroelastic half-space to steady-state harmonic surface tractions.” Int. J. Numer. Anal. Geomech., 10(6), 609–632.
Jin, B., and Liu, H. (2001a). “Dynamic response of a poroelastic half-space to horizontal buried loading.” Int. J. Solids Struct., 38(44–45), 8053–8064.
Jin, B., and Liu, H. (2001b). “Dynamic response of a poroelastic half-space to tangential surface loading.” Mech. Res. Commun., 28(1), 63–70.
Johnson, L. R. (1974). “Green’s function for Lamb’s problem.” Geophys. J. Int., 37(1), 99–131.
Lamb, H. (1904). “On the propagation tremors over the surface of an elastic solid.” Philos. Trans. R. Soc. London, 203(359–371), 1–42.
Pak, Y. S. R. (1987). “Asymmetric wave propagation in an elastic half-space by a method of potentials.” J. Appl. Mech., 54(1), 121–126.
Paul, S. (1976a). “On the displacements produced in a porous elastic half-space by an impulsive line load. (Non-dissipative case).” Pure. Appl. Geophys., 114(4), 605–614.
Paul, S. (1976b). “On the disturbance produced in a semi-infinite poroelastic medium by a surface load.” Pure. Appl. Geophys., 114(4), 615–627.
Philippacopoulos, A. J. (1997). “Buried point source in a poroelastic half-space.” J. Eng. Mech., 860–869.
Pooladi, A., Rahimian, M., and Pak, Y. S. R. (2016). “Three-dimensional time-harmonic fundamental solutions for a fluid-saturated poroelastic half-space with partially permeable free surface.” Int. J. Numer. Anal. Meth. Geomech., 40(14), 1903–1935.
Puswewala, U. G. A., and Rajapakse, R. K. N. D. (1988). “Axisymmetric fundamental solutions for a completely saturated porous elastic solid.” Int. J. Eng. Sci., 26(5), 419–436.
Senjuntichai, T., and Rajapakse, R. K. N. D. (1994). “Dynamic Green’s functions of homogeneous poroelastic half-plane.” J. Eng. Mech., 2381–2404.
Wilmanski, K. (2006). “A few remarks on Biot’s model and linear acoustics of poroelastic saturated materials.” Soil. Dyn. Earthquake Eng., 26(6–7), 509–536.
Zheng, P., Ding, B. Y., and Zhao, S. X. (2014). “Frequency domain fundamental solutions for a poroelastic half-space.” Acta Mech. Sin., 30(2), 206–213.
Zheng, P., Zhao, S. X., and Ding, D. (2013). “Dynamic Green’s functions for a poroelastic half-space.” Acta. Mech., 224(1), 17–39.
Zhou, X. L., Wang, J. H., and Lu, J. F. (2002). “Transient foundation solution of saturated soil to impulsive concentrated loading.” Soil. Dyn. Earthquake Eng., 22(4), 273–281.
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Published In
Journal of Engineering Mechanics
Volume 144 • Issue 6 • June 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Jul 20, 2017
Accepted: Nov 30, 2017
Published online: Mar 29, 2018
Published in print: Jun 1, 2018
Discussion open until: Aug 29, 2018
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