Abstract
In this paper, the dynamic response of an infinite cylindrical hole embedded in a porous medium and subjected to an axisymmetric ring load is investigated. Two scalar potentials and two vector potentials are introduced to decouple the governing equations of Biot’s theory. By taking a Fourier transform with respect to time and the axial coordinate, we derive general solutions for the potentials, displacements, stresses and pore pressures in the frequency-wave-number domain. Using the general solutions and a set of boundary conditions applied at the hole surface, the frequency-wave-number domain solutions for the proposed problem are determined. Numerical inversion of the Fourier transform with respect to the axial wave number yields the frequency domain solutions, while a double inverse Fourier transform with respect to frequency as well as the axial wave number generates the time-space domain solution. The numerical results of this paper indicate that the dynamic response of a porous medium surrounding an infinite hole is dependant upon many factors including the parameters of the porous media, the location of receivers, the boundary conditions along the hole surface as well as the load characteristics.
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References
Tranter C.J. (1946). On the elastic distortion of a cylindrical hole by a localized hydrostatic pressure. Q Appl Math 4:298–302
Bowie O.L. (1947). Elastic stresses due to a semi-infinite band of hydrostatic pressure acting over a cylindrical hole in an infinite solid. Q Appl Math 5:100–101
Parnes R. (1983). Applied tractions on the surface of an infinite cylindrical bore. Int J Solids Structures 19:165–177
Selberg W.L. (1952). Transient compression waves from spherical and cylindrical cavities. Ark Fys 5:97–108
Jordan D.W. (1962). The stress wave from a finite cylindrical explosive source. J Math Mech 11:503–551
Parnes R. (1969). Response of an infinite elastic medium to traveling loads in a cylindrical bore. ASME J Appl Mech 36:51–58
Parnes R. (1986). Steady-state ring-load pressure on a borehole surface. Int J Solids Struct 22:73–86
Parnes R. (1983). Elastic response to a time-harmonic torsion-force acting on a bore surface. Int J Solids Struct 19:925–934
Rajapakse R.K.N.D. (1993). Stress analysis of borehole in poroelastic medium. ASCE J Eng Mech 119:1205–1227
Cui L., Cheng A.H.D., Abousleiman Y. (1997). Poroelastic solution for an inclined borehole. ASME J Appl Mech 64:32–38
Biot M.A. (1956). Theory of propagation of elastic waves in a fluid-saturated porous solid, I, Low frenquency range. J Acoust Soc Am 28:168–178
Biot M.A. (1956). Theory of propagation of elastic waves in a fluid-saturated porous solid, II: Higher frenquency range. J Acoust Soc Am 28:179–191
Biot M.A. (1962). Mechanics of deformation and acoustic propagation in porous media. J Appl Phys 33:1482–1498
Biot M.A. (1941). General theory of three-dimensional consolidation. J Appl Phys 12:155–164
Truesdell C., Noll W. (1965). The non-linear field theories of mechanics. In: Flügge S. (eds) Principles of classical mechanics and field theory, Handbuck der Physik, vol III/3. Springer, Berlin Heidelberg New York
Morland L.W. (1972). A simple constitutive theory for a fluid-saturated porous solid. J Geophys Res 77:890–900
Bowen R.M. (1980). Incompressible porous media models by use of the theory of mixtures. Int J Eng Sci 18:1129–1148
Bowen R.M. (1982). Compressible porous media models by use of the theory of mixtures. Int J Eng Sci 20:697–735
Passman, S.L., Nunziato, E.W., Walsh, E.K.: A theory of multiphase mixtures, Appendix. In: Truesdell, C.A. (ed.) Rational thermodynamics, Hopkins University Press, 2nd edn. pp. 286–325 (1984).
de Boer R. (2000). Theory of porous media – highlights in the historical development and current state. Springer, Berlin Heidelberg New York
Ehlers W., Bluhm J. (2002). Porous media: theory, experiments, and numerical applications. Springer, Berlin Heidelberg New York
O‘Connell R.J., Budiansky B. (1977). Viscoelastic properties of fluid-saturated cracked solids. J Geophys Res 82:5719–5735
Christensen R.M. (1979). Mechanics of composite materials. Wiley, New York
Hudson J.A., Liu E., Crampin S. (1996). The mechanical properties of materials with interconnected cracks and pores. Geophys J Int 124:105–112
Jakobsen M., Johansen T.A., McCann C. (2003). The acoustic signature of fluid flow in complex porous media. J Appl Geophys 54:219–246
Mura T. (1982). Micromechanics of defects in solids. Martinus-NijhoK, Derdrecht
Nemat-Nasser, S., Hori, M.: Micromechanics: overall properties of heterogeneous materials. 2nd edn. Amsterdam: North-Holland, Amsterdam (1999)
Johnson D.L., Koplik J., Dashen R. (1987). Theory of dynamic permeability and tortuosity in fluid-saturated porous-media. J Fluid Mech 176:379–402
Pride S.R., Morgan F.D., Gangi A.F. (1993). Drag forces of porous-medium acoustics. Phys Rev B 47:4964–4978
Sneddon I.N. (1951). Fourier transforms. McGraw-Hill, New York
Oppenheim A.V., Schafer R.W. (1999). Discrete-time signal processing. Prentice-Hall Inc, Englewood Cliffs
Ricker N.H. (1977). Transient waves in visco-elastic media. Elsevier, Amsterdam
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Lu, JF., Jeng, DS. Dynamic Analysis of an Infinite Cylindrical Hole in a Saturated Poroelastic Medium. Arch Appl Mech 76, 263–276 (2006). https://doi.org/10.1007/s00419-006-0025-9
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DOI: https://doi.org/10.1007/s00419-006-0025-9