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On the response of a poro-elastic bed to water waves

  • Tokuo Yamamoto (a1) (a2), H. L. Koning (a3), Hans Sellmeijer (a1) and Ep Van Hijum (a4)
Abstract

The problem of the response of a porous elastic bed to water waves is treated analytically on the basis of the three-dimensional consolidation theory of Biot (1941). Exact solutions for the pore-water pressure and the displacements of the porous medium are obtained in closed form for the case of waves propagating over the poro-elastic bed. The theoretical results indicate that the bed response to waves is strongly dependent on the permeability k and the stiffness ratio G/K’, where G is the shear modulus of the porous medium and K’ is the apparent bulk modulus of elasticity of the pore fluid. The earlier solutions for pore-water pressure by various authors are given as the limiting cases of the present solution. For the limits G/K′ → 0 or k→ ∞, the present solution for pressure approaches the solution of the Laplace equation by Putnam (1949). For the limit G/K′→ ∞, the present solution approaches the solution of the heat conduction equation by Nakamura et al. (1973) and Moshagen & Tørum (1975).

The theoretical results are compared with wave tank experimental data on pore-water pressure in coarse and fine sand beds which contain small amounts of air. Good agreement between theory and experiment is obtained.

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References
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Biot, M. A. 1941 General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155164.
Koning, H. L. 1968 Rep. Delft Soil Mech. Lab. (c) 0–14683–II.
Liu, P. L. 1973 Damping of water waves over porous bed. Proc. A.S.C.E., J. Hydraul. Div. 99(HY12), 2263–2271.
Mallaid, W. W. & Dalrymple, R. A. 1977 Water waves propagating over a deformable bottom. Offshore Tech. Conf. OTC 2895, Houston, Texas.
Massel, S. B. 1976 Gravity waves propagated over permeable bottom. Proc. A.S.C.E., J. Waterways, Harbors & Coastal Engng 102(WW2), 11–121.
Moshagen, H. & TøRUM, A. 1975 Wave induced pressures in permeable seabeds. Proc. A.S.C.E., J. Waterways, Harbours & Coastal Engng 101(WW1), 49–57.
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Prevost, J. H. et al. 1975 Discussion of ‘Wave induced pressures in permeable seabeds’ (by H. Moshagen & A. Tørum, paper no. 11099). Proc. A.S.C.E., J. Waterways, Harbours & Coastal Engng 101(WW1), 464–465.
Putnam, J. A. 1949 Loss of wave energy due to percolation in a permeable sea bottom. Trans. Am. Geophys. Un. 30, 349356.
Reid, R. O. & Kajiura, K. 1957 On the damping of gravity waves over a permeable seabed. Trans. Am. Geophys. Un. 30, 662666.
Sleath, J. F. A. 1970 Wave induced pressures in beds of sand. Proc. A.S.C.E., J. Hydraul. Div. 96(HY2), 367–378.
Verruijt, A. 1969 Elastic storage of aquifers. In Flow Through Porous Media (ed. R. J. M. DeWiest), chap. 8. Academic Press.
Yamamoto, T. 1977 Wave induced instability in seabeds. Proc. A.S.C.E. Spec. Conf.: Coastal Sediments 77, Charleston, SC.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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