Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T19:03:32.634Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  12 April 2006

Tokuo Yamamoto ,
H. L. Koning ,
Hans Sellmeijer  and
Ep Van Hijum
Tokuo Yamamoto
Affiliation:
Department of Civil Engineering, Oregon State University, Corvallis Present address: Department of Civil Engineering, University of Houston, Texas 77004.
H. L. Koning
Affiliation:
Delft Soil Mechanics Laboratory, Delft, The Netherlands
Hans Sellmeijer
Affiliation:
Department of Civil Engineering, Oregon State University, Corvallis
Ep Van Hijum
Affiliation:
DeVoorst Hydraulics Laboratory, Emmeloord, The Netherlands
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 1 , 12 July 1978 , pp. 193 - 206
Copyright
© 1978 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Biot, M. A. 1941 General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155–164.Google Scholar
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.Google Scholar
Mallaid, W. W. & Dalrymple, R. A. 1977 Water waves propagating over a deformable bottom. Offshore Tech. Conf. OTC 2895, Houston, Texas.Google Scholar
Massel, S. B. 1976 Gravity waves propagated over permeable bottom. Proc. A.S.C.E., J. Waterways, Harbors & Coastal Engng 102(WW2), 11–121.Google Scholar
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.Google Scholar
Nakamura, M. et al. 1973 On the seepage in the seabed due to waves. Proc. 20th Japan Soc. Civil Engrs Coastal Engng Conf. pp. 421–428 (in Japanese).Google Scholar
Nath, J. H. et al. 1977 Pressures in sand from waves and caisson motion. Rep. Lab. Testing for Delft Hydraul. Lab. (See also Tech. Rep., School Engng, Oregon State Univ.)Google Scholar
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.Google Scholar
Putnam, J. A. 1949 Loss of wave energy due to percolation in a permeable sea bottom. Trans. Am. Geophys. Un. 30, 349–356.Google Scholar
Reid, R. O. & Kajiura, K. 1957 On the damping of gravity waves over a permeable seabed. Trans. Am. Geophys. Un. 30, 662–666.Google Scholar
Sleath, J. F. A. 1970 Wave induced pressures in beds of sand. Proc. A.S.C.E., J. Hydraul. Div. 96(HY2), 367–378.Google Scholar
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.Google Scholar