Sea Bed Instability From Waves

Abstract

The pressures and the effective stresses in seabeds induced by waves are treated analytically based on Biot's three-dimensional consolidation theory. The wave induced pressures and stresses in a bed are strongly influenced by the permeability and the shear modulus of the soil, the compressibility of pore water, and the thickness of the bed. As a design example, a stress analysis is made for the North Sea design wave and seabed conditions. The numerical results indicate that the North Sea design waves will liquefy the top up to 2 m of the sand beds and induce the sliding failures in the top up to 8.0 m of the sand beds. The theory has been verified by a laboratory experiment for the wave induced pressures. INTRODUCTION The subject of wave induced pressures and stresses in seabeds is important with regard to the design of foundations for various ocean and near shore structures, such as gravity type breakwaters, offshore oil storage tanks, and drilling rigs like EKOFISH at North Sea. The subject is also important when one considers the problems of the flotation of buried pipelines and the burial of rubble mounds, tetorapods, and other blocks by waves. However, the subject is not well understood because the dynamic behavior of soils is difficult to express mathematically. When the water waves propagate over a porous bed such as a sand bed, the flow of fluid is induced in the porous medium and the porous medium itself is forced to deform. Thus, the bed response to water waves is actually a combination of fluid and solid mechanical effects. There have been numerous investigations of the problem of the flow induced in a porous bed by water waves, including Liu (1973), Massel (1976), Moshagen and Tørum (1975), Nakamura, et al. (1973), Putnam (1949), Reid and Kajiura (l957) and Sleath (1970). However, they all assumed that the porous beds are rigid and non deformable. In addition, all except Moshagen and Tørum (1975) and Nakamura, et al. (1973) assumed that the pore fluid is, incompressib1e. The fluid motion in the porous bed is usually expressed by Darcy's law which, with the assumption of a rigid bed with isotropic permeability and incompessible water, leads to the Laplace equation for the pore water pressure. The consequence of this theory is that the pore-water pressure response is independent of the permeability of the bed material. The approach taken by Nakamura, et al. (1973) and Moshagen and Tørum (1975) is based on the assumption that the water is compressible while the porous bed is non deformable which leads to the heat conduction equation for the pore-water pressure. The conclusion from this assumption was that the pore-water pressure response is strongly dependent on the permeability of the bed material. This approach provides no information on the wave induced stresses in seabeds.

Analysis of wave-induced liquefaction in seabed deposits of silt

“…The stress at a point can be readily determined by the classical solutions by Boussinesq for the two-dimensional plane strain problems (Yamamoto, 1978;Madsen, 1978). The harmonic wave-load can be expressed as:…”

Transient wave-induced pore-water-pressure and soil responses in a shallow unsaturated poroelastic seabed

“…Within the framework of the poroelastic theory and the linear wave assumption, analytical solutions for the displacements of the soil skeleton and pore pressure were first obtained by Yamamoto et al (1978), in which the soil was assumed to be homogeneous and isotropic. Their solutions were applied to evaluate the shear failure potential inside the sandy seabed under the North Sea design conditions (Yamamoto 1978). Madsen (1978) derived similar analytical solutions for a hydraulically anisotropic seabed.…”

Travelling wave-induced liquefaction of sand deposits

“…Henkel (1970) was one of the first to carry out a total stress analysis for sea floor under wave loads following the classical procedure of limit equilibrium slope stability analysis. Analytical solutions of effective stress analysis for two-phase coupled response of a poro-elastic bed to water wave were provided by Yamamoto (1978) applying the Biot theory of consoli-NOTE: Written discussion of this paper is welcomed and will be received by the Editor until August 31, 1994 (address inside front cover).…”