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 permeabilitykand the stiffness ratioG/K’, whereGis the shear modulus of the porous medium andK’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 limitsG/K′→ 0 ork→ ∞, the present solution for pressure approaches the solution of the Laplace equation by Putnam (1949). For the limitG/K′→ ∞, the present solution approaches the solution of the heat conduction equation by Nakamuraet 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.
In the Biot theory, the effect of frequency on the oscillatory viscous forces within a porous medium is treated by replacing the kinematic viscosity ν by an oscillatory viscosity νF. Here, F is a function of angular frequency ω, the kinematic viscosity ν, and the single pore size a. In this paper, a mathematical expression of F is presented for arbitrary distribution of pore sizes that can be used in the Biot theory without modification. It is shown that porous media with a given permeability and porosity may be represented by an infinite number of pore-size distributions. The dispersion and attenuation of acoustic waves through such porous media are independent of the pore-size distribution at the low- and high-frequency limits, while they are strongly dependent on the pore-size distribution in the intermediate frequency range. For porous media with φ-normal pore size distributions having a given value of permeability, the maximum specific attenuation decreases and the bandwith of dispersion increases with an increasing standard deviation of the pore-size distribution. Finally, the generalized Biot theory for arbitrary distribution of pore sizes is compared with the entire data of compressional wave attenuation through surficial marine sediments given by E. Hamilton. Comparison between his data and the predictions from this theory show good agreement. [Work supported by ONR.]
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.
Measurements of ambient seismic noise levels in the range 0.03–1.0 Hz were made using ocean-bottom seismometers (OBS) at four shallow-water (<100 m) locations on the New Jersey Shelf and George’s Bank. Surface gravity-wave-induced seabed motion (single-frequency microseism) was found to be dominant in the frequency range 0.03–0.3 Hz, with the high-frequency cutoff strongly dependent on water depth. The peak seismic level in the water wave band was measured at 2.0×10−8 (m/s2)2/Hz in 12 m of water. This level was observed to decrease rapidly with greater water depth. Seismic interface waves (microseisms) of power level approximately 5×10−10 (m/s2)2/Hz were observed in the range 0.25–1.0 Hz. This microseism power level was found to be roughly constant in water depths from 12 to 70 m. A quiet ‘‘notch’’ between the two wave bands, in the range 0.15–0.3 Hz, was observed. The background seismic level in this notch was determined to be less than 5×10−12 (m/s2)2/Hz. Extrapolations of the observed pressures and seabed motions into deeper water conditions are made.
Where wake effects are negligjble. potential flow calculations predict well the lift and added mass forces acting on pipelines near the ocean floor when subjected to time dependent flows. Wake effects have a significant influence on the flow conditions and measured frequencies of vortex shedding can predict the drag force acting on the cylinder. The Strouhal number is a function of the gap below the cylinder. The added mass coefficient is much larger when the cylinder is near the boundary than when it is a free stream. -
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