Wave Attenuation over a Rigid Porous Medium on a Sandy Seabed

In this study, an analytic solution of wave interaction with a rigid porous medium above a poro-elastic sandy bottom is derived to investigate the attenuation of the surface wave and the wave-induced soil response. In the model, both inertial and damping effects of the flow are considered in the rigid porous region using the potential theory, while the consolidation theory is adopted in the sand region. A new complex dispersion relation involving parameters of the rigid porous and the poro-elastic medium is obtained. The analytic solutions are verified by some special cases, such as wave interaction with a porous structure over an impermeable bottom or wave interaction with a poro-elastic medium only. Numerical results indicate that the wave attenuation is highly dependent upon the thickness of the rigid porous layer, the soil stiffness, and their respective coefficients of permeability. Increasing the thickness of the rigid porous layer will shorten the wavelength of the surface wave regardless of the sand coarseness. The pore pressure in fine-sand is larger than in coarse sand, with both decaying with wave progression. It is also found that increasing the thickness of the rigid porous medium will effectively reduce the pore pressure in the sand. For the applications, an extended hyperbolic mild-slope equation is finally obtained, based on the basic analytic solutions. Examples of the wave height transformation over submerged permeable breakwaters on a slope sandy seabed are given. The simulated results show that the wave decay of the coarse sand seabed is larger than those of fine-sand and impermeable seabeds when waves pass after the submerged porous breakwater. The wave damping versus the friction factor for various height of the submerged breakwater is discussed.     

Wave Interaction with a Flexible Porous Breakwater in a Two-Layer Fluid

An analysis has been carried out to study the performance of a flexible porous plate breakwater in a two-layer fluid where each fluid is assumed to be of finite depth and the breakwater is extended over the entire water depth. The problem is analyzed in two dimensions with the assumption of small amplitude wave theory and plate response. The effects of both surface and internal waves are taken into account in the present study. The associated mixed boundary value problem is reduced to a linear system of equations by utilizing a more general orthogonal relation along with least squares approximation method. The reflection and transmission coefficients for the surface and internal modes, wave load, and breakwater response are computed for various physical parameters of interest to analyze the efficiency of the flexible porous plate as a breakwater in the two-layer fluid.     

Wave Diffraction by a Vertical Cylinder with a Porous Ring Plate

Linearized potential wave theory is applied to investigate the phenomenon of wave diffraction by a vertical circular cylinder with a thin ring plate in water of finite depth. By means of the eigenfunction expansion method, harmonic expressions for the velocity potential are obtained. The numerical results for the wave loads and the wave height surrounding the body are discussed. It is found that the presence of a thin ring plate causes the focusing of wave energy near the rear edge of the cylinder for small dimensionless porous-effect parameters. A porous ring plate behaves as a wave absorber, which leads to a decrease of the wave height until setdown occurs. The ring plate can decrease not only the horizontal wave force but also the moment on the cylinder. In general, the mechanism of decreasing the wave loads on the cylinder by a porous ring plate is different from that by an impermeable ring plate. An impermeable ring plate attached to the cylinder causes wave focusing near the rear edge of the cylinder so that the difference between wave heights at the front edge and at the rear edge of the cylinder becomes small; hence the wave loads on the cylinder are decreased. A porous ring plate behaves as a wave absorber, which decreases the wave height at the front edge of the cylinder, and thus leads to a decrease of wave loads on the cylinder.     

Propagation of Love Waves in an Inhomogeneous Fluid Saturated Porous Layered Half-Space with Properties Varying Exponentially

Based on Biot’s theory for transversely isotropic fluid saturated porous media, the complex dispersion equation for Love waves in a transversely isotropic fluid-saturated porous layered half-space is derived with the consideration of the inhomogeneity of the layer. The equation is solved by an iterative method. Detailed numerical calculation is presented for an inhomogeneous fluid-saturated porous layer overlying a purely elastic half-space. The dispersion and attenuation of Love waves are discussed. In addition, the upper and lower bounds of Love wave speed are also explored.     

Joined Influences of Nonlinearity and Dilation on the Ultimate Pullout Capacity of Horizontal Shallow Plate Anchors by Energy Dissipation Method

The ultimate pullout capacity (UPC) and the shape modification factors of horizontal plate anchors were calculated by using upper-bound limit analysis, in which the assumptions of both a nonlinear failure criterion and the nonassociated flow rule were made upon the soil mass above the anchor plate. Three types of anchor plates, including strip anchors, circle anchors, and rectangle anchors, and the corresponding failure mechanisms are taken into consideration. The anchor breakout factors were obtained according to the principle of virtual power, which was realized numerically by the nonlinear sequential quadratic programming algorithm. The shape modification factors for different kinds of anchors were given through a multiple nonlinear regression method. Numerical experiments demonstrate the validity of the solutions by reducing the solutions (nonlinear criterion and nonassociated flow rule) into their special cases (linear criterion and associated flow rule), which matches well with existing work. The dilation and nonlinearity of soil mass should be considered because it plays a remarkable role in the UPC of anchor plates.     

Saturation Effects of Soils on Ground Motion at Free Surface Due to Incident SV Waves

A study is presented of saturation effects of subsoil on seismic motions at the free surface of a half space due to an inclined (SV) wave. By treating the soil as a partially water-saturated porous medium that is characterized by its degree of saturation, porosity, permeability, viscosity, and compressibility, a theoretical formulation is developed for the computation of free-surface amplitudes in both the horizontal and vertical components, which are defined as a function of the degree of saturation, the angle of incidence, and the frequency. Numerical results are presented using typical sand properties. It is shown that even a slight decrease of full saturation may lead to a substantial influence on the free-surface amplitudes in both the components and the amplitude ratios between them, and this influence is dependent on the angle of incidence. Significant phase shift between the horizontal and vertical components may also occur due to this slight change in saturation. At small incident angles, partial saturation of subsoil generally may cause a greater vertical-to-horizontal ratio compared with a fully saturated model. It is suggested that one may need to carefully take into account the saturation condition in the interpretation of field observations on seismic ground motions.     

Viscous Flow Past a Porous Spherical Shell—Effect of Stress Jump Boundary Condition

Using the stress jump boundary condition for the tangential stresses at the porous liquid interface along with the continuity of the velocity components and normal stress, the uniform viscous flow past a porous spherical shell with external radius r1, internal radius r2 is studied. The flow inside the porous region is governed by Brinkman equation. The flow in the liquid region is governed by the Stokes equation. The flow field is computed by matching the boundary conditions at the porous-fluid interface. The effect of stress jump coefficient β on the flow field is very much felt. An increase in the drag with permeability is found for different R, different ratio of r1/r2, and also a change in magnitude of the drag for different values of stress jump coefficient β is observed. Also, the variation of torque and shear stress with permeability and the stress jump coefficient is discussed.