Effect of Gravity and Initial Stress on Torsional Surface Waves in Dry Sandy Medium

This problem studies the effect of gravity and initial stress on the propagation of torsional surface waves in dry sandy medium. The mathematical analysis of the problem has been dealt with the Whittaker function. Assuming the expansion of the Whittaker function up to linear term, it is concluded that the gravity field will always allow torsional waves to propagate. The expansion of the Whittaker function up to quadratic terms shows that two such wave fronts may exist in the medium. Finally, it is concluded that the sandy medium without support of a gravity field cannot allow the propagation of torsional surface waves, where as the presence of a gravity field always supports the propagation of torsional surface waves regardless of whether the medium is elastic or dry sandy.     

Torsional Surface Waves in Nonhomogeneous Anisotropic Medium under Initial Stress

This paper studies the possibilities of propagation of torsional surface waves in nonhomogeneous anisotropic half-space under compressive initial stress. Two types of variations in nonhomogeneity, mainly hyperbolic and quadratic, have been discussed, and it is observed that in both cases the torsional surface wave will propagate in the media under consideration. The velocities of propagation have been computed and are presented in graphs. The study shows that for hyperbolic variation of nonhomogeneity, the increase of the anisotropic factor, increases the velocity of propagation, always keeping it more than that of shear wave in homogeneous medium. The presence of initial stress increases the velocity of propagation. In the case of quadratic variation it is found that the presence of initial stresses increases the velocity of propagation. The increase of anisotropy decreases the velocity, and the decrease in the nonhomogeneity factor increases the velocity, always keeping the velocity of torsional surface waves less than that of shear wave in the homogeneous medium.     

Scattering of Harmonic Waves by a Circular Cavity in a Porous Medium: Complex Functions Theory Approach

An analytical solution for the evaluation of scattering of waves by a circular cavity in infinite isotropic elastic porous media is presented. Two groups of complex functions for solid skeleton and pore fluid in a two-dimensional complex plane are introduced in order to solve the Biot equations. Stress, displacement, and pore pressure fields induced by incident and scattered waves in the medium and especially in the vicinity of the cavity are evaluated in this complex plane. The validation of the proposed solution is shown by various numerical examples. A parametric study including the effects of fluid compressibility changes, shear modulus, and permeability variations, several wave numbers, and wave types (fast, slow, and shear waves) is performed.     

Pressure Waves in Porous Medium Saturated with Liquid Containing Gas Bubbles

Theoretical analyses on nonlinear pressure waves evolution in porous medium saturated with a liquid containing gas bubbles is carried out. The evolution equations for fast and slow longitudinal modes are derived for slightly nonlinear, disperse, and dissipation processes. The pressure wave distribution in gas bubble liquid-saturated porous media was investigated experimentally. It was revealed that both modes might have oscillating structure induced by bubble oscillation in the wave. It is shown that the wave damping is determined by a combined impact of heat losses due to gas cooling in the bubbles and dissipation due to longitudinal displacement of liquid and porous skeleton, both influenced by the wave. Experimental data on the velocity and structure of fast and slow modes are compared with results of theoretical modeling.     

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.     

Oblique Impact of Water Waves on Thin Porous Walls

There is a paradoxical phenomenon in earlier studies when the incoming water wave is parallel to a porous breakwater, the water wave permeates completely without regard to the largeness of the the porosity of the porous breakwater. For solving the problem of the water waves obliquely impacting upon the thin porous wall, a new boundary condition on the thin porous wall—which can remedy the above mentioned paradoxical phenomenon—is proposed based on the concept that the incident angle remains unchanged when the water wave permeates into the wall. According to this new boundary condition, an analytic solution of an oblique water wave impacting on a thin porous wall of any permeability is obtained. It is found that the above paradoxical phenomenon, as the water wave is parallel to a thin porous wall, disappears. And, as the incident angle approaches 90°, the reflection coefficient and the transmission coefficient reasonably converge to 1 and 0, respectively, while on the contrary, those in the earlier investigations converge to 0 and 1.     

Fully Nonlinear Boussinesq-Type Equations for Waves and Currents over Porous Beds

The paper introduces a complete set of Boussinesq-type equations suitable for water waves and wave-induced nearshore circulation over an inhomogeneous, permeable bottom. The derivation starts with the conventional expansion of the fluid particle velocity as a polynomial of the vertical coordinate z followed by the depth integration of the vertical components of the Euler equations for the fluid layer and the volume-averaged equations for the porous layer to obtain the pressure field. Inserting the kinematics and pressure field into the Euler and volume-averaged equations on the horizontal plane results in a set of Boussinesq-type momentum equations with vertical vorticity and z-dependent terms. A new approach to eliminating the z dependency in the Boussinesq-type equations is introduced. It allows for the existence and advection of the vertical vorticity in the flow field with the accuracy consistent with the level of approximation in the Boussinesq-type equations for the pure wave motion. Examination of the scaling of the resistance force reveals the significance of the vertical velocity to the pressure field in the porous layer and leads to the retention of higher-order terms associated with the resistance force. The equations are truncated at O(μ4), where μ = measure of frequency dispersion. An analysis of the vortical property of the resultant equations indicates that the energy dissipation in the porous layer can serve as a source of vertical vorticity up to the leading order. In comparison with the existing Boussinesq-type equations for both permeable and impermeable bottoms, the complete set of equations improve the accuracy of potential vorticity as well as the damping rate. The new equations retain the conservation of potential vorticity up to O(μ2). Such a property is desirable for modeling wave-induced nearshore circulation but is absent in existing Boussinesq-type equations.     

Turbulent Boundary Layer Flows Above a Porous Surface Subject to Flow Injection

A new analytical expression for velocity profile in a fully developed turbulent boundary layer above a porous surface subject to flow injection is derived by solving the coupled Reynolds equations and turbulent kinetic energy equation. The advection of turbulent kinetic energy is considered during the derivation, whereas the earlier studies have neglected it. The new solution reduces to the universal logarithmic law in the case of no flow injection. For the small injection, the solution can be expanded into a series form in terms of the normalized injection velocity. The leading order terms are found to be equivalent to those in the earlier works in which the advection of turbulent kinetic energy has been neglected in the derivation. The new solution can provide more accurate prediction of bed shear stress for a wide range of flow injection rate, fluid type (e.g., from air to water), and surface roughness. On the other hand, the earlier theories may significantly underestimate bed shear stress under high injection rates.     

Poromechanics of Anisotropic Hollow Cylinders

It has been known that inherent material anisotropy influences the mechanics of geoengineering applications. Aiming at the experimental studies associated with geoengineering applications in anisotropic materials, this paper proposes a poromechanics analysis of a fully saturated transversely isotropic hollow cylinder. Closed-form analytical solutions for the pore pressure and stress fields were derived. These solutions are obtained under various loading conditions that are encountered in laboratory testing procedures. Numerical analyses were carried out to demonstrate the material anisotropy effect on stress, displacement, and pore pressure distributions in the cylinder. It is also shown that uncertainties in the estimation or measurements of the poromechanical parameters have proven effects on the time-dependent responses of the hollow cylinder geometry during laboratory testing.     

In Situ Estimate of Shear Wave Velocity Using Borehole Spectral Analysis of Surface Waves Tool

In situ field testing has been performed over the past several years at a silty sand site in Austin, Tex. using the borehole spectral analysis of surface waves (SASW) tool to develop the technique and assess the validity of the method. The borehole SASW tool is an inflatable pressuremeterlike device that allows surface wave measurements to be performed along the wall of an uncased borehole while varying the in situ states of stress. Field results demonstrate the applicability of borehole SASW testing as a method to characterize soil sites and provide information about in situ shear wave velocity and the relationship between shear wave velocity and state of stress. Results from a borehole SASW test conducted at the Austin site are presented herein to demonstrate the applicability and validity of the method.     

Celerity and Amplification of Supercritical Surface Waves

The amplification of supercritical waves in steep channels is examined analytically using a one-dimensional dynamic solution of the Saint-Venant equations. Existing methods were modified to describe the amplification of surface waves over a normalized channel length rather than over a single wavelength. The results are strikingly different, and a generalized graph shows that short waves amplify the most over a fixed channel length. The maximum amplification parameter over a normalized channel length is 0.53 when F = 3.44. Applications to the flood drainage channel F1 in Las Vegas indicate that the amplitude of waves shorter than 100 m would increase by 65% over a channel length of 543 m. These theoretical results await field verification. Supercritical waves could be dampened by increasing channel roughness to reduce the Froude number below 1.5.     

Fully Nonhydrostatic Modeling of Surface Waves

A fully nonhydrostatic model is tested by simulating a range of surface-wave motions, including linear dispersive waves, nonlinear Stokes waves, wave propagation over bottom topographies, and wave–current interaction. The model uses an efficient implicit method to solve the unsteady, three-dimensional, Navier-Stokes equations and the fully nonlinear free-surface boundary conditions. A new top-layer pressure treatment is incorporated to fully include the nonhydrostatic pressure effect. The model results are verified against either analytical solutions or experimental data. It is found that the model using a small number of vertical layers is capable of accurately simulating both the free-surface elevation and vertical flow structure. By further examining the model’s performance of resolving wave dispersion and nonlinearity, the model’s efficiency and accuracy are demonstrated.     

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.     

Experimental Evidence for Slow Compressional Waves

One of the most conspicuous aspects of the Biot–Frenkel theory is the existence of the slow compressional wave. An overview is given of the various experimental techniques that were/are used to study its appearance and properties.     

Extended Boussinesq Equations for Water-Wave Propagation in Porous Media

This paper presents a new Boussinesq-type model equations for describing nonlinear surface wave motions in porous media. The mathematical model based on perturbation approach reported by Hsiao et al. is derived. The drag force and turbulence effect suggested by Sollitt and Cross are incorporated for observing the flow behaviors within porous media. Additionally, the approach of Chen for eliminating the depth-dependent terms in the momentum equations is also adopted. The model capability on an applicable water depth range is satisfactorily validated against the linear wave theory. The nonlinear properties of model equations are numerically confirmed by the weakly nonlinear theory of Liu and Wen. Numerical experiments of regular waves propagating in porous media over an impermeable submerged breakwater are performed and the nonlinear behaviors of wave energy transfer between different harmonics are also examined.     

Effective Medium Theories for Multicomponent Poroelastic Composites

It is demonstrated that effective medium theories for poroelastic composites such as rocks can be formulated easily by analogy to well-established methods used for elastic composites. An identity analogous to Eshelby’s classic result has been derived previously for use in composites containing arbitrary ellipsoidal-shaped inclusions. This result is the starting point for new methods of estimation, including generalizations of the coherent potential approximation, differential effective medium theory, and two explicit schemes. Results are presented for estimating drained shear and bulk modulus, the Biot–Willis parameter, and Skempton’s coefficient. Three of the methods considered appear to be quite reliable estimators, while one of the explicit schemes is found to have some undesirable characteristics. Furthermore, the results obtained show that the actual microstructure should be taken carefully into account when trying to decide which of these methods to apply in a given situation.     

Improving the Uniqueness of Surface Wave Inversion Using Multiple-Mode Dispersion Data

The use of multiple-mode dispersion data in surface wave inversion to derive shear-wave velocity (vs) profiles has increased in the past decade as the inclusion of higher mode data can improve the accuracy of the inversion results. However, the error associated with nonuniqueness in the multiple-mode inversion has not been clarified and quantified. This research focuses on the attempt to improve the accuracy of multiple-mode surface wave inversion result by optimizing the use of multiple-mode dispersion data to reduce the error associated with the nonuniqueness in inversion. In this research, an alternative approach was used where inversion of surface wave dispersion data was performed using three distinct modes. Four different vs profiles, representing regular and irregular cases, were used, and multiple-mode dispersion data were synthesized from these profiles using the dynamic stiffness matrix method as the theoretical model. The dispersion data were then inverted using the Levenberg–Marquardt method. The results demonstrated that, as expected, inclusion of higher modes did not improve the accuracy of the inversion results for the regular profiles. However, inclusion of higher modes significantly improved the uniqueness of the inversions for the irregular profiles. The results also demonstrate that regardless of the nature of the profile, the accuracy of the inversion improves when the starting profile more closely matches the true profile. Of all the inversion approaches investigated, the best approach was one where three successive inversions, using one, two, and three modes, respectively, was used, where the inverted profile from one inversion was used as a starting model for a subsequent inversion that used one additional mode.     

Laminar Water Wave and Current Passing Over Porous Bed

The problem of the dynamic interaction of water waves, current, and a hard poroelastic bed is dealt with in this study. Finite-depth homogeneous water with harmonic linear water waves passing over a semi-infinite poroelastic bed is investigated. In order to reveal the importance of viscous effect for different bed forms, viscosity of water is considered herein. In a boundary layer correction approach, the governing equations of the poroelastic material are decoupled without losing physical generality. The contribution of pressure effect and shear effect to the hard poroelastic bed, which is a valuable indication to the mechanism of ripple formation, is clarified in the present study. This approach will be helpful in saving time and storage capacity when it is applied to numerical computation.     

One-Dimensional Model of Shallow Water Surface Waves Generated by Landslides

A numerical model is presented as the basis for the study of surface waves generated by bank and bottom landslides in rivers. The flow is assumed to be properly modeled by the shallow water equations. The solid movement is introduced in the model as an external action, and assumed rigid and impervious. Two situations are identified in the flow subsequent to a solid movement: longitudinal and transversal sliding. A discussion on the modeling difficulties associated with the latter is included. The flow equations are solved by means of an upwind scheme specially adapted to advancing fronts over dry irregular beds.