Antiplane Diffraction from Canyon above Subsurface Unlined Tunnel

The 2D scattering and diffraction of plane shear horizontal waves by a surface semicircular canyon on top of an underground circular unlined tunnel (cavity) in a homogeneous elastic half-space has been analyzed. Using an exact analytic series solution of the problem for a general angle of wave incidence, the ground motions of the half-space surface on and near the canyon and that of the underground cavity were evaluated. These surface motions depend on the following parameters: (1) The angle of incidence ζ of the plane shear horizontal waves; (2) the dimensionless frequency or wave number ka; (3) a0∕a, the ratio of the radius of the surface canyon to that of the underground cavity; and (4) D∕a, the ratio of the depth of the cavity to its radius.     

Pore Pressure Response Following Undrained uCPT Sounding in a Dilating Soil

The generation and dissipation of pore fluid pressures following standard piezocone sounding (uCPT) sounding in silty sands are observed to exhibit many of the characteristics of undrained penetration in dilatant materials; steady excess pore pressures may be subhydrostatic, or may become subhydrostatic during dissipation, and are slow to decay. Enigmatic pore pressure dissipation histories which transit from sub- to supra- and again to subhydrostatic before equilibrating at hydrostatic are consistent with a response where undrained pressures are maximally negative remote from the penetrometer tip. This surprising distribution of induced pore fluid pressures is accommodated in cavity expansion models for a dilating soil. A Mohr-Coulomb constitutive model is established for undrained loading of a soil with pore pressure response defined by Skempton pore pressure parameters. Defined in terms of effective stresses, this allows undrained stresses and pore pressures to be determined following cavity expansion in a c–? soil. Pore pressures are conditioned by the shear modulus, Skempton A parameter, and the “undrained shear strength.” The undrained shear strength is additionally modulated by the magnitudes of c, ?, A, and of the initial in situ effective stress, σ0′. Cavity expansion stresses, and pore pressures may be backcalculated. Undrained pore pressures are shown to decay loglinearly with radius from the cavity wall; they may be either supra- or subhydrostatic at the cavity wall, and where suprahydrostatic may become subhydrostatic close to the transition to the elastic region. This initial pressure distribution contributes to the observed switching between supra- and subhydrostatic pore pressures recorded during dissipation. “Type curves” that reflect the dissipation response enable the consolidation coefficient, undrained strength, and shear modulus to be computed from observed pore pressure data, and confirmed against independent measurements. In addition to representing the dilatory response of cohesionless silts, the method applies equally to recovering the pressure generation and dissipation response of overconsolidated clays.     

Purging of a Neutrally Buoyant or a Dense Miscible Contaminant from a Rectangular Cavity. I: Case of an Incoming Laminar Boundary Layer

The flow past two-dimensional (2D) channel cavities along with the removal of neutrally buoyant or dense miscible contaminants introduced instantaneously inside the cavity are studied using eddy resolving techniques. In the simulations, the incoming boundary layer is laminar and the flow is observed not to transition to turbulence as it is convected over the cavity. As for these flow conditions the main coherent structures in the separated shear layer over the cavity are quasi-dimensional, 2D simulations are performed. It is found that the mechanism of removal of the contaminant is very different between the neutrally buoyant and buoyant cases. In the neutrally buoyant case the contaminant is purged from the cavity mostly due to the interactions between the vortices shed in the separated shear layer with the main recirculation eddies inside the cavity and with the trailing edge corner. In the simulations in which a dense contaminant is introduced inside the cavity, after the initial stages of the mass exchange process, the main phenomenon is the presence of a large amplitude internal wave motion which interacts with a strong cavity vortex situated near the trailing edge corner in between the shear layer and the density interface. The density variation across this oscillatory interface is strong. Through this interaction wisps of denser contaminant are extracted from the region beneath the density interface, before being ejected from the cavity by the separated shear layer vortices. The values of the global mass exchange coefficients for the different phases of the purging process are estimated from simple dead-zone models. As expected, the purging process is delayed in the case in which the density of the contaminant is larger than the one of the carrying fluid.     

In Situ Measurement of Damping Ratio Using Surface Waves

Measurements of surface wave attenuation provide a means to determine the in situ material damping ratio profile of near-surface soils. Frequency-dependent surface wave attenuation coefficients are determined from measurements of seismic wave amplitudes at various offsets from a swept-sine source. The accuracy of the measured attenuation coefficients is improved by properly accounting for the geometric attenuation of multimode Rayleigh waves. Once the frequency-dependent attenuation coefficients are determined, the shear damping ratio profile is calculated using a constrained inversion analysis. Application of the method is illustrated at the Treasure Island National Geotechnical Experimentation Site. Values of shear damping ratio, obtained using surface wave measurements, were less than those measured using cross hole tests, possibly because the higher frequencies used in cross hole tests result in more apparent attenuation due to scattering and because fluid losses contribute to damping at higher frequencies. Damping ratios from surface wave tests agree more closely with resonant column and torsional shear test results.     

Dynamic Stress Concentrations in Lined Twin Tunnels within Fluid-Saturated Soil

An exact analysis for three-dimensional dynamic interaction of monochromatic seismic plane waves with two lined circular parallel tunnels within a boundless fluid-saturated porous elastic medium is presented. The novel features of Biot dynamic theory of poroelasticity along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorems for cylindrical wave functions are employed to obtain a closed-form solution in the form of infinite series. The analytical results are illustrated with numerical examples in which two identical tunnels, lined with concrete and embedded within water-saturated soils of distinct frame properties (i.e., soft or stiff soils), are insonified by plane fast compressional or shear waves at end-on incidence. The basic dynamic field quantities such as the hoop and axial stress amplitudes are evaluated and discussed for representative values of the parameters characterizing the system. The effects of formation material type, angle of incidence, incident wave frequency, and the proximity of the two tunnels on the liner stresses are examined. Particular attention is paid to the influence of bonding and drainage conditions at the liner/soil interface on the dynamic stress concentrations. Limiting cases are considered and good agreement with the solutions available in the literature is obtained.     

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.     

Effects of shear elasticity on sea bed scattering: numerical examples

It is known that marine sediments can support both compressional and shear waves. However, published work on scattering from irregular elastic media has not examined the influence of shear on sea bed scattering in detail. A perturbation model previously developed by the authors for joint roughness-volume scattering is used to study the effects of elasticity for three sea bed types: sedimentary rock, sand with high shear speed, and sand with "normal" shear wave speed. Both bistatic and monostatic cases are considered. For sedimentary rock it is found that shear elasticity tends to increase the importance of volume scattering and decrease the importance of roughness scattering relative to the fluid case. Shear effects are shown to be small for sands.     

The acoustoelastic response of a textured material during elastic-plastic deformation

Acoustoelasticity is a technique for the nondestructive evaluation of stress which relates changes in the speeds at which plane waves propagate through a solid to variations in the stress state. In the present work, the acoustoelastic behavior of a polycrystalline aggregate during elasticplastic deformation is investigated. Results are reported for a series of uniaxial tests in which the velocities of longitudinal and shear waves were monitored during elastic-plastic deformation of aluminum 5086-H32. A specific microstructural mechanism—the reorientation of grains due to plastic deformation—is investigated as a cause for the observed changes in acoustoelastic response which occur during elastic-plastic deformation. The Taylor theory analysis of the grain reorientation predicts velocity changes that are of the same sign and order of magnitude as the experimental results for shear waves but not for longitudinal waves.     

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.     

Viscoelastic Wave Dispersion and Rheometry of Cohesive Sediments

The interpretation of in situ rheometry based on shear wave propagation techniques is examined in terms of various viscoelastic model assumptions concerning sediment behavior under water waves. It is shown that, due to viscoelastic wave dispersion, measurements of shear wave velocity by pulse techniques are unsuitable as a basis for in situ rheometry, and that resonance-based techniques are unreliable.     

Laboratory Studies on the Coupled Oscillations between an Internal Density Interface and a Shear Layer

The results from experiments conducted in a 2?m high flow compartment at large Reynolds numbers are reported in this paper. Flow entered the compartment through an opening at the base on one side of the compartment and exited from an opening at the bottom of the opposite wall of the compartment. A shear layer is formed at the boundary between the incoming flow and the ambient fluid in the compartment. The impingement of the shear layer on the opposite wall of the compartment gives rise to periodic vortex formation and highly organized oscillations in the shear layer. When a density interface is present inside the compartment, resonance conditions were set up when the oscillations of the internal standing waves were “locked in” with the shear layer oscillations. Under resonance conditions, internal standing waves with amplitudes of up to 0.1?m were observed. The formation of the internal standing waves is linked to the shear layer oscillations. Resonance conditions result when the shear layer is oscillating close to the natural frequency of the stratified fluid system in the compartment. The results of this investigation are applicable for fresh water storage in floating bottom-opened tanks in the sea, where under resonance conditions, entrainment rates could be significantly increased.     

Spatial and Temporal Characteristics of Transient Extreme Wave Profiles on Depth-Varying Currents

The results of laboratory experiments on transient (short lived), extreme (highest nonbreaking) waves on depth-varying currents are reported. A new feedback control wave focusing method on currents was developed to create transient, extreme waves in the presence of desired depth-varying currents at the prescribed position. Both wave profiles and time series of surface displacements were measured to examine the spatial and temporal characteristics of extreme waves. Wavelengths estimated from dispersion relations consistently underestimated those measured directly from the video images of transient extreme waves. This underestimation well correlates with a proposed wavelength asymmetry parameter ξ (a ratio of the trough length to the crest length), suggesting the rapid change of a transient wave profile during a wave cycle. The effects of the current shear on transient, extreme wave profiles are recognized. The negative shear increased the limiting wave steepness but reduced the vertical asymmetry. The vertical asymmetry could be remarkably augmented by the positive current shear, while the limiting wave steepness was reduced. These results were clearly observed in the spatial wave profiles, but not in the time series of the surface displacement.     

Damping Effect on Waves Propagating Past a Submerged Horizontal Plate and a Vertical Porous Wall

A set of analytical solutions for waves propagating past a combined submerged horizontal plate and vertical porous wall breakwater system is presented. The wave damping effect caused by the horizontal plate induced flow constriction is considered in the analysis. The velocity potentials in each fluid domain are derived based on the linear wave theory and the unknown coefficients are determined from the matching conditions using three sets of orthogonal eigenfunctions. Reflection and transmission coefficients are presented to evaluate the performance of the breakwater system. The analytical solutions in terms of the reflection and transmission coefficients as well as the hydrodynamic force on the vertical porous wall are found in good agreement with published laboratory measurements. In comparison with the solutions without taking into account the wave damping effect, the present analytical solutions significantly improve the accuracy of the wave predictions, especially for the reflected waves.     

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.     

Oblique and Herringbone Buckling Analysis of Steel Strip by Spline FEM

 The tilted waves in steel strip during rolling and leveling of sheet metal can be classified into two different types of buckling, oblique and herringbone buckling, respectively. Numerical considerations of oblique and herringbone buckling phenomena are dealt with by the spline finite element method (FEM). It is pointed out that the shear stress due to residual strains caused by the rolling process or applied non-uniform loading is the main reason of oblique and herringbone buckle. According to the analysis of stress distribution in plane, the appropriate initial strain patterns are adopted and the corresponding buckling modes are calculated by the spline FEM. The developed numerical model provides an estimation of buckling critical load and wave configuration.     

Behavior of Nonbuoyant Jets in a Wave Environment

This paper presents experimental results of a turbulent neutrally buoyant jet vertically discharged in a stagnant ambient and of the same jet discharged in a flow field of regular waves, in the intermediate range between deep and shallow water. A number of such studies have been performed on this configuration in the past, but mostly limited to concentration (dilution) measurements. Thus one could argue the need for a detailed analysis of this problem with modern instrumentation. This paper will address the deficiency and will present the results of a new experimental study into wave-induced mixing. Velocity jet components were measured with a backscatter, two-component four-beam laser Doppler anemometer system. For the cases of jets with waves, ensemble-averaged velocities were obtained by phase averaging the measured signals separated by the wave period over about 500 waves. The main results of the present study indicate the following: (1) the entrained flow is higher in the case of jet with waves; (2) oscillating velocity components cannot be described by classic wave motion theories; (3) comparison of the root-mean square of turbulent velocity components indicates the effect of wave presence; (4) in the case of jet-wave interaction, the reduction of the jet momentum shown in literature can be explained by the presence of the turbulent Reynolds normal stresses (which are not as small as in the case of stagnant ambient and, consequently, cannot be ignored) and the wave Reynolds normal stresses; and (5) the analysis of the wave Reynolds shear stresses shows that it is not always right to apply a wave motion theory to obtain the statistical contribution of the wave field; a conclusion particularly interesting in order to enable the improvement of mathematical models present in literature.     

Poroelastic Model for Production- and Injection-Induced Stresses in Reservoirs with Elastic Properties Different from the Surrounding Rock

Closed-form and semianalytical solutions for induced poroelastic stresses and strains are extremely useful for the design of subsurface fluid storage in caverns because of their relative ease of implementation and their suitability for parameter sensitivity analyses. This paper describes the use of Eshelby’s inhomogeneity theory to derive equations that can be used to predict the induced stresses and strains for reservoirs that are elliptical in cross section, under plane strain conditions. Sensitivity analyses demonstrate that the induced stresses are relatively insensitive to the Poisson’s ratio of the surrounding rock, but they are strongly affected by the Poisson’s ratio of the reservoir, and the ratio of shear modulus of the reservoir to that of the surrounding rock. Results are presented in terms of dimensionless parameters, which facilitate their application to a broad range of reservoir dimensions and pressure-change magnitudes. These equations can also be used to predict the induced stresses around a cavity, which represents the special case of an inhomogeneity with a shear modulus of zero.     

Resonant Column Testing of Sands with Different Viscosity Pore Fluids

The effect of pore fluid viscosity on the stiffness, damping, and liquefaction characteristics of sands was investigated to assess the potential contributions to a centrifuge model seismic response for soils saturated with high-viscosity pore fluid. Resonant column tests with cyclic loading frequencies in the range of 20–45 Hz were performed on a variety of fluids and sand sizes. At a strain level less than 2 × 10?4, the damping increased with pore fluid viscosity and shear strain amplitude, and it decreased with sand particle size. However, at shear strain greater than about 2 × 10?4, the increased skeleton damping tended to mask any effect of additional damping due to fluid viscosity. The liquefaction tests on fine silica sand revealed that the increase in total energy dissipation was not more than 10% for 100 cS oil when compared with water at a driving frequency of 25 Hz. Based on the experimental results, a simple model is proposed to examine the dependency of viscous damping on pore fluid viscosity, loading frequency, particle size, and shear strain amplitude.     

Instabilities of the metal surface in electrolytic alumina reduction cells

Transient waves on the metal surface in electrolytic cells are studied by simulation on a computer model. The model used is a semidynamic modification of a model for stationary flow and surface calculation. The simulation results clearly show that any wave once started by some disturbance, will turn into a transient wave rotating along the edge of the cell cavity, resulting in a tilting movement of the whole metal surface. The mechanism of the rotating wave is explained. It is further demonstrated that there exists a stability limit above which the rotating waves are amplified instead of being damped, leading to an unstable situation known as “shaky pot”. A simple empirical stability formula is presented, showing the interrelation of the decisive cell parameters. General estimation curves for typical cells are also given.