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.     

Dispersive and Nonhydrostatic Pressure Effects at the Front of Surge

Undular bores and shocks generated by dam-break flows or tsunamis are examined considering nonhydrostatic pressure and dispersive effects in one- and two-horizontal-dimensional space. The fully nonlinear Boussinesq-type equations based on a weakly nonhydrostatic pressure assumption are chosen as the governing equations. The equation set is solved by a fourth-order accurate finite-volume method with an approximate Riemann solver. Several typical benchmark problems such as dam-break flows and tsunami wave fission are tested in one- and two-horizontal-dimensional space. The computed results by the Boussinesq-type model are at least as accurate as the results by the hydrostatic shallow water equations. This is particularly evident near the steep front of the wave, where frequency dispersion can play an important role. The magnitude of this nonhydrostatic pressure and dispersive effect near the front is quantified, and the engineering implications of neglecting these physics, as would be done through the use of a hydrostatic model, are discussed.     

Forced Vertical Vibration of Circular Plate in Multilayered Poroelastic Medium

This paper considers the vertical vibrations of an elastic circular plate in a multilayered poroelastic half space. The plate is subjected to axisymmetric time–harmonic vertical loading and its response is governed by the classical thin-plate theory. The contact surface between the plate and the multilayered half space is assumed to be smooth and either fully permeable or impermeable. The half space under consideration consists of a number of layers with different thicknesses and material properties and is governed by Biot’s poroelastodynamic theory. The vertical displacement of the plate is represented by an admissible function containing a set of generalized coordinates. Contact stress and pore pressure jump are established in terms of generalized coordinates through the solution of flexibility equations based on the influence functions corresponding to vertical and pore pressure loading. Solutions for generalized coordinates are obtained by establishing the equation of motion of the plate through the application of Lagrange’s equations of motion. Selected numerical results are presented to portray the influence of various parameters on dynamic interaction between an elastic plate and a multilayered poroelastic half space.     

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.     

Effects of Weakly Nonlinear Water Waves on Soft Poroelastic Bed with Finite Thickness

Since porous material is usually of a finite thickness in nature, the effects of periodically nonlinear water waves propagating over a soft poroelastic bed with finite thickness are hence noticed and studied in this work. The water waves are simulated by potential theory while the porous bed is governed by Biot’s theory of poroelasticity herein. The conventional Stokes expansion of water waves based on a one-parameter perturbation expansion fails to solve the soft poroelastic bed problem; therefore, the boundary layer correction approach combined with a two-parameter perturbation expansion is proposed, which enables us to solve the problem of soft poroelastic bed with finite thickness. The results are compared to the similar problem with an infinite-thickness porous bed. The boundary effects of the impervious rock are significant on wave-induced pore water pressure and effective stresses, but are of very little significance on wave profiles at the free surface and the porous bed surface. However, the rigid boundary is insignificant to the pore water pressure and effective stresses when the thickness of porous bed is larger than about one wavelength.     

多孔介质模型在稀土电解槽优化模拟中的应用

针对熔盐电解法制取稀土金属钕槽型结构,首次提出了多孔介质模型与表面化学反应相结合的方法研究阳极电解反应过程,通过在靠近阳极表面取1~2mm的薄层设立为多孔介质层,并在多孔介质层上增设化学反应,模拟研究阳极表面的化学反应、槽体内部流场运动情况以及气泡上浮过程,同时对比欧拉法的模拟结果得到了该模拟法与欧拉法模拟的区别及该法研究的优势。模拟结果表明,该方法更能反映实际电解过程气泡生成和运动规律。     

Macroscopic Turbulence Models and Their Application in Turbulent Vegetated Flows

Turbulent flow in porous media, terrestrial and aquatic canopies, and urbanlike roughness is usually investigated using the macroscopic approach, which is based on the volume average theory (VAT). Two different methodologies have been developed in the past leading to different equations for both the mean and the turbulence quantities: time-averaging the volume-averaged equations and volume-averaging the time-averaged equations. In this study four models of the volume-averaging methodology are applied for modeling the flow in open channels with submerged vegetation. The vegetation is considered rigid, simulated as cylindrical roughness in a staggered or nonstaggered arrangement. Three of the models are of the k-ε type and one is of the Reynolds stress type. The latter has been applied using a modified ε equation to account for the extra dissipation attributable to vegetation. Numerical results for both mean and turbulence flow characteristics are compared against available experimental measurements for dense canopies under shallow and deep flow conditions. In addition, relevant characteristics (displacement thickness, canopy shear layer parameter, mixing length, penetration length scale, and etc.) are calculated for both computed and experimental data for assessing the performance of the models.     

Laboratory Measurements on Turbulent Pressure Fluctuations in and above Gravel Beds

The statistics of pressure fluctuations above and within three types of porous granular beds such as in gravel bed streams, rivers, and man-made canals are investigated by data gained via laboratory flume experiments. The flow conditions examined include a diversity of hydrodynamic loads that increase up to the point where single grains are moving from time to time, without causing severe modification to the bed texture and the related positions of the pressure sensors. Analysis is performed by means of histograms and spectral techniques and vertical intensity profiles. Two simplified equations are found that describe the vertical decrease for the standard deviation of the measured fluctuations indicating drag and lift, respectively, nondimensionalized by the mean bed shear stress. The former fluctuation is described by a crude linear fit, whereas the latter clearly shows that the lift intensity decreases exponentially in the porous bed with a decay distance of one to two times the equivalent grain roughness. Within the subsurface layer the standard deviation reaches a nonzero constant, mainly dominated by long-wave pressure fields that are convected in the outer flow. These findings can be used in future sediment transport models that use force balance approaches to determine incipient motion conditions.     

Method of Fundamental Solutions for Three-Dimensional Stokes Flow in Exterior Field

The main purpose of the present paper is to provide practical and numerical implementations of the method of fundamental solutions for three-dimensional exterior Stokes problems with quiet far-field condition and discuss the issues therein. The solutions of the steady Stokes problems are obtained by utilizing the boundary collocation method as well as the expansion of Stokeslets, which are the fundamental solutions of the steady Stokes equations. To validate the proposed model, numerical results of a lid-driven cavity flow, uniform flow passing a sphere, and a rotating dumbbell-shaped body show good agreement with the numerical and analytical solutions available in the literature. Also, a hypothetical problem with both vorticity and velocity boundary conditions is solved and compared with the analytical solution. The proposed model is then properly exploited to obtain the flow results of uniform flow passing a pair of vertical spheres in tandem and uniform flow passing a pair of horizontal spheres in tandem. Furthermore, the accuracy of the present numerical scheme is addressed and the detail flow characteristics, such as pressure distribution, streamline contour, velocity field, and vorticity fields are sketched.     

Response of Inhomogeneous Seabed around Buried Pipeline under Ocean Waves

Recently, considerable efforts have been devoted to the phenomenon of wave-seabed-pipeline interaction. However, conventional investigations for this problem have been concerned with a uniform seabed, despite the strong evidences of variable permeability and shear modulus. In this paper, a finite-element model is proposed to investigate the wave-induced pore pressure, effective stresses, and soil displacements in the vicinity of a buried pipeline in a porous seabed with variable permeability and shear modulus. The numerical results indicate that the inclusion of variable permeability and shear modulus significantly affects the wave-induced soil response around the pipeline. The influence of the variable permeability and shear modulus and geometry of the pipe on the wave-induced soil response around a buried pipeline are also detailed.     

Multilayer Averaged and Moment Equations for One-Dimensional Open-Channel Flows

A model is developed to account for the vertical distribution of velocity and nonhydrostatic pressure in one-dimensional open-channel flows. The model is based on both classical multilayer models and depth-averaged and moment equations. The establishment of its governing equations and the flow simulation are performed over a number of flow layers as in classical multilayer models. However, the model also allows for vertical distributions within a flow layer by including both Boussinesq terms and effective stress terms due to depth-averaging operations. These terms are evaluated on the basis of vertically linearly approximated profiles of velocity and pressure. The resulting additional coefficients can be solved by the moment equations for the relevant layers. Three verifications demonstrate satisfactory simulations for water surface profile, as well as vertical distributions for horizontal velocity, vertical velocity, and nonhydrostatic pressure. Sensitivity analysis shows that the model can be applied with fewer flow layers, more flexibility of layer division, and less computational cost than classical multilayer models, without a remarkable compromise in accuracy.     

Vertical Vibration of a Flexible Plate with Rigid Core on Saturated Ground

In this paper, the vertical vibration of a flexible plate with rigid core resting on a semi-infinite saturated soil is studied analytically. The behavior of the soil is assumed to follow Biot’s poroelastodynamic theory with compressible soil skeleton and pore water, and the response of the time-harmonic excited plate is governed by the classical thin-plate theory. By virtue of the Hankel transform technique, the fundamental solutions of the skeleton displacements, stresses, and pore pressure are derived, and a set of dual integral equations associated with the relaxed boundary and completely drained condition at the soil-foundation contact interface are also developed. These governing integral equations are further reduced to the standard Fredholm integral equations of the second kind and solved by numerical procedures. Comparison with existing solutions for a rigid permeable plate on saturated soil confirms the accuracy of the present solution. Selected numerical results are presented to show the influence of the permeability, the size of the rigid core, and the plate flexibility on the dynamic interaction between the elastic plate with rigid core and the underlying saturated soil.     

Leachate Recirculation Using Permeable Blankets in Engineered Landfills

Subsurface leachate recirculation or liquid injection methods for municipal solid waste (MSW) landfills are horizontal trenches, vertical wells, and permeable blankets. In this study, results of field-scale testing and numerical modeling of a recently developed subsurface leachate recirculation system called permeable blankets have been presented. In the field, at a MSW landfill located in Michigan, the travel of injected leachate in a 60-m-wide by 9-m-long by 0.15-m-deep blanket made up of crushed recycled glass was measured using an automated sensing system consisting of sensors embedded in the blanket. Leachate injection rates used in the field and simulated in this study ranged from 1.1 to 3.6?m3/h per meter length of the injection pipe embedded in the permeable blanket. HYDRUS-2D was used to simulate the travel and pressure head of injected leachate in permeable blankets. The influence of the following parameters on the hydraulic performance of permeable blankets was evaluated: (1) hydraulic properties of permeable blanket and waste; (2) geometry of permeable blanket; (3) settlement of permeable blanket; (4) leachate dosing frequency; and (5) initial degrees of saturation of permeable blanket and waste. The key findings of the study are: (1) the rate and maximum distance of travel of injected leachate are a strong function of the relative hydraulic properties of the permeable blanket and underlying waste and the rate and frequency of leachate injection; and (2) the maximum pressure head in the blanket due to liquid injection does not exceed the injection pressure. The field data and the numerical modeling results indicated that permeable blankets can be designed to inject liquids or recirculate leachate in MSW landfills. Long-term performance of such blankets needs to be evaluated.     

Influence of High-Permeability Layers for Enhancing Landfill Gas Capture and Reducing Fugitive Methane Emissions from Landfills

Gas collection systems of various designs have been used to control landfill gas emissions, which can be problematic, particularly before installation of final landfill covers. In this work, an innovative gas collection system that includes a permeable layer near the top surface of landfills was evaluated for enhancing capture of landfill gas and reducing fugitive methane emissions. A computational model that accounts for advective and diffusive fluxes of multiple gas components was used to evaluate the efficiency of this new design for intermediate landfill covers. The utility of the high-permeability gas-conductive layer was illustrated for several conditions of interest including varying refuse permeability, varying degrees of permeability anisotropy, and temporal atmospheric pressure changes. Simulations showed that the permeable layer decreased methane emissions by 43% when the horizontal to vertical permeability ratio for refuse was kh/kv = 3 and the domain average kh = 3×10?12?m2, while reductions in methane emissions decreased to 17% for the same anisotropy but with kh = 10?11?m2. With this design, barometric pressure changes did not significantly affect oxygen intrusion or methane emission rates.     

Turbulent Flow Over and Within a Porous Bed

The characteristics of turbulent flow in open channels with a porous bed are studied numerically and experimentally. The “microscopic” approach is followed, by which the Reynolds-averaged Navier-Stokes equations are solved numerically in conjunction with a low-Re k-ε turbulence model above and within the porous bed. The latter is represented by a bundle of cylindrical rods of certain diameter and spacing, resulting in permeability K ranging from 5.5490×10?7 to 4.1070×10?4?m2 and porosity ? from 0.4404 to 0.8286. Mean velocities and turbulent stresses are measured for ? = 0.8286 using hot-film anemometry. Emphasis is given to the effect of Darcy number Da on the flow properties over and within the porous region. Computed and experimental velocities in the free flow are shown to decrease with increasing Da due to the strong momentum exchange near the porous medium/free flow interface and the corresponding penetration of turbulence into the porous layer for highly permeable beds. Computed discharge indicates the significant reduction of the channel capacity, compared to the situation with an impermeable bed. On the contrary, laminar flow computations, along with analytical solutions and measurements, indicate opposite effects of the porous medium on the free flow.     

Analytical Solution of a Pressure Transmission Experiment on Shale Using Electrochemomechanical Theory

Analytical solutions are derived for a pressure transmission experiment of a saturated charged compressible porous medium. The governing equations describe infinitesimal deformations of charged porous media saturated with a monovalent ionic solution. From the governing equations a coupled diffusion equation is derived for the three electrochemical potentials, which is decoupled introducing a set of normal parameters. The magnitude of the eigenvalues of the diffusivity matrix corresponds to the time scales for Darcy flow, diffusion of ionic constituents, and diffusion of electrical potential. The radial strain is very sensitive to the ionization.     

Leachate Recirculation in Bioreactor Landfills Using Geocomposite Drainage Material

The key purpose of this study was to test the use of a permeable blanket made up of a geocomposite drainage layer (GDL) for leachate recirculation in municipal solid waste (MSW) landfills and to predict the observed leachate travel in the blanket using a numerical model. A 34?m long by 12?m wide permeable blanket made up of GDL was constructed at an active MSW landfill located in Michigan. Leachate was injected in the GDL using a perforated pipe placed centrally above the GDL along its length. Moisture content sensors, pressure transducers, thermistors, thermocouple sensors, and a vertical load sensor were embedded immediately below the GDL blanket to monitor the flow of injected leachate. After the blanket was covered with waste, leachate was injected into the blanket at rates ranging from 0.9 to 2.6?m3/h per meter length of the blanket. Data collected from the embedded sensors indicated that the injected leachate traveled at rates ranging from 5 to 18?m/h through the blanket depending upon the leachate injection rate. Only pressure transducers and thermistors were consistently able to detect migration of injected leachate once the blanket got saturated. Moisture content sensors could not register any change in readings once the blanket became saturated. Leachate injection pressure monitored over a period of about 12 months indicated no signs of clogging of the blanket. The leachate pressures measured immediately below the blanket were less than the net leachate injection pressure indicting that there was a head loss in the GDL blanket. Numerical modeling of liquid flow in the blanket indicated that predicted leachate travel in the blanket was consistent with the field data for assumed values of the waste hydraulic conductivity. In the absence of measured representative hydraulic properties of the waste, absolute verification of the field data was not possible.     

General Approach to Dynamic Analysis of Rotorcraft

This paper presents a general‐purpose mathematical formulation for the dynamic analysis of a rotorcraft consisting of flexible or rigid components, or both, that may undergo large rotations. In this formulation, two sets of coordinates are used, namely rigid‐body coordinates and elastic coordinates. The rigid‐body coordinates define the location and the orientation of a body frame with respect to an inertial frame. The rigid‐body rotational coordinates may be Euler angles, Euler‐like angles, or Euler parameters. The elastic coordinates define the elastic deformations with respect to the body frame. Nonlinear strain‐displacement relations are considered in order to be able to incorporate the effect of geometric stiffening. A systematic methodology that combines the traditional finite element and multibody approaches is developed to obtain a set of differential and algebraic equations governing the dynamics of the system. The resulting set of equations is highly nonlinear. Numerical schemes to solve this set of equations are also discussed. The formulation presented is general and allows the development of a modular code. The formulation also allows the code to be updated and grow without reformulation of the problem.     

Laminar and Turbulent Bottom Boundary Layer Induced by Nonlinear Water Waves

Results of a numerical study to investigate wave-induced boundary layer flows are reported. In this study, the writers consider a coupled viscous-inviscid approach, in which the fully nonlinear free surface boundary conditions are satisfied in the inviscid flow calculation, while the viscous flow near the seabed is solved via the Reynolds-averaged Navier-Stokes equations, instead of the thin boundary layer equation. To simulate the turbulent flow, a two-layer k-ε model is applied. Coupling of the viscous and inviscid computations is accomplished by the direct matching of the velocity and pressure distributions on the matching boundaries. Validation of the numerical model is carried out separately for the inviscid and viscous models, and the coupling approach as a whole. The numerical results are compared with theoretical solutions and available experimental data. A parametric study of the laminar and turbulent boundary layers for highly and weakly nonlinear waves is performed using the coupled viscous-inviscid approach. The results are compared with corresponding U-tube simulations, and the discrepancy is highlighted and discussed.     

Dynamic Numerical Analysis of Antimoisture-Damage Mechanism of Permeable Pavement Base

As a permeable base material of pavement, the large stone porous asphalt mixture (LSPM) is used widely in China to lessen the moisture damage of the asphalt pavement. However, the dynamics mechanism of the inhibitory effect of permeable base on moisture damage is not clear yet. The dynamic fluid-solid coupling analysis of the saturated pavement with LSPM base course, considering the asphalt mixtures as the porous medium, was performed using the finite difference numerical code FLAC3D. Numerical results revealed that the positive and negative dynamic pore pressure alternated in the pavement with the approaching and leaving of the wheel loads. The phenomenon of water pumping out of and sucking into the pavement under the moving loads was proved. The flow of fluid in pavement can be regarded as the laminar flow. The presence of the LSPM base course greatly decreased the dynamic pore pressure and the scouring force in the surface course because of the large permeability coefficient of the LSPM. The location of the maximum dynamic pore pressure also changed due to the LSPM base course. Due to the permeable base, the dissipation of the dynamic pore pressure was accelerated and thus the moisture damage was lessened.