Effective Porosity Measurement of a Marine Clay

Effective porosity commonly represents only the voids in soils or rock that contribute to the advective transport of groundwater. In the extreme case, all the pores or fractures are interconnected and contribute to the transport of groundwater. However, in most cases, some pores or fractures are dead-ended or isolated and, therefore, do not contribute to the advective movement of water through the soil or rock mass. The effective porosity is often estimated to be some fraction of the total porosity. The purpose of this study was to compare a glacial marine clay deposit’s effective and total porosities. The inner connection of the soil pores and the importance of the clay minerals on the pore spaces are at the root of the effective porosity testing described herein. Based on the results of three tracer tests on a low-plasticity, glacial marine clay, the effective porosity was found to be approximately equal to the total porosity within an error of less than 10%. Based on visual appearance of this uniform clay, the longitudinal dispersivity was assumed to be small compared to the tracer specimen length. However, it was found that larger test specimens would have made the tracer breakthrough curves less complicated.     

Permeable Pavement as a Hydraulic and Filtration Interface for Urban Drainage

Permeable pavement, specifically cementitious permeable pavement (CPP), is a passive structural low impact development material and green infrastructure system for rainfall-runoff control. Multifunctional engineered CPP can fulfill requirements as a load-transmitting surface while serving as a more environmentally conscious infrastructure material that functions to restore the in situ hydrology while also functioning as a passive treatment unit operation and process. As an infrastructure material; CPP reduces runoff, filters, and treats infiltrating runoff, reduces thermal pollution and temperature, provides the load-carrying capacity of conventional rigid concrete pavement, and leaches environmentally beneficial Ca and alkalinity, as compared to flexible asphalt. In this study, pore characteristics of CPP, including effective porosity (?e), pore size distribution and tortuosity (τ) are examined using x-ray tomography and gravimetric-geometric methods. Total porosity (?t) is measured and utilized as a comparative index. Results provide insight when modeling CPP as an infiltration and evaporation interface, a conveyance/storage medium for liquid and gas, and with admixtures or coatings an adsorptive-filtration medium for pollutants such as phosphorus and metals. Results indicate that high particle separation and significant hydraulic conductivities can be achieved with CPP. The effectiveness of CPP for particle removal also requires that these particle deposits are managed on a periodic basis through practices such as pavement cleaning.     

Dual Porosity and Secondary Consolidation

In this paper, the results of a series of experiments using one-dimensional oedometer testing, mercury intrusion porosimetry (MIP), and scanning electron microscopy are reported on kaolinite samples with known and controlled fabric associations to reexamine the dual-porosity hypothesis for the underlying mechanisms of secondary consolidation. The oedometer testing results indicate that the pH 7.8 sample (face-to-face aggregated structure) has the smallest values of compression index, Cc, and secondary compression index, Cα. The pH 4 sample (flocculated but dispersed structure) has the largest values, while the pH 7.8 with salt sample (flocculated and aggregated structure) has medium values. The Cα/Cc ratios for these three samples are similar regardless of the structure and consolidation pressure. The MIP results on pore-size evolution in the pH 7.8 with salt sample show that both primary and secondary consolidation processes preferentially occur in the larger and weaker interaggregated pores instead of in the smaller and stronger intraaggregate pores. These oedometer testing and MIP results do not support the dual-porosity hypothesis, whereas they suggest that the primary and secondary consolidation processes involve the same physical factors.     

High-Order Compact Difference Scheme for Convection–Diffusion Problems on Nonuniform Grids

In this study, a high-order compact (HOC) scheme for solving the convection–diffusion equation (CDE) under a nonuniform grid setting is developed. To eliminate the difficulty in dealing with convection terms through traditional numerical methods, an upwind function is provided to turn the steady CDE into its equivalent diffusion equation (DE). After obtaining the HOC scheme for this DE through an extension of the optimal difference method to a nonuniform grid, the corresponding HOC scheme for the steady CDE is derived through converse transformation. The proposed scheme is of the upwind feature related to the convection–diffusion phenomena, where the convective–diffusion flux in the upstream has larger contributions than that in the downstream. Such a feature can help eliminate nonphysical oscillations that may often occur when dealing with convection terms through traditional numerical methods. Two examples have been presented to test performance of the proposed scheme. Under the same grid settings, the proposed scheme can produce more accurate results than the upwind-difference, central-difference, and perturbational schemes. The proposed scheme is suitable for solving both convection- and the diffusion-dominated flow problems. In addition, it can be extended for solving unsteady CDE. It is also revealed that efforts in optimizing the grid configuration and allocation can help improve solution accuracy and efficiency. Consequently, with the proposed method, solutions under nonuniform grid settings would be more accurate than those under uniform manipulations, given the same number of grid points.     

Determination of Source Strength of Landfill Gas: A Numerical Modeling Approach

An accurate estimation of source strength of gas in a landfill is necessary to design gas extraction systems. A one-dimensional mathematical model to estimate source strength of landfill gas is presented. The model is based on fundamental principles of gas transport through porous media, and incorporates methane oxidation in landfill cover soils. The nonlinear mathematical equation for gas migration through layered soil was linearized and solved using the partially implicit Crank Nicolson technique. Apart from source strength, concentration and pressure as functions of depth and gas emissions into the atmosphere were computed. Laboratory experiments were conducted to generate data for model calibration and verification for mono- and two-layered systems. Other model parameters were estimated using information from published literature. The model data were in agreement with laboratory test results obtained for both systems.     

Application of an Intraparticle Diffusion Model to Describe the Release of Polyaromatic Hydrocarbons from Field Soils

The fate and transport of chemicals of concern released from field soils must be known to protect human and ecological receptors. A mechanistic approach to modeling chemical release from soil is advantageous to implement effective remediation strategies at an impacted site. The focus of this research was to gain an understanding of the processes causing slow release of polyaromatic hydrocarbons (PAHs) from field soils collected at sites with historical releases. A mechanistically based intraparticle diffusion model was applied to experimentally measured hydrocarbon release data and particle size distributions obtained from three field soils. For these field soils, the intraparticle diffusion model was able to describe the measured chemical release data. Fitted effective diffusion coefficients (Deff) of the intraparticle diffusion model correlated to expected results. Trends were found to exist between the Deff and both the molecular weight (MW) and the octanol–water partition coefficient (Kow) of the PAH analyzed for the field soils with low organic carbon content. For these soils, the relationships suggest that intraparticle diffusion processes may be responsible for slow desorption and it may be possible to estimate Deff values for a soil or contaminated media with similar intraparticle properties using a readily measured chemical characteristic such as MW and Kow.     

Diagnosis of the Transition from Rock to Soil in a Granodiorite

This paper describes an attempt to develop a method to define when granodiorite loses its properties as a rock and transforms into soil material. The research program approached the problem from a mechanistic point of view by comparing the pore water pressures generated during isotropic compression with the apparent—and micro—porosities, in terms of a newly proposed pore size distribution index as well as the compressive strengths of the specimens tested. A site was selected for study where weathering of the rock is not accompanied by the production of clay minerals, thus eliminating the complications introduced by the presence of highly compressive zones in the matrix. Samples tested using various criteria indicated that changes in the pore-size distribution can realistically reflect the transformation sought. It appears that further studies should be directed towards determination of the changes in the pore geometry, whereby a scientific definition of the transformation from rock to soil can be made.     

Digital Image Analysis to Determine Pore Opening Size Distribution of Nonwoven Geotextiles

The filtration performance of a geotextile is controlled by its pore opening size distribution (PSD). Current methods for determining PSD are mostly indirect and contain inherent disadvantages. Recent technological advancements in image analysis offer great potential for a more accurate and direct way of determining the PSD of nonwoven geotextiles. A new and accurate method of image analysis for PSD determination of nonwoven geotextiles is presented in this paper. The image analysis method was developed using various mathematical morphology algorithms to provide a complete PSD curve for each geotextile. The two characteristic pore opening sizes, O95 and O50, were determined from image analysis and were compared to the results from laboratory tests, analytical equations, as well as manufacturer’s reported apparent opening sizes (AOS). The image-based O95 pore opening size of various geotextiles was comparable to the manufacturer’s reported AOS as well as to those determined from the laboratory dry sieving test. However, the measured O50 pore opening size was lower than the one determined using the analytical equations developed by two previous researchers. Overall, the image analysis method presented provides a unique and accurate method that can measure fiber thickness and pore opening sizes in a cross-sectional image of a woven geotextile.     

Reducing Numerical Diffusion Effects with Pycnocline Filter

Numerical or artificial diffusion is the unintentional smoothing of gradients associated with the discretization of the transport equations. In lakes and reservoirs where through-flow is small, the effects of numerical diffusion of mass are cumulative, leading to a progressive weakening of vertical density stratification. This density field misrepresentation precludes accurate, long-term, three-dimensional (3D), hydrodynamic simulations on fixed grids in closed basins with an active thermocline. An ad hoc technique to limit the destratifying effects of numerical diffusion of mass is presented and tested for a 3D, hydrostatic, Z-coordinate numerical model. The technique quantifies the domain-integrated numerical diffusion by assessing the change in the background potential energy Eb. At each time step, the change in Eb associated with numerical diffusion is calculated, then removed using a sharpening filter applied to each water column. In idealized test cases, the filtering technique is effective in maintaining density stratification over one year while undergoing periodic, large-amplitude forcing by internal waves. Forty-day simulations of Lake Kinneret compared to field measurements demonstrate improved representation of density stratification using the filtering technique.     

Model for Consolidation-Induced Solute Transport with Nonlinear and Nonequilibrium Sorption

A numerical model, called CST2, is presented for coupled large strain consolidation and solute transport in saturated porous media. The consolidation and solute transport algorithms include the capabilities of a previous model, CST1, with the addition of a variable effective diffusion coefficient during consolidation and nonlinear nonequilibrium sorption. The model is based on a dual-Lagrangian framework that tracks separately the motions of fluid and solid phases. Verification checks of CST2 show excellent agreement with analytical and numerical solutions for solute transport in rigid porous media. A parametric study illustrates that, for the test cases considered, variation of effective diffusion coefficient during consolidation has an important effect on solute transport, whereas nonlinearity of the sorption isotherm has a less important effect. Additional simulations show that nonequilibrium sorption can have a strong effect on consolidation-induced solute transport and that this effect becomes more important as the rate of consolidation increases. The simulations also corroborate previous findings that consolidation can have a lasting effect on solute migration because transient advective flows change the distribution of solute mass which then becomes the initial condition for subsequent transport processes.     

Equivalent Stress Equation for Unsaturated Soils. II: Solid-Porous Model

Based on the study of the equilibrium of the particles of a soil showing a bimodal structure and subject to certain suction, it was possible to establish an analytical expression for the value of Bishop’s parameter χ (see the companion paper). This parameter can be written as a function of the saturated fraction and the degree of saturation of the unsaturated fraction of the soil. However, the determination of these last two parameters cannot be made from current experimental procedures. Therefore, a solid-porous model simulating the structure of the soil is proposed herein and used to determine these parameters. The data required for the solid-porous model are obtained from the grain and pore size distributions, void ratios, and secondary soil–water retention curves of the soil. The plots of the deviator stress versus equivalent stress shows a unique failure line for a series of tests performed at different confining net stresses and suctions, confirming that the proposed equivalent stress equation is adequate to predict the shear strength of unsaturated soils. It also results in different strengths for wetting and drying, as the experimental evidence suggests.     

Equivalent Stress Equation for Unsaturated Soils. I: Equivalent Stress

In 1959 Bishop stated his effective stress equation for unsaturated soils. However, the difficulties in estimating the value of its main parameter χ, made this equation useless and it was abandoned for some time. Only recently, it has been recognized that the use of Bishop’s stress equation can lead to simpler and more realistic constitutive models for unsaturated soils. However, up to now the most successful equations to quantify the value of parameter χ are empirical and not satisfactory for most soils. Based on the analysis of the equilibrium of the solid particles of a soil showing a bimodal structure and subject to certain suction, it was possible to establish an analytical expression for Bishop’s parameter χ. The resulting stress has been called equivalent stress (in contrast with effective stress) and can be used to predict the shear strength of unsaturated soils. The equivalent stress is written as a function of the net stress and suction and requires two parameters: the saturated fraction and the degree of saturation of the unsaturated fraction of the soil. This equivalent stress clarifies some features of the strength of unsaturated soils that up to now had no apparent explanation. However, the determination of its two parameters cannot be made from current experimental procedures. A method for the determination of these parameters and a comparison between experimental and theoretical results for the shear strength of unsaturated soils are presented in a companion paper.     

In Situ Partial Exfiltration of Rainfall Runoff. II: Particle Separation

Metal elements or other constituents transported in urban and transportation land use rainfall runoff are often adsorbed on or incorporated with entrained particles that are ubiquitous in such runoff. Infiltration–exfiltration can be an effective in situ particle separation and quantity control structural best management practices or low impact development practices allowing runoff to return to soil after passive physical-chemical treatment. The in situ partial exfiltration reactor (PER), which combined the surface straining of the cementitious porous pavement (CPP) layer with filtration of oxide coated sand media beneath, provided control of water quantity and quality. Particle analyses were carried out for both influent and effluent to examine filter efficiency as a function of particle size and hydrology. Influent dm/dp ratios suggest that the dominant PER particle separation mechanisms were unsaturated physical–chemical filtration with the CPP layer functioning as a straining surface. Particle size distributions were modeled based on a two-parameter cumulative power-law function. The performance of the PER as a filter is shown to be a function of the unsteady site hydrology. Temporal variation in the filter coefficient and the volumetric particle fraction remaining were directly related to the unsteady influent loading rate. Particle removal efficiency by the PER based on concentration ranged from 71 to 96% on a mass-based concentration and 92–99% on a number based concentration. Results suggest that a properly designed PER can provide effective in situ control for particles and could be combined with or function separately from source control (i.e., pavement cleaning or a mass trading framework).     

Hyporheic Exchange with Gravel Beds: Basic Hydrodynamic Interactions and Bedform-Induced Advective Flows

Stream-subsurface exchange processes are important because of their role in controlling the transport of contaminants and ecologically relevant substances in streams. Laboratory flume experiments were conducted to examine solute exchange with gravel streambeds. Two morphologies were studied: flat beds and beds covered by dune-shaped bedforms. High rates of exchange were observed with flat beds under a wide range of stream flow conditions, indicating that there was considerable turbulent coupling of stream and pore water flows. The presence of bedforms produced additional exchange under all flow conditions. The exchange with bedforms could be represented well by considering solute flux caused by bedform-induced advective pumping. Pumping exchange was enhanced by inertial effects, including non-Darcy flow and turbulent diffusion. For the flat bed case, dye injections showed that exchange also occurred by a combination of advective pore water flow and turbulent diffusion near the stream–subsurface interface. The relative effects of advective and diffusive transport processes could not be separated due to the complex nature of the induced flows in the gravel bed. However, exchange was found to scale with the square of the stream Reynolds number in all cases. Comparison of these results with those obtained with coarser and finer sediments demonstrated that the exchange rate is also proportional to the square of the characteristic bed sediment size. These scaling relationships can be used to improve interpretation of solute transport observed in natural rivers.     

Plane-Strain Propagation of a Fluid-Driven Crack in a Permeable Rock with Fracture Toughness

A solution to the problem of a plane-strain fluid-driven crack propagation in elastic permeable rock with resistance to fracture is presented. The fracture is driven by injection of an incompressible Newtonian fluid at a constant rate. The solution, restricted to the case of zero lag between the fluid front and the fracture tip, evolves from the early-time regime when the fluid flow takes place mostly inside the crack toward the large-time response when most of the injected fluid is leaking from the crack into the surrounding rock. This transition further depends on a time-invariant partitioning between the energy expanded to overcome the rock fracture toughness and the energy dissipated in the viscous fluid flow in the fracture. A numerical approach is used to compute the solution for the normalized crack length and crack opening and net-fluid pressure profiles as a function of two dimensionless parameters: the leak-off/storage evolution parameter and the toughness/viscosity number. Relation of this solution to the various available asymptotic solutions is discussed. Obtained mapping of the solution onto the problem parametric space has a potential to simplify the tasks of design, modeling, and data inversion for hydraulic fracturing treatments and laboratory experiments.     

Is P-Wave Velocity an Indicator of Saturation in Sand with Viscous Pore Fluid?

It is commonly assumed that within inundated sand the Skempton B value and P-wave velocity decrease with decrease in saturation. In centrifuge tests a common saturation procedure is to inundate the specimen with carbon dioxide while under a vacuum and then slowly introduce the viscous pore fluid. The B value and related saturation is difficult to measure in centrifuge models and P-wave velocity—saturation correlations have been used for this purpose. A laboratory emulation of centrifuge saturation procedures was made using a triaxial cell with top and bottom bender elements and a viscous methyl cellulose–water pore fluid. Contrary to expectations, the laboratory tests showed high P-wave velocities indicative of full saturation when B values were low. Numerical modeling of the laboratory tests indicated that if air bubbles within the pore fluid are numerous and closely spaced then there is a good correlation between saturation, B value, and P-wave velocity. However if the air bubbles are larger and only present in some of the pores then the P-wave velocity is not a good indicator of B value and average saturation. The laboratory tests also showed that placing the specimen under backpressure for several days increased saturation and related B values. It is suggested that this common laboratory procedure should be considered for saturating centrifuge test specimens.     

Ceramic Filter for Small System Drinking Water Treatment: Evaluation of Membrane Pore Size and Importance of Integrity Monitoring

Ceramic filtration has recently been identified as a promising technology for drinking water treatment in households and small communities. This paper summarizes the results of a pilot-scale study conducted at the U.S. Environmental Protection Agency’s (EPA) Test & Evaluation (T&E) Facility in Cincinnati on two ceramic filtration cartridges with pore sizes of 0.05 and 0.01?μm to evaluate their ability to remove turbidity and microbiological contaminants such as bacteria [Bacillus subtilis ( ≈ 1.0?μm) and Escherichia coli ( ≈ 1.4?μm)], Cryptosporidium oocysts (4–6?μm), polystyrene latex (PSL) beads (2.85?μm) (a surrogate for Cryptosporidium), and MS2 bacteriophage ( ≈ 0.02?μm) (a surrogate for enteric viruses). The results demonstrated that the relatively tighter 0.01-μm cartridge performed better than the 0.05-μm cartridge in removing all the biological contaminants and surrogates. For turbidity removal, the 0.01-μm cartridge performed slightly better than the 0.05-μm cartridge; however, the permeate rate in the 0.01-μm cartridge reduced rapidly at higher feed water turbidity levels indicating that a tighter membrane should only be used with adequate pretreatment or at a low feed water turbidity to prolong membrane life. Microbiological monitoring was identified as a more sensitive indirect integrity monitoring method than turbidity and particle count monitoring to ensure effective treatment of water by ceramic filtration. Both PSL beads and B. subtilis showed potential as effective surrogates for Cryptosporidium, with B. subtilis showing higher degree of conservatism. Any opinions expressed in this article are those of the writer(s) and do not necessarily reflect the official positions and policies of the EPA. Any mention of products or trade names does not constitute recommendation for use by EPA. This document has been reviewed in accordance with EPA’s peer and administrative review policies and approved for publication.     

Immiscible Displacement Model for Anisotropic and Correlated Porous Media

Immiscible flow governs the macroscopic behavior of aqueous and non-aqueous phase liquids inside the porous media. Ganglia generation and movement of the advancing front during fluid displacement can only be described by means of microscopic models. In this study, a pore network cellular automata is used to simulate the displacement of a nonaqueous phase liquid by water inside a porous media. Pore sizes are generated using random and stochastic fields. The numerical model captures the evolution of interfaces and fluid movement for each pressure applied to the displacing fluid. Observed trends suggest that ganglia size and shape, and fingering are directly related to anisotropy, pore size spatial variability and correlation length. The results show that micro- and mesoscale porous media properties control the nonaqueous phase residual saturation and observed macoscopic behavior.