Unsaturated Media Research Articles

Axisymmetric consolidation behavior of multilayered unsaturated soils with transversely isotropic permeability

Time-dependent consolidation behavior of unsaturated soils is a vital problem in the geotechnical engineering. With the aid of the Fredlund consolidation theory, this work further assumes the total stress of soils skeleton freely change, and extends the Fredlund consolidation theory to a Biot-type theory, establishing the fully-coupled equation model of multilayered unsaturated poroelastic media with transversely isotropic permeability. To convert the partial differential governing equation into ordinary differential equations, the integration transform technology is applied. Subsequently, the precise integration method is used to acquire the time-dependent consolidation solution of multilayered unsaturated media with transversely isotropic permeability in the transformed domain, which is further solved in the actual domain by the inverse Hankel transform. A verification examples is provided to compare the present results with the existing work in the literature, showing a great coincidence and proving the feasibility of the present solution. Finally, numerous numerical examples are presented to investigate the evolution of excess pore pressure and settlement under quasi-static loads, revealing the consolidation behavior of unsaturated soils. The results demonstrates that the ramping time, stratification, permeability, depth and m1w have a significant effect on the consolidation behavior.

Evaluation of a practical approach for field scale moisture flow modeling in heterogeneous media at a semiarid site

AbstractA practical approach for modeling field‐scale moisture flow in a highly heterogeneous unsaturated medium is described in this study. The validity of this approach is demonstrated through comparison of the numerical simulations with field observations at a semiarid site located in southcentral Washington State. The methodology is based on upscaling the core scale hydraulic properties and combining power‐law and tensorial connectivity‐tortuosity (PA‐TCT) approaches to derive macroscopic anisotropy parameters for each hydrostratigraphic unit (HSU) identified in the field. Each heterogeneous HSU is approximated by an equivalent homogeneous medium (EHM) model for which PA‐TCT parameters are used in the flow simulations. The available field data on moisture content and matric potential are compared with steady‐state flow simulations based on the mean form of Richards' equation. While the homogenization or averaging of heterogeneities, embedded in the EHM modeling approximation, cannot capture all of the field‐scale variability, the simulated steady‐state moisture and matric potential profiles capture well the central tendency of the field data. This approach is deemed practical for assessing the fate and transport of contaminants in highly heterogeneous unsaturated media at the transport scale of hundreds of meters.

Delivery of imiquimod to intestinal lymph nodes following oral administration.

Intestinal lymph nodes are involved in the progression of colorectal cancer (CRC). Tumours suppress the activation of dendritic cells (DCs) in draining lymph nodes, diminishing anti-cancer immune response. Imiquimod (IMQ) facilitates DCs activation via toll-like receptor 7, suggesting that targeted delivery of IMQ to intestinal lymph nodes can improve the treatment of CRC. This study aims to enhance the delivery of IMQ to intestinal lymph nodes by a highly lipophilic prodrug approach. Amide prodrugs were synthesised by conjugating IMQ with saturated and unsaturated medium- to long-chain fatty acids. Their potential for intestinal lymphatic transport was assessed by their affinity to chylomicrons and solubility in long-chain triglycerides. Further selection of prodrug candidates was determined by resistance to enzymatic hydrolysis in intestinal lumen and release of IMQ in the lymphatics using fasting state simulated intestinal fluid supplemented with esterases, brush border enzyme vesicles and plasma. Key pharmacokinetic parameters and biodistribution in rats were assessed for the most promising compounds, prodrugs 5 and 8. The plasma concentration-time profile of IMQ following oral administration of the prodrugs was less erratic in comparison to the administration of unmodified IMQ. The lymph-to-plasma ratios of IMQ concentration increased 1.9- and 1.7-fold using prodrugs 5 and 8 in comparison to administration of unmodified IMQ, respectively. Importantly, the average concentration of IMQ in mesenteric lymph nodes (MLN) was 11.2- and 7.6-fold higher than in plasma following the administration of prodrugs 5 and 8, respectively. Additionally, the non-specific wide distribution of IMQ into various organs and tissues was reduced with prodrugs. This work suggests that the highly lipophilic prodrug approach can efficiently deliver IMQ to intestinal lymphatics. In addition, this study demonstrates the feasibility of an amide prodrug approach for intestinal lymphatic targeting.

Two Nitsche-based mixed finite element discretizations for the seepage problem in Richards’ equation

This paper proposes two algorithms to impose seepage boundary conditions in the context of Richards’ equation for groundwater flows in unsaturated media. Seepage conditions are non-linear boundary conditions, that can be formulated as a set of unilateral constraints on both the pressure head and the water flux at the ground surface, together with a complementarity condition: these conditions in practice require switching between Neumann and Dirichlet boundary conditions on unknown portions on the boundary. Upon realizing the similarities of these conditions with unilateral contact problems in mechanics, we take inspiration from that literature to propose two approaches: the first method relies on a strongly consistent penalization term, whereas the second one is obtained by an hybridization approach, in which the value of the pressure on the surface is treated as a separate set of unknowns. The flow problem is discretized in mixed form with div-conforming elements so that the water mass is preserved. Numerical experiments show the validity of the proposed strategy in handling the seepage boundary conditions on geometries with increasing complexity.

Diffraction of P1, SV, or Rayleigh waves by an arbitrary-shaped canyon in an unsaturated half-plane

The diffraction of P1, SV, or Rayleigh waves by an arbitrary-shaped canyon in an unsaturated half-plane is investigated in this paper. The scattered wave potentials with unknown coefficients are solved by Fredlund’s theory and the Helmholtz’s decomposition. The general expressions of displacements, stresses, pore pressures, and seepage are obtained using complex variable method. The half-surface and the canyon surface are mapped onto semi-circles in the image plane with Möbius transformation and Schwarz–Christoffel mapping. The boundary-valued problems yield an infinite series of linear algebraic equations with unknown coefficients. The truncating numbers are selected to assure the convergence and accuracy of the solution. A parametric study is performed to investigate the site responses of the canyons by incident P1 waves in an unsaturated half-plane. Numerical results show that the aspect ratio, saturation degree, circular frequency, and angle of incident wave significantly affect the site response of the canyon. The effects of saturation degree on the ground motions are significant owing to the complex tri-interaction of the three phases in the unsaturated medium. The dynamic concentrations occur at the corner region of the canyon. The shielding effect of the canyon to obliquely incident P1 waves is obvious.

Influence of Tension-Driven Flow on the Transport of AFFF in Unsaturated Media

Influence of Tension-Driven Flow on the Transport of AFFF in Unsaturated Media

Dynamic response of cylindrical deep buried tunnels in unsaturated soil under axisymmetric explosion loading

This study established a calculation model for a cylindrical tunnel subjected to internal explosion loading in an unsaturated medium, assuming that the transient load exponentially decays along the tunnel direction. The governing equations for the lining tunnel and the surrounding unsaturated soil under explosion load were derived based on continuum mechanics and the theory of porous media mixtures. Laplace inverse transformation and Fourier inverse transformation were employed to derive the dynamic response of the lining and soil in the time-space domain. Furthermore, the effects of unsaturated medium saturation on the explosion response of the lining and the surrounding region were investigated. The results demonstrate that the analytical solution can be used to explain the dynamic response of an underground tunnel surrounded by unsaturated soil, during an internal explosion. The solutions can be extended to further advancements considering different boundary conditions.

Impact of Pressure Waves on Water Imbibition and Flow in Unsaturated Porous Media

AbstractThe wetting front dynamics during water imbibition in dry porous media affect the ultimate water distribution pattern. In this study, we investigate the impact of pressure pulses that emit waves in the water phase on the water distribution and imbibition patterns in porous media. We present experimental results of water spatial distribution in sand columns following infiltration under abrupt pressured‐water pulses and compare them with those of continuous inflow. Applying pressure waves during infiltration increases pressure gradients behind the wetting front, which can overcome capillary and gravitational forces, leading to uniform imbibition. To simulate the process, we developed a pore‐network model incorporating an analytical solution of pressure wave attenuation to predict the imbibition pattern. Our results demonstrate that the amplitude of the pressure wave is associated with a sharp wetting front, resulting in higher water content compared to Darcy‐type continuous flow. The findings suggest that pressure waves have the potential to achieve high water content in unsaturated media and provide insights into the spatial extent of their impact on water distribution.

Dynamic response of a shallow lined circular tunnel by incident P1 and SV waves in an unsaturated half-plane

The dynamic response of a shallow lined circular tunnel in the unsaturated half-plane during earthquakes is investigated in this paper using the complex function method. The wave fields of the unsaturated medium with unknown coefficients are solved by Fredlund’s theory and Helmholtz’s decomposition based on the momentum and mass balance equations. General expressions for the displacements and total stresses of the solid skeleton, pore pressures, and seepage are derived using the complex function method and conformal mapping technique. The half-plane surface and the tunnel in the physical domain are mapped onto two bonded ring regions in the image plane using two conformal mapping functions. The boundary value problem yields a series of algebraic equations by the boundary conditions and the continuity conditions along the liner-medium interface. The unknown coefficients in the infinite series of algebraic equations can be solved numerically by truncating the series number. A parametric study is performed to investigate the dynamic responses of the medium and the liner by the incident P1 waves. Numerical results reveal that the embedded depth of the tunnel, the saturation degree of the medium, the liner-medium rigidity ratio, the frequency and angle of the incident P1 waves significantly affect the dynamic responses of the medium and the liner. The shielding effect on the tunnel to the incident P1 waves is obvious. The response of the liner-medium system to the incident waves is independent of the saturation degree of the unsaturated medium when its value is high. The effect of the liner-medium rigidity ratio is great on the dynamic stress concentrations of the liner-medium system and weak on the displacements along the half surface. The frequency of the incident excitation has a great influence on the displacements of the half surface.

Stability of shallow sub-surface cavities under surface loading using granular media through model testing

Buried cavities are one of the commonly occurring Ground related issues. Every year, thousands of cave-in episodes are documented as a result of the collapse of underground cavities, damaging infrastructure and frequently resulting in fatalities. Cavities at shallow depths are critical and can seriously harm the surface infrastructure, which in most cases are the highways and the roads with traffic loadings. The fault or cracks in subsurface structures, such as box girders, pipelines, etc., primarily contribute to the cavity initiation at shallow depths. The cavities remain stable until the soil arching and the capillary forces in the unsaturated media can collectively resist the pressure of overburden soil. The stability of the shallow cavity is of concern when it lies beneath the heavy traffic loads of the highways. In this study, a particular model test equipment was prepared, having a soil chamber, water level indicator, and a base with a slit opening to induce a cavity in the soil. Model tests were performed using granular media of spherical and non-spherical (clumped and deformed) glass particles under unsaturated conditions to form a stable shallow cavity. The resultant cavity was tested with surface loading using surface plates and having variable loading rates. It was found that particle shape has a significant effect when surface loading is applied to the stable cavity. Clumped particles showed approx. Ten times higher peak resistance to surface loading compared to the spherical particles, both having equivalent mean particle size. The loading rate was found to be effective for the cases with unsaturated conditions; however, for dry samples, the loading rate was found to have insignificant effects on surface loading.

Complex function method for the scattering of harmonic plane waves by an arbitrary-shaped cavity in an unsaturated medium

General formulations of the complex function method for the scattering of harmonic waves by an arbitrary-shaped cavity in the unsaturated medium are constructed. In light of the momentum and the mass balance equations, the wave fields of the unsaturated medium with unknown coefficients are solved by Fredlund’s theory and Helmholtz’s decomposition. Complex-valued expressions for the displacements and the total stresses of the solid skeleton, the pore pressures, and the seepages of the unsaturated medium are obtained by the conformal transformation technique to map the arbitrary cavity onto a unit circle in the complex plane. The boundary value problem results in a series of infinite algebraic equations with unknown coefficients by considering the stress, displacement, and permeable conditions along the cavity. A parametric study for the scattering of the incident P1 waves around a rectangular cavity in an unsaturated medium is performed to investigate the dynamic stress concentrations, displacements, and pore pressures. Numerical results show that the saturation degree of the unsaturated medium has a considerable influence on the dynamic response of the cavity by the incident P1 waves. With the increase of the saturation degree, the dynamic stress concentration around the rectangular cavity decreases, and the equivalent pore pressure increases. For obliquely incident P1 waves, the shielding effect of the rectangular cavity is obvious.

Model of water transfer in concrete and rock based on a single state variable to consider simultaneous positive pressure and drying boundary conditions

During their service life, concrete structures may be subjected to positive pressure and drying boundary conditions simultaneously. This phenomenon is likely to occur in civil engineering structures, such as tunnels for nuclear waste storage, dams, and piles, where the simultaneous phenomena of drying and saturation must be considered because of their strong effects on the short- and long-term behavior of the structure. The water transport model proposed in this paper predicts the mass transfer and water field in the material. It provides a continuous description of saturated and unsaturated media using liquid pressure as the only state variable and also considers the effects of temperature variations. A formulation for water transfer with a single state variable is presented, followed by an illustration of its numerical implementation and a procedure for the calibration of parameters. The model is compared with experimental and numerical results to validate its efficiency. For this purpose, several applications dealing with drying and saturation phenomena are used. The results obtained show the potential of the proposed water transfer model to evaluate the water transport in the material under study at different temperatures by simulating a mock-up of nuclear power plant wall. It is finally used to predict the re-saturation of an underground nuclear waste disposal structure.

Research on Displacement Diffusion Model of Time-Varying Slurry with Rheological Parameters in Unsaturated Media

Research on Displacement Diffusion Model of Time-Varying Slurry with Rheological Parameters in Unsaturated Media

In situ monitoring of internal water storage reveals nitrogen first flush phenomena, intermittent denitrification, and seasonal ammonium flushing

Internal water storage (IWS) can be included in bioretention practices to increase storage capacity or promote denitrification—the microbial reduction of nitrate to nitrogen gas. IWS and nitrate dynamics are well studied in laboratory systems. However, the investigation of field environments, consideration of multiple nitrogen species, and determination between mixing versus denitrification is lacking. This study employs in situ monitoring (∼24 h duration) of water level, dissolved oxygen (DO), conductivity, nitrogen species, and dual isotopes of a field bioretention IWS system for nine storms events over a year period. Rapid peaks in IWS conductivity, DO, and total nitrogen (TN) concentrations occurred along the rising limb of the IWS water level and indicated a first flush effect. TN concentrations generally peaked during the first ∼0.33 h of sampling and the average peak IWS TN concentration (Cmax = 4.82 ± 2.46 mg-N/L) was 38% and 64% greater than the average TN along the IWS rising and falling limb, respectively. Dissolved organic nitrogen (DON) and nitrate plus nitrite (NOx) were the dominant nitrogen species of IWS samples. However, average IWS peak ammonium (NH4+) concentrations August through November (0.28 ± 0.47 mg-N/L) demonstrated statistically significant shifts compared to February through May (2.72 ± 0.95 mg-N/L). Average lysimeter conductivity measurements were more than ten times higher February through May. The sustained presence of sodium observed in lysimeters, from road salt application, contributed to NH4+ flushing from the unsaturated media layer. Dual isotope analysis showed denitrification occurred for discrete time intervals along the tail of the NOx concentration profile and the hydrologic falling limb. Longer antecedent dry periods (17 days) did not correlate to enhanced denitrification but did correspond to more leaching of soil organic nitrogen. Results from field monitoring highlight the complexities of nitrogen management in bioretention systems. First flush behavior into the IWS suggests management to prevent TN export is most critical during the onset of a storm.

Hydromechanical behavior of unsaturated swelling clays: review

Expansive soils are materials composed mainly of active minerals of the smectite family, where montmorillonite is an essential member of that group. These types of soils tend to undergo volumetric changes due to variations in moisture content. Many geotechnical engineering practices, such as dam core design or subgrade compaction, require a thorough evaluation of the response of these soils to determine placement conditions. However, the main problem in evaluating the mechanical response of this type of soil lies in the nonlinear nature, which limits the use of most classical constitutive models that apply the basic rules of elastoplasticity. In this study, an analysis is carried out to understand the hydromechanical behavior of expansive soils in saturated and unsaturated conditions. Direct and indirect physical evidence is presented and discussed to evaluate the hydraulic response of the soil structural elements responsible for these adverse dynamics from a global (expansive phenomena as a whole) and individual (swelling and shrinkage) perspective. Since the response of these soils is hydrostatic dependent, the locus of water movement in porous media is examined, starting from the Richards equation (1931), in order to consider the flow mechanisms in unsaturated media under transient conditions.

Isolation Effect of P-Wave By Double-Layer Wave Impeding Barrier in Unsaturated Foundations

Wave impeding block (WIB) barriers are often used to reduce vibration from different sources, but traditional vibration isolation of WIB has been limited to homogeneous materials and single-phase elastic or two-phase saturated foundations by many researchers. In fact, soils in nature are usually tri-phase unsaturated materials, and the propagation characteristics of elastic waves in unsaturated medium are completely different from those in single-phase elastic medium or two-phase saturated porous medium. In addition, the conventional WIB barrier has better vibration isolation only at low frequencies. Therefore, this paper improves the vibration isolation of the WIB by double-layer WIB with the same thickness on the basis of traditional WIB. Based on the wave theory of unsaturated porous media and elastic media, and according to the Helmholtz principle, we can obtain the solution of surface vertical displacement after setting double-layer WIB in unsaturated foundation, and then the isolation effect of double-layer WIB in unsaturated foundation under [Formula: see text]-wave incidence is investigated. The wave impedance ratio at the interface between WIB and unsaturated soil and wave impedance ratio at the interfaces among the layers of WIB is first analyzed on the vibration isolation effect of double-layer WIB, and the wave impedance ratio corresponding to the optimal vibration isolation effect of WIB barrier is achieved. Then the key factors such as incidence angle, incidence frequency, saturation, thickness, and burial depth of the double-layer WIB are evaluated on its vibration isolation properties. Finally, the isolation effects of single-layer homogeneous WIB and double-layer non-homogeneous WIB with the same thickness are compared. For the same thickness isolation barrier, the vibration isolation efficiency of double-layer WIB is 42.73% higher than single-layer at the incidence angle of [Formula: see text]–[Formula: see text]. The double-layer WIB has better isolation effect at low, medium and high frequencies than single-layer WIB.

Daisy-shaped liquid bridges in foam-filled granular packings

HypothesisMany applications of liquid foams use them to fill the porosity of various granular media. How is the liquid distributed in such foam-filled systems, in which the geometry of the bubble assembly can be strongly constrained by pore confinement? ExperimentsWe study how the liquid is distributed in a grain packing filled with liquid foam, as a function of both liquid content and bubble-to-grain size ratio. Moreover, Surface Evolver simulations are carried out at the scale of a single bubble confined into a tetrahedral pore. FindingsWe reveal that foam-filled granular assemblies exhibit a robust pendular-like regime, which is reminiscent of the pendular regime in unsaturated media. The main difference is that here the liquid bridges are daisy-shaped, i.e. with a liquid core bounded by bubbly petals. A simple theoretical model is proposed to describe the foam liquid bridges between contacting grains. In the case of large bubbles, the model is compared with the Surface Evolver simulation. The model is also applied to the case of wall liquid bridge, which is compared with the experimental observation. Beyond their geometrical characteristics, the presence of these liquid bridges, which can represent almost 25% of the liquid contained in the porosity, makes it possible to imagine a new approach (binder foam-based) to bind granular assemblies and turn them to solid materials.

An Iterative Approach for Numerical Solution to the Time-fractional Richards Equation with Implicit Neumann Boundary Conditions

In this paper, we develop an iterative method of lines scheme for the numerical solution to the time fractional Richards equation with implicit Neumann boundary conditions, which is an effective tool for describing a process of flow through unsaturated media. A numerical example is provided to show the effectiveness of the presented method for different model parameters and inputs. The method illustrated here can be applied to other types Richards equation with various input functions and Dirichlet boundary conditions.

Numerical analysis of wave propagation and vibration attenuation effects of periodic scattering piles in unsaturated poroviscoelastic ground

ABSTRACT The elastic wave propagation and vibration attenuation zones for periodically scattering piles in unsaturated ground were investigated using Finite-Element Method (FEM) and Bloch periodic theory. The unsaturated ground was modelled by unsaturated poroviscoelastic medium with the weak form governing equations derived from the mass and momentum conservative equations using Galerkin method and Fourier transform. The quadratic polynomial eigenvalue equations for the unsaturated medium were obtained using the Bloch periodic theory, and solved by FEM for the complex eigenvalues to evaluate the band gaps of the pile-soil system. The eigenvalue bands combined with the frequency response function were used to analyse the mitigation effects of piles in unsaturated ground with different soil properties and piles parameters. This research found that the pile-soil system has three propagational waves, in which the shear wave and the slow longitudinal wave carry low-frequency vibrations that undermine the attenuation effects of the piles barrier. The increasing soil saturation degree affects the attenuation effects by reducing the soil modulus and increasing the fluid content. And both of those two mechanisms reduce the frequency of the attenuation zones (AZ), which improves the low-frequency vibration attenuation, and reduces the width of AZ that could reduce the vibration mitigation effects.

Effects of solution chemistry and humic acid on transport and deposition of aged microplastics in unsaturated porous media

Microplastics (MPs) are susceptible to aging in the environment, and aged MPs are highly migratory in soil due to their smaller particle size and more negative surface charge, but the effects of soil environmental factors on the fate and transport of aged MPs are still unclear. In this study, the transport behavior of pristine/aged MPs in unsaturated sandy porous media was examined under different ionic strength (IS), cationic type (Na+, Ca2+) and humic acid (HA) conditions. The results indicated that the surface charge, surface oxygen-containing functional groups and surface morphology of MPs changed significantly after aging, and that the mobility of aged MPs was significantly enhanced than the pristine MPs under all test conditions. The retention amounts of pristine/aged MPs in unsaturated porous media increased with IS, and IS had a less inhibitory effect on the transport of aged MPs than pristine MPs. The mobility of pristine/aged MPs in Ca2+ solutions was significantly weaker than that in Na+ solutions due to enhanced straining and electrostatic adsorption. HA promoted the mobility of pristine/aged MPs in unsaturated porous media under all IS Na+ (1, 10, and 25 mM) solutions and lower IS (1 mM) Ca2+ solutions, and the ability of HA to promote the transport of aged MPs was significantly stronger than that of pristine MPs due to the higher adsorption of HA on the surface of aged MPs. However, at higher IS (10 mM) Ca2+ solution conditions, the bridging effect of Ca2+ led to the formation of HA-MPs complexes, which altered the hydrophobicity of the pristine/aged MPs surface and the pristine/aged MPs were mainly retained on the air-water interface (AWI). CFT theory and two-site kinetic retention models indicated that the retention of pristine/aged MPs in unsaturated media was dominated by monolayer adsorption, straining and clogging effects. The current research findings may provide insights into the fate and transport of aged MPs in soil and their potential risk of groundwater contamination.