Consolidation-Induced Solute Transport Research Articles

Two-Dimensional Model for Consolidation-Induced Solute Transport in an Unsaturated Porous Medium

Solute transport through porous media is usually described by well-established conventional transport models with the ability to account for advection, dispersion, and sorption. In this study, we further extend our previous one-dimensional model for solute transport in an unsaturated porous medium to two dimensions. The present model is based on a small-strain approach. The proposed model is validated with previous work. Both homogeneous landfill and pointed landfill conditions are considered. A detailed parametric study shows the differences between the present model and previous one-dimensional model.

Numerical modeling of contaminant advection impact on hydrodynamic diffusion in a deformable medium

The self-weight of solid waste or machine-rolled compaction can induce or trigger contaminant migration in the landfill. Although the consolidation-induced hydraulic gradient driving solution transport has been extensively investigated, little attention has been paid to ion migration caused by its concentration gradient variation. It is necessary to more precisely predict the multi-stage contaminant transports in deforming porous material. Based on the modified Cam-clay model, the proposed fluid-solid coupled model can simulate the elastoplastic deformation behavior of layered kaolinite and KBr solution transport/sorption, and its modeling results were validated by published laboratory data. The solid-fluid interactions were analyzed by comparing various transport manners of K + and Br − from excess pore pressure generation to dissipation. Results reveal that the consolidation process can accelerate KBr solute advection from the contaminated layer into the uncontaminated layer, and then affects the subsequent diffusion, mechanical dispersion and sorption for K + and Br − . The simulations also indicate that consolidation-induced solute transport is time-dependent, and therefore the ion diffusion and mechanical dispersion should receive more attention.

Fully transient analytical solution for solute transport in 1D deforming saturated porous media considering nonlinear compressibility and permeability

In this study, a series of analytical solutions for coupled consolidation and solute transport in 1D saturated deformable porous media considering nonlinear compressibility and permeability relationships is presented. The proposed analytical solutions consider the combined effects of consolidation, diffusion, advection, dispersion, sorption and degradation. The proposed analytical solutions are successfully validated against the experimental results of consolidation-induced solute transport tests and verified against the CST3 numerical model. The results in model verification indicate that the proposed analytical solution shows good efficiency and accuracy and the assumptions taken in deriving the analytical solution of consolidation governing equation have a limited impact on the accuracy of the proposed analytical solution. Using the verified analytical solution, a series of simulations is conducted to investigate the effects of consolidation and solute transport mechanisms (i.e., advection, dispersion, sorption and degradation) on trichloroethylene (TCE) transport through the compacted clay liner (CCL) system. The results indicate that, regardless of which solute transport mechanism is considered, the consolidation of CCL can substantially affect the TCE transport through the CCL liner system. The advection induced by the leachate head and the sorption of CCL increase the effect of consolidation on TCE transport through the CCL liner system, whereas the dispersion of TCE decreases this effect. Moreover, degradation (both the degradation of dissolved and sorbed TCE masses) can barely affect the effect of consolidation on TCE transport.

Numerical Modelling of consolidation-induced solute transport in unsaturated soil with dynamic hydraulic conductivity and degree of saturation

The effects of the pore pressure related dynamic hydraulic conductivity and dynamic degree of saturation on the consolidation-induced solute transport in deformable unsaturated soils are investigated. The storage equation and solute transport equations are revised to account for the dependence of these two soil parameters on pore pressures. Three dynamic models were conducted for dynamic hydraulic conductivity, dynamic degree of saturation, and both. Compared with the conventional model, the simulation results showed that both hydraulic conductivity and degree of saturation increased near the soil surface where pore pressure exceeded air-entry value. Dynamic hydraulic conductivity results in a slightly slower solute transport while dynamic degree of saturation accelerates the migration of contaminants. Including both dynamic effects produced limited differences in solute concentration, while consolidation results were affected significantly. Although dynamic degree of saturation has some influences on consolidation-induced solute transport, the correlation of the dynamic path is less significant. The air-entry value is an important parameter to determine when soil parameters become dynamic, and it affects the soil consolidation process in certain extent. This study provides new methods to incorporate in-homogeneous soil parameters, which are not only spatiotemporal variables, but also dynamic variations with pore pressure.

Benchmark Problem for Large Strain Consolidation-Induced Solute Transport

AbstractConsolidation-induced solute transport is an important process for a variety of engineering applications involving contaminated soil and other compressible porous media. This note presents ...

Consolidation-Induced Solute Transport for Constant Rate of Strain. II: Comparison with Incremental Loading

AbstractThis paper presents a numerical investigation of one-dimensional large strain consolidation-induced solute transport for incremental loading (IL) and constant rate of strain (CRS) conditions. Solute transport accounts for advection, diffusion, dispersion, linear and nonlinear sorption, and equilibrium and nonequilibrium sorption, and is consistent with temporal and spatial variations of porosity and seepage velocity in the consolidating soil. Simulations were conducted using material properties for kaolinite clay and indicate that IL and CRS conditions produce significantly different responses during the course of consolidation, including applied stress, rate of settlement, excess pore pressure, and local strain. However, for a given set of initial and boundary conditions, final solute mass outflows and final solute concentration profiles for IL and CRS conditions were generally in close agreement, provided that total elapsed time and final average strain were matched for both loading procedures. ...

Consolidation-Induced Solute Transport for Constant Rate of Strain. I: Model Development and Simulation Results

AbstractA numerical model, called CSTCRS1, is presented for coupled one-dimensional consolidation and solute transport under constant rate of strain (CRS) loading conditions. The consolidation algorithm accounts for vertical strain, general constitutive relationships, relative fluid velocity, changing compressibility and hydraulic conductivity during consolidation, and an external hydraulic gradient. The solute transport algorithm accounts for advection, dispersion, linear and nonlinear sorption, and equilibrium and nonequilibrium sorption. Soil compressibility is rate-independent and as such CSTCRS1 is more appropriate for less-structured soils. The model is based on a dual-Lagrangian framework that separately tracks the motions of sold and fluid phases. The development of CSTCRS1 is first described, and is followed by verification checks. Numeric examples are then presented to illustrate the effects of initial contamination distribution, transport conditions, applied strain rate, initial specimen height...

Discussion of “Investigation of Consolidation-Induced Solute Transport. I: Effect of Consolidation on Transport Parameters” by J. Lee, P. J. Fox, and J. J. Lenhart

Discussion of “Investigation of Consolidation-Induced Solute Transport. I: Effect of Consolidation on Transport Parameters” by J. Lee, P. J. Fox, and J. J. Lenhart

Closure to “Investigation of Consolidation-Induced Solute Transport. I: Effect of Consolidation on Transport Parameters” by J. Lee, P. J. Fox, and J. J. Lenhart

Closure to “Investigation of Consolidation-Induced Solute Transport. I: Effect of Consolidation on Transport Parameters” by J. Lee, P. J. Fox, and J. J. Lenhart

Investigation of Consolidation-Induced Solute Transport. II: Experimental and Numerical Results

This paper presents an experimental and numerical investigation of consolidation-induced solute transport. Diffusion and large strain consolidation tests were performed on composite specimens of kaolinite clay consisting of an upper uncontaminated layer and a lower layer contaminated with potassium bromide. Experimental measurements of effluent concentration, solute mass outflow, and final concentration profiles were obtained for a variety of initial, boundary, and loading conditions, including unload/reload. Numerical simulations were conducted using a computational model in which solute transport occurs by advection, dispersion, and sorption and is consistent with temporal and spatial variations of porosity and seepage velocity in the consolidating layer. Large strains were taken into account as well as variation of effective diffusion coefficient with porosity and nonlinear nonequilibrium sorption effects. The numerical simulations are in good to excellent agreement with the experimental measurements. Results indicate that, depending on conditions, diffusion and consolidation-induced advection can make important contributions to solute transport and mass outflow. Thus, both mechanisms should be considered for transport analyses involving soft contaminated clays undergoing large volume change. Results also indicate that nonequilibrium sorption effects were not significant for the materials and test conditions used in this study.

Investigation of Consolidation-Induced Solute Transport. I: Effect of Consolidation on Transport Parameters

This paper presents an experimental investigation of the effect of clay consolidation on parameters that govern the advective-dispersive transport of an inorganic solute. Batch, diffusion, dispersion, and solute transport tests were conducted using kaolinite clay and dilute solutions of potassium bromide (KBr). Batch tests produced the highest levels of K+ sorption and indicated that equilibrium sorption was achieved in approximately 10–30 min. The increase in sorption observed in the batch tests, as compared to the dispersion or solute transport tests, reflects the significantly lower solids-to-solution ratio and more efficient mixing process. By comparison, kaolinite consolidation had little effect on sorption due to the relatively small change in porosity. Values of hydrodynamic dispersion coefficient ( Dh ) , effective diffusion coefficient ( D∗ ) , and apparent tortuosity factor decreased with decreasing porosity. Values of D∗ obtained for Br− were generally larger than for K+ , whereas Dh values for...

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.

Coupled Large Strain Consolidation and Solute Transport. I: Model Development

The development of a numerical model, CST1, for coupled large strain consolidation and solute transport in saturated porous media is presented. The consolidation algorithm is one-dimensional and includes the capabilities of a previous code, CS2, with the addition of time-dependent loading, unload/reload effects, and an externally-applied hydraulic gradient. The solute transport algorithm is two-dimensional and accounts for advection, longitudinal and transverse dispersion, first-order decay reactions, and linear equilibrium sorption. Solute transport is consistent with temporal and spatial variations of porosity and seepage velocity in the consolidating layer. The key to the transport model is the definition of two Lagrangian fields of elements that follow the motions of fluid and solid phases separately. This reduces numerical dispersion and simplifies transport calculations to that of dispersion mass flow between contiguous fluid elements. The effect of relative numerical resolution of fluid and solid elements on the accuracy of sorption/desorption is also discussed. This paper presents the theoretical and numerical development of the CST1 model. A companion paper presents verification checks of CST1 and the results of simulations that illustrate the significance of consolidation-induced solute transport for some interesting numeric examples.

Coupled Large Strain Consolidation and Solute Transport. II: Model Verification and Simulation Results

The results of numerical simulations for coupled large strain consolidation and solute transport, obtained using the CST1 model, are presented. CST1 accounts for advection, longitudinal and transverse dispersion, first-order decay reactions, and linear equilibrium sorption. Verification checks of CST1 show excellent agreement with analytical solutions for one-dimensional (1D) transport in rigid porous media, including various Peclet numbers and concentration boundary conditions. Similarly excellent agreement is observed for two-dimensional advection-dispersion transport in rigid media and 1D advection-dispersion transport in compressible media undergoing large strain consolidation. CST1 is then used to investigate consolidation-induced solute transport for a single composite liner system and a confined disposal facility for dredged contaminated sediments. In both cases, solute transport was found to be strongly affected by consolidation-induced advection both during and after the consolidation period. Consolidation has 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.