Analytical Solution for Conservative Solute Transport in One-Dimensional Homogeneous Porous Formations with Time-Dependent Velocity

The space-time variation in contaminant concentration in unsteady flow in a homogeneous finite aquifer subjected to point source contamination is analytically derived under two conditions: (1) the flow velocity in the aquifer is of sinusoidal form; and (2) the flow velocity is an exponentially decreasing function. The analytical solution is illustrated using an example. Analytical solutions are perhaps most useful for benchmarking numerical codes and solutions.     

Analytical Solution for Two-Dimensional Solute Transport in Finite Aquifer with Time-Dependent Source Concentration

Using the Hankel Transform Technique, an analytical solution is derived for two-dimensional solute transport in a homogeneous isotropic aquifer. The aquifer is subjected to time-dependent point source contamination. The solution is derived under two conditions: (1) the flow velocity in the aquifer is a sinusoidally varying function and (2) the flow velocity is an exponentially decreasing function. Initially the aquifer is assumed solute free. The analytical solution is illustrated using an example.     

Parametric Study of One-Dimensional Solute Transport in Deformable Porous Media

Formulation for the effect of dissipation of excess pore water pressure on one-dimensional advective-diffusive transport of solutes in clays is presented. The formulation is based on the effect of the rate of consolidation or swelling and excess pore pressure or suction dissipation on transient, nonlinear advective component of transport through clay. One partial differential equation is presented for advective diffusive transport that is dependent upon soil/solute properties and transient hydraulic head gradient, which is calculated from the Terzaghi consolidation equation. Finite difference method is used to solve the system of partial differential equations for consolidation and solute transport. Four hypothetical cases are evaluated to demonstrate the effect of consolidation under loading and swelling under hydraulic gradient on advective-diffusive transport and breakthrough in single and double drainage clay layer. The results show that consolidation in doubly drained clay impacts concentration profiles, but does not significantly impact breakthrough of the diffusive flux. Consolidation under single drainage conditions, significantly impacts the diffusional flux. When drainage path is the same as the diffusional flux, consolidation accelerates transport and breakthrough time can be less than 5% of the diffusional breakthrough time under no consolidation. Swelling under hydraulic gradient application can either accelerate or retard the advective diffusive flux, depending upon the ratio of the effective diffusion coefficient relative to the coefficient of consolidation. Higher the effective diffusion coefficient and lower the coefficient of consolidation result in an increase in the effect of pressure dissipation on transport.     

Groundwater Modeling for the Analysis of Active Slow-Moving Landslides

Active slow-moving landslides in clayey soils exhibit continuous movements generally controlled both in the accelerating and decelerating phases by the pore-water pressure regime that, in turn, is strictly correlated to the net rainfall regime. The paper stresses the importance of a reliable groundwater model to predict these types of movements. To this aim a procedure is proposed to define the transient groundwater regime in the slope on the basis of recorded rainfall and monitoring data; the model is then used to derive the time-dependent shear strength along the main slip surfaces. The displacements at selected points along the slip surface are computed using a phenomenological (i.e., empirical) relationship between the local factor of safety and the displacement rate at those points. The procedure is employed for the analysis of a well-documented case history: the Porta Cassia landslide (central Italy).     

Analytical Solutions of Linear Finite-Strain One-Dimensional Consolidation

Numerical solutions of linear finite-strain one-dimensional consolidation of both initially unconsolidated and initially fully consolidated soil layers with both one-way and two-way drainage have been available for some time. However, no solutions of the limiting cases for initially unconsolidated soil have been available. Nor, except for the limiting cases corresponding to small-strain consolidation of initially fully consolidated layers, has the accuracy of these solutions and the solution charts based on them been evaluated. Analytical counterparts of the earlier numerical solutions and solution charts, analytical solutions of the limiting cases for initially unconsolidated soil, and analytical solutions of the small-strain Terzaghi equation expressed in material coordinates are presented in this paper. The analytical solutions clarify aspects of the numerical solutions, improve marginally the accuracy of the solution charts, and enable the latter to be easily replicated and extended. They may also be applied to the validation of numerical solutions of nonlinear finite-strain consolidation.     

Comparing Three Models for Treatment of Stagnant Zones in Riverine Transport

The modified advection dispersion equation (MADE) model is compared to the transient storage model (TSM) and fractional advection dispersion equation (FRADE) model for modeling riverine transport. The comparisons are illustrated using field examples. The parameter F of the FRADE model is found to be inconsistent to its physical meaning and is unrelated to dead zone fraction. Also, the estimated parameters of TSM are found to be inconsistent to their physical meaning. On the contrary, the parameters of MADE are consistent and related to the dead zone fraction. It is observed that the MADE model is easy to use and yields reliable and consistent results.     

Efficient Solution of the Coupled One-Dimensional Surface—Two-Dimensional Subsurface Flow during Furrow Irrigation Advance

Physically based modeling of the coupled one-dimensional surface and two-dimensional (2D) subsurface flow during furrow irrigation advance often causes numerical instabilities and nonconvergence problems. This is particularly the case for low irrigation advance rates when infiltration consumes a predominant part of the inflow volume. The proposed furrow advance phase model (FAPS) further develops the concepts of a previous study. An analytical zero-inertia surface flow model is iteratively coupled with the 2D subsurface water transport model HYDRUS-2. In contrast to the previous study, the flow domain is discretized using fixed space increments and the resulting set of nonlinear flow equations is solved using the Newton method. The complexity of the model was reduced by process adequate simplifications. FAPS exhibited better convergence, numerical stability, and less computational time than the original fixed time interval solution. The new solution converged rapidly for a number of model tests with various inflow rates including runs with very slow irrigation advance. Simulation model predictions agree very well with advance times measured in laboratory and field tests.     

Analytical Solutions for Constant-Flux and Constant-Head Tests at a Finite-Diameter Well in a Wedge-Shaped Aquifer

Neglecting the effect of well radius may lead to a significant error in the predicted drawdown distribution near the pumping well area. New analytical solutions describing aquifer responses to a constant pumping or a constant head maintained at a finite-diameter well in a wedge-shaped aquifer are derived based on the image-well method and applicable to an arbitrarily located well in the system. The solutions are useful for quantifying groundwater exploitation from a wedge-shaped aquifer and for determining the hydrogeological parameters of a wedge-shaped aquifer in inverse problems.     

Analytical Solutions for Unsteady Transport Dispersion of Nonconservative Pollutant with Time-Dependent Periodic Waste Discharge Concentration

Analytical solutions have been obtained by the Fourier transform method for the case of unsteady transport dispersion of nonconservative pollutant/biochemical oxygen demand with first-order decay under each of the sine and cosine variation of waste discharge concentration at upstream boundary and nonzero initial condition throughout the river. The solutions give correct results along the whole length of the river for all times in contrast to those available in the literature which yield sensible results under quasisteady-state assumption and for large times only. Appropriate expressions for memory length and memory time have been derived so as to include the effect of decay rate of the pollutant in terms of the Thomann number.     

Generalized Analytical Solutions for Groundwater Head in Inclined Aquifers in the Presence of Subsurface Drains

Analytical solutions for groundwater head in the presence of subsurface drains are important in assessing the effectiveness of an existing drainage system under a probable extreme variation in the rate of recharge and designing a new drainage system. Generalized analytical solutions for groundwater head in inclined aquifers in the presence of parallel subsurface drains are obtained considering the transient rate of recharge as a power series (polynomial) function and depth-dependent rate of evapotranspiration. An appropriate function, new to analytical drainage studies, is used for correctly representing the depth-dependent rate of evapotranspiration. The solutions are obtained considering the practical situation of drains placed at shallow depth in a considerable depth of aquifer. Two conditions of large and small saturated thicknesses in comparison to the increase in groundwater head are considered. A mathematical criterion is proposed to distinguish between large and small saturated thicknesses. The analytical equations for discharge to drains for different cases considered are also obtained. The discharge equations used by prior investigators are found inappropriate.     

Diameter and Surcharge Effects on Solute Transport across Surcharged Manholes

New data are presented describing the retention time and longitudinal dispersion of a solute tracer across circular surcharged manhole structures of different diameters. The variations with both discharge and surcharge level are described and the relationships quantified. The variation of the longitudinal dispersion coefficient exhibits poorly defined trends, however using an aggregated dead zone technique both the reach time delay and travel time show clear variations. A surcharge threshold level for these parameters is evident at the larger manhole diameters and this is explained in relation to jet theory. The variation of the surcharge mean time delay and postthreshold mean travel time are quantified, while the prethreshold travel times are shown to be dependent on both discharge and surcharge. The relationships allow for inclusion in sewer water quality modeling and provide a method for improving predictive techniques.     

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.     

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.     

Analytical Method for Predicting the Mobility of Slow-Moving Landslides owing to Groundwater Fluctuations

This paper deals with the active landslides that are controlled by pore water pressure changes owing to groundwater fluctuations. These landslides are usually characterized by low displacement rate with deformations essentially concentrated within a narrow shear zone, above which the unstable soil mass moves as a rigid body. Taking advantage of some original analytical solutions, a method is developed for a preliminary prediction of the landslide mobility. This method is based on a simple sliding-block model and allows the landslide velocity to be readily evaluated once pore water pressure measurements are available. An application to a case study documented in the literature is also shown.     

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.     

Approach Using Active Groundwater Storage for Hydrologic Model Calibration in West-Central Florida

Hydrologic model calibration is always a challenging and tedious process especially for the calibration of complex models, which includes continuous hydrograph models, requires sophisticated calibration methods. The Hydrologic Simulation Program-FORTRAN (HSPF) is one of the popular and powerful time variable hydrologic models. However, in order to improve the assessment of hydrologic activities in shallow ground water settings, the model needs to be reliably calibrated for ground water contribution. Little guidance is provided in the literature concerning the manner of this contribution. In fact, the most common calibration of HSPF uses subjective parameter fitting and focuses on the attainment of statistical goodness of fit of runoff fluxes and water levels, ignoring ground water components. The goal of this research is using a different approach to calibrate HSPF with observed water table records. In this study, HSPF is applied on a small area in west-central Florida and calibrated by comparing active ground water storage to well elevation records in range land and forested land covers. The Nash-Sutcliffe efficiency and correlation coefficient computed using observed and simulated daily flows are 0.91 and 0.96 at Peace River, respectively, also with good fair results for other stations in the model domain. The study shows that improved calibration of the model can be achieved if active ground water storage and well records are compared for timing and magnitude of fluctuations.     

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.     

Modeling Fate and Transport of Roadside-Applied Herbicides

A physically based, one-dimensional, mathematical model is developed to simulate transport of herbicides applied to roadsides into adjacent surface water. Herbicide transport by overland flow, infiltrating water, and subsurface flow is considered. The model accounts for advection, dispersion, equilibrium linear sorption in the soil, and first-order decay of the herbicides. Chemical transport between soil and overland flow is described using a rate-limited mass exchange between the two compartments that is proportional to the difference between the chemical concentration in overland flow and the pore water with a proportionality constant that is a function of overland flow characteristics and rain intensity. For simulating overland and subsurface flow, the kinematic wave equation is solved using a Crank–Nicolson finite difference scheme. Richards’ equation is solved using a Galerkin finite element method to model infiltration, and the transport equation is solved using a finite difference method. The model is calibrated and verified using extensive field data on the runoff of five herbicides with a range of physical–chemical properties at two field sites. Good agreement is obtained between predicted and measured event-mean concentrations in runoff and the herbicide concentration remaining in the application-zone soil.     

Rapid Graphical Detection of Weakness Problems in Numerical Simulation Infiltration Models Using a Linearized Form Equation

Recently, Valiantzas proposed a new two-parameter vertical infiltration equation that can be transformed to a linearized-form equation that essentially states that the shape of the cumulative infiltration data, when presented in the form of (i2/t) versus i, is linear. In this paper, the presentation of the numerical data to the Valiantzas linearized-form equation is proposed as an additional criterion to detect easily and rapidly possible errors of the numerical solutions and eventually to choose the best spatial discretization for a simulated infiltration event that is used as setup parameter to the numerical infiltration models. Numerical data and analytical solutions were used to validate the proposed method.