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.     

Distribution of Discharge Intensity along Small-Diameter Collector Well Laterals in a Model Riverbed Filtration

Experiments were performed to evaluate flow and head variations along perforated screens (10–30?mm in diameter) using sand tanks which were connected and a perforated screen extended through these tanks to form a model collector well lateral up to 2.6?m in length. Hydraulic heads and discharge along the lateral and production rates of the model collector well were measured as the water level in the well, the lateral length, and diameter, and the hydraulic conductivity of the filter sand were varied. A mathematical model was developed to predict the axial flow velocity distribution and the discharge intensity variation along the lateral using the head distribution. Results showed that the production rate increased as the lateral length and diameter and the drawdown at the well increased. However, the production rate increase was not linearly related to these factors. When larger-diameter laterals were used, the axial flow velocity in the laterals decreased. This caused the hydraulic heads along the lateral to become more flattened, resulting in a lateral of high efficiency in terms of water production. This condition is similar to the assumption of the uniform discharge intensity along the lateral that many researchers have used in the analysis of the horizontal wells. Under the conditions of this study, a critical axial flow velocity was determined to be 1?m/s. Hydraulic efficiency decreased drastically when the velocity exceeded 1?m/s. The roughness coefficient (the Manning’s n value) of the lateral varied as a function of factors such as axial velocity and discharge intensity, and it ranged from 0.010 to 0.015.     

Transient Flow into a Partially Penetrating Well during the Constant-Head Test in Unconfined Aquifers

This study derives a semianalytical solution for drawdown distribution during a constant-head test at a partially penetrating well in an unconfined aquifer. The constant-head condition is used to describe the boundary along the screen. In addition, a free-surface condition is used to delineate the upper boundary of the unconfined aquifer. The Laplace-domain solution is then derived using separation of variables and Laplace transform. This solution can be used to identify the aquifer parameters from the data of the constant-head test when integrated with an optimization scheme or to investigate the effects of vertical flow caused by the partially penetrating well and free-surface boundary in an unconfined aquifer.     

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.     

Unsteady Solution for Well Recharge in a Low Diffusive Aquifer

Finite aquifer solution exists for the constant head in a fully penetrating well. Their use for well recharge is limited, as they do not permit simultaneous computation of unsteady wellhead pressure and variable recharge rate. In the present paper semianalytical solutions are presented for well recharge under variable head boundary condition. These solutions were developed using the method of separation of variables and Duhamel’s convolution theorem. The solution developed in the paper was verified with the Jacob-Lohman solution and subsequently validated using field data pertinent to constant-head boundary conditions. Subsequently for variable head boundary condition such an appropriate background was found missing in the literature.     

Approximation of Well Function and Identification of Leaky Aquifer Parameters

The existing equation for leaky aquifers is transformed into a nondimensional form using new parameters and a scaled well function for leaky aquifers is proposed. A computationally simple function is developed for accurately approximating the scaled well function for the practical range of the parameters. Utilizing this function (approximation), an optimization method is proposed for identifying the leaky-aquifer parameters from observed drawdowns. The new function has an enhanced utility when a repetitive numerical evaluation of the well function for leaky aquifers is needed, e.g., while estimating the aquifer parameters using optimization or Kalman filter or artificial neural network methods. The application of the proposed method is illustrated using a few sets of published data. The proposed method outperforms the extended Kalman filter method, based on the reported results in the literature.     

Kernel Method for Transient Rate and Volume of Well Discharge under Constant Drawdown

A kernel method is proposed for calculating transient rate and cumulative volume of well discharge under constant drawdown. The new method can also be used for obtaining the drawdown (in pressure head) in the aquifer at some distance away from the well. Employing the new method, an optimization method is used to estimate the aquifer parameters from transient well discharge or drawdown in the aquifer pressure head. The proposed method can also be used to model the recovery of drawdown (in aquifer pressure head) after the plug-in of the well.     

Flow Depletion Induced by Pumping Well from Stream Perpendicularly Intersecting Impermeable/Recharge Boundary

Analytical solutions for rate and volume of flow depletion induced by pumping a well from a stream that intersects an impermeable or a recharge boundary at right angles are derived using the basic flow depletion factor defined earlier by the author. A new concept of directly obtaining stream flow depletion using the method of images is proposed. The solutions are derived for five different management cases of a stream and boundary intersecting at right-angles, assuming the aquifer to be confined with semi-infinite areal extent. A computationally simple function is proposed for accurately approximating the error function. The existing analytical solution in the case of a right-angle bend of stream given by Hantush was obtained for unconfined aquifers using a linearization of the governing partial differential equation. The solution for this case obtained using the proposed method for confined aquifer is the same as obtained by Hantush for unconfined aquifers, which shows that the linearization adopted by Hantush does not actually solve this problem for unconfined aquifers.     

Drawdown due to Pumping a Partially Penetrating Large-Diameter Well Using MODFLOW

The approach by the author for modeling the large-diameter wells using MODFLOW is extended to the partially penetrating large-diameter wells. The temporal variation of drawdown due to a steady pumping is presented in the form of diagnostic curves for different penetration. These diagnostic curves can also be used to estimate the aquifer parameters from the observed drawdowns in a partially penetrating large-diameter well.     

Analytical Solution for Tidal Propagation in a Leaky Aquifer Extending Finite Distance under the Sea

This paper focuses on groundwater dynamics in response to the tidal fluctuation in a coastal aquifer system. An analytical solution is derived to describe groundwater level fluctuation in a leaky aquifer extending finite distance under the sea. Based on this solution, the joint effects of various parameters, such as the dynamic effect of water table fluctuation and the leakages of the inland and offshore, on the behavior of the groundwater level fluctuations in the inland part of the leaky confined aquifer can be thoroughly analyzed. When the roof length is increased, the dynamic effect of the water table fluctuation on the dimensionless groundwater amplitude, intrusion distance, and fixed phase shift in the unconfined aquifer become more important and the water table fluctuation approaches constant values when the roof length is greater than a threshold value. However, given the same values of dimensionless leakage and roof length, the dimensionless groundwater amplitude, intrusion distance, and fixed phase shift in the leaky aquifer with considering the dynamic effects are always larger than those of neglecting such effects.     

Water Table Fluctuation in the Presence of a Time-Varying Exponential Recharge and Depth-Dependent ET in a Two-Dimensional Aquifer System with an Inclined Base

An analytical solution is presented for water table fluctuation between ditch drains in presence of exponential recharge and depth-dependent evapotranspiration (ET) from groundwater table in a two-dimensional gently sloping aquifer. The groundwater head above the drain is small compared to the saturated thickness of the aquifer. A sound mathematical transformation is devised to transform the two-dimensional groundwater flow equation into a simple form, which makes possible to obtain an analytical solution. The transient midpoint water table variations from the proposed solution compare well with the already existing solutions for horizontal aquifer. A numerical example is used to illustrate the combined effect of depth-dependent ET coupled with a time-varying exponential recharge on the water table fluctuation. The inclusion of a depth-dependent ET in the solution results in water table decline at a faster rate as compared to the case when ET is not considered. With an increase in slope of the aquifer base, water table profiles become asymmetric and the water table divide shifts towards the lower drain. The height of the water table profiles increases on moving away from the boundary of the aquifer and the highest level of the ground water table is obtained in the central portion of the aquifer basin due to the presence of drainage ditches on the aquifer boundary. When the effect of ET is incorporated in combination with recharge, the analytical solution results in accurate and reliable estimates of water table fluctuations under situations subjected to a number of controlling factors. This study will be useful for alleviation of drainage problems of the aquifers receiving surface recharge and surrounded by streams.     

Simple Method for Quick Estimation of Leaky-Aquifer Parameters

Simple method and explicit equations are proposed for estimating the parameters of leaky aquifers from drawdown at an observation well, which avoid the curve matching or initial estimate of the parameter. The proposed method is computationally simple and the calculations can be performed even on a handheld calculator. The application of the methods is illustrated, using published data sets. The new method yields quick and accurate estimates of the leaky-aquifer parameters, if observed drawdowns do not contain large errors. The proposed method can also analyze the early drawdowns for accurate characteristics/parameters of a confined aquifer, if the conductance of the aquitard is assigned a zero value. It is hoped that the proposed method would be of help to field engineers and practitioners.     

Generalized Analytical Solutions for Groundwater Head in a Horizontal Aquifer in the Presence of Subsurface Drains

Generalized analytical solutions for groundwater head in horizontal aquifers in the presence of parallel subsurface drains are obtained considering a transient rate of recharge as a power series (polynomial) function and depth-dependent rate of evapotranspiration. A function, new to analytical drainage studies, is proposed for correctly representing the depth-dependent rate of evapotranspiration. The solutions are obtained considering the practical situation of drains placed at a shallow depth in a considerable depth of aquifer. Two conditions of large and small saturated thicknesses in comparison to the changes in groundwater head are considered. A mathematical criterion is proposed to distinguish between large and small saturated thicknesses.     

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.     

Fractional Steps Scheme of Finite Analytic Method for Advection–Diffusion Equation

For simply finding local analytic solution, the time derivative in the traditional finite analytic (FA) method is generally replaced with a first-order finite difference approximation as a source term. However, this may induce excessive numerical diffusion, especially for advection-dominated transport problems. In this paper, a fractional steps scheme of the FA method without using the finite difference approximation to time derivative is proposed by applying the one-dimensional FA method whose local analytic solution is obtained from both spatial and time domains, together with the method of fractional steps. Four hypothetical examples, including two-dimensional and three-dimensional cases, are employed to investigate this newly proposed method as compared with the traditional FA method, the optimal unsteady FA method, and the alternating direction scheme of the hybrid FA method. The results show that the fractional steps scheme of the FA method can greatly diminish numerical diffusion and is superior to the other methods compared herein.     

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.     

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.     

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.     

Remediation of TCE-Contaminated Groundwater in a Sandy Aquifer Using Pulsed Air Sparging: Laboratory and Numerical Studies

The objective of this study was to investigate, through laboratory and numerical investigations, the effectiveness of a pulsed air sparging system for remediation of groundwater contaminated with trichloroethylene (TCE) in a sandy aquifer. In laboratory experiments, air was pulsed into TCE source zone on a daily basis in order to remediate TCE-contaminated groundwater. Most dissolved TCE was removed at the end of experiments although its concentrations fluctuated due to the air pulsing. The measured gaseous phase TCE concentration increased whereas the aqueous phase TCE concentration decreased during air sparging pulses. Experimental data were assessed by using a numerical code STOMP (subsurface transport over multiphases) with some modification based on the TCE dissolution kinetics. The unmeasured residual TCE mass was predicted through numerical simulations. Results show that aqueous concentrations for TCE are still much higher than the maximum contaminant level in spite of successful removal of 95% of residual TCE. It may imply that it would be more appropriate to apply air sparging combined with other remediation technologies such as bioremediation for remediation of TCE-contaminated groundwater.     

Undrained Limit States of Shallow Foundations Acting in Consort

There is no established procedure for the calculation of bearing capacity of a shallow foundation system comprising cojoined footings. Ad hoc approaches are relied on and may simply involve summing the ultimate limit states of the individual footings as if they acted independently; neglecting additional capacity of the system available from the kinematic constraint provided by the structural connection between the footings. In this study, the undrained capacity under general loading of rigidly connected two-footing systems at various separations has been investigated with finite-element analyses. Results are presented in terms of ultimate limit states under pure vertical (V), horizontal (H), and moment (M) loading, and failure envelopes defining limiting load states under combined VH, VM, HM, and VHM loads. Kinematic failure mechanisms observed in the finite-element analyses are presented and in cases used to provide the basis for upper bound solutions.