One-dimensional Groundwater Flow Research Articles

Numerical modeling of groundwater flow based on explicit and fully implicit schemes of finite volume method

This paper documents a novel numerical model for calculating the behavior of unsteady, one-dimensional groundwater flow by using the finite volume method. The developed model determined water table fluctuations for different scenarios as follows: Drainage and recession from an unconfined aquifer, and water table fluctuations above an inclined leaky layer due to ditch recharge with a constant and variable upper boundary condition. The Boussinesq equation, which is the governing equation in this domain, is linearized and solved numerically in both of the explicit and fully implicit conditions. Meanwhile, the upwind scheme is employed to discretize the governing equation. The computed outcomes of both the explicit and implicit approaches agreed well with the results of analytical solution and laboratory experiments. The main reason is that in the first half of simulation process explicit scheme obtains slightly better results and in the second half of the simulation process fully implicit scheme predicts more reliable outcomes that are hidden in the neighbor node points. As a final point, the numerical outcomes confirm that the developed model is capable of calculating satisfactory outcomes in engineering and science applications.

Can we infer the age of karst conduit from the profile of potentiometric surface?

The Floridan aquifer consists of a high presence of karst features that make the landscape prone to sinkholes. Karst conduits can conduct high amounts of water and affect processes such as groundwater transport. A karst conduit evolution model based on dissolution chemistry is applied to the Silver Springs springshed in Ocala, Florida. The model is able to reproduce the observed potentiometric head profiles more accurately than the one-dimensional groundwater flow model for confined aquifer with leaky conditions. In addition, based on the initial fracture geometry and dissolution chemistry, the model predicts the age of the conduits from the analyzed head profiles to be approximately 9–60 Myrs old. The understanding of the karst conduit geometric evolution and mapping can improve conduit age prediction as well as better characterize conduit flow patterns and subsequent groundwater processes.

Quantitative Assessment of the Mechanisms of Earthquake-Induced Groundwater-Level Change in the MP Well, Three Gorges Area

Earthquake-induced groundwater-level changes have been widely studied, though the mechanisms causing coseismic responses are still debated. In this study, we employ several models to fit the coseismic groundwater-level changes caused by the 2008 Wenchuan earthquake in the MP well, located in the Three Gorges Dam. The fits for all models are about the same. By comparing the model results with the results from tidal response and baseflow recession analyses, we conclude that a transient permeability model can best describe the coseismic groundwater-level changes in the MP well. The discharge from the Changmutuo fault zone estimated from the one-dimensional groundwater flow model during the 20 days following the earthquake is about 310 ± 90 m3.

Non-Steady One-Dimensional Groundwater Flow In Confined Aquafer Induced By Time Delayed Water Level Changes In Bounding Channel

Unsteady state one dimensional flow of ground water induced by changes in water level in two channels bounding an isotropic homogeneous confined aquifer was studied. The water level in the two channels varies gradually with time and defined by mathematical functions with inbuilt time delay parameters. Exact solution to the problem was sought analytically, using the Laplace transform method. Results were obtained for pressure heads in error functions at various times and places in the aquifer. The equations obtained in the study were in agreement with those obtained by other researchers in previous studies. Using a numerical example, actual head values were determined for varying set values of delay parameters and these were plotted and compared.

Screening-level estimates of mass discharge uncertainty from point measurement methods

The uncertainty of mass discharge measurements associated with point-scale measurement techniques was investigated by deriving analytical solutions for the mass discharge coefficient of variation for two simplified, conceptual models. In the first case, a depth-averaged domain was assumed, consisting of one-dimensional groundwater flow perpendicular to a one-dimensional control plane of uniformly spaced sampling points. The contaminant flux along the control plane was assumed to be normally distributed. The second case consisted of one-dimensional groundwater flow perpendicular to a two-dimensional control plane of uniformly spaced sampling points. The contaminant flux in this case was assumed to be distributed according to a bivariate normal distribution. The center point for the flux distributions in both cases was allowed to vary in the domain of the control plane as a uniform random variable. Simplified equations for the uncertainty were investigated to facilitate screening-level evaluations of uncertainty as a function of sampling network design. Results were used to express uncertainty as a function of the length of the control plane and number of wells, or alternatively as a function of the sample spacing. Uncertainty was also expressed as a function of a new dimensionless parameter, Ω, defined as the ratio of the maximum local flux to the product of mass discharge and sample density. Expressing uncertainty as a function of Ω provided a convenient means to demonstrate the relationship between uncertainty, the magnitude of a local hot spot, magnitude of mass discharge, distribution of the contaminant across the control plane, and the sampling density.

Effects of Water Seepage on the Stability of Soil-slopes

Landslide is a kind of severe natural disaster and societal hazard throughout the world.Among various effecting factors, water is commonly known as one of the major triggers for landslide failures. In this paper, a coupling model of water-seepage and stability analysis has been developed for analyzing the effect of water on the stability of slopes. A combination of spline curves and genetic algorithm is used to locate the critical slip surface for slope stability calculations. A new analytical solution of the linearized Boussinesq equation was developed for one-dimensional groundwater flow in unconfined aquifer. An actual landslidelocated in the Three Gorges Reservoir was analyzed by simulating the changes of the seepage field caused by rainfall and water level fluctuation. The influences of water seepage on the stability of landslide were discussed with emphasis.The results show that rainfall infiltration and the variation of water level can tremendously influence the stability of slopes.

Induced groundwater flux by increases in the aquifer's total stress.

Fluid-filled granular soils experience changes in total stress because of earth and oceanic tides, earthquakes, erosion, sedimentation, and changes in atmospheric pressure. The pore volume may deform in response to the changes in stress and this may lead to changes in pore fluid pressure. The transient fluid flow can therefore be induced by the gradient in excess pressure in a fluid-saturated porous medium. This work demonstrates the use of stochastic methodology in prediction of induced one-dimensional field-scale groundwater flow through a heterogeneous aquifer. A closed-form of mean groundwater flux is developed to quantify the induced field-scale mean behavior of groundwater flow and analyze the impacts of the spatial correlation length scale of log hydraulic conductivity and the pore compressibility. The findings provided here could be useful for the rational planning and management of groundwater resources in aquifers that contain lenses with large vertical aquifer matrix compressibility values.

Parameter-independent model reduction of transient groundwater flow models: Application to inverse problems

A new methodology is proposed for the development of parameter-independent reduced models for transient groundwater flow models. The model reduction technique is based on Galerkin projection of a highly discretized model onto a subspace spanned by a small number of optimally chosen basis functions. We propose two greedy algorithms that iteratively select optimal parameter sets and snapshot times between the parameter space and the time domain in order to generate snapshots. The snapshots are used to build the Galerkin projection matrix, which covers the entire parameter space in the full model. We then apply the reduced subspace model to solve two inverse problems: a deterministic inverse problem and a Bayesian inverse problem with a Markov Chain Monte Carlo (MCMC) method. The proposed methodology is validated with a conceptual one-dimensional groundwater flow model. We then apply the methodology to a basin-scale, conceptual aquifer in the Oristano plain of Sardinia, Italy. Using the methodology, the full model governed by 29,197 ordinary differential equations is reduced by two to three orders of magnitude, resulting in a drastic reduction in computational requirements.

Ensemble average and ensemble variance behavior of unsteady, one-dimensional groundwater flow in unconfined, heterogeneous aquifers: an exact second-order model

A new stochastic model for unconfined groundwater flow is proposed. The developed evolution equation for the probabilistic behavior of unconfined groundwater flow results from random variations in hydraulic conductivity, and the probabilistic description for the state variable of the nonlinear stochastic unconfined flow process becomes a mixed Eulerian–Lagrangian–Fokker–Planck equation (FPE). Furthermore, the FPE is a deterministic, linear partial differential equation (PDE) and has the advantage of providing the probabilistic solution in the form of evolutionary probability density functions. Subsequently, the Boussinesq equation for one-dimensional unconfined groundwater flow is converted into a nonlinear ordinary differential equation (ODE) and a two-point boundary value problem through the Boltzmann transformation. The resulting nonlinear ODE is converted to the FPE by means of ensemble average conservation equations. The numerical solutions of the FPE are validated with Monte Carlo simulations under varying stochastic hydraulic conductivity fields. Results from the model application to groundwater flow in heterogeneous unconfined aquifers illustrate that the time–space behavior of the mean and variance of the hydraulic head are in good agreement for both the stochastic model and the Monte Carlo solutions. This indicates that the derived FPE, as a stochastic model of the ensemble behavior of unconfined groundwater flow, can express the spatial variability of the unconfined groundwater flow process in heterogeneous aquifers adequately. Modeling of the hydraulic head variance, as shown here, will provide a measure of confidence around the ensemble mean behavior of the hydraulic head.

Determination of the parameter pattern and values for a one-dimensional multi-zone unconfined aquifer

In an aquifer, heterogeneity plays an important role in governing groundwater flow. Hence, aquifer characterization should involve both the pattern and values of the hydrogeological parameters. A new analytical solution describing the one-dimensional groundwater flow in a multi-zone unconfined aquifer is presented, and a methodology developed from the analytical solution and a heuristic approach for determining the pattern and values of the aquifer parameters are proposed. The analytical solution demonstrates that the hydraulic head varies spatially and is influenced by aquifer heterogeneity. Simulated annealing, a heuristic approach, is incorporated with the solution to simultaneously identify the pattern and values of the hydraulic conductivity for a horizontal multi-zone unconfined aquifer. This approach may be used to give an approximate result for a two-dimensional problem by dividing the model area into a number of transects along the transverse direction, identifying the parameter values along the longitudinal direction for each transect, and then smoothing the identified results.

Modeling the flow and leachate transport in the vadose and saturated zones of a municipal landfill

The purpose of the present study was to evaluate the groundwater contamination due to the construction and operation of the municipal landfill of Amari, Rethymno, Crete. The groundwater flow and leachate transport in the vadose and saturated zones were studied and simulated, using three different models: the one-dimensional groundwater flow and contaminant transport model for the vadose zone Pesticide Root Zone Model (PRZM-3), the Geographical Information System (GIS) Argus ONE and the three-dimensional groundwater flow and contaminant transport model Princeton Transport Code (PTC). The simulation time was 30 and 20 years, and the results obtained, according to the models and the existing hydrogeological conditions, were very encouraging and reassuring about the groundwater quality of the broad region.

Analytical Models for the Design of Iron-Based Permeable Reactive Barriers

The preliminary design of iron-based permeable reactive barriers is often accomplished using analytic expressions for one-dimensional groundwater flow and contaminant transport. Typically, one or more of the governing processes is simplified or neglected to facilitate development of a tractable solution. This paper presents a set of improved design equations that include the effects of dispersion, finite domain boundary, sequential decay, and production processes, and increased flow through high conductivity barriers. When applied to realistic example problems, application of the expanded design equations typically results in the specification of a larger permeable reactive barrier thickness than obtained using conventional approaches.

Stochastic analysis of spatial variability in unconfined groundwater flow

In this paper, spatial variability in steady one-dimensional unconfined groundwater flow in heterogeneous formations is investigated. An approach to deriving the variance of the hydraulic head is developed using the nonlinear filter theory. The nonlinear governing equation describing the one-dimensional unconfined groundwater flow is decomposed into three linear partial differential equations using the perturbation method. The linear and quadratic frequency response functions are obtained from the first- and second-order perturbation equations using the spectral method. Furthermore, under the assumption of the exponential covariance function of log hydraulic conductivity, the analytical solutions of both the spectrum and the variance of the hydraulic head produced from the linear system are derived. The results show that the variance derived herein is less than that of Gelhar (1977). The reason is that the log transmissivity is linearized in Gelhar’s work. In addition, the analytical solutions of both the spectrum and the variance of the hydraulic head produced from the quadratic system are derived as well. It is found that the correlation scale and the trend in mean of log hydraulic conductivity are important to the dimensionless variance ratio.

A two‐dimensional analytical solution for groundwater flow in a leaky confined aquifer system near open tidal water

AbstractGroundwater in coastal areas is commonly disturbed by tidal fluctuations. A two‐dimensional analytical solution is derived to describe the groundwater fluctuation in a leaky confined aquifer system near open tidal water under the assumption that the groundwater head in the confined aquifer fluctuates in response to sea tide whereas that of the overlying unconfined aquifer remains constant. The analytical solution presented here is an extension of the solution by Sun for two‐dimensional groundwater flow in a confined aquifer and the solution by Jiao and Tang for one‐dimensional groundwater flow in a leaky confined aquifer. The analytical solution is compared with a two‐dimensional finite difference solution. On the basis of the analytical solution, the groundwater head distribution in a leaky confined aquifer in response to tidal boundaries is examined and the influence of leakage on groundwater fluctuation is discussed. Copyright © 2001 John Wiley & Sons, Ltd.

Modeling flow over an initially dry bed

The one-dimensional groundwater flow equations are coupled with the St. Venant equations to simulate the flow resulting from a sudden removal of a dam over an initially dry downstream bed. The St. Venant equations are solved using a Petrov-Galerkin finite element scheme, while the groundwater flow equations are solved using the Bubnov-Galerkin finite element scheme. The comparison of the computed water surface and discharge per unit width profiles with the corresponding analytical solutions, for a dambreak over frictionless horizontal bed, show that the model possesses excellent phase accuracy, for both positive and negative waves, and can predict the discharge distribution accurately. Also, the computed water surface profiles are compared with the available measured data for the dambreak flows over smooth and rough surfaces of horizontal and sloping channels. In addition, the results obtained from only the St. Venant equations with minimum depth criteria are presented for comparison with the above model.

Uncertainty of One-Dimensional Ground-Water Flow in Strongly Heterogeneous Formations

The writers have formulated quasi-analytical nonlinear solutions to investigate the uncertainty of one-dimensional ground water flow in heterogeneous formulations in which the standard deviation of the log hydraulic conductivity σ\Dln(\iK)\N > 1. The writers have studied three cases for fixed boundary conditions: a semibounded domain, a free domain, and a both-side-bounded domain. The writers have also studied the random boundary conditions for the bounded domain. The writers have obtained variances and covariances of head for semibounded and free domains, and have calculated variances of head for the both-side-bounded domain. Monte Carlo simulations are generated to obtain the head variances and are used to verify the quasi-analytical solutions. The ergodicity assumption is proven to be rigorously correct in a semibounded or a free domain but not correct in a both-side-bounded domain by using a linear autocorrelation function.

Analysis of One-Dimensional Ground-Water Flow in a Nonuniform Aquifer

A one-dimensional (1D) flow, resulting from a sudden rise or decline in the water stage of a flood channel in a composite aquifer, which consists of two different regions separated by a linear discontinuity parallel to the channel, is considered. Governing equations are solved analytically for appropriate initial and boundary conditions. The obtained solution allows the determination of water level fluctuations in both regions of the composite aquifer and the time-dependent flow rate to (or from) the aquifer. It is shown that three other solutions found in the literature (solutions for uniform finite aquifer with impervious boundary, uniform finite aquifer with recharge boundary, and uniform semiinfinite aquifer) are special cases of the proposed solution, and they are unified in one form. The proposed solution is a relatively simple means of predicting the variations in the water levels in the aquifer as well as evaluating the time-dependent flow rate. It may also be used for the identification of the aquifer properties and for numerical model validation.

Subdomain Integration Model of Ground-Water Flow

The subdomain numerical integration method is applied to the nonlinear one-dimensional saturated groundwater flow equation (Boussinesq equation). Because the state variable of the resulting numerical analog can be cast in terms of spatial coordinates, nonlinearity can be eliminated, greatly increasing accuracy and simplifying the numerical code. As a result, the solution can be performed on hand held programmable calculators. Good results were obtained when applying the method to confined and unconfined (nonlinear) aquifer examples.