Dupuit Assumption Research Articles

Fuzzy Estimators of Drain spacing in Subsoil Drainage using Fuzzy Logic and Possibility Theories

In the permanent flow of subsoil drainage, a lot of equations are used, most of them based on the Dupuit assumption. All related mathematical models present uncertainties and fuzziness, which create problems in the design of drainage networks. Fuzzy Logic deals with this problem and allows the management of uncertain information. This paper presents the solution of the Hooghout equation based on Fuzzy Logic and Possibility theories, using the Reduced Transformation Method for the related numerical calculations. This results in a fuzzy estimator for the drain spacing, whose α-cuts, provide, according to Possibility Theory, the confidence intervals of the drain spacing with a certain strong probability. Results on subsoil drainage in the case of soils with parallel drains located at any position from the impermeable bottom are presented. The possibility theory application enables the engineers and designers of irrigation, drainage, and water resources projects to gain knowledge of hydraulic properties (e.g., water level, outflow volume) and make the right decision for rational and productive engineering studies.

Analysis of the impact of groundwater-level decrease caused by drainage on tunnel water inflow

Affected by excavation, the phenomenon of groundwater-level drop around mountain tunnels is widespread, resulting in poor accuracy of the existing water-inflow calculation formula derived when the groundwater level is fixed. Based on this, a simplified calculation model of tunnel water inflow is constructed that considers drainage; and the tunnel water inflow is calculated according to the Dupuit assumption and conformal transformation. The law of conservation of fluid mass is used to solve the equivalent water head around the tunnel after drainage and the Taylor formula is used for degradation analysis, and the rationality of the model construction and the correctness of the formula derivation are verified through the tunnel under construction and numerical simulation. Finally, the sensitivity of the characteristic parameters is studied, the evolution law of the equivalent head is revealed and the influence mechanism is discussed. The research shows that the error between the calculated value of tunnel water inflow and the field measured value can be reduced from 16.1 to 8.9%, which improves the prediction accuracy of tunnel water inflow to a certain extent.

The Steady Seepage Line Equation of Ionic Rare Earth Ore (IREO) In Situ Leached with Long Strip Bare Feet and Its Application

Without a reliable design method for the leaching and seepage step of in situ leaching (ISL), problems such as low comprehensive resource recovery rate and frequent geological disasters such as landslides are prominent. This study established a simplified “liquid injection-collection” plane model of ISL with a linear barefoot type rare earth mine as the research object. The steady seepage line equation was derived based on groundwater dynamics and the Dupuit assumption. Then, engineering verification and calculation error analysis were performed. The seepage line equation is expressed as a piecewise function, where the seepage line in the liquid injection area is the upper half of the ellipse line, and the one in the non-liquid injection area is a parabola. The calculation error increases along the flow field direction. The seepage gradient, bedrock gradient, liquid injection range, and relative permeability coefficient have limited influence on the calculation error of the equation. The seepage line equation can be fairly applied in ISL. The seepage line equation can provide a theoretical basis for the “prior prediction (design)” of the “liquid injection/collection” leaching and seepage process in ISL.

An Analytical Solution to Two-Region Flow Induced by Constant-Head Pumping in an Unconfined Aquifer

This paper proposes an analytical solution to the problem of two-region flow induced by constant-head pumping tests in an unconfined aquifer based on the Dupuit assumption. The two-region flow includes a finite non-Darcian pattern near the pumping well and a semi-finite Darcian pattern in the rest region. By Izbash’s equation, the solution to the two-region flow is derived using the Boltzmann method. The reliability of the proposed solution is investigated through comparisons with the numerical solution by COMSOL Multiphysics and the hydraulic head−time data from the pumping test in Wisconsin. The influences of the finite non-Darcian flow pattern on the hydraulic head and pumping rate are also discussed. The results demonstrate that a greater degree of non-Darcian turbulence can effectively increase the pumping flow rate, although such influence can be reduced over time. A method for determining the range of the non-Darcian region has been developed and validated by the specific discharge and Reynolds number.

An analytical and meshless model for 3D transient flow in a confined aquifer with nonuniform thickness: Application to stream depletion due to groundwater extraction

This study proposes an analytical and meshless model for three-dimensional transient flow induced by multiple wells in a stream-confined aquifer system with arbitrary nonuniform aquifer thickness. The model involves allocating external image wells near the aquifer boundary. The aquifer drawdown is defined as Theis’ solution plus a simple series expanded by complementary error functions reflecting the boundary effects of the stream and impervious stratum. The solution for stream depletion rate (SDR) can be derived based on the drawdown solution. Results suggest the Dupuit assumption of no vertical flow is valid to estimate SDRs affected by the landward exponentially decreasing thickness. The SDR induced by multiple wells is the same as that by a single well if the total well discharge rate and stream-well distances in the multiple well case are identical to those in the single well case. The present solution outperforms a finite difference solution in computational efficiency.

Experimental investigation of steady-state flow with ditch-drainage and surface recharge

This paper experimentally investigates the variations of the groundwater table when uniform surface recharge with vertical drainage occurs in an unconfined aquifer. Homogenous and layered soil was considered for the soil profile in the experiments. A large-scale flume with 5.5 m length, 0.6 m width and 1 m height, was used for experiments of the groundwater flow. The effects of soil type, stratification and water level on the groundwater flow were examined under ditch-drainage. For the layered soil, the water table height depends significantly on the properties of the soil layer which is adjacent to the impermeable bed. The results of the experiments were compared with the theoretical solutions, and the precision of various equations for determining the water table height was evaluated and a reliable equation for different conditions was proposed. The results shows that the Dupuit approximate is able to precisely predict the water table level in fine sand, however, it is not capable of predicting the water table level in coarse sand. The vertical water velocity, which is neglected by Dupuit assumption, in the coarse sand is considerable, so this approximation is not able to appropriately predict the phreatic surface. In addition, three well-known equations of Engelund (1951), Knight (2005), and Castro-Orgaz et al., (2012) are used to predict the phreatic water surface. These equations precisely forecast water level height in homogenous coarse sand. Engelund’s solution is applicable merely in free drainage conditions. Eventually, Knight (2005), Castro-Orgaz et al., (2012), and Dupuit solutions yield the best estimation to find the locations of the groundwater in top layer fine sand, top layer coarse sand, and vertically layered sand, respectively.

Groundwater Flow Analysis for Inclined Aquifers.

Sedimentary deposits that have water in subsurface groundwater system are not often completely horizontal because of the geological features such as: bedding and folding. These deposits typically overlay on sloped impervious layers, and therefore; additional research is necessary for these situations. In this research an analytical model is presented for groundwater flow on inclined impermeable layer. The presented model is preferable to the Paolowsky method regarding its applicability and accuracy. The Dupuit's assumption is used for the formulation. The presented model can be generalized for the situation, having surficial infiltration into and exfiltration from the groundwater system. Several problems of different slope situations and boundary conditions are addressed by the presented model and the results are shown here. The model is compared with numerical model Seep/w and good agreements are obtained when possible.

Groundwater table fluctuations in a coastal unconfined aquifer with depth-varying hydraulic properties

While many analytical studies have been carried out to examine groundwater table fluctuations in tidally-influenced coastal unconfined aquifers, they generally focused on homogeneous aquifers and overlooked actual field situations with sound physical underpinnings. Taking the inelastic intergranular movement into account, this study presented a new governing equation under the Dupuit assumption, in which the compressibility factor was considered to incorporate the vertical variations of both effective porosity and hydraulic conductivity. An analytical solution was derived using Taylor expansion and the perturbation method. Time-varying groundwater table from the present model lies in between the homogeneous solutions predicted using grain parameters in the upper and bottom aquifer layers, which is almost overlapped with the homogeneous solution if applying the grain parameters in the middle layer. Effects of depth-varying hydraulic properties were further examined with respect to the total fluctuation range and phase shift of the groundwater table, which quantitatively present the differences between the present solution and Nielsen (1990) homogeneous solution. Such differences become significant for the large compressibility factor. In addition, it was mathematically proved that compressibility factor has no effect on the mean water surface as landward distance approaches infinity.

A calculation method for seepage of vertical wells with concentric rings in horizontal rock layers

Some vertical wells are excavated in the horizontal rock layers with different thicknesses and permeability coefficients, and have concentric rings such as lining and grouting circle. The exiting formulas, which are derived for the unlined wells in homogeneous body, are inapplicable to such complex wells. Therefore, a calculation method is developed. Based on the Dupuit assumption, the vertical velocity of groundwater is ignored, and only the horizontal flow is considered. Consequently, each layer is assumed to be independent of the other during seepage. The water inflow and the water pressure of each layer are obtained according to the Darcy law. The total water inflow is the sum of those of all layers. Then, the seepage analysis of a vertical well is carried out by using this method and numerical simulation. The two results are in good agreement. It is found that the water pressure on the lining or that on the grouting ring generally increases with depth and also changes with the permeability coefficient of each layer. The impact of grouting circle parameters on water inflow is discussed. The research in this paper can provide useful references for well seepage analysis and design of grouting circle.

A simple model for the simulation of the flow behavior in unconfined double porosity aquifers

The flow processes in unconfined double porosity aquifers consisting of a porous matrix and a dense network of fractures are investigated using the equivalent continuum approach, the Dupuit assumption and a depth-integrated formulation. We show that, unlike in the case of confined double porosity aquifers, in the case we investigate the term describing the internal flux between the two equivalent continua is non-linear. For the case of dewatering processes, a system of Partial Differential Equations, which involves only four parameters is developed. It is demonstrated that for the opposite case of recharging aquifer, at least for some cases, a much more complicated mathematical description is necessary. For the dewatering aquifer case fully explicit analytical solutions for both the variations of water table and discharge to an adjacent water body are developed. We verified the accuracy of the solutions for the head by comparison against numerical results.

Assessment of the hydrodynamics role for groundwater quality using an integration of GIS, water quality index and multivariate statistical techniques

To explore the impact of groundwater hydrodynamics on water quality, a cost-effective geospatial model was developed using geographic information system (GIS) technology and the Dupuit assumption. Meanwhile, the groundwater quality in the Dagu River Basin was evaluated based on the water quality index (WQI) and multivariate statistical analyses. In April (dry season) and September (rainy season) 2017, the groundwater level was automatically monitored from 115 wells, and the water quality including 21 hydrochemical parameters was sampled from 37 wells. Results reveal that the WQI values varied from 35.01 to 64.74, with mean values of 51.89 and 47.87 in the rainy and dry seasons. Approximately 80% of the samples exhibited moderate water quality, with no significant difference between the rainy and dry seasons. Nitrate pollution and the integrated water quality in the central and northern regions were generally worse than that in the southern region. The Darcy velocity in the central and northern regions was relatively high with a maximum rate of 0.56 m/d, compared with the southern region. This correlation illustrates the effect of groundwater hydrodynamics on quality. The sowing of greater chemical fertilizers combined with faster groundwater movement is likely responsible for the large–scale nitrate pollution in the central and northern regions. Results also proved the accuracy of the geospatial model with a valid uncertainty. The geospatial model provides a valuable alternative for the spatial analysis of the effect of groundwater hydrodynamics on water quality.

Seepage Face in Steady-State Groundwater Flow between Two Water Bodies

AbstractAn implicit solution determining the seepage-face dimension formed in steady-state flow through an aquifer connecting two water bodies is achieved based on the Dupuit assumption and conserv...

Proof of Dupuit's Assumption for the Free Boundary Problem in an Inhomogeneous Porous Medium

Для задач со свободной границей, описывающих стационарные течения грунтовых вод, исследуется асимптотическое поведение решений в ситуации, когда масштаб по одному из пространственных направлений намного меньше, чем по другим. Доказана сходимость решений к некоторому пределу. Свойства этого предельного решения соответствуют предположению, которое в инженерных приложениях называется гипотезой Дюпюи и на основе которого принято строить приближенные модели течений грунтовых вод в тонких водоносных горизонтах. Библиография: 13 названий.

Analysis of the Seepage Due to the Thawing of Permafrost, Considering the Gradient of the Impermeable Layer

Topographical deformation due to global warming has become a serious problem. However, scientific studies have not been sufficiently conducted to understand the mechanisms. Solifluction, a gradual mass movement related to freeze-thaw processes, is known as a typical topographical deformation. The purpose of this study is to simulate the solifluction process considering the seepage influence, and then establish a predictive numerical model. The authors adopted the Finite Volume Method (FVM) and Dupuit's assumption in order to precisely simulate the seepage flow. Consequently, according to this study, the authors suggested to adopt a non-linear assumption for appropriate estimation of seepage flow velocity.

Estimation of the position of the sharp interface in littoral aquifers with hydraulic head differences within the fresh-water zone

In littoral zones where fresh groundwater discharges into the sea, a vertical difference in hydraulic head always exists within the fresh-water zone, i.e., the Dupuit assumption is not satisfied. The hydraulic head difference may affect the sharp interface and needs to be taken into account when position of the interface is determined. Examination of the equilibrium status of a point on the interface reveals that the location of the interface in a homogeneous and isotropic coastal unconfined aquifer can be determined based on the fresh-water head and the salt-water head at one point on the sharp interface. Considering a linear increase or decrease in the hydraulic head within the fresh-water zone, a method for estimating the position of the sharp interface is described on the basis of the fresh hydraulic heads at two arbitrary points in the fresh-water zone and the salt hydraulic head at one arbitrary point in the salt-water zone in the same vertical straight line in the littoral zone. The method using corresponding pressures at the points is also given. The Ghyben-Herzberg model is a specific case of the method. This method requires three nearest observation wells, two revealing the fresh-water zone and one tapping the deeper salt-water zone, or three transducers installed in one well, two in the fresh-water zone and one in the deeper salt-water zone. The Observations of piezometric heads in the northwest Beihai coast in China are used to illustrate the application of the method to determine the position of the sharp interface, which ranges from 32.56 to 49.15 m under the mean sea level during the specific observation period.

An Analysis on Groundwater Recharge by Mathematical Model in Inclined Porous Media

The present paper discusses the analysis of solution of groundwater flow in inclined porous media. The problem related to groundwater flow in inclined aquifers is usually common in geotechnical and hydrogeology engineering activities. The governing partial differential equation of one-dimensional groundwater recharge problem has been formed by Dupuit's assumption. Three cases have been discussed with suitable boundary conditions and different slopes of impervious incline boundary. The numerical as well as graphical interpretation has been given and its coding is done in MATLAB.

Is the Dupuit assumption suitable for predicting the groundwater seepage area in hillslopes?

AbstractMany physically based hydrological/hydrogeological models used for predicting groundwater seepage areas, including topography‐based index models such as TOPMODEL, rely on the Dupuit assumption. To ensure the sound use of these simplified models, knowledge of the conditions under which they provide a reasonable approximation is critical. In this study, a Dupuit solution for the seepage length in hillslope cross sections is tested against a full‐depth solution of saturated groundwater flow. In homogeneous hillslopes with horizontal impervious base and constant‐slope topography, the comparison reveals that the validity of the Dupuit solution depends not only on the ratio of depth to hillslope length d/L (as might be expected), but also on the ratio of hydraulic conductivity to recharge K/R and on the topographic slope s. The validity of the Dupuit solution is shown to be in fact a unique function of another ratio, the ratio of depth to seepage length d/LS. For d/LS < 0.2, the relative difference between the two solutions is quite small (<14% for the wide range of parameter values tested), whereas for d/LS > 0.2, it increases dramatically. In practice, this criterion can be used to test the validity of Dupuit solutions. When d/LS increases beyond that cutoff, the ratio of seepage length to hillslope length LS/L given by the full‐depth solution tends toward a nonzero asymptotic value. This asymptotic value is shown to be controlled by (and in many cases equal to) the parameter R/(sK). Generalization of the findings to cases featuring heterogeneity, nonhorizontal impervious base and variable‐slope topography is discussed.

Estimation of maximum saturated depth in two-layered drainage blankets over the barrier in landfill cover system

For accurately calculating the maximum saturated depth over the landfill barrier and analyzing the variation of liquid head with inflow time, a new method is presented that considers the unsteady-state condition. Based on the principle of water balance and the extended Dupuit assumption, the solution of the new method can be calculated. Also, this method is capable of revealing the effect of the multilayered drainage media. One of the advantages of the method presented in this paper is that it can be used to draw a phreatic surface in layered drainage media under unsteady-state condition and estimate the location of the maximum liquid depth, for both homogeneous conditions and two-layered drainage conditions. Based on the developed analysis method, the effects of a parametric variation on the maximum saturated depth and the variation of saturated depth with time are presented. The calculated results show that with the increase of slope gradients of cover system, the saturated depth of cover system is easy to reach a stable value. Moreover, when the drainage layer consists of two layers with different thickness and hydraulic conductivity, the increase of hydraulic conductivity of the upper drainage layer will make it easier for the saturated depth of cover system to reach a stable and lower value.

An Analysis of River Bank Slope and Unsaturated Flow Effects on Bank Storage

Recognizing the underlying mechanisms of bank storage and return flow is important for understanding streamflow hydrographs. Analytical models have been widely used to estimate the impacts of bank storage, but are often based on assumptions of conditions that are rarely found in the field, such as vertical river banks and saturated flow. Numerical simulations of bank storage and return flow in river-aquifer cross sections with vertical and sloping banks were undertaken using a fully-coupled, surface-subsurface flow model. Sloping river banks were found to increase the bank infiltration rates by 98% and storage volume by 40% for a bank slope of 3.4° from horizontal, and for a slope of 8.5°, delay bank return flow by more than four times compared with vertical river banks and saturated flow. The results suggested that conventional analytical approximations cannot adequately be used to quantify bank storage when bank slope is less than 60° from horizontal. Additionally, in the unconfined aquifers modeled, the analytical solutions did not accurately model bank storage and return flow even in rivers with vertical banks due to a violation of the dupuit assumption. Bank storage and return flow were also modeled for more realistic cross sections and river hydrograph from the Fitzroy River, Western Australia, to indicate the importance of accurately modeling sloping river banks at a field scale. Following a single wet season flood event of 12 m, results showed that it may take over 3.5 years for 50% of the bank storage volume to return to the river.

A method for estimating the fresh water–salt water interface with hydraulic heads in a coastal aquifer and its application

Examining the descriptions of piezometric heads at two points in both the salt water and fresh water zones reveals that when the groundwater flow system is in steady state and satisfies the Dupuit assumption, the location of the fresh water–salt water interface in a homogeneous, isotropic, and unconfined coastal aquifer can be estimated based on a piezometric head of fresh water at a point in the fresh water zone (from the water table to the interface) vertically lined up with a piezometric head of salt water at a point in the salt water zone (from the interface down). Research shows that the new method is a general relation and that both the Hubbert relation describing the location of the interface and the Ghyben–Herzberg relation are special cases of this method. The method requires two piezometric wells to be close to each other and each tapping into a different zone. Measurements of piezometric heads at a well cluster consisting of piezometric wells tapping separately into fresh water and salt water zones near Beihai, China at 5-day intervals for 15 months are used to illustrate the estimation of interface location. The depth of the interface for well H5 ranges from 32 to 72 m below the sea level.