An analytical solution for predicting transient seepage into ditch drains from a ponded field

Barua, Gautam; Alam, Wazir

doi:10.1016/j.advwatres.2012.09.002

Cited by 23 publications

(32 citation statements)

References 20 publications

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“…This solution is somewhat complex as, due to non-symmetry of flow in the flow space in between the drains, the entire flow domain OABCDHKJO was required to be considered in their analysis, running three different Fourier series to accommodate the boundaries at the ditch faces as well as on the surface of the soil. The solution provided here, however, as can be seen, is developed by considering only one half (because of symmetry of flow in the considered flow space) of the flow domain and is, hence, relatively much simpler than the one provided by Barua and Alam [11]. Further, it is important to note that these two solutions are totally independent of one another and the one obtained here cannot be reduced from Barua and Alam's solution [11] as the flow domains, as mentioned before, over which these solutions are being developed are not the same.…”

Section: Mathematical Analysismentioning

confidence: 99%

“…We would like to mention here that Barua and Alam [11] solved the flow problem of fig. 1 by considering a variable ponding field over the surface of the soil and unequal water level heights in the adjacent ditch drains.…”

Section: Mathematical Analysismentioning

confidence: 99%

“…Most of these solutions, however, are for the steady state situation and thus not applicable to study the transient dynamics associated with a ponded ditch drainage scenario. Barua and Alam [11] provided a comprehensive analytical solution to the ditch drainage problem considering unequal water level heights in between adjacent drains as well as a variable depth of ponding over the surface of the soil. However, because of the general nature of this solution, it is somewhat demanding on its computational requirements and as such there lies a necessity of developing a relatively simple solution to the problem.…”

Section: Introductionmentioning

confidence: 99%

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An analytical model for predicting transient flow into equally spaced ditch drains receiving water from a uniformly ponded field

Barua

Alam

2013

Water Resources Management VII

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An analytical solution is worked out for predicting transient seepage into a network of parallely spaced ditch drains in a homogeneous and anisotropic soil overlying an impervious barrier and receiving water from a uniformly ponded field. The distance between the adjacent drains is assumed to be the same and the level of water in all the ditches are all considered as equal in the analysis. In order that only two-dimensional flow prevails in the flow spaces in between the drains, it is further assumed in the mathematical procedure that the field is of infinite extent. The correctness of the develop model is established by performing a MODFLOW check on it for a considered ditch drainage situation. The study shows that the rate of water entry at the surface of a soil from a uniformly ponded field to the ditch drains is of a relatively better uniformity at early times of a simulation and that this uniformity gets progressively reduced with the passage of time, particularly for situations where the anisotropy ratio (it is a quotient between the horizontal and vertical saturated hydraulic conductivities of a soil) of the soil is low. Further, the transient state duration of a ponded ditch drainage scenario may be considerable if the drains are being laid in a soil having low directional conductivity values and a high anisotropy ratio, more so if the drains are being installed relatively deeper into the ground. The solution provided here is important as it can be successfully employed for designing a network of ditch drains for cleaning a salt affected soil and also in reclaiming a water-stagnated area.

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Section: Mathematical Analysismentioning

confidence: 99%

Section: Mathematical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An analytical model for predicting transient flow into equally spaced ditch drains receiving water from a uniformly ponded field

Barua

Alam

2013

Water Resources Management VII

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“…A comprehensive analytical treatment to the transient ditch drainage problem was provided by Barua and Alam [19] by considering a variable ponding field over the surface of the soil and unequal water level heights in between the adjacent drains. The application of this solution, however, is computationally demanding as the solution requires evaluation of three Fourier coefficient sets related to the three boundaries associated with the face of the ditches and to the surface of the soil, along with the estimation of a double Fourier series related to the initial condition of the problem.…”

Section: Introductionmentioning

confidence: 99%

Analysis of transient seepage into equally spaced ditch drains from a ponded field

Barua¹,

Alam²

2015

Int. J. SDP

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An analytical solution is proposed for simulating transient seepage into a system of ditch drains placed in parallel in a homogeneous and anisotropic soil confined by an impermeable layer and receiving water from an infinitely extended ponded field. The solution assumes the ponding depth over the surface of the soil to be uniform and the soil fluid to be of constant density. The model can be applied for both equal and unequal water levels in adjacent drains. The accuracy of the developed solution is checked by comparing for a flow situation the hydraulic heads and streamlines as obtained from the proposed model with the corresponding results obtained from an available steady state solution of the problem as provided by Kirkham [14]. A numerical check on the proposed solution is also performed for a particular flow configuration of the problem in the transient zone. The study shows that flow in a ponded ditch drainage system is greatly influenced by anisotropy and directional conductivities of soils. The uniformity of surface flux distribution is found to be quite sensitive to the anisotropy ratio (the ratio of horizontal and vertical saturated hydraulic conductivities of soil) of a soil column -a higher anisotropy ratio favors and a low anisotropy ratio weakens this distribution. Furthermore, the time to attain steady state by a ditch drainage system can be considerable, particularly for situations where the drains are dug relatively deeper into a soil having a high anisotropy ratio. The analytical model presented here is significant as it can be used to design ditch drainage networks for reclaiming a salt-affected and/or waterlogged soil within a specified time.

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“…Subsurface drainage is also often used for reclaiming waterlogged and saline soils and in mitigating phosphorous and pesticide loads of agricultural fields (Youngs 1994;Dils and Heathwaite 1999;Heathwaite and Dils 2000;Kroger et al 2008). Washing of a salt-affected soil often involves subjecting the surface of the soil to a uniformly recharged or ponded field so that sufficient head is being provided to force water though the soil profile with the intention that the moving water takes away a portion of the salt present in the soil profile, the salt-enriched water is then drained with the help of a network of subsurface drains put into the soil for the purpose (Martinez Beltran 1978;Rao and Leeds-Harrison 1991;Youngs 1994;Barua and Tiwari 1995;Youngs and Leeds-Harrison 2000;Barua and Alam 2013). Thus, during reclamation of a contaminated soil profile also, an accurate estimation of groundwater travel times for water particles originating at different locations on the surface of the soil is essential as this distribution provides information based on which the time of leaching of a contaminated soil profile may be worked out.…”

Section: Introductionmentioning

confidence: 99%

An iterative method for estimating solute travel times to ditch drains under steady recharge and ponded conditions

Barua

Patidar

2015

Appl Water Sci

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An iterative procedure is worked out for estimating solute travel times in a subsurface system by making use of the velocity and streamline distributions pertinent to the system. The developed method is then being applied to study the solute travel times to ditch drains originating from a field being subjected to a uniform (1) recharge and (2) ponding field over the surface of the soil. For case (1), both single and layered soils are being considered to estimate the travel times. The developed mathematical procedure is simple to use, robust, reasonably accurate even if being used with a lesser division of a streamline and completely eliminates the necessity of determination of any integrals for estimating the travel times-integrals which, in the methods generally been employed for estimating the travel times from steady-state analytical groundwater models, would otherwise need be evaluated. The study shows that travel times of water particles traversing through a layered soil being subjected to a uniform recharge at the surface are sensitive to the directional conductivities, anisotropy ratio (defined here as the ratio between horizontal and vertical hydraulic conductivities of soil) and thickness of individual layers of a soil profile as well as to the magnitude of the steady-state recharge on the surface of the soil. For the ponded drainage scenarios also, directional conductivities and thickness of a soil profile, extent of partial penetration and width of the ditch drains, levels of water head at the surface of the soil as well as on the ditches are observed to influence the travel times in a noticeable way. The proposed method is important as it provides simple and accurate estimations of migration times of pollutants to subsurface drains under different drainage situations; it can also be used to assess the time of reclamation of a salt-affected or waterlogged soil being drained by a network of subsurface drains being installed for the purpose from the available hydraulic theory relevant to the concerned drainage situation.

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An analytical solution for predicting transient seepage into ditch drains from a ponded field

Cited by 23 publications

References 20 publications

An analytical model for predicting transient flow into equally spaced ditch drains receiving water from a uniformly ponded field

An analytical model for predicting transient flow into equally spaced ditch drains receiving water from a uniformly ponded field

Analysis of transient seepage into equally spaced ditch drains from a ponded field

An iterative method for estimating solute travel times to ditch drains under steady recharge and ponded conditions

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