Extension of a Recent Method for Obtaining Exact Solutions of the Bruce and Klute Equation

Barry, David Andrew; Parlange, Jean‐Yves; Prevedello, Celso Luiz; Loyola, Jocely Maria Thomazoni; Reichardt, Klaus; Nielsen, D. R.

doi:10.2136/vzj2009.0055

Cited by 6 publications

(63 citation statements)

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“…The theory proposed by Barry et al (2010) is very simple in its essence, inspired in its formulation, complex in its solution, but easy to apply. The technique consists of introducing a nonzero value of air‐entry pressure h a , such that for h < h a and θ < θ s the soil is not saturated, while it is saturated for h ≥ h a and θ = θ s .…”

Section: Theoretical Considerationsmentioning

confidence: 99%

“…Many equations are part of the theory of Barry et al (2010), but regarding those that define the water content profile at the WF of horizontal infiltration, we have:

λ = λ_{normala} {(\frac{h - h_{normalb}}{h_{normala} - h_{normalb}})}^{α}, λ > λ_{normala}

where h is the matric potential at the WF profile, λ a is the value of the Boltzmann's transformation variable (λ) for h = h a , and h b and α are the fitting parameters, wherein:

h_{normalb} = h_{normala} (1 - α)

In the theory of Barry et al (2010), the parameter α in Eq. [1] can assume any value, while in the theory of similarity the value of λ is defined by Eq.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

“…On the other hand, this similarity between functions does not occur for porous media (PM) with finer textures and, therefore, the soil water content profiles in these media end up being overestimated by the theory of similarity. Barry et al (2010) analyzed the theory of Prevedello et al (2008) from the perspective of Bruce and Klute's (1956) equation and concluded that there is a singularity in the saturated area, notably at x = 0. They extended the theory of Prevedello et al (2008) to define the function θ( h ) of the WF in an exact way, without any relation of similarity or resemblance to the retention curve.…”

mentioning

confidence: 99%

“…For this reason, the concept of air‐entry pressure ( h a ) was introduced in that work to solve the Bruce and Klute (1956) equation in two soil water content domains, without physical singularities, although assuming the initial soil water content (θ i ) to be zero before the infiltration process. This work aims to apply the theory of Prevedello et al (2008), with the extension proposed by Barry et al (2010), for the analytical determination of the soil water content profile at any time of horizontal infiltration, analyzing the results of such application in different PM considering θ i values different from zero before the infiltration process.…”

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confidence: 99%

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Generalization of the Green–Ampt Theory for Horizontal Infiltration into Homogeneous Soils

Prevedello

Armindo

2016

Vadose Zone Journal

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Core Ideas The Green–Ampt theory may be now generalized for the unsaturated zone. This theory is applicable in any homogeneous soil for θi ≠ 0. The centenary limitation of the Green–Ampt theory for horizontal infiltration has been solved. In past work, an analytic solution of the Boltzmann transform as a function of matric potential was proposed to estimate the soil water content profile for horizontal water infiltration into porous media. However, it could only be successfully described for sands, but with singularity at position x = 0. Later, others introduced the concept of air‐entry pressure to divide the soil water retention curve into saturated and unsaturated domains to provide an exact solution of the Bruce and Klute equation, with no restrictions, while assuming the initial soil water content to be zero before the infiltration process. The problem remained that the above‐mentioned analytical solution was limited to sands, while the Bruce‐ and Klute‐based approach was limited to zero water content at the beginning. This study was based on both previous studies, and the objective was to develop a solution that works for all soil types and does not depend on zero initial soil moisture content. As a result, an alternative solution is presented that generalizes the centenary theory of Green and Ampt for any homogeneous soil.

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Section: Theoretical Considerationsmentioning

confidence: 99%

“…Many equations are part of the theory of Barry et al (2010), but regarding those that define the water content profile at the WF of horizontal infiltration, we have:

λ = λ_{normala} {(\frac{h - h_{normalb}}{h_{normala} - h_{normalb}})}^{α}, λ > λ_{normala}

where h is the matric potential at the WF profile, λ a is the value of the Boltzmann's transformation variable (λ) for h = h a , and h b and α are the fitting parameters, wherein:

h_{normalb} = h_{normala} (1 - α)

In the theory of Barry et al (2010), the parameter α in Eq. [1] can assume any value, while in the theory of similarity the value of λ is defined by Eq.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Generalization of the Green–Ampt Theory for Horizontal Infiltration into Homogeneous Soils

Prevedello

Armindo

2016

Vadose Zone Journal

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“…It must be highlighted that Eq. (6) is valid solely for the unsaturated zone; an analytical solution for the Richards' equation without gravity including the saturated zone was given recently by Barry et al (2010). The dependence of h with θ was obtained using the empirical relationship given by van Genutchen (1980):…”

Section: Hydraulic Descriptionmentioning

confidence: 99%

Modelling of acid mine drainage (AMD) in columns

Souza

Mansur

2011

Braz. J. Chem. Eng.

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-A model is proposed in this paper to describe the generation of acid mine drainage (AMD) in leaching columns. The model considers: (i) Water flow through the column, which is calculated using the 1-D analytic solution of the Richards' equation assuming the existence of a similarity relationship between the water retention function and the water content profiles at a given time; and (ii) Pyrite oxidation weighted by microbiological effects occurring in spherical particles according to the shrinking core model. Mass balances of oxygen and pyrite were derived in order to evaluate the intrinsic oxidation rate and the pyrite fraction reacted with time and column position. The model was used to simulate a six month operation of a leaching column, which comprised successive weekly cycles of dry and wet periods. Simulation results demonstrated that AMD generation is strongly affected by the presence of microorganisms. A relative deviation of 5% between simulation and experimental data was obtained.

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Counter-current imbibition and non-linear diffusion in fractured porous media: Analysis of early- and late-time regimes and application to inter-porosity flux

Douarche

Braconnier

Momeni

et al. 2022

Advances in Water Resources

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Extension of a Recent Method for Obtaining Exact Solutions of the Bruce and Klute Equation

Abstract: Fig. 2. Normalized moisture content θ/θ s as a function of the normalized Boltzmann variable ϕ/ϕ a (solid line). Th e dashes show θ/θ s = 0.

Cited by 6 publications

References 6 publications

Generalization of the Green–Ampt Theory for Horizontal Infiltration into Homogeneous Soils

Generalization of the Green–Ampt Theory for Horizontal Infiltration into Homogeneous Soils

Modelling of acid mine drainage (AMD) in columns

Counter-current imbibition and non-linear diffusion in fractured porous media: Analysis of early- and late-time regimes and application to inter-porosity flux

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