Drainage equations and non-Darcian modelling in coarse porous media or geosynthetic materials

Bordier, C.; Zimmer, Daniel

doi:10.1016/s0022-1694(00)00151-7

Cited by 115 publications

(57 citation statements)

References 8 publications

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“…From the Sidiropoulou et al (2007) dataset, the data for granular sands, gravel and round river gravel by Ahmed and Sunada (1969) (data by Ahmed); Ranganadha Rao and Suresh (1970), Ahmed and Sunada (1969) (data by Ahmed), Ranganadha Rao and Suresh (1970), Tyagi and Todd (1970) and Arbhabhirama and Dinoy (1973). 2) Data from Sidiropoulou et al (2007) by Ahmed and Sunada (1969), Venkataraman and Rao (1998) and Bordier and Zimmer (2000) Tyagi and Todd (1970) and Arbhabhirama and Dinoy (1973) correspond well. Sedghi-Asl et al (2014) and the rest of the dataset of Sidiropoulou et al (2007) (Ahmed and Sunada 1969;Venkataraman and Rao 1998;Bordier and Zimmer 2000), which mainly consists of glass spheres and crystalline rock, underestimate b for a given a, compared to our dataset.…”

Section: Comparison With the Literaturementioning

confidence: 81%

“…2) Data from Sidiropoulou et al (2007) by Ahmed and Sunada (1969), Venkataraman and Rao (1998) and Bordier and Zimmer (2000) Tyagi and Todd (1970) and Arbhabhirama and Dinoy (1973) correspond well. Sedghi-Asl et al (2014) and the rest of the dataset of Sidiropoulou et al (2007) (Ahmed and Sunada 1969;Venkataraman and Rao 1998;Bordier and Zimmer 2000), which mainly consists of glass spheres and crystalline rock, underestimate b for a given a, compared to our dataset. Similar to the current study, the effect of the grain size distribution on nonlinear flow behavior was shown by Moutsopoulos et al (2009) …”

Section: Comparison With the Literaturementioning

confidence: 81%

“…For example, the Izbash equation'[initially proposed by Forchheimer (1901)], which is a nonlinear power law function, is widely used to model the non-Darcy flow (e.g., Bordier and Zimmer 2000;Wen et al 2013). Despite the experimental validity of the Izbash equation, it lacks any physical base (Bordier and Zimmer 2000).…”

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confidence: 99%

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The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

et al. 2017

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The current study provides new experimental data on nonlinear flow behavior in various uniformly graded granular materials (20 samples) ranging from medium sands (d 50 > 0.39 mm) to gravel (d 50 = 6.3 mm). Generally, theoretical equations relate the Forchheimer parameters a and b to the porosity, as well as the characteristic pore length, which is assumed to be the median grain size (d 50 ) of the porous medium. However, numerical and experimental studies show that flow resistance in porous media is largely determined by the geometry of the pore structure. In this study, the effect of the grain size distribution was analyzed using subangular-subrounded sands and approximately equal compaction grades. We have used a reference dataset of 11 uniformly graded filter sands. Mixtures of filter sands were used to obtain a slightly more well-graded composite sand (increased C u values by a factor of 1.19 up to 2.32) with respect to its associated reference sand at equal median grain size (d 50 ) and porosity. For all composite sands, the observed flow resistance was higher than in the corresponding reference sand at equal d 50 , resulting in increased a coefficients by factors up to 1.68, as well as increased b coefficients by factors up to 1.44. A modified Ergun relationship with Ergun constants of 139.1 for A and 2.2 for B, as well as the use of d m − σ as characteristic pore length predicted the coefficients a and b accurately.

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Section: Comparison With the Literaturementioning

confidence: 81%

Section: Comparison With the Literaturementioning

confidence: 81%

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The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

et al. 2017

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“…The aim of this work is to verify the ability of Stephenson's formula to reproduce the water profile in large porous media. The flow regime in a riprap is generally turbulent, which limits Darcy's relation (Bordier and Zimmer, 2000). It is then necessary to analyze the hydrodynamics in an experimental channel.…”

Section: Introductionmentioning

confidence: 99%

An analytical model for water profile calculations in free surface flows through rockfills

Soualmia

Jouini

Masbernat

et al. 2015

jtam

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In this study, an analytical model to resolve the water profiles equation of free surface flows through riprap has been developed. This model is based on Stephenson's relation to determine the head loss for different flow states in order to see its ability to reproduce the water profiles. This analytical model has been applied to experimental series realized in a rectangular channel built at the National Agronomic Institute of Tunisia (INAT) in collaboration with engineering consultants of the firm MECATER and in partnership with the INP Toulouse. MECATER is interested in these flows within the framework of a project with the nickel company SLN of ERAMET group in New Caledonia, concerning the protection of mining sterols against water flows at high mountains.

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“…However, many evidences from the laboratory and field experiments show that this linear law may be invalid in some situations, especially when the groundwater flow velocity is sufficiently high or sufficiently low, where non-Darcian flow prevails (Basak, 1977;Bordier and Zimmer, 2000;Engelund, 1953;Forchheimer, 1901;Izbash, 1931;Liu et al, 2012;Soni et al, 1978).…”

Section: Introductionmentioning

confidence: 99%

Forchheimer flow to a well-considering time-dependent critical radius

Wang

Zhan

Tang

2014

Hydrol. Earth Syst. Sci.

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Abstract. Previous studies on the non-Darcian flow into a pumping well assumed that critical radius (R CD ) was a constant or infinity, where R CD represents the location of the interface between the non-Darcian flow region and Darcian flow region. In this study, a two-region model considering time-dependent R CD was established, where the non-Darcian flow was described by the Forchheimer equation. A new iteration method was proposed to estimate R CD based on the finite-difference method. The results showed that R CD increased with time until reaching the quasi steady-state flow, and the asymptotic value of R CD only depended on the critical specific discharge beyond which flow became nonDarcian. A larger inertial force would reduce the change rate of R CD with time, and resulted in a smaller R CD at a specific time during the transient flow. The difference between the new solution and previous solutions were obvious in the early pumping stage. The new solution agreed very well with the solution of the previous two-region model with a constant R CD under quasi steady flow. It agreed with the solution of the fully Darcian flow model in the Darcian flow region.

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Drainage equations and non-Darcian modelling in coarse porous media or geosynthetic materials

Cited by 115 publications

References 8 publications

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

An analytical model for water profile calculations in free surface flows through rockfills

Forchheimer flow to a well-considering time-dependent critical radius

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