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Modeling of Particle Migration in Porous Media: Application to Soil Suffusion

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Abstract

The suffusion phenomenon occurs when fine soil particles are detached by seepage flow and transported away from the matrix. This process is one of the main causes of failure of hydraulic structures and road embankments. This study aimed to build a numerical model for simulating the suffusion within a porous medium. This model combines a flow law and an erosion equation related to the evolution of soil porosity. In addition, the dispersion and the deposition kinetics of eroded particles were combined with detachability process. The equations describe the evolution of the instantaneous concentration of the fluidized solid and the variation of eroded mass. Sensitivity analysis allows highlighting the influence of the different parameters on the suffusion, particularly that deposition kinetics starts acting only below a given hydraulic gradient and beyond a sample length. The simulation results indicate that the suffusion process is strongly related to hydraulic conditions, physical soil characteristics and pore water chemicals. The adjustment of numerical results with experimental data from laboratory tests provides a good agreement. This model is devoted to investigate conditions leading hydraulic works to avoid suffering suffusion.

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Abbreviations

C :

Volume concentration of eroded particles (volume fraction)

\(C_k\) :

Constant in Kozeny–Carman equation

\(C_\mathrm{me}\) :

Maximum erodibility coefficient

D :

Dispersion coefficient (\(\hbox {m}^2\,\hbox {s}^{-1}\))

\(f_0\) :

Initial fine fraction

\(f_\mathrm{max}\) :

Maximum erodible mass fraction

gradH:

Hydraulic gradient (m m\(^{-1}\))

H :

Hydraulic head (m)

j :

Mass flow rate from erosion, per unit volume (\(\hbox {kg\,m}^{-3}\,\hbox {s}^{-1}\))

k :

Hydraulic permeability (m s\(^{-1}\))

K :

Intrinsic permeability (\(\hbox {m}^{2}\))

\(k_{d0}\) :

Initial deposition kinetic coefficient (\(\hbox {s}^{-1}\))

\(m_0\) :

Initial fine mass (mg)

m :

Eroded cumulative mass (mg)

\(m/m_0\) :

Eroded mass fraction (relative cumulative mass)

q :

Darcy velocity (\(\hbox {m\,s}^{-1}\))

\(R_\mathrm{fine}\) :

Volume fraction of erodible fine fraction

u :

Pore velocity (m s\(^{-1}\))

\(u_\mathrm{fs}\) :

Velocity of fluidized solid (eroded fine particles) (m s\(^{-1}\))

\(\alpha \) :

Dispersivity coefficient (m)

\( \gamma _w\) :

Specific weight of water (\(\hbox {N\,m}^{-3}\))

\(\mu \) :

Instantaneous dynamic viscosity of water (\(\hbox {kg\,m}^{-1}\,\hbox {s}^{-1}\))

\( \mu _0\) :

Initial dynamic viscosity of water (\(\hbox {kg\,m}^{-1}\,\hbox {s}^{-1}\))

\(\rho _\mathrm{f}\) :

Fluid density (\(\hbox {kg\,m}^{-3}\))

\(\rho _\mathrm{s}\) :

Solid density (\(\hbox {kg\,m}^{-3}\))

\(\lambda \) :

Empirical coefficient of erosion (\(\hbox {m}^{-1}\))

\(\phi \) :

Instantaneous porosity of soil

\(\phi _0\) :

Initial porosity of soil

\(\Delta t\) :

Time increment

\(\Delta x\) :

Space increment

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Acknowledgments

The research described in this paper was realized in the laboratory Waves and Complex Media Laboratory, FRE 3102 CNRS, University of Le Havre—France

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Authors and Affiliations

  1. University of Sciences and Technology of Oran “Mohammed Boudiaf”, Oran, Algeria

    Ahmed Chetti

  2. Waves and Complex Media Laboratory, FRE 3102 CNRS, University of Le Havre, Le Havre, France

    Ahmed Benamar

  3. Modeling and Computational Methods Laboratory, University of Saida, Saida, Algeria

    Abdelkrim Hazzab

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  1. Ahmed Chetti
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  2. Ahmed Benamar
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  3. Abdelkrim Hazzab
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Correspondence to Ahmed Chetti.

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Chetti, A., Benamar, A. & Hazzab, A. Modeling of Particle Migration in Porous Media: Application to Soil Suffusion. Transp Porous Med 113, 591–606 (2016). https://doi.org/10.1007/s11242-016-0714-y

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