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A DEM-based approach for modeling the evolution process of seepage-induced erosion in clayey sand

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Abstract

In this paper, a predictive model for simulating temporal behaviors of clayey sand during seepage-induced erosion has been developed by coupling discrete element method (DEM) with computational fluid dynamics (CFD). In this model, the particle–fluid coupling simulation is solved by a “fixed coarse-grid” scheme in 3D particle flow code (PFC3D), and the suffusion of clay matrix in the initiation of erosion is converted to a degradation process of bonding strength between particles according to a degradation law. The law is derived from the well-known shear stress threshold law dealing with soil internal erosion, which is based on two erosion parameters—the critical shear stress and the erosion coefficient. Then the degradation law is implemented in the CFD–DEM model via developing customized code using the Python language. The ability of the model to predict the interfacial erosion of soils is confirmed by two numerical tests. The results are seen to match the empirical criteria, such as revealing a clearly defined critical tangential shear stress, beyond which erosion occurs, and a positive correlation between the rate of erosion and the pressure gradient. It is believed that the numerical model is able to reproduce the time-dependent evolution process of seepage-induced erosion in clayey sand.

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Abbreviations

m :

Soil erosion velocity

H :

Erodibility factor

X :

Flow variable

\(k_{\text{er}}\) :

Coefficient of surface erosion

\(\varvec{\tau}\) :

Shear stress at the interface

\(\tau_{c}\) :

Threshold shear stress

b :

Exponent

\(\Delta P_{j}\) :

Pressure drop

n :

Cell porosity

\(x_{j} \;(j = 1,2,3) \,\) :

Cell size in three directions (m)

K :

Matrix permeability (m2)

d eff :

Effective diameter of particle (m)

S 0 :

Specific surface area (m2)

r i, r j, r k :

Particle radius

n b :

Number of particles in a cell

N :

Total number of particles in the model

n c :

Number of fluid cells

\(V_{{i\_{\text{overlop}}}}\) :

Volume of overlap between a ball and a fluid cell

\(\tau_{{{\text{cell}}\_i}}\) :

Tangential shear stress of the fluid cell i

\(M_{\text{clay}}\) :

Mass of clay matrix

\(M_{\text{grain}}\) :

Mass of grain matrix

\(\omega\) :

Clay–aggregate ratio

\(m_{{j\_{\text{clay}}}}\) :

Clay mass “occupied” by ball j

\(\lambda ,\lambda_{\text{coh}} ,\lambda_{\text{ten}}\) :

Coefficients of bonding strength

\(R_{j\_s}\) :

Shear strength of the bonds around ball j

\(R_{j\_t}\) :

Tensile strength of the bonds around ball j

\(C_{i}\) :

Cohesion of contact i

\(T_{i}\) :

Tensile strength of contact i

n j :

Contact number associated with ball j

n k :

Contact number associated with ball k

\(\beta\) :

The contact radius multiplier

S i :

Area of contact i

\(\tau_{j} ,\tau_{k}\) :

Shear stress at the surface of ball j and ball k

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 41672300, 41472245, 41602301, and 51622803), the Fundamental Research Funds for the Central Universities (No. 106112016CDJZR208804), and the China Postdoctoral Science Foundation (No. 2018M643414).

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Authors and Affiliations

  1. School of Civil Engineering, Chongqing University, Chongqing, 400045, China

    Dong Ming Gu, Han Long Liu, Wen Gang Zhang & Xue Cheng Gao

  2. National Joint Engineering Research Center of Geohazards Prevention in the Reservoir Areas, Chongqing, 400045, China

    Dong Ming Gu, Han Long Liu, Wen Gang Zhang & Xue Cheng Gao

  3. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400044, China

    Da Huang

  4. School of Civil and Transportation Engineering, Hebei University of Technology, Tianjin, 300401, China

    Da Huang

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  1. Dong Ming Gu
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Gu, D.M., Huang, D., Liu, H.L. et al. A DEM-based approach for modeling the evolution process of seepage-induced erosion in clayey sand. Acta Geotech. 14, 1629–1641 (2019). https://doi.org/10.1007/s11440-019-00848-0

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