Acta Geotechnica

, Volume 14, Issue 6, pp 1629–1641 | Cite as

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

  • Dong Ming Gu
  • Da HuangEmail author
  • Han Long Liu
  • Wen Gang Zhang
  • Xue Cheng Gao
Research Paper


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.


Coupling CFD–DEM Erosion law Soil erosion Time-dependent 

List of symbols


Soil erosion velocity


Erodibility factor


Flow variable


Coefficient of surface erosion


Shear stress at the interface


Threshold shear stress



\(\Delta P_{j}\)

Pressure drop


Cell porosity

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

Cell size in three directions (m)


Matrix permeability (m2)


Effective diameter of particle (m)


Specific surface area (m2)

ri, rj, rk

Particle radius


Number of particles in a cell


Total number of particles in the model


Number of fluid cells


Volume of overlap between a ball and a fluid cell


Tangential shear stress of the fluid cell i


Mass of clay matrix


Mass of grain matrix


Clay–aggregate ratio


Clay mass “occupied” by ball j

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

Coefficients of bonding strength


Shear strength of the bonds around ball j


Tensile strength of the bonds around ball j


Cohesion of contact i


Tensile strength of contact i


Contact number associated with ball j


Contact number associated with ball k


The contact radius multiplier


Area of contact i

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

Shear stress at the surface of ball j and ball k



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Civil EngineeringChongqing UniversityChongqingChina
  2. 2.National Joint Engineering Research Center of Geohazards Prevention in the Reservoir AreasChongqingChina
  3. 3.State Key Laboratory of Coal Mine Disaster Dynamics and ControlChongqing UniversityChongqingChina
  4. 4.School of Civil and Transportation EngineeringHebei University of TechnologyTianjinChina

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