SCIENCE CHINA Technological Sciences, Volume 63 , Issue 2 : 329-340(2020) https://doi.org/10.1007/s11431-018-9387-2

LEM-DEM coupling for slope stability analysis

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  • ReceivedMay 8, 2018
  • AcceptedNov 1, 2018
  • PublishedFeb 25, 2019


Slope stability analysis is a keen area of interest to researchers of geotechnical engineering and geological hazards. To date, the most popular approach applied in slope engineering design is the limit equilibrium method (LEM). However, for this method, some assumptions are required when obtaining the sliding force and the resistance force on the slide face. The discrete element method (DEM) presents an advantage in the calculation of the interaction forces between adjacent blocks without assumptions. This paper introduces a new slope stability analysis based on coupling of both approaches, herein referred to as LEM-DEM. The main LEM-DEM procedure is to transform the slice model of a slope in LEM into the DEM model and obtain the sliding force and the resistance force to calculate the factor of stability (Fos). The sensitivity analysis of the parameters in DEM, such as normal and shear stiffness, was conducted to illustrate that LEM-DEM suggests higher contact stiffness. A comparison between the Fos values in DEM and LEM-DEM was also conducted to indicate the rationality and advantages of LEM-DEM, especially for a gentle slope with a changing shear force direction in the slice model where the interslice forces in LEM are unreasonable. Furthermore, this study carried out a 3D landslide stability analysis extension, along with the results, for the proposed method.

Funded by

the National Natural Science Foundation of China(Grant,Nos.,51679123,51479095)


This work was supported by the National Natural Science Foundation of China (Grant Nos. 51679123, 51479095, 51879142).


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  • Figure 1

    The generation process of slices in 2D LEM-DEM.

  • Figure 2

    (Color online) The splitting method of slope in 3D LEM-DEM model.

  • Figure 3

    (Color online) The spatial topological relations of the slope surface and slide face.

  • Figure 4

    (Color online) Illustration of the treatment for one situation of boundary columns. (a) The slide face intersects with boundary column; (b) identification of the part inside the slide body; (c) the column after the removal of excess part.

  • Figure 5

    (Color online) Illustration of the boundary columns with different type.

  • Figure 6

    (Color online) Comparison of model before and after removal treatment. (a) Model before removal treatment; (b) model after removal treatment.

  • Figure 7

    The data transmission of LEM-DEM method.

  • Figure 8

    (Color online) The 2D model of a slope.

  • Figure 9

    (Color online) The influence of contact stiffness (Kn, Kn/Ks) on Fos. (a) Original shear strength of slide face; (b) reinforced shear strength of slide face.

  • Figure 10

    (Color online) The influence of the reinforcement of slide face’s shear strength parameters during the calculation of contact forces in DEM simulation on Fos.

  • Figure 11

    (Color online) Slice model with different slice width. (a) Slice width=1 m; (b) slice width=10 m.

  • Figure 12

    (Color online) Influence of the slice width on Fos.

  • Figure 13

    (Color online) Contact forces on the slide face of each slice. (a) Normal force; (b) shear force.

  • Figure 14

    (Color online) Interaction forces between adjacent slices (the positive direction of shear force is defined as clockwise). (a) Shear force; (b) normal force.

  • Figure 15

    (Color online) Distribution of Fos based on LEM-DEM method.

  • Figure 16

    (Color online) An example of gentle slope with 1.0% gradient.

  • Figure 17

    (Color online) The shear forces on the slide face of the slope in Figure 16 with different methods (the positive direction of the shear force is defined as rightward).

  • Figure 18

    (Color online) The FEM-DEM computing model of slope model of Figure 8.

  • Figure 19

    (Color online) Contact force on the slide face of each slice. (a) Shear force on the slide surface; (b) normal force on the slide surface.

  • Figure 20

    (Color online) 3D model and the shear forces distribution on the slide face of the Bu-Le landslide. (a) 3D landslide model; (b) shear forces distribution on the slide face.

  • Figure 21

    (Color online) Distributions of shear force, normal force and Fos of each slice of the Bu-Le landslide. (a) Shear force; (b) normal force; (c) Fos.

  • Table 1   All possible types of 3D block of slice model

    Number of special node (node outside lanslide body)

    Special node type



    Inside slide body

    triangular prism block


    Right-angle node

    Pentahedron block

    Acute-angle node

    Obtuse-angle node


    Right-angle node

    Tetrahedron block

    Acute-angle node

    Obtuse-angle node


    Outside slide body

    Total types


  • Table 2   Main characteristics of common LE methods


    Equilibrium condition satisfied




    Inter-slice forces can be ignored

    Bishop simplified

    Vertical and overall moment

    Side forces are horizontal

    Janbu simplified

    Vertical and horizontal

    Side forces are horizontal


    Vertical, horizontal and overall moment

    Inter-slice forces are parallel and normal force acts at the center of the base of the slice

    Morgenstern & Price’s

    Vertical, horizontal and overall moment

    Inter-slice shear force is related to the inter-slice normal force by X/E =λf(x)

  • Table 3   Results comparison of the gentle slope based onLEM and LEM-DEM


    Resistant force (kN)

    Slide force (kN)






    Morgenstern & Price








  • Table 4   The Fos of Bule landslide based on different methods


    Resistant force (1011 kN)

    Sliding force (1011 kN)











    3D LEM









    2D LEM









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