SCIENCE CHINA Technological Sciences, Volume 63 , Issue 5 : 777-790(2020) https://doi.org/10.1007/s11431-019-9598-2

Study on meso-mechanical behavior of sand based on its 2D geometrical model

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  • ReceivedJun 3, 2019
  • AcceptedJul 29, 2019
  • PublishedJan 2, 2020


A comprehensive study on the meso-mechanical behaviors of sand with its 2D geometrical models was presented in this study. Based on the 2D geometrical models’ database of sand particles, quantitative analysis on the geometrical characteristics of the studied sand particles was performed. A new clump generation algorithm based on fewer multiple overlapping circles was provided to accurately model the shape of sand particles, and was used to build the discrete element method (DEM) numerical model of the sand sample for DEM biaxial tests. The macro- and meso-mechanical behaviors of the studied sand samples were systematically analyzed. Deformation was mainly localized in a X-shaped shear zone, in which the particles experienced large displacements and rotations. Development of stress-induced anisotropy in particle and void orientations, as well as the mesoscopic fabric, was significant during the shearing process. Continuous collapse, generation, reduction, and extension of force chains occurred during the shearing process, especially after the peak stress was reached. This led to the fluctuations in the evolution of deviatoric stress and volumetric strain at macroscale, as well as the fabric anisotropy at mesoscale.

Funded by

the National Key Research and Development Program during the 13th Five-Year Plan of China(Grant,No.,2017YFC0805406)

and the Natural Science Foundation of China(Grant,Nos.,51879142,51679123,&,51479095)


This work was supported by the National Key Research and Development Program during the 13th Five-Year Plan of China (Grant No. 2017YFC0805406), and the National Natural Science Foundation of China (Grant Nos. 51879142, 51679123 & 51479095).


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  • Figure 1

    (Color online) Illustration of particle morphology terminology modified after Barrett (1980).

  • Figure 2

    (Color online) Sand particles used in study from Fujian province, China.

  • Figure 3

    (Color online) Shape characteristics of sand particles. (a) Relationship among particle length, aspect ratio and roundness; (b) relationship between aspect ratio and roundness.

  • Figure 4

    (Color online) Fourier descriptors of sand particles. (a) Relationship among aspect ratio, shape factor and texture factor; (b) static analysis of angularity factor and texture factor.

  • Figure 5

    (Color online) Relationship of the morphological descriptors with the length of the sand particles in statistical average.

  • Figure 6

    (Color online) Discretizing of a 2D particle. (a) Particle discretization; (b) generating reference circles.

  • Figure 7

    Flowchart of the MOC algorithm.

  • Figure 8

    (Color online) MOC clump model of a real particle.

  • Figure 9

    (Color online) DEM biaxial model of the sand.

  • Figure 10

    (Color online) Comparisons of the macro mechanical behaviors between the laboratory triaxial tests and DEM biaxial tests of the sand sample (in (a) and (b), the dots are the laboratory triaxial tests, and lines are the DEM numerical tests). (a) Deviatoric stress-axial strain; (b) volumetric strain-axial strain; (c) p-q curves.

  • Figure 11

    (Color online) Localization of the sample in meso-scale during the shearing process. (a) Displacement of particles; (b) rotation of particles (positive if counterclockwise); (c) porosity increment in meso-scale (positive if dilation).

  • Figure 12

    (Color online) Calculation of the particle’s area based on Voronoi cell.

  • Figure 13

    (Color online) Spatial orientation schematic of the particles and voids.

  • Figure 14

    (Color online) Evolution of the anisotropic behaviors of the particles and voids. (a) Principal direction of anisotropy; (b) coefficient of anisotropy; (c) polar distribution of the average number of the principle axial direction.

  • Figure 15

    (Color online) Development of the anisotropy parameters of contact normal, average normal force and average tangential force. (a) Principal direction of anisotropy; (b) coefficient of anisotropy; (c) polar distribution of the average normal contact force and average tangential contact force under confining stress 200 kPa.

  • Figure 16

    (Color online) Development of the force chain of the sample under different confining stress (the colors and the thickness of the chains show the magnitude of the normal contact force with unit of N).

  • Figure 17

    (Color online) Development of the average contact number of particles.

  • Table 1   Statistical analysis of the morphology characteristics of sand particles



    Standard deviation



    Aspect ratio










    Shape factor





    Angularity factor





    Texture factor





  • Table 2   Meso-mechanical parameters of materials used in DEM biaxial test





    Density of particle (kg/m3)


    Elastic modulus of particle contact, Ec (GPa)


    Poisson’s ratio of particle contact, v


    Friction angle of particle contact (°)



    Density of particle (kg/m3)


    Elastic modulus of particle contact, Ec (GPa)


    Poisson’s ratio of particle contact, v


    Friction angle of particle contact (°)



    Density (kg/m3)


    Elastic modulus of contact, Ec (GPa)


    Poisson’s ratio of contact, v


    Friction angle of contact (°)


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