Discrete Element Study of Particle Size Distribution Shape Governing Critical State Behavior of Granular Material

Jiang, Mingdong; Barreto, Daniel; Ding, Zhi; Yang, Kaifang

Abstract

Granular soil is a porous medium composed of particles with different sizes and self-similar structures, exhibiting fractal characteristics. It is well established that variations in these fractal properties, such as particle size distribution (PSD), significantly influence the mechanical behavior of the soil. In this paper, a three-dimensional (3D) Discrete Element Method (DEM) is applied to study the mechanical and critical-state behavior of the idealized granular assemblages, in which various PSD shape parameters are considered, including the coefficient of uniformity (Cu), the coefficient of curvature (Cc), and the coefficient of size span (Cs). In addition, the same PSDs but with different mean particle sizes (D50) are also employed in the numerical simulations to examine the particle size effect on the mechanical behavior of the granular media. Numerical triaxial tests are carried out by imposing axial compression under constant mean effective pressure conditions. A unique critical-state stress ratio in p′-q space is observed, indicating that the critical friction angle is independent of the shape of the PSD. However, in the e-p′ plane, the critical state line (CSL) shifts downward and rotates counterclockwise, as the grading becomes more widely distributed, i.e., the increasing coefficient of span (Cs). Additionally, a decrease in the coefficient of curvature (Cc) would also move the CSL downward but with negligible rotation. However, it is found that the variations in the mean particle size (D50) and coefficient of uniformity (Cu) do not affect the position of the CSL in the e-p′ plane. The numerical findings may shed some light on the development of constitutive models of sand that undergo variations in the grading due to crushing and erosion, and address fractal problems related to micro-mechanics in soils.

Citation

Jiang, M., Barreto, D., Ding, Z., & Yang, K. (2025). Discrete Element Study of Particle Size Distribution Shape Governing Critical State Behavior of Granular Material. Fractal and Fractional, 9(1), Article 26. https://doi.org/10.3390/fractalfract9010026

• Journal Article Type: Article
• Acceptance Date: Jan 3, 2025
• Online Publication Date: Jan 6, 2025
• Publication Date: 2025
• Deposit Date: Jan 6, 2025
• Publicly Available Date: Jan 6, 2025
• Journal: Fractal and Fractional
• Electronic ISSN: 2504-3110
• Publisher: MDPI
• Peer Reviewed: Peer Reviewed
• Volume: 9
• Issue: 1
• Article Number: 26
• DOI: https://doi.org/10.3390/fractalfract9010026
• Keywords: particle size distribution; granular material; discrete element method; critical state theory