Shear Mechanism and Optimal Estimation of the Fractal Dimension of Glass Bead-Simulated Sand

Abstract

Spherical glass beads weaken the influences of particle morphology, surface properties, and microscopic fabric on shear strength, which is significant for revealing the relationship between macroscopic particle friction mechanisms and the particle size distribution of sand. This paper explores the shear mechanical properties of glass beads with different particle size ratios under different confining pressures. It obtains the particle size ratio and fractal dimension D through an optimal mechanical response. Simultaneously, we explore the range of the fractal dimension D under well-graded conditions. The test results show that the strain-softening degree of Rs is more obvious under a highly effective confining pressure, and the strain-softening degree of Rs can reach 0.669 when the average particle size d¯ is 0.5 mm. The changes in the normalized modulus ratio Eu/Eu50 indicate that the particle ratio and arrangement are the fundamental reasons for the different macroscopic shear behaviors of particles. The range of the peak effective internal friction angle φ is 23 °~35 °, and it first increases and then decreases with the increase in the effective confining pressure. As the average particle size increases, the peak stress ratio MFL and the peak effective internal friction angle φ first increase and then decrease, and both can be expressed using the Gaussian function. The range of the fractal dimension D for well-graded particles is 1.873 to 2.612, and the corresponding average particle size d¯ ranges from 0.433 to 0.598. Under the optimal mechanical properties of glass beads, the particle size ratio of 0.25 mm to 0.75 mm is 23:27, and the fractal dimension D is 2.368. The study results provide a reference for exploring friction mechanics mechanisms and the optimal particle size distributions of isotropic sand.