Evolution of Power-Law Particle-Size Distributions in Dense Grain-Flow Experiments

Abstract

Understanding particle fragmentation and its resulting particle-size distribution is essential for comprehending shear zone formation, structure, and frictional behavior in faults and landslides, particularly at high normal stresses. 3-D fractal dimension (D₃) is used as a measure of particle-size distribution, and for the potential self-similarity physics. Previous research suggests D₃ – 2.58 based on the “constrained comminution” model, or D3 = 3.00 considering large shear displacement. However, field data from rock avalanches reveal scattered D₃ that deviate from these predictions, possibly due to the neglection of the underlying fragmented physics, such as the particle-size-dependent fragmentation probability. Herein, we conducted rotary shear experiments to investigate the evolution of D₃ under varying normal stresses, velocities, and mineral compositions. Experimental results demonstrate that D₃ monotonically increases with shear displacement and converges to an ultimate value, significantly influenced by mineral composition but less affected by shear velocity and confining stress within the experimental conditions. A modified large-strain model that considered size-dependent grain-breakage probability was proposed, which may explain the observed divergence of D₃ from previous predictions. This model highlights the complex mechanisms involved in particle breakage within dense grain-flows, resulting in the high but scattered D₃ observed in natural shear zones. Furthermore, we recognize that additional mechanisms, such as abrasion and grinding, can contribute to the particle size reduction and influence the ultimate fractal dimension. This study provides valuable insights into the dynamics of particle fragmentation in shear zones and has implications for understanding various geological processes.