Fractal Dimension Evolution in Dense Granular Flows: Insights from Rotary Shear Experiments

Understanding particle fragmentation and its resulting particle-size distribution is crucial for interpreting shear zone behavior in geological processes like faulting and landslides, especially under high-stress conditions. This study uses the 3-D fractal dimension (D3) to measure particle-size distribution and potential self-similarity. While previous models predict D3 values around 2.58 or 3.0, field data show significant variation. We conducted rotary shear experiments to investigate how D3 evolves with shear displacement under different normal stresses, velocities, and mineral compositions. Our results show that D3 increases monotonically with shear displacement, converging to an ultimate value highly dependent on mineral composition, but much less affected by normal stress and shear velocity. A modified large-strain model incorporating size-dependent grain-breakage probability is proposed, which explains the divergence of D3 from previous predictions. This model highlights the complexity of particle fragmentation in dense grain flows and provides a possible explanation for the high but variable D3 observed in natural shear zones. Further, we acknowledge that additional mechanisms, such as abrasion and grinding, can further contribute to particle size reduction. This study offers valuable insights into the dynamics of particle fragmentation in geological shear zones.