Structural hierarchy and mechanical properties of rocks. Part I. Structural hierarchy and viscosity

Rock masses have a complex structural hierarchy that strongly affects their physical and mechanical properties. The present paper studies the relationship between viscosity and the structural hierarchy. The study shows that different structural levels correspond to different viscosities and characteristic strain rates. High viscosity and low strain rate correspond to the macroscopic structural level, while the meso- and microlevels are characterized by low viscosity and high strain rate. Generally, with an increase of external actions the strain rate grows as well, deformation and fracture gradually cover the meso- and microlevels, and viscosity smoothly decreases. At a high strain rate viscosity is inversely proportional to strain rate. Based on the analysis of viscosity at different structural levels, we propose an asymptotic intermediate approximation of viscosity at different levels. In the limiting cases, the approximation formula becomes valid for the continental structural level and microlevel. This suggests that the approximation is adequate for the description of viscosity at different structural levels.