Evaluation of Small-Scale Damage Evolution in Uniaxial Compression Based on Damage Connectivity

ABSTRACT: Intact rock specimens exhibit multiple stages of deformation when subjected to unconfined compression. Crack initiation (CI) marks the onset of microcrack nucleation at low-stress levels (~%30-%50 of unconfined compressive strength (UCS)) while crack damage (CD) refers to the stage where cracks coalesce and interact, occurring near the ultimate strength of the rock (~%70-%90 of UCS). The processes of nucleation, interaction, and coalescence of cracks during the monotonic loading of intact rocks can be viewed through the lens of percolation theory, which assesses the connectivity of elements within a network system and is independent of boundary conditions. However, a gap remains in understanding how percolation site and bond ratios evolve during loading and, specifically, the correlation of the percolation ratios with different stages of the damage such as CI and CD in different rock types. To address this, the present study investigates the evolution of the percolation ratios during loading in Stanstead granite (SG), Barre granite (BG), and Lyons sandstone (LS) under unconfined loading conditions. We utilized two-dimensional digital image correlation (2D-DIC) to evaluate damage development in individual regions of the specimens and then used percolation theory to quantify the connectedness of these damaged regions. The results reveal consistent percolation ratio values at CI and CD levels in BG and SG specimens, regardless of rock type. However, in LS specimens, the percolation ratios values were lower due to the heterogeneity and anisotropy of the LS specimens, which contrasts with the assumptions of percolation theory.