Application of fractal dimensions in predicting the drying shrinkage of metakaolin-based geopolymers

This study develops a fractal dimension-based model for predicting drying shrinkage in metakaolin-based geopolymers (MKBGs) through mercury intrusion porosimetry and thermodynamic analysis. The micropore surface fractal dimension Ds2 (pore diameter ≤30 nm, dimension range: 2.27–2.97) demonstrates significant correlations with pore structure parameters: strong negative relationships with porosity (R2 = −0.8923), sub-30-nm pore volume (R2 = −0.8293), and most probable pore size (R2 = −0.7120), alongside a moderate positive correlation with specific surface area (R2 = 0.5892). Ds2 further serves as a robust indicator of macroscopic properties, exhibiting a linear correlation with compressive strength (R2 = 0.9392) and effectively characterizing pore connectivity through chloride migration coefficients (R2 = 0.7388) and internal humidity decay kinetics (daily R2 > 0.9 at 50 % RH). By establishing a Ds2-dependent humidity evolution model (R2 > 0.95), we achieve drying shrinkage prediction with minimal deviations (e.g., 481 με for 40 % activator concentration). This approach provides a practical framework for geopolymer durability optimization while circumventing complex humidity measurements.