Time-Dependent Porosity–Fractal Coupling and Brittleness Evolution in Cementitious Materials with Slag Dosage Variation: From Pore Geometry to Strength

Understanding how pore-system geometry governs mechanical performance remains essential for designing slag-blended cementitious materials. This study investigates the time-dependent coupling between porosity P and fractal dimension D and its implications for strength development and brittleness evolution in cementitious materials with slag dosage variation (0–40%). Compressive strength (f_c), flexural strength (f_f), the compressive-to-flexural strength ratio (f_c/f_f, used as a practical brittleness proxy), porosity (%), fractal dimension, and low-field nuclear magnetic resonance (LF-NMR) permeability (k, mD) were evaluated at 3, 7, and 28 days. Results reveal a pronounced age dependence in microstructure–property relationships. At 28 days, increasing slag dosage led to monotonic pore refinement and geometric reorganization, evidenced by reduced porosity (4.84% → 3.88%), increased fractal dimension (2.754 → 2.820), and decreased permeability (0.00025 → 0.00011 mD), accompanied by enhanced mechanical performance (47.73 → 49.33 MPa in f_c; 6.34 → 7.11 MPa in f_f) and reduced brittleness (f_c/f_f: 7.53 → 6.94). In contrast, a critical 7-day decoupling was observed: slag mixtures exhibited substantially lower porosity (≈5.42–5.69% vs. 7.07% for the reference) yet lower compressive strength (≈34.81–35.29 MPa vs. 38.65 MPa), indicating that porosity alone is insufficient to interpret early-age compressive capacity. Across ages, permeability and fractal trends highlight the role of pore-network connectivity and geometric complexity in governing transport resistance and fracture-related behavior. Overall, the findings demonstrate that a time-dependent porosity–fractal coupling framework provides a coherent pathway “from pore geometry to strength,” particularly for brittleness-relevant indices where geometric effects are amplified. © 2026 by the authors.