Beyond Surface Modulus: Shape-Aware Crack-Index Assessment of Mass Concrete Foundations Under Early-Age Thermal Stress

Early-age thermal cracking is a major serviceability and durability concern in mass-concrete foundations, especially under hot-weather construction conditions. Although surface modulus is widely used as a massivity descriptor, its ability to predict stress-based cracking risk across different member geometries remains unclear. This study presents a coupled MIDAS Civil three-dimensional hydration-heat and thermal-stress workflow with Python-based post-processing to evaluate the peak core temperature T_max,core, the maximum core-to-surface temperature differential ΔT_cs,max, and the thermal crack index I_cr,min for eight representative foundation geometries. For the 3 × 3 × 3 m reference block, the workflow predicts T_max,core = 65.2 °C, ΔT_cs,max = 26.2 °C, and I_cr,min = 1.79 (limit-cracking band). Surface modulus alone is an unreliable predictor across mixed geometries, with R² ≤ 0.23 for all three responses. Response-specific models improve accuracy substantially: T_max,core follows a d_min-quadratic relation (R² = 0.94), ΔT_cs,max a combined M–d_min model (R² = 0.87), and I_cr,min an inverse thermal-differential relation (R² = 0.95). Surface modulus remains suitable for preliminary massivity screening of cubic foundations, but non-cubic geometries require explicit shape-aware three-dimensional assessment for design-level crack control. Among controllable inputs, placement temperature and cement content dominate thermal risk, a 20 °C rise in placement temperature increases T_max,core by 19.1 °C, while the convection coefficient and foundation geometry govern ΔT_cs,max and I_cr,min; all relationships are condition-specific screening tools requiring recalibration beyond the stated parametric range.