Constitutive modelling of foamed concrete under true-triaxial compression based on statistical damage theory

Foamed concrete possesses a failure mode distinct from the brittle failure of ordinary concrete, with its highly porous skeleton leading to progressive air-void collapse, local crushing, and subsequent densification. Therefore, constitutive models developed for dense brittle concrete cannot be directly transferred to foamed concrete. A statistical damage constitutive model was developed for foamed concrete under true-triaxial compression by combining continuum damage mechanics with statistical strength theory. The mesoscale collapse threshold was described by a two-parameter Weibull distribution, and the Drucker–Prager and Mogi-Coulomb criteria were introduced as alternative stress-state functions to account for true-triaxial stress effects. Model parameters were calibrated using a genetic algorithm and compared with experimental stress–strain curves of foamed concrete with wet densities of 600 and 1000 kg/m³. The proposed model reproduced the main features of the tested responses, including the peak, post-peak stress drop, and residual plateau. The Drucker–Prager-based formulation showed slightly lower average fitting errors within the present dataset, particularly for the 600 kg/m³ series, while both criteria captured the main stress–strain characteristics after calibration. Parametric analysis clarified the roles of the Weibull shape factor, Weibull scale factor, and residual stress parameter in controlling the curve shape. This study advances constitutive modelling of foamed concrete by establishing a mesoscale framework for interpreting true-triaxial stress–strain responses associated with pore collapse and skeleton compaction.