A diffusion–reaction–damage model for chloride transport in concrete under coupled sulfate–chloride attack

Chloride transport in concrete under coupled Cl - - SO 4 2- exposure is difficult to predict because ion diffusion, chemical reactions, and damage evolution occur simultaneously. A diffusion–reaction–damage model was therefore developed based on Fick’s second law, reaction kinetics, and expansion-induced cracking. A one-dimensional transient diffusion–reaction equation was used to describe sulfate ingress and the depletion of reactive aluminate phases. The expansion associated with AFt formation was related to crack-density evolution and subsequently incorporated into the effective Cl⁻ diffusion coefficient. The proposed model was validated using mixed chloride–sulfate exposure tests conducted at Cl⁻-SO₄²⁻ molar ratios of 0.2, 0.5, 0.7, and 1.0 over exposure periods of 30, 90, 180, 270, and 360 days. Within the investigated SO₄²⁻/Cl⁻ molar-ratio range of 0.2-1.0 and exposure periods of 30-360 d, increasing the sulfate concentration and exposure duration progressively advanced the sulfate penetration front and extended the reactive-aluminate-depleted zone into the concrete. The results show that higher sulfate concentrations and longer exposure durations increase sulfate penetration, accelerate aluminate depletion, and promote corrosion-product accumulation. The resulting expansion and cracking gradually extend into the concrete and enhance Cl⁻ transport. Beyond approximately 22.5 mm from the exposed surface, sulfate-induced effects diminished markedly, with C₃A consumption approaching zero. The predicted chloride profiles generally agree with the experimental results, although localized deviations occur within the 0–5 mm surface layer because of non-ideal surface mass transfer, chloride binding, and layered-sampling effects. The proposed model provides a mechanistic framework for durability assessment and service-life prediction of concrete structures exposed to complex saline environments.