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• The influences of moisture variations on ion transport and physical crystallization were discussed. • The respective contributions of chemical and physical attack to crystallization pressure were distinguished. • The deterioration in concrete performance was considered under the combined impacts of external sulfate attack and drying–wetting cycles. • A transport-chemical-physical–mechanical model was developed to evaluate and predict damage progression to concrete. When coupled with drying–wetting cycles, the deterioration process of concrete subjected to external sulfate attack (ESA) is significantly accelerated. The impact of moisture variations on ion transport was considered to establish a mass conservation equation with pore solution concentration as the variable. The contributions of chemical and physical attack to crystallization pressure were distinguished, and a bulk modulus reduction function was introduced to ascertain the stiffness deterioration. An ESA model was proposed and verified by comparing it to published experimental data, which could accurately predict the deterioration process of concrete under ESA and drying–wetting cycles. [ABSTRACT FROM AUTHOR]