## 1 Introduction  
Service life in PSC (prestressed concrete) and RC (reinforced concrete) structures is very important for securing the performance of the structures during their use period, and each country plans these structures with consideration of the target performance and intended service life [1, 2]. Concrete is a porous construction material, which partially permits the transport of moisture and harmful ions, and concrete structures have been exposed to various deterioration environments. In the deterioration of chloride attack and carbonation, embedded steel corrosion is initiated and accelerated through penetrated chloride ions and carbon dioxide from outside, so they are considered as major deterioration in each country [3, 4, 5]. Particularly, these two deterioration mechanisms have clear critical conditions since they accelerate reinforcement corrosion, and the service life can be evaluated or determined based on the critical threshold, such as critical chloride content, which initiates corrosion in outer steel and carbonation depth, which exceeds the cover depth. In the case of freezing-thawing action and chemical erosion for concrete, which cause the decomposition of the cement matrix, concrete strength and porosity play an important role in resistance to these deteriorations. In particular, chemical erosion, which is mainly caused by sulfate ions, leads to the penetration of sulfate ions, expansion of cement hydrates, micro cracking in the pore structure, and acceleration of deterioration. Sulfate ions from outside react with the cement hydrates to produce gypsum and ettringite, which results in the swelling and disintegration of the pore structure [6; 7; 8]. Many studies have been performed on these reactions, and various research results have been reported on deterioration modeling using thermodynamic equations, strength degradation modeling, and combined deterioration with freeze-thawing action [9; 10; 11]. For chloride attack and carbonation, many studies have been proposed for evaluating service life from semi-empirical models with experimental parameters to thermodynamic models considering moisture transport and ion reactions with absorption [3; 5; 12; 13; 14]; however, regarding sulfate attack, a clear model has not been adopted for international codes or specification. It is very difficult to quantify the deterioration in the design stage since the deteriorated concrete depth and sulfate diffusion change simultaneously, and the complex reactions between the cement hydrates and the sulfuric acid ions in liquid and gaseous phases occur with micro cracking at the same time [3; 5; 7; 11]. For service life design at the meso-level, multilayer diffusion theory and the linear degradation depth method are widely used [15; 16; 17], where the diffusion coefficient and cover depth are recognized as key parameters. In the former theory [15; 16], the time-dependent diffusion of sulfate ions was assumed, and the intruded sulfate ions were compared with the critical concentration, like the evaluation technique for chloride penetration based on the skin depth theory [18]. In the latter theory [5; 17], it is assumed that the deterioration depth due to sulfate ions linearly increases with the exposure period and diffusion coefficient, considering the reaction of cement component (Al\({}_{2}\)O\({}_{3}\)) and sulfate concentration. In previous studies and tests [6; 7], several models were proposed with regression analysis of the test parameters, but it is difficult to apply them to various concrete mixtures and exposure conditions. The ion transport is greatly affected by exterior conditions and the deterioration depth due to sulfate ions and also varies with the temperature. The diffusion behavior trend with increasing temperature is known to follow the Arrhenius Law, and the variation in the measured diffusion coefficient significantly increases as well, which yields a change in service life [19; 20; 21].