## 1 Introduction  
Many countries are experiencing dramatic and swift urbanization in the worldwide, the result of which is followed by massive construction and demolition wastes (C&DWs) and a huge demand of natural aggregate (NA). These C&DWs cause serious environmental loads. The demand of NA results in overexploitation and shortage of NA resources, which greatly damages the ecological balance of aggregate-producing areas [1, 2]. Utilizing these C&DWs as recycled aggregates to prepare the recycled aggregate concrete (RAC) is an effective and proven method to solve the environmental and resource crises and realize a circular economy in conventional concrete industries [3, 4, 5, 6, 7]. Many countries around the world including USA, China, and EU are gradually extending RAC to practical projects [8; 9; 10; 11]. At present, RAC has been widely used in building structures and pavements [12; 13; 14]. In this situation, the RAC utilization rate around the world is growing progressively with each passing year [15; 16]. However, when such RAC reaches its service life, it will face the problem of being dismantled and becoming waste concrete again. To achieve the strategy of sustainable development, multiple recycling of RAC emerges, attracting widespread attention from scholars. Obtaining the utmost out of waste RAC and converting it to produce repeatedly recycled aggregate concrete (RRAC) will further improve the utilization rate of C&DWs and conserve natural resources effectively. Therefore, it is quite necessary to explore the multiple recycling potential of RAC. Carbonation resistance is a key index affecting the durability of reinforced concrete structures [17; 18]. Exploring the carbonation behavior of RRAC is an indispensable step which determines the application potential of RRAC. Concrete carbonation is a process in which CO\({}_{2}\) in the atmosphere reacts with the alkali in the cement to make the pore water more acidic, thus lowering the pH and leading to the loss of passivation film for reinforcements [19; 20]. In the previous work, the carbonation behavior of three generations of RRAC with 100% replacement rate were reported [21]. It was found that with the increasing of the recycling number, the repeatedly recycled concrete aggregate (RRCA) quality degraded seriously and the carbonation resistance of RRAC gradually declined. But this study only considered the effect of a single factor on the carbonation resistance of RRAC. In an actual engineering, the occurrence of concrete carbonation is always accompanied with other environmental factors [22; 23]. In a micro-frozen region whose average monthly temperature of the coldest month is between 0\(\sim\)\(-\)4 \({}^{\circ}\)C, the concrete always inevitably suffers from freeze-thaw cycles. These regions make up about a third of China's territory. Therefore, it is necessary to investigate the effect of freeze-thaw cycles on the carbonation behavior of concrete used in micro-frozen regions. Previous research has pointed out that the carbonation resistance of concrete in the cold region was worse than that only in the atmospheric environment [24; 25; 26]. This is attributed to the damages caused by freeze-thaw cycles in the cold environment. [PERSON] et al. [27] and [PERSON] et al. [28] reported that the mechanical properties and relative dynamic elastic modulus of RAC decreased and the mass loss increased with the rise of freeze-thaw cycles. [PERSON] et al. [29] concluded that the porosity of recycled concrete increased with the increasing number of freeze-thaw cycles and proportion of recycled coarse aggregate. The freeze-thaw cycle is believed to bring about some micro- or macro-cracks in the concrete, which can immediately provide pathways for further migration of CO\({}_{2}\)[24]. [PERSON] [30] studied the carbonation behavior of natural aggregate concrete (NAC) in freeze-thaw circumstances.