Bond Behavior of Recycled Fiber Recycled Concrete with Reinforcement after Freeze-Thaw Cycles

: Freeze-thaw (F-T) damage is the major factor destroying the bond behavior of reinforced concrete in the cold areas of China. The bond behavior between recycled ﬁber recycled concrete (RFRC) and reinforcement after F-T cycles was investigated in this paper. The pull-out tests were undertaken with the replacement rate (0, 50%, and 100%) of recycled aggregates (RA) and volume content (0, 0.12%, and 0.24%) of recycled ﬁbers (RFs) as test variables. The results demonstrate that the F-T cycles will reduce the bond strength between RFRC and reinforcement. Bond strength decreases by 69.41% after 150 cycles. Moreover, RF can improve the bond strength between RFRC and reinforcing steel. Bonding strength increases by 11.35% with the addition of 0.12% RF. A simpliﬁed two-phase bond-slip model between RFRC and reinforced steel after F-T cycles was eventually established, and it correlated well with the experimental results. This research presents a theoretical basis for the application of RFRC in building structures in cold areas. bond is, compared with effect


Introduction
The booming construction industry has accelerated the consumption of natural resources, while generating huge amounts of construction and demolition waste (C&DW) [1]. According to statistics, each year, on a global scale, over 1.5 billion tons of C&DW are produced, of which, nearly 700 million tons are in China, as shown in Figure 1a, and this number keeps growing [2]. Such a huge amount of C&DW-occupied land, as seen in Figure 1b, pollutes air and water resources as well [3]. Not only is this a problem for China, but it is also a global problem [4]. Therefore, specialists from various countries actively explore the treatment of recycling mode of C&DW [5,6], research on the performance of recycled concrete (RC), and ensure sustainable economic development.
Bond behavior is one of the key factors that determine whether recycled aggregates (RA) can be used in concrete structures [7][8][9]. The findings have been achieved as follows: the bond strength correlates well with the crushing index of RA [10]. The bond strength of recycled concrete with 100% RA is approximately 15% lower than natural aggregates (NA) [11]. Kim et al. found that, the smaller the aggregate size, the higher the bond strength through pull-out test [12]. Early in 1987, Shima et al. proposed the application of bond stress, slip, and reinforcement strain to characterize the bond-slip relationship between concrete and reinforcement [13]. As the research progressed, Kankam obtained the relationship between bond stress and slip through experiments [14], i.e., the τ-s relationship equation. Seara-Paz et al. established a modified expression for predicting the maximum bond strength, considering RA replacement rate and compressive strength [15]. Guizani et al. conducted pull-out tests under monotonic and cyclic loading, respectively, and investigated the influence of the degree of restraint and the number of initial loadings on and investigated the influence of the degree of restraint and the number of initial loadings on the test, thereby establishing a bond--slip constitutive model [16]. Gao et al. established the bond strength model between RC and reinforcement based on natural concrete (NC) [17]. Moreover, the model proposed by Hu et al. was obtained with an experiment [18]. As we all know, freeze-thaw (F-T) damage is part of the main factor that affects the durability of reinforced concrete [19]. Moreover, F-T cycles accelerate the generation and development of concrete cracks, lead to a decrease in bond properties, and are particularly severe in the frozen regions of Northeast China [20]. Hanjari et al. noted that F-T cycles harm bond properties of concrete materials, whether coarse aggregate is NA or RA [21]. Liu et al. points out that, the more RA there is, the more damage caused by F-T cycles [22]. Shi et al. believe the cement paste attached to the surface of RA is the key factor causing the decline in frost resistance [23]. Meanwhile, the experimental results of Reference [18] also support this view. Huaishuai et al. researched the bond performance of fully recycled concrete and various types of steel bars; subsequently, corresponding bond-slip trend curves were given [24]. Wang et al. expressed the bond-slip relationship in terms of the relative dynamic modulus of elasticity loss rate based on the bond-degradation law produced by F-T cycles [25]. In addition, based on the influence of different reinforcement diameters and concrete protective layer thickness on the bond performance, a corresponding empirical model was given by Ren et al. [26]. In summary, most research has been conducted on the negative impact of F-T environments on bond behavior. However, relatively few works have been performed to enhance the bond behavior of recycled concrete and reinforcing steel under F-T conditions. Studies revealed that fibers have a beneficial effect on the performance of concrete [27]. In actual projects, steel fibers, polypropylene fibers, etc., are utilized to enhance the properties of concrete structures [28]. Especially steel fibers can enhance the frost resistance of concrete [29,30], and with steel fibers, the bond stress of concrete is enhanced by up to 5~20% [31]. Gao et al. investigated the bonding performance of reinforcement with recycled concrete, using RA replacement rate and steel fibers volume content as variables, and finally, a bond-slip model was derived [32]. However, it is mostly used for high-strength and ultra-high-strength concrete, while RC has low in strength, particularly under cold environments, and is more prone to damage, so the role of steel fibers cannot be fully utilized. Fortunately, polypropylene fibers promote the homogeneity of concrete; therefore, the crack and frost resistance were strengthened [33]. Test by Afroughsabet et al. shows that the bond behavior of polypropylene and steel fibers was higher than that of steel fiber [34]. Relatively little research has been conducted, nonetheless, on the bond performance of single-mixed polypropylene fibers with concrete [35], but undoubtedly, polypropylene is a good choice for improving the bonding performance of recycled concrete in cold environments. As we all know, freeze-thaw (F-T) damage is part of the main factor that affects the durability of reinforced concrete [19]. Moreover, F-T cycles accelerate the generation and development of concrete cracks, lead to a decrease in bond properties, and are particularly severe in the frozen regions of Northeast China [20]. Hanjari et al. noted that F-T cycles harm bond properties of concrete materials, whether coarse aggregate is NA or RA [21]. Liu et al. points out that, the more RA there is, the more damage caused by F-T cycles [22]. Shi et al. believe the cement paste attached to the surface of RA is the key factor causing the decline in frost resistance [23]. Meanwhile, the experimental results of Reference [18] also support this view. Huaishuai et al. researched the bond performance of fully recycled concrete and various types of steel bars; subsequently, corresponding bond-slip trend curves were given [24]. Wang et al. expressed the bond-slip relationship in terms of the relative dynamic modulus of elasticity loss rate based on the bond-degradation law produced by F-T cycles [25]. In addition, based on the influence of different reinforcement diameters and concrete protective layer thickness on the bond performance, a corresponding empirical model was given by Ren et al. [26]. In summary, most research has been conducted on the negative impact of F-T environments on bond behavior. However, relatively few works have been performed to enhance the bond behavior of recycled concrete and reinforcing steel under F-T conditions. Studies revealed that fibers have a beneficial effect on the performance of concrete [27]. In actual projects, steel fibers, polypropylene fibers, etc., are utilized to enhance the properties of concrete structures [28]. Especially steel fibers can enhance the frost resistance of concrete [29,30], and with steel fibers, the bond stress of concrete is enhanced by up to 5~20% [31]. Gao et al. investigated the bonding performance of reinforcement with recycled concrete, using RA replacement rate and steel fibers volume content as variables, and finally, a bond-slip model was derived [32]. However, it is mostly used for highstrength and ultra-high-strength concrete, while RC has low in strength, particularly under cold environments, and is more prone to damage, so the role of steel fibers cannot be fully utilized. Fortunately, polypropylene fibers promote the homogeneity of concrete; therefore, the crack and frost resistance were strengthened [33]. Test by Afroughsabet et al. shows that the bond behavior of polypropylene and steel fibers was higher than that of steel fiber [34]. Relatively little research has been conducted, nonetheless, on the bond performance of single-mixed polypropylene fibers with concrete [35], but undoubtedly, polypropylene is a good choice for improving the bonding performance of recycled concrete in cold environments.
Meanwhile, carpets are generally used in households, hotels, and other live and workplaces in China. Moreover, with convenience comes the problem. Each year, more Crystals 2021, 11, 1506 3 of 17 than 13 million tons of waste carpets are produced, of which, mainly polypropylene fibers carpet [36]. In addition to disposal by the landfill, incineration will cause serious pollution to the ecological environment ( Figure 2) [37]; regrettably, an economical and environmentally friendly solution has not yet been proposed. It is a thorny problem, with the goal of "carbon neutrality" and "carbon peaking" [38]. Meanwhile, carpets are generally used in households, hotels, and other live and workplaces in China. Moreover, with convenience comes the problem. Each year, more than 13 million tons of waste carpets are produced, of which, mainly polypropylene fibers carpet [36]. In addition to disposal by the landfill, incineration will cause serious pollution to the ecological environment ( Figure 2) [37]; regrettably, an economical and environmentally friendly solution has not yet been proposed. It is a thorny problem, with the goal of "carbon neutrality" and "carbon peaking" [38]. The waste carpet is treated, and the recycled fibers (RFs) that are obtained are used in RC; on the one hand, this improves the performance of concrete, but on the other hand, it reduces resource consumption and promotes waste recycling, achieving a win-win situation. Therefore, this paper proposes the concept of recycled fiber recycled concrete (RFRC). Fibers are taken from the waste carpet, firstly; cleaned and disinfected, secondly; and mechanically and manually cut, finally, to acquire fiber segments. Coarse aggregates come from C&DW. Simulating the harsh cold environment of Northeast China, we performed F-T tests (0, 50, 100, 150 cycles) with RA replacement rates of 0, 50%, and 100%; RF volume contents of 0, 0.12%, and 0.24% as variables; and five groups, with 60 specimens in total. The bond behavior between RFRC and reinforcement under F-T cycles was studied. Additionally, local bond-slip tests were conducted to investigate the distribution law of bond stress with RFRC50-12 series. A bond-slip model under F-T condition was established. In this paper, we provide new ideas for the application of waste carpet and C&DW and promote in-depth research on the recycling of the solid waste in cold regions.

Materials
In this study, ordinary Portland cement P•O 42.5(Sunnsy Group, Shenyang, China) was used as the cement, which meets GB175-2018 [39]: natural river sand as fine aggregates, fineness modulus 2.7, mud content <2%, and apparent density 2615 kg/m 3 . Two types of coarse aggregates, NA and RA were used: NA from crushed gravel, and RA from the structural laboratory of Shenyang Jianzhu University, original-strength grade C40. Crushed by manual and jaw crusher, cleaned, and sieved; maximum particle size 25 mm, conforms to GB/T 25177-2010 [40] and GB/T 14685-2011 [41]. Figure 3 shows the grading curves of aggregates. Performance indicators are shown in Table 1. Reinforcing steel was used, with 10 and 16 mm. Mechanical properties are shown in Table 2. Mixing water was ordinary tap water. The waste carpet is treated, and the recycled fibers (RFs) that are obtained are used in RC; on the one hand, this improves the performance of concrete, but on the other hand, it reduces resource consumption and promotes waste recycling, achieving a win-win situation. Therefore, this paper proposes the concept of recycled fiber recycled concrete (RFRC). Fibers are taken from the waste carpet, firstly; cleaned and disinfected, secondly; and mechanically and manually cut, finally, to acquire fiber segments. Coarse aggregates come from C&DW. Simulating the harsh cold environment of Northeast China, we performed F-T tests (0, 50, 100, 150 cycles) with RA replacement rates of 0, 50%, and 100%; RF volume contents of 0, 0.12%, and 0.24% as variables; and five groups, with 60 specimens in total. The bond behavior between RFRC and reinforcement under F-T cycles was studied. Additionally, local bond-slip tests were conducted to investigate the distribution law of bond stress with RFRC50-12 series. A bond-slip model under F-T condition was established. In this paper, we provide new ideas for the application of waste carpet and C&DW and promote in-depth research on the recycling of the solid waste in cold regions.

Materials
In this study, ordinary Portland cement P•O 42.5(Sunnsy Group, Shenyang, China) was used as the cement, which meets GB175-2018 [39]: natural river sand as fine aggregates, fineness modulus 2.7, mud content < 2%, and apparent density 2615 kg/m 3 . Two types of coarse aggregates, NA and RA were used: NA from crushed gravel, and RA from the structural laboratory of Shenyang Jianzhu University, original-strength grade C40. Crushed by manual and jaw crusher, cleaned, and sieved; maximum particle size 25 mm, conforms to GB/T 25177-2010 [40] and GB/T 14685-2011 [41]. Figure 3 shows the grading curves of aggregates. Performance indicators are shown in Table 1. Reinforcing steel was used, with 10 and 16 mm. Mechanical properties are shown in Table 2. Mixing water was ordinary tap water. The recycled fibers (RFs) from waste carpet, polypropylene material, density 0.91 kg/m 3 , modulus of elasticity 3.5 × 10 3 MPa, water absorption <0.1%, cleaned and cuts, obtain waste fiber bundles, with length 18 to 20 mm; the preparation process is shown in Figure 4.

Concrete Mixture
Due to the old cement mortar attached to the surface of RA, it has a higher water absorption rate. According to Table 1, the water absorption rate of RA is 3.9 times than NA. DG/T J08-2018 [42] stipulates that the mix ratio of recycled concrete should consider the adsorbed water of the aggregates. Being dependent on the standard, every 50% increase of RA is 10 kg/m 3 of additional water approximately. Water absorption of fibers <0.1%; its influence on water consumption can be ignored. The concrete mixture is shown in Table 3. Specimen preparation process is in Figure 5; the machine was JW350 forced  The recycled fibers (RFs) from waste carpet, polypropylene material, density 0.91 kg/m 3 , modulus of elasticity 3.5 × 10 3 MPa, water absorption <0.1%, cleaned and cuts, obtain waste fiber bundles, with length 18 to 20 mm; the preparation process is shown in Figure 4. The recycled fibers (RFs) from waste carpet, polypropylene material, density 0.91 kg/m 3 , modulus of elasticity 3.5 × 10 3 MPa, water absorption <0.1%, cleaned and cuts, obtain waste fiber bundles, with length 18 to 20 mm; the preparation process is shown in Figure 4.

Concrete Mixture
Due to the old cement mortar attached to the surface of RA, it has a higher water absorption rate. According to Table 1, the water absorption rate of RA is 3.9 times than NA. DG/T J08-2018 [42] stipulates that the mix ratio of recycled concrete should consider the adsorbed water of the aggregates. Being dependent on the standard, every 50% increase of RA is 10 kg/m 3 of additional water approximately. Water absorption of fibers <0.1%; its influence on water consumption can be ignored. The concrete mixture is shown in Table 3. Specimen preparation process is in Figure 5; the machine was JW350 forced

Concrete Mixture
Due to the old cement mortar attached to the surface of RA, it has a higher water absorption rate. According to Table 1, the water absorption rate of RA is 3.9 times than NA. DG/T J08-2018 [42] stipulates that the mix ratio of recycled concrete should consider the adsorbed water of the aggregates. Being dependent on the standard, every 50% increase of RA is 10 kg/m 3 of additional water approximately. Water absorption of fibers < 0.1%; its influence on water consumption can be ignored. The concrete mixture is shown in Table 3. Specimen preparation process is in Figure 5; the machine was JW350 forced multifunctional mixer (Qianchen Machinery Equipment, Shenyang, China), rotational speed 60 r/min.

Test Specimens
According to the mixture, prepare 100 × 100 × 100 mm pull-out specimen, 5 series, 3 parallel tests per series, 4 F-T cycles (0, 50, 100, 150), 60 in total. Figure 6 shows the details of the specimen: anchorage length 5 times the diameter of reinforcing steel (50 mm). With PVC pipes embedded at each end of the mold, we sealed with paraffin wax to eliminate influence on the test results.
Meanwhile, according to the results of F-T cycles, 8 pull-out specimens for bondstress distribution were made with 100 × 100 × 160 mm. The treatment of reinforcing steel refers to Liu [43] and Tang [44]. Firstly, reinforcing steel is pretreated by cutting along the axis, slotted. Strain gauges inside, spaced 20 mm, 9 pieces. Closed after waterproofing, anchorage length 10 times the diameter of reinforcement (160 mm). Figure 7a shows the steel-bar handling process. Figure 7b shows details of the stress distribution specimen.

Test Specimens
According to the mixture, prepare 100 × 100 × 100 mm pull-out specimen, 5 series, 3 parallel tests per series, 4 F-T cycles (0, 50, 100, 150), 60 in total. Figure 6 shows the details of the specimen: anchorage length 5 times the diameter of reinforcing steel (50 mm). With PVC pipes embedded at each end of the mold, we sealed with paraffin wax to eliminate influence on the test results.

Test Specimens
According to the mixture, prepare 100 × 100 × 100 mm pull-out specimen, 5 series, 3 parallel tests per series, 4 F-T cycles (0, 50, 100, 150), 60 in total. Figure 6 shows the details of the specimen: anchorage length 5 times the diameter of reinforcing steel (50 mm). With PVC pipes embedded at each end of the mold, we sealed with paraffin wax to eliminate influence on the test results.
Meanwhile, according to the results of F-T cycles, 8 pull-out specimens for bondstress distribution were made with 100 × 100 × 160 mm. The treatment of reinforcing steel refers to Liu [43] and Tang [44]. Firstly, reinforcing steel is pretreated by cutting along the axis, slotted. Strain gauges inside, spaced 20 mm, 9 pieces. Closed after waterproofing, anchorage length 10 times the diameter of reinforcement (160 mm). Figure 7a shows the steel-bar handling process. Figure 7b shows details of the stress distribution specimen. Meanwhile, according to the results of F-T cycles, 8 pull-out specimens for bond-stress distribution were made with 100 × 100 × 160 mm. The treatment of reinforcing steel refers to Liu [43] and Tang [44]. Firstly, reinforcing steel is pretreated by cutting along the axis, slotted. Strain gauges inside, spaced 20 mm, 9 pieces. Closed after waterproofing, anchorage length 10 times the diameter of reinforcement (160 mm). Figure 7a shows the steel-bar handling process. Figure 7b shows details of the stress distribution specimen.

Rapid Freeze-Thaw Cycles Test
Twenty-four hours later, the specimens were demolded and transferred to standard conditions for 23 days of curing. Subsequently, they were immersed in water for 4 days. The test was performed by the quick-freeze method, dependent on the GB/T50082-2009 [45]. The apparatus used a type KDR-V9 concrete rapid freeze-thaw testing machine (Shuzhi Instrument Company, Shenyang, China), as shown in Figure 8. Temperature ranged from −17 to 5 °C, every 50 F-T cycles for one period.

Pull-Out Test
The pull-out test with WAW-600C electro-hydraulic servo universal testing machine(Jinan Times Co. Ltd., Jinan, China), as shown in Figure 9, using displacement control method, loading speed 0.3 mm/min. Linear Variable Differential Transformer (LVDT) #1 tests the displacement of loading end. LVDT #2 tests the free end, with automatic data collection. The experiment was carried out with GB/T 50152-2012 [46]; before loading, slowly pressurize the specimen; after the reading of LVDT #1 stable, reset the reading and start. Assume that the bond strength is uniformly distributed over the entire bonded section of steel bar. The bond strength is calculated as in Equation (1):

Rapid Freeze-Thaw Cycles Test
Twenty-four hours later, the specimens were demolded and transferred to standard conditions for 23 days of curing. Subsequently, they were immersed in water for 4 days. The test was performed by the quick-freeze method, dependent on the GB/T50082-2009 [45]. The apparatus used a type KDR-V9 concrete rapid freeze-thaw testing machine (Shuzhi Instrument Company, Shenyang, China), as shown in Figure 8. Temperature ranged from −17 to 5 • C, every 50 F-T cycles for one period.

Rapid Freeze-Thaw Cycles Test
Twenty-four hours later, the specimens were demolded and transferred to standard conditions for 23 days of curing. Subsequently, they were immersed in water for 4 days. The test was performed by the quick-freeze method, dependent on the GB/T50082-2009 [45]. The apparatus used a type KDR-V9 concrete rapid freeze-thaw testing machine (Shuzhi Instrument Company, Shenyang, China), as shown in Figure 8. Temperature ranged from −17 to 5 °C, every 50 F-T cycles for one period.

Pull-Out Test
The pull-out test with WAW-600C electro-hydraulic servo universal testing machine(Jinan Times Co. Ltd., Jinan, China), as shown in Figure 9, using displacement control method, loading speed 0.3 mm/min. Linear Variable Differential Transformer (LVDT) #1 tests the displacement of loading end. LVDT #2 tests the free end, with automatic data collection. The experiment was carried out with GB/T 50152-2012 [46]; before loading, slowly pressurize the specimen; after the reading of LVDT #1 stable, reset the reading and start. Assume that the bond strength is uniformly distributed over the entire bonded section of steel bar. The bond strength is calculated as in Equation (1):

Pull-Out Test
The pull-out test with WAW-600C electro-hydraulic servo universal testing machine (Jinan Times Co. Ltd., Jinan, China), as shown in Figure 9, using displacement control method, loading speed 0.3 mm/min. Linear Variable Differential Transformer (LVDT) #1 tests the displacement of loading end. LVDT #2 tests the free end, with automatic data collection. The experiment was carried out with GB/T 50152-2012 [46]; before loading, slowly pressurize the specimen; after the reading of LVDT #1 stable, reset the reading and start. Assume that the bond strength is uniformly distributed over the entire bonded section of steel bar. The bond strength is calculated as in Equation (1): where τ is the bond strength between concrete and reinforcement (MPa), P is pull-out force (kN), d is diameter of reinforcement (mm), and l a is bond length of reinforcement (mm). The slip of the reinforcement can be calculated by the average value of the loading end (S 1 ) and free end (S 2 ), as Equation (2). S 1 and S 2 correspond to the data collected by LVDT #1 and LVDT #2.
where τ is the bond strength between concrete and reinforcement (MPa), P is pull-out force (kN), d is diameter of reinforcement (mm), and la is bond length of reinforcement (mm). The slip of the reinforcement can be calculated by the average value of the loading end (S1) and free end (S2), as Equation (2). S1 and S2 correspond to the data collected by LVDT #1 and LVDT #2. Figure 9. Pull-out test machine of type WAW-600C.

Failure Modes
Changes in apparent morphology can reflect the damage process of RFRC during -T cycles. The morphology for 50, 100, and 150 cycles is shown in Figure 10. At 50 cycles, the peel degree of cement mortar on the surface of the specimen is different; coarse aggregates of the NC, RC50, and RC100 series are exposed. At 100 cycles, the more RA, the more exposure; RC50 coarse aggregates fall off partial, and RC100 edge incomplete. At 150 cycles, a large amount of fine aggregates is spalling, coarse aggregates are exposed obviously, and the surface of the specimen is uneven; RFRC50-12 and RFRC50-24 are less damaged, and RC100 has the most serious damage. The results showed that the -T cycles caused damage to the NC and RC series; the degree was positively correlated with the number of F-T cycles. Furthermore, it is also related to the amount of RA and RF: the greater of the amount of RA, the more serious the damage is, and it should be noted. The addition of RF can improve RC frost resistance to a certain extent.

Failure Modes
Changes in apparent morphology can reflect the damage process of RFRC during -T cycles. The morphology for 50, 100, and 150 cycles is shown in Figure 10. At 50 cycles, the peel degree of cement mortar on the surface of the specimen is different; coarse aggregates of the NC, RC50, and RC100 series are exposed. At 100 cycles, the more RA, the more exposure; RC50 coarse aggregates fall off partial, and RC100 edge incomplete. At 150 cycles, a large amount of fine aggregates is spalling, coarse aggregates are exposed obviously, and the surface of the specimen is uneven; RFRC50-12 and RFRC50-24 are less damaged, and RC100 has the most serious damage. The results showed that the -T cycles caused damage to the NC and RC series; the degree was positively correlated with the number of F-T cycles. Furthermore, it is also related to the amount of RA and RF: the greater of the amount of RA, the more serious the damage is, and it should be noted. The addition of RF can improve RC frost resistance to a certain extent.

Failure Modes
Changes in apparent morphology can reflect the damage process of RFRC durin cycles. The morphology for 50, 100, and 150 cycles is shown in Figure 10. At 50 cycles peel degree of cement mortar on the surface of the specimen is different; coarse aggreg of the NC, RC50, and RC100 series are exposed. At 100 cycles, the more RA, the m exposure; RC50 coarse aggregates fall off partial, and RC100 edge incomplete. At 150 cles, a large amount of fine aggregates is spalling, coarse aggregates are exposed o ously, and the surface of the specimen is uneven; RFRC50-12 and RFRC50-24 are less d aged, and RC100 has the most serious damage. The results showed that the -T cy caused damage to the NC and RC series; the degree was positively correlated with number of F-T cycles. Furthermore, it is also related to the amount of RA and RF greater of the amount of RA, the more serious the damage is, and it should be noted. addition of RF can improve RC frost resistance to a certain extent. The pull-out test was be conducted every 50 F-T cycles. The results are shown in Table 4. The data are the average of three specimens, and there are two types of damage: split and split/pull-out ( Figure 11). Split failure produces wide through cracks; the specimen separates into two halves during damaged, with a bursting sound. With split/pull-out failure, there are narrow through cracks, no obvious sound when destroyed, and the specimen can still maintain the integrity after the reinforcement is pulled out. It should be noted that, under 150 F-T cycles, one case of a split occurred in three specimens with the RC100 series, and two cases in the RFRC50-24 series.  The pull-out test was be conducted every 50 F-T cycles. The results are shown in Table 4. The data are the average of three specimens, and there are two types of damage: split and split/pull-out ( Figure 11). Split failure produces wide through cracks; the specimen separates into two halves during damaged, with a bursting sound. With split/pullout failure, there are narrow through cracks, no obvious sound when destroyed, and the specimen can still maintain the integrity after the reinforcement is pulled out. It should be noted that, under 150 F-T cycles, one case of a split occurred in three specimens with the RC100 series, and two cases in the RFRC50-24 series.   Figure 12 presents the relationship between the bond strength and F-T cycles. It can be observed that, as the number of F-T cycles increases, the bond strength gradually decreases. As shown in Figure 12a, the bond-strength loss is 45.24%, 48.79%, and 69.41% for NC, RC50, and RC100 series after 150 F-T cycles. Additionally, with a fixed number of F-  Figure 12 presents the relationship between the bond strength and F-T cycles. It can be observed that, as the number of F-T cycles increases, the bond strength gradually decreases. As shown in Figure 12a, the bond-strength loss is 45.24%, 48.79%, and 69.41% for NC, RC50, and RC100 series after 150 F-T cycles. Additionally, with a fixed number of F-T cycles, the bond strength between RC and reinforcement is less than that of the NC series and decreases with the increase of RA. The addition of RA increases the area of the interface transition zone (ITZ) of the material; meanwhile, this part is the weakest area of concrete material performance. Therefore, with the F-T cycles environment, the specimen is more likely to be damaged when subjected to external loads. This is consistent with the failure modes of the specimen. Over 150 F-T cycles later, the reduction in bond strength is lower than 5% for NC and RC50, about 30% for RC100. That is, compared with F-T cycles, the effect of RA on the bond-strength loss is low and negligible at 50% RA replacement. increased by 11.35%, while RFRC50-24 increased by 4.78% and decreased by 7.03% before and after cycles. It is shown that the incorporation of RF plays a positive role in the bond behavior of recycled concrete with reinforcement, but it is related to the RF content. A small amount of RF enhances the bonding strength, while excessive RF has a discouraging effect. RF ameliorates the internal structure of recycled concrete, optimizes the mixing of aggregate and mortar, slows down the generation and development of cracks, and plays a certain role in dissipating the energy generated by the force. Moreover, excess RF, which reduces the homogeneity of the mixture, accelerates structural damage in F-T cycles environment, thus resulting in bond-strength reduction.  Figure 13 demonstrates the relationship between slip and F-T cycles. It can be observed that the development trends of curves are similar, and the slip extends with the number of F-T cycles. The reason why is that F-T cycles cause damage to the concrete matrix and reduce the restraining effect of the concrete to the reinforcement. In addition, a fixed number of cycles, increased RA, and decreased slip are related. As shown in Figure  13a, after 150 F-T cycles, the RC50 and RC100 series were reduced by 9.76% and 14.63%, respectively, compared with the NC series. During the loading process, RA between the ribs was more easily crushed, reducing the friction between concrete and reinforcement, which is consistent with the conclusion of [22]. Figure 13b reflects the influence of RF on slip under F-T cycles conditions. After 150 F-T cycles, the RFRC50-12 slip increased significantly, 13.89% improvement over RC50 series. Whereas the variation of RFRC50-24 slip is not significant. To a certain extent, the addition of RF plays a role in tensile crack resistance and energy consumption but is related to the content.  Figure 12b shows the influence of RF on bond strength under F-T cycles' conditions. After 150 F-T cycles, the bond-strength loss was 48.79%, 39.63%, and 54.56% for the RC50, RFRC50-12, and RFRC50-24 series. Compared to RC50, the bond strength of FRC50-12 increased by 11.35%, while RFRC50-24 increased by 4.78% and decreased by 7.03% before and after cycles. It is shown that the incorporation of RF plays a positive role in the bond behavior of recycled concrete with reinforcement, but it is related to the RF content. A small amount of RF enhances the bonding strength, while excessive RF has a discouraging effect. RF ameliorates the internal structure of recycled concrete, optimizes the mixing of aggregate and mortar, slows down the generation and development of cracks, and plays a certain role in dissipating the energy generated by the force. Moreover, excess RF, which reduces the homogeneity of the mixture, accelerates structural damage in F-T cycles environment, thus resulting in bond-strength reduction. Figure 13 demonstrates the relationship between slip and F-T cycles. It can be observed that the development trends of curves are similar, and the slip extends with the number of F-T cycles. The reason why is that F-T cycles cause damage to the concrete matrix and reduce the restraining effect of the concrete to the reinforcement. In addition, a fixed number of cycles, increased RA, and decreased slip are related. As shown in Figure 13a, after 150 F-T cycles, the RC50 and RC100 series were reduced by 9.76% and 14.63%, respectively, compared with the NC series. During the loading process, RA between the ribs was more easily crushed, reducing the friction between concrete and reinforcement, which is consistent with the conclusion of [22].

Bond-Slip Curves
The bond-slip curves of specimens are shown in Figure 14. Each curve has a similar trend. Overall, the curve can be separated into micro-slip stage, slip stage, extracted stage, descend stage, and residual stage, in accordance with the model of Reference [47]. In the micro-slip stage, pull-out force is quite small, and there is no visible slippage at the free  Figure 13b reflects the influence of RF on slip under F-T cycles conditions. After 150 F-T cycles, the RFRC50-12 slip increased significantly, 13.89% improvement over RC50 series. Whereas the variation of RFRC50-24 slip is not significant. To a certain extent, the addition of RF plays a role in tensile crack resistance and energy consumption but is related to the content.

Bond-Slip Curves
The bond-slip curves of specimens are shown in Figure 14. Each curve has a similar trend. Overall, the curve can be separated into micro-slip stage, slip stage, extracted stage, descend stage, and residual stage, in accordance with the model of Reference [47]. In the micro-slip stage, pull-out force is quite small, and there is no visible slippage at the free end; the curve varies linearly. At the slip stage, the pull-out force gradually increases, the free end starts to slide, and the curve grows non-linearly. At the pull-out stage, as the force grows to a certain value, the peak strength appears; subsequently, the specimen is damaged, the curve enters descend stage, and the peak strength decreases speedily. In the residual stage, the bond strength decreases slowly and remains stable. It should be noted that, after the F-T cycles, RFRC50-24 failure modes showed split and pull-out.

Bond-Slip Curves
The bond-slip curves of specimens are shown in Figure 14. Each curve has a sim trend. Overall, the curve can be separated into micro-slip stage, slip stage, extracted sta descend stage, and residual stage, in accordance with the model of Reference [47]. In micro-slip stage, pull-out force is quite small, and there is no visible slippage at the f end; the curve varies linearly. At the slip stage, the pull-out force gradually increases, free end starts to slide, and the curve grows non-linearly. At the pull-out stage, as the fo grows to a certain value, the peak strength appears; subsequently, the specimen is da aged, the curve enters descend stage, and the peak strength decreases speedily. In residual stage, the bond strength decreases slowly and remains stable. It should be no that, after the F-T cycles, RFRC50-24 failure modes showed split and pull-out.  Figure 15 shows the influence of RA on the bond-slip curve under F-T conditio The curve RC is lower than NC. The more RA there is, the flatter the curve is, as is c sistent with the conclusion of the literature [48]. In Figure 15a, we can see that there w no remarkable difference between the curves in the micro-slip stage before the F-T cyc In the slip stage, with the RA increases, the elastic modulus of the curve decreases; co spondingly, the bond strength decreases. In the slip stage, the difference between cur becomes more significant; the residual strength was 50.87%, 43.04%, and 31.01% of ultimate strength, respectively. After 150 F-T cycles, each curve becomes flat, as shown Figure 15b. The percentage of residual strength decreased by 18.98%, 6.77%, and 3.9 That is, the damage of the NC series' residual strength by F-T cycles is relatively obvio  Figure 15 shows the influence of RA on the bond-slip curve under F-T conditions. The curve RC is lower than NC. The more RA there is, the flatter the curve is, as is consistent with the conclusion of the literature [48]. In Figure 15a, we can see that there was no remarkable difference between the curves in the micro-slip stage before the F-T cycles. In the slip stage, with the RA increases, the elastic modulus of the curve decreases; correspondingly, the bond strength decreases. In the slip stage, the difference between curves becomes more significant; the residual strength was 50.87%, 43.04%, and 31.01% of the ultimate strength, respectively. After 150 F-T cycles, each curve becomes flat, as shown in Figure 15b. The percentage of residual strength decreased by 18.98%, 6.77%, and 3.96%. That is, the damage of the NC series' residual strength by F-T cycles is relatively obvious.
The effect of RF content on the bond-slip curve is illustrated in Figure 16. Before the F-T cycles, the development trend of the curve is not much different, but after the F-T cycles, RFRC50-24 damage is the most significant; even the failure mode changes, while RFRC50-12 had good bond behavior. The effect of RF content on the bond-slip curve is illustrated in Figure 16. Before the F-T cycles, the development trend of the curve is not much different, but after the F-T cycles, RFRC50-24 damage is the most significant; even the failure mode changes, while RFRC50-12 had good bond behavior.

Bond Stress Distribution
Take RFRC50-12 series for the bond-stress distribution test under F-T cycles conditions and NC as a control test. Since the bond stress cannot be obtained directly through experiments, it is hypothesized that the stress is uniformly distributed. The stress-equilibrium conditions of the reinforcement are shown in Figure 17, and the bond stress is calculated as follows. The effect of RF content on the bond-slip curve is illustrated in Figure 16. Before the F-T cycles, the development trend of the curve is not much different, but after the F-T cycles, RFRC50-24 damage is the most significant; even the failure mode changes, while RFRC50-12 had good bond behavior.

Bond Stress Distribution
Take RFRC50-12 series for the bond-stress distribution test under F-T cycles conditions and NC as a control test. Since the bond stress cannot be obtained directly through experiments, it is hypothesized that the stress is uniformly distributed. The stress-equilibrium conditions of the reinforcement are shown in Figure 17, and the bond stress is calculated as follows.

Bond Stress Distribution
Take RFRC50-12 series for the bond-stress distribution test under F-T cycles conditions and NC as a control test. Since the bond stress cannot be obtained directly through experiments, it is hypothesized that the stress is uniformly distributed. The stress-equilibrium conditions of the reinforcement are shown in Figure 17, and the bond stress is calculated as follows.
where σ s is the tensile stress, dx is the length of the isolated body, and ε s is the tensile strain. For the convenience of calculation, Equation (4) is mostly utilized to simplify the bond stress of τ(x) along the anchoring length, la.
where ∆x i is the distance between the two measuring points of the i section; ε j and ε j+1 are the strains of the steel bars at the j and j + 1; and P j and P j+1 are the tensile force at the j and j + 1. Figure 18 shows the bond-stress-distribution curve of RFRC50-12 before and after the F-T cycles. The bond stress is not uniformly distributed throughout the anchorage section, and with the increase of the pull-out force, the stress peak appears in the middle of the bonding area in the curve. At the beginning of loading, there is a negligible difference in bond stress at each position, and as the load increases, the peak point starts to be prominent, and the location does not change with the increase of load. The reason is that the bond stress in this region plays a key role in the load transfer process, and the increase in load does not change this state. Compared with the free end, the bond stress near the loading end increases significantly. Because the loading end is loaded first and then transferred to the free end, while the main bond stress is carried by the intermediate region less bond is transferred to the free end, there is slow growth for the bond stress in this region.

Bond Stress Distribution
Take RFRC50-12 series for the bond-stress distribution test under F-T cycles conditions and NC as a control test. Since the bond stress cannot be obtained directly through experiments, it is hypothesized that the stress is uniformly distributed. The stress-equilibrium conditions of the reinforcement are shown in Figure 17, and the bond stress is calculated as follows.
where Δxi is the distance between the two measuring points of the i section; εj and εj + 1 are the strains of the steel bars at the j and j + 1; and Pj and Pj + 1 are the tensile force at the j and j + 1. Figure 18 shows the bond-stress-distribution curve of RFRC50-12 before and after the F-T cycles. The bond stress is not uniformly distributed throughout the anchorage section, and with the increase of the pull-out force, the stress peak appears in the middle of the bonding area in the curve. At the beginning of loading, there is a negligible difference in bond stress at each position, and as the load increases, the peak point starts to be prominent, and the location does not change with the increase of load. The reason is that the bond stress in this region plays a key role in the load transfer process, and the increase in load does not change this state. Compared with the free end, the bond stress near the loading end increases significantly. Because the loading end is loaded first and then transferred to the free end, while the main bond stress is carried by the intermediate region less bond is transferred to the free end, there is slow growth for the bond stress in this region.
The F-T cycles changed the position of the peak point, as it shifted in the direction of the loading end. The reason may be that the specimen can only be fixed in the direction of F-T cycles; as the test proceeds, the loading end of the F-T damage becomes more serious, so the peak position is shifted. The higher the number of F-T cycles, the more dramatic the decrease in peak bond stress. That is, F-T cycles cause internal damage to the RFRC, and the more serious the damage, the more noticeable the decrease in bonding performance. When the average bond stress is the same, the more uniform the distribution of bond stress, indicating that the utilization rate of bond strength is higher and the ductility is better. To verify the inhomogeneity of the RA to improve the bond stress, this paper introduces μ1, μ2, and μ3 bondstress inhomogeneity coefficients for analysis, and they are calculated as follows.  15kN 20kN 25kN  30kN  35kN  40kN  45kN 50kN 55kN  60kN  65kN Bond stress (MPa) Distance from the loading end (mm) The F-T cycles changed the position of the peak point, as it shifted in the direction of the loading end. The reason may be that the specimen can only be fixed in the direction of F-T cycles; as the test proceeds, the loading end of the F-T damage becomes more serious, so the peak position is shifted. The higher the number of F-T cycles, the more dramatic the decrease in peak bond stress. That is, F-T cycles cause internal damage to the RFRC, and the more serious the damage, the more noticeable the decrease in bonding performance.
When the average bond stress is the same, the more uniform the distribution of bond stress, indicating that the utilization rate of bond strength is higher and the ductility is better. To verify the inhomogeneity of the RA to improve the bond stress, this paper introduces µ 1 , µ 2 , and µ 3 bondstress inhomogeneity coefficients for analysis, and they are calculated as follows.
where τ max , τ min , and τ av are the maximum, minimum, and average bond stress generated under the ultimate load. The closer µ 3 is to 1, the more uniform the bondstress distribution is. The µ 3 of each specimen is illustrated in Figure 19. The µ 3 increases as the number of F-T cycles increases. That is, F-T damage is a gradual accumulation process. The more F-T cycles there are, the more serious the damage and the more uneven the bond-stress distribution. Under the same conditions, RFRC50-12 is higher than NC. This indicates that the addition of RA also improves the inhomogeneity of the material. When the average bond stress is the same, the more uniform the distribution of bond stress, indicating that the utilization rate of bond strength is higher and the ductility is better. To verify the inhomogeneity of the RA to improve the bond stress, this paper introduces μ1, μ2, and μ3 bondstress inhomogeneity coefficients for analysis, and they are calculated as follows.
where τMax, τMin, and τav are the maximum, minimum, and average bond stress generated under the ultimate load. The closer μ3 is to 1, the more uniform the bondstress distribution is. The μ3 of each specimen is illustrated in Figure 19. The μ3 increases as the number of F-T cycles increases. That is, F-T damage is a gradual accumulation process. The more F-T cycles there are, the more serious the damage and the more uneven the bond-stress distribution. Under the same conditions, RFRC50-12 is higher than NC. This indicates that the addition of RA also improves the inhomogeneity of the material.

Freeze-Thaw Damage Mechanism of Bond Stress
The bond stress between concrete and reinforcement is composed of a chemical adhesive force, friction resistance, and mechanical interaction force. Initially, F-T damage acts only on the outer surface of the concrete. With the increase of F-T cycles, cracks are generated in the concrete, thus weakening the restraint effect of the concrete on the internal steel bars and reducing the bond stress. Once the number of F-T cycles reaches a particular value, F-T cracks appear on the interface between concrete and reinforcement, destroying the adhesion and friction forces. Moreover, the bonding stress decreases significantly.
The RA has higher water absorption, and compared with the NC series, the RC series has poorer frost resistance and more significant bond-stress loss. In addition, the relative sliding of the reinforcement when it is pulled out causes the spalled concrete, which is scattered on the surface of the reinforcement, to form a "spherical effect", which increases the friction coefficient and enhances the frictional resistance [1]. RA is easier to crush and easily crushed into powder when subjected to force, thus promoting the relative sliding between concrete and steel bars and reduces friction. At the same time, the loss of mechanical bite force is evident.
The addition of RF does not alter the properties of recycled concrete, but it prevents the generation and development of cracks, as shown in Figure 20; it also has the effect of absorbing energy and enhancing the mix compatibility, thus enhancing the frost resistance of concrete and reducing F-T damage. This complies with fiber spacing theory; that is, at a certain range, the larger the volume of fibers, the smaller the spacing of fiber distribution in the concrete, and the gap between the matrix material is also reduced. In addition, the fibers across the cracks have an inhibitory effect on the development of oblique cracks [49].
sistance of concrete and reducing F-T damage. This complies with fiber spacing theory; that is, at a certain range, the larger the volume of fibers, the smaller the spacing of fiber distribution in the concrete, and the gap between the matrix material is also reduced. In addition, the fibers across the cracks have an inhibitory effect on the development of oblique cracks [49].
In summary, the influence of RA on the bond behavior is primarily concentrated in frictional resistance and mechanical interaction force, while RF is the chemical adhesion force.

Bond Stress-Slip Model for RFRC
The development trend of the bond-slip curve of each group is the same; it can be simplified into ascending and descending segments. Therefore, a corresponding bond-slip model can be established to determine the bond performance between RFRC and the steel bar interface after F-T cycles. In this paper, depending on the dimensionless parameter bond-slip model proposed by Reference [47], the bond-slip model is shown in Equation (8).
where τu is ultimate bond stress, and su is the ultimate slip. The measured data are fitted according to Equation (8). The fitting results are shown in Table 5. Moreover, Figure 21 shows the comparison between test results and predicted results, which are well fitted, and it is suitable for simulating the bond performance between RFRC and reinforcement. In summary, the influence of RA on the bond behavior is primarily concentrated in frictional resistance and mechanical interaction force, while RF is the chemical adhesion force.

Bond Stress-Slip Model for RFRC
The development trend of the bond-slip curve of each group is the same; it can be simplified into ascending and descending segments. Therefore, a corresponding bond-slip model can be established to determine the bond performance between RFRC and the steel bar interface after F-T cycles. In this paper, depending on the dimensionless parameter bond-slip model proposed by Reference [47], the bond-slip model is shown in Equation (8).
where τ u is ultimate bond stress, and s u is the ultimate slip. The measured data are fitted according to Equation (8). The fitting results are shown in Table 5. Moreover, Figure 21 shows the comparison between test results and predicted results, which are well fitted, and it is suitable for simulating the bond performance between RFRC and reinforcement.

Conclusions
The bond behavior of RFRC and reinforcement after the F-T cycle was investigated by using the pull-out test. From the experimental results, we determined the major conclusions to be as follows: (1) The bond strength decreases as the number of F-T cycles increases, whether there are natural or recycled aggregates. For fixed F-T cycles, the bond strength loss of natural aggregates was less than that of recycled aggregate concrete. Compared with F-T cycles, the effect of recycled aggregates' replacement rate on bond strength was not significant; RC50 bond strength is 95% of NC. (2) The addition of fibers slows down the generation and development of cracks, and it promotes the bond performance under F-T conditions and the optimal dosing of 0.12% in this test. (3) The NC bond stress distribution is bimodal, the recycled concrete bond-stress distribution is unimodal, that is, the addition of recycled aggregates increases the unevenness of the bond stress. Moreover, the pullout force increases, and the local stress concentration is obvious. (4) A simplified two-phase bond-slip model is proposed to characterize the bond performance between RFRC and reinforcement after F-T cycles, as it correlates well with the test results.