Mechanical Properties and Uniaxial Compression Stress—Strain Relation of Recycled Coarse Aggregate Concrete after Carbonation

The application of recycled coarse aggregate (RCA) made from waste concrete to replace natural coarse aggregate (NCA) in concrete structures can essentially reduce the excessive consumption of natural resources and environmental pollution. Similar to normal concrete structures, recycled concrete structures would also suffer from the damage of carbonation, which leads to the deterioration of durability and the reduction of service life. This paper presents the experimental results of the cubic compressive strength, the static elastic modulus and the stress–strain relation of recycled coarse aggregate concrete (RAC) after carbonation. The results show that the cubic compressive strength and the static elastic modulus of carbonated RAC gradually increased with the carbonation depth. The uncarbonated and fully carbonated RAC show smaller static elastic modulus than natural aggregate concrete (NAC). As the carbonation depth increased, the peak stress increased, while the peak strain decreased and the descending part of the curves gradually became steeper. As the content of RCA became larger, the peak stress decreased, while the peak strain increased and the descending part of the curves gradually became steeper. An equation for stress–strain curves of RAC after carbonation was proposed, and it was in good agreement with the test results.


Introduction
With the acceleration of the modernization process, the demand for concrete in the construction market is increasing. A large amount of natural coarse aggregate (NCA) was produced and then consumed, which leads to an increasing shortage of natural aggregate resources and brings huge challenges to sustainable development [1]. Meanwhile, the construction and demolition of buildings has also brought about more construction waste. Currently, the application of recycled coarse aggregate (RCA) instead of NCA in actual engineering can significantly decrease the amount of NCA [2] and further alleviate the severe shortage of resources, therefore, the engineering application of recycled coarse aggregate concrete (RAC) had received widespread attention and was actively promoted.
The construction industry, which consumes huge natural resources, is not only the main source of CO 2 emissions, but also suffers from severe durability due to carbonation. It is widely known that carbonation of concrete is essentially a chemical reaction process of Ca(OH) 2 and C-S-H with carbon dioxide, respectively [3,4]. This will lead to the decrease of the concentration of hydroxide in the pore solution, which means that the pH value is reduced, and induces the increase of chloride ion concentration, further resulting in the corrosion of embedded reinforcements. Immense efforts are being made to reduce the harm of carbonation to concrete by trying different methods. For example, the replacement of ordinary Portland cement by alkali-activated materials may decrease the emission of carbon dioxide from the root [5]; the application of red ceramics could weaken the carbonation

Coarse Aggregate
The RCA provided by Nanjing Shoujia Renewable Resources Utilization Company (Nanjing, China) was made from waste concrete through mechanical crushing, cleaning, grading and processing. RCA and NCA were continuous-graded crushed gravel with a size from 2.5 to 26.5 mm. The basic properties of RCA and NCA tested according to JGJ 52-2006 [22] fulfilled the requirements. Figure 1 depicts the grading distributions of RCA and NCA, and Table 2 shows the basic properties of RCA and NCA.

Cement
The cement applied in this test was 32.5 ordinary Portland cement manufac China Cement, Co., Ltd. (Nanjing, China). The physical and chemical characterist cement are presented in Table 1.

Coarse Aggregate
The RCA provided by Nanjing Shoujia Renewable Resources Utilization C (Nanjing, China) was made from waste concrete through mechanical crushing, c grading and processing. RCA and NCA were continuous-graded crushed grave size from 2.5 to 26.5 mm. The basic properties of RCA and NCA tested accordin 52-2006 [22] fulfilled the requirements. Figure 1 depicts the grading distributions and NCA, and Table 2 shows the basic properties of RCA and NCA.   Natural river sand with fineness modulus of 2.60 was selected as fine aggregate (FA). Figure 1 shows the grading distribution of FA, and Table 2 displays the basic properties of FA.

Mix Proportion
The mix proportion of the RAC was designed according to the method proposed in JGJ-55-2011 [23]. In order to achieve a target 28d cubic compressive strength (f cu,28 ) of 20 MPa for RAC with 100% RCA content, the water-cement ratio was determined to be 0.53 by tests. Additionally, considering the high water absorption characteristics of RCA, a suitable method should be sought to compensate the loss of water content, so as to reduce the influence of water loss on the mix design and improve the workability of RAC. Referring to the existing research literature, two effective methods were proposed to solve the aforementioned problem. One method was to add more water in the process of mixing the mixture [24,25], and the other method was to prewet the RCA with dry surfaces [26]. Referring to the research results of Poon et al. [27], Brand et al. [28] and Oliveira et al. [29], the RCA was soaked in water for 10 min, then taken out of the water and dried for 10 min before mixing. The concrete mixtures and properties are shown in Table 3.

Specimens
Four degrees of carbonation were designed including non-carbonation, partial carbonation with lower carbonation depth, partial carbonation with larger carbonated depth and full carbonation (non-carbonation represents a target carbonation depth of 0 mm; partial carbonation with lower carbonated depth represents a target carbonation depth of 15 mm; partial carbonation with larger carbonated depth represents a target carbonation depth of 35 mm; full carbonation represents a target carbonation depth of 50 mm).
Corresponding to each degree of carbonation, a total of four batches of concrete specimens were cast. Each batch consisted of six groups of concrete specimens with different replacement ratios of RCA (0%, 20%, 40%, 60%, 80% and 100%). Within each group, 3 cubic specimens (100 mm × 100 mm × 100 mm) were used to obtained the measured carbonation depth (MD), 3 cubic specimens were used to obtain the f cu,28 , 6 cubic specimens were used to measure the cubic compressive strength after carbonation (f cu ) and 6 prismatic specimens (100 mm × 100 mm × 300 mm) were applied for the tests of static elastic modulus (E c ) and stress-strain curves after carbonation. A total of 288 cubic specimens and 144 prismatic specimens were prepared. All specimens were cured for 24 h, demolded, then covered with wet straw-matting for the first 7 days and placed in the laboratory until the 28th day.

Accelerated Carbonation Test
Accelerated carbonation test was carried out in accordance with the method proposed in Chinese code GB/T 50082-2009 [30]. After 28 days of natural curing, the concrete specimens were placed in an air-dry oven for 48 h (60 • C). The concrete specimens were taken out of the oven, five sides of the specimen were sealed with heated paraffin, and the remaining unsealed side allowed the carbon dioxide to enter the inside of the specimen in one direction. Then the prepared concrete specimens were placed on the bracket of the HTX-12X carbonation chamber with CO 2 concentration, relative humidity and temperature of (20 ± 2)%, (70 ± 5)% and (20 ± 5) • C, respectively. The distance between each concrete specimen was more than 50 mm.
The initial model for predicting the carbonation depth established based on the diffusion law shows that there is a good correlation between the carbonation rate and the carbonation duration [31]. A similar conclusion was also found by Neves et al. [32]. Therefore, the specimen could reach the expected carbonation depth by setting the predetermined carbonation duration. When the test carbonation duration approached the predetermined value, one cubic specimen was taken out every 15 d and split to test whether the carbonation depth reached the expected value.

Carbonation Depth Measurement
As shown in Figure 2, the prepared cubic concrete specimens were split and the cross sections were sprayed with 1% phenolphthalein alcohol solution (Nanjing, China). After the color change was stable, the length from the edge of the specimen to the edge of the red-purple area was measured at intervals of 10 mm along the edge of the specimen. The mean value of the measured results was taken as the original carbonation depth. The average value of the carbonation depth of three identical samples was taken as the final measurement result. Table 4 lists the carbonation depth values of each batch of concrete specimens.

Degree of Carbonation
Property Type Note: S-the standard deviation for mean values among cubic concrete specimens; T-the time which concrete specimens were exposed to carbonation; MD-measured carbonation depth; D-the relative carbonation depth. Carbonation depth was used as a single index to measure the degree of carbonation of concrete. For concrete structures or components with different cross-section dimensions, their mechanical properties were different to a certain extent although the measured carbonation depth values were the same. Therefore, the size of concrete structure and component should be considered when measuring the degree of concrete carbonation. Considering the size effect and more reasonably describing the change of mechanical properties of concrete after carbonation, the relative carbonation depth (D) of concrete, which is the ratio of the MD to half of the section side length of the cubic specimen, was defined as the analytical parameter to study the performance of carbonated concrete. The experimental results of the D of concrete specimens are listed in Table 4.

Uniaxial Compressive Loading Test
After the carbonation test, the uniaxial compressive loading test was carried out. In order to avoid the friction force produced in the process of top-load application from affecting the stress state of the entire concrete specimen [33], two displacement sensors with a range of 200 mm were installed to measure the strain in the midspan of the specimen under uniaxial compression. In addition, two strain gauges were placed in the midspan of the other two sides of the specimen to measure transverse strain. A load sensor was placed between the bottom of the specimen and the loading plate to measure the axial load during the loading process. The digital display pressure testing machine with the capacity of 1000 kN was used to apply uniaxial compressive force to the specimen at the loading rate of 1.0 kN/s. The test data, which consisted of the longitudinal strain, the transverse strain and the axial load on the specimens, was collected by the dynamic signal acquisition and analysis system (20 points per second). Figure 3 shows the f cu,28 of the RAC in dependence on the replacement ratio of RCA. It can be clearly seen that the f cu,28 of RAC presents a downward trend as the content of RCA increased. Compared with NAC, the f cu,28 of RAC with replacement ratio of 20%, 40%, 60%, 80% and 100% decreased by 8.9%, 18.2%, 25.6%, 25.2% and 28.6%, respectively. Similar experimental results were also reported by Akbarnezhad et al. [34].

28d Cubic Compressive Strength
tributed to the following three aspects. Firstly, the bond between RCA and old and new mortar is weak, which is not conducive to the development of bond strength. Secondly, at the initial stage of mixing concrete, the excess water contained in RCA was released during the hydration process, leading to an increase in water-cement ratio, thus reducing the fcu,28 of RAC. Thirdly, RCA has large porosity, high crushing value and its strength is lower than NCA. With the increase of replacement ratio, stress concentration can easily occur in the process of axial pressure loading due to the accumulated damage existing in RCA. As analyzed by Hu et al. [35], due to the randomness of the experiment and the complex interaction mechanism between RCA and NCA, there is no monotonic relationship between fcu,28 and RCA substitution percentage. In this study, the ratio of the 28d cubic compressive strength of RAC (fcu,28-RAC) to the 28d cubic compressive strength of NAC (fcu,28-NAC) was defined as the relative fcu, 28. Figure 4 shows the relationship between relative fcu, 28 and RCA substitution percentage. The correlation coefficient (R 2 ) of the fitted curve is higher than 0.9, indicating that the formula shown in Figure 4 could quantitatively measure the loss of fcu,28 at each RCA substitution rate. As can be observed from Figure 5, the decrease in relative fcu,28 with the replacement ratio ranging from 0% to 60% was significantly greater than that of the replacement ratio varying from 60% to 100%. This illustrates that the low content of RCA has a great impact on the fcu,28-RAC. This is closely related to the development path and process of internal cracks. In the process of exerting uniaxial compressive force, the initial cracks inside RAC specimens expanded, widened, and gradually penetrated the RCA and weak zones. The reduction of the f cu,28 of RAC due to the incorporation of RCA was mainly attributed to the following three aspects. Firstly, the bond between RCA and old and new mortar is weak, which is not conducive to the development of bond strength. Secondly, at the initial stage of mixing concrete, the excess water contained in RCA was released during the hydration process, leading to an increase in water-cement ratio, thus reducing the f cu,28 of RAC. Thirdly, RCA has large porosity, high crushing value and its strength is lower than NCA. With the increase of replacement ratio, stress concentration can easily occur in the process of axial pressure loading due to the accumulated damage existing in RCA.
As analyzed by Hu et al. [35], due to the randomness of the experiment and the complex interaction mechanism between RCA and NCA, there is no monotonic relationship between f cu,28 and RCA substitution percentage. In this study, the ratio of the 28d cubic compressive strength of RAC (f cu,28-RAC ) to the 28d cubic compressive strength of NAC (f cu,28-NAC ) was defined as the relative f cu, 28 . Figure 4 shows the relationship between relative f cu, 28 and RCA substitution percentage. The correlation coefficient (R 2 ) of the fitted curve is higher than 0.9, indicating that the formula shown in Figure 4 could quantitatively measure the loss of f cu,28 at each RCA substitution rate. As can be observed from Figure 5, the decrease in relative f cu,28 with the replacement ratio ranging from 0% to 60% was significantly greater than that of the replacement ratio varying from 60% to 100%. This illustrates that the low content of RCA has a great impact on the f cu,28-RAC . This is closely related to the development path and process of internal cracks. In the process of exerting uniaxial compressive force, the initial cracks inside RAC specimens expanded, widened, and gradually penetrated the RCA and weak zones.

Cubic Compressive Strength after Carbonation
In this paper, under the same RCA substitution ratio, the ratio of the cubic compressive strength of carbonated concrete (fcu-carbonated) to that of uncarbonated concrete (fcu-uncarbonated) was defined as the relative cubic compressive strength after carbonation. Figure 5 shows the relative cubic compressive strength of RAC after carbonation in dependence on the MD at each specific RCA replacement ratio. As shown in Figure 5, at each specific substitution ratio, the relative cubic compressive strength of the RAC after carbonation presents an increasing trend with the increase of the MD. In terms of the RAC with 40% replacement ratio, the fcu of RAC with the carbonation depth of 17.3 mm, 25.5 mm and 50 mm were 10.7%, 14.3% and 22.2% higher than that of uncarbonated RAC, respectively.
In the process of carbonation, CO2 in the form of gas phase and liquid phase entered the concrete specimen mainly through the pores and cracks. The insoluble substance, CaCO3, formed by the chemical reaction between Ca(OH)2 and CO2 deposited in the pore structure; on the one hand, they could refine the size of the pores, on the other hand, their presence helps to reduce the volume of pores in cement-based material. Besides, the porosity of the loose concrete in ITZ was higher than that of the cement matrix, which was more conducive to the transmission of CO2 in the ITZ. The greater degree of carbonation further increased the strength of the concrete in ITZ. Therefore, the carbonated RAC shows higher compressive strength than uncarbonated RAC.

Cubic Compressive Strength after Carbonation
In this paper, under the same RCA substitution ratio, the ratio of the cubic compressive strength of carbonated concrete (f cu-carbonated ) to that of uncarbonated concrete (f cu-uncarbonated ) was defined as the relative cubic compressive strength after carbonation. Figure 5 shows the relative cubic compressive strength of RAC after carbonation in dependence on the MD at each specific RCA replacement ratio. As shown in Figure 5, at each specific substitution ratio, the relative cubic compressive strength of the RAC after carbonation presents an increasing trend with the increase of the MD. In terms of the RAC with 40% replacement ratio, the f cu of RAC with the carbonation depth of 17.3 mm, 25.5 mm and 50 mm were 10.7%, 14.3% and 22.2% higher than that of uncarbonated RAC, respectively.
In the process of carbonation, CO 2 in the form of gas phase and liquid phase entered the concrete specimen mainly through the pores and cracks. The insoluble substance, CaCO 3 , formed by the chemical reaction between Ca(OH) 2 and CO 2 deposited in the pore structure; on the one hand, they could refine the size of the pores, on the other hand, their presence helps to reduce the volume of pores in cement-based material. Besides, the porosity of the loose concrete in ITZ was higher than that of the cement matrix, which was more conducive to the transmission of CO 2 in the ITZ. The greater degree of carbonation further increased the strength of the concrete in ITZ. Therefore, the carbonated RAC shows higher compressive strength than uncarbonated RAC. Figure 6 vividly depicts the relationship between the RCA substitution ratio and the cubic compressive strength of RAC after full carbonation (f cu-fully ). As the content of RCA increased, the value of f cu-fully showed a gradual decline. This means that with the increase of RCA content, the f cu-fully was less affected by carbonation. This can be explained by the fact that most of the insoluble CaCO 3 generated in the carbonation process was filled in the new mortar in RAC, and a very small part was filled in the old mortar and the interface between the new mortar and the old mortar. Compared with the new mortar, the bonding interface between the new and old mortar as well as the internal cracks of RAC were less affected by carbonation. Therefore, in a word, the defect of RCA was responsible for the strength loss of concrete specimens. cubic compressive strength of RAC after full carbonation (fcu-fully). As the content of RCA increased, the value of fcu-fully showed a gradual decline. This means that with the increase of RCA content, the fcu-fully was less affected by carbonation. This can be explained by the fact that most of the insoluble CaCO3 generated in the carbonation process was filled in the new mortar in RAC, and a very small part was filled in the old mortar and the interface between the new mortar and the old mortar. Compared with the new mortar, the bonding interface between the new and old mortar as well as the internal cracks of RAC were less affected by carbonation. Therefore, in a word, the defect of RCA was responsible for the strength loss of concrete specimens. Figure 6. The fcu-fully versus the replacement ratio of RCA. Table 5 lists the test results of Ec measured according to the method proposed in Chinese code GB/T 50082-2009 [30]. It can be seen that, the Ec of NAC with relative carbonation depths of 0.31, 0.62 and 1 are 5.8%, 21.5% and 37.6% higher than that of uncarbonated NAC, respectively. For RAC with 100% replacement ratio, the Ec of RAC with relative carbonation depths of 0.41, 0.77 and 1 are 4.9%, 9.6% and 13.5% higher than that of uncarbonated RAC, respectively. This is because the insoluble substance, CaCO3, generated in the process of carbonation constantly filled the pores of concrete, further improving the compactness of concrete, thus increasing the Ec of the concrete.   Table 5 lists the test results of E c measured according to the method proposed in Chinese code GB/T 50082-2009 [30]. It can be seen that, the E c of NAC with relative carbonation depths of 0.31, 0.62 and 1 are 5.8%, 21.5% and 37.6% higher than that of uncarbonated NAC, respectively. For RAC with 100% replacement ratio, the E c of RAC with relative carbonation depths of 0.41, 0.77 and 1 are 4.9%, 9.6% and 13.5% higher than that of uncarbonated RAC, respectively. This is because the insoluble substance, CaCO 3 , generated in the process of carbonation constantly filled the pores of concrete, further improving the compactness of concrete, thus increasing the E c of the concrete.  Figure 7 shows the relationship between the E c and the MD of the carbonated RAC. It can be clearly observed that, under the condition of non-carbonation and complete carbonation, the E c of RAC with different replacement ratios was lower than that of NAC. Specifically, when the replacement ratio was 100%, the E c of uncarbonated RAC and fully carbonated RAC was 16.8% and 31.4% lower than that of NAC, respectively. Consistent research results were obtained by Chen et al. [36]. From Figure 8, it can also be concluded that greater replacement ratio of RCA led to smaller E c for RAC with the same carbonation degree. This is closely related to the porosity of the aggregate. The greater content of dense aggregate with high modulus of elasticity, the greater the E c of the concrete. The old mortar with high porosity attached to the surface of RCA and the original cracks inside RCA directly cause the elastic modulus of RCA to be lower than that of NAC.  Figure 7 shows the relationship between the Ec and the MD of the carbonated RAC. It can be clearly observed that, under the condition of non-carbonation and complete carbonation, the Ec of RAC with different replacement ratios was lower than that of NAC. Specifically, when the replacement ratio was 100%, the Ec of uncarbonated RAC and fully carbonated RAC was 16.8% and 31.4% lower than that of NAC, respectively. Consistent research results were obtained by Chen et al. [36]. From Figure 8, it can also be concluded that greater replacement ratio of RCA led to smaller Ec for RAC with the same carbonation degree. This is closely related to the porosity of the aggregate. The greater content of dense aggregate with high modulus of elasticity, the greater the Ec of the concrete. The old mortar with high porosity attached to the surface of RCA and the original cracks inside RCA directly cause the elastic modulus of RCA to be lower than that of NAC.   Due to the different sources of RCA and the small number of test specimens, various forms of equations have been proposed by authors to characterize the relationship between the elastic modulus and the cubic compressive strength of carbonated RAC, as shown in Table 6. Based on the existing research results and the experimental results of this paper, the elastic modulus in dependence on the cubic compressive strength of carbonated RAC was depicted in Figure 8.  Due to the different sources of RCA and the small number of test specimens, various forms of equations have been proposed by authors to characterize the relationship between the elastic modulus and the cubic compressive strength of carbonated RAC, as shown in Table 6. Based on the existing research results and the experimental results of this paper, the elastic modulus in dependence on the cubic compressive strength of carbonated RAC was depicted in Figure 8.

Static Elastic Modulus
It can be seen intuitively that the existing proposed formulas cannot fit the experimental results well. In this paper, the alternative regression analysis was performed based on Equation (2), Equation (4) and Equation (6). The regression equation was as follows.
where the regression coefficients a and b are 0.414 and 9.516, respectively. The correlation coefficient is R 2 = 0.93. Thus, the following relationship was recommended to reckon the relationship between the static elastic modulus and the cubic compressive strength of carbonated RAC. E c = 0.414 · f cu + 9.516 (9) Figure 9 shows the failure patterns of carbonated concrete specimens subjected to uniaxial compression load. With the increase of axial load, the carbonated NAC and RAC showed a similar failure process. When the applied stress exceeded the peak stress, tiny cracks parallel to the axial pressure appeared on the surface of the specimen. As the axial strain increased, these fine cracks gradually extended, widened and interconnected with each other. At last, an obvious oblique crack appeared on the surface of the specimen when failure occurred.

Failure Pattern
Compared with NAC, RAC specimens with high replacement ratios presented serious failure mode. Furthermore, the broken old and new mortar as well as RCA can be clearly seen on the fracture surface of the damaged RAC specimens. With respect to the failure process of the RAC with high substitution ratio, concrete specimens show brittle failure, marked by the rapid development of cracks and loss of bearing capacity. As can be seen in Figure 9e-h, compared with uncarbonated RAC, the surface spalling of concrete specimens with larger carbonation depth was observed, which was accompanied by a loud splitting sound in test, indicating that the carbonated RAC exhibits brittle characteristics. In general, failure planes observed from failed specimens indicate that the quality of the RCA is poor. clearly seen on the fracture surface of the damaged RAC specimens. With respect to the failure process of the RAC with high substitution ratio, concrete specimens show brittle failure, marked by the rapid development of cracks and loss of bearing capacity. As can be seen in Figure 9e-h, compared with uncarbonated RAC, the surface spalling of concrete specimens with larger carbonation depth was observed, which was accompanied by a loud splitting sound in test, indicating that the carbonated RAC exhibits brittle characteristics. In general, failure planes observed from failed specimens indicate that the quality of the RCA is poor.   Figure 10 shows the stress-strain curves of the carbonated concrete specimens under uniaxial compression. With the increase of vertical deformation, the stress of NAC and RAC with different carbonation depths shows a trend of first increasing and then decreasing. The peak stress (σ p ) of NAC with relative carbonation depths of 0.31, 0.62 and 1 were 10.2%, 30.5% and 46.8% higher than that of uncarbonated concrete, respectively, and the corresponding peak strains (ε p ) were 7.3%, 9.2% and 7.5% lower than that of uncarbonated concrete, respectively. Similar phenomenon could be seen from the comparison between the stress-stain curves of RAC with different carbonation depths in each figure. Furthermore, the greater the carbonation depth, the steeper the descending section of the stress-strain curve. This indicates that the carbonation would increase the brittleness of NAC and RAC. The reason for this was that the insoluble substances generated by carbonation gradually filled the pores and the cracks inside the concrete. With the increasing carbonation degree, the internal density of the concrete increased, resulting in a gradual increase in the ability of the entire specimen to bear external load, but a decrease in the ability to resist deformation. the stress-stain curves of RAC with different carbonation depths in each figure. Furthermore, the greater the carbonation depth, the steeper the descending section of the stressstrain curve. This indicates that the carbonation would increase the brittleness of NAC and RAC. The reason for this was that the insoluble substances generated by carbonation gradually filled the pores and the cracks inside the concrete. With the increasing carbonation degree, the internal density of the concrete increased, resulting in a gradual increase in the ability of the entire specimen to bear external load, but a decrease in the ability to resist deformation. It can be observed from Figure 10b-f that, with regard to the stress-strain curves of RAC with various carbonation depths, the difference was gradually reduced with the increasing replacement ratio. This illustrates that the stress-strain curves of RAC was less affected by carbonation with the increase of replacement ratio. This can be explained by the fact that the aforementioned insoluble substances produced during the carbonation process continuously filled the voids inside the mortar and the voids at the ITZ. Although the strength of concrete can be improved to a certain extent, the strength of RCA and the existence of original cracks inside RAC were not influenced by the carbonation process. Under the action of the external load, new cracks in RAC would continue to expand on the basis of these original cracks. Therefore, the original cracks existing in the interior of original natural aggregate inside RCA are the main cause of failure of RAC after carbonation.

The Influence of Carbonation on Stress-Strain Curves of RAC
3.5.2. The Influence of Replacement Ratio on Stress-strain Curves of RAC Figure 11 shows the stress-strain curves of uncarbonated concrete and fully carbonated concrete with different substitution ratios. As can be seen from the stress-strain curve of the uncarbonated concrete shown in Figure 11a, the σp decreased and the corresponding εp increased with the increase of replacement ratio. The σp of RAC with replace- It can be observed from Figure 10b-f that, with regard to the stress-strain curves of RAC with various carbonation depths, the difference was gradually reduced with the increasing replacement ratio. This illustrates that the stress-strain curves of RAC was less affected by carbonation with the increase of replacement ratio. This can be explained by the fact that the aforementioned insoluble substances produced during the carbonation process continuously filled the voids inside the mortar and the voids at the ITZ. Although the strength of concrete can be improved to a certain extent, the strength of RCA and the existence of original cracks inside RAC were not influenced by the carbonation process. Under the action of the external load, new cracks in RAC would continue to expand on the basis of these original cracks. Therefore, the original cracks existing in the interior of original natural aggregate inside RCA are the main cause of failure of RAC after carbonation. Figure 11 shows the stress-strain curves of uncarbonated concrete and fully carbonated concrete with different substitution ratios. As can be seen from the stress-strain curve of the uncarbonated concrete shown in Figure 11a, the σ p decreased and the corresponding ε p increased with the increase of replacement ratio. The σ p of RAC with replacement ratios of 20%, 40%, 60%, 80% and 100% were 15.2%, 10.6%, 17.1%, 20.3% and 27.4% lower than that of NAC, respectively, and the corresponding ε p of RAC with replacement ratios of 20%, 40%, 60%, 80% and 100% were −0.8%, 3.8%, 9.4%, 16.8% and 25.6% higher than that of NAC, respectively. Suryawanshi et al. [18], Xiao et al. [20], Belén et al. [21] and Luo et al. [44] revealed a similar conclusion that the σ p of uncarbonated RAC was no more than 30% lower than that of NAC, and the ε p of RAC was no more than 25% higher than that of NAC. It was because with increasing content of RCA, in addition to the rising number of cracks inside mortar and ITZ, the effective water-cement ratio around RCA was larger than that around NCA due to the adopted prewetting method before mixing, thus leading to a decrease in σ p . With the increase of replacement ratio, the increase in ε p was attributed to two aspects. Firstly, under the action of external load, the progressive development of origin micro-cracks in RCA results in a tendency to increase the longitudinal strain at a faster rate than the applied stress. Additionally, compared with NCA, the larger water-cement ratio around RCA makes the RCA smoother, allowing the increase of strain in the ascending branch.  Figure 11b shows the stress-strain curves of fully carbonated concrete. A conclusion similar to the test results of uncarbonated concrete was obtained. For example, on the basis of the data analysis in Table 5, it can be found that the σp of RAC with replacement ratios of 20%, 40%, 60%, 80% and 100% were 12.8%, 22.4%, 39.4%, 40.5% and 42.6% lower than that of NAC, respectively, and the corresponding εp of RAC were 2.4%, 12.4%, 19.9%, 14.1% and 34.9% higher than that of NAC, respectively. Meanwhile, experimental results also illustrate that although the interior of the fully carbonated concrete has a high degree of compactness, a large amount of original cracks inside RCA was responsible for the failure of carbonated RAC. In addition, under the premise of the same degree of carbonation, the descending of the stress-strain curves of RAC gradually became steeper with the increasing replacement ratios of RCA, indicating that the brittleness of RAC increases due to the defect of RCA.

Fitting Analysis of Stress-Strain Relation of RAC after Carbonation
In previous studies, researchers were devoted to the investigation on the stress-strain relationship of RAC and proposed corresponding models [18,20,21]. The model proposed by Guo [45] was used to describe the stress-strain curves of RAC after carbonation. The normalized equation is shown as follows:  Figure 11b shows the stress-strain curves of fully carbonated concrete. A conclusion similar to the test results of uncarbonated concrete was obtained. For example, on the basis of the data analysis in Table 5, it can be found that the σ p of RAC with replacement ratios of 20%, 40%, 60%, 80% and 100% were 12.8%, 22.4%, 39.4%, 40.5% and 42.6% lower than that of NAC, respectively, and the corresponding ε p of RAC were 2.4%, 12.4%, 19.9%, 14.1% and 34.9% higher than that of NAC, respectively. Meanwhile, experimental results also illustrate that although the interior of the fully carbonated concrete has a high degree of compactness, a large amount of original cracks inside RCA was responsible for the failure of carbonated RAC. In addition, under the premise of the same degree of carbonation, the descending of the stress-strain curves of RAC gradually became steeper with the increasing replacement ratios of RCA, indicating that the brittleness of RAC increases due to the defect of RCA.

Fitting Analysis of Stress-Strain Relation of RAC after Carbonation
In previous studies, researchers were devoted to the investigation on the stress-strain relationship of RAC and proposed corresponding models [18,20,21]. The model proposed by Guo [45] was used to describe the stress-strain curves of RAC after carbonation. The normalized equation is shown as follows: where a and b denote the shape parameters of the ascending branch and descending branch of curves, respectively. Combined with the experimental results and applying Equations (10) and (11), the optimal values of shape parameters a, b and the corresponding correlation coefficient (R 2 ) were obtained through data regression analysis, which were all listed in Table 7, respectively. As shown in Table 7, the corresponding correlation coefficients are greater than 0.9, demonstrating that the application of the model proposed by Guo [45] could better describe the stress-strain relationship of RAC after carbonation. To investigate the influence of the two factors of replacement ratio and carbonation degree on the stress-strain relationship of RAC, the parameters a, b in dependence on the replacement ratio (R) and the value D are depicted in Figure 12, respectively. The fitting equations are shown as follows: Experimental results show that replacing NCA with RCA in concrete mix and conducting carbonation would significantly increase the brittleness of RAC. With regard to the increase of replacement ratio of RCA increasing the brittleness of RAC, it was because the RCA particles are softer than the NCA particles, the path of crack development was to penetrate the interior of the aggregate instead of extending along the periphery of the aggregate, which results in a reduction in fracture energy and ductility. Regarding the carbonation behavior increasing the brittleness of RAC, it may be related to the product of hydration reaction. In the process of hydration reaction, a large amount of Ca(OH)2 crystal, 3CaO·2SiO2·3H2O and 2CaO·SiO2·4H2O cementitious material with good deformation performance was generated inside the concrete. However, these crystals and cementitious materials would be consumed during the process of carbonation. In the absence of external force, the CaCO3 precipitates on the pore wall due to the reaction, further reducing the deformation performance of concrete. Figure 13 shows the comparison between the calculated dimensionless stress-strain curves and the experimental stress-strain curves for RAC with 40% and 100% substitution ratio at different carbonation depths. There is a high degree of agreement between the experimental curves and the calculated curves. Therefore, the stress-strain model put forward in this paper could be adopted to obtain the dimensionless stress-strain curves of RAC after carbonation. As shown in Figure 12a, the value of parameter a, which represents the slope of the initial tangent of the stress-strain curve, decreased gradually with the increase of replacement ratio and carbonation degree, demonstrating that the plastic deformation characteristic of RAC specimens is more obvious. As for parameter b shown in Figure 12b, it shows an increasing trend with the increasing replacement ratio and carbonation degree, indicating that the RAC specimen exhibited poor ductility [44]. However, some data points are not in good agreement with the fitting results. The reason for this was that the cracks inside specimens and microcracks in RCA developed randomly when the stress-strain curve entered the descending phase, which significantly affected the deformation of the concrete. In addition, this was explained clearly by Xiao et al. [46], that the stress-strain relationship of RAC, which consists of the ascending and descending branch, had larger variability than that of NAC.
Experimental results show that replacing NCA with RCA in concrete mix and conducting carbonation would significantly increase the brittleness of RAC. With regard to the increase of replacement ratio of RCA increasing the brittleness of RAC, it was because the RCA particles are softer than the NCA particles, the path of crack development was to penetrate the interior of the aggregate instead of extending along the periphery of the aggregate, which results in a reduction in fracture energy and ductility. Regarding the carbonation behavior increasing the brittleness of RAC, it may be related to the product of hydration reaction. In the process of hydration reaction, a large amount of Ca(OH) 2 crystal, 3CaO·2SiO 2 ·3H 2 O and 2CaO·SiO 2 ·4H 2 O cementitious material with good deformation performance was generated inside the concrete. However, these crystals and cementitious materials would be consumed during the process of carbonation. In the absence of external force, the CaCO 3 precipitates on the pore wall due to the reaction, further reducing the deformation performance of concrete. Figure 13 shows the comparison between the calculated dimensionless stress-strain curves and the experimental stress-strain curves for RAC with 40% and 100% substitution ratio at different carbonation depths. There is a high degree of agreement between the experimental curves and the calculated curves. Therefore, the stress-strain model put forward in this paper could be adopted to obtain the dimensionless stress-strain curves of RAC after carbonation. mentitious materials would be consumed during the process of carbonation. In the absence of external force, the CaCO3 precipitates on the pore wall due to the reaction, further reducing the deformation performance of concrete. Figure 13 shows the comparison between the calculated dimensionless stress-strain curves and the experimental stress-strain curves for RAC with 40% and 100% substitution ratio at different carbonation depths. There is a high degree of agreement between the experimental curves and the calculated curves. Therefore, the stress-strain model put forward in this paper could be adopted to obtain the dimensionless stress-strain curves of RAC after carbonation.

Conclusions and Prospectives
With regard to the 28d cubic compressive strength of RAC with replacement ratio less than 60%, it decreased sharply with the increasing replacement ratio. When the content of RCA was larger than 60%, the 28d cubic compressive strength of RAC showed a slow decline with the replacement ratio. With regard to the NAC or RAC at a specific replacement ratio, greater degree of carbonation could further increase the cubic compressive strength.
The static elastic modulus of carbonated RAC gradually increased with the increasing carbonation depth. For uncarbonated or fully carbonated RAC, the static elastic modulus decreased with the increase of RCA content. The model for the relationship between static elastic modulus and cubic compressive strength was established according to the experimental results in this study.
Compared with the stress-strain curve of uncarbonated concrete, the influence of carbonation on the stress-strain curve of carbonated concrete was mainly reflected in the increase of stress value and the decrease of strain value. For RAC with high content of RCA, the stress-strain curves of RAC with various carbonation depth exhibited a small difference, indicating that the carbonation caused a lower impact. Under the condition of the same carbonation degree, the influence of RCA replacement ratio on the stress-strain curves was mainly reflected in the decrease of peak stress and the increase of peak strain.
The comparison results of the calculated stress-strain curves and the experimental stress-strain curves illustrates that the application of the existing model could better describe the stress-strain relationship of RAC after carbonation.
The mathematical model of the stress-strain curve for carbonated RAC proposed in this paper was established based on the existing test data. Reliability analysis should be added to further research if this model was applied to actual engineering. Additionally, the water-cement ratio of RAC was determined based on the adaptation of C20 strength

Conclusions and Prospectives
With regard to the 28d cubic compressive strength of RAC with replacement ratio less than 60%, it decreased sharply with the increasing replacement ratio. When the content of RCA was larger than 60%, the 28d cubic compressive strength of RAC showed a slow decline with the replacement ratio. With regard to the NAC or RAC at a specific replacement ratio, greater degree of carbonation could further increase the cubic compressive strength.
The static elastic modulus of carbonated RAC gradually increased with the increasing carbonation depth. For uncarbonated or fully carbonated RAC, the static elastic modulus decreased with the increase of RCA content. The model for the relationship between static elastic modulus and cubic compressive strength was established according to the experimental results in this study.
Compared with the stress-strain curve of uncarbonated concrete, the influence of carbonation on the stress-strain curve of carbonated concrete was mainly reflected in the increase of stress value and the decrease of strain value. For RAC with high content of RCA, the stress-strain curves of RAC with various carbonation depth exhibited a small difference, indicating that the carbonation caused a lower impact. Under the condition of the same carbonation degree, the influence of RCA replacement ratio on the stress-strain curves was mainly reflected in the decrease of peak stress and the increase of peak strain.
The comparison results of the calculated stress-strain curves and the experimental stress-strain curves illustrates that the application of the existing model could better describe the stress-strain relationship of RAC after carbonation.