3.3.3. Elastic Modulus

Figure 11 shows the relationship between the elastic modulus and carbonation depth. It can be observed that the elastic modulus of RAC50 is significantly lower than that of NAC. The reasons are as follows. On the one hand, the decrease in the elastic modulus of RAC50 was attributed to the weak and porous recycled coarse aggregates [5,44]. On the other hand, the elastic modulus may decrease due to the cracks between old mortar and aggregates and the micro-cracks which occur in the process of the production of RCA [45].

**Figure 11.** Elastic modulus versus carbonation depth.

Moreover, the elastic modulus of NAC, RAC50, and RAC100 specimens increased with the increase of carbonation depth. O ˘guzhan Çopuro ˘glu [46] and Han Jian De [47] obtained similar results by using nanoindentation technology. Concrete specimens become denser with the increase of carbonation depth, which is due to the carbonation of concrete. In the carbonation, the chemical reaction between CO2 entered in the concrete and Ca(OH)2 in the cement produces insoluble CaCO3, which deposits in the pores of concrete.

When the carbonation depth reached about 20 mm, the elastic modulus of NAC, RAC50, and RAC100 specimens increased by about 15.8%, 10.2%, and 12.6%, respectively, compared to uncarbonated specimens. The result shows that the elastic modulus of NAC is higher than that of RAC50 with the same carbonation depth. When the RAC100 is fully carbonated, its elastic modulus has increased by about 28.3%.

#### 3.3.4. Relative Toughness

The area under the stress–strain curve can generally be considered as a measure of the toughness of materials [48]. However, researchers' definition of toughness is not universal. Wengui Li [41] and Sufen Dong [49] regarded the area under the stress–strain curve as toughness directly. Zemei Wu [50] and Jinyang Jiang [51] defined the relative toughness as the ratio of the area under the curve to that of the ascending portion before the peak stress.

To avoid misjudgment due to much higher peak stress after carbonation, the ratio of the area under the curve before 50% of peak stress at the descending part to that of before peak stress was defined as relative toughness in this study. Figure 12 shows the relationship between relative toughness and carbonation depth. The relative toughness of uncarbonated NAC is higher than that of RAC50. This may be due to the weak and porous RCA. The relative toughness of NAC, RAC50, and RAC100 specimens decreased overall with the increase of carbonation depth. When the carbonation depth reached about 20 mm, the relative toughness of NAC, RAC50, and RAC100 specimens decreased by about 14.6%, 7.1%, and 16.2%, respectively, compared with non-carbonated specimens. The results show that the relative toughness of NAC reduced faster than that of RAC50 with the increase of carbonation depth.

**Figure 12.** Relative toughness versus carbonation depth.

#### **4. Stress–Strain Relation of Carbonated RAC and NAC**

Xiao [29] and Wu [31] found that the analytical equations proposed by Guo [52] and adopted by the code for design of concrete structures (GB 50010-2002) in China to describe the complete stress–strain curve of NAC were also applicable to RAC. Hence, in this study, the equations are adopted to analyze the stress–strain relation of carbonated RAC and NAC are shown as follows:

$$y = \begin{cases} ax + (3 - 2a)x^2 + (a - 2)x^3, x \le 1\\ \frac{x}{b(x - 1)^2 + x}, x \ge 1\\ x = \frac{\varepsilon}{\varepsilon\_c}, y = \frac{\sigma}{\sigma\_c} \end{cases} \tag{3}$$

where *a* and *b* are parameters affecting the ascending and descending part of the curve, respectively; *ε*<sup>0</sup> is the peak strain; *σ*<sup>0</sup> is the peak stress.

The First Optimization software developed by 7D-Soft High Technology Inc. was used to find the optimum parameters of the ascending part and the descending part according to the test data based on Equation (3). Parameter *a*, *b* and corresponding correlation coefficients are shown in Table 4. The fitting results of the stress–strain relation are shown in Figure 13. The results show that the test values are in good agreement with the theoretical values and correlation coefficients are over 0.9. It is proven that Equation (3) is also applicable to carbonated RAC and NAC.


**Table 4.** Fitting results.

Parameter *a* represents the relative slope of the ascending part of the curve, and a smaller value means a flatter ascending part [50]. Parameter *a* of uncarbonated NAC and RAC50 are similar, whereas that of RAC100 is nearly 70% higher than them. This potentially indicates that parameter *a* depends on the compressive strength more than the replacement rate of RCA. Besides, parameter *a* generally shows a downward trend with the increases in the carbonation depth. This means carbonation increased the relative flatness of the ascending part of stress–strain curves.

Parameter *b* presents the relative slope of the descending part of the curve. A bigger *b* value means a steeper descending part of the curve and therefore poorer toughness performance [51]. It can be clearly observed that parameter *b* increases with the increase of carbonation depth, meaning that carbonation increased the relative steepness of the descending part of stress–strain curves.

**Figure 13.** *Cont.*

**Figure 13.** *Cont.*

**Figure 13.** *Cont.*

**Figure 13.** The fitting results of stress–strain relation. (**a**) NAC-0.0 mm; (**b**) NAC-4.9 mm; (**c**) NAC-9.0 mm; (**d**) NAC-12.2 mm; (**e**) NAC-14.5 mm; (**f**) NAC-17.5 mm; (**g**) NAC-19.8 mm; (**h**) RAC50- 0.0 mm; (**i**) RAC50-9.3 mm; (**j**) RAC50-15.3 mm; (**k**) RAC50-19.4 mm; (**l**) RAC50-21.3 mm; (**m**) RAC50- 29.1 mm; (**n**) RAC50-31.0 mm; (**o**) RAC100-0.0 mm; (**p**) RAC100-11.4 mm; (**q**) RAC100-16.8 mm; (**r**) RAC100-21.5 mm; (**s**) RAC100-25.2 mm; (**t**) RAC100-28.9 mm; and (**u**) RAC100-35.0 mm.

In addition, the correlation coefficients of NAC are higher than those of RAC50 and RAC100, which may be due to the discreteness of RAC [28].

The research results show that low strength of interfacial transition zone is the main factor of the size effect of concrete. Consequently, the size effect on the strength of recycled aggregate concrete becomes obvious because the strength of interfacial transition zone of recycled aggregate concrete is lower than that of ordinary concrete [53]. The compressive stress–strain model of recycled coarse aggregate concrete in this study is mainly used in the finite element method (FEM) analysis of concrete structure. The element size in the concrete structure analysis is small, so the size effect on strength and brittleness will be small. Therefore, the experimental results in Figure 13 will be directly applied to FEM analysis of concrete structure in the engineering practice.

#### **5. Summary**

In this study, the uniaxial compressive behavior of RAC with different carbonation depths was experimentally investigated, and the effects of carbonation depths on NAC and RAC were compared by experimental results. The main results are summarized as follows.


of ultimate strain to peak strain and relative toughness of RAC and NAC specimens decreased overall with the increase of carbonation depth. When the carbonation depth reached about 20 mm, the relative toughness of RAC50 and RAC100 specimens decreased by about 7.1% and 16.2%, respectively, compared with non-carbonated specimens.

(3) Stress–strain models of recycled aggregate concrete with different carbonation depths were established, and the experimental values are in good agreement with the theoretical values and correlation coefficients are over 0.9. Carbonation decreased the relative slope of the ascending part and increased the relative steepness of the descending part of stress–strain curves of recycled aggregate concrete.

**Author Contributions:** Conceptualization, J.W.; Data curation, H.D.; Formal analysis, K.T.; Investigation, K.T. and H.D.; Methodology, Y.W.; Resources, K.T., J.W., Y.W. and R.Z.; Supervision, J.W.; Validation, H.D.; Visualization, H.D.; Writing—original draft, H.D.; Writing—review & editing, H.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the subproject of the 13th Five-Year Plan National Key R&D Plan: Study on recycled aggregate concrete for construction waste and preparation of composite wall panel (2018YFD1101001-2), 2018–2022.

**Acknowledgments:** This work was supported by the subproject of the 13th Five-Year Plan National Key R&D Plan: Study on recycled aggregate concrete for construction waste and preparation of composite wall panel (2018YFD1101001-2), 2018–2022.

**Conflicts of Interest:** The authors declare no conflict of interest.
