*4.2. Analysis of AE Energy Distribution*

From the data in Figure 5, the AE accumulative energy distribution of the RC column was calculated on the area under three ranges of the load level (0–0.3, 0.3–0.6 and 0.6–0.9), as shown in Figure 6. In order to reduce the influence of machine error and environmental noise on the critical failure, this paper focuses on the analysis of energy release within the load level of 0–0.9 [32]. The loading process is divided into three phases: preloading (0–0.3), middle loading (0.3–0.6) and late loading (0.6–0.9). The proportion of the AE accumulative energy in three phases is calculated accordingly.

As shown in Figure 6, regardless of the degree of corrosion, the proportion of energy released in the late loading period is the largest but the smallest in the preloading period. The result shows that the internal damage degree of the RC column increases with the increase of the load level. Comparing among the four groups, the energy proportion of Z-0 is 5% and 6%. When the corrosion rate reaches 15% (Z-15), the preloading energy proportion only increases by 6%, which indicates that the corrosion of the reinforcement has little impact on internal damage in the preloading period. Although the internal crack increases with the increment of the corrosion degree on the reinforcement, the crack propagation is not obvious due to the low load level, which may explain the small increase in energy [33].

In the middle loading period, the energy proportion of Z-0 is 6% and 8%. As the corrosion rate increases, the energy proportion in the middle loading period can increase to 26% and 23% at a growth rate of 20%. This indicates that the load in the middle loading period can enlarge the original microcracks, resulting in a large AE energy release. The corrosion in Z-10 and Z-15 is much more than Z-0 and Z-5, which strengthens the release of AE energy from Z-5 to Z-10. In this case, the AE signals before the middle loading period can be affected by the corrosion degree of specimens. Hence, the AE signals in the middle loading period can reflect the initial health condition of the corroded RC column.

of AE energy from Z-5 to Z-10. In this case, the AE signals before the middle loading period can be affected by the corrosion degree of specimens. Hence, the AE signals in the middle loading period can reflect the initial health condition of the corroded RC column.

**Figure** *6.* AE accumulative energy distribution of the reinforced concrete column for different corrosion rates (two specimens per corrosion rate)*.*  **Figure 6.** AE accumulative energy distribution of the reinforced concrete column for different corrosion rates (two specimens per corrosion rate).

### *4.3. Damage Evolution Model of Corroded RC*

After taking the derivative of the curve shown in Figure 7a, the curve of slope change could be obtained, shown in Figure 7b. It can be seen that as the corrosion rate increases, at the load level of 0.9, the curve form changes from exponential to linear. As shown in Figure 7b, the slope of the load over the accumulative hit curve increases linearly with the increase of the load level. According to the results of the experiment, the corrosion rate also has an effect on the initial slope. The initial slopes of Z-0, Z-5, Z-10 and Z-15 are 125, 500, 800 and 1700, respectively. It can be found that within a certain corrosion rate range, the higher the corrosion rate, the greater the initial slope of the AE accumulation signal can be achieved. Meanwhile, since the initial slope represents AE activity at the initial low load level, a higher corrosion rate refers to stronger AE activity of the RC columns during the initial loading period. Although there is little variation between the two specimens for each corrosion rate, trends among different corrosion rates are apparent. *Crystals* **2021**, *11*, x FOR PEER REVIEW 10 of 17 ' *<sup>V</sup> N pe q* <sup>−</sup> = + 0.40871 **Table 3.** AE accumulative parameters. **Parameter Z-0 Z-0 Z-5 Z-5 Z-10 Z-10 Z-15 Z-15**  m 2985 3324 1684 1935 1885 1382 683 1256 n −120 24 256 504 832 450 1833 1836

**Figure 7.** *Cont*.

Z-5-2

0.0 0.2 0.4 0.6 0.8 1.0 0 1000 2000 3000 4000 5000 Specimen:Z-10-2 Accumulative hit number Load level

Z-10-1

Z-10-2

**Figure 7.** *Cont*.

**Figure 7.** Load accumulative hit curve and slope curve for different corrosion rates (two specimens **Figure 7.** Load accumulative hit curve and slope curve for different corrosion rates (two specimens per corrosion rate).

The variation of the parameters with the corrosion rate is shown in Figure 8. As the corrosion increases, m decreases from 3500 to 540, and at the same time, n increases from –120 to 2000. This indicates that parameters m and n are related to the change of the corrosion rate, and their approximate linear function can be expressed as [34]: *m* = − 2931 134ρ (11) *n* =− + 234 118ρ (12) Comparing the slope changes of each group, it can be seen that the slope of Z-0 increases from 125 to 2750. The slope of the Z-15 increases little from 1750 to 2800, but the growth rate remains at a high level. Therefore, it can be inferred that corrosion of the reinforcement can affect the whole service life of RC columns. When the corrosion rate is low or zero, the deterioration of internal damage is a dynamic process, from slow to fast. As a response, the AE signal changes from low to high. With the increase of the corrosion rate, the internal damage evolution of the RC column is accelerated, and the AE signal maintains a high level.

where *ρ* is the corrosion rate. By substituting m and n into Equation (10), N' can be expressed as ' *N mV n V V* = += − − − 2931 234 (134 118) ρ By integrating Equation (13), the relationship between load and accumulative hit can be expressed as follows: After considering the slope change trend, two slope relationship models are selected to fit the data [31]. The fitting results are shown in Table 2. Comparing these two models, the R<sup>2</sup> value of *N*<sup>0</sup> = *pe*−*<sup>V</sup>* + *q* is generally lower than that of *N*<sup>0</sup> = *mV* + *n*. Therefore, based on the characteristics of the above relationships, the binomial is adopted to establish the slope relation curve.

$$N'=mV+n\tag{10}$$

<sup>1</sup> 22 2 1465 234 (67 118 ) <sup>2</sup> *N mV nV V V V V* = += − − − ρ (13) where *N*' is the slope of accumulative AE hit number, and m and n are the AE accumulative parameters, which can be obtained by fitting, as shown in Table 3.

where *N* is the accumulative AE hit number, V is the load level, *ρ* is the corrosion rate and


m and n are the AE accumulative parameters. Combining Equations (14) and (2), the prob-**Table 2.** Fitting results of the slope.

per corrosion rate).

**Table 3.** AE accumulative parameters.


The variation of the parameters with the corrosion rate is shown in Figure 8. As the corrosion increases, m decreases from 3500 to 540, and at the same time, n increases from –120 to 2000. This indicates that parameters m and n are related to the change of the corrosion rate, and their approximate linear function can be expressed as [34]:

$$m = 2931 - 134\rho \tag{11}$$

$$n = -234 + 118\rho \tag{12}$$

where *ρ* is the corrosion rate. By substituting m and n into Equation (10), N' can be expressed as *N*<sup>0</sup> = *mV* + *n* = 2931*V* − 234 − *ρ*(134*V* − 118). *Crystals* **2021**, *11*, x FOR PEER REVIEW 13 of 16

**Figure 8.** Parameter variation with the corrosion rate. (**a**) *m* variation with corrosion rate, (**b**) *n* **Figure 8.** Parameter variation with the corrosion rate. (**a**) *m* variation with corrosion rate, (**b**) *n* variation with corrosion rate

variation with corrosion rate

0.0

10.

a = -0.15 b = 3.64 c = 41.72

0.0 0.2 0.4 0.6 0.8 1.0

Load level

Accumulative hit number

0.4

By integrating Equation (13), the relationship between load and accumulative hit can be expressed as follows:

$$N = \frac{1}{2}mV^2 + nV = 1465V^2 - 234V - \rho(67V^2 - 118V) \tag{13}$$

0.6 0.8 10% Corrosion rate 15% Corrosion rate Damage degree D where *N* is the accumulative AE hit number, V is the load level, *ρ* is the corrosion rate and m and n are the AE accumulative parameters. Combining Equations (14) and (2), the probability density function of the AE event can be obtained [35]:

$$f(V) = \frac{1}{N\_0} \frac{ds(V)}{dV} = \frac{2931V - 234 - \rho(134V - 118)}{N\_0} \tag{14}$$

0.2 The integral of Equation (15) is the damage evolution model of corroded RC:

$$D = \frac{1}{N\_0} \int\_0^V ds(V) = \frac{N}{N\_0} \tag{15}$$

0.0 0.2 0.4 0.6 0.8 1.0

Load level

Load level **Figure 9.** Correlation curve of the load and damage degree. *4.4. Initial Damage of Corroded RC*  The number of AE events in different corrosion rates is shown in Figure 10. In order to reduce the effect of system noise and eliminate the instability of the failed concrete, the The relationship of the load and damage degree under different corrosion rates for the RC column is shown in Figure 9. It can be seen that corrosion of reinforcement has a great influence on the damage evolution of the RC column. At the beginning, at the lower load level, the damage evolution is very slow. As the load level increases, the internal damage increases until the late loading period. Compared with the uncorroded specimens at the lower load level, with the increase in the corrosion rate, the damage factor of specimens is significantly increased, which leads to great damage accumulation before initial loading.

AE signal is collected under the load level of 0.1–0.9. Based on Ohtsu's model, the data at different corrosion rates are fitted. The fitting parameters a, b and c are shown in Figure

> a = -0.86 b = 0.24 c = 92.88

Accumulative hit number

Z-0-1 Z-0-2

Parameter

*m*

Parameter

*m*

0 2 4 6 8 10 12 14 16 18

variation with corrosion rate

Corrosion rate( %)

10.

a = -0.15 b = 3.64 c = 41.72

Accumulative hit number

**Figure 8.** Parameter variation with the corrosion rate. (**a**) *m* variation with corrosion rate, (**b**) *n*

Parameter *n*

Parameter *n*

*Crystals* **2021**, *11*, x FOR PEER REVIEW 13 of 16

(**a**) (**b**)

**Figure 9.** Correlation curve of the load and damage degree. **Figure 9.** Correlation curve of the load and damage degree.

### *4.4. Initial Damage of Corroded RC* 0.2

0.4

*4.4. Initial Damage of Corroded RC*  The number of AE events in different corrosion rates is shown in Figure 10. In order to reduce the effect of system noise and eliminate the instability of the failed concrete, the AE signal is collected under the load level of 0.1–0.9. Based on Ohtsu's model, the data at The number of AE events in different corrosion rates is shown in Figure 10. In order to reduce the effect of system noise and eliminate the instability of the failed concrete, the AE signal is collected under the load level of 0.1–0.9. Based on Ohtsu's model, the data at different corrosion rates are fitted. The fitting parameters a, b and c are shown in Figure 10. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 Load level

0 2 4 6 8 10 12 14 16 18 -500

Corrosion rate( %)

different corrosion rates are fitted. The fitting parameters a, b and c are shown in Figure 1500 2000 2500 3000 3500 4000 Accumulative hit number a = -0.86 b = 0.24 c = 92.88 It can be seen that the values of the uncorroded column are −0.15 and −0.86, which indicates that the AE rate of the specimens is very low at the lower load level. The initial microcracks of the two uncorroded columns are very few. The values of specimens at a 5% corrosion rate are −0.06 and 0.88. The AE rate increased with the increase of the corrosion rate, indicating that the number of microcracks also increased. The values of a for specimens at a 10% and 15% corrosion rate are both greater than 0, and the microcracks propagated. Therefore, comparing the results of the AE rate process theory theoretically proves that the different reinforcement corrosion degrees cause different initial damage to RC columns before axial compression. As a result, the diversity in the internal damage evolution of the corroded column obtained by Equation (10) is verified. **Figure 9.** Correlation curve of the load and damage degree. *4.4. Initial Damage of Corroded RC*  The number of AE events in different corrosion rates is shown in Figure 10. In order to reduce the effect of system noise and eliminate the instability of the failed concrete, the AE signal is collected under the load level of 0.1–0.9. Based on Ohtsu's model, the data at different corrosion rates are fitted. The fitting parameters a, b and c are shown in Figure 10.

**Figure 10.** *Cont*.

**Figure 10.** AE events in different corrosion rates and N–V fitting curves. **Figure 10.** AE events in different corrosion rates and N–V fitting curves.

### It can be seen that the values of the uncorroded column are −0.15 and −0.86, which **5. Conclusions**

indicates that the AE rate of the specimens is very low at the lower load level. The initial microcracks of the two uncorroded columns are very few. The values of specimens at a 5% corrosion rate are −0.06 and 0.88. The AE rate increased with the increase of the corro-Based on the experimental investigation, the following findings can be drawn from this study:


**Author Contributions:** Conceptualization, Y.C. and S.Z.; investigation, Y.C.; data curation, C.F., Y.L. and S.Y.; methodology, X.J.; visualization, Y.L.; formal analysis, D.W.; software, C.F.; writing—original draft, Y.C. and S.Z.; writing—review and editing, Y.L., G.Z., N.D., X.J. and S.Z.; project administration, Y.C.; funding acquisition, C.F.; validation, X.J., Y.L. and G.Z.; resources, Y.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** The financial support from the National Key R&D Program of China (No. SQ2019YFB160077), and the Natural Science Foundation of Zhejiang Province (Grant No. LR21E080002, LZ20E080003), and the National Natural Science Foundation (Grant Nos. 51678529 and 51978620) are gratefully acknowledged.

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

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