## 3 Results and Discussion
### Ib-Value Analysis  
A B-value analysis method was first applied for analyzing seismic waves, and it has been recognized extensively by scholars for its advantages in quantifying seismicity [31]. The B-value analysis method can also be applied in the AE field for cases when the waves in acoustic emission are similar to the waves in an earthquake [21]. The B-value can be defined as follows:  
\[\log_{10}N=a-b\left(\frac{A_{dB}}{20}\right) \tag{5}\]  
where \(A_{dB}\) is the amplitude of AE signal; \(N\) is the number of AE signals with the amplitude above \(A_{dB}\), \(a\) and \(b\) are the parameters of linear fitting, \(a\) is the intercept of the regression line, and \(b\) is the slope of the regression line, also called the b-value of these AE events. Ib-value (improved b-value) method, which is evolved from the B-value analysis method, has been applied in the civil engineering field in the past few years [32]. The Ib-value is a calculated statistical value from AE events, which can be obtained by:  
\[lb=\frac{\log_{10}N(\mu-\alpha_{1}\cdot\sigma)-\log_{10}N(\mu+\alpha_{2}\cdot \sigma)}{(\alpha_{1}+\alpha_{2})\cdot\sigma} \tag{6}\]  
where \(\mu\) and \(\sigma\) are the mean and standard deviation of the amplitude distribution in recent \(N\) AE signals; usually the \(\alpha_{1}\) and \(\alpha_{2}\) are constant values between 0 and 1, in this paper, the two parameters are given the values of 0 and 1, respectively; \(N\) is set to 100, which is the population of recent hits. The Ib-value is a transient feature, and the value will be updated with each new AE signal recorded during the cracking process of the material. When micro-cracks (smaller-scale and weaker damage) begin to form, bigger Ib-values can be obtained. The reason for this is that during the cracking process of micro-cracks, the cracked surfaces rub against each other, although the number of AE events is large, the amplitude of AE signals is small. On the contrary, when macro-cracks (larger-scale and stronger damage) forms, smaller Ib-values can be obtained. Thus, the Ib-value analysis method (as a statistical analysis method) can effectively distinguish the internal damage type throughout the entire loading process. Figure 10 shows the Ib-value curves of RC beams with different corrosion ratios under the load of 0.05 kN/s. The maximum and minimum values of the five Ib-value curves are listed in Table 3.  
Figure 10: _Cont._  
From Figure 10 and Table 3, it can be considered that the maximum and minimum values of the five Ib-value curves are decreased with the increasing of the steel corrosion ratio. According to the physical meaning of the Ib-value, steel corrosion increases the proportion of the large amplitude of AE events in the fracture process, which infers that the proportion of macro-cracks is increased along with the steel corrosion ratio. Furthermore, even without loading, there are a large number of micro-cracks that form in concrete due to steel corrosion. Once the mechanical loading process begins, the micro-cracks could increase together rapidly and develop into macro-cracks, which demonstrates that steel corrosion seriously reduces the flexural properties of the RC beam. In the early load stage from 0 s to 100 s of the uncorroded RC specimen, the Ib-value curve falls sharply, which indicates a large amount of large-amplitude AE events, in other words, there are lots of macro-cracks formed during this stage. Then, in the 100-150 s load stage, the sharply increasing curve indicates that there are lots of micro-cracks formed. Later on, in the 150-350 s load stage, the  
Figure 10: Ib-value curves of corroded RC beams: (**a**) Uncorroded RC beam; (**b**) 10% corroded RC beam; (**c**) 20% corroded RC beam; (**d**) 30% corroded RC beam; (**e**) 40% corroded RC beam.