# Acoustic Emission Analysis of Fracture and Size Effect in Cementitious Mortars
## 4 AE Analysis: Results and Discussion
### b-Value Analysis
#### 4.4.1 Role of Sensor-Source Distance in the \(b\)-Value Analysis  
In the Brazilian splitting test, cracking may start at one side of the sample and quickly propagate to the other side (y-direction). Hence, the \(b\)-value of AE hits captured by sensors located close to the fracturing region and those positioned on the other end are compared in this section to verify the effect of source-sensor distance. When approaching the peak load, micro-cracks will localize and coalesce to form macro-cracks. These macro-cracks typically start to form between 70 to 95% of the peak load. This is shown on the localization plot in Figure 11.  
The resulting \(b\)-value evolution for AE hits captured by separate channels is presented in Figure 12. From Figure 12a,b it can be seen that, for hits coming from channels closer to the fracturing region (Ch-1 and Ch-4), the \(b\)-value drops below 1 before reaching the peak load. This drop occurred when the load was between 70 to 95% of the peak load, indicating the macro-crack formation observed at the side of channels 1 and 4 in the localization plot. This clearly shows the capability of \(b\)-value analysis in identifying the fracture progression. On the other hand, this \(b\)-value drop was not captured less distinctively for hits coming from the sensors positioned at the other end of the sample, further from the fracturing region. This is shown in Figure 12c,d for channels 2 and 3, respectively. A drop in \(b\)-value requires the occurrence of high-amplitude hits. Due to the attenuation of signals when traveling to reach these sensors, this drop is not clearly observed. Hence, quantifying fracture behavior using AE \(b\)-value analysis requires signals that have not been subjected to a significant attenuation. The sensitivity of \(b\)-value analysis to AE amplitude attenuation has been observed by [PERSON] [57], on AE data acquired during a compression creep test on ice. Thus, designing an AE sensor layout requires a preliminary investigation on the possible location of fracture (initial damaged zone, a region with high-stress concentration or notches). In the current work, to avoid the impact of attenuation, only the sensor close to the fracturing region is used for further \(b\)-value analysis. However, the difference in sample size can also play a role in the variation of AE attenuation. This is because compared to the smallest sample, the AE signals within the larger sample can travel 35 to 50 mm more. The attenuation coefficient for the material was determined using the PLB test and was found to be 0.1 dB/mm. Thus, to avoid the impact of attenuation in the \(b\)-value analysis,  
Figure 11: Sensor (Ch) layout and AE source localization plots for a Brazilian splitting test at three stages of the loading on a large sample (\(L_{1}\)). The three loading stages are defined as a percentage of the peak load. All views are top views, and four of the six sensors (Ch) are indicated. only the AE hits captured by the sensors closer to the fracture region were used. Hence, the signals in the larger sample can attenuate by 3.5 to 5 dB more than the smallest sample. This can be assumed as sufficiently lower than the possible difference in AE due to size variation. As the sample size increases, the fracture energy is also expected to increase. Hence, AE of higher amplitudes are also expected. There is a tradeoff between attenuation and this increment in amplitude. Hence, this analysis is within the assumption that, for this sample size and the material attenuation coefficient, there is more increment in amplitude than the possible attenuation. This assumption is corroborated with the fact that in the larger samples, a similar amount of AE signals with higher amplitudes were still detected compared to the smaller samples, as exemplified in Figure 13.  
Figure 12: \(b\)-value analysis of AE hits detected on sensors (Ch) found close to and further from the fracture region on a large sample (\(L_{1}\)) for a Brazilian splitting test.