## 3 Results and Discussion
### Strain Localization  
The DICM results in terms of strain fields in the circumferential direction \(e_{xx}\) and radial displacement \(dR\) are provided. Using the method, the strain of any point within the observation area of the concrete is computed, so the initiation and development of the cracks are investigated through the full-field contour images where the \(e_{xx}\) and \(dR\) change under different loadings. Figure 9 shows the strain and displacement fields. The color scale bar presents positive and negative values corresponding to different colors, and the direction of movement can be determined in accordance with a coordinate system depicted in Figure 5: a positive value indicates that the sample is subjected to expansion and the displacement is moving to the radial direction in the color map. In this figure, the strain and displacement contours are represented at different strain energy levels which are inflection points on the AE energy trend (Figure 8). Figure 8: AE energy release rate \(f_{e}(U)\) and cumulative AE energy \(F_{e}(U)\): (**a**) AE energy release in sample No. 5; (**b**) AE energy release in sample No. 8; (**c**) AE energy release in sample No. 9; (**d**) AE energy release in sample No. 11; (**e**) AE energy release in sample No. 12. For sample No. 5 (Figure 9a), the strain in the x and z directions appeared to be a localization phenomenon at 50% of the strain energy level and the strain localization area concentrated along the center of the pre-existing flaw in the internal structure during the loading process. It indicates the main crack pattern which started from this location. The AE energy release at the strain energy level of 50% showed a sudden increase which means the significant crack development and the final failure corresponds to the high AE energy  
Figure 9: Circumferential strain \(e_{xx}\) and radial displacement \(dR\): (**a**) Distribution in sample No. 5; (**b**) Distribution in sample No. 8; (**c**) Distribution in sample No. 9; (**d**) Distribution in sample No. 11; (**e**) Distribution in sample No. 12.  
emission event near 100% of the strain energy level (Figure 8a). The localized displacement has also started from the 50% of strain energy level which is concentrated in the central part of the sample and moved to the bottom side implying the expansion of the radial surface caused by the pre-existing defects' modifications. The strain \(e_{xx}\) and radial displacement \(dR\) of damaged and non-damaged areas illustrate the significant difference in the values from the crack occurrence event (40% of the strain energy level). In sample No. 11, the same strain distribution can be mentioned: the circumferential strain localizes near the internal defects forming the main fracture pattern (Figure 9d). However, here, strain started to localize before the high AE event occurred. AE energy release had a sudden skip near 40% of strain energy level that demonstrates that fracture processes evolved faster (Figure 8d). Sample No. 8 illustrates the different strain and displacement phenomena: the main failure evolved on the specimen's upside and the edge popping out is clearly visible (Figure 9b). This process started at 20% of the strain energy level and dominated until the final failure as the mainly strain-concentrated and deformable area. According to the AE energy release behavior, the fracture events accompanied the loading process which is expressed in the continuous AE emission (Figure 8b). Rapid AE energy release occurred at 20% of the strain energy level corresponding to the edge deformation beginning, and at 40%, the popping-out was completed. Afterward, this place became a prevalent weak zone where cracks developed. In sample No. 9 (Figure 9c), strain localization can be detected immediately in different parts: the edge and back sides of the concrete core. It also can be mentioned that the cracking development processes occur faster and the coalescence can be detected, which says about an unstable failure stage leading to rapid failure.