# A Novel Approach to Quantifying the Failure Modes of Concrete-Epoxy Interface
## 2 Materials and Methods
### Fracture Surface Analysis
#### 2.2.3 Failure Modes Detection and Quantification  
After the images of the CEI failure surfaces were pre-processed, the pre-processed images were analyzed to determine and quantify the failure modes with HVS, CIE L*a*b*, YCbCr, or RGB color space image segmentation and manual approaches. The manual approach is to validate the image segmentation-based process and determine the most suitable color space for evaluating the failure modes. * Color space image segmentation-based image processing approach  
The methodology for the color spaces segmentation approach is itemized in the following steps. Figure 5: A typical image of the fracture surface failure sides. Figure 6: Preprocessed images of the failure side designated as (**a**) A and (**b**) B. Step 1: Modelling the epoxy areas on the sides of CEI fracture surfaces with a white mask using HSV, CIE L*a*b*, YCbCr, or RGB color space-based segmentation technique. Step 2: Changing the color of the model of the epoxy areas to distinct primary color on either of the failure sides. The color of the model of sides A and B was changed to red and green, respectively. Step 3: Superimposing the new model of sides A and B at equal intensity. That, when any area covered by either green or red color overlays, a secondary color (i.e., yellow) is formed. The regions covered in yellow imply failure within the epoxy (CE), and those covered in red and green indicate a failure within the interface of concrete substrate and epoxy (IF). Step 4: Modelling the identified failure modes (IF and CE) with a white mask using HSV, CIE L*a*b, YCbCr or RGB color space-based segmentation technique. Step 5: Quantifying the failure modes. The IF, CE, and CC were evaluated with Equation (1) through (4). \[\text{Net area}=(\text{area covered by failure side A and B})/2, \tag{1}\]  
\[\text{IF}=(\text{area covered by IF}/\text{net area})100, \tag{2}\]  
\[\text{CE}=(\text{area covered by CE}/\text{net area})100, \tag{3}\]  
\[\text{CE}=(\text{ net area}-[\text{area covered by }(\text{CE}+\text{IF})]/\text{Net area})100, \tag{4}\]  
For conciseness, only the steps for the HSV color space image segmentation-based image processing technique is expressed graphically in Figures 7-10. The models with the concrete edges were not used in the failure mode evaluation, they are provided to monitor the overlapping of the concrete edges. * Manual approach  
The use of color space image segmentation techniques for CEI failure surface analysis is novel and there is a need to evaluate the performance of the color spaces for the proposed application. As a result, a manual or traditional approach was used to analyze the CEI failure surfaces to validate the novel image segmentation-based approach. However, due to the rigorous computational effort required by the manual approach, only one of the three failure modes was assessed. The failure surface analysis using the manual approach was limited to the evaluation of CE due to its computational ease compared to the other failure modes. The steps for evaluating the CE failure using the manual approach are itemized below. Step 1: Printing the pre-processed images of the failed CEI surfaces on 210 mm by 297 mm (A4) papers. Step 2: Modelling the concrete edges and epoxy areas on each CEI failure surface sides with blue and black A4-sized carbon paper, respectively. The models produced by the black and blue carbon papers were such that each represented either of the failure sides. Step 3: Highlighting the intersection of the epoxy area on either side. As shown in Figure 7, the overlaps of the two models were highlighted in green. The green highlights imply the region where failure within the epoxy (CE) occurred. Step 4: Evaluating CE. The ratio of the CE was evaluated with the aid of Equation (5). Figure 10: Step 4: modeling the (**a**) CE and (**b**) IF. Figure 9: Step 3: overlapped models of the (**a**) epoxy areas and (**b**) epoxy areas and concrete edges of the failure sides A and B.