## 2 Materials and Methods
### Mechanical Characterisation of the Concrete
#### 2.2.2 Digital Image Correlation Fundaments and Prototype  
The mechanical characterisation tests were complemented with the digital image correlation technique to measure the displacements and strains of the specimens. DIC allows these measurements to be calculated from images acquired during the testing process, comparing an initial reference image without strain with that corresponding to each of the loading states [30].  
Taking into account the type of specimens used and the existence of flat and curved specimens, a different approach was used for each of them. A 2D-DIC approach was used to measure the in-plane displacements and strains of the cubic specimens, while a 3-DIC approach was used for the cylindrical specimens.  
In both cases, it is necessary to carry out a preliminary preparation of the specimens. Firstly, the surface is primed with a matt white paint, and after that a speckle pattern is generated on it. In this case, the spray technique with matt black paint was used, which makes possible to generate a stable greyscale pattern on the surface whose speckle is random, unique and non-periodic [50]. In order to evaluate the quality of the generated pattern, the Mean Intensity Gradient (MIG) parameter [51] and the coverage factor were calculated. The value obtained for the MIG was higher than 30 for all samples, with a coverage factor between 45 and 55%, considered optimal according to [PERSON] et al. [52].  
The prototype used for image acquisition consisted of high-resolution cameras Manta G-917B 1\" (Allied Vision, Stadtroda, Germany) Monochrome CCD equipped with 50 mm macro lens and neutral LED lights to enhance illumination and facilitate acquisition (Figure 4). The synchronisation of the image acquisition and the data provided by the test machine was achieved using a Quantum data acquisition system plus an Omron CP1 Hprogrammable logic controller (PLC) that allowed the synchronisation and programming of the triggering of the different cameras.  
For the 2D-DIC approach (Figure 4a), a single camera was used and positioned perpendicular to the measurement plane using a micrometric ball joint. For the 3D-DIC approach (Figure 4b), two cameras with a stereo angle of 15\({}^{\circ}\) were used. In order to achieve the highest possible accuracy in the measurements, similar to a strain gauge [53], in both cases the device was placed at a distance of 1.25 m from the specimens, which allowed capturing the entire specimen surface with a GSD of 0.09 mm/px. A lens aperture of 8 and a shutter speed of 1/100 s were set to allow image acquisition with adequate illumination, depth of field and sharpness.  
Once images were captured, image analysis was performed for subsets of pixels within a region of interest (ROI). DIC uses Zero mean Normalised Cross-Correlation (ZNCC) [54] to analyse and compare the subsets. This process is facilitated by the greyscale speckle pattern. The application of this criterion to all subsets of the ROI and successive images is performed by optimisation algorithms, which are combined with interpolations to achieve sub-pixel accuracy [55].  
While for the 2D-DIC approach this process is carried out directly for flat images, in the 3D-DIC approach, it is necessary to carry out an orientation process prior to image acquisition that allows the conversion of image coordinates to three-dimensional coordinates. In this case, an approach similar to the one established by [PERSON] et al. [56] was used, which combines the Bundle Adjustment (BA) algorithm with the Direct Liner Transformation (DLT) algorithm. This methodology allows obtaining the distortion and the internal and external parameters of the cameras, which are used for the three-dimensional reconstruction of the ROI points for which the displacements and strains were calculated using the procedure described above.  
Figure 4: Digital image correlation prototype: (**a**) 2D-DIC; and (**b**) 3D-DIC.