# Use of Image Correlation to Measure Macroscopic Strains by Hygric Swelling in Sandstone Rocks
## 1 Introduction  
Hygric swelling is a process that some sandstone rocks undergo when humidity rises. It implies the volume increment of some rock particles, which causes strains, stresses and, depending on the rock composition, a global volume increment in rock. This process can produce small cracks, which is quite a common phenomenon in Europe [1, 2]. Consequently, strain measurement due to hygric swelling is an important parameter to assess the suitability of a particular sandstone rock in the construction and restoration of historic buildings. The most straightforward way to measure hygric swelling is to partially or completely submerge a rock probe in water and measure the vertical displacement of the upper probe boundary with a linear variable displacement transformer (LVDT) [3]. Given the total vertical probe length, and by assuming a zero displacement of its basis, a global vertical strain can be easily calculated as the mean value for all the points on the rock. However, on the one hand, not all points undergo the same strain, and on the other hand, only vertical strains can be measured by this simple procedure. Horizontal swelling measurements by LVDT need more complex devices that are not always suitable for the rock probe under study [4]. Those inconveniences can be overcome by methods based on imaging techniques. Measuring strains by image processing with the proper setup and calculation methods allows the strain to be found for each point in the image according to time [5]. However, image procedures followed to find strains also have some drawbacks. Some are related to the calculation method for tracking a specific detail with time. To this end, the most widely used operation is normalized digital image cross-correlation (DIC), which is implemented herein by the normalized cross-correlation algorithm, _normxcorr2_, in MATLAB [6]. Although DIC has a nominal accuracy of one pixel, accuracy can increase by subpixel techniques. These techniques consist of interpolating the image or interpolation peak. In both cases, the result is biased toward the nearer integer to, thus, introduce a symmetric error with a sigmoid shape to determine the subpixel position. Some errors may also appear during image recording, such as unexpected camera movements due to mechanical drifts, overheating, changes in ambient light or image distortion due to the camera lens. Therefore, a thorough error study that considers all these factors should be conducted as part of any image procedure. Image methods for measuring rock swelling have been implemented in very different ways in the literature: generally, probe size determines the most convenient imaging device for acquiring images, ranging from microscope to commercial cameras, and even different image setups can be used for the same probe size. In [7], scanning electron microscope images were used to compare the rock microstructure to the strains measured on a sample of centimeters in size. To measure strains, a 5 Mpx camera with a telecentric lens was used on the same probe side. The resolution for DIC calculation images was 0.5 px/um. Those images were analyzed by a DIC method developed by [8], which considers the possible cracks that were expected in the analyzed sample. Strains were calculated by displacement derivation using the correlation results. The results showed a very heterogeneous strain distribution during desiccation, probably due to the presence of heterogeneous water and microstructural non-homogenous distribution. Images directly taken by electron microscopy have also been used to perform DIC strain calculations [9]. In [10], a sample slice (1 mm thick and few millimeters on plane) of an argilaceous rock was recorded during swelling by electron microscopy with a 13.8 Mpx size and a resolution of 0.06 px/um. The results showed that the macroscopic swelling strain was the combined result of the local free swelling strains and the additional mechanical strains induced by particle interactions.