# Use of Image Correlation to Measure Macroscopic Strains by Hygric Swelling in Sandstone Rocks
## 4 Conclusions  
This manuscript discusses a method to measure the deformation of a sandstone rock partially submerged in water due to hygric swelling. This method uses a simple camera and a telecentric objective, which allows macroscopic deformations to be measured. The method uses digital image cross-correlation on small rock areas so that changes in both the vertical and horizontal directions can take place.  
Both the numerical and experimental procedures are described, and possible errors were analyzed. According to our calculations, the calculation error method was below 0.1 px or the equivalent to 0.04 \(\upmu\)m. Experimental implementation requires long time sequences, which means that marked mechanical and thermal stability conditions are required. In our case, the required stability was not achieved, and an image drift was observed. However, the key parameter in our measurement was strain, which is a relative magnitude, and therefore, rigid body movements did not affect measurements.  
Four sandstone rock samples were measured by the herein presented methods. The horizontal strain demonstrated that rock deformation was not uniform, which became larger the closer it was to the submerged part. Our measurements showed a clear dilation in the horizontal direction, which is expected for a partially submerged porous body. The strain measurements in the vertical direction displayed unexpected behavior, so deformation maps at different moments during the experiment were calculated. The maps showed clearly the distribution of the deformations and revealed important inhomogeneities in their distribution, reflecting the composition of the rock.  
The method showed good capabilities in measuring local displacement and, from this, the strain of a small rock sample in both the vertical and horizontal directions. The methods herein followed, despite the limitations described, are simpler to implement than those that involve microscopic analyses and may be of much interest for analyzing macroscopic rock dynamics as construction material.  
Note that, with the exception of the telecentric lens, which can be replaced by a standard objective with proper distortion calibration, the setup is relatively cheap, which makes this procedure affordable for students or for preliminary tests in research labs. The main drawback of the method is the thermal drift observed. Future works should pay attention to compensate this issue without increasing the price and the complexity of the setup.  
Finally, we would like to add that the proposal demonstrates that natural textures can be used as reliable targets for DIC techniques. Further analysis and characterization of textures is needed in order to optimize the subpixel correlation results.  
Conceptualization, D.M. and B.F.; methodology, B.F.; software, D.M.; validation, M.-B.T., D.M. and B.F.; formal analysis, B.F.; investigation, M.-B.T.; resources, B.F.; data curation, D.M.; writing--original draft preparation, B.F.; writing--review and editing, D.M.; visualization, M.-B.T.; supervision, D.M.; project administration, B.F.; funding acquisition, M.-B.T. and B.F. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Generalitat Valenciana and the European Social Fund (FSE) through the Recruitment of Predoctoral Research Staff ACIF/2018/211 included in the FSE Operational Program 2014-2020 of the Valencian Community (Spain). [PERSON] and [PERSON] acknowledge the support from the Generalitat Valenciana through Project GV/2020/077.