# Use of Image Correlation to Measure Macroscopic Strains by Hygric Swelling in Sandstone Rocks
## 3 Results and Discussion
For the vertical displacement, we see a clear movement due to hydration in the vertical direction. The curve is the typical one that has been observed in other experiments [15], with rapid swelling and a slow stabilization phase. Horizontal displacements were more difficult to interpret as the ROIs on the left and right sides were expected to move in opposite directions. However, the obtained results showed that the movement of all the ROIs went in the same direction, although the displacement of the three ROIs on the left was always less than that on the right. This effect could be due to sample rotation from the irregular expansion of the base or a composition camera drift effect and rock expansion. In order to better understand this situation, Figure 11 represents the horizontal and vertical strains obtained for all four samples. As strains represent relative displacement between ROIs, all the global effects on the sample (rigid body movements) can be cancelled out, and all the observable effects may be due to internal forces. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Vertical Strain Error (\(\times\)10\({}^{-3}\))**} \\ \hline
**ROIs** & **MEAN** & **STD** \\ \hline
1–2 & 0.1167 & 0.1467 \\
2–3 & 0.1841 & 0.1172 \\
1–3 & 0.1504 & 0.0833 \\
4–5 & \(-\)0.5586 & 0.1580 \\
5–6 & 0.0938 & 0.1461 \\
4–6 & 0.2313 & 0.0823 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Vertical strain error for a long-term still sequence of the recorded images. Figure 10: Measured vertical (left) and horizontal (right) shifts for each ROI in a wet experiment. The results are shown for sample 1, but similar graphs were obtained for all the measured samples. As the sample was submerged at the bottom, horizontal swelling was expected to be greater at the bottom than at the upper top. This was observed in all the horizontal displacement graphs, where each pair of ROIs presented minor deformations, because they were further away from water. The observed behavior was similar for all the samples, and the observed variability can be explained by rock non-homogeneity, which can produce samples with slightly different compositions and structures. Note that the upper part of all the samples, which corresponded to ROIs #1 and #4, was much less affected by hygric swelling. The results for the vertical strains were not so clear. Once again, it would seem that the upper part of samples, which corresponded to the strains between ROIs 1-2 and 4-5 (depicted in blue in Figure 12), were less affected by swelling. The green line, which represents the strains for the ROIs closer to the water level, presented a positive strain during the first 2 h, which means that the rock expanded. After this time, however, the strain decreased, possibly because an early capillary pressure effect was followed by relaxation and water circulation through pores to cause slight shrinkage in the vertical direction but maintained expansion in the horizontal direction. We underline that the strains observed in the vertical directions were of the same order as the peak error limits observed in the dry test (see Figure 9), hence the possibility of the oscillations herein shown not being so marked. However, the trend was very clear, and this behavior was repeated in all four samples with the same shape approximately 2 h after the experiment starts. At that time, as the drift was not as important, the effect cannot be fully explained by experimental errors, and the total displacement in Figure 10 is several orders of magnitude larger than the total displacement observed in the dry experiment (see Figure 8). Figure 11: Measured horizontal strains for the four hydrated samples. In order to get more insight about the rock behavior, we have calculated different deformation maps of sample 1. In Figure 13, we present the results obtained for the horizontal and vertical deformations at 1, 2 and 3 h after the water addition.