## 4 Results  
### Tensile Failure Mode  
The tensile stress-strain curves for the specimens with a dry density of 1.6 g/cm\({}^{3}\) are shown in Figure 6, where \(\varepsilon\) and \(\sigma\) refer to the tensile strain and tensile stress, respectively. For the specimens that were prepared using the WM (i.e., along the wetting path), their tensile stress-strain curves were found to have a similar pattern. It was shown that the tensile stress increased gradually until a peak stress value was reached and then the stain-softening behavior appeared at the post-peak stage. The analogously plastic deformation after reaching the peak tensile stress indicates the ductile behavior of all of the specimens that were prepared using the wetting method. Their tensile failures can be described approximately as ductile failures. It was noted that the ductile failure was more evident as the water content increased. Unlike the WM samples, the tensile stress-strain responses for the specimens that were prepared using the DM present two distinct patterns: (1) when the water content was more than 18%, the tensile failure was, in general, ductile, similar to that of the WM  
Figure 5: The methodology employed in this study. Figure 6: Tensile stress–strain curves for specimens with different water contents (\(\rho=1.6\) g/cm\({}^{3}\)). samples; (2) when the water content was less than 18%, the tensile stress initially increased almost linearly with the tensile strain until the peak value was reached. Then, the tensile stress decreased abruptly to 0 kPa with no plastic strains following afterward, apparently indicating a brittle failure mode. The tensile deformation process of loess is accompanied by the evolution of the strain field and the development of tensile cracks; two traits that are well captured by using PIV analysis. Combined with the obtained PIV results, the tensile stress-strain curve that is related to the ductile failure mode can be divided into four stages: the fabric adjustment stage (I), micro-crack formation stage (II), macro-crack formation stage (III) and crack penetration stage (IV), as are indicated in Figure 7. The PIV analysis results from the central neck part of the soil specimen for these four stages are illustrated in Figure 8, wherein Part A shows the development of the surface cracks while Parts B and C present the distribution of the displacement vector and strain contours at the region of interest (ROI). It was seen that, in stage I, the difference between the tensile displacement vectors, along with a relatively greater tensile strain, appeared at the upper part of the ROI, implying that the soil fabric was being adjusted due to the external tensile force and that the forthcoming tensile crack may develop from the upper part. In stage II, the tensile stress gradually increased to its peak value and micro-cracks were expectedly formed at the upper part of the specimen. The strain contour plot shows that the larger strain was mainly concentrated within the region wherein the micro-cracks emerged and that the tensile strain was at its largest near the crack's tip. In this stage, the local structure of the specimen was destroyed. In stage III, macro-cracks gradually formed, leading to a rapid decrease in the tensile stress. There was a noticeable displacement difference between the two sides of the crack and the direction of displacement was nearly perpendicular to the crack. Furthermore, a relatively greater tensile strain occurred at the bottom of the ROI, indicating the potential propagation of the crack from the upper part of the sample to the bottom. After the specimen entered stage IV, the crack extended downward and the tensile stress gradually decreased to zero. The larger tensile strain that appeared at the bottom of the sample indicated the formation of the connected crack. At this stage, the tensile displacement on the left side of the crack was close to zero, implying the splitting of the specimen and the occurrence of complete tensile failure.