## 3 Damage Characteristics
### Mesoscale Damage  
The characteristics of cracks in the soil are one of the main manifestations of the mesoscale properties of the soil. They represent a type of characteristic that lies between the macro- and micro- scales. Utilizing high-definition photographs to extract crack data is economically advantageous. The processing steps for this method are shown in Figure 6.  
(i) Image Extraction: Due to the tendency of sandy red clay to swell upon water absorption and shrink during dehydration, cracks gradually close during the humidification process [32]. Therefore, crack images are extracted only after the sample has been completely desiccated. Following each complete dehydration cycle, the upper surface of the sample is photographed, recorded, and analyzed. During the photographic process,  
Figure 5: XRD test results of sandy red clay under cycles. Figure 6: Flowchart of crack image processing. the sample is positioned within an lightbox. A digital camera, securely mounted on an iron stand, is positioned approximately 10 cm above the center of the ring sample. All ambient light sources are excluded, and the upper surface of the sample is captured solely under light illumination within the light-box. The pixel resolution and focal length are maintained consistently across all photographs. (ii) Image Processing: The detailed procedure is outlined as follows: The original image was first imported into Adobe Photoshop 2020 (PS) for initial processing, the goal of this step was to crop the image along its borders to extract the sample section. The cropped image was then imported into Matlab, where it was converted to grayscale. Subsequently, the grayscale image underwent several processes, including grayscale correction, initial denoising, image sharpening, and grayscale inversion. The processed grayscale image was binarized, and filtering methods were applied to remove small noise points, resulting in a cleaner image. Finally, the cracks within the image were connected, and image closing and deburring operations were performed. (iii) Signal Conversion: The image signals were converted into a digital format. Image-Pro-Plus 6.0 (IPP) software demonstrated advantages such as a high accuracy in edge detection and the ability to concurrently and precisely quantify multiple parameters of irregular shapes, which enabled the precise extraction of image features. After the images processed by Matlab were imported into IPP software and its measure function was employed, the desired parameters were specified, which facilitated the extraction of crack characteristics. In order to quantitatively analyze the development law of the crack using wet-dry cyclic action, the following basic indexes are proposed: (i) Maximum crack width (\(w_{max}\)), defined as the maximum value of the distance between the curves on both sides of the crack along the width direction, generally located near the intersection of the main crack. (ii) The mean crack width (\(w_{avg}\)), defined as the ratio of the total cleft area to the longitudinal cleft length. The crack length was calculated from the ossified crack images. (iii) The crack ratio (\(r_{c}\)), defined as the ratio of the area of the crack to the surface area of the specimen. In this study, the white area represents the crack, so the ratio of the number of white pixel points to the total number of pixel points was used to represent the crack rate. Note that the scale was calibrated by the average diameter of the specimen measured by vernier calipers. It is noteworthy that, upon analyzing the crack evolution patterns of each specimen, all specimens exhibited a common three-stage law of crack evolution: initiation stage (\(N\leq 1\)), propagation stage (\(1<N\leq 4\)), and stable stage (\(N>4\)), despite the discrete nature of the absolute fracture parameters among the specimens. During the initiation stage, the cracks are minute, with a sparse distribution of a few tiny cracks, and the crack network has not yet developed.