Geometrical size effect of desiccation cracks in purple soil in the Three Gorges Reservoir areas

Purple soil is one kind of agricultural soil that is widely distributed in the Three Gorges Reservoir area. The drying desiccation cracks in the purple soil can be easy to form under the rainfall-evaporation cycle. Hydraulic and mechanical properties of the soil can also be significantly exacerbated by natural disasters, such as soil erosion. Three Gorges Reservoir area also shares the complex topographical characteristics. Geometric size has been the most common environmental factor in the development of desiccation cracks in purple soil. Additionally, the recurrent persistent heavy rainfall often leads to severe hydraulic erosion in the purple soil, leasing to the dispersion of soil aggregates, the migration of fine particle runoff, and significant soil structural damage. The soil saturation can be localized, due to waterlogging. This study aims to investigate the geometric size effect of desiccation cracking under hydraulic erosion using the response surface method (RSM). A series of indoor drying experiments were conducted on 13 groups of purple soil mud samples with different thicknesses (10, 20, and 30 mm) and diameters (100, 200, and 300 mm). The crack morphologies were quantitatively characterized using digital image processing. The results show that: 1) Geometry posed an outstanding effect on the crack ratio, length density, average width density, and fractal dimension of desiccation cracks. Thickness was the main influencing factor on crack ratio and fractal dimension, while there was a more pronounced effect of the diameter on the crack length and width development. All crack ratio, average width density, and fractal dimension showed linear growth with an increase in thickness, whereas, ρl decreased linearly. length density decreased linearly with an increase in diameter, while average width density, and fractal dimension decreased nonlinearly, and crack ratio increased linearly. There was an interaction effect of diameter and thickness on crack ratio, average width density, and fractal dimension; 2) The cracks mainly presented in three forms of “I”, “T”, and “Y”, where the “T” type cracks were the highest proportion. The smaller the thickness was, the denser the crack distribution and the more irregular the crack network was. The smaller the diameter was, the more single the crack network and the more the cracks distributed toward the edge of the soil mass. The proportion of single crack area was mainly less than 0.2%, with a frequency exceeding 0.5. The probability density of the proportion of single crack area decreased exponentially with the increase of crack area. The frequency distribution followed the Expdec function curve. A random orientation was found in the initiation and propagation of cracks. However the size of the soil specimens significantly affected the uniformity of the crack direction distribution; 3) The geometric dimensions had a significant impact on the ease of cracking in purple soil, indicating a smaller average cracking stress with a larger diameter. The soil was more prone to desiccation cracking. However, the large thickness was selected to diminish the geometric size effect of diameter on the average cracking stress. The mechanical mechanism behind crack development was determined, according to the inter-particle unsaturated soil mechanics. The soil shrinkage and eventual cracking were attributed to the imbalance in the tensile stress field caused by an increase in the matric suction, due to the moisture evaporation. Geometric dimensions significantly impacted the rate of moisture evaporation. The finding can provide a strong reference for the morphology and development of cracks in purple soil in the Three Gorges Reservoir area.