Construction of the three-dimensional soil shrinkage cracking model and its parameter sensitivity analysis

Soil desiccation and cracking can be one of the most common physical phenomena during natural and man-made damage processes. There is the a significant effect on the mechanical and hydraulic properties of soil in modern agriculture. This study aimed to reveal the development and formation mechanism of desiccation cracking in farmland soil along the depth direction. The Hookean spring model proposed by Vogel was improved to construct the triangular prism network structure with the nodes under the gravity. A three-dimensional soil desiccation cracking model was established to simulate the crack depth. The crack along the depth direction was assumed as the vertical development during simulation. The farm soil desiccation cracking experiment was carried out in the Tongxin County (105°54′E, 36°58′N), Ningxia, China. The ponded water was exerted at the soil surface, until the soil was saturated at the upper 10 cm layer. Camera photography was used to capture the images of crack formation and development at 2-hour intervals for three days. The steps of digital image processing included: the non-experimental part of the image was cropped, the image size was processed to 2048×2048 pixels, while the image was applied geometrically corrected, and a color image of the crack patterns was converted into a gray image, which was then converted into a binary image using the threshold division, and finally the image was processed through the noise removal. The white areas and black pixels in the binary image were represented by the aggregates and crack skeleton, respectively. After that, the Minkowski densities were adopted to quantify the surface crack patterns. Three basic characteristics of cracks were divided into the area A, the length L, and the Euler number E of the crack (representing connectivity in the two-dimensional crack structure). The difference between the Minkowski density and crack depth of the experimental and simulated image was quantified by four evaluation indicators: the coefficient of determination, R², the consistency index, IA, and the root mean square error, RMSE. Finally, a systematic analysis was implemented on the influence of the longitudinal elastic coefficients, K_z (representing the elasticity of soil along the depth direction on the model output. Parameters The parameters of the model were calibrated and verified by the field experimental measurement and photograph. The precision of the simulation was also evaluated. The results show that: The coefficients of determination, R² for the area, length, and Euler number density were between 0.849-0.959. RMSE was between 0.005-0.083, while the BIAS was between 0.103-0.190, and the consistency index IA was 0.965-0.988. As such, the improved 3D model calibration was fully met the requirement of calibration. The model was effective to simulate the formation and development of cracks in farmland soils along the depth direction. The simulated surface crack morphology was consistent with the development of natural cracks. The smaller the longitudinal elastic coefficient was, the more outstanding the trend of crack development along the depth direction was. The peak of crack depth frequency was at soil depth of 6 cm, and the proportion of deep cracks (soil depth of 5-10 cm) was larger. On the contrary, the crack generation and development along the depth direction were inhibited, with the peak of crack depth frequency at (soil depth of 1cm) and a greater proportion of shallow cracks (soil depth of 1-4 cm). The finding can provide an ideal way to predict the development and formation of soil cracks along the depth direction