土壤干缩开裂三维模型构建及其参数敏感性分析

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

    • 摘要: 为揭示农田土壤干缩裂隙沿深度方向的发展规律及形成机理,该研究改进了Vogel提出的Hookean弹簧模型,通过构建由节点组成的三棱柱状网格结构,并考虑重力的影响,建立了可以模拟裂隙深度的三维农田土壤干缩开裂模型,分析了纵向弹性系数(与土壤沿深度的弹性有关)对模拟裂隙深度的影响,通过Minkowski密度(即面积密度、长度密度和欧拉数密度)量化分析裂隙形态。结果表明:试验与模拟裂隙图像的面积、长度、欧拉数密度及裂隙深度频率的决定系数在0.849~0.959之间,一致性指标在0.965~0.988之间,偏差在0.103~0.189之间,均方根误差在0.005~0.083之间,说明改进后的三维模型达到率定要求,该三维物理模型可以模拟出裂隙沿深度的拓展情况,模拟的表层裂隙形态特征符合自然裂隙的发育规律。敏感性分析中,纵向弹性系数越小,裂隙沿深度方向发育的趋势越明显,深裂缝(土深5~10 cm)的占比越大。研究可为模拟农田土壤裂隙沿纵向的发育和形成提供算法参考。

       

      Abstract: 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, Kz (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

       

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