Numerical simulation of vertical crack propagation in paddy fields based on nonlinear fracture mechanics

用断口照片测得的裂缝尖端张开角(CTOA)描述了裂缝形成的机理。断裂试验使用了深槽弯曲试件，该试件是将钙基膨润土和硅砂的混合物与液限的水稻土模制成矩形棒，与土壤吸力在5~50 kPA之间保持平衡(有些50kPa试件湿化到5kPa时)，并插入0.4倍试件厚度的缺陷。从一系列图像中量化了裂纹的生长和几何形状。在裂纹稳定扩展过程中测得的CTOA随干燥程度的增加而减小。当最初平衡到50kPa的样品被重新润湿到5kpa时，CTOA甚至进一步下降。这些结果表明，CTOA主要由硬度决定，尽管再湿作用可能会改变裂纹尖端之前的毛细应力。安装在容器中的土壤通过压缩压力进行固结。解除压力后，在中心形成一个垂直的缺陷，然后试件受到由渗透性陶瓷制成的两侧的水吸入。将观察到的CTOA值与弯曲试验测得的值进行比较。收缩时的CTOA值与弯曲时的CTOA值相近，说明用弯曲试验得到的CTOA值来模拟收缩裂缝是可行的。该模型由一个主程序和一个模块组成，主程序用于计算土壤水分耗竭引起的土体变形，模块通过参考当前CTOA和临界CTOA来确定裂纹尖端的发展。模型的试运行证明，预测的裂缝深度与现场测量的裂缝深度基本一致，为模拟提供了参数。

Mechanics of crack formation were described using Crack Tip Opening Angle (CTOA) measured with fractography soil were used. Fracture testing used deep-notch bend specimens formed by moulding a mixture of Ca-bentonite and silica sand, and a paddy soil at the liquid limit into rectangular bars, equilibrating to soil water suction ranging from 5 kPa to 50 kPa (with some 50kPa specimens wetted to 5kPa), and inserting a flaw 0.4 x specimen thickness. The growth and geometry of the cracks were quantified from a series of images. CTOA measured during stable crack growth decreased with drying. CTOA decreased even further when specimens equilibrated initially to 50 kPa were rewetted to 5 kPa. These results suggested CTOA was primarily governed by the stiffness, although rewetting probably altered the capillary stresses in advance of the crack tip.Vertical crack propagation was studied in a laboratory-scale model subject to shrinkage. Soil installed in a container was consolidated by compression pressure. After removing the pressure, a vertical flaw was formed at the center, and then the specimen was subject to water suction imposed to both sides made of permeable ceramics. Observed CTOA values were compared with those measured by the bending tests. CTOA values in shrinkage were similar to those in bending, suggesting it is practically sufficient to use CTOA obtained by the bending tests for the simulation of shrinkage-induced cracking.A numerical model was developed based on the coupled mechanical and hydraulic analysis of soil. The model is consists of a main program which calculates the deformation of soil due to depletion of soil water, and a module which determines progress of the crack tip by referring to current and critical CTOA. Test runs of the model proved that the predicted crack depths were practically corresponded to those measured in the field where parameters for the simulation were obtained