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基于多边形比例边界有限元法和粘聚裂缝模型提出了混凝土坝坝基界面在随缝宽非线性变化的水压力驱动下的非线性断裂数值模型。混凝土和基岩采用多边形比例边界单元模拟,界面裂缝的断裂过程区采用粘性界面单元模拟。因为界面裂缝总是处于复合断裂模态,故同时引入了法向和切向的界面单元,且考虑了裂纹面作用有法向和切向任意荷载时的应力强度因子求解。以裂尖为原点,裂尖附近的位移场和应力场在径向上解析求解,在环向具有有限元精度。因此无需在裂尖附近加密网格或采用富集技术即可求得高精度的解。对于界面断裂,可模拟出与两种材料差异性相关的非1/2奇异性。断裂过程区的水压力随缝面宽度变化,采用指数函数的形式进行表征,通过参数调整可实现不同分布的水压力的模拟。水压力与粘聚力考虑为与裂缝宽度相关的组合函数,便于非线性迭代的实现。结合多边形网格生成和重剖分技术,可方便地模拟界面裂缝在水力驱动下的扩展过程。算例研究表明了该文模型的有效性,从中也可看出考虑缝内水压及其具体分布形式对研究坝的稳定性具有重要影响。
Based on the finite element method of polygon boundary and the model of cohesive fracture, a numerical model of nonlinear failure of concrete dam foundation interface driven by water pressure with nonlinear changes of slot width is proposed. The concrete and bedrock are modeled by a polygon proportional boundary element, and the fracture process area of the interface crack is simulated by a viscous interface element. Because the interface cracks are always in the complex fracture mode, both normal and tangential interface elements are introduced at the same time, and the stress intensity factor when the crack surface acts with normal and tangential loads is considered. With the crack tip as the starting point, the displacement field and stress field near the crack tip are resolved analytically in the radial direction and have finite element accuracy in the circumferential direction. Therefore, it is not necessary to encrypt the mesh near the crack tip or use the enrichment technique to obtain a high-precision solution. For interfacial fracture, non-½ singularities associated with the variability of the two materials can be simulated. The water pressure in the fracture zone changes with the width of the seam, and is characterized by an exponential function. Through the parameter adjustment, the simulation of water pressure with different distribution can be realized. Water pressure and cohesion are considered as a combinatorial function related to the crack width to facilitate the realization of nonlinear iterations. Combined with polygon mesh generation and re-segmentation technology, interface crack propagation under hydraulic driving can be simulated conveniently. The case study shows the validity of the model. It can also be seen that considering the pressure and the specific distribution of the fractures have an important influence on the stability of the dam.