中文摘要：

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。

英文摘要：

A model for the water fracture modeling at dam-foundation interface is proposed based on Scaled Boundary Polygons and Cohesive Crack Model. Both the dam and foundation rock are modelled by Scaled Boundary polygons, while the fracture process zone of the interfacial crack is modeled by interface elements embodying a cohesive softening law. Since interfacial crack is always in mixed mode loading, interface elements are introduced in both the normal and tangential directions. The stress intensity factors are solved for cracks subscribed with arbitrary side-face tractions. The displacement field and stress field are solved semi-analytically, contributing to the high precision of the solution without asymptotic enrichment or local mesh refinement. The polygon generation and remeshing technique facilitates convenient modeling of the crack propagation process. The proposed model is verified by a numerical example, which also shows that the water pressure and its distribution pattern inside the crack influence remarkably the stability of the crack.