基于多边形比例边界有限元的重力坝裂缝扩展过程模拟

Modelling of crack propagation of gravity dams based on scaled boundary polygons

本文基于多边形比例边界有限元方法(Polygon SBFEM)模拟了水力超载作用下混凝土重力坝的断裂过程。SBFEM有降维和半解析求解的特点,在求解裂缝尖端的应力场及位移场时有半解析解,可根据定义直接导出应力强度因子,对于界面材料和各向异性材料均可有效模拟。结合多边形单元生成和重剖分策略可使裂缝扩展过程的模拟非常灵活、便捷。Koyna大坝的水力超载算例表明,本模型仅用粗网格即可获得满意的精度,且计算结果对裂缝扩展步长不敏感,适用于实际混凝土坝工程的断裂分析。模拟所得裂缝扩展路径和荷载-位移曲线与现有文献结果一致,证明了本文模型的有效性。

The fracture process of concrete gravity dam under overflow loading is modeled by the PolygonScaled Boundary Finite Element Method(Polygon SBFEM). The domain is discretized with polygon ele-ments,each of which is considered as a subdomain of the SBFEM. The singular stress field and displace-ment field in the vicinity of a crack tip are obtained semi-analytically. The stress intensity factors are ob-tained directly from their definition. Different types of stress singularities can be represented in a uniformform. By introducing the polygon element scheme, it becomes flexible and convenient to predict the crackpropagation. Only local remeshing that introduces minimum changes to the global mesh is involved. Throughthe numerical simulation of Koyna dam subjected to reservoir overflow, it was found that different meshdensities and crack propagation lengths led to consistent results. The predicted crack trajectories and thestructural responses show a good agreement with other numerical simulations reported in the literature,which demonstrates the effectiveness of the model.