Abstract Extended finite element method (XFEM) and time integration by α-method are coupled in the direct integration scheme to study the 2D dynamic fracture of concrete gravity dam-foundation-reservoir interaction. The advantages of XFEM for the strong displacement discontinuity description of a crack and α-method for the time integration in dynamic analysis to dissipate the shockwaves after crack growth are combined together. The proposed method can improve the computation efficiency and can avoid numerical instability to judge the crack propagation orientation of XFEM. Obtained results show by increasing the value of α in time integration, the shock waves after crack growth are decreased and the stability of numerical solution is increased. In addition the accuracy of the dynamic fracture simulation using the proposed method is investigated in comparison with other reported in the literature. To apply the interaction in finite element model, zero thickness six-nodal contact elements are used in which the dam, foundation and reservoir are formulated with Lagrangian approach. Also, to predict dynamic fracture behavior of a cracked dam, dynamic stress intensity factors (DSIFs) are used. The interaction integral (conservation integral) originally proposed to evaluate SIFs to incorporate dynamic effects is utilized to evaluate DSIFs. Effective parameters in problem-solving such as the contribution of each distinct term in the interaction integral, crack tip element, length of crack growth, integration radius, location of initial crack, angle of initial crack, internal damping ratio of the dam, and fracture energy based on proposed method are discussed.

中文翻译：

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XFEM与时间积分α法相结合的坝基水库地震分析

摘要 扩展有限元法(XFEM)和α法时间积分耦合在直接积分方案中，研究混凝土重力坝-地基-水库相互作用的二维动态断裂。XFEM 用于裂纹强位移不连续性描述的优点和用于动态分析中时间积分以消散裂纹扩展后的冲击波的 α 方法的优点结合在一起。提出的方法可以提高计算效率，避免数值不稳定对XFEM裂纹扩展方向的判断。得到的结果表明，在时间积分中增加α的值，裂纹扩展后的冲击波减小，数值解的稳定性增加。此外，与文献中报道的其他方法相比，研究了使用所提出方法的动态断裂模拟的准确性。为了在有限元模型中应用相互作用，使用零厚度六节点接触单元，其中大坝、地基和水库用拉格朗日方法制定。此外，为了预测开裂大坝的动态破裂行为，使用了动态应力强度因子 (DSIF)。最初提出用于评估 SIF 以结合动态效应的相互作用积分（守恒积分）被用来评估 DSIF。解决问题的有效参数，例如相互作用积分中每个不同项的贡献、裂纹尖端元素、裂纹扩展长度、积分半径、初始裂纹位置、初始裂纹角度、