Combining XFEM and time integration by α-method for seismic analysis of dam-foundation-reservoir

•A numerical solution using the XFEM and time integration by α-method are coupled to study the 2D dynamic fracture of dam-foundation-reservoir problem.•The proposed method can improve the computation efficiency and avoid numerical instability.•Obtained results show by increasing the value of α in time integration, the shock waves after crack growth are decreased.•The effect of dynamic term is small and only increases at crack propagation times, but cracking profile with dynamic term oscillates around the static path. 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.