13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Stability and fracture analysis of arch dam based on deformation reinforcement theory Yuanwei Pan1,*, Yaoru Liu1, Qiang Yang1 1 Department of Hydraulic Engineering, Tsinghua University, 100084, China * Corresponding author: pyw10@mails.tsinghua.edu.cn Abstract Fracture is a common and significant failure mode of high arch dam. Current theories are still limited in fracture analysis of 3-D structure. In this paper, deformation reinforcement theory (DRT) is deduced and elaborated with a definition of stability that an elasto-plastic structure is stable if equilibrium condition, kinematical admissibility and constitutive equations can simultaneously be satisfied under given external loads. Furthermore, a global stability analysis method of elasto-plastic structure based on DRT is presented. Unbalanced forces can be used to evaluate the stability of structure and indicate fracture initiation and propagation. FEM expression of DRT is deduced and implemented in a three dimensional nonlinear FEM program, and successfully applied in dam heel cracking and multi-crack analysis of arch dam. As statically indeterminate structure, high arch dam is capable of stress redistribution to some extent while cracking occur. This process was expressed in FEM program by iteration and convergence of unbalanced forces. Both elasto-plastic FEM analysis and geo-mechanical experiments are performed on Baihetan and Xiaowan arch dams. Results show that unbalanced forces can be used as the indication of fracture initiation and propagation. Keywords arch dam, cracks, fracture, stability, unbalanced force 1. Introduction From the point of view of failure analysis, fracture is a common and significant failure mode of high arch dam, which may result in many problems. In fracture analysis, various factors should be taken into consideration, e.g., material properties, surface notches, cracks, shape and size of structure and working conditions. Those factors present many challenging problems of practical importance range from the micro-scale cavity of materials to macro-scale cracks in engineering structures. Fracture mechanics has now developed many branches such as linear elastic fracture mechanics (LEFM), nonlinear fracture mechanics, fatigue analysis (e.g., lifetime prediction) and dynamic fracture mechanics. Irwin and Orowan extended Griffith’s classical work on brittle materials and proposed both stress and energetic criterions to analyze cracking [1–3], i.e., the stress intensity factor (SIF) and energy release rate, which provided precise measure of fracture toughness and succeeded in predicting cracking behavior. Some significant advances were made by theoretical and experimental mechanics researchers in nonlinear fracture analysis. Wells suggested to assess ductile fracture toughness with crack opening displacement (COD) [4]. Rice proposed J-integral that characterize the intensity of near tip elastic-plastic deformation fields [5]. Besides, numerical methods have developed rapidly, including Finite Element Method (FEM), Discrete Element Method (DEM), Boundary Element Method, eXtended FEM, Numerical Manifold Method and etc. Those theories mentioned above are based on planar analysis. There is still severe limitation on the applicability of those theories when extended to three-dimension structure. Besides, very little progress has yet been made on understanding the nucleation, growth and interaction of cracks. The description of multi-crack behavior involves complex nonlinear overall deformation, which is beyond the capacity of common numerical methods based on linear plastic. This paper presents a new approach to deal with cracks in stability and fracture analysis of 3-D structure. Unbalanced force, derived from the Deformation Reinforcement Theory (DRT) [6, 7], could be the criterion of initiation of fracture, the distribution area and magnitude of which could indicate fracture propagation direction [8]. FEM expression of DRT was deduced and implemented
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