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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 658160, 12 pages
Research Article

Fracture Analysis of Brittle Materials Based on Nonlinear FEM and Application in Arch Dam with Fractures

1State Key Laboratory of Hydroscience and Hydraulic Engineering, Tsinghua University, Beijing 100084, China
2State Grid Xin Yuan Construction Co., Ltd., Beijing 100761, China
3China University of Mining & Technology, Beijing 100083, China

Received 7 June 2013; Revised 2 September 2013; Accepted 4 September 2013

Academic Editor: Pengcheng Fu

Copyright © 2013 Yuanwei Pan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Current fracture analysis models based on fracture mechanics or continuum damage mechanics are still limited in the application to three-dimensional structure. Based on deformation reinforcement theory coming from elastoperfect plastic theory, unbalanced force is proposed to predict initiation and propagation of cracks. Unbalanced force is the driving force of time-dependent deformation according to Perzyna’s viscoplasticity theory. It is also related to the damage driving force in viscoplastic damage model. The distribution of unbalanced force indicates cracks initiation area, while its direction predicts possible cracks propagation path. Uniaxial compression test of precrack specimen is performed as verification to this method. The trend and distribution of cracks are in good agreement with numerical results, proving that unbalanced force is feasible and effective for fracture analysis. The method is applied in fracture analysis of Xiaowan high arch dam, which is subjected to some cracks in dam due to the temperature control program. The results show that the deformation and stress of cracks and the stress characteristics of dam are insensitive to grouting of cracks. The existing cracks are stable and dam heel is still the most possible cracking position.