Abstract
Traditional fracture analysis is based on fracture mechanics and damage mechanics. They focus on the propagation of the fracture. However, their propagation criterions are not easily applied in practice and the current analysis is limited in planar problem. This paper presents a new theory that the occurrence of the unbalanced force (derived from the Deformation Reinforcement Theory) could be the criterion of the initiation of the fracture, and the distribution area and propagation of the unbalanced force could be the indication of the fracture propagation direction. By aggregate analysis with Stress Intensity Factor (SIF) criterion, the unbalanced force actually is the opposite external load that is the SIF difference incurred between the external loads and permitted by the structure. Numerical simulation and physical experiments on pre-fracture cuboid rock specimens proved that the occurrence of the unbalanced force could be the initiation of the fracture. Mesh size dependence was also considered by analysis of different mesh size finite element gravity dam models. Furthermore, the theory was applied to the feasibility analysis of the Baihetan arch dam together with physical experiments in order to evaluate the fracture propagation of dam heel. The results show that it is an effective way to use unbalanced force to analyze the fracture initiation and propagation when performing 3-dimensional nonlinear FEM calculation.
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References
Yang W. Macro-micro Fracture Mechanics (in Chinese). Beijing: National Industry Press, 1995
Geersa M G D, De Borst R, Peerlings R H J. Damage and crack modeling in single-edge and double-edge notched concrete beams. Eng Fract Mech, 2000, 65: 247–261
Tang C A. Numerical tests of progressive failure in brittle materials (in Chinese). Mech Eng, 1999, 21(2): 21–24
Chen Y Q, Zheng X P, Yao Z H. Explanation of strain softening and numerical modeling to the failure process of laminated composite material (in Chinese). Chin J Comput Phys, 2003, 20(1): 14–20
Dumstorffz P, Meschke G. Crack propagation criteria in the framework of X-FEM-based structural analyses. Int J Numer Anal Meth Geomech, 2007, 31: 239–259
Fang X J, Jin F, Wang J T. Simulation of mixed-mode fracture of concrete using extended finite element method (in Chinese). Eng Mech, 2007, 24(Supp I): 46–52
Kou X D, Zhou W Y. The application of element-free method to approximate calculation of arch dam crack propagation (in Chinese). J Hydraul Eng, 2000, 10: 28–35
Huang Y S, Zhou W Y, Hu Y J. Crack propagation tracing by using 3-D element-free Galerkin method(in Chinese). J Hydraul Eng, 2006, 37(1): 63–69
Xiao H T, Yue Z Q. Boundary element analysis of 3D crack problems in layered materials (in Chinese). Chin J Comput Mech, 2003, 20(6): 721–724
Hou Y L, Zhou Y D, Zhang C H. Tensile shear mixed mode fracture analysis of concrete rock material by distinct element method (in Chinese). Chin J Comput Mech, 2007, 24(6): 773–778, 784
Wang S L, Ge X R. Application of manifold method in simulating crack propagation (in Chinese). Chin J Rock Mech Eng, 1997, 16(5): 319–332
Yang Q, Zhang H, Wu R Z. Lattice model simulation of fracture in disordered brittle materials (in Chinese). Chin J Rock Mech Eng, 2000, 19(Supp): 941–945
Hillerborg A, Modéer M, Peterson P E. Analysis of crack propagation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res, 1976, 6: 773–782
Bazant Z P. Crack band model for fracture of geomaterial. In: Eisenstein Z, ed. Proc 4th Int Conf on Numerical Methods in Geomechanics, Edmonton: Univ of Alberta, 1982, 3: 1137–1152
Blackburn W S. A remeshing algorithm for three-dimensional crack growth and intersection with surfaces or cracks in non-coplanar planes. Eng Anal Bound Elem, 2000, 24: 343–350
Bouchard P O, Bay F, Chastel Y. Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria. Comput Method Appl Mech Eng, 2003, 192: 3887–3908
Van Vroonhovena J C W, De Borst R. Combination of fracture and damage mechanics for numerical failure analysis. Int J Solids Struct, 1999, 36: 1169–1191
Erdogan F, Sih G C. On the crack extension in plates under plane loading and transverse shear. ASME J Basic Eng, 1963, 85(4): 519–527
Hussain M A, Pu S L, Underwood J. Strain energy release rate for a crack under combined mode I and mode II. In: Paris P C, Irwin G R, eds. Fracture Analysis, ASTM STP 560, 2–28, Philadelphia, PA. American Society for Testing and Materials, 1993
Palaniswamy K, Knauss W G. On the problem of crack extension in brittle solids under general loading. In: Nemat-Nasser S, ed. Mechanics Today, vol 4. Oxford: Pergamon Press, 1978. 87–148
Sih G C. Strain energy density factor applied to mixed mode crack problems. Int J Fract, 1974, 10(3): 305–321
Cotterell B, Rice J R. Slightly curved or kinked cracks. Int J Fract, 1980, 16(2): 155–169
Theocaris P S, Andrianopoulos N P. The Mises elastic-plastic boundary as the core region in fracture criteria. Eng Fract Mech, 1982, 16(3): 425–432
Yang Q, Liu Y R, Chen Y R, et al. Deformation reinforcement theory and global stability and reinforcement of high arch dams. Chin J Rock Mech Eng (in Chinese), 2008, 27(6): 1121–1136
Yang Q, Chen X, Zhou W Y, et al. On unbalanced forces in 3D elastoplastic finite element analysis(in Chinese). Chin J Geotech Eng, 2004, 26(3): 323–326
Lin P. Brittle failure behaviour of medium contaiming flaws and pore (in Chinese). Doctoral Thesis. Shengyang: The Northeastern University, 2002
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Liu, Y., Chang, Q., Yang, Q. et al. Fracture analysis of rock mass based on 3-D nonlinear Finite Element Method. Sci. China Technol. Sci. 54, 556–564 (2011). https://doi.org/10.1007/s11431-010-4278-8
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DOI: https://doi.org/10.1007/s11431-010-4278-8