| Some problems related to crack stability of concrete dams in the field of dam monitoring are studied in this dissertation using theories and mathematics such as chaos theory, fractal geometry, artificial neural networks, grey system theory, motion stability theory, catastrophe theory, and so on. The main contents are as follows.(1) The method of the phase space reconstruction and determination of its parameters of crack dynamic system are investigated. Calculation is made about the characteristic invariants such as correlation dimension, maximal Lyapunov exponent and Kolmogorov entropy of the crack dynamic system. The results indicate that the time series of cracks are chaotic ones.(2) Owing to the low prediction precision of the conventional statistic model for crack opening displacements, three statistic model and chaos theory - based hybrid prediction models with higher precision are presented. Aiming at the deficiencies in the CTOD criterion applied to analysis of critical crack propagation, a new fracture criterion is established.(3) The methods of detecting sub-critical propagation of cracks in concrete dams are explored by use of grey system theory, motion stability theory and catastrophe theory, and three criteria for sub-critical crack propagation are given.(4) Because calculation of stress intensity factors using the finite element method of the linear elastic fracture mechanics cannot satisfy the need for the real-time monitoring and the real-time analysis of cracks in concrete dams, a four-layer neural network optimized by genetic algorithm and chaos optimization algorithm is proposed. The example shows that the optimized neural network can yield good results.(5) Aiming at irregularity of a real fracture surface or a real crack profile, applying Griffith's criterion and fractal geometry, the real asymptotic expression at the crack tip is developed, and it is discovered that the fractality of the crack reduces the stress singularity at the crack tip.
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