Calculation Model Of Equivalent Fracture Toughness Of Concrete And Detection Method Of Cracks In RC Beam

The integrity of a structure may be destructed by cracks induced by fracture of concrete, some mechanical fracture surfaces may be formed within the structure, and the stress condition of the structure may be deteriorated. This may induce serious engineering accidents as collapse of bridges and destroy of buildings constantly. Beam is the most basic member in structures. The cracks existed within reinforced concrete (RC) beam generally may threaten the safety of RC structures. Therefore, systematical studies on fracture mechanism of concrete and crack detection of RC beam have important theoretical significance and engineering value for guaranteeing the safety of large civil structures.The researches on calculation model of equivalent fracture toughness of concrete and detection method of cracks of RC beam are performed systematically in this dissertation. The main research work and innovative achievements are summarized as follows:(1) Based on fracture mechanics of concrete and composite material mechanics, the analytical model is built to solve the equivalent fracture toughness of concrete. The modified shear lag model is used to build the layered shear lag model of the concrete specimen with a crack. The fictitious crack model is used to modify the boundary condition of stress of the analytical model. Combined with other boundary condition of stress and displacement, displacement and stress functions of layers of the analytical model are obtained. Using energy method, the analytical expression of the equivalent fracture toughness of concrete is obtained. Analytical solutions of the equivalent fracture toughness of concrete are obtained using the analytical calculation model with the experimental data of 8 specimens. The calculated results show that mean square errors and variation coefficients of the calculated values with different volumes are lower than 0.0398 and 0.0384 respectively, and those with different heights are lower than 0.0394 and 0.0363 respectively. Being lower mean square errors and variation coefficients, the analytical solutions are more robust than the numerical solutions based on the coherent experiment. Therefore, the analytical model provides a reliable practical analytical method to solve the equivalent fracture toughness of concrete.(2) Considering the length of the subcritical growth of the main crack and the cohesive strength of the fictitious crack of concrete, and using the analytical relationship between the J integral and the stress intensity factor, a numerical algorithm based on the element free Galerkin method with wavelet basis to solve the equivalent fracture toughness of concrete is built. The third order B spline function is taken as the wavelet function to substitute the traditional polynomial basis in the element free Galerkin method, which is used to build the element free Galerkin method with wavelet basis. The numerical model to solve the equivalent fracture toughness of concrete is deduced using J integral theory. The influence of different resolution of wavelet basis on the calculated values is investigated. The calculated results for 8 specimens with crack show that in the case of identical resolution of wavelet basis, the mean square derivations and the coefficients of variation of the calculated values of the 4 volume series specimens are smaller than 0.0244 and 0.0231 respectively, and the those of the 4 height series specimens are smaller than 0.0384 and 0.0362, so to have good consistency. By comparing with the analytical solutions, the maximum relative error of the calculated values of 8 specimens is about 5%, so the precision of the calculated results is high. And the influence of different resolution of wavelet basis on the calculated results is little. Therefore, the element free Galerkin method with wavelet basis is a reliable numerical algorithm with high precision to solve the equivalent fracture toughness of concrete.(3) Based on fracture mechanics, the analytical relationship of the stress intensity factor and strain energy is used to obtain the analytical expression of additional strain energy induced by straight or diagonal crack in element of RC beam. Considering the influence of steel bar, the virtual work principle is used to deduce the stiffness matrix of element with a straight or diagonal crack of RC beam. Some test beams with different straight or diagonal cracks damage cases are fabricated, whose results of model test verify the applicability of the stiffness matrix of the element with a straight or diagonal crack. The tested results show that frequencies of test beams are reduced and the influence of the second order frequency is bigger than the influence of the first frequency for cracks, which is consistent with conclusions given by others. This proofs the model test is valid. The modal analysis for test beams is given based on the deduced elemental stiffness matrix with a crack. The calculated results show that the maximum value of relative error between the computational frequencies and experiment frequencies is only 2.76% and the values of MAC of correlative model shapes between experimental and calculation are bigger than 0.9. This verifies good relativity between the tested and calculated modal shapes. Therefore, the deduced elemental stiffness matrix of RC beam with a crack can be used in the calculation of infinite element and the calculation precision is higher.(4) A two-stage detection method in time domain for straight cracks of RC beam is established using the linear elastic fracture theory and displacement responses of RC beam in time domain. Firstly, normalized method and hypothesis testing are used to build a damage index with relation to the mean curvature change ratio to locate cracks based on displacement responses in time domain. Secondly, the analytical relationships of the strain energy release rate, stress intensity factor and depth of crack are used to obtain a crack depth model in time domain to detect the depth of crack. The stiffness matrix of cracked element is used to simulate the cracked RC beams to verify the feasibility of the algorithm of straight crack detection. The calculated results show that the algorithm could locate cracks precisely with high confidence interval. 80% of locations of cracks are detected successfully when the threshold of the normalized parameter is put to 1.0. Combining the diagram of damage index, all of locations of cracks can be detected precisely. Depths of cracks can be detected in a certain accurate degree. Meanwhile the contaminated displacement responses are used to analyze the robustness of the damage index and the crack depth model, which demonstrates that the method is robust against even if 5% noise level. Therefore, the two-stage detection method in time domain is a method with high efficiency to detect the depths and locations of straight cracks in RC beam.(5) A genetic neural network-based detection method in frequency domain for diagonal cracks within RC beams is built. The topological structure, weight and threshold of the BP neural network are optimized using the genetic algorithm. Normalized ratios of variations of the frequencies, normalized ratios of variations of the square of same order frequencies and components of mode of the cracked RC beam are used as the damage indices to train the genetic neural network. The method based on the genetic neural network is built to detect the location, depth and angle of the diagonal crack. The stiffness matrix of cracked element is used to obtain frequencies and model shapes of the cracked RC beams to verify the feasibility of the method of diagonal crack detection. The numerical simulation shows that the method detects the location, depth and angle of the diagonal crack successfully with a high detection precision and robust. In the 5% noise level, the successful rate of location detection is 100%, and the detection error of crack depth is controlled in 25%, and the detection error of crack angle is controlled in 12%. Therefore, the genetic neural network-based detection method in frequency domain is an effective method to detect the diagonal cracks within RC beams.