【作者】 刘永光；

【导师】 李忠献；

【作者基本信息】 天津大学 ， 结构工程， 2007， 博士

【摘要】 混凝土断裂引起的结构裂缝会破坏结构的整体性,形成结构内部的力学断面,导致结构应力状态的恶化,由此引起的桥梁坍塌、建筑毁坏等重大工程事故不断发生。梁是结构中最基本的构件,钢筋混凝土梁中普遍存在的裂缝,严重威胁钢筋混凝土结构的安全性。因此,深入研究混凝土的断裂机理以及钢筋混凝土梁的裂缝诊断,对保证大型土木工程结构的安全性,具有重要的理论意义和工程价值。本文全面系统地开展混凝土等效断裂韧度的计算模式和钢筋混凝土梁的裂缝诊断方法的研究,主要研究工作与创新成果包括以下几个方面:(1)基于混凝土断裂力学与复合材料力学,建立了求解混凝土等效断裂韧度的解析计算模式。运用修正的剪滞理论,建立了带裂缝混凝土梁的分层剪滞模型;采用虚拟裂缝模型,修正了求解混凝土断裂韧度的应力边界条件;结合剪滞模型的应力、位移边界条件,得到了分层解析模型各子层的位移和应力的分布函数;运用能量法则,建立了求解混凝土等效断裂韧度的解析表达式。运用所建立的解析模型对8根带裂缝试件的试验数据进行数值仿真分析,得到了混凝土等效断裂韧度的解析解。计算结果表明,4根体积系列试件的混凝土等效断裂韧度的均方差和变异系数分别小于0.0398和0.0384,4根高度系列试件的混凝土等效断裂韧度的均方差和变异系数分别小于0.0394和0.0363,与相关试验对应的数值解相比,解析解的均方差和变异系数更小,且具有更好的鲁棒性。因此,所建立的解析计算模式为求解混凝土等效断裂韧度提供了一种可靠的实用解析方法。(2)考虑混凝土主裂缝亚临界扩展长度及虚拟裂缝区粘聚力,利用J积分与应力强度因子的解析关系,建立了基于小波基无单元方法求解混凝土等效断裂韧度的数值计算模式。运用三阶B样条函数作为小波基函数,取代了传统无单元方法中的多项式基,建立了小波基无单元方法;结合J积分原理,推导了混凝土等效断裂韧度的数值计算模式。研究了不同基底小波分辨率对混凝土等效断裂韧度计算值的影响。运用所建立的数值计算模式对8根带裂缝试件的试验数据进行数值仿真分析,得到了混凝土等效断裂韧度的数值解。结果表明,在相同基底小波分辨率下,4根体积系列试件计算值的均方差和变异系数分别小于0.0244和0.0231,4根高度系列试件计算值的均方差和变异系数分别小于0.0384和0.0362,计算结果的一致性好;与解析解相比,8个试件的计算值的最大相对误差均在5%左右,计算结果的精度高;且不同基底小波分辨率对计算结果影响不大。因此,所建立的数值计算方法是求解混凝土等效断裂韧度的一种可靠的高精度数值方法。(3)基于断裂力学理论,考虑钢筋的影响因素,运用应力强度因子与应变能的解析关系,得到了钢筋混凝土梁单元由于直裂缝或斜裂缝所产生的附加应变能的解析表达式,结合虚功原理,推导出了含直裂缝或斜裂缝的钢筋混凝土梁的单元刚度矩阵。制作了含不同直或斜裂缝损伤工况的模型梁,通过模态试验验证了所建立的含裂缝梁单元刚度矩阵的适用性。试验结果显示,裂缝使得梁的频率降低,且裂缝对第二阶频率的影响大于第一阶频率,这与既有研究结论相吻合,说明了试验的有效性。运用所建立的含裂缝梁的单元刚度矩阵对试验梁进行了模态分析,计算结果显示,频率计算值与试验值的最大相对误差仅为2.76%,计算振型与对应实测振型的MAC值均大于0.9,显示了二者较好的相关性,充分说明所建立的含裂缝钢筋混凝土梁的单元刚度矩阵,可以用于结构有限元计算,并且具有良好的计算精度。(4)运用线弹性断裂理论,结合时域内的位移响应,建立了钢筋混凝土梁直裂缝的时域两阶段诊断方法。首先,基于时域内的位移响应,结合正则化技术和假设检验,建立了用平均曲率变化比表示的损伤指标,用于诊断直裂缝的位置;其次,结合线弹性断裂力学中应变能释放率、应力强度因子与裂缝深度的解析关系式,建立了直裂缝深度的时域模型,用于识别裂缝的深度。运用所建立的带直裂缝梁的单元刚度矩阵对裂缝梁进行了仿真分析,进而验证了所建立方法的有效性,结果表明,该方法能够在较高的置信区间内准确识别钢筋混凝土梁中多处裂缝的位置,当正则化参量的阈值为1.0时,成功诊断了80%的裂缝位置;通过结合损伤指标图,裂缝位置诊断成功率达到了100%;运用所建立的尺寸诊断模型,也可以在一定精度内诊断出裂缝的深度。通过对含测量噪声的损伤指标与深度模型的诊断结果的分析表明,该方法在5%噪声的影响下仍具有良好的鲁棒性。因此,所建立的时域两阶段诊断方法是诊断钢筋混凝土梁直裂缝位置和深度的一种高效方法。(5)建立了基于遗传神经网络的钢筋混凝土梁斜裂缝的频域诊断方法。运用遗传算法,优化了BP神经网络的拓扑结构、权值和阈值;用归一化的损伤前后的频率变化比、同阶频率平方变化比和振型分量作为损伤指标,对所构造的遗传神经网络进行训练,建立了基于遗传神经网络的钢筋混凝土梁斜裂缝的频域诊断方法,用以识别斜裂缝的位置、深度和角度。运用所建立的带斜裂缝梁的单元刚度矩阵进行了模态分析,验证了所建立的频域诊断方法的有效性进行,结果表明,该方法可以成功诊断出斜裂缝的位置、深度和角度,且诊断精度高、鲁棒性强;在5%测量噪声影响下,对斜裂缝位置诊断的正确率为100%,对斜裂缝深度的诊断误差在25%以内,对斜裂缝角度的诊断误差在12%以内。因此,所建立的基于遗传神经网络的频域诊断方法是诊断钢筋混凝土梁中斜裂缝的一种有效方法。更多还原

【Abstract】 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.更多还原