【作者】 刘钧玉；

【导师】 林皋；

【作者基本信息】 大连理工大学 ， 结构工程， 2008， 博士

【摘要】 在实际工程中,混凝土坝等结构由于温度、地震、干缩等原因不可避免地会出现表面裂纹,裂纹的出现改变了坝体的受力状态,并在裂纹尖端将产生较大的应力集中现象,对坝和结构的安全造成不利影响。水库蓄水以后裂纹内的水压力作用将引起额外的材料损伤而降低结构抵抗开裂的能力。尽管人们已经认识到裂纹内水压可能改变结构的抗力强度,但是由于缺少现场实测、实验室试验、数值分析的数据,裂纹内水压力对结构的影响仍然是结构设计和安全评价中的一个不确定因素。因此,研究裂纹内水压力对结构安全性的影响将具有重要的意义。比例边界有限元法(Scaled Boundary Finite Elemem Method,简称SBFEM)是最近发展起来的一种新的数值方法,它不仅集合了传统有限元法和边界元法的优点,同时具有自己独特的优势。首先,它只需离散部分边界使问题降低一维,从而减小了计算工作量以及前处理的工作量。其次它避免了基本解求解的复杂性和奇异积分,可以方便地处理各向异性材料。在无限域模拟方面,它精确满足无穷远处的辐射条件,且不需要增加任何计算量就能够方便地模拟一类非均质无限地基。在断裂力学方面当相似中心选在裂尖处时裂纹面不需要离散,且在径向位移和应力具有完全精确的解析解,使得裂纹尖端应力强度因子的计算既准确又方便,处理应力奇异性问题是比例边界有限元法的另一个突出优点。本文应用比例边界有限元法在断裂力学应用中的优势,联合子结构法(超单元)对弹性多裂纹问题进行了分析,进一步推广了比例边界有限元法的应用范围,使得应用比例边界有限元法分析水坝的水力劈裂问题成为可能。由于比例边界有限元法具有半解析的特点,对于一大类体荷载和面荷载可以解析地求解不需要引入额外的近似,本文建立了含裂纹内水压的重力坝应力强度因子的比例边界有限元计算方程,该方程由二阶齐次常微分方程转变为二阶非齐次常微分方程,求解方法发生一定的变化,通过典型算例验证了收敛性和精度。并计算了正交异性材料,双材料交界面及多裂纹有裂纹面荷载作用情况下的应力强度因子。最后研究了不同裂纹长度、不同水压分布、不同坝体坝基弹模比的情况下应力强度因子的变化规律,得到一些有意义的结论。在研究坝体的地震响应时,通常要研究无限地基对坝体响应的影响,一般计算公式中只包含了弹性刚度与阻尼项,而忽略了迟滞效应。本文应用比例边界有限元方法建立了考虑迟滞效应影响的无限地基动力相互作用方程。通过一种新的高阶透射边界对无限地基进行模拟。该透射边界是基于无限域动力刚度矩阵的连分式解形式。连分式的系数通过以动力刚度矩阵表示的比例边界有限元方程递推计算。数值算例验证了该透射边界的收敛性,并与解析解进行比较表明该方法具有较高的精度。并将该透射边界应用于重力坝—地基—库水系统动力分析,将计算结果与工程上常用的无质量地基进行了对比。该方法可以方便有效的进行二维和三维大型结构—地基相互作用分析。在以上研究的基础上,本文充分利用比例边界有限元法在结构—地基相互作用分析中及断裂力学中应用的两大优势,对重力坝—地基—库水系统进行了动态断裂分析,给出了裂纹尖端应力强度因子时程变化规律,以及坝体的最大应力分布。表明比例边界有限元法可以有效应用于坝体的动态断裂分析。更多还原

【Abstract】 In the practical engineering, the concrete dam will suffer various kinds of damage such as dents, corrosion pits, cracks, deformation, etc. through years of environmental impact of soil reactions, earthquakes, water pressure, etc. The presence of these cracks or geometrical changes, such as notches may result in reduction of the stiffness of the cracked structures, and thus influence the degree of safety. Furthermore, any water pressure inside cracks will cause additional material damage and therefore reduce resistance against further cracking. Although it is anticipated that water pressure in cracks might change the strength of the structures, due to lack of historical, experimental and numerical evidences the influence of water pressure in cracks on the structures remains a major factor of uncertainty in the design and safety assessment of concrete structures. Therefore it has very important meaning to study the effect of the water pressure in the crack on the safety of the structure.The scaled Boundary Finite Element Method (abbr. SBFEM) is a new numerical method developed in recently. It has the advantages of both the finite element method and the boundary element method, at the same time it has its own characters. Firstly, it discretizes only boundaries of the investigated domain, reduces the cost of prepare process. Secondly, no fundamental solution and its complexity are required, anisotropic materials are handled without additional computational efforts. In the modeling of unbounded domain, the method permits the boundary condition at infinity to be enforced analytically, non-homogeneous unbounded domains with the elasticity modulus and mass density varying as power functions of spatial coordinates can be considered easily. When it is applied to fracture mechanics problems, the scaling centre is chosen on the part of the boundary, no discretization is required. In the radial direction the displacements and stress can be evaluated analytically, the stress intensity factors and T-stress can be calculated based on their determination. It is another prominent character of SBFEM to represent the stress singularities.In the paper the elastic multi-crack problem is analyzed using SBFEM combining the sub-technique (or super-element). The scope of application of the SBFEM has been extended, and it makes it feasible to analyze the hydraulic fracture problem using the SBFEM. For a kind of loads varying as power functions in the radial coordinate, the SBFEM remains semi-anlytical and no additional approximations are introduced. The scaled boundary finite element equations for evaluating the SIF of the gravity dam with the effect of water pressure inside the crack is established and solved. The equation is the second order heterogeneous ordinary differential equation. Its solving process is different from the second order homogeneous ordinary differential equation. The comparison with the analytical solution and numerical examples show that SBFEM is effective and possesses high accuracy for the calculation of stress intensity factor with the contribution of surface tractions. The stress intensity factors of the anisotropic materials and bi-material with the contribution of surface tractions are also evaluated. The fracture analysis for the interfacial cracks in the vicinity of the dam heel combining the sub-structure technique (or super-element) is made. The effect of different water pressure distributing in the crack is studied and some useful conclusions are obtained by comparisons.When subjected to earthquake ground motion, wether considering the dynamic interaction of structure-foundation plays a vital important role to the response of the dam. Generally, the formula for calculating the interaction force includes the elastic stiffness matrix and damp matrix only, the lingering effect is disregarded. The equation of the structure-unbounded foundation interaction which can consider the lingering effect, namely the action of the time coupling, is established. In the paper the unbounded foundation is considered by a new high-order transmitting boundary based on the continued-fraction solution of the dynamic-stiffness matrix. The coefficient matrices of the continued fraction are evaluated recursively through the scaled boundary finite element equation in dynamic stiffness. The convergence of the high-order transmitting boundary is demonstrated by the numerical examples. Comparisons with the analytical solutions show that the method possesses high accuracy. The system of the gravity dam-reservoir-foundation is calculated and the results are compared with the mass-less base model. In conclusion the approach is effective and suitable for 2D and 3D large-scale structure-foundation interaction analysis.At last, making the best use of advantage that SBFEM can simulate the unbounded media and the stress singularity expediently, the system of the gravity dam-reservoir-foundation with the crack in the dam heel is evaluated dynamically, the time history of the DSIFs and the stress distributing of the dam with crack are provided for the infinite foundation and mass-less foundation. The approach is applicable for the 2D dynamic fracture analysis.更多还原