Effect Of The Water Pressure Inside The Crack On The Fracture Behavior Of Concrete Gravity Dam

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.