The Dynamic Interaction Analysis Of Dam-Reservoir-Foundation Based On SBFEM

When subjected to earthquake ground motion, wether considering the dynamicinteraction of structure-foundation plays a vital important role to the response of the structure,especially for the large-scale spatial structures, for example, large hydraulic dams, long-spanbridges, high buildings, underground structures, etc. However, with the development ofscience and technology and the increase of difficulty in engineering, present methods ofmodeling the unbounded foundation can't meet the needs of science research and engineeringapplication. The Scaled Boundary Finite Element Method (abbr. SBFEM) is a new numericalmethod developed in recently. It has the advantages those the finite element method can'texceed. For example, reducing spatial dimension by one, satisfying the infinite boundarycondition of wave transmitting, simulating the inhomogeneous media, etc. So it is suitable forapplying in the structure-foundation interaction. But, due to the basement of the theory in thismethod, there are so many limitation that it can't apply in practical engineering expediently.This paper brings the advantages of this method into play and overcomes its limitations;ultimate purpose is proposing an effective process to analyze dam-water-foundation dynamicinteraction by SBFEM and dealing with some problems in practical engineering.The hydrodynamic pressures have to be taken into account in the seismic responseanalysis of dams subjected to earthquake excitation. In this paper, the basic formulae forcalculating hydrodynamic pressure were derived by SBFEM, which included thecompressibility and boundary absorb of reservoir. On the assumption of incompressibility ofreservoir water, the added mass matrix was also derived. Numerical examples of gravity damsand arch dams show that this approach is simple, effective and appropriate for engineeringpurpose.Limited by the similarity in SBFEM, for the structures with complicated geometry shape,for example arch dam, it is difficult to analyze structure-foundation dynamic interaction bySBFEM. In this paper, the sub-structuring approach was studied. The structure was dividedinto some sub-structures. Obtaining the stiffness matrix and mass matrix of each sub-structureby SBFEM, then assembling them to global matrices of the structure. The shape and materialproperty of unbounded foundation of arch dam are very complex. It is impossible to simulatethe arch dam's foundation by SBFEM directly due to the same reason. Based on the dynamic cone theory developed by Meek and Wolf, a reasonable three-dimensional unboundedfoundation model of arch dam was proposed. The interaction to arch dam by unboundedfoundation was simulated reasonably, but the structure-foundation interface shrinked to agreat extent. By introducing the processes mentioned above, the problem of the dynamicinteraction analysis of dam-reservoir-foundation was reduced by one dimension. Sequentially,the work of pro-process was saved to a great extent.In the numerical method for dynamic analysis of structure-foundation interaction intime-domain by above approach, the convolution integral makes the computation veryinefficient. In this paper, two improved methods were proposed based on sub-structuringapproach and reduced set of base functions, respectively. The computational efficiency wasincreased greatly by them. Then the comparisons between the two improved methods ofaccuracy and efficiency were performed and the reasonable choice was made.At last, making the best use of advantage that SBFEM can simulate inhomogeneousunbounded media expediently, the reasonable inhomogeneous unbounded foundation of damswas proposed. Based on the efficient approach developed above, cases of foundationinhomogeneity with stiffness varying according to an exponential function along the radialdirection, and cases of foundation inhomogeneity with stiffness discontinuity and with weakinterlayer strata on the earthquake response of concrete arch dams as well as gravity damswere analyzed. It is found that taking into account the effect of foundation inhomegeneity forthe earthquake safety assessment of concrete arch and gravity dams has great significance.The general tend of the conclusions is applicable for the design of great dams located in highseismic area.