Abstract
In the present paper, the seismic response of a large underground hydropower plant, which is located in southeast China, is investigated and a high performance recursive procedure based on the damping-solvent extraction method (DSE) is proposed for the study of the dynamic stiffness matrix of unbounded rock medium. An analytical formula for the derivative of the dynamic stiffness matrix of unbounded medium with respect to frequency is given, which can reduce the computational cost for a specified frequency. Then a recursive procedure is derived to converse the solving of the inverse matrix at a series of frequencies to step-by-step matrices multiplication, which can reduce the computational cost dramatically. The proposed procedure incorporated with substructure method is implemented in a finite element code for the dynamic analysis of a large three-dimensional underground hydropower plant caverns subjected to seismic excitation. Numerical tests on several representative unbounded domain wave problems demonstrate excellent accuracy and efficiency.
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