| Abstract: | A direct boundary element procedure is presented to determine the impedance matrix for a three-dimensional foundation supported on an infinitely-long canyon of uniform cross-section cut in a homogeneous half-space. The uniform cross-section of the canyon permits analytical integration along the canyon axis leading to a series of two-dimensional boundary problems involving Fourier transforms of the full-space Green's functions. Solution of these two-dimensional boundary problems leads to a dynamic flexibility influence matrix which is inverted to determine the impedance matrix. The accuracy of the procedure is demonstrated by comparison with previous solutions for a surface-supported, square foundation and results obtained by a three-dimensional boundary element method (BEM) for a foundation of finite-width supported on an infinitely-long canyon. Compared with the three-dimensional BEM, the present method requires less computer storage and is more accurate and efficient. The foundation impedance matrix determined by this procedure can be incorporated in a substructure method for earthquake analysis of arch dams. |
