Impedance functions for three‐dimensional foundations supported on an infinitely‐long canyon of uniform cross‐section in a homogeneous half‐space

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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.

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