Computation of Spatially Varying Ground Motion and Foundation-Rock ImpedanceMatrices for Seismic Analysis of Arch Dams

摘要

The first part presents a direct boundary element method (BEM) to determine thethree-dimensional seismic response of an infinitely-long canyon of arbitrary but uniform cross-section cut in a homogeneous viscoelastic half-space, to P, SV, SH or Rayleigh wave excitations at arbitrary angles with respect to the axis of the canyon. The accuracy of the procedure and implementing computer program is demonstrated. The procedure would enable analytical estimation of the spatial variation of ground motions around the canyon and hence the possibility of exploring the effects of such variation on earthquake response of arch dams. The second part presents a direct boundary element procedure to determine the foundation impedance matrix defined at the nodal points on the dam-foundation rock interface. The uniform cross-section of the infinitely-long 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. Compared with the three-dimensional BEM, the present method requires less computer storage and is more accurate and efficient.