Analysis of pile foundations under dynamic loads

A method is presented for the analysis of pile foundations which are subjected to horizontal dynamic loads from earthquakes, airplane impact, gas explosion or other sources. The motion of the pile cap and the pile forces are computed. - The loads may be applied to the pile cap or directly to the piles (e.g. by earthquake wave motion). The soil may be stratified and is considered to be an elastic or visco-elastic medium. The piles are assumed vertical. The method makes use of an approximate fundamental solution for displacements caused by a dynamic point load in a layered visco-elastic medium. The approximation involves a discretization of the medium in the vertical direction. In horizontal directions the medium is treated by continuum theory. The soil medium supports each pile at about 10 to 20 nodes. A dynamic flexiblity matrix for the soil is derived which relates the elastic, damping and inertial forces of the soil to the displacements at each node. It includes effects of radiation damping. All piles are coupled through the soil flexibility matrix. The piles are modelled by beam elements. Transient response is computed using fast discrete Fourier transforms. The arrangement of the piles is arbitrary. However, simple and double symmetry can be accounted for by the computer program. When the pile arrangement is axisymmetric, the degrees of freedom can be reduced to only those of two piles per ring. The influence of the number of piles and the influence of the pile spacing on group stiffness and on pile forces is presented for two soil profiles. Dynamic effects on pile forces of a foundation for a reactor building are studied. They are significant when soils are soft. (orig.)