Frequency-dependent impedance of a strip foundation group and its representation in time domain

A semi-analytical procedure is presented to study the dynamic cross-interference among a group of long strip foundations on an elastic half-space, which is simplified as a two-dimensional problem. In addition to analytical solutions in terms of Green functions, a discretization method is applied to determine the lateral/rocking dynamic impedances of a foundation group. To determine the unknown contact stresses between the foundations and the supporting medium, the soil-foundation interfaces are discretized into a series of strip elements which are only subjected to constant lateral and vertical tractions. Multiple foundations with different widths and separation distances are considered in the formulations. For the time history analysis of those strongly frequency-dependent impedances of a foundation group through a substructure approach, complex Chebyshev polynomials are used to fit the lumped-parameter (L-P) model in the domain-transformation. Numerical results over a wide range of vibration frequencies for impedance calculation are verified with the existing methods. The effects of cross-interference on contact stress distributions and impedances for a group of two and three rigid foundations are discussed in detail. Finally, the accuracy and the validity of the L-P model are rigorously studied by simulating adjacent foundations on an elastic half-space within a close distance.