Dynamical Characteristics of Soil-Structure Cross-Interaction System, I

Abstract

This paper deals with the cross-interaction problem which means the dynamic interaction problem among the multi-structure system through soilground. The model of such a soil-structure system is supposed to be a multi-mass or multi-spring-mass system on a visco-elastic stratum over the rigid bed rock. Two types of excitation are considered ; force excitation at one of masses or basement masses and the other is the uniform displacement excitation at the free surface or the soilrock interface of the stratum. All the dynamical characteristics of the soil-structure system are discussed in the form of dimensionless transfer functions. In order to formulate such cross-interaction problem, the dynamical ground compliance matrix associated with multi-foundation system on the Voigt type visco-elastic stratum, which is a complexvalued symmetric matrix representing the set of displacement transfer functions of foundation areas to the force excitation on each foundation area, the displacement transfer function at the free surface of the visco-elastic stratum to the uniform displacement excitation at the soil-rock interface, and the displacement and force transfer functions of an elastic shear type spring-mass system to the displacement excitation at the basement, are determined. And then, the transfer functions of the horizontal displacements of the soil-structure cross-interaction system subjected to the two types of excitation in the same horizontal direction are expressed in terms of the above-mentioned basic transfer functions associated with the visco-elastic stratum and the elastic structures. The numerical analyses are carried out in the cases of identical two and seven-mass systems and of identical and different two-spring-mass systems, all of which have the same square foundations on the visco-elastic stratum, and also in the cases of a single mass and a single spring-mass system for the sake of comparison. From the amplitude characteristics of the dimensionless transfer functions of the soil-structure system, the following remarks are obtained : (1) The effects of the cross-interaction on the dynamical characteristics of the soil-structure system are different considerably depending on whether the lowest natural frequency due to the structuresubsoil interaction is smaller or not than the fundamental natural frequency of the stratum, If the lowest natural frequency is in the lower frequency range, the amplitude characteristics are sharp and the cross-interaction effect appears in the neighbourhood of the natural frequency. If contrary, the amplitude characteristics are broadened and the cross-interaction effect covers the wide frequency range containing the lower natural frequencies of the soil-structure system. (2) The cross-interaction effects depend on the type of excitation, the number of structures and the dynamical characteristics of structures. In the case of the identical two structures subjected to the uniform displacement excitation at the free surface of the stratum, the cross-interaction effect is smaller as compared with the case of the force excitation at one of the two structures. In the case of different structures, however, the effects are rather large for the displacement excitation than for the force excitation. (3) As the number of structures increases, the cross-interaction becomes complicated and the maximum peak value of the amplitude characteristics in the case of the uniform displacement excitation becomes large because of the increase of the transmitted energy as well as the dispersion of the peak values. (4) The amplitude characteristics of a structure are considerably influenced by the cross-interaction in the vicinity of the fundamental natural frequency of the adjacent structures. The cross-interaction effect becomes remarkable as the fundamental frequencies of the structures are close to each other and their masses are large as compared with the foundation area.