Evaluation of kinematic interaction of soil-foundation systems by a stochastic model

Abstract

At the present practice, the earthquake response analysis of structures is generally based on an assumption that the ground just beneath a foundation vibrates in the same phase and with the same amplitude everywhere. However, it is very doubtful that a structure vibrates as if it were set on a shaking table. As the foundation slab, which is relatively stiff compared with the soil, works to constrain such ground motions, short period components of the ground motions whose wave length is short to the dimension of the slab are naturally weakened. Consequently the slab has the effect of a kind of low pass filter on the ground motions. This effect is called ‘kinematic interaction’.¹ In the past, many studies have been made on the kinematic interaction both theoretically and experimentally,^2–9 and characteristics of the kinematic interaction have become clearer. However, since the effect of kinematic interaction is so complicated to depend totally on a geometrical pattern of a foundation slab, ground characteristics and the excitation, further researches are needed for incorporation of the effect into dynamic design practice.

This paper formulates the kinematic interaction of embedded rectangular foundations by the random vibration theory, and discusses the effect by examining field data obtained in earthquakes. Since the formulation is based on the fact that statistical correlation of ground motions at different points decreases as the distance between the different points increase, and especially when components of high frequency are contained in ground motions, characteristics of mutual correlations of the motions of different points are first investigated. Next, the formulation of the kinematic interaction is investigated. In order to justify a low pass filter by this stochastic model, earthquake records observed at a large scale inground tank and a foundation, whose material is cement-mixed soil-improved-ground, are analysed as examples of deep and shallow embedded foundations respectively. Also the filtering effect on microtermor records observed at a reinforced concrete four-storey school building are investigated as another example of more general structures.