Dynamic Stiffness of Foundations on Inhomogeneous Soils for a Realistic Prediction of Vertical Building Resonance

Abstract

The aim of this contribution is a practice-oriented prediction of environmental building vibrations. A Green's functions method for layered soils is used to build the dynamic stiffness matrix of the soil area that is covered by the foundation. A simple building model is proposed by adding a building mass to the dynamic stiffness of the soil. The vertical soil-building transfer functions with building-soil resonances are calculated and compared with a number of measurements of technically induced vibrations of residential buildings. In a parametrical study, realistic foundation geometries are modeled and the influence of incompressible soil, deep stiff soil layering, soft top layers, and increasing soil stiffness with depth is analyzed. All these special soil models reduce the resonant frequency compared to a standard homogeneous soil. A physically motivated model of a naturally sedimented soil has a stiffness increasing with the square root of the depth and yields a foundation stiffness that decreases with foundation area considerably stronger than the relatively insensitive homogeneous soil. This soil model is suited for the Berlin measuring sites and reproduces satisfactorily the experimental results.