Numerical assessment of the applicability of the vertical cone model for foundation vibration analysis (in German)

When designing dynamically exited foundations, the soil-foundation interaction must be taken into account to ensure sufficient load-bearing capacity and, above all, serviceability of the foundations. It is therefore necessary to consider the dynamic properties of the soil during the design process. One possibility is to fully model the subsoil in the calculation models used for the design. However, this approach usually leads to very extensive models, which result in uneconomically long computing times. An alternative way to avoid this is to replace the soil with a simple mechanical system consisting of springs, dampers and masses. Such a model was proposed in the literature in 1942, then further developed by several authors until 1993 and subsequently successfully applied in the field of soil-structure-interaction and soil-machine-interaction. The subsoil is regarded as a linearly elastic isotropic homogeneous half-space, from which however only a truncated cone-shaped section is considered. The top surface of the downwardly infinite truncated cone forms the vibrating foundation which is converted into a circular foundation of the same area. Assuming a one-dimensional wave propagation in this cone, this model is equivalent to a spring-damper-mass-system with frequency-independent coefficients. A further development based on this one-dimensional wave propagation in cones is a transfer function for foundation vibrations on stratified half-spaces developed in 1994.

The aim of this master thesis is to investigate the applicability of these cone models using finite element (FE) modelling. In particular, the half-space replacement models for vertical vibrations are examined. At the beginning, a FE-model for a homogeneous and stratified subsoil using a rotationally symmetric model, in which the infinite region of the half-space is modelled using infinite elements, is developed. These FE-models are then used to carry out parameter studies, the results of which are compared with the cone model or the transfer function.

For homogeneous half-spaces, a very good agreement with the FE-results is achieved, whereby the vibration amplitudes tend to be slightly overestimated by the cone model. In the domain around the resonant frequency of the foundation-subsoil system, however, large deviations occur, which may be due to the different damping coefficients. The transfer function for stratified half-spaces also shows good agreement with the FE-results. Here, the deviations are in the same order of magnitude, in the case of “soft” layers on “stiff” half-spaces the deviations are at their greatest.



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