Numerical Simulation of Displacement Functions of Strip Footings

The risk associated with structures subjected to dynamic loading needs a rigorous analysis that takes into account dynamic soil-structure interaction. A key step of this analysis consists of estimating the dynamic response of the foundations by calculating their impedance (i.e. dynamic stiffness K and damping C) or displacement functions (real part F₁ and imaginary part F₂). The purpose of this work is to evaluate the displacement functions (inverse of impedance functions) of strip footings on the surface of some homogeneous soil. Validation studies indicate the accuracy and versatility of the models performed with the software FLAC (Fast Lagrangian Analysis of Continua). It is known that the assumption of homogenous layer or half space with constant shear modulus G may not be realistic as the shear wave velocity increases as a function of the effective overburden stress. In this paper, three soil models are considered. For each case, the adopted mechanical characteristics correspond to a type of soil with constant or variable shear wave velocity. Calculations are performed over a practically sufficient range of oscillating frequency ratios a_o. Comparison of results obtained with varying and constant shear wave velocity shows the importance to consider this velocity increasing with depth. Additional calculations conducted on two-layer soil are also presented in order to recommend the thickness of soil that is required in the model to capture soil-structure interaction.