Low computational cost formulation for the analysis of the soil-structure interaction in frames considering the equilibrium in the deformed soil condition

Abstract

Lattice structures have a wide range of applications in real structures. For example, concrete buildings can be modeled as flat or spatial frames, while lattice or ribbed slabs can be modeled as grids. Computer programs frequently used for the design of buildings in Brazil allow the design to be carried out in spatial gantry and grid. Also, some include the possibility of applying calculated support settlements or manually introducing an elastic spring to simulate the behavior of the foundation. However, it is not possible to insert geotechnical data together with the structure for the geotechnical evaluation of soil deformation in an integrated way to obtain an analysis of the interaction between the stresses in the structure and the soil deformations, as well as to take into account the overlapping of stresses applied in the soil mass to evaluate settlements. In this context, classical solutions to analyze these domains together have been proposed with the use of the Finite Element Method (FEM) and by the coupling between the Boundary Element Method (SEM) and FEM. Despite being robust, these techniques are not yet commonly used in calculation offices, due to the high computational cost. In this sense, alternative formulations with lower computational cost, such as the one proposed herein, can be a viable alternative for the analysis of the effects of soil-structure interaction in conventional structures without significantly impairing computational performance. Thus, to approximate the computational analysis to the real behavior of structures, this article proposes an efficient and low-cost computational matrix analysis solution for the integration between structural and geotechnical models, considering the soil-structure interaction. Thus, the integrated model considers the compatibility between the forces calculated in the structure and the settlement prediction, carried out, considering the soil deformation caused by the global contribution of stresses, in such a way as to consider in the analysis of the soil, both the tensions arising from the support itself and those transmitted by the other foundation elements. The proposed alternative formulation was verified for isolated structural analyses, geotechnical isolates and finally considering the coupled form with equilibrium in the deformed condition of the soil, paying attention to the robustness of the implementation.