# Pseudo-analytical model for sliding immersed structures under time-history earthquake loadings

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## Abstract

Some specific projects require that the structures being constructed are not anchored while being immersed. It is the case for recent bridges designed for large earthquake loadings, masonry structures, unanchored immersed storage structures. This solution gives more flexibility in the localization and in the use of such structures and a decrease in the internal stress. However, one has to evaluate precisely the behavior of this sliding structure, and in particular, the cumulative sliding displacement during a seismic event in order to prevent any impact or loss of stability. Given the highly non-linear behavior of such immersed sliding structures, the computational time and capacity to estimate the cumulative sliding displacement is important. It is then almost impossible to do easily a predimensioning of the structure or to apply a stochastic method in order to cover the possible time-history earthquakes corresponding to the dimensioning spectrum. The aim of this paper is to present a pseudo-analytical model to estimate the sliding amplitudes of different simplified systems which represent a given dynamic behavior: a single immersed sliding mass and an immersed sliding beam system. In each model, the fluid-structure interaction between the immersed body and the pool is modeled as hydrodynamic masses. The sliding is represented by a solid Coulomb friction. The seismic loading can be any 3D time-history accelerograms. The pseudo-analytical solutions are obtained considering the different phases of the movement and the continuity between each phase. The results are then compared to the values computed using \(ANSYS^{TM}\). The analytical curves show a good fit of the computational results. A comparison between 3 models is shown (single immersed sliding mass, immersed sliding mass-spring system, immersed sliding beam) stressing the importance of the model on the estimated sliding displacement.

## Keywords

Analytical solutions Sliding structures Fluid-structure interaction Tri-dimensional seismic loading## References

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