Reliability-based analysis of circular footings using response surface methodology
Résumé
In this paper, a reliability-based analysis of a circular foundation resting on a $(c,ϕ)$ soil and subjected to a vertical load is presented. Both the ultimate and the serviceability limit states are considered. The two deterministic models used are based on numerical simulations using the finite difference code FLAC 3D . The first model computes the ultimate bearing capacity of the foundation and the second one calculates the footing vertical displacement due an applied vertical load. The Hasofer-Lind reliability index is adopted for the assessment of the foundation reliability. The random variables considered are the soil shear strength parameters for the ultimate limit state and the soil elastic properties for the serviceability limit state. The response surface methodology is used to find an approximation of the analytically-unknown limit state surfaces and the corresponding reliability indexes. The numerical results have shown that the assumption of uncorrelated soil parameters is conservative in comparison to the one of negatively correlated variables. The failure probability was highly influenced by the coefficient of variation of the angle of internal friction for the ultimate limit state and the Young modulus for the serviceability limit state. The computation of the system failure probability involving both the ultimate and the serviceability limit states was also presented and discussed.
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