The thesis proposes to study the accuracy of the finite element method (FEM) analyses by means of « quality indicators ». The quality indicators represent simple mathematical formulas that are designed to evaluate the reliability of the numerical analyses. The accuracy of the discretization modeling of these analyses is determined ; the mathematical model is considered correct and the errors resulting from the choice of the mechanical properties of the soil are not taken into account. We proposed the mathematical formulations of the quality indicators and also established their lower and upper bounds. Due to their simple mathematical formulation, the quality indicators are easily implemented in any finite element computer code. We have introduced them in the CESAR-LCPC finite element computer code, namely in the nonlinear mechanical execution module. The proposed quality indicators are used on a number of simple 2D and 3D problems elastic and elastoplastic problems in order to assess the jump in stress values in the nodes of the generated mesh. After testing the accuracy of the discretization modeling of these numerical analyses, we evaluated the discretization modeling quality of a braced sheetpile excavation (Hochstetten experimental site, near Karlsruhe). The accuracy of the results based on the mechanical properties of the soil and the structure has not been studied. Also, we proved that the quality indicator results are independent of the chosen mechanical properties for the soil or structure
Development of quality indicators for the finite element method : application to retaining structures