Utilisation de la methode des elements finis non-lineaires pour la conception des structures en beton arme: Application aux structures massives

Nonlinear finite elements for concrete structures have seen a remarkable advancement in the last half century with more emphasis on constitutive modelling of reinforced and non-reinforced concrete. Applications were restricted to the analysis of simple structures (beams, columns, slabs...etc.), comparisons to experimental tests, and rarely extended to the design of complex structures. Many reasons lie behind this fact. The first is the difficulty to implement such analyses for complex structures: large computation time with respect to conventional linear analyses, and convergence problems generally related to concrete softening. The second important reason is the complexity of the concrete material and the existence of a multitude of models and theories in the literature. Finally, there is a lack in the literature and international codes concerning the reliability framework and the limit state design using nonlinear analyses. The current work presents solutions to these issues and applications in the field of large reinforced concrete structures. To address the first problem, the quasi-static explicit solver algorithm is presented in this work, as an alternative to the conventional static implicit solver. Effectiveness of the explicit solver algorithm compared to the standard implicit one is demonstrated. It is shown through validations that, analysis of complex models with highly non-linear behaviour is being possible without the need for iterations. To address the second and third problems, a methodology that uses nonlinear finite elements analysis for determining a global resistance factor for the design of reinforced concrete structures is suggested. A new reliability approach is introduced, which takes into account the uncertainties of the material properties and the performance of the concrete model used in the calculations. In a first step, estimation of the coefficient of variation of the prediction error is performed for a given concrete model, nonlinear finite element package and a target design structure (TDS). In a second step, the global resistance factor is computed following a procedure in which the coefficient of variation of the calculated resistance is estimated using Rosenblueth's point estimate method. Robustness and simplicity of this method are demonstrated. The suggested methodology is well suited for structural engineers having access to non-linear deterministic finite element packages with concrete models.;Application of this general methodology is presented for the case of large hydraulic structures. The draft tube structure which is a typical component of a powerhouse with large members and non conventional boundary conditions is taken as the TDS. Following the two-step procedure, the model error is firstly computed for two candidate concrete models: EPM3D and CDP. The validation process is undertaken from material to structural levels. Importance of considering the statistical size effect of the concrete is outlined in the calibration procedure at the material level and a new expression for the equivalent tensile strength is suggested. It is shown through this process that the use of only the compressive strength of the concrete and the yield strength of reinforcement are sufficient with EPM3D model to obtain relatively low coefficient of variation of model error. Using this selected concrete model and its corresponding model error, the global resistance factor is computed in a second step for the TDS. Effects of temperature, nominal shear reinforcement and lateral confinement are discussed. As an additional application, the shear size effect is investigated for very large concrete members without shear reinforcement. It is shown that, contrarily to some recent design code equations, the tendency of shear strength is much less sensitive to size effects for very large members. It is shown that for the case of a uniformly loaded beam, the macro size effect in shear tends asymptotically to the meso statistical size effect in tension previously identified at the material level in the first step.;Keywords: nonlinear analysis, finite element, concrete model, explicit algorithm, global safety factor, limit state design, hydraulic structures, design and assessment, verification & validation, size effect.