In order to make non-linear finite element analyses applicable during assessments of the ultimate load capacity or the structural reliability of large reinforced concrete structures, there is need for an efficient solution strategy with a low modelling uncertainty. A solution strategy comprises choices regarding force equilibrium, kinematic compatibility and constitutive relations. This contribution demonstrates four important steps in the process of developing a proper solution strategy: (1) definition, (2) verification by numerical experiments, (3) validation by benchmark analyses and (4) demonstration of applicability. A complete solution strategy is presented in detail, including a fully triaxial material model for concrete, which was adapted to facilitate its implementation in a standard finite-element software. Insignificant sensitivity to finite element discretisation, load step size, iteration method and convergence tolerance were found by numerical experiments. A low modelling uncertainty, denoted by the ratio of experimental to predicted capacity, was found by comparing the results from a range of experiments to results from non-linear finite element predictions. The applicability to large reinforced concrete structures is demonstrated by an analysis of an offshore concrete shell structure.

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A hierarchical model for the variability of material properties in ready-mixed concrete is formulated. The model distinguishes between variation on the batch, recipe, plant, producer, durability class, strength class, and regional standard level. By considering Bayesian inference and maximum likelihood estimators, the contributions from the different hierarchical levels to the variability can be estimated. The methodology is demonstrated by considering more than 14,000 compressive strength recordings from Norwegian ready-mixed concrete plants. The results suggest that the compressive cube strength of lab-cured specimens can be represented by a log-normally distributed variable with mean 1.28f_ck,cube and coefficient of variation V_c,cube=0.13. Prior parameters for Bayesian updating are given for a range of strength and durability classes. The application of the results is demonstrated in two examples. Since the durability class gives a required maximum water-binder ratio, and the strength of the concrete is governed by the water-binder ratio, the durability class introduces a strength potential if the concrete is subject to strict durability requirements and low-strength requirements. It is suggested that the designer should specify a strength class that utilizes this strength potential, and it is expected that a closer collaboration between the designer, contractor, and producer will result in improved concrete specifications.

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In order to make non-linear finite element analyses applicable during assessment of the global resistance of large concrete structures, there is need for a solution strategy with a low modelling uncertainty. A solution strategy comprises choices regarding force equilibrium, kinematic compatibility and constitutive relations. Relatively large solid finite elements and a fully triaxial material model for concrete were used in the present work. Bayesian inference was applied to results from 38 benchmark analyses. The results indicated that the modelling uncertainty could be represented as a log-normally distributed random variable with mean 1.10 and standard deviation of 0.12. A new method for characterizing the failure mode was developed. The results indicated that the physical uncertainties influenced the estimated parameters of the modelling uncertainty, and that this should be considered when other uncertainties are included in a reliability assessment.

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A fully triaxial material model for concrete was implemented in a commercial finite element code. The only required input parameter was the cylinder compressive strength. The material model was suitable for non-linear finite element analyses of large concrete structures. The importance of including a crack closure algorithm was demonstrated on a case involving sequential loading. Bayesian inference was applied to results from a series of benchmark analyses, and the results indicate that the modelling uncertainty can be represented by a log-normal variable with a mean 1.10 and a coefficient of variation of 10.9%.@en