Nineteen 2D nonlinear finite element analysis (NLFEA) solution strategies were benchmarked against a wide variety of 101 experiments on reinforced concrete beams failing in bending, flexural shear, or shear compression. The relatively high number of solution strategies was motivated by the conviction that choices for the constitutive models, the finite element kinematics and equilibrium settings will interact, and must therefore be tested in conjunction. Modeling uncertainty distribution parameters are presented for the 19 solution strategies, using all beams, and using beams with and without stirrups separately. The resulting statistics are discussed against the correctness of the simulated failure modes and failure loads, revealing that rotating crack models perform well for the relatively ductile failures in beams with stirrups, while fixed crack models perform better for the more brittle failures in beams without stirrups. The tailored solution strategies that predict failure modes correctly, imply a log-normal distribution of the modeling uncertainty with relatively low coefficients of variation. The outlook is that these estimates of the statistical properties of the modeling uncertainties could serve as a basis within safety formats.

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When non-linear finite element analyses are used in design of new or assessment of existing concrete structures, one should account for the modelling uncertainty before conclusions are drawn based on the results. The present article describes the basis for how this topic is treated in the draft of fib Model Code 2020. There are two components of the modelling uncertainty: (i) within-model, and (ii) between-model. The within-model uncertainty was estimated from a range of series of benchmark analyses gathered from the literature. Each series was assumed analyzed in a consistent manner, termed as the solution strategy. The main result for the within-model component, is a set of prior parameters for Bayesian updating. In an application setting, the prior parameters should be updated after validating the selected solution strategy with a suite of relevant benchmark analyses, before using the mean and coefficient of variation in the Global Factor Method or calculating the modelling uncertainty factor (Formula presented.) to be used in the Partial Factors Method. Finally, results from blind-prediction competitions were studied. With the present data, it cannot be concluded that a-priori knowledge of the experimental outcome reduces the uncertainty in the prediction. Hence, there is no need for compensating for this effect by a separate partial factor.

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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