The effect of uncertainty in material properties and model error on the reliability of strength and ductility of reinforced concrete members

Abstract

The application of reliability-based code calibration procedures in the design of reinforced concrete (RC) structures has enjoyed increasing attention in the past three decades. All of the current design codes implement limit state design, in which the load factors and the resistance reduction factors are calibrated using probabilistic procedures. However, limit states involving strength-related measures have received the most consideration in these code calibration procedures, while less attention has been paid to the probabilistic evaluation of deformation-based measures, such as ductility. Generally, the calculation of deformation-based measures requires a more advanced nonlinear analysis method. It is generally accepted that the uncertainty in predicting deformation-related measures is higher than for strength-related measures. Furthermore, deformation-based measures depend on variables with higher uncertainty, for which fewer probabilistic models can be found in the literature. These issues have been major obstacles in tackling deformation-based limit states in the design of RC members.This study was planned to not only investigate the effect of uncertainty in material properties and of analysis model error on the reliability of strength and ductility, but to complement the current gaps in knowledge in the area of probabilistic models for material properties and model errors, especially those affecting ductility. Three important applications, in which both the strength and ductility measures are of importance, are considered. These applications are: i) the minimum ductility requirements in RC beams; ii) moment redistribution in continuous RC beams; and iii) the behaviour of FRP-confined circular columns.The mechanical properties of concrete, especially the ultimate strain and the strain at peak stress, are very important in evaluating the ductility of RC members. Based on experimental data from the current literature, new probabilistic models for these variables were calibrated. Furthermore, an updated experimental database of more than 240 test data was used for calibrating new models for all of the Equivalent Rectangular Stress Block (ERSB) parameters. It was observed that design code models for the ERSB parameters have nearly the same level of accuracy when compared with the experimental data. The design code models and the fibre model were used for calculating the strength and ductility of RC sections and, using an experimental database, probabilistic model errors associated with these models were evaluated. It was shown that the uncertainty in predicting the ductility of RC sections is more than three times that for strength. A reliability analysis on the flexural strength and curvature ductility of RC sections (designed based on the minimum ductility requirements of the current design codes) showed that, although design codes agree on the level of safety for strength-based limit states, there is noticeable disparity between design codes when it comes to the reliability of ductility limit states. Furthermore, while the RC cross-sections are adequately safe against flexural failure, there is a relatively high probability of experiencing brittle failure.Based on experimental data from the current literature, a new probabilistic model for the plastic hinge length of RC structures subjected to gravity loads was calibrated. According to the collected experimental data, there is high scatter in the calculated plastic hinge length. The calibrated model for the plastic hinge was then used in an analytical procedure, based on demand and capacity rotations, for calculating the moment redistribution capacity in continuous RC beams. Reliability analysis on the moment redistribution factor (MRF) showed that even if the average span-to-depth ratio is considered, the code-specified values for MRF are not generally safe. Furthermore, uncertainty in the MRF can cause a reduction in the reliability index of the strength limit state that is comparable to the reduction resulting from a high live-to-dead load ratio.Based on a database of more than 560 data, new probabilistic models for the strength of confined concrete, based on Drucker-Prager and Richart’s models, were proposed. The dilation behaviour of FRP-confined concrete was investigated using another experimental database with more than 200 test data. New models for the plastic potential function of the Drucker-Prager criterion and the dilation rate of FRP-confined concrete were proposed. The new models were then used to calibrate new analytical and finite element (FE)-based models for predicting the ductility of FRP-confined concrete. A database with more than 640 test data of FRP-confined concrete was used to calibrate the model error associated with the proposed strength and ductility models, and those models showed very good performance, outperforming the existing models. Probabilistic analytical and FE-based procedures for evaluating the nominal and lower bound values of strength and ductility in FRP-confined columns were proposed. It was shown that the uncertainty in predicting the ductility of FRP-confined columns is more than twice that for strength and that the uncertainty in material properties and model error has considerable effect on the probabilistic lower bound values of strength and ductility.