Objective - To quantify the influences of uncertainties in material properties, loads, and modeling techniques on the predicted performance of reinforced concrete columns under lateral seismic and axial loads from gravity. This project also investigates the possible improvements in order to increase the efficiency of the framework that incorporates the three sources of uncertainty. By Q4 of FY2018, the results of this study will establish a framework to quantify uncertainty for structural components in PBSE.
What is the Technical Idea? The key technical ideas of this project are to (1) extend the framework on incorporating three main sources of uncertainty to be applicable for reinforced concrete columns, (2) improve the existing component-level uncertainty quantification framework, (3) investigate the impact of loading uncertainty in more detail, and (3) integrate the results of this project with those of the exploratory work on steel beam-columns into a framework to inform future project work by EEG concerning inclusion of uncertainty in projects concerning assessment of buildings.
The main critical innovation of this project is to incorporate material, modeling, and loading uncertainties into the evaluation of the collapse risk of reinforced concrete columns. The material uncertainty will be quantified by collecting test data on the material properties of concrete and reinforcement with the same nominal strength, and presented in terms of a set of distribution. The material uncertainty will be propagated through the modeling uncertainty using stochastic simulation techniques at three levels of modeling resolution (i.e. three separate modeling techniques with varying degrees of approximation), including lumped plasticity, component-based models, and detailed finite element models. A set of probability distributions will be developed to represent the response of the structure as a function of material and modeling uncertainties. These probability distributions will be integrated with the uncertainty in the imposed ground motion to evaluate the overall uncertainty in the response of the reinforced concrete components. This task is a continuation of the exploratory project that is being completed by the PIs. The uncertainty in the response predicted for reinforced concrete columns is expected to be larger than that for steel beam-columns due to the higher natural uncertainty in the material properties and modeling schemes for reinforced concrete buildings.
This project will also investigate the impact of record-to-record (RTR) variability, i.e. loading uncertainty). The exploratory project used Incremental Dynamic Analysis (Vamvatsikos and Cornell 2002) to quantify the RTR variability. One of the questions raised during the exploratory project was how using different ground motion sets or different ground motion selection methods will impact the RTR uncertainty. Moreover, Bradley (2013) suggested that the use of IDA and a single set of ground motions without consideration of the variation of the ground motion characteristics with respect to the intensity of the ground motion, can lead to lower variance in the response prediction but potentially higher bias. However, he did not provide any data to support his hypothesis. This study will investigate the impact of the selected ground motions and the hazard level associated to the motions on the magnitude of RTR uncertainty. The technical contributions from this research would help fill critical knowledge gaps which currently prevent researchers and engineers from evaluating the influences of the underlying sources of uncertainty in full-scale system- and subsystem-level experiments as well as numerical analysis.
What is the Research Plan? This project investigates the potential improvements required to enhance the the framework for incorporating three main sources of uncertainty in the collapse assessment of steel columns. These improvements involve but not limited to investigating the impact of using fitted distributions instead of empirical cumulative distributions on generating random numbers (Q2 of FY 2017) and investigating the influence of different loading scenarios on the measured RTR uncertainty (Q3 of FY 2017).
A parallel effort will be initiated to extend the applicability of this framework to reinforced concrete columns. A comprehensive literature review and data mining will be conducted to quantify the uncertainty associated with the material properties of concrete and steel reinforcing bars in form of a set of probability distribution functions (Q2 of FY 17). The uncertainty embedded in the modeling procedure for concrete columns will be quantified by developing and validating computational models of reinforced concrete columns under gravity and seismic loads at three levels of modeling resolution from reduced-order to detailed finite elements. This task is planned to be accomplished in Q4 of FY 2017. A set of probability distribution functions for reinforced concrete columns that incorporate the influences of material and modeling uncertainties will be developed by performing analyses with probabilistically varied input material properties at each level of modeling resolution under an amplifying acceleration time history record. The integrated material and modeling uncertainty will be propagated through the RTR uncertainty, quantified based on the responses of a reinforced concrete column to a suite of imposed ground motions, to evaluate the total resulting uncertainty in the response of concrete columns. This task will be completed in Q3 of FY 2018.
The uncertainty quantified for reinforced concrete columns will be integrated with the results of the exploratory project on the uncertainty quantification of steel beam-columns to ensure the feasibility and generality of the proposed framework to quantify the component level uncertainty. This task will be conducted in Q4 of FY 2018. A pilot study will be conducted in Q2 of 2019 to propagate the component-level material uncertainty to the system-level to identify the impact of one of the sources of uncertainty embedded in the collapse prediction results for a structural system. This task will be conducted to explore the challenges and feasibility of moving from component to the system level uncertainty. The outcomes of this task will provide recommendations for the future projects in EEG concerning incorporating uncertainty in the PBSE framework.