Performance-Based Earthquake Engineering (PBEE) has provided a probabilistic framework to predict the response of the structural systems by incorporating the influences of various sources of uncertainty. Among the sources of uncertainty, the effects of uncertainty in the applied loads (i.e., loading uncertainty) on the performance assessments of structures is well established. However, the influences of material and modeling uncertainties have not yet been systematically integrated into PBEE. Sattar et al. (2015) proposed a framework to incorporate three sources of uncertainty (loading, material and modeling) in the collapse assessment of steel beam-columns. This framework was developed in a joint effort between the Earthquake Engineering and Structures Groups at NIST. The proposed project will modify this framework to be applied for response prediction of reinforced concrete column components and frame systems under axial loading from gravity and lateral loading from earthquake ground motions. In addition, this project will conduct a comprehensive literature review on the previous studies conducted on the uncertainty quantification of the structural response and explore various research ideas on the field of uncertainty quantification for future consideration by the Earthquake Engineering Group at NIST.
Objective - To quantify the influences of uncertainties in material properties, loads, and modeling techniques on the performance of reinforced concrete column components and frame systems under lateral seismic and axial loads from gravity. The results of this study will be integrated with the findings of the exploratory project concerning steel beam-columns to establish a framework to quantify uncertainty for isolated structural components and structural systems 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 and frames, (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 seismic performance assessment of reinforced concrete column components and frame systems. 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. 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 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? As part of this project, potential improvements required to enhance the framework developed for incorporating three main sources of uncertainty in the seismic performance assessment of steel columns will be investigated. One of these improvements will involve investigating the influence of different loading scenarios on the measured RTR uncertainty (completed in Q3 of FY 2017).
A comprehensive literature review and data mining is conducted in the first year of the project to quantify uncertainty in material properties of concrete and steel reinforcing bars in the form of a set of probability distribution functions (completed in Q3 of FY 18).
The uncertainty embedded in the modeling procedure for concrete columns will be quantified by analyzing the predictions submitted to the blind prediction contest on a bridge column specimen tested at UCSD. The predictions submitted to the blind prediction contest provide a unique opportunity to quantify the impact of different modeling approaches on the predicted response of structures. As an alternative approach, the impact of modeling uncertainty on the response of 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 (completed in Q3 of FY 2018).
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 Q4 of FY 2018.
The uncertainty quantified for reinforced concrete columns will be integrated with the results of the exploratory project on uncertainty in the seismic performance 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 Q1 of FY 2020.
The uncertainty quantification framework will be extended from the component level (i.e., column) to the system level by improving the framework to enable studying the uncertainty in the seismic performance of a reinforced concrete frame system. The first task will consist of collecting seismic response data from shake table tests that have been conducted on reinforced concrete frames. One or more shake table test frames will be selected to be used for model validation activities. This task will be completed in Q2 of FY 2020.
Similar to the component level uncertainty study, uncertainty related to materials, modeling, and record-to-record variability will be quantified by developing and validating computational models that will be analyzed for their response under combined gravity and seismic loads.
Models will be developed at different resolution levels including lumped plasticity formulations (i.e., plastic hinge models) and distributed plasticity formulations (i.e., fiber models), and may also include more detailed finite element models. For each modeling approach, an analytical model of the shake table test selected for model validation will be developed and validated against measured response data. This task will be completed in Q4 of FY 2020.
Material uncertainty will be assessed in a manner similar to that of the reinforced concrete bridge column component with some additional considerations that will need to be addressed. One of the primary differences between the component level and system level uncertainty quantification studies will be the need to consider the relationships and interdependencies between material properties of individual components in the frame system (e.g., the correlation between concrete strength in a column and beam in a single story; the correlation between concrete strength in columns in different stories). The framework developed for system level uncertainty quantification will be improved and expanded to account for these additional relationships. This task will be completed in Q4 of FY 2020.
The impact of RTR variability will be quantified by subjecting a single validated model to a suite of ground motion records. This task will be completed in Q1 of FY 2021.
The impact of modeling uncertainty will be quantified by subjecting each of the validated models to a single ground motion record scaled to different loading intensities. This task will be completed in Q2 of FY 2021.
A set of probability distribution functions for reinforced concrete frames 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 frame to a suite of imposed ground motions, to evaluate the total resulting uncertainty in the response of concrete frame system. This task will be completed in Q4 of FY 2021.