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Quantitative risk analysis (QRA) is a systematic approach to quantify risks associated with the operation of an engineering process. QRA is an essential tool to support the understanding of exposure of risk to the environment and assets which helps making cost effective decisions to manage the risks for the entire asset lifecycle [Ho et al., 2000 and Salzano et al., 2003]. In structural engineering, QRA typically involves multiple tasks including inspection, testing, numerical modeling, and probabilistic analysis. The risk evaluation results will identify the need for risk mitigation and retrofit plans. As a result, risk evaluation and mitigation are complementary tasks that lead to improving the resilience of the built environment.

This project covers three “Research Tasks” (RT) concerning risk evaluation and mitigation of structures that lead to improving the state-of-art-and-practice for implementing the performance-based earthquake engineering (PBEE) framework. RT1 entitled “Quantification of Material, Loading, and Modeling Uncertainties of RC Structural Components and Systems” focuses on improving the measurement of sources of uncertainties and their impact on structural response. RT2 entitled “Developing Intensifying Artificial Acceleration for Rapid Risk Evaluation” focuses on accelerating the risk evaluation of any type of structure or lifeline by subjecting them to a pre-designed intensifying ground motion. RT3 entitled “Reliability of Fiber Reinforced Composite Systems in Resilient Infrastructure” addresses short- and long-term performance of fiber reinforced polymer (FRP) retrofitted buildings and infrastructure. The 3 RTs are focused on reinforced concrete (RC) structures; however, in a broader perspective, the framework is applied to other structural systems. Figure 1 illustrates the connection among 3 RTs and their contribution in the PBEE framework, with RTs 1 and 2 focused on improving risk evaluation techniques; and RT3 on improving the mitigation techniques.


Connection among three tasks under the main research plan.


This project aims to improve techniques currently used for risk evaluation (including uncertainty quantification) and mitigation (including FRP retrofit) of structural systems and integrate them within the PBEE framework. The first phase of the project is focused on development and enhancement of methods and quantifiers for uncertainty evaluation as well as data on the impact of FRP retrofit systems.

What is the Problem?

The problem statement of this project is three-fold. 1) The impact of ground motion uncertainty is well understood in the earthquake engineering field and there are well-developed methods to consider and quantify its impact. However, the impact of other sources of uncertainty (including modeling and material) as well as their interaction and combined impact on the structural response is less understood. There is a need to quantify the impact of various sources of uncertainty on the structural response. 2) Implementation of probabilistic seismic assessment methods (such as PBSD) is computationally expensive as it requires multiple analysis of the structure for a suite of ground motions. There is a need to develop alternative approaches that reduce the computational cost while still maintaining the accuracy of the assessment. 3) There is a lack of data and methods to quantify the short- and long-term performance of FRP retrofitted structures which hinder reliable assessment of FRP retrofitted structures.  

What is the Technical Idea?

The technical idea for each of the three research tasks are described separately:

RT1- Quantification of Material, Loading, and Modeling Uncertainties of RC Structural Components and Systems:

This project develops a method to quantify the impact of three individual sources of uncertainty, as well as their combined impact, on seismic performance assessments of structures: (1) uncertainty associated with variability in construction material properties; (2) uncertainty associated to the analytical model; and (3) uncertainty in earthquake loading (i.e., record-to-record (RTR) variability). Material uncertainty is quantified by collecting test data on important construction material properties (e.g., concrete compressive, reinforcing steel yield strengths) and developing a set of probability distributions to describe the properties. Modeling uncertainty is quantified by developing several “parent models” and a set of corresponding “children models” by varying modeling parameters (e.g., constitutive model, damping model, mesh size) of the corresponding parent model. The impact of record-to-record (RTR) uncertainty is quantified using the multi stripe analysis (MSA) method, where the numerical model is analyzed for multiple sets of ground motions selected at different seismic hazard levels. The project investigates the impact of the individual sources of uncertainty (e.g., material uncertainty only), the impact of pairs of uncertainty sources (e.g., material and modeling), and the combined impact of all three sources of uncertainty on the structural response.

As part of the project, a framework to incorporate uncertainty in seismic performance evaluations will be developed and refined at a structural component level (i.e., bridge pier) and then applied to a system level (i.e., building frame). The system level study will use two RC frame structures with different heights. Project outcomes will include the development of dispersion parameters describing uncertainty in important engineering demand parameters (e.g., lateral story drift ratio) and guidance for considering uncertainty in research and practical applications of the PBEE framework.

The technical contributions from this research will help to 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.

RT2- Developing Intensifying Artificial Acceleration (IAA) for Rapid Risk Evaluation:

Development of a framework, as part of the PBEE philosophy, has provided a new mechanism for incorporating the influences of various sources of uncertainty, such as ground motion (GM) uncertainty, into structural assessment. This framework requires multiple nonlinear transient structural analyses for a suite of GMs at different seismic hazard levels. Multiple approaches have been developed in the last two decades for GM selection and scaling. A well-established method is incremental dynamic analysis (IDA) where a model is subjected to a GM record, and the transient analysis is repeated, each time increasing the scale factor on the input GM until that motion causes collapse [Sattar et al., 2015]. The challenge in implementing the framework using IDA methods is the need for conducting numerous dynamic analyses (in the order 400-500) to properly address the GM record-to-record variability. This has been the main obstacle for full adoption of this approach in the practice (especially at system level).

A faster procedure is needed to perform probabilistic risk assessment and turn the cost-efficient PBEE as the standard of practice. Developing an alternative method is challenging because it needs to substantially reduce the computational time while capturing (1) the uncertainty in the response, and (2) the unique characteristics of the recorded GMs including intensity, time, and frequency domain features. A new method will be used, i.e. intensifying artificial accelerations (IAAs). This method is similar to the classical pushover analysis; however, it will be implemented in the dynamic condition. Therefore, it is appropriate to call it a dynamic pushover procedure. In this technique, an acceleration signal increases as time goes by, which can be used for nonlinear assessment of structural systems. Using this method, with only a single time history analysis, a full picture of system response from linear elastic to nonlinear, and finally collapse, can be created [Vamvatsikos and Cornell, 2002].

The application of intensifying dynamic functions have shown promising results in the collapse assessment [Hariri et al., 2014; Mirzaee and Estekanchi, 2015; He et al., 2020]; however, they currently do not capture unique anatomy of the GM records such as duration or frequency content. The basic concept of IAA is inspired by the medical “stress (treadmill) test”. In this exercise test, patients (or athletes) run on a treadmill, while the speed and slope of the treadmill are gradually increased until the patient reaches complete exhaustion. The physician measures the patient’s cardiovascular health based on the maximum endured intensity. The human body is a complex system with many unknown factors, yet such a simple exercise test can provide important information about general health status despite the inherent uncertainty in our knowledge.

The IAAs can be generated, used, and validated in three levels: (1) generic IAA, (2) site-specific IAAs, and (3) ground motion dependent IAAs. The generic IAA can be used for dynamic analysis of the systems regardless of the location of the structure. The site-specific IAA would be developed based on the response spectra of the site and possibly incorporate the fundamental period of the structures. This method can be then validated against the results from the conditional ground motion selection method. The ground motion dependent IAA establishes a relationship between different ground motion intensity measures (IMs) at different scaling levels. These relationships will be used to optimize the ground motion specific IAA at different time intervals.

The main goal of this project is to develop a series of site-specific intensifying artificial acceleration functions to be used for continuous limit state development and collapse evaluation of frame structures and lifeline systems. The results of the IAA method will be compared and validated with available techniques such as incremental dynamic analysis, multiple stripe analysis and cloud analysis.

RT3- Reliability of Fiber Reinforced Polymer (FRP) Composite Systems in Resilient Infrastructure:

FR composites have been used in infrastructure applications to repair, seismically retrofit, and strengthen new and existing structures, as well as build lightweight bridge decks, and provide corrosion-resistant internal reinforcement (i.e. as reinforcing bars) for concrete [Want et al., 2015; Ma et al., 2017; Ebead et al., 2016; Chandrasekaran and Banerjee, 2015]. In comparison to steel, FR composites offer the advantage of being corrosion-resistant, lightweight, easy to apply to a variety of support structures, adaptable for a particular need, and elastically responsive to seismic activity [Want et al., 2015; O’Connor and Frankhauser, 2016; Zaman et al., 1988].

In infrastructure, carbon fibers are most commonly employed in the form of fabric, laminate, or individual tow. These fibers have a high strength and stiffness-to-mass ratio [Zaman et al., 1988]. Fibers are typically combined with a matrix before (prepreg) or during (wet layup) application. [Ebead et al., 2016, Zaman et al., 1988; Bilotta et al., 2017; Pino, 2016; Awani et al., 2017] Several organizations, such as the American Concrete Institute (ACI) committee 440, the International Federation for Structural Concrete (fib), the American Association of State Highway and Transportation Officials (AASHTO) and the Transportation Research Board (TRB), have an active presence in FR composite research. It is well known that FR composites can strengthen structures, but durability of retrofitted structures is not fully addressed.

The durability of FR composite retrofits and the systems they are applied to are critical to both the functionality and safety of our nation’s building stock and infrastructure. Factors that affect durability may include age, freeze/thaw exposure, moisture-induced damage, thermal damage, UV radiation exposure, indoor air quality, and flammability during fire exposure. [Ma et al., 2015; Zaman et al., 1988; Barbosa et al., 2017; Kim and Alqurashi, 2017; Lau et al., 2016] To date, some durability research studies have been conducted and acceptance criteria have been proposed for buildings by the International Code Council (ICC) Evaluation Service, but are somewhat limited in their applicability to FR composites in the field [Barbosa et al., 2017; AC125, 2007; AC343, 2016]. Durability depends on the specific material constituents of the FR composite and conditions during matrix curing [Tumialanand De Luca, 2014]. Since strength retention (e.g., modulus and ultimate strain at rupture) of FR composites alone (micro-level) and when bonded to concrete (meso-level) are key requirements to sustaining the performance of the FR composite system, mechanical measurements in these configurations are important. Furthermore, chemical measurements that provide mechanistic understanding of the changes in FR composite systems can enable broader understanding of performance loss and failure modes [Zaman et al., 2988]. 

In addition to the gaps in knowledge concerning durability of retrofitted components, the extent of short-term performance improvement of some structural components, such as reinforced concrete shear walls, is less understood. The ASCE 41, Seismic Evaluation and Retrofit of Existing Buildings, which is the main U.S. standard for retrofit of existing buildings, currently provides no guidance on simulating the response of retrofitted components. Methods to measure the structural improvement by FR composites applied to existing structural components such as masonry and reinforced concrete walls are also needed.

Currently, a general lack of data, test methods, and standards to assess the health and performance of FR composite materials in indoor and outdoor environments is a major barrier to their use [Zaman et al., 2988]. An evaluation of performance and health of FR composites in actual systems requires investigation to inform stakeholders and make progress on implementing the necessary method development and testing for this relatively new material. Once the performance and health of FR composite systems have been grounded in measurement science, the resilience of FR composite systems to earthquakes and other extreme events can be modeled and evaluated [Wang et al., 2016].

What is the Research Plan?

The research plans for each of the three research tasks are described separately:

RT1: Quantification of Material, Loading, and Modeling Uncertainties of RC Structural Components and Systems:

The uncertainty quantification framework for the component level was completed in early 2022. In the next phase of the project, the framework will be extended to the system level by improving the framework to enable studying the uncertainty in the seismic performance of RC frame systems. The first task will consist of selecting archetype buildings for the system level study. An extensive literature review will be conducted in order to quantify the uncertainty sources in the system level and to distinguish its unique differences from component level. Similar to the component level uncertainty study, uncertainty related to materials, modeling, and RTR variability will be quantified by developing and validating computational models that will be analyzed 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. The models will be validated and sensitivity analyses will be performed to identify important parameters. For system level evaluations, material uncertainty will be assessed in a similar way to the component level evaluations. Some additional considerations will need to be addressed to account for spatial uncertainty in material properties (e.g., differences in material properties among beams and columns at different locations in the frame). The framework developed for system level uncertainty quantification will be improved and expanded to account for these additional relationships. The impact of modeling uncertainty will be quantified by subjecting each parent model and its children to a set of artificial acceleration time histories. RTR variability will be evaluated by applying the MSA analysis method to the parent and children models and comparing statistical parameters for important engineering demand parameters considering the impact of: (1) individual sources of uncertainty (e.g., material only); (2) pairs of uncertainty sources (e.g., material and modeling); and (3) combination of all three sources of uncertainty.

RT2: Developing Intensifying Artificial Acceleration (IAA) for Rapid Risk Evaluation:

As discussed in the Technical Idea section, the generation and application of IAAs can be conducted in three main levels. In the generic form, the IAAs will be implemented on component level RC columns with different characteristics (e.g. fundamental period, ductility, etc.) and the results will be compared with three other seismic probabilistic analysis technique (i.e. incremental dynamic analysis, multiple strip analysis and cloud analysis). Accuracy and computational times of these methods will be compared.

Next, the site-specific IAAs will be generated. A Matlab code will be developed to generate the synthetic IAA with (1) desired duration (i.e. longer IAA for stiffer structures), (2) any envelope function (i.e. linearly or nonlinear increasing of signal intensity), and (3) any desired location with specific response spectra (i.e., depending on soil type). The procedure is based on nonlinear unconstrained optimization technique which controls characteristic parameters of a ground motion (e.g., acceleration and displacement) over time. The site-specific IAAs will be applied to the component level models in the first step, and the results will be compared and contrasted with current ground motion selection and scaling methods such as conditional and unconditional ground motion selection based on a target response spectrum.

Both the generic and site-specific IAAs are developed based on a target response spectrum and explicitly account for ground motion characteristics. The next generation of IAAs should be developed based on unique ground motion dynamic fingerprints. This includes the significant duration of the motion, as well as all the significant intensity measure parameters. Therefore, a relation should be first established between different ground motion intensity measure parameters and the scaling factor which is used for the record itself. This relation might be linear for some intensity measure and nonlinear (either concave down or up) for others. Next, a series of statistical and machine learning models should be run to fully quantify the meta-model which describes the time-dependent GM intensity measures. Such a meta-model will be sought by analyzing thousands of ground motion records in the PEER website.

In the first out-year, the Matlab code for optimization of the IAA functions from the site-specific model will be combined with intensifying nature of ground motion intensity measure parameters to generate the ground motion-specific IAA records. This task is targeted for a large number of unique real ground motion records including the short and long duration records, near and far-field motions. Finally, upon validation, this method will be propagated to all the records in the PEER website and a parallel website will be created, hosted by NIST, to manage and maintain all these records for public use.

RT 3: Reliability of Fiber Reinforced Polymer (FRP) Composite Systems in Resilient Infrastructure:

This project will seek to implement a strategic plan that prioritizes the current research needs for fiber reinforced (FR) composites used in structural systems (NIST SP-1244). The research plan will 1) investigate FR composite use in the field, 2) design durability experiments of FR composite systems from micro to macro level that focus on the critical modes of failure identified, and 3) assess performance of FR composites in structural systems using laboratory tests and numerical analysis.

RT3-1: Investigate FR use in the field and prioritize research needs [Completed]

RT3-2: Design durability experiments of FR composite systems

The IMG is uniquely equipped to measure polymeric materials and concrete as they age under different conditions using environmental chambers (high temperature, humidity, low temperature, and freeze/thaw) such as the NIST SPHERE (UV, temperature, humidity) at multiple material scales (micro to meso scales). Durability studies of stand-alone composites (fibers + resin) and FR composites bonded to concrete will be conducted to evaluate changes to both micro- and meso-levels, respectively. Durability studies will include outdoor weathering in 2 to 3 climatic zones with several types of glass and carbon FRP materials representative of externally bonded FRP products used nationally. Changes in material properties such as adhesion to concrete and strength retention of FRP composite/concrete assemblies under different environmental loads may provide improvement  to strength reduction factors for retrofit design [Dai et al. 2005]. Accelerated conditioning protocols will also be employed using at least two environmental conditions with high potential for causing FRP composite degradation. Degradation modes from accelerated conditioning tests will be compared to modes observed in outdoor tests to determine if accelerated conditioning can realistically determine FRP composite failure at a more accessible time scale than outdoor testing. Metrology that indicates FRP composite performance level will be incorporated into durability studies to measure performance loss due to degradation and potentially predict the point at which FRP composite failure occurs. Chemical tests can be used, when needed, to determine mechanistic changes of FRP composites during degradation. Non-invasive metrology, such as ultrasonic techniques and infrared thermography, may be investigated for measuring FRP composite bond adhesion and be related to strength retention depending on identified performance metrics.

RT3-3: Bond quality testing

The quality of the bond between the FRP material and the substrate can be critical to the performance of the FRP retrofit. Oftentimes, the bond can be the limit state of the FRP retrofit. The quality of the bond can be affected by installation practices, environmental degradation, and hazard events such as earthquakes. Currently, the industry standard for assessing bond quality is the pull-off test, which is a pass/fail test that places direct tension on a disc adhered to the FRP surface and requires a failure in the concrete above a certain threshold strength. Based on input at the NIST stakeholder workshop, variability in the results of this test method leads to difficulty interpreting the actual quality of the bond, and further information is needed to understand the test’s limitations. An ongoing sensitivity analysis is underway to assess variables that may affect the test method’s results. Future work will include determining if there are available alternatives to the pull-off tests for bond quality assessment such as non-destructive testing, peel tests, and shear tests. It is important that new test methods are practical for field testing.

RT3-4: Develop a database of FRP retrofitted shear walls and modeling parameters

All available data on the experimental testing of FRP-retrofitted shear walls will be collected for inclusion in a database. The database will include all relevant information on the tests, including specimen data, design of FRP retrofit, test parameters, and experimental results. This database will be published for public use. One of the uses of the database in this project will be the development of modeling parameters of retrofitted shear walls. This is important because there are currently no modeling parameters in the standards used for design that are directly applicable to retrofitted components. The modeling parameters will be developed using regression analysis of key design parameters of the walls in the database against control points of an idealized backbone curve. Once modeling parameters are determined, we will engage with stakeholders and code committees, such as the ACI 369 Seismic Repair and Rehabilitation committee (which provides concrete-specific content for ASCE 41), to discuss our findings and develop a change proposal to integrate into future versions of the design codes.

RT3-5: Assess performance of FR composites in structural systems

A set of macro- (component) level tests will be developed using the findings of micro- and meso- level phases of the study to measure the performance of wall structural components enhanced by FR composites. These tests will be conducted with the goal of quantifying the improvement in the response of retrofitted components in existing structures. The experiments will be designed and conducted to quantify the change in the force-displacement response of structural components retrofitted by FRP with and without consideration of deterioration over time. Three types of tests specimens will be assembled  for each test, where the first specimen is not retrofitted, the second specimen is retrofitted, and the third specimen is retrofitted and exposed to the accelerated degradation to simulate field observations [note: testing of the third specimen would be part of the long-term plan for this project]. The force-displacement response of two tests will be measured under cyclic and monotonic loading to quantify the improvement in the response of the structural components retrofitted by FR composites. The experimental results will be used to inform/validate the modeling parameter equations developed in RT3-4.

RT3-6: Develop a pre-standard for seismic assessment of FRP-retrofitted concrete structures

This RT is intended to produce design procedures for common high-use seismic retrofit techniques involving FRP materials. Of particular interest for this task is the seismic retrofit of deficient reinforced concrete buildings. The final product is intended to be a standardization-ready document targeted for adoption by ACI 369.1 (Guide for Seismic Rehabilitation of Existing Concrete Frame Buildings and Commentary) and ASCE/SEI 41 (Standards of Seismic Safety for Existing Federally Owned and Leased Buildings) standards, as well as the ACI 440 standard for retrofit of concrete structures using externally applied FRP. The envisioned document would have pre-standard language for ease of adoption in the standards, while also providing a robust background/commentary section. A possible format for the document may follow the NCHRP Report 6553 that was the precursor to an AASHTO guide on non-seismic retrofit of bridges using FRP. Under this RT, the project team will form a working group of subject matter experts (SMEs) from academia and industry to work with NIST researchers on developing the pre-standard document.


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Created January 6, 2023