Performance-based Earthquake Engineering Methodology Research Articles

Artificial Neural Network Technique For Seismic Fragility Analysis Of A Storage Tank Supported By Multi-Storey Frame

Abstract Fragility function, which defines the conditional probability of exceeding a limit state given an intensity measure (IM) of the earthquake, is an essential ingredient of modern approaches like the performance-based earthquake engineering methodology. However, the generation of such curves generally entails a high computational effort to account for epistemic and aleatory uncertainties associated with structural analysis and seismic load. Moreover, a certain probability function, such as the log-normal distribution, is usually assumed in order to carry out the conditional probability of failure of a structure, without any prior information on the correct probability distribution. In this paper, an artificial neural network (ANN) model is proposed to carry out fragility curves in order to avoid the aforementioned problems. In this respect, this paper investigates the following aspects: (i) implementation of an efficient algorithm to select proper seismic intensity measures as inputs for ANN, (ii) derivation of surrogate models by using the ANN techniques, (iii) computation of fragility curves by means Monte Carlo Simulations and (iv) validation phase.

Lifetime response of a liquefiable soil foundation-embankment system subjected to sequences of mainshocks and aftershocks

During their typical design working life, structures are subjected to multiple sequential earthquakes that are divided into clusters of mainshocks and aftershocks. In consequence, the induced seismic damage accumulates due to these several events in each cluster. On the other hand, the Performance Based Earthquake Engineering (PBEE) methodology presents limitations in accounting for the damage issued from multiple events and the fragility curves represent the failure probability only in one event of a given intensity.For this purpose, this work studies the response of a given structure subjected to sequences of mainshocks–aftershocks during its lifetime. The used time histories (mainshocks) were stochastically generated from a synthetic ground motion model, whereas the aftershocks were generated from the Branching Aftershock Sequence (BASS) model. The cumulative damage measure of the embankment is calculated after the tested sequences. More importantly, its lifetime distribution is estimated and compared with previous results. Finally, to be compatible with the PBEE methodology, the fragility evolution of the embankment over its lifetime was calculated as to emphasize its evolution with the loading history in the soil.

Seismic fatality risk evaluation framework for existing buildings in Switzerland

The Swiss code SIA 269/8 for the seismic evaluation of existing structures is risk-based. It relies on the compliance factor αeff, defined as the ratio of the seismic capacity of an existing structure to the required seismic capacity of a hypothetical identical new structure, to indirectly evaluate the casualty risk posed by the existing structure. While it is convenient to have a direct relationship between the casualty risk and the degree of code compliance of the existing structure, it is debatable if the contributions of the seismic hazard, structural performance and occupancy to the casualty risk should be merged into a single quantity, conflicting with the multi-component nature of seismic risk. This paper presents a graphical framework to evaluate the seismic fatality risk for existing buildings. The framework is based on the PEER Center performance-based earthquake engineering methodology to provide a transparent view of the contributions of different sources of hazard and risk. Starting from a seismic hazard model, probabilistic seismic demand, damage and loss models are introduced, taking the uncertainty into account at each step. The final product of the proposed framework, a loss curve representing the (annual) exceedance rate of fatality counts, enables engineers and building owners to make better, risk-based decisions. The proposed framework is demonstrated for an existing building in Switzerland. Notably, in addition to the SIA 269/8 evaluation method, this demonstration compares eight hybrid approaches differentiated by the utilized structural assessment techniques (nonlinear static pushover vs. incremental dynamic analysis), uncertainty propagation in the demand model (record variability only vs. record variability and epistemic uncertainty) and solution strategies (closed-form vs. numerical) to find a practical compromise between the accuracy and the computational effort. A comparison of the obtained results shows that the SIA 269/8 evaluation method underestimates the fatality risk for the presented building and identifies a practical alternative based on the proposed graphical framework.

On the relevance of incorporating bar slip, bar buckling and low-cycle fatigue effects in seismic fragility assessment of RC bridge piers

The paper reports the results of a numerical investigation on the relevance of including bar slip, bar buckling and low-cycle fatigue in seismic fragility assessment of RC bridge piers. The numerical study is completed on a series of well-confined circular RC bridge column with different configurations where the main variables included are the longitudinal reinforcement ratio, the axial load ratio, the spiral reinforcement ratio and the aspect ratio. Moreover, calculations are performed in several options, namely: (i) Model considering perfect bond (ii) Model considering perfect bond + buckling + fatigue (iii) Model incorporating bar slip only (iv) Model incorporating bar slip + buckling and (v) Model incorporating bar slip + buckling + fatigue. The significance of each individual or combined effect is assessed through comparison of the results from two calculation options. The response of the RC bridge is firstly evaluated through cyclic and monotonic analyses giving indication whether its inherent individual or combined effects should be explicitly considered or if it may be neglected in the probabilistic risk assessment analyses. By considering the main conclusions of the preliminary sensitivity study, the fragility curves are the developed using the Performance-Based Earthquake Engineering (PBEE) methodology. The sensitivity of results to the modelling strategy are discussed in terms of (i) the inelastic seismic demands under strong ground motions using the incremental dynamic analysis (IDA) and (ii) the relative vulnerability developed using probabilistic demand models (PSDM) extracted from the results of the IDA analyses. Based on these studies recommendations are made for the development of reliable and efficient modelling strategy when evaluating the performance of RC bridge piers for use in PBEE.

A framework for the rapid assessment of seismic upgrade viability using performance-based earthquake engineering

The performance-based earthquake engineering (PBEE) methodology allows designers to deaggregate expected seismic losses in a building to a component level. This deaggregated information provides the opportunity to tailor upgrade strategies to individual structures based on sources of losses. However, the optimization of an upgrade strategy becomes difficult because of the relationship between a structure and its nonstructural components; hence, multiple competing upgrade options must be considered. To address this obstacle, this article proposes a framework to guide the assessment of the viability of both structural and nonstructural upgrade strategies, while accounting for limited design resources likely encountered in the early stages of the design process. The framework utilizes the median shift probability (MSP) method, a modified version of the PBEE method introduced in this article, to rapidly summarize the effects of structural upgrades on nonstructural components by considering the impacts of structural modifications on the floor hazards. While accounting for this relationship, the MSP method utilizes the deaggregation of loss across different source categories to identify the benefit of combined structural and nonstructural upgrades, increasing a designer’s understanding of the impact of structural upgrades on losses and allowing for the rapid determination of optimized upgrade strategies unique to the owner’s conditions. A case study example of the implementation of the framework is provided, and the results obtained from the MSP method are compared with those obtained from more rigorous but resource-intensive optimization analysis. An implementation of the MSP method in Microsoft Excel is provided with this article.

Examining the accuracy and validity of loss estimations using the PBEE methodology for wood residential buildings through integrated experimental findings and expert panel solicitation

ABSTRACT The validity and accuracy of loss estimations using the Performance Based Earthquake Engineering (PBEE) approach is studied through integrated experimental findings and expert panel solicitation. The expert panel study had two parts focusing on component- and building-level studies. At the component-level, the experts estimated damage to the building components and provided repair specifications with associated costs and times based on the initial damage state. At the building-level study, the experts assessed the building and component damage in detail using the damage dataset collected during the experiments and prepared a repair schedule. The resulting repair cost and time for the building were then used to evaluate the accuracy of loss estimations using the PBEE method. Various combinations of damage and loss models were considered in the PBEE analysis. It was shown that non-representative/inaccurate damage or loss models even for one component type can cause significant discrepancies in the loss estimations.

Updated probabilistic seismic performance assessment framework for ordinary standard bridges in California

AbstractWith the recent advent of performance‐based earthquake engineering (PBEE) in seismic design practice of buildings serving as an impetus for this work, initial steps toward a fully probabilistic performance‐based seismic design (PBSD) method for bridges, a less trodden area in terms of PBEE applications, are taken herein by assembling an updated probabilistic seismic performance assessment framework for ordinary standard bridges (OSBs) in California. The framework stems from the comprehensive PBEE methodology developed under the auspices of the Pacific Earthquake Engineering Research (PEER) Center. With performance measures defined as the risk associated with the exceedance of a set of damage/limit‐states (LSs), improvements from the state‐of‐the‐art literature on the PEER PBEE methodology are incorporated, including (1) introduction of an improved intensity measure ‐ average spectral acceleration over a period range, (2) conditional mean spectrum‐based hazard‐consistent and site‐specific ground motion selection, (3) introduction of material strain‐based engineering demand parameters, (4) use of practical LSs pertinent to seismic damage evaluation of bridges, and (5) development of strain‐based normalized fragility functions for the considered LSs. The updated framework, assembled herein using a specific testbed California OSB as a case in point, is general within its scope and is applicable to the gamut of design situations representative of the population of OSBs in California. With the PEER PBEE framework implemented for OSBs in an updated and rigorous form, the groundwork for utilizing this framework in the context of PBSD of such bridges is laid.

Performance-based earthquake engineering methodology for seismic analysis of nuclear cable tray system

The Pacific Earthquake Engineering Research (PEER) Center has been developing a performance-based earthquake engineering (PBEE) methodology, which is based on explicit determination of performance, e.g., monetary losses, in a probabilistic manner where uncertainties in earthquake ground motion, structural response, damage estimation, and losses are explicitly considered. To carry out the PEER PBEE procedure for a component of the nuclear power plant (NPP) such as the cable tray system, hazard curve and spectra were defined for two hazard levels of the ground motions, namely, operation basis earthquake, and safe shutdown earthquake. Accordingly, two sets of spectral compatible ground motions were selected for dynamic analysis of the cable tray system. In general, the PBEE analysis of the cable tray in NPP was introduced where the resulting floor motions from the time history analysis (THA) of the NPP structure should be used as the input motion to the cable tray. However, for simplicity, a finite element model of the cable tray was developed for THA under the effect of the selected ground motions. Based on the structural analysis results, fragility curves were generated in terms of specific engineering demand parameters. Loss analysis was performed considering monetary losses corresponding to the predefined damage states. Then, overall losses were evaluated for different damage groups using the PEER PBEE methodology.

Epistemic Uncertainty Treatment Using Group Method of Data Handling Algorithm in Seismic Collapse Fragility

Abstract Developing fragility functions is the essential step in incorporating important uncertainties in next-generation performance-based earthquake engineering (PBEE) methodology. The present paper is aimed to involve record-to-record variability as well as modelling uncertainty sources in developing the fragility curves at the collapse limit state. In this article, in order to reduce the dispersion of uncertainties, Group Method of Data Handling (GMDH) in combination with Monte Carlo Simulation (MCS) is used to develop structural collapse fragility curve, considering effects of epistemic and aleatory uncertainties. A Steel Moment Resisting Frame (SMRF) is chosen as the tested structure. The fragility curves obtained by the proposed method which belongs to GMDH approaches are compared with those resulted from simple and well-known available methods such as First-Order Second-Moment (FOSM), Approximate Second-Order Second-Moment (ASOSM) and Monte Carlo (MC)/Response Surface Method (RSM), somehow, as an accurate method. The results of the application of the proposed approach indicate increasing accuracy and precision of the outputs as well as power with the same computational time compared to aforementioned methods. The GMDH method introduced here can be applied to the other performance levels.

Seismic loss analysis of buildings with post-tensioned cross-laminated timber walls

The FEMA P-58 performance-based earthquake engineering methodology was used to assess the economic losses associated with earthquake damage to nonstructural components of two prototype buildings with post-tensioned cross-laminated timber rocking walls. A suite of 22 far-field ground motions were used for nonlinear time history (NLTH) analysis. Truncated incremental dynamic analysis was used to scale the ground motions, and results of the NLTH analyses were used to develop cumulative distribution functions for inter-story drift and peak floor accelerations. The economic factors assessed in the risk analysis included the expected repair cost with respect to spectral acceleration, the probability of exceeding an expected repair cost for selected time periods, and the expected annual loss over different time periods considering various discount factors. It was determined that the ratio of nonstructural repair cost to total building cost at the design earthquake and maximum considered earthquake was lower for the low-rise building than the mid-rise building. However, the probability of nonstructural damage at the service-level earthquake was lower for the mid-rise building than the low-rise building.

Performance Evaluation of Chinese High-Speed Railway Bridges Under Seismic Loads

The multi-span simply supported (MSSS) box girder bridge is the most used structural form for the high-speed railway (HSR) in China. In structural design, it is required that the MSSS bridge system has high stiffness and low deflection under the operation loads. With the expansion of the HSR network to regions that are seismically active, the seismic performance of MSSS bridges in these regions is an issue of great concern. In this study, the performance-based earthquake engineering (PBEE) methodology originally developed to quantify the seismic performance of buildings and bridges has been adopted to quantify the seismic performance of the HSR MSSS bridges in China. Typically, a four-span MSSS bridge used in China’s Sichuan–Yunnan HSR lines has been extensively assessed by the PBEE approach. This study is the first of its kind to systematically identify and quantify the damage states, repair actions, repair costs and travel delay losses for China’s HSR MSSS bridge system. The results reveal that the financial loss from the MSSS bridge system is highly dependent on the anchorage capacity of the fixed bearings. Overall, the costs of travel delay outweigh those for structural repair. Most of the financial loss can be attributed to the functional loss of the track-slab components and bearings of the HSR MSSS bridge system.

Ground motion selection and modification evaluation for highway bridges subjected to Bi-directional horizontal excitation

Reinforced concrete (RC) highway bridges are primary lifeline infrastructures where accurate seismic structural analysis is essential to ensure the safety of bridges. The nonlinear seismic behavior of bridge structures generally exhibits distinct differences in the longitudinal and transverse directions, and thus studies on bi-directional ground motion excitation are needed. Performance-based earthquake engineering (PBEE) methodology explicitly takes into account uncertainties in hazard, structural response, damage, and loss estimation such that enables a comprehensive understanding of the structural performance in a probabilistic manner. For a given large ground motion scenario, this study takes advantage of the PBEE methodology (the first two stages of hazard and structural response) to develop a benchmark probability distribution of the seismic demands (PDSD) for a given bridge structure considering different assumed intercept angles of the input ground motions with the bridge longitudinal axis. The accuracy and reliability of the PDSD estimates from various ground motion selection and modification procedures for the purpose of future bridge designs are evaluated against this reference benchmark PDSD. Such an evaluation is conducted for several engineering demand parameters of three representative RC bridges in California.

Nationwide Earthquake Risk Model for Wood-Frame Houses in Canada

Quantitative seismic risk assessments involve hazard characterization, exposure database, vulnerability assessment, and uncertainty modelling, and promote consistent risk management actions, when conducted systematically across a country. This study implements a performance-based earthquake engineering methodology to develop a nationwide earthquake risk model for Canadian wood-frame houses by integrating probabilistic seismic hazard analysis results provided by the Geological Survey of Canada and seismic fragility functions derived from incremental dynamic analysis. To facilitate the implementation of the seismic risk analysis method, an in-house probabilistic seismic hazard analysis tool for Canada is developed and used to verify the accuracy of the adopted approach of approximating the upper tail of the seismic intensity measure distribution and to generate detailed seismic disaggregation results for ground motion record selection and seismic fragility modelling purposes. By integrating the preceding two elements via Monte Carlo methods, a full seismic risk curve can be obtained in a computationally efficient manner. The approach is applied to 1,620 representative locations used for the 2016 Canadian Census and thus facilitates the development of seismic risk maps of key risk metrics that are derived from exceedance probability curves in terms of earthquake damage/loss ratio. The developed seismic risk maps serve as valuable decision-support tools to implement risk-based management strategies consistently across Canada.

Seismic risk mitigation in buildings using a new method to encode a joint weighting function in multi-attribute utility theory

This paper provides a new simple, nonparametric method that directly elicits a joint weighting function to be immediately associated with multi-attribute utility under uncertainty. The method allows to include the subjective perception of probabilities and consequences in the decision-making process while dealing with multi-attributes. The concept was only possible when dealing with one outcome; this study demonstrates that it can be achieved for multiple outcomes by mean of a parametric method. First, the newly proposed procedure is described. Then, the experimental protocol is presented while applied to the performance-based earthquake engineering (PBEE) methodology. The decision-making process of PBEE is improved by including the preferences of the decision maker, which is usually the owner. This improvement is important, especially in seismic risk mitigation, because the problem involves low probabilities, which may be inaccurately estimated or even unknown, and these are coupled with catastrophic events. Such combined factors, when objectively weighed, lead to decisions counter to the distorted perception of probabilities and consequences that reflect the implicit desires of the decision maker. Using the newly proposed method, the owner, whose own preferences are elicited, is more likely to embrace the solution since he is involved in the decision process. The results and implications of the analysis are discussed showing the difference in results while including the joint weighting function in the decision-making procedure. The method, which is a step forward in multi-attribute utility theory, is not restricted to the decision-making process applied to PBEE but can be implemented to any multi-attribute decision analysis problem.

On the cyclic behaviour of new pier-to-deck connections for short-medium span composite I-girder bridges

Abstract Short-medium span steel–concrete composite I-girder bridges are becoming more and more popular, because of the reduced construction time and costs. The light weight renders them particularly suitable also is seismic areas, even though this advantage has not been yet adequately investigated. In fact, in case of seismic loading, significant tensile forces might be exhibited at the bottom flange of the steel girder, especially when monolithic connection between deck and pier is adopted, and the connection, conceived for sustaining prevailing hogging bending moments, could experience an excessive damage. With this aim, the cyclic behaviour of new pier-to-deck joints involving the use of concrete cross-beams (CCB) has been recently analysed within the European project (SEQBRI). This paper deals with the results of a wide experimental investigation of these new joints, performed with the aim of characterizing their hysteretic behaviour. Three different typologies were tested: one designed according to the German standard DIN-FB-104, generally utilized for gravity loads only, and other two types proposed for bridges located in low (VAR-1) and medium (VAR-2) seismicity. A series of displacement-imposed cyclic tests highlighted a good seismic behaviour of all the tested solutions. In particular, the DIN-FB-104 VAR C and VAR-2 displayed a similar global behaviour in terms of maximum force and displacement, but with a more pronounced crack development and buckling of steel girders of the first solution. The VAR-2 also avoids possible pull-out phenomena in the CCB thanks to the beneficial action of pre-stressing bars. A damage analysis of the proposed connections was finally performed in view of the application of the performance-based earthquake engineering methodology and the quantification the seismic performance of this bridge typology, which was among the aims of SEQBRI project.

Financial risk evaluation of non-ductile reinforced concrete buildings in eastern and western Canada

Financial risks due to catastrophic earthquakes can be severe. This is particularly applicable to existing buildings that were constructed prior to modern seismic hazard maps and seismic design provisions. Pre-1970 non-ductile reinforced concrete (RC) frame buildings in Canada are of typical examples, where design base shear coefficients were essentially the same across the country, despite very diverse seismic hazards in the east and the west. This study implements a comprehensive performance-based earthquake engineering methodology to evaluate the financial risks of non-ductile RC frame buildings with different numbers of stories for seismicity in Montreal and Victoria. In addition to seismic loss curves that consider a comprehensive event set of regional seismicity, conditional loss distributions for critical scenarios are developed. The results of the financial risk evaluations for the buildings strongly indicate the effects of regional seismicity are significant and overall seismic risks for buildings in Victoria are greater than those in Montreal. Nevertheless, seismic vulnerability of these buildings remains to be high for both locations, meaning that should a major earthquake strike near the location, the buildings studied will suffer major damage. The results from the detailed risk assessments are also useful for developing effective financial risk mitigation strategies through earthquake insurance.

The Effects of Viscous Damping Modeling Methods on Seismic Performance of RC Moment Frames Using Different Nonlinear Formulations

Nonlinear response history analysis, contributing to seismic performance assessment, is a constructive tool for evaluating buildings' behavior and damages due to the earthquake. Applying an accurate viscous damping model constitutes a crucial part in this regard. The seismic response and performance of two reinforced concrete moment frames considering various damping modeling techniques and nonlinear elements are investigated. Two basic approaches to consider nonlinearity are selected: distributed and concentrated plasticity, using force and displacement-based fiber elements and elements that contain two end springs and elastic parts to which zero and modified initial stiffness proportional damping are allocated respectively. Rayleigh damping with mass and four different stiffness matrices are applied in fiber elements. The results of Incremental Dynamic Analysis and loss estimation, considering performance-based earthquake engineering methodology, indicate that Rayleigh damping with mass and initial stiffness overestimates collapse capacity and underestimates performance parameters, while, the model with mass and tangent stiffness with updated proportionality terms shows the opposite trend. In concentrated plasticity models, the more flexible the springs, the more conservative the evaluation of building performance.

A numerical simulation strategy on occupant evacuation behaviors and casualty prediction in a building during earthquakes

Casualty prediction in a building during earthquakes benefits to implement the economic loss estimation in the performance-based earthquake engineering methodology. Although after-earthquake observations reveal that the evacuation has effects on the quantity of occupant casualties during earthquakes, few current studies consider occupant movements in the building in casualty prediction procedures. To bridge this knowledge gap, a numerical simulation method using refined cellular automata model is presented, which can describe various occupant dynamic behaviors and building dimensions. The simulation on the occupant evacuation is verified by a recorded evacuation process from a school classroom in real-life 2013 Ya’an earthquake in China. The occupant casualties in the building under earthquakes are evaluated by coupling the building collapse process simulation by finite element method, the occupant evacuation simulation, and the casualty occurrence criteria with time and space synchronization. A case study of casualty prediction in a building during an earthquake is provided to demonstrate the effect of occupant movements on casualty prediction.

Effects of viscous damping models on a single-layer latticed dome during earthquakes

Rayleigh damping model is recommended in the recently developed Performance-Based Earthquake Engineering (PBEE) methodology, but this methodology does not provide sufficient information due to the complexity of the damping mechanism. Furthermore, each Rayleigh-type damping model may have its individual limitations. In this study, Rayleigh-type damping models that are used widely in engineering practice are discussed. The seismic performance of a large-span single-layer latticed dome subjected to earthquake ground motions is investigated using different Rayleigh damping models. Herein a simulation technique is developed considering low cycle fatigue (LCF) in steel material. In the simulation technique, Ramberg-Osgood steel material model with the low cycle fatigue effect is used to simulate the non-uniformly distributed material damping and low cycle fatigue damage in the structure. Subsequently, the damping forces of the structure generated by different damping models are compared and discussed; the effects of the damping ratio and roof load on the damping forces are evaluated. Finally, the low cycle fatigue damage values in sections of members are given using these damping models. Through a comparative analysis, an appropriate Rayleigh-type damping model used for a large span single-layer latticed dome subjected to earthquake ground motions is determined in terms of the existing damping models.

Seismic assessment of existing tall buildings: A case study of a 35-story steel building with pre-Northridge connection

The Tall Buildings Initiative (TBI) program of Pacific Earthquake Engineering Research Center has been expanded to consider the seismic performance of existing tall buildings. This paper selects a 35-story steel moment resisting frame (SMRF), designed in 1968 with construction details representative of that period, for detailed seismic evaluation in the framework of Performance Based Earthquake Engineering (PBEE). A three-dimensional numerical model capturing the mechanical properties of the most critical structural elements was generated using the program: Open System for Earthquake Engineering Simulation (OpenSees). Systematic nonlinear response history analysis (NRHA) under two basic safety earthquake (BSE) hazard levels for existing buildings were performed following ASCE 41-13 guideline. Probabilistic checks on the confidence levels of the building to achieve collapse prevention (CP) and immediate occupancy (IO) at different hazard levels were conducted based on FEMA 351. In addition, damage and loss analysis was carried out using FEMA P-58 PBEE methodology. Analysis results following different procedures all predicted that the case-study building failed to meet the recommended performance objectives and had a variety of seismic vulnerabilities, and possible retrofits were needed.