Probabilistic Seismic Risk Assessment Research Articles

Damping‐dependent correlations between horizontal‐horizontal, horizontal‐vertical, and vertical‐vertical pairs of spectral accelerations

AbstractCorrelation coefficients for 5%‐damped spectral accelerations (SAs) of horizontal ground‐motion components have been extensively studied and applied in probabilistic seismic analysis using vector‐valued intensity measures (IMs). Such correlations are, however, not sufficient for structures with different damping ratios under multidirectional earthquake shakings. This paper presents a comprehensive study on the correlations between horizontal‐horizontal (H‐H), horizontal‐vertical (H‐V), and vertical‐vertical (V‐V) pairs of SAs for different damping ratios based on the NGA‐West2 ground motion database. The correlations of SAs with peak ground acceleration (PGA) and peak ground velocity (PGV) are also investigated. The uncertainty in correlations is measured by integrating the bootstrap method into the logic‐tree framework. Comparative results indicate that the correlation coefficients generally increase for IMs of larger damping ratios. The relative difference between the damping‐dependent and conventional 5%‐damped correlation coefficients can be notable, reaching 100% and 35% in the SA‐SA and SA‐PGV (or PGA) pairs, respectively. Based on the empirical correlation results, an artificial neural network is utilized to develop parametric models of the correlations and the executive files for implementing these models are provided. The ANN‐aided damping‐dependent correlation models developed can be considered as a generalization of the conventional 5%‐damped correlation models, and may serve as useful tool in applications such as ground‐motion selection and vector‐valued probabilistic seismic risk assessment for structure systems.

Reference prior for Bayesian estimation of seismic fragility curves

One of the key elements of probabilistic seismic risk assessment studies is the fragility curve, which represents the conditional probability of failure of a mechanical structure for a given scalar measure derived from seismic ground motion. For many structures of interest, estimating these curves is a daunting task because of the limited amount of data available; data which is only binary in our framework, i.e., only describing the structure as being in a failure or non-failure state. A large number of methods described in the literature tackle this challenging framework through parametric log-normal models. Bayesian approaches, on the other hand, allow model parameters to be learned more efficiently. However, the impact of the choice of the prior distribution on the posterior distribution cannot be readily neglected and, consequently, neither can its impact on any resulting estimation. This paper proposes a comprehensive study of this parametric Bayesian estimation problem for limited and binary data. Using the reference prior theory as a cornerstone, this study develops an objective approach to choosing the prior. This approach leads to the Jeffreys prior, which is derived for this problem for the first time. The posterior distribution is proven to be proper (i.e., it integrates to unity) with the Jeffreys prior but improper with some traditional priors found in the literature. With the Jeffreys prior, the posterior distribution is also shown to vanish at the boundaries of the parameters’ domain, which means that sampling the posterior distribution of the parameters does not result in anomalously small or large values. Therefore, the use of the Jeffreys prior does not result in degenerate fragility curves such as unit-step functions, and leads to more robust credibility intervals. The numerical results obtained from two different case studies—including an industrial example—illustrate the theoretical predictions.

Seismic fragility analysis of slopes based on large-scale shaking table model tests

Seismic fragility analysis is one probabilistic method that represents the conditional probabilities of exceeding different predetermined damage states for various given earthquake hazard levels, which is the essential part of probabilistic seismic risk assessment. It has gained much popularity recently because much more comprehensive and richer results than traditional probabilistic methods can be provided. The classical seismic fragility analysis of slopes is always performed through analytical approaches. In the present study, a novel seismic fragility analysis framework combined with shaking table model test results is proposed for probabilistic seismic performance and risk assessment of slopes. The shaking table model tests of a rock slope reinforced by pile-anchor structures were firstly performed subjected to a suite of real earthquake records with different intensity levels. Subsequently, the seismic responses from shaking table model tests were then gathered for the optimal analysis to determine the optimal engineering demand parameter (EDP) and earthquake intensity measure (IM) for seismic fragility analysis of slopes. At last, the identified most appropriate IM and EDP were selected to construct the scalar-valued fragility curves, vector-valued fragility surfaces and fragility surfaces considering acceleration elevation amplification effect by the proposed framework. The results indicate that using single IM to construct scalar-valued fragility functions may result in different failure probabilities depending on the chosen earthquake IM. The vector-valued fragility surfaces provide more information than ordinary fragility curves, and lead to more proper and realistic evaluations of seismic hazard of slopes. The methods and results presented in this paper also provide the basis for the probabilistic seismic risk and loss assessment of earthquake-induced slope geological disaster.

Probabilistic seismic collapse risk assessment of non-engineered masonry buildings in Malawi

This study presents the most recent development of a nationwide earthquake risk model for non-engineered masonry buildings in Malawi. Due to its location within the East African Rift, Malawi experienced several moderate earthquakes that caused seismic damage and loss. Recently, a new probabilistic seismic hazard model has been developed by considering fault-based seismic sources, in addition to conventional areal sources. The most recent 2018 national census data provide accurate exposure information for Malawian people and their assets at detailed spatial resolutions. To develop seismic fragility functions that are applicable to Malawian housing stocks, building surveys and experimental tests of local construction materials have been conducted. By integrating these new developments of seismic hazard, exposure, and vulnerability modules, a quantitative seismic building collapse risk model for Malawi is developed on a national scale. For the rapid computation of seismic risk curves at individual locations, an efficient statistical approach for approximating the upper tail distribution of a seismic hazard curve is implemented. Using this technique, a seismic risk curve for a single location can be obtained in a few seconds, thereby, this can be easily expanded to the whole country with reasonable computational times. The results from this new quantitative assessment tool for seismic impact will provide a sound basis for risk-based disaster mitigation policies in Malawi.

UNCERTAINTY QUANTIFICATION AND GLOBAL SENSITIVITY ANALYSIS OF SEISMIC FRAGILITY CURVES USING KRIGING

Seismic fragility curves have been introduced as key components of seismic probabilistic risk assessment studies. They express the probability of failure of mechanical structures conditional to a seismic intensity measure and must take into account various sources of uncertainties, the so-called epistemic uncertainties (i.e., coming from the uncertainty on the mechanical parameters of the structure) and the aleatory uncertainties (i.e., coming from the randomness of the seismic ground motions). For simulation-based approaches we propose a methodology to build and calibrate a Gaussian process surrogate model to estimate a family of nonparametric seismic fragility curves for a mechanical structure by propagating both the surrogate model uncertainty and the epistemic ones. Gaussian processes have indeed the main advantage to propose both a predictor and an assessment of the uncertainty of its predictions. In addition, we extend this methodology to sensitivity analysis. Global sensitivity indices such as aggregated Sobol' indices and kernel-based indices are proposed to know how the uncertainty on the seismic fragility curves is apportioned according to each uncertain mechanical parameter. This comprehensive uncertainty quantification framework is finally applied to an industrial test case consisting of a part of a piping system of a pressurized water reactor.

Probabilistic Seismic Risk Assessment of a reinforced concrete building considering hazard level and the resulting vulnerability using Bayesian Belief Network

Probabilistic Seismic Risk Assessment of a reinforced concrete building considering hazard level and the resulting vulnerability using Bayesian Belief Network

Seismic excitation model in probabilistic risk assessment of civil infrastructure

AbstractRealistic risk assessment of civil infrastructure subjected to catastrophic events plays a crucial role in strategic asset management. In this process, visualization of the asset and its environment always possesses some epistemic uncertainty associated with the modeler's simplification/abstraction. The present paper aims at providing a critical perspective into the characterization of the seismic excitation model for risk assessment of civil infrastructures and identifying gaps in the present knowledge. For this purpose, the main factors that influence the development of a comprehensive framework for the simulation of seismic excitation are highlighted. The coupling effect of the spatial variability of ground motions and the substructure's footprint on the realization of the seismic excitation model is illustrated. Finally, the necessity of direct incorporation of the load analysis subtask in the probabilistic seismic risk assessment of civil infrastructures is discussed. In addition, simplified probability density functions are proposed for the simulation of the seismic excitation model.

Life-cycle dynamic analysis and probabilistic seismic risk assessment of cross-fault hydraulic tunnels considering AAR-induced deterioration

The alkali-aggregate reaction (AAR) triggered the deterioration of the machinistic property of concrete materials is among the major negative factor that results in the reduction of structural serviceability and performance for concrete structures, especially for those hydraulic engineering in contact with water for service life-cycle. Hydraulic tunnels, being a vital component of hydraulic engineering, are frequently employed in various lifeline projects around the world. Once the AAR effect renders the hydraulic tunnel inoperable, the government and society will suffer enormous economic losses, delaying the achievement of carbon neutrality. However, current specification for seismic design does not account for the degradation of structural performance parameters induced by AAR effects, which cannot fully reveal the earthquake performance of AAR-affected tunnels during use. Having realized this challenge, this work presents a mechanical model of the AAR effect integrating the concrete elastic-plastic damage model to conduct the inelastic dynamic response and random earthquake risk assessment of AAR-affected cross-fault hydraulic tunnels with design life-cycle. To this end, a study of the AAR-affected hydraulic tunnels, which consider the fluid-structure-surrounding rock coupling systems throughout the service period, is undertaken to associate the structural reaction with the predefined evaluation index directly. Subsequently, The nonlinear dynamic assessment of cross-fault hydraulic tunnel is conducted by using increased dynamic method to generate several data. Besides, this research constructs the three-dimensional (3D) time-dependent fragility surfaces considering the AAR effect and seismic intensity level. The results of this study underscore this point that the AAR effect possesses the capability to aggravate the response of relative displacement and extend the cumulative damage cracking area of the cross-fault hydraulic tunnels (CFHTs) with the increase in service time. Similarly, the 3D time-varying fragility surfaces show that the longer the service time of AAR-affected cross-fault hydraulic tunnels, the more likely they are to collapse. The above phenomena demonstrate that the AAR effect can be recommended for the utilization in estimating the likelihood of the erosion of the building during service life-cycle and future seismic design code.

A database and empirical model for earthquake post-loss amplification

The impact of destructive earthquakes might exceed the local capacity to cope with disasters and lead to an increase in the reconstruction costs. This phenomenon is commonly termed as post-loss amplification, and its main causes include the increase in the cost of construction materials and labor due to the sudden demand, the need to reconstruct following higher standards, or other unexpected costs. We reviewed 70 past earthquakes to identify events where post-loss amplification was observed, and collected a set of seismogenic, socio-economic, geographical, and impact variables for those events. Using this database, we developed two models to predict post-loss amplification, using a composite indicator that reflects the level of destruction in the region, or a parameter that characterizes the frequency of the event. This study indicates increased costs (>10%) for events where the economic losses exceed 1% of the regional gross domestic product, or for events with an estimated return period of at least 10 years. These models can be applied directly in the amplification of economic losses in earthquake scenarios or in probabilistic seismic risk assessment.

Performance based probabilistic seismic risk assessment for urban heritage. An example in Pla del Remei Area (Valencia)

The assessment of the seismic behaviour of historic residential buildings and the estimation of their possible losses in the event of an earthquake, is a must for defining strategic mitigation plans to prevent irreplaceable heritage losses. In this study an integrated performance based probabilistic risk assessment methodology is developed. An archival study and a field survey allow to identify architectural and construction characteristics of heritage residential buildings in urban areas and determine realistic structural models. These are analysed by using a limit state approach, coded in the FaMIVE method, considering different construction hypotheses, to produce capacity curves which support the identification of a discrete number of typologies representative of the entire building stock in the area. Their fragility functions are then derived using the modified N2 method. Because of the difficulty in quantifying the expected probable losses in purely economic terms, given the heritage value of these assets, losses are computed in terms of damaged floor surface area and mean damage ratio. These have been obtained through the earthquake loss estimation platform SELENA, considering different possible seismic scenarios. The procedure is applied to masonry residential buildings in Pla del Remei area of Valencia, Spain, built between the end of the 19th Century and the end of the Spanish War (1939). This neighbourhood embodies the cultural values, construction techniques and historic legacy of a new and brief era of modernity, inspired by the new urban theories and architectural styles of Eclecticism and Modernism. Despite Valencia being located in an area of low to moderate seismicity, the results show that the maximum percentage of built damaged area ranges from 5.8 to 11.6% for 475 years return period, increasing to 33.59–51.59% for 975 years return period. The high level of resolution of the study allows mapping and identifying the structures at higher risk and is therefore a valuable tool to support sensitive and targeted retrofitting policies.

Probabilistic seismic hazard and risk assessment of Mizoram, North East India

This paper presents seismic hazard and risk assessment for the state of Mizoram based on a classical probabilistic seismic hazard analysis and event-based probabilistic seismic risk analysis. For the seismic hazard estimation, analysis has been performed considering the areal source model, fault zone polygon, and smoothed gridded seismicity model. The earthquake activity rates for these source zones and smoothed gridded seismicity sources are estimated from the homogenized and declustered earthquake catalogue. The logic tree framework is applied in the seismic source models and Ground Motion Prediction equations (GMPEs) to account for the epistemic uncertainties. Five Next-generation attenuation (NGA) GMPEs for the active shallow region and three GMPEs for the Indo-Burma subduction zone have been used to evaluate the hazard at the reference rock condition (Vs30 ​= ​760 ​m/s). Peak Ground Acceleration (PGA) and Spectral Acceleration (SA) at 0.2 s and 1s are estimated for each eight districts headquarters of Mizoram for a 2% and 10% probability of exceedance in 50 years. The hazard curves and Uniform Hazard Spectra (UHS) are also presented. For seismic risk analysis, building exposure data are based on digitized building footprint and 2011 Housing Census data of India. All the buildings are classified into three classes, and seismic vulnerability functions are assigned to each building class. The area per building class is assigned from the digitized footprint. Building replacement costs per square meter have been chosen based on expert input and values identified from past study. Lastly, the study conducted a seismic risk analysis using the Open Quake-engine's probabilistic event-based methodology to estimate risk metrics at the district level, such as average annual losses and probability curves for loss exceedance. The study's findings provide valuable insights into the most high-risk areas, the building construction types that are most vulnerable to seismic activity, and the anticipated economic losses in the state of Mizoram. These results can serve as a guide for local government authorities in developing future city plans and implementing earthquake risk mitigation strategies.

Multi-unit seismic probabilistic risk assessment: A Bayesian network perspective

The Fukushima Dai-ichi highlighted multi-unit accidents in nuclear power plant (NPP) probabilistic risk assessment (PRA). This paper focuses on multi-unit seismic PRA because seismic events are contributors to NPP site risk. This paper integrates works on modeling ground motion spatial variability at a NPP site and dependent seismic failures into a coherent and rigorous framework using Bayesian networks, and explores the relative importance of different types of correlation on NPP site-based risk metrics. A study of a hypothetical dual unit NPP site considered 15 cases with varying degrees of correlation in spatial ground motion (GM) and seismic failures. Based on the results, the current assumption of perfect GM correlation across a NPP site underestimates risk metrics that consider either unit experiencing core damage (CD) (site CD), which is not conservative. The risk metric that considers both units experiencing CD (concurrent CD) shows differences between the partial and perfect GM correlation assumptions when multiple component failures contribute to the CD in each unit. Within a GM correlation assumption, the site CD increases as the fragility correlation increases, a counterintuitive trend. The risk assessment case outlined in this paper provides more realistic results than the cases reflecting the current state of practice.

The new seismic hazard model ESHM20 of Europe: Investigating the implications to the seismic design and risk assessment of major industrial facilities across Europe

AbstractThe seismic performance and safety of major European industrial facilities have a global interest for the whole of Europe and its citizens. However, the seismic design of these facilities is based on national, sometimes outdated seismic hazard analyses. The results of the commonly developed, fully harmonized newly released European Seismic Hazard Model ESHM20 provide a pertinent reference for seismic hazard at European scale and have been officially adopted as an “acceptable representation of the seismic hazard in Europe” in the ongoing revision of Eurocode 8. This study presents a large-scale investigation of the impact of the potential adoption of ESHM20 on the design of new industrial facilities as well as on the potential seismic risk of existing facilities at European level with respect to the current seismic codes. The horizontal elastic response spectra using ESHM20 in combination with the revised Eurocode 8 for selected industrial sites are compared with the respective response spectra of the national regulations for return periods of 475, 2500 and 5000 years. In addition, a single containment LNG tank is analysed for an industrial site in Germany using the design approach for liquid filled tanks according to the revised Eurocode 8. Furthermore, a deterministic and probabilistic seismic risk assessment of a vessel installed in a five-storey frame is performed for industrial sites in Greece and Germany. The examples show that a consistent procedure all over Europe would be desirable and a benefit for engineers in terms of comparability and achievement of the same safety targets. Based on the conducted illustrative studies, the consequences of a potential adoption of the revised Eurocode 8 and ESHM20 hazard maps are discussed and summarized with respect to the standard harmonisation process in Europe.

Probabilistic seismic risk assessment framework: case study Adapazari, Turkey

While earthquakes can have a devastating impact on the economic growth and social welfare of earthquake prone regions, probabilistic seismic risk assessment can be employed to assess and mitigate such risks from future destructive events. In a previous study (Sianko et al. in Bull Earthq Eng 18:2523–2555, 2020), a probabilistic seismic hazard analysis (PSHA) tool based on the Monte-Carlo approach, was developed to predict the seismic hazard for high seismicity areas. In this study, a seismic risk assessment framework is developed incorporating the previously developed PSHA tool, with vulnerability functions based on various damage criteria, exposures and casualty models. Epistemic uncertainty is addressed using logic trees and distribution functions. The developed seismic risk assessment framework can estimate human and economic losses for particular return periods using an event-based stochastic procedure. The framework is applied to a case study area, the city of Adapazari in Turkey. Seismic risk assessment is carried out for different return periods to identify the most vulnerable areas of the city. The verification of the developed seismic risk framework is performed by comparing the predicted seismic losses to those observed during the 1999 Kocaeli earthquake that severely affected the city of Adapazari. The results of the study indicate that while overall predictions for extensive and complete damage states demonstrate strong correlation with the observed data, accurate risk predictions at the district level are not achievable without microzonation studies.

A cost-benefit analysis for the appraisal of social and market prices in the probabilistic seismic risk assessment of building portfolios: A methodology for the evaluation of disaster risk reduction programs

A cost-benefit analysis can be a milestone for the probabilistic seismic risk assessment of building portfolios. This approach appraises social, economic, and technical aspects as evaluation criteria, becoming a reliable method for more accurate feasibility evaluation of Disaster Risk Reduction (DRR) programs. This paper proposes a simplified methodological approach to estimate the feasibility of intervention campaigns directed to seismic retrofitting for building portfolios. Its feature is the number of variables it encompasses such as: multiple intervention levels, resource distribution, maximum repair time, direct and indirect losses, simplified seismic resilience, number of casualties, amount of replacement buildings, and expected service life. Then, all these factors are analyzed using a conventional probabilistic seismic risk assessment, followed by the estimation of net cash flows in terms of social and market prices. The final profitability and feasibility are determined based on investment indicators (Net Present Value, Internal Rate of Return, and Cost-Benefit ratio). In addition, plots of maximum repair time and simplified seismic resilience (as a function of the resource distribution) are proposed as novel decision-making tools. To illustrate the methodology, a case study of six building portfolios grouped into two categories is presented. The portfolios are conformed by a Peruvian school typology designated as 780-PRE, typically two-story high with reinforced concrete moment-resisting frames plus infill-walls and confined masonry walls. The demonstrative case included eleven target scenarios to assess the as-built and several intervention conditions, based on incremental seismic retrofitting measures. Results confirm that social prices influence the decision-making process, even making feasible projects that were initially unfeasible (when solely appraised under market prices). Finally, the authors propose further applications of this methodology as a tool to support the development of reliable DRR-programs.

A fragility curve based on the transformation of a random variable

ABSTRACT There are two failure criteria in seismic probabilistic risk assessment of a nuclear power plant to define component failure caused by an earthquake. The first is in terms of peak ground acceleration and peak ground acceleration capacity. The second is in terms of seismic response and component capacity. These criteria are closely related, but they are not equivalent. One can derive a different fragility curve from the second criterion. First, this study analytically shows the relation of these failure criteria, pointing out that a fragility curve may not represent the uncertainty of a failure probability derived from the second criterion. In addition, we propose a probability density function of a failure probability based on the second criterion using the transformation of a random variable method applied to probability density functions of seismic response and component capacity. Then, we derive a new fragility curve based on the derived probability density function. Also, we show that the derived probability density function links to a likelihood function based on a mean fragility curve used in the literature. Finally, we discuss the non-identifiability of uncertainties of response and capacity, and we propose a Bayesian model utilizing a local response to overcome the non-identifiability.

Performance-Based Characterization and Quantification of Uncertainty in Damage Plasticity Model for Seismic Fragility Assessment of Concrete Structures

Seismic probabilistic risk assessment requires explicit consideration and quantification of all sources of uncertainty. Although uncertainties in earthquakes and basic material properties, such as nominal concrete compressive strength, strain at maximum stress, and modulus of elasticity of concrete, have been considered in some studies, uncertainties in parameters used to model the nonlinear behavior of concrete are often not considered. Recent recommendations in design standards have incorporated performance-based limit states in the design and risk assessment of nuclear power plants. These recommendations have implicitly mandated that the uncertainty in the nonlinear behavior of concrete needs to be characterized and quantified in accordance with different performance limit states. This study focused on nonlinear model parameters in the concrete damage plasticity model (CDPM) and their characterization in terms of material strength parameters. Furthermore, a performance-based characterization and quantification of uncertainties in nonlinear model parameters was also conducted. Data from existing experimental studies were used to study the uncertainties in CDPM and were used as a basis for the proposed quantification.

A framework to quantify the effectiveness of earthquake early warning in mitigating seismic risk

Earthquake early warning systems (EEWSs) aim to rapidly detect earthquakes and provide timely alerts, so that users can take protective actions prior to the onset of strong ground shaking. The promise and limitations of EEWSs have both been widely debated. On one hand, an operational EEWS could mitigate earthquake damage by triggering potentially cost- and life-saving actions. These range from automated system responses such as slowing down trains to the actions of individuals that receive the alerts and take protective measures. On the other hand, the effectiveness of an EEWS is conditional on the ability to issue warnings that are sufficiently accurate and timely to facilitate an appropriate action. The refinement of earthquake early warning (EEW) algorithms and the installation of denser and faster seismic networks have improved performance; however, the benefit in risk reduction that an EEWS could achieve remains unquantified. In this study, we leverage upon regional event-based probabilistic seismic risk assessment to devise a quantitative and fully customizable framework for evaluating the effectiveness of EEW in mitigating seismic risk. We demonstrate this framework using Switzerland as a testbed, for which we compute and contrast human loss exceedance curves with and without EEW.

Estimating annualized earthquake loss for residential buildings in Tehran, Iran

A probabilistic seismic risk assessment is conducted in this study to quantify Annualized Earthquake Loss (AEL) of Tehran, the capital of Iran. To do so, a comprehensive review of three main components of risk assessment including the seismic hazard analysis, exposure model and vulnerability functions is performed. The classical seismic hazard analysis is carried out based on the most recent earthquake catalog by considering the available uncertainties. A high-quality building exposure model based on recent census data with geographic resolution of census blocks is also compiled. According to available information, buildings are classified into 19 groups by considering their construction material, quality and height. The results show that sum of AEL in Tehran is about 10,488 million USD, which is equivalent to 0.16% of exposed economic value. The spatial distribution of AEL indicated that value of AEL in the eastern districts is higher; however, the relative seismic risk in term of AELR in the southern districts of the city is much higher. In addition, a disaggregation analysis per building typology is performed to identify the contribution of different building taxonomies in AEL. The results show that the masonry and low-quality steel and concrete structures with poor designing specifications have the highest contribution in AEL. The finding from this study can be used by local authorities, government and insurance sector in order to develop effective risk mitigation plans and a robust insurance scheme for Tehran, Iran.

Application of quasi-Monte Carlo and importance sampling to Monte Carlo-based fault tree quantification for seismic probabilistic risk assessment of nuclear power plants

Application of quasi-Monte Carlo and importance sampling to Monte Carlo-based fault tree quantification for seismic probabilistic risk assessment of nuclear power plants