Performance-based Earthquake Engineering Framework Research Articles

Long‐range Ising model for regional‐scale seismic risk analysis

AbstractThis study introduces the long‐range Ising model from statistical mechanics to the performance‐based earthquake engineering (PBEE) framework for regional seismic damage analysis. The application of the PBEE framework at a regional scale involves estimating the damage states () of numerous structures, typically performed using fragility function‐based stochastic simulations. However, these simulations often assume conditional independence or employ simplistic dependency models among the of structures, leading to significant misrepresentation of regional risk. The Ising model addresses this issue by converting the available information on binary (safe or failure) into a joint probability mass function, leveraging the principle of maximum entropy. The Ising model offers two main benefits: (1) it requires only the first‐ and second‐order cross‐moments, enabling seamless integration with the existing PBEE framework, and (2) it provides meaningful physical interpretations of the model parameters, facilitating the uncovering of insights not apparent from data. To demonstrate the proposed method, we applied the Ising model to 156 buildings in Antakya, Turkey, using post‐hazard damage evaluation data, and to 182 buildings in Pacific Heights, San Francisco, using simulated data from the Regional Resilience Determination tool. In both instances, the Ising model accurately reproduces the provided information and generates meaningful insights into regional damage. The study also investigates the change in Ising model parameters under varying earthquake magnitudes, along with the mean‐field approximation, further facilitating the applicability of the proposed approach.

Optimal intensity measure for seismic performance assessment of shield tunnels in liquefiable and non-liquefiable soils

Relating the ground motion intensity measure (IM) and the structural engineering demand parameter is a crucial step in the performance-based earthquake engineering framework. This study investigates the selection of IM for development of probabilistic seismic demand model of urban shield tunnels subjected to earthquake ground motions in liquefiable and non-liquefiable soils. Nonlinear dynamic effective stress analyses are conducted to develop a database of the intensity measures and structural seismic responses exposed to ground shaking and soil liquefaction. Two advanced soil constitutive models (i.e., Pressure DependMultiYield03 and PressureIndependMultiYield for liquefiable and non-liquefiable soils, respectively) are employed to capture the nonlinear behavior. A suite of 23ground motion intensity measures is selected and assessed based on the evaluation criteria of correlation, efficiency, practicality and proficiency. Eventually, the multi-level fuzzy comprehensive evaluation method is employed to comprehensively consider the four evaluation criteria and establish the optimal ground motion IM suitable for probabilistic seismic demand analysis of shield tunnel structures. The obtained results show that the sustained maximum acceleration is the optimal IM for evaluating the structural seismic response, followed by the peak ground acceleration in both liquefiable and non-liquefiable soils. Peak pseudo velocity spectrum, displacement square integral and Housner spectral intensity are found to be not suitable for the probabilistic seismic demand analysis of shield tunnel structures.

Collapse mechanisms and fragility curves based on Lumped Damage Mechanics for RC frames subjected to earthquakes

Reinforced concrete structures under earthquakes present nonlinear behavior with cracking evolution and plastic strains that can lead to failure due to large displacements with development of collapse mechanisms. This manuscript presents a methodology to apply Lumped Damage Mechanics (LDM) in a Performance-Based Earthquake Engineering (PBEE) framework, to evaluate the seismic vulnerability of reinforced concrete frames. The lumped damage model represents the evolution of damage and plasticity lumped into local inelastic hinges at the nodes of the elements. This paper proposes a novel procedure to identify and characterize global collapse mechanisms from the internal variables of damage using system reliability theory. In this way, the internal variables of damage are used as engineering demand parameters (EDPs) to calculate the fragility curves of the structure, which are also compared with usual interstory drift fragilities. To evaluate the seismic vulnerability, incremental dynamic analyses are conducted. The main results demonstrate efficiency of LDM in a PBEE framework, and that the internal variables of damage are objective indicators of collapse for RC frames. Results show how to identify the global failure mechanisms that are more likely to appear for each frame. For regular frames, high correlation is observed between the local hinges forming each global collapse mechanism. This allows collapse mechanisms to be readily characterized by the strongest link in a parallel system.

Selection of optimal intensity measures for seismic performance evaluation of underground utility tunnel and internal pipeline system

Seismic intensity measures (IMs), which are closely related to both earthquake hazards and structural responses, play a critical role in the performance-based earthquake engineering (PBEE) framework. This paper aims to investigate and define the most representative IMs for probabilistic seismic demand model (PSDM) for the longitudinal utility tunnel and internal pipeline system. Similar to the requirements by the Chinese Code for seismic design of urban rail transit structures, the utility tunnel in this study is assumed being buried in four typical engineering site classes for the analyses. Soil-tunnel-pipeline interactions are simulated using a double-beam system resting on a nonlinear foundation. Soil-tunnel interaction, tunnel-pipeline interaction and joint connections are modeled as nonlinear springs with different mechanical properties. A series of 17 pairs of outcrop ground-motion records and 27 commonly used IMs are selected in the analyses. Engineering demand parameter (EDP) is defined based on the maximum joint opening and the maximum strain of the utility tunnel and internal pipeline, respectively. The selected IMs for predicting the seismic responses of tunnel-pipeline systems are tested using different criteria, i.e., correction, efficiency, practicality, and proficiency. The final decision-making procedure employs a fuzzy multi-criteria decision method. The numerical results indicate that: (1) The velocity-related IMs are the most representative IMs based on the four criteria for structures buried in four sites of different conditions; (2) The optimal seismic IMs vary with different criteria, site classes and structure types. According to the fuzzy multi-criteria decision approach, optimal IMs for the tunnel-pipeline system are PGV, PGV, EPV and HI for site classes I – IV, respectively. The proposed optimal IMs can be utilized to construct seismic fragility curves of utility tunnel, internal pipeline and tunnel-pipeline systems in four different site classes.

Seismic fragility analysis of structures via an Adaptive Gaussian Mixture Model and its application to resilience assessment

Seismic fragility analysis and seismic resilience assessment are pivotal tasks within the performance-based earthquake engineering framework. The former aims to quantitatively assess the probability of engineering structures sustaining various degrees of damage when subjected to earthquakes of varying intensity levels. In contrast to many traditional seismic fragility methods, this paper introduces a precise and versatile approach grounded in reliability analysis, with the goal of eliminating the restrictive lognormal assumption. Initially, the proposed method involves conducting seismic reliability analysis of structures using the Fractional Exponential Moments-based Maximum Entropy Method (FEM-MEM). This approach efficiently yields failure probabilities. Subsequently, an Adaptive Gaussian Mixture Model (AGMM) is presented for fitting a set of failure probability points, producing comprehensive and continuous seismic fragility curves. Notably, AGMM offers remarkable flexibility in modeling fragility curves, ensuring precise estimations for subsequent resilience assessments. Building upon the results of the fragility analysis, the paper proceeds to assess the seismic resilience of structures. The proposed method’s feasibility and effectiveness are validated through two illustrative numerical examples. The results demonstrate that, in comparison to the conventional lognormal assumption, the proposed method offers superior accuracy and broader applicability for conducting seismic fragility analyses of structures.

Earthquake-induced loss assessment of hybrid self-centering piston-based braced frame with friction springs and SMA bars

A novel Self‐Centering Piston-Based Bracing (SC-PBB), integrating Friction Springs (FSs) and Shape Memory Alloy (SMA) bars, offers a promising solution for curtailing seismic damage in braced frame structures. Nevertheless, this hybrid SC-PBB may incur higher construction costs compared to conventional bracing archetypes. Accordingly, it is imperative to investigate whether the initial cost increase can be offset over the structure's lifespan. This study quantifies earthquake-induced financial losses in braced frames equipped with SC-PBBs (SC-PBBFs) compared to those equipped with Buckling-Restrained Bracings (BRBs). A building-specific Performance-Based Earthquake Engineering (PBEE) framework is employed to evaluate potential economic losses under far-field ground motions. The analysis quantifies total, collapse, irreparable, and repair losses by incorporating seismic hazards, structural demands, and damage consequences. Results reveal higher total and collapse losses for BRBFs, although their lower repair costs for non-structural components mitigate repair loss. Additionally, the low-rise SC-PBBF archetype could recoup initial construction expenses over its expected lifespan, unlike its BRBF counterpart.

Predictive models for assessment of buried pipeline response under seismic landslides in Iran

In seismic regions both in Iran and around the world, subterranean gas pipelines inevitably extend through high-risk areas prone to seismic landslides. The seismic landslide-pipe failure mechanism constitutes a continuum geomechanical challenge influenced by factors such as sliding mass configuration, pipe positioning relative to potential slope failure surfaces, and seismic input characteristics. In this study, response of steel pipeline buried in sand under seismic landslide action is analyzed by finite difference models using an advanced soil constitutive model. The numerical model is first validated based on the shaking table test results and then several dynamic analyses are performed using the selected records of the Iranian ground motions database. The outcomes of the dynamic analysis demonstrate that Arias Intensity (Ia) can be identified as an optimal intensity measure (IM) for predicting the seismic response of a slope-pipe system in terms of maximum pipe deflection, axial strain, and shear stress. Predictive models are then developed based on the optimal IM for estimating the pipe deflection, axial strain, and shear stress subjected to a seismic landslide. These proposed predictive models offer valuable insights for assessing the response of buried pipelines to seismic landslides in Iran within the framework of performance-based earthquake engineering.

Seismic risk assessment of highway bridges in western Canada under crustal, subcrustal, and subduction earthquakes

This study conducts seismic risk assessment of highway bridges in western Canada. The performance-based earthquake engineering (PBEE) framework is enhanced to assess the expected annual repair cost ratio (ARCR) and annual restoration time (ART) of a benchmark bridge class under the region’s three types of earthquakes - shallow crustal earthquakes (CEs), deep subcrustal earthquakes (SCEs), and megathrust Cascadia subduction earthquakes (CSEs). First, event-specific seismic hazard models are considered, whereas event-consistent ground motions are selected for non-linear time history analyses. Compared with those from CEs and SCEs, CSE ground motions feature a much longer duration. This long-duration effect is captured by validating the numerical model of the bridge column against (1) a cyclic pushover test under standard versus long-duration loading protocols and (2) a shaking table test excited by six consecutive ground motions. Besides, the Park and Ang damage index is utilized as the column’s engineering demand parameter (EDP) and updated as a demand-capacity ratio model when reaching four different damage states. A comprehensive list of ground motion intensity measures (IMs) is considered where the spectra acceleration at one second, Sa(1.0), is chosen as the most suitable IM based on its performance in proficiency, efficiency, practicality, and EDP-IM correlation across all three earthquake events. Subsequently, component- and system-level fragility models are derived under each earthquake type using the cloud analysis that convolves the seismic demands with capacity models for multiple bridge components. To further quantify and propagate the epistemic uncertainty associated with the development of probabilistic seismic demand models (PSDMs), the bootstrap resampling technique is utilized to generate numerous seismic demand datasets and develop a stochastic set of seismic fragility curves. Finally, the bootstrapped, event-dependent fragility models are combined with the respective hazard models and probabilistic loss functions to assess the expected ARCR and ART for the benchmark bridge class. This study underscores the significantly higher seismic risk of highway bridges when facing CSEs, followed by CEs and SCEs.

Seismic loss assessment of code-compliant moment-resisting RC buildings located on different soil conditions of Mexico City

This research aims to estimate the expected economic losses associated with the repair cost of a set of code-compliant moment-resisting reinforced concrete buildings located on different soil conditions in Mexico City. The loss assessment methodology is based on the second generation of the Performance-Based Earthquake Engineering (PBEE) framework, which quantifies the seismic performance of buildings in terms of metrics such as economic losses, downtime, and casualties, which are more meaningful to owners and stakeholders for the decision-making process. The methodology uses a probabilistic approach that takes into account uncertainties in seismic intensity, structural response, component damage, and consequence prediction. The seismic response of structures was calculated in terms of inter-story drifts and floor accelerations to assess the damage to their structural and non-structural components. In addition, taking into account the seismic hazard of the site, the expected annual losses (EAL) are calculated to provide insight into the seismic performance evaluation of structures with different characteristics in terms of the financial impact in seismic-prone regions like Mexico City.

Optimal intensity measures in probabilistic seismic demand model of subway station

Ground motion intensity measure (IM), which is a key link between the seismic hazard analysis and structural seismic response analysis, plays an important role in the performance-based earthquake engineering framework. The objective of this paper is to evaluate the most commonly used IMs with respect to their capability to predict the seismic response of underground subway station structures. Because the properties of the surrounding soil has significant influence on the seismic response of subway station structure, four typical classes of engineering sites ranging from Class I to IV according to Chinese code for seismic design of urban rail transit structures are selected in this study. Dynamic time history analyses considering nonlinear soil-structure interaction (SSI) are performed on four two-dimensional finite element models consisting of two-storey three-span subway stations embedded in four different engineering sites in this paper. Both the near-fault without velocity pulse and far-fault ground motions are used as the seismic inputs for the nonlinear SSI models in this study. Ground motion excitation is converted into equivalent seismic load at the artificial boundary for the discretized finite element model to realize the seismic load input. The applicability of 20 ground motion IMs commonly used in earthquake engineering research are investigated in this study. Statistical regression analysis is carried out for those IMs and engineering demand parameters (EDPs) of the subway station structure measured by maximum inter-storey displacement ratio obtained from nonlinear time history analyses. Based on the criteria of efficiency, practicality, proficiency and sufficiency, the optimal IMs in probabilistic seismic demand model that can best estimate the seismic response of the subway station structure are identified among those commonly used IMs. It is found that for sites of Class I and Class II, the Arias intensity followed by the velocity spectrum intensity are the optimal candidates, and for sites of Class III and Class IV, the Arias intensity is the optimal IM.

Modelling of non-structural components of an industrial multi-storey frame for seismic risk assessment

Seismic risk assessment of industrial facilities is complex due to the presence of different types of equipment. It represents a research issue that requires further investigation. To this end, some analytical approaches have been developed in the framework of performance-based earthquake engineering. Nonetheless, their accuracy in the case of complex critical facilities, such as nuclear and non-nuclear industrial plants, is still under investigation. Thus, the proposed study intends to research in depth, in a risk assessment framework, some critical aspects related to: (1) modelling of industrial facilities and their secondary equipment with different degrees of accuracy, also taking into account their dynamic interaction; (2) selection of seismic records for fragility analysis, due to the narrow distribution of frequency values for non-structural components; (3) effectiveness of performance-based earthquake engineering applied to this particular class of coupled structure-equipment for risk assessment. In this context, the proper selection of seismic records becomes relevant, and SCoRes, an innovative algorithm for accelerograms selection is worthy of investigation. On these premises, two different configurations of a primary industrial structure, i.e. a moment resisting frame and a braced frame, equipped with non-structural components and subjected to shake table test campaigns are selected as case studies. For the two configurations, a vulnerability assessment of two vertical tanks installed on the first floor was carried out. Along these lines, to establish the effectiveness of the proposed method for both the moment resisting frame and braced frame configurations, the mean annual frequency of exceedance of the bottom-wall strain of the above-mentioned tanks, both at the design basis and safe shutdown earthquake has been evaluated.

Probabilistic assessment of the rules used to combine peak floor responses of special concentrically braced frames under orthogonal seismic effects

AbstractEstimating seismic demands and the associated damage to nonstructural components (NSCs) is a critical step in the performance‐based earthquake engineering (PBEE) framework. To facilitate this type of assessment, NSCs are classified as being acceleration, velocity, or displacement sensitive. When two‐dimensional structural models and response history analyses are used in the PBEE framework, heuristics are used to combine the orthogonal responses. Although there has been significant research to develop and evaluate combination rules for structural component responses, comparatively much less attention has been placed on NSC demands. FEMA P‐58 does provide a combination rule specifically for NSC seismic demands; however, the basis and accuracy of these provisions have never been examined. In this paper, the effectiveness of three popular combination rules used to estimate peak floor acceleration (PFA) and peak floor velocity (PFV) is investigated. Incremental dynamics analyses under unidirectional and bidirectional record‐sets are performed on six special concentrically braced frame buildings with different heights and torsional irregularity. The associated floor responses are used to examine the efficacy of the combination rules. Subsequently, a probabilistic approach is proposed to enhance the accuracy of combination rules. The performance of the enhanced combination rules is compared to that of a surrogate model that estimates PFA and PFV under orthogonal seismic effects. The results show that the performance of existing combination rules is slightly affected by building height and plan irregularity. Also, the combination rule suggested by FEMA P58 is found to overestimate the PFA and PFV demands by 10–15% compared to the demands derived from bidirectional response history analysis.

Comparative assessment of alternative methods for evaluating the optimality of ground motion intensity measures using woodframe buildings

Selection of an optimal ground motion intensity measure (IM) is one of the preliminary yet integral steps in minimizing uncertainty propagation through the probabilistic performance-based earthquake engineering framework. The optimal IM is evaluated and selected based on two widely known evaluation metrics: efficiency and sufficiency. In this study, the univariate regression- and entropy-based methods that are currently available to compute efficiency and sufficiency are presented. More importantly, the existing methods are expanded to account for multivariate relationships between various engineering demand parameters (EDPs), the IM, and the causal parameters. Finally, a comparative assessment of alternative methods is performed based on 10 different IMs and 10 woodframe archetype buildings. The univariate and multivariate methods produce comparable results for the efficiency-based assessment with SaT1 and ASI performing comparably well. Also, for all IMs, both the dispersion and joint entropy are found to be lower in the single-family dwellings (SFDs) compared to the multi-family dwellings (MFDs). This observation can be explained by the higher ductility demands in the latter of the two building types. Similar results are also obtained between the univariate and multivariate entropy-based sufficiency evaluations. In both cases (univariate and multivariate), SaT1 and PGA are the most sufficient IMs for SFDs and MFDs with Saavg also performing well for the MFDs.

RPBEE: Performance-based earthquake engineering on a regional scale

Over the last two decades, the performance-based earthquake engineering (PBEE) framework developed by the Pacific Earthquake Engineering Research (PEER) Center has gained the attention of researchers and practitioners worldwide. This framework was originally focused on quantifying the seismic risk of individual structures. However, with the advent of the “seismic resilience” concept, broader definitions of stakeholders and performance metrics on a regional scale are desirable. In this context, we present a formalized extension of the PEER PBEE framework for its use in groups of structures spatially distributed over a region, herein referred to as RPBEE framework. As an example, we use the RPBEE framework for computing the total number of damaged structures, the expected total economic loss, and the probability distribution of total economic losses within a region. We highlight differences with the original PEER framework and challenges arising from the implementation of the new RPBEE framework for future research and adoption, along with potential ways to overcome them.

Assessing seismic performance of code-compliant steel special moment frames using ASCE 41-17

ASCE 41 standard, increasingly used by practitioners, is a desirable tool to evaluate the seismic performance of different types of structures according to the Performance-Based Earthquake Engineering framework. The latest edition of this standard (ASCE 41-17) has undergone significant changes with respect to its previous versions, which could substantially affect the results of structural performance evaluation. Within this context, the present study performs a comprehensive quantitative investigation of the seismic performance of steel structures based on the component-level Tier 3 systematic evaluation procedure of ASCE 41-17, using both nonlinear static (conventional and enhanced pushover analyses) and dynamic analyses. The evaluation is conducted on six ASCE 7 code-compliant steel special moment frames considering different heights (i.e., 6, 12, and 18 stories) and two versions of the seismic design code (i.e., ASCE 7-10 and -16). The results of the nonlinear dynamic procedure demonstrate that both the ASCE 7-10 and -16 designed buildings satisfy the acceptance criteria of ASCE 41-17. It is also shown that the linear dynamic procedure recommended by ASCE 41-17 to supplement the results of the nonlinear static procedure for buildings with significant higher modes effect cannot provide an accurate estimation of the structural performance compared to enhanced pushover procedures. Additionally, the comparison of the structural performance evaluation between the ASCE 41-13 and -17 indicated that the previous edition of this code (ASCE 41-13) is overly conservative for columns compared to ASCE 41-17. Finally, the applicability of using the modeling parameters recommended by ASCE 41 for simulating the elements’ behavior in case of the lack of sufficient available experimental data is demonstrated.

EESD special issue: AI and data‐driven methods in earthquake engineering – (Part 1)

EESD special issue: AI and data‐driven methods in earthquake engineering – (Part 1)

Optimal Intensity Measures for Probabilistic Seismic Stability Assessment of Large Open-Pit Mine Slopes under Different Mining Depths

The dynamic stability of slopes is the key to ensure the safety of a large open-pit mine during and after a strong earthquake. This study was mainly focused on the identification of optimal intensity measures (IMs) for the probabilistic seismic stability assessment of large open-pit mine slopes within the framework of performance-based earthquake engineering (PBEE). To this end, four open-pit slopes with different mining depths were constructed as the reference cases for the numerical investigation. The randomness of input ground motions and the uncertainty of material properties of the slopes were also considered. A total of 96 ground-motion records and 29 common IMs were selected for testing. By a series of nonlinear time-history analyses, the probabilistic seismic demand models (PSDMs) between the minimum factor of safety (FOS) of slopes and all considered IMs were developed. The optimal IMs with respect to FOS were identified based on the evaluation of five criteria: correlation, efficiency, practicality, proficiency, and sufficiency. The impacts on seismic fragility and FOS response hazard of the slopes were discussed when using different IMs. The results reveal that sustained maximum velocity (SMV) and velocity spectrum intensity (VSI) are recognized as the optimal IM for a mining depth of 50 m and 100 m, respectively. However, Housner intensity (HI) is observed to have the best predictability for both the mining depths of 200 m and 300 m. Moreover, for the three most commonly used IMs, peak ground velocity (PGV) is superior to peak ground acceleration (PGA) and spectral acceleration at first mode period (Sa (T1)) for different mining depths. Finally, based on the evaluations of seismic fragility and FOS response hazard, the uncertainty of seismic stability prediction of open-pit slopes can be greatly reduced when using a more appropriate or optimal IM.

Towards seismic performance quantification of viscous damped steel structure: Site-specific hazard analysis and response prediction

With an emphasis on predictable performance, the paramount importance of performance-based earthquake engineering (PBEE) in quantifying earthquake risks and facilitating the better-informed design of the built environment to achieve earthquake resilience has been widely acknowledged. And the uses of damping systems, i.e., structures incorporated with supplemental damping devices, have been recognized as an effective structural development to increase the resilience of structures to earthquakes. This paper presents a uniform hazard spectrum (UHS) based site-specific ground motion selection procedure, to implement the PBEE framework to relate earthquake hazard to structural performance for structures with variable dynamic properties. This ground motion selection procedure accounts for the effect of variable structural dynamic properties on hazard characterization for structures with damping systems. A paradigm building site, on which the site-specific hazard from the probabilistic seismic hazard analysis (PSHA) is consistent with the risk-targeted hazard from the design maps of ASCE/SEI 7-10, is selected for the implementation of the procedure. Three suites of 40 ground motions representing various hazard intensities at the building site are selected for time history dynamic analysis of a prototype structure with nonlinear viscous damping system. Evaluated is the probability distribution of major engineering demand parameters (EDPs) including story drift, residual story drift, floor velocity, and floor acceleration. The results demonstrated that the major EDPs of a building structure with supplemental nonlinear viscous dampers at a paradigm site can be estimated using the lognormal probability distribution, and the proposed UHS-based site-specific ground motion selection procedure is critical to the performance assessment of structures with variable dynamic properties in the PBEE framework.

SVD enabled data augmentation for machine learning based surrogate modeling of non-linear structures

The computationally expensive estimation of engineering demand parameters (EDPs) via finite element (FE) models, while considering earthquake and material parameter uncertainty limits the use of the Performance Based Earthquake Engineering framework. Attempts have been made to substitute FE models with surrogate models, however, most of these models are a function of building parameters only. This necessitates re-training for earthquakes not previously seen by the surrogate. In this paper, the authors propose a machine learning based surrogate model framework, which considers both these uncertainties in order to predict for unseen earthquakes. Accordingly, earthquakes are characterized by their projections on an orthonormal basis, computed using SVD of a representative ground motion suite. This enables one to generate varieties of earthquakes by randomly sampling these weights and multiplying them with the basis, resulting in a large data set that is needed to train machine learning models. The weights along with the constitutive parameters serve as inputs to a machine learning model with EDPs as the desired output. Four competing machine learning models were tested and it was observed that a deep neural network (DNN) gave the most accurate prediction. The framework is validated by using it to successfully predict the peak response of one-story and three-story shear frame buildings represented using nonlinear spring–mass–damper systems, subjected to unseen far-field ground motions.

Seismic fragility analysis using stochastic polynomial chaos expansions

Within the performance-based earthquake engineering (PBEE) framework, the fragility model plays a pivotal role. Such a model represents the probability that the engineering demand parameter (EDP) exceeds a certain safety threshold given a set of selected intensity measures (IMs) that characterize the earthquake load. The-state-of-the art methods for fragility computation rely on full non-linear time–history analyses. Within this perimeter, there are two main approaches: the first relies on the selection and scaling of recorded ground motions; the second, based on random vibration theory, characterizes the seismic input with a parametric stochastic ground motion model (SGMM). The latter case has the great advantage that the problem of seismic risk analysis is framed as a forward uncertainty quantification problem. However, running classical full-scale Monte Carlo simulations is intractable because of the prohibitive computational cost of typical finite element models. Therefore, it is of great interest to define fragility models that link an EDP of interest with the SGMM parameters — which are regarded as IMs in this context. The computation of such fragility models is a challenge on its own and, despite a few recent studies, there is still an important research gap in this domain. This comes with no surprise as classical surrogate modeling techniques cannot be applied due to the stochastic nature of SGMM. This study tackles this computational challenge by using stochastic polynomial chaos expansions to represent the statistical dependence of EDP on IMs. More precisely, this surrogate model estimates the full conditional probability distribution of EDP conditioned on IMs. We compare the proposed approach with some state-of-the-art methods in two case studies. The numerical results show that the new method prevails over its competitors in estimating both the conditional distribution and the fragility functions.