Stochastic Ground Motion Research Articles

A full‐probabilistic cloud analysis for structural seismic fragility via decoupled M‐PDEM

AbstractPerformance‐based earthquake engineering (PBEE) is essential for ensuring engineering safety. Conducting seismic fragility analysis within this framework is imperative. Existing methods for seismic fragility analysis often rely heavily on double loop reanalysis and empirical data fitting, leading to challenges in obtaining high‐precision results with a limited number of representative structural analysis instances. In this context, a new methodology for seismic fragility based on a full‐probabilistic cloud analysis is proposed via the decoupled multi‐probability density evolution method (M‐PDEM). In the proposed method, the assumption of a log‐normal distribution is not required. According to the random event description of the principle of preservation of probability, the transient probability density functions (PDFs) of intensity measure (IM) and engineering demand parameter (EDP), as key response quantities of the seismic‐structural system, are governed by one‐dimensional Li‐Chen equations, where the physics‐driven forces are determined by representative analysis data of the stochastic dynamic system. By generating ground motions based on representative points of basic random variables and performing structural dynamic analysis, the decoupled M‐PDEM is employed to solve the one‐dimensional Li‐Chen equations. This yields the joint PDF of IM and EDP, as well as the conditional PDF of EDP given IM, resulting in seismic fragility analysis outcomes. The numerical implementation procedure is elaborated in detail, and validation is performed using a six‐story nonlinear reinforced concrete (RC) frame subjected to non‐stationary stochastic ground motions. Comparative analysis against Monte Carlo simulation (MCS) and traditional cloud analysis based on least squares regression (LSR) reveals that the proposed method achieves higher computational precision at comparable structural analysis costs. By directly solving the physics‐driven Li‐Chen equations, the method provides the full‐probabilistic joint information of IM and EDP required for cloud analysis, surpassing the accuracy achieved by traditional methods based on statistical moment fitting and empirical distribution assumptions.

Regionally adjusted stochastic earthquake ground motion models, associated variabilities and epistemic uncertainties

An optimisation-based calibration technique, using the area metric, is applied to determine the input parameters of a stochastic earthquake-waveform simulation method. The calibration algorithm updates a model prior, specifically an estimate of a region’s seismological (source, path and site) parameters, typically developed using waveform data, or existing models, from a wide range of sources. In the absence of calibration, this can result in overestimates of a target region’s ground motion variability, and in some cases, introduce biases. The proposed method simultaneously attains optimum estimates of median, range and distribution (uncertainty) of these seismological parameters, and resultant ground motions, for a specific target region, through calibration of physically constrained parametric models to local ground motion data. We apply the method to Italy, a region of moderate seismicity, using response spectra recorded in the European Strong Motion (ESM) dataset. As a prior, we utilise independent seismological models developed using strong motion data across a wider European context. The calibration obtains values of each seismological parameter considered (such as, but not limited to, quality factor, geometrical spreading and stress drop), to develop a suite of optimal parameters for locally adjusted stochastic ground motion simulation. We consider both the epistemic and aleatory variability associated with the calibration process. We were able to reduce the area metric (misfit) value by up to 88% for the simulations using updated parameters, compared to the initial prior. This framework for the calibration and updating of seismological models can help achieve robust and transparent regionally adjusted estimates of ground motion, and to consider epistemic uncertainty through correlated parameters.

Stochastic ground motion simulation of the 26 September 2019 Mw 5.8 Silivri (Istanbul) earthquake

Stochastic ground motion simulation of the 26 September 2019 Mw 5.8 Silivri (Istanbul) earthquake

Ground motion simulations of the 1887 Pinal de Amoles (MW = 5.53) and the 1989 Landa de Matamoros (MW = 4.94) earthquakes, Querétaro, Mexico

Ground motions characteristics of the 1887 Pinal de Amoles (MW = 5.53) and the 1989 Landa de Matamoros (MW = 4.94) Querétaro earthquakes were studied. For this purpose, the specific barrier model (SBM) was implemented in the context of the stochastic ground motion representation of earthquakes. The SBM was calibrated by modeling the peak ground acceleration (PGA) and the Fourier acceleration spectra (FAS) of the 11 May 2016 (MW = 4.80) Guadalajara earthquake. The calibration results showed that the SBM and selected source and path parameters were able to reproduce synthetic PGA and spectra in good agreement with observed waveforms; in particular, a stress drop of 160 bars fits the results better. Several rupture scenarios for the 1887 and 1989 events were performed by obtaining synthetic seismograms considering different values of stress drop (10, 30, 50, 100, 150, 200, 300, and 500 bars). For a typical stress-drop value of 100 bars, the PGA at distances of 10 and 200 km are in the following intervals: 2.57–295 cm/s2 and 1.72–186 cm/s2 for the Pinal de Amoles and Landa de Matamoros earthquakes, respectively. The results obtained in this study contribute toward a better understanding of strong ground motions in the region.

Reliability-based design optimization for seismic structures considering randomness associated with ground motions

When addressing the dynamic reliability analysis of structures, it becomes necessary to account for multiple limit state functions or their combinations. In scenarios where structures are subjected to random excitation, this can lead to intricate inter-dependencies among different limit states, and the computational workload can pose a substantial challenge in ensuring sufficient precision. Code-based design primarily ensures safety at the member level, while deterministic optimization fails to accommodate the inherent uncertainties associated with external excitation or the system as a whole. Therefore, in such cases, to address both the uncertainties in excitations and the presence of multiple limit states while mitigating computational challenges, equivalent extreme-value criteria are employed within the framework of the probability density evolution method to calculate the global reliability of the structure subjected to stochastic ground motions generated from the physically motivated stochastic ground motion model. Numerical optimization is subsequently conducted using genetic algorithms, aiming to minimize the cost of the superstructure while adhering to the design performance criteria related to the inter-story drift ratio and considering global reliability. Additionally, multi-objective optimization is carried out using NSGA-II, permitting the generation of multiple solutions, from which one can select the most suitable solution as needed. The numerical results illustrate the effectiveness of this technique in achieving an optimal balance between the cost of the structure and the consideration of global reliability, providing a comprehensive solution for dynamic reliability analysis and design optimization of structures under random excitations.

Reliability-based design optimization of tuned mass-damper-inerter for mitigating structural vibration

The tuned mass-damper-inerter (TMDI), comprising mass blocks, springs, dampers, and two-terminal inertial elements, has garnered significant attention as an advanced iteration of the tuned mass damper (TMD) in recent years. However, previous studies of TMDI's design are primarily conducted according to the theoretical formulas based on deterministic analysis assuming harmonic excitations or stochastic analysis assuming Gaussian white noise type excitations. This treatment falls short of capturing the non-stationary and non-Gaussian characteristics exhibited by engineering excitations and thus cannot ensure the safety of controlled structure. A few studies considering non-stationary excitations and based on reliability metrics, in conjunction with stochastic simulation methods, often confront excessive computational overhead. Aiming at such a challenge, the reliability-based design optimization (RBDO) of TMDI system, combining the probability density evolution method (PDEM) and genetic algorithm (GA), for mitigating structural vibration under non-stationary excitations is performed in this study. For the purposes of illustration, a single-degree-of-freedom system attached the TMDI and subjected to stochastic ground motions is studied. Considering the cases of different levels of inertance-to-mass ratios, the RBDO of the TMDI is carried out. The solutions by the theoretical formulas and by the variance-based design optimization are compared to verify the superiority of the proposed method. For assessing the seismic mitigation performance of the optimized TMDI system, probability density evolution analysis of structure-TMDI system with three levels of inertance-to-mass ratios is performed. Comparison between the RBDO of TMDI and that of TMD under consistent mass ratio is further addressed. Numerical results reveal the technical advantages of TMDI in a probabilistic sense, i.e., high vibration mitigation performance, considerable mass reduction, and less stroke demand.

Stochastic simulation of earthquake ground motions based on improved finite-fault model

In the seismic reliability analysis of engineering structures, it is often necessary to adopt stochastic ground motions as inputs. However, the current methods used to generate stochastic samples, such as the spectral representation method, the spectral transfer method, the dynamic source method, the physical source method, and the comprehensive method, etc., are not very convincing since they do not contain the complete information of seismic occurrence and propagation. In this study, an improved finite-fault model for stochastic simulation of ground motions is proposed. Compared to existing stochastic finite-fault model, the improved model considers the propagation law of phase spectrum, local site effect, and the impact of wave velocity on the arrival time of seismic waves. Besides, identification and statistics of model parameters are carried out based on ground motion records. Reasonable samples of stochastic ground motions are then obtained. In addition, parameter sensitivity analysis is conducted to determine critical random variables, which reduces the complexity of stochastic simulation. Simulation results are compared with recorded accelerograms from the 1999 Chi-Chi earthquake. It is shown that the improved stochastic finite-fault model is reliable, and the acceleration response spectra of simulated samples are consistent with those of station records collected at various site classes and the design spectra.

Simulation of non-stationary ground motions and its applications in high concrete faced rockfill dams via direct probability integral method

Many high concrete face rockfill dams (CFRDs) have been constructed in earthquake-prone areas in recent years, and it is essential to evaluate the seismic safety performance of these dams considering the randomness of seismic excitation. In this paper, the relationship between the stochastic ground motion generation method and the direct probability integral method (DPIM) is established by using the number theory point selection method as the bridge. The DPIM is introduced into the field of stochastic dynamic analysis and multi-index reliability evaluation of high CFRD for the first time. First, a non-stationary stochastic excitation model at five sites is established based on the latest standard for the seismic design of hydraulic structures. Then, taking a practical project as an example, stochastic dynamic response analysis and reliability assessment based on dam crest settlement deformation and dam slope cumulative slippage are conducted by using DIPM. Finally, the influence of these two indexes on reliability is explored by drawing the equal failure probability curve. The results show that the stochastic dynamic analysis and reliability assessment framework established in this paper can provide probabilistic seismic safety assessments for high CFRDs. Sliding damage of the dam slope is more likely than the deformation damage of the rockfill from the perspective of probability.

Regional spectral characteristics, quality factor and site responses in western-central Sichuan, China (II): Application to stochastic ground motion simulation

The stochastic finite-fault approach was used to model the 2022 Luding earthquake with a magnitude of Mw 6.6 in China at 16 selected near-field stations. To investigate the impact of the site effect on the synthetic results, two models were taken into account: One model was obtained from the generalized inversion technique, and the other model was obtained from the horizontal-to-vertical spectral ratio method. The high-frequency attenuation parameter was estimated to be 0.040 s and the value of 4.0 MPa for the stress parameter was adopted. Comparisons of the recorded and simulated Fourier amplitude spectrum, pseudospectral acceleration, peak ground acceleration, and peak ground velocity were performed to investigate the capability of the selected input parameters. In addition, the model bias, simulated peak ground acceleration and peak ground velocity were calculated by the local site amplification estimated by the two methods. The results show that the site effects estimated by the generalized inversion technique can well simulate the high-frequency response spectra and Fourier amplitude spectrum and can provide peak ground acceleration and peak ground velocity values consistent with the recorded values, while the local site amplification roughly calculated by the horizontal-to-vertical ratio method underestimates the main ground motion characteristics. Furthermore, strong-motion records with the same magnitude but different hypocentral distance ranges in the generalized inversion technique are used to estimate near-surface site effects, which shows that the distance range has a small impact on the estimation of local site amplification. Model parameters that performed well in this study provide confidence in understanding and quantifying seismic hazards in the Luding area from earthquake scenarios with different magnitudes.

Integrating real‐time hybrid simulation with multi‐fidelity Monte Carlo predictor for seismic fragility assessment

AbstractSeismic fragility evaluates the performance of a structure regarding to its capability to withstand earthquake loads by describing the exceedance probability for selected engineering demand parameters. High‐fidelity (HF) models are essential for simulation‐based techniques to obtain accurate fragility assessment in the presence of uncertainties. Dynamic structural behavior however is often difficult to replicate realistically through numerical simulation, especially when parts of the structure are difficult for accurate modeling due to their inherent complex nonlinearity. This study presents the integration of real‐time hybrid simulation (RTHS) with multi‐fidelity Monte Carlo (MFMC) predictor for seismic fragility analysis. RTHS combines physical testing of experimental substructures and numerical modeling of analytical substructures thus presenting a cyber‐physical alternative for HF seismic performance evaluation. The MFMC predictor provides an optimized allocation algorithm that makes full use of data from both HF and low‐fidelity (LF) models to achieve unbiased estimation for response quantities of interests. Experimentally expensive HF data from RTHS is thus integrated with computationally cheap simulation of LF numerical models through MFMC to facilitate seismic fragility analysis. A two‐story steel moment resisting frame (MRF) with self‐centering viscous dampers (SC‐VDs) is utilized to demonstrate the effectiveness and efficiency of the proposed method. Computational simulation is first performed to numerically verify the feasibility of the proposed method for the MRF subjected to non‐stationary stochastic ground motions. RTHS is then conducted experimentally as HF model and integrated with linear elastic LF models through MFMC for fragility analysis of the MRF equipped with SC‐VDs. Both computational and experimental analysis demonstrate that the proposed method provides a promising technique for seismic fragility assessment especially when accurate modeling is not available due to complex structural behavior.

Generating ground motions using the Fourier amplitude spectrum

AbstractIn this paper, a simplified method aimed at generating ground motions records using a Fourier amplitude spectrum model obtained by a response spectrum is presented. The use of white noise with specific conditions on the variance and inter‐frequency correlation allows to get a realistic variability of the Fourier amplitude spectrum. Moreover, a two‐corner frequency model is defined from empirical ground‐motion data and a filter is applied to capture the attenuation at high frequencies. The generated series of stochastic ground motions accurately match the mean value of the target response spectrum. The procedure was tested on an Italian site and results showed excellent matching in terms of mean and dispersion values with either the median obtained from ground motion prediction equations (GMPE) and conditional mean spectra (CMS). The advantage of the proposed methodology is that time‐histories can be generated with low computational effort, they do not need scaling or frequency content adjustments and are spectrum compatible with a given target spectrum.

Verification of a stochastic dynamic analysis method by shaking table tests of a slope retaining system

Various sources of uncertainty can greatly affect the seismic responses and seismic reliability of slope retaining systems. Many studies have observed and highlighted that ignoring the effect of uncertainties, especially the randomness of ground motions, would cause an inaccurate evaluation of seismic performance of slope retaining system. It is thus of great significance to employ the stochastic dynamic analysis method to quantify these uncertainties and corresponding effect. A recently developed stochastic dynamic analysis method, namely probability density evolution method (PDEM), have been proposed for the stochastic seismic responses analysis of geotechnical engineering. Although its efficiency and accuracy have already been proved by numerical cases, its feasibility and accuracy has not been verified from the experimental perspective, and its application in the stochastic seismic responses analysis using the field monitor data and experiment results in geotechnical engineering has not yet been studied. In the present study, a hard-strength rock slope model reinforced by pile-anchor structures is firstly constructed for the repeating shaking under a series of ground motions. A set of fully non-stationary stochastic ground motions are generated to quantify the randomness of input ground motions. Then, the stochastic seismic responses of the slope retaining system, including acceleration responses, amplification effect and earth pressure along pile-anchor structures, are analyzed and compared by the PDEM and various assumed probabilistic distribution models to illustrate the feasibility and accuracy of PDEM from the experimental perspective. The results demonstrate that the PDEM can obtain relatively more accurate stochastic seismic response results, and can also be used to analyze the experimental data from the probabilistic perspective.

Probabilistic analysis of seismic mitigation of base‐isolated structure with sliding hydromagnetic bearings based on finite element simulations

AbstractBase isolation is one of the most efficient methods for seismic mitigation of building and bridge structures in high‐intensity areas. However, the base‐isolated structure designed according to current codes based on the local seismic hazard and a few station records might not guarantee the performance of the base isolation system and ensure the safety of the structure. Carrying out a probabilistic analysis of seismic mitigation of base‐isolated structures, considering the randomness associated with earthquake ground motions, is thus necessary. To this end, the stochastic seismic response and reliability analysis of base‐isolated structures subjected to stochastic ground motions are conducted in this study, in conjunction with the probability density evolution method and the principle of equivalent extreme value event. The recently developed sliding hydromagnetic bearing is employed to constitute the base isolation layer of the base‐isolated structure. A refined finite element analysis is carried out to accurately reveal the dynamic characteristics of the base‐isolated structure. It is shown that the base‐isolated structure can be well simulated by the finite element model, which is verified through a comparative study with the results of shaking‐table tests. The base‐isolated structure gains a sound seismic mitigation compared to the base‐fixed structure in a probabilistic sense, and can ensure the safety of the structure by deploying a moderately designed base isolation system.

Stochastic Ground-Motion Simulation of the 2021 Mw 5.9 Woods Point Earthquake: Facilitating Local Probabilistic Seismic Hazard Analysis in Australia

ABSTRACT The 2021 Mw 5.9 Woods Point event is the largest onshore earthquake that has occurred in the recorded history of southeastern Australia since European settlement. To study its source and ground-motion characteristics and to extract information for local seismic hazard analysis, we employ a stochastic finite-fault simulation approach to simulate ground motions for this event based on the observations collected from 36 onshore stations. We determine the regional distance-dependent attenuation parameters using the horizontal Fourier acceleration amplitude spectrum in the frequency range of 0.1–20 Hz. We parameterize path parameters using different models to consider uncertainties and sensitivities. To investigate local site effects, we construct a VS30-based site amplification model. Source parameters are then determined by fitting the theoretical Brune’s ω2 model with a reference Fourier source spectrum at 1.0 km. The κ0 value for the reference rock site is estimated as κ0=0.01 s, and dynamic stress drop is found to be 41.0 MPa by minimizing the overall absolute residual of 5% damped pseudospectral acceleration. We validate the simulations by comparing simulated and observed ground motions in terms of various intensity measurements; analyses of residuals show that the simulations are in good agreement with observations (average residual is close to 0). To facilitate future probabilistic seismic hazard analysis, six selected ground-motion models are ranked using the deviance information criteria based on an independent data set consisting of field observations and simulated ground motions.

Seismic failure probability analysis of slopes via stochastic material point method

Earthquakes, an important factor in inducing landslides, usually have great randomness. Moreover, landslides are investigated as large deformations, and traditional grid-based methods encounter mesh distortions when dealing with such problems. In this context, the spectral expression method and random functions are introduced to generate stochastic ground motions, and the material point method is adopted to perform probabilistic slope analysis. First, the dry aluminum bar collapse test and the Chiu-fen-erh-shan landslide were simulated to verify the effectiveness of this improved procedure. Then, three typical stochastic ground motions were selected to investigate the effects of material parameters (internal friction angle and cohesion) and slope geometry (slope inclination and height) on the sliding distance of the slope. Finally, the uncertainty of ground motions was taken into account when conducting the probabilistic analysis of earthquake-induced landslides. The results demonstrate that the sliding distance of slopes varies with earthquake action, exhibiting certain randomness, particularly in strong earthquakes. In addition, slope geometry influences sliding distances more than material parameters, and slope geometry should be the prior consideration for slope prevention and mitigation.

A non-ergodic spectral acceleration ground motion model for California developed with random vibration theory

A new approach for creating a non-ergodic pseudo-spectral acceleration (PSA) ground-motion model (GMM) is presented, which accounts for the magnitude dependence of the non-ergodic effects. In this approach, the average PSA scaling is controlled by an ergodic PSA GMM, and the non-ergodic effects are captured with non-ergodic PSA factors, which are the adjustment that needs to be applied to an ergodic PSA GMM to incorporate the non-ergodic effects. The non-ergodic PSA factors are based on the effective amplitude spectrum (EAS) non-ergodic effects and are converted to PSA through Random Vibration Theory (RVT). The advantage of this approach is that it better captures the non-ergodic source, path, and site effects through small-magnitude earthquakes. Due to the linear properties of the Fourier Transform, the EAS non-ergodic effects of the small events can be applied directly to the large magnitude events. This is not the case for PSA, as response spectra are controlled by a range of frequencies, making PSA non-ergodic effects dependent on the spectral shape, which in turn is magnitude-dependent. Two PSA non-ergodic GMMs are derived using the ASK14 (Abrahamson et al. in Earthq Spectra 30:1025–1055, 2014) and CY14 (Chiou and Youngs in Earthq Spectra 30:1117–1153, 2014) GMMs as backbone models, respectively. The non-ergodic EAS effects are estimated with the LAK21 (Lavrentiadis et al. in Bull Earthq Eng ) GMM. The RVT calculations are performed with the V75 (Vanmarcke in ASCE Mech Eng Mech Division 98:425–446, 1972) peak factor model, the D_{a0.05-0.85} estimate of AS96 (Abrahamson and Silva in Apendix A: empirical ground motion models, description and validation of the stochastic ground motion model. Tech. rep.,. Brookhaven National Laboratory, New York) for the ground-motion duration, and BT15 (Boore and Thompson in Bull Seismol Soc Am 105:1029–1041, 2015) oscillator-duration model. The California subset of the NGAWest2 database (Ancheta et al. in Earthq Spectra 30:989–1005, 2014) is used to fit both models. The total aleatory standard deviation of each of the two non-ergodic PSA GMMs is approximately 25% smaller than the total aleatory standard deviation of the corresponding ergodic PSA GMMs. This reduction has a significant impact on hazard calculations at large return periods. In remote areas, far from stations and past events, the reduction of aleatory variability is accompanied by an increase in epistemic uncertainty.

Influence of source uncertainty on stochastic ground motion simulation: a case study of the 2022 Mw 6.6 Luding, China, earthquake

Influence of source uncertainty on stochastic ground motion simulation: a case study of the 2022 Mw 6.6 Luding, China, earthquake

Consistent seismic hazard and fragility analysis considering combined capacity-demand uncertainties via probability density evolution method

A consistent seismic hazard and fragility framework considering combined capacity-demand uncertainties is proposed, in light of the probability density evolution method (PDEM). The PDEM has solid theoretical basis in the reliability field, and it is integrated within the performance-based earthquake engineering (PBEE) for hazard-fragility assessment in this paper. During the analysis, the sample sets with different assigned probability are required to determine in advance, and the equivalent extreme events with virtual stochastic process are required to establish for solution. Both the uncertainties of capacity and demand are considered, and a combined performance index (CPI) is defined as concerned physical variable in PDEM, through pushover static and timehistory dynamic analyses. A non-stationary stochastic earthquake model is introduced using spectral representation of random functions, and the real characteristics of ground motions are reflected by one or two variables for each probability space. The peak ground acceleration (PGA) and spectral acceleration of the first period [Sa(T1)] of non-stationary stochastic ground motions are then obtained for each earthquake level, and the equivalent extreme events are also performed to discuss the statistical information of PGA or Sa(T1) through PDEM. The exceeding probability of PGA or Sa(T1) for each earthquake level is acquired, and a connection between the fragility value and hazard extent is built. The final 3D consistent hazard-fragility curves are then given, and the exceeding probability for different limit states, earthquake levels as well as intensity exceeding conditions can be predicted. Moreover, a comparison with the four classic approaches in the state-of-the-art is performed to verify the accuracy of PDEM procedure. In general, the framework avoids the pre-defined lognormal fragility shape and proves the combined efficiency and accuracy with the Monte Carlo simulation (MCS). The consistency from probabilistic hazard to fragility is realized without re-selecting earthquake waves, which is mainly attributed to the application of PDEM and non-stationary ground motions. The proposed framework provides new ideas for the consistent non-parametric hazard and fragility assessment scheme in the PBEE.

Stochastic dynamic response and seismic fragility analysis for high concrete face rockfill dams considering earthquake and parameter uncertainties

The multiple uncertainties of soil properties and ground motions significantly affect the seismic response of high concrete face rockfill dams (CFRDs). Three types of randomness (the material parameter randomness, stochastic seismic excitation, and their coupling) are generated by stochastic ground motion model and generalized F-discrepancy (GF-discrepancy) method. The generalized probability density evolution method (GPDEM) is used to analyze the influence of randomness on the stochastic dynamic response and system reliability of high CFRDs. The limit state of CFRD is defined according to the crest subsidence and the stress of face-slab, and a performance-based reliability evaluation framework is established. The results show that the randomness of ground motions dominates stochastic dynamic response of the CFRD and the dynamic reliability at different safety thresholds can be obtained by the above methods. Moreover, the proposed seismic safety evaluation framework provides a significant guidance for designing and analyzing practical engineering projects.

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.