Ground Motion Uncertainty Research Articles

Uncertainty quantification for seismic response using dimensionality reduction‐based stochastic simulator

AbstractThis paper introduces a stochastic simulator for seismic uncertainty quantification, which is crucial for performance‐based earthquake engineering. The proposed simulator extends the recently developed dimensionality reduction‐based surrogate modeling method (DR‐SM) to address high‐dimensional ground motion uncertainties and the high computational demands associated with nonlinear response history analyses. By integrating physics‐based dimensionality reduction with multivariate conditional distribution models, the proposed simulator efficiently propagates seismic input into multivariate response quantities of interest. The simulator can incorporate both aleatory and epistemic uncertainties and does not assume distribution models for the seismic responses. The method is demonstrated through three finite element building models subjected to synthetic and recorded ground motions. The proposed method effectively predicts multivariate seismic responses and quantifies uncertainties, including correlations among responses.

Probabilistic seismic demand analysis for bridges based on earthquake scenarios

The current probabilistic seismic demand analysis of structures predominantly considers the correlation between the ground motion intensity measure (IM) and structural seismic demand, but fails to effectively capture regional source characteristics. It is essential to integrate earthquake engineering with seismic response of structures using source parameters to quantify regional ground motion uncertainties and determine appropriate IMs. This study presented a probabilistic seismic demand analysis method for structures based on earthquake scenarios, characterized by 1) utilizing the stochastic finite-fault method to simulate ground motions at a specific site instead of employing multiple seismic waves from different source areas, and 2) incorporating the correlation between IMs and the key indicator of source parameters, stress drop, into the probabilistic seismic demand analysis. Taking a continuous girder bridge as an example, the performance of the stress drop and 14 individual IMs in predicting the longitudinal seismic demand and reflecting source characteristics was evaluated. The results revealed that it was difficult to establish a reliable relationship between the stress drop and structural seismic demand. Owing to the complexities of ground motion and structural parameters, the individual IMs were challenging to effectively capture their characteristics simultaneously. Therefore, composite IMs have been proposed to cover the characteristics of both the source and seismic demand. The optimal solutions were derived using a multi-objective genetic algorithm, which exhibited desirable capabilities in both aspects, providing a comprehensive guide for the seismic performance assessment of regional transportation networks.

Estimation of Earthquake-Induced Direct Economic Losses of Portfolio Buildings Based on Seismic Fragility Surface

Regional seismic loss assessment is crucial for developing earthquake emergency plans, which can significantly reduce casualties and socioeconomic losses in urban communities. Due to the complex types of building structures in a region, it is not possible to accurately measure the damage state of building structures using a single scalar ground motion intensity measure (IM). To more accurately reflect the responses of structures under earthquake excitations, the seismic fragility surface models for 4 typical RC frame structures are developed based on the vector ground motion IMs. The results indicate that the fragility surface model offers a superior level of precision in capturing the inherent uncertainty of ground motion and subsequently determines a more precise probability of structural failure, outperforming traditional single scalar ground motion IM fragility curve models. This enhanced accuracy holds significant implications for regional loss assessment. To fully consider the spatial cross-correlation of vector ground motion IMs, based on the established ground motion database of 8778 records, principal component analysis (PCA) and geostatistical analysis methods are used to construct a spatial cross-correlation influence field that simultaneously considers multiple ground motion IMs to simulate more realistic earthquake scenarios. Considering the impact of uncertainty in loss ratio on earthquake-induced direct economic loss estimation results, the maximum entropy technique is used in conjunction with an improved Latin Hypercube Sampling (LHS) to achieve spatially uniform sampling of loss ratio (LR). This study proposes an assessment framework for regional seismic direct economic loss for portfolio buildings based on the seismic fragility surface model considering spatial cross-correlation and uncertainty of loss ratio. The proposed framework is verified by numerical examples, and it is proven that the regional portfolio buildings considering multiple ground motion IMs is more reliable and robust than those merely considering a single ground motion IM, and when spatial cross-correlation is not considered, the probability of serious economic losses will be underestimated.

Efficient seismic fragility analysis considering uncertainties in structural systems and ground motions

AbstractFragility plays a pivotal role in performance‐based earthquake engineering, which represents the seismic performance of structural systems. To comprehensively understand the structural performance under seismic events, it is necessary to consider uncertainties in the structural model, i.e., epistemic uncertainties. However, considering such uncertainties is challenging due to computational complexity, leading most fragility analyses only to consider the chaotic behavior of ground motions on structural responses, i.e., aleatoric uncertainties. To address this challenge, this study proposes an adaptive algorithm that intertwines with the conventional fragility analysis procedures to consider both aleatoric and epistemic uncertainties. The algorithm introduces Gaussian process‐based metamodels to efficiently consider epistemic uncertainties with a small number of time history analyses. Steel moment‐resisting frame structures and a reinforced concrete building are used to demonstrate the improved efficiency and wide applicability of the proposed method. In each case, the proposed method yields fragility curves consistent with reference solutions but with substantially lower computational effort. Comprehensive discussions are provided regarding ground motion sets, structural types, and definitions of limit‐states to demonstrate the robustness of the proposed approach.

Uncertain seismic response and robustness analysis of isolated continuous girder bridges

When calculating the seismic response of structures, conventional methods often neglect uncertainty and suffer from excessive computation. Although robustness metrics have been effective in evaluating structural safety, they are not suitable for isolated continuous girder bridges (ICGB). To address this issue, this paper introduces an uncertain seismic response and robustness assessment method tailored to ICGB: Firstly, the method considers uncertainty in material parameters and ground motion by constructing a data set using Monte Carlo simulation. Secondly, a genetic algorithm for parallel optimisation of radial basis function neural network (GAPO-RBFNN) is trained to predict the seismic responses of the bridges. Thirdly, a robustness metric specifically designed for bridges is derived and applied to bridge. Finally, the proposed robustness metric is validated on lead rubber bearing (LRB) and shape memory alloy-lead rubber bearing (SMA-LRB) bridges. Results indicate that the GAPO-RBFNN model accurately approximates the mapping relationship between structural parameters and seismic response, with an average error of only 0.32% and a 70% reduction in computation time compared with traditional methods. Moreover, the new robustness metric overcomes the limitations of the dismantled member method and is applicable to bridge. The robustness of the SMA-LRB-ICGB, strengthened by SMA, is improved, providing evidence of the effectiveness of the proposed robustness metric.

Seismic fragility estimation through real-time hybrid simulation and surrogate-based multi-fidelity Monte Carlo predictor

The intricate dynamic responses of structures, particularly when confronted with uncertainty, poses significant challenges in constructing reliable analytical models, thus resulting in unreliable fragility assessment. This study presents an approach that integrates data-driven techniques with real-time hybrid simulation (RTHS) to achieve reliable fragility analysis. RTHS data and imprecise surrogate models are fused using a multi-fidelity Monte Carlo predictor (MFMC), yielding unbiased estimations for parameters of fragility curve. The MFMC predictor can be considered as an optimized forecasting tool that harnesses the computational efficiency of low-fidelity simulations and the precision of high-fidelity experiments. RTHS is utilized for obtaining high-fidelity experimental data, part of which is leveraged to establish low-fidelity surrogate models, ultimately enabling multi-fidelity analysis through direct data-to-data analysis. A two-story steel moment-resisting frame equipped with self-centering viscous dampers is used as a proof-of-concept to demonstrate the proposed method. Structural and ground motion uncertainties are incorporated to reflect practical engineering environment. The low-fidelity Kriging models were built using portion of high-fidelity RTHS data. Simulation and experimental investigations were conducted to evaluate the effectiveness and efficiency of the proposed approach. The results suggest that the proposed method provides a promising tool for accurately evaluating seismic fragility, particularly when simulation-based methods are not feasible.

Impact of ground motion uncertainty evolution from post-earthquake data on building damage assessment

Accurate damage assessment after an earthquake is crucial for effective emergency response. Using ground motion information enables rapid building damage assessment when detailed damage data are unavailable. While uncertainty in earthquake parameters plays a significant role in the accuracy of rapid estimations, it is usually treated as a constant parameter rather than as a dynamic parameter that considers the amount of ground motion data collected that evolve over time. This work investigates the impact of incorporating evolving ground motion uncertainty in ground motion estimations from US Geological Survey’s (USGS) ShakeMap on post-disaster damage assessments from two methodologies: the revised Thiel–Zsutty (TZR) model and Federal Emergency Management Agency’s (FEMA) Hazus. Using data from the 2020 Indios earthquake in Puerto Rico and the 2014 Napa earthquake, we find that changes in uncertainty in estimates of peak ground acceleration reach 65% between early and late versions of the ShakeMap. We propose a process to integrate this evolution with the two damage assessment methodologies through a Monte Carlo simulation-based approach, demonstrating that it is critical to introduce dynamic ground motion uncertainty in the damage assessment process to avoid propagating unreliable measures. Both methodologies show that resulting damage estimates can be characterized by narrower distributions, indicative of reduced uncertainty and increased precision in damage estimates. For the TZR model, an improved estimate of post-disaster loss is achieved with narrower bounds in distributions of expected high scenario loss. For Hazus, the results show potential changes in the most probable damage state with an average change of 13% in the most probable damage state. The described methodology also demonstrates how uncertainty in the resulting damage state distributions can be reduced compared with the use of the current Hazus methodology.

Accounting for ground-motion uncertainty in empirical seismic fragility modeling

Seismic fragility models provide a probabilistic relation between ground-motion intensity and damage, making them a crucial component of many regional risk assessments. Estimating such models from damage data gathered after past earthquakes is challenging because of uncertainty in the ground-motion intensity the structures were subjected to. Here, we develop a Bayesian estimation procedure that performs joint inference over ground-motion intensity and fragility model parameters. When applied to simulated damage data, the proposed method can recover the data-generating fragility functions, while the traditionally used method, employing fixed, best-estimate, intensity values, fails to do so. Analyses using synthetic data with known properties show that the traditional method results in flatter fragility functions that overestimate damage probabilities for low-intensity values and underestimate probabilities for large values. Similar trends are observed when comparing both methods on real damage data. The results suggest that neglecting ground-motion uncertainty manifests in apparent dispersion in the estimated fragility functions. This undesirable feature can be mitigated through the proposed Bayesian procedure.

Hierarchical and mixed uncertainty quantification for simulation-based structural seismic fragility analysis

Seismic fragility assessments (SFA) encompass significant uncertainties, including ground motions, materials, geometry, boundaries, and modeling, which impart inherent uncertainties to the fragility curve. Quantifying these uncertainties is essential for informed decision-making in earthquake disaster mitigation. This paper presents a hierarchical uncertainty quantification (UQ) framework for simulation-based SFA, which can address mixed aleatory and epistemic uncertainties. The framework comprises two levels: At Level 1, ground motion uncertainties are accounted for through record-to-record variation, while structural parameter uncertainties are captured using well-defined probability distributions. The quantification of uncertainty in seismic fragility is accomplished using mean and quantile fragility curves, representing the average outcome and the dispersion of structural fragility, respectively. Fuzziness is also introduced to enhance the objectivity of failure determination. Level 2 addresses uncertainties in the distribution hyper-parameters of structural variables through evidence theory, facilitating an understanding of their influence on the seismic fragility curve and quantifying uncertainty in mean and quantile fragility curves. This UQ framework builds upon the multivariate seismic fragility analysis method, integrating Kriging regression for seismic demand prediction and logistic regression for generating multivariate seismic fragility functions. The proposed framework is validated numerically on an existing three-span reinforced concrete continuous girder bridge, affirming its practical utility and reliability.

Horizontal ground-motion model for subduction slab earthquakes using offshore ground motions in the Japan Trench area

The S-net, a large-scale network of permanent ocean-bottom seismographs in the Japan Trench, consisting of 150 stations, has recorded a large number of offshore ground motions that can be used to establish the empirical attenuation relationship of offshore ground motions in the subduction zone. Due to the different attenuation characteristics among different earthquake types in subduction zones, the earthquakes are classified into four tectonic types of subduction slab, interface, shallow crustal, and upper-mantle earthquakes according to the classification scheme of Zhao et al. (2015). Predictive models and uncertainties in offshore ground motions were investigated for different earthquake types. This study establishes a horizontal offshore subduction slab earthquake ground-motion model (GMM) and compares the offshore and onshore slab earthquake GMMs. As the site conditions at ocean-bottom stations are different from those at land stations, the effects of water depth and sediment thickness are taken into account in the offshore slab earthquake GMM. Due to differences in the burial methods of ocean-bottom stations, stations were divided into buried and unburied to investigate the effects of the burial methods. Therefore, regression analysis was used to propose an offshore slab earthquake GMM considering the magnitude, focal depth, distance, water depth, sediment thickness, and burial method. By separating the within-event residuals, the single-station standard deviation is presented. Compared to the onshore GMM, the predicted spectra of the offshore GMM are significantly larger at long periods. For the attenuation rate, the offshore attenuation rate is lower than that of the onshore attenuation rate for short periods, but is basically consistent with the onshore attenuation rate for long periods. The proposed GMM can be used to predict the offshore ground motions for slab earthquakes with rupture distances less than 300 km, focal depths less than 110 km, and moment magnitude between 4 and 7.4.

Seismic safety of RC piers with parameter uncertainties: Assessing dimensionless response using Bayesian linear regression

Both maximum and residual deformations are essential for seismic safety during and following strong earthquakes, especially in the near field. These parameters are often calculated per unidirectional analysis, albeit bidirectional analysis may be carried out for important systems with the availability of growing computational power. However, a pressing challenge in earthquake engineering that continues to exist in the face of several uncertainties is to represent these response statistics – essentially with wide dispersion - in an expressive and effective format. The present paper aims to represent the maximum and residual deformation to unidirectional and bidirectional shaking in a rational format, even when uncertainties in ground motion and structural characteristics are prevalent. To this end, a bridge pier with uncertain material parameters is subjected to a wide range of stochastically simulated near-field motions with forward-directive signature, and the responses are computed to unidirectional and bidirectional shaking. In an attempt to develop predictive models, the responses are regressed first in terms ofprimary parameterscharacterizing structural material and ground motions. Next, by standard principles of mechanics, the response is recast in a dimensionless and orientationally consistent format in terms ofderived parameters. This reduces the number of independent variables yet connotes a sound basis of mechanics. The predictive model in terms of derived dimensionless parameters is further extended in the Bayesian framework to improve the predictive model in a probabilistic sense.

Seismic fragility analysis of rocking buckling-resistant braced structures subjected to far-field and near-field ground motions

To address the inadequate seismic performance of traditional buckling-restrained braced frame structures (BRBFS), this study introduces a novel structure, the rocking buckling-restrained braced frame structure (RBRBFS). The RBRBFS achieves effective control of main structure damage and enhances structural energy dissipation and seismic resilience by disconnecting the column feet from the foundation in the BRBFS and using friction energy dissipation devices as rocking column feet. This research aims to quantitatively assess the seismic performance and collapse safety margin of the new RBRBFS under different types of ground motions. To achieve this goal, two eight-story structures, one is traditional BRBFS and the other is RBRBFS, were designed. Incremental Dynamic Analysis (IDA) was employed, accounting for ground motion uncertainty, to conduct a comparative study of the seismic fragility of both structures subjected to near-fault pulse-like and far-field earthquake ground motions. Nonlinear dynamic analysis results indicate that under high-intensity ground motions, the RBRBFS significantly improves structural ductility and effectively controls structural damage. Compared to BRBF structures, the BRBFS exhibit a reduction of 26.5% and 18.3% in damage probability deviation under the two seismic excitations, highlighting their more stable structural response under varying seismic conditions. Furthermore, this novel RBRBFS increases the collapse margin ratio by 25% to 30%, demonstrating its higher seismic collapse resistance capacity

Lateral variations of shear wave velocity (VS) profile and VS30 over gentle terrain

Lateral variations of shear wave velocity (VS) profile and time-averaged shear wave velocity in the upper 30 m (VS30) are important indicators of site condition and significant contributors to uncertainty in earthquake ground motion and seismic hazards. Few previous studies involved in quantifying these lateral variations, especially at short distances, due to limited data at closely spaced sites. This study quantitatively investigated the lateral variation of VS profile and VS30 over plain and piedmont terrains, focusing on short distances ranging from hundreds of meters to several kilometers. 2510 plain and 749 piedmont borehole profiles from the mainland China borehole profile database were employed to examine these variations using the variogram as the geo-statistics tool. The main findings include: 1) Over plain terrain, the variation in site conditions between sites does not significantly increase with separation distance within a certain range (typically from 1 km to 3–5 km). Over piedmont terrain, site condition variation steadily increases with distance. 2) The variation of site condition over piedmont terrain is higher than that over plain terrain. Nonetheless, for both terrains, the dispersion of site condition between sites at distance of <1 km is engineering negligible, and the correlation of site conditions between sites within 5 km remains strong; 3) For both terrains, the lateral variation of VS in deeper layers is higher than that in shallower layers. The study outcomes emphasize the importance of incorporating the information of nearby measurements in site condition estimations. The study outcomes can also be utilized in the optimization of borehole sampling design for microzonation projects and the evaluation of site condition dispersion at inferred sites.

Quantification of material modeling uncertainty on seismic performance of SMA-based self-centering concentrically braced frames

Shape memory alloys (SMAs) combine super-elasticity and energy dissipation capacity therefore is favored in seismic hazard mitigation. Simplifications are necessary to incorporate acquired material properties through material testing for dynamic analysis. This study presents a methodology to integrate SMA material testing, model inference, and probabilistic seismic analysis for uncertainty quantification of SMA model uncertainty on SMA based structures. The proposed methodology is applied to a SMA-based self-centering concentrically braced frame (SC-CBF). The posterior distribution of SMA modeling parameters is first obtained through the MCMC algorithm. Considering computational cost of MCMC algorithm, linear moments method is introduced to sample SMA modeling parameters. Extensive time-history analysis is then performed to quantify the effect of SMA modelling uncertainty and ground motions on the performance of SC-CBF. Significant response changes can be observed in SC-CBF due to the effect of uncertainty, which inevitably affect the reliability assessment of the structure. These analysis results also show that modeling uncertainty will affect seismic performance of SMA-based SC-CBF but its influence is less significant than that caused by ground motion uncertainty for the braced frame investigated in this study.

Selection of hazard-consistent ground motions for risk-based analyses of structures

In seismic risk analysis, probabilistic seismic demand analysis (PSDA) is required to determine the probability distribution of structural seismic responses. One of the key steps in PSDA is to select a suite of ground motions that are consistent with seismic hazards at a target site. Current methods for selecting hazard-consistent ground motions only achieve consistency at one or several predefined periods and choose several discrete intensity levels to consider uncertainty of ground motions. To avoid drawbacks of the current methods, this study proposes a novel method for selecting hazard-consistent ground motions. In this method, a scenario earthquake set for ground motion selection is firstly obtained from seismic hazard disaggregation to a hazard level corresponding to a very small value of spectral acceleration at a specific period. Then, a suite of random target response spectra that are consistent with target site seismic hazards are simulated based on the scenario earthquake set. Finally, one suite of hazard-consistent ground motions are selected from a ground motion database. Through a numerical example, this study concludes, a suite of selected ground motions using the proposed method presents very good consistency with the target site seismic hazards. Since hazard-consistent ground motions selected using the proposed method do not depend on the building information, they can be used to accurately perform PSDA of any building and accurately predict structural seismic responses.

Fragility analysis of masonry infill R.C. frame using incremental dynamic approach

The current study aims to investigate damage assessment of the RC frames with brick masonry infill (BMI). The effects of near-source ground motions (GMs) are considerably predominant in the seismic response of the structure as related to far-source ground motion due to their forward directivity plus long period. The near-source ground motion is characterized by enormous everlasting ground translation, strong peak ground acceleration (PGA), and a very low-frequency pulse. The Indian codes have not yet incorporated the influence of near-source GM into their design response spectra. Hence, IDA curves that represent ground motion uncertainty have been established for ten near-field ground motion records. Further, the fragility curves have been constructed to envisage progressive damage to the structure. The spectral acceleration-based fragility curves for the ten-story RC frames without BMI, with BMI, and with the open ground story are developed. It is proved that the BMI frame shows better performance during seismic motions. The probability of damage for the collapse prevention state is reduced for frames with BMI, and with open-ground story frames as compared to a frame without BMI.

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.

MSA-based seismic fragility analysis of RC structures considering soil nonlinearity effects and time histories compatible to uniform hazard spectra

In the present study, an updated ground motion simulation framework based on spectral compatible time histories is proposed for the evaluation of seismic performance of mid-rise reinforced concrete structures with multi-stripe analysis (MSA) based probabilistic seismic hazard analysis. The seismic fragility functions are generated for two numbers of three storied instrumented test buildings of which one is founded on individual flexible footings and other one is a base isolated building. The fragility analysis is carried out for different performance levels under a series of input ground motions (IGMs) by considering uncertainty in soil structure interaction and uncertainty in ground motion. IGMs are obtained from the uniform hazard response spectrum (UHRS) with different return period thus conserving the frequency content of input motion during the scaling of high intensity earthquakes. The UHRS compatible synthetic time histories are applied at rock level and amplified surface motion obtained from soil amplification studies considering soil nonlinearity are applied to the buildings supported on soil springs. Nonlinear time history analysis is performed by modelling hysteretic characteristic of columns using modified Takeda model. The fragility curves obtained from the proposed methodology are compared with that using simple scaling of accelerograms generally performed in literature. The proposed technique gives conservative result for structure with individual flexible footings while no marked differences are observed for base isolated structure.

Seismic response analysis of subway station structure under random excitation based on probability density evolution method

The subway station structure mainly faces the uncertainty of ground motion and surrounding soil mass. Comprehensive analysis of the seismic response of subway station structures under random excitation is the key to ensuring the safety of urban people's lives and property. In this paper, the random shear wave velocity profile model and the random ground motion model characterizing uncertainty are established. Using a high-dimensional space optimization point selection strategy significantly reduces the number of sample points and computational costs of nonlinear time history analysis (NLTHA). Combining the probability density evolution method (PDEM) with finite element analysis, the stochastic seismic response analysis of the subway station structure under dual random excitations is realized. In addition, statistical methods are used to analyze the distribution characteristics of the most unfavorable seismic responses of the subway station structure. The research results show that when random excitation is not considered, the adverse seismic damage risk of subway station structures will be ignored. The evolution of the seismic dynamic response of subway station structures is mainly controlled by the amplitude of random ground motion acceleration. Additional random shear wave velocities can increase the lateral deformation range of the subway station structure, leading to a decrease in the dynamic reliability of the structure. PDEM can conduct stochastic seismic response analysis of the subway station structure from both time and response dimensions. The proposed method provides strong support for a comprehensive analysis of the seismic response of underground structures.

Seismic performance and fragility of two-story and three-span underground structures using a random forest model and a new damage description method

This paper proposes a new method for evaluating the seismic performance and fragility of large underground structures. A typical underground subway station consisting of a two-story and three-span structure was used as the research subject. Considering the variation of sites and the uncertainty of input ground motions, we developed a finite element model of a nonlinear dynamic soil-underground structure interaction system. Based on the incremental dynamic analysis method, the nonlinear seismic responses of the subway station structure were calculated for 900 cases. Python (software) was used to accelerate the processing of the large number of numerical simulation data. Based on the seismic damage characteristics of an underground structure, this paper proposes a new concept of average seismic damage value to evaluate the damage condition of the underground structure to overcome the inadequacies induced by an expert’s intuitive judgment. Meanwhile, the random forest prediction model was adopted to predict the seismic performance levels (SPLs) of the underground structure, and a non-parametric test was performed to verify the correlation between the degree of seismic damage and the inter-story drift ratios (IDR) of the large underground structure. This proved that the IDR could describe the seismic damage of shallow-buried underground structures; we advanced a precise quantification system of the SPL for shallow-buried subway station structures with two-story and three-span using probability statistics. The peak ground velocity (PGV) is more suitable than the peak ground acceleration (PGA) for use as the seismic intensity measure (IM) for large underground structures when the stiffness of the soil foundation becomes soft. In addition, the seismic fragility curves of the shallow-buried subway station structure were constructed and analyzed using the developed quantification system for the SPL.