Seismic fragility denotes the probabilities of a system exceeding some prescribed damage levels under a range of seismic intensities. Classical seismic fragility studies in slope engineering usually construct fragility functions by making some assumptions for fragility curve shape, and always neglect spatial variability of soil materials. In this study, an assumption-free method on the basis of probability density evolution theory (PDET) is proposed for seismic fragility assessment of slopes. The random input earthquakes and spatially-variable soil parameters in slope are simultaneously quantified. By the proposed method, assumption-free fragility curves of a slope are established without limiting the fragility curve shape. The obtained fragility results are also compared with those from two classic parametric fragility methods (linear regression and maximum likelihood estimation) and Monte Carlo simulation. The results demonstrate that the proposed assumption-free method has potential to gives more rigorous and accurate fragility results than classical parametric fragility analysis methods. With the proposed method, more reliable fragility results can be obtained for slope seismic risk assessment.

The nonlinear mechanical behaviour of pipeline joints influences the seismic response of water supply pipelines. This study presents an experimental investigation of the tensile behaviour of push-on joints of ductile iron (DI) pipelines, subjected to axial tensile forces and internal water pressure. The axial performance and damage states of joints are determined for push-on joints with different diameters. A statistical analysis is then conducted to determine the correlation between tensile strength and joint opening. An empirical equation for estimating the tensile strength of pipeline joints is proposed, along with a normalized failure criterion for joint opening considering water leakage. Moreover, a numerical model for buried pipelines considering nonlinear soil-pipe interaction is developed. Incremental dynamic analysis (IDA) is performed on DI pipelines with explicit consideration of the uncertainty of joint mechanical properties. Seismic fragility curves are developed based on the IDA results. The effect of mechanical parameter uncertainty of pipeline joints on seismic risk assessment of segmented pipelines is quantitatively evaluated. The numerical results indicated that the failure probability of the pipeline considering the uncertainty of joint mechanical properties is approximately 1.5 to 2 times larger than that predicted by a deterministic model.

Cloud and incremental dynamic analysis (IDA) are the two most commonly used methods for seismic fragility analysis. The two methods differ significantly in the number of ground motions and whether these motions are scaled. This paper designed a random selection procedure to thoroughly discuss the influence of ground motion combinations encompassing different numbers of motions on the Cloud-based and IDA-based seismic fragility analysis for underground subway station structures. Focusing on a shallow-buried single-story station structure, a nonlinear dynamic time-history finite element analysis model of soil-structure interaction was developed. 400 ground motions were selected for random combination to perform Cloud-based seismic fragility analysis, and 20 ground motions were selected for random combination to perform IDA-based analysis. The results showed that the number of ground motions has a significant influence on the seismic fragility analysis in both Cloud and IDA, especially on the prediction of damage probability for higher seismic performance levels and when the PGA exceeded 0.3 g. In regions with a low probability of strong earthquakes, this paper recommended using no fewer than 10 and 220 ground motions in the IDA-based and Cloud-based seismic fragility analyses, respectively. In regions with a high probability of strong earthquakes, the optimal number of ground motions should be increased to 300 for Cloud-based analysis and 15 for IDA-based analysis.

As an important coastal protective structure, the breakwater is prone to failure due to foundation damage under seismic actions. However, the seismic performance evaluation of breakwaters has received little attention. This study conducts a seismic fragility analysis of composite breakwaters constructed on liquefiable foundations. By adopting a performance-based seismic design (PBSD) approach and considering the record-to-record (RTR) variability of ground motions, the seismic performance of the breakwaters is assessed over their entire lifecycle. Based on the results of the parameter sensitivity analysis, the reinforcement schemes were proposed in terms of delaying foundation liquefaction and limiting the lateral displacement of liquefied soil. The results of the seismic intensity measure (IM) parameter selection indicate that the commonly used peak ground acceleration (PGA) exhibits a weak correlation with the seismic response of the breakwater, whereas the cumulative absolute velocity (CAV) has a strong correlation. The comparison of the reinforcement schemes shows that the Dense Sand Column (DC) scheme provides significant reinforcement effects, while the Concrete Sheet Pile (CSP) scheme is more suitable for reinforcing existing breakwaters. The seismic performance assessment framework can also be applied to other structures where structural damage is closely related to foundation deformation, such as caisson quays and embankments.

The recurring occurrence of seismic hazards constitutes a significant and imminent threat to subway stations. Consequently, a meticulous assessment of the seismic resilience of subway stations becomes imperative for enhancing urban safety and ensuring sustained functionality. This study strives to introduce a probabilistic framework tailored to assess the seismic resilience of stations when confronted with seismic hazards. The framework aims to precisely quantify station resilience by determining the integral ratio between the station performance curve and the corresponding station recovery time. To achieve this goal, a series of finite element models of the soil-station system were developed and employed to investigate the impact of site type, seismic intensity, and station structural type on the dynamic response of the station. Then, the seismic fragility functions were generated by developing the relationships between seismic intensity and damage index, taking into account multidimensional uncertainties encompassing factors such as earthquake characteristics and construction quality. The resilience assessment was subsequently conducted based on the station's fragility and the corresponding economic loss, while also considering the recovery path and recoverability. Additionally, the impacts of diverse factors, including structural characteristics, site types, functional recovery models, and peak ground acceleration (PGA) intensities, on the resilience of stations with distinct structural forms were also discussed. This work contributes to the resilience-based design and management of metro networks to support adaptation to seismic hazards, thereby facilitating the efficient allocation of resources by relevant decision makers.

Despite the emergence of recent advancements, machine learning (ML) based methods for estimating the fragility curves of structures through probabilistic ground motion selection techniques pose a challenge due to the computational cost associated with data preparation. The primary aim of this research is to reduce the data preparation time involved in estimating the fragility curves of structures using a ground motion selection approach that considers earthquake magnitude, distance from the seismic source, and shear wave velocity of soil as essential parameters. To achieve this objective, ML algorithms are employed to calculate the fragility curves of various reinforced concrete moment resisting (RC/MR) frames with different periods, utilizing codebased and generalized conditional intensity measure (GCIM) ground motion selection methods. The SMOTE-ENN technique, a data resampling method, is used to balance the training data for the ML algorithms to address potential bias resulting from imbalanced training data. To validate the fragility curves obtained through ML, analytical fragility curves are derived for a specific structure at three damage levels and compared with the ML curves. The results demonstrate that the percentage of the enclosed area between the analytical and ML curves, relative to the area under the analytical curve, is below 10 % and 5 % for the GCIM and code-based methods, respectively. Fragility curves were generated for various structures, including regular and irregular buildings, to investigate the generalizability. Results indicate that, for the specific structures analyzed in this study, excluding torsional ones, the structure's period is a sufficient structural feature for generating fragility curves.

Selecting the optimal intensity measure (IM) is essential for accurately assessing the seismic performance of the submarine shield tunnels in the layered liquefiable seabed. However, current research relies on simplistic ranking or filtering methods that neglect the different contributions of each evaluation criterion on IM's overall performance. To address this, this study begins by developing a numerical simulation method for nonlinear dynamic analysis, considering joint deformation, ocean environmental loads, and soil liquefaction, which is validated by experimental and theoretical methods. Subsequently, a fuzzy multiple criteria decision-making (FMCDM) method based on fuzzy probabilistic seismic demand models (FPSDM) is proposed, which integrates the fuzzy analytical hierarchical process (FAHP) for calculating weights and the fuzzy technique for order preference by similarity to ideal solution (FTOPSIS) for ranking IM alternatives. Finally, tunnel damage is classified into four states employing joint opening as the index for measuring damage, then the seismic fragility analysis is conducted. The results indicate that the optimal IM of a submarine shield tunnel situated in layered liquefiable seabed is sustained maximum velocity (SMV). Furthermore, the comparison between the fragility curves established using SMV and peak ground acceleration (PGA) reveals PGA, a frequently employed IM, notably undervaluing the seismic hazard.

Although the influence of duration of ground motion on the seismic response of aboveground structures is clearly recognized, its influence on underground structures remains unclear. To this end, this study performs incremental dynamic analyses under both short and long duration ground motions, to quantify the significance of the duration effect on the seismic fragility of subway stations. A two-dimensional soil-structure system is established on the basis of the Daikai subway station, consisting of an elastoplastic soil model and a concrete damage plasticity model. A set of thirty spectrally matched ground motions with varying significant durations (D5-95) are employed. In particular, using the center column total compressive damage index (DTCD) and peak inter-story drift ratio (IDR) as structural demand measures (DM), the percentage difference in fragility curves between long and short duration is evaluated by accounting for six suits of damage state thresholds. Correlations between the two DMs and D5-95 show that ground motion duration affects significantly the seismic fragility of subway stations. Overall, the duration effect is not detected in the minor damage state and becomes more pronounced in the collapse state, suggesting that the duration effect increases as the damage state threshold increases. The median collapse capacity for long duration ground motions is up to approximately 60% or 37% lower than that for short duration ground motions, when a peak IDR or DTCD are adopted, respectively. The results of this study highlight the great importance of properly considering duration when selecting earthquake records for seismic fragility assessment of subway stations.

Concrete gravity dams, forming a quarter of the ICOLD database with over 61,000 dams, often surpass 50 years of service, necessitating increased maintenance and safety scrutiny. Given the aging and advancing seismic safety methods, reevaluating their seismic resilience, considering material degradation and concrete heterogeneity, is imperative. This study conducts a comprehensive seismic fragility assessment of the Pine Flat Dam at lifecycle stages of 1, 50 and 100 years, accounting for material degradation due to aging and uncertainties from concrete heterogeneity. It develops a 2D dam-foundation-reservoir model with fluid-structure-soil interaction and material nonlinearity using the concrete damage plasticity model. The assessment includes 55 ground motions, selected via the conditional mean spectrum method, representing five return periods from 475 to 10,000 years. Fragility curves are developed by fitting a lognormal distribution to failure probabilities at varying intensities. These curves are compared using damage indices like crest displacement and stress at the dam's neck and heel. Aging increases failure probability, correlating with age and return period, as shown by the leftward shift of fragility curves, while concrete heterogeneity adds uncertainty. The results emphasize the critical need for ongoing seismic fragility reassessments, accounting for aging, environmental exposure, and seismic demands on dam safety.

Seismic risk assessment is pivotal for ensuring the reliability of prefabricated subway stations, where selecting optimal intensity measures (IMs) critically enhances probabilistic seismic demand models and fragility analysis. While peak ground acceleration (PGA) is widely adopted for above-ground structures, its suitability for underground systems remains debated due to distinct dynamic behaviors. This study identifies the most appropriate IMs for soft soil-embedded prefabricated subway stations at varying depths through nonlinear finite element modeling and develops corresponding fragility curves. A soil-structure interaction model was developed to systematically compare seismic responses of shallow-buried, medium-buried, and deep-buried stations under diverse intensities. Incremental dynamic analysis was employed to construct probabilistic demand models, while candidate IMs (PGA, PGV, and vrms) were evaluated using a multi-criteria framework assessing correlation, efficiency, practicality, and proficiency. The results demonstrate that burial depth significantly influences IM selection: PGA performs optimally for shallow depths, peak ground velocity (PGV) excels for medium depths, and root mean square velocity (vrms) proves most effective for deep-buried stations. Based on these optimized IMs, seismic fragility curves were generated, quantifying damage probability characteristics across burial conditions. The study provides a transferable IM selection methodology, advancing seismic risk assessment accuracy for prefabricated underground infrastructure. Through a systematic investigation of the correlation between IM applicability and burial depth, coupled with the development of fragility relationships, this study establishes a robust technical framework for enhancing the seismic performance of subway stations, and provides valuable insights for seismic risk assessment methodologies in underground infrastructure systems.