This study quantifies the seismic fragility assessment of shallow-founded buildings in liquefiable and treated soils, enhanced by drainage and densification, considering both short-and long-term behaviors. A conceptual framework is proposed for developing seismic fragility curves based on engineering demand parameters (EDPs) of buildings subjected to various earthquake magnitudes. The framework for establishing seismic fragility curves involves three essential steps. First, nonlinear dynamic analyses of soil-building systems are performed to assess both the short-term response, which occurs immediately following an earthquake, and the longterm response, when excess pore water pressure completely dissipates, and generate a dataset of building settlements. The seismic responses are compared in terms of excess pore water pressure buildup, immediate and residual ground deformation, and building settlement to explore the dynamic mechanisms of soil-building systems and evaluate the performance of enhanced drainage and densification over short-and long-term periods. Second, 38 commonly used and newly proposed intensity measures (IMs) of ground motions (GMs) are comprehensively evaluated using five statistical measures, such as correlation, efficiency, practicality, proficiency, and sufficiency, to identify optimal IMs of GMs. Third, fragility curves are developed to quantify probability of exceeding various capacity limit states, based on structural damage observed in Taiwan, for both liquefaction-induced immediate and residual settlements of buildings under different levels of IMs. Overall, this study proposes a rapid and straightforward probabilistic assessment approach for buildings in liquefiable soils, along with remedial countermeasures to enhance seismic resilience.

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.

Shallow subway tunnels in both the intermediate and far fields are significantly affected by Rayleigh surface waves, which typically induce substantial vertical seismic motion and exhibit high seismic destructiveness. However, current vulnerability assessments of underground tunnels primarily focus on body waves. This study aims to identify the optimal ground motion intensity measures (IMs) for evaluating the seismic fragility of shallow circular subway tunnels subjected to Rayleigh waves. A detailed dynamic analysis of soil-tunnel interaction is performed using the two-dimensional Finite Element Method, with particular emphasis on the influence of tunnel burial depth and site classification on the tunnel's response to Rayleigh waves. The input of Rayleigh wave motion is modeled by transforming the motion into a series of equivalent forces, applied through viscoelastic boundaries. This study examines 15 widely used ground motion IMs, with diameter deformation ratio (DDR) serving as the damage measure (DM). Linear regression analysis is conducted to explore the relationship between IMs and DDR. The optimal IMs are evaluated based on criteria including efficiency, practicality, proficiency, and correlation. The results indicate that for sites classified as Class III and IV, the optimal IM is root mean square velocity (vrms), while for Class II sites, spectral mean velocity (SMV) is more suitable. Fragility curves for shallow-buried tunnels in Class II, III, and IV sites are presented. These curves demonstrate that tunnels are most vulnerable to damage in Class II sites, followed by Class IV, and least vulnerable in Class III sites. In Class II sites, shallower tunnel depths are associated with increased seismic damage, while deeper tunnels in Class III and IV sites experience greater seismic damage. The primary factor influencing seismic damage to tunnels is the vertical relative deformation of the surrounding soil layers.

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.

In the processes of seismic design of underground structures, selecting a reasonable input ground motion is very important, which can cause severe damage to underground structures. To quantitatively evaluate the seismic damage potential of ground motions on multi-storey underground structures and solve the problem that single intensity measures are inadequate in accurately indicating the seismic damage potential of ground motions, this paper taking the input ground motions in the seismic design of underground structures as the research object, and constructing some composite intensity measures that can effectively characterize the damage potential of input ground motion. Firstly, considering that the underground structures in different characteristic period-type sites will exhibit different seismic responses under the same excitation, the soil-structure system is divided into four-period bands. Then, four representative periods are selected from four-period bands respectively, and the corresponding four soil-structure system numerical models are established. Subsequently, 40 ground motions are selected for elastoplastic numerical analysis, and the results of the numerical analysis were used as sample data to construct composite intensity measures corresponding to soil-structure systems in each period band using the partial least squares regression method. Finally, 100 additional ground motions were used to verify the correlation between the composite intensity measures and the seismic damage of underground structures. The results show that the correlation coefficient between the composite intensity measures and the seismic damage of multi-storey underground structures is better than those of commonly used single intensity measures.

The selection of representative ground motion intensity measure (IM) and structural engineering demand parameter (EDP) is the crucial prerequisite for evaluating structural seismic performance within the performance-based earthquake engineering (PBEE) framework. This study focuses on this crucial step in developing the probabilistic seismic demand model for two-story and three-span subway stations exposed to transverse seismic loadings in three different ground conditions. The equivalent linearization approach is used to simulate the shear modulus degradation and the increase in damping characteristics of the soil under seismic excitation. Nonlinear fiber beam-column elements are adopted to characterize the nonlinear hysteretic degradation of the subway station structure during seismic events. A total of 21 far-field ground motions are selected from the PEER strong ground motion database. Nonlinear incremental dynamic analyses (IDAs) are conducted to evaluate the seismic response of the subway station. A suite of 23 ground motion IMs is evaluated using the criteria of correlation, efficiency, practicality, and proficiency. Then, a multi-level fuzzy evaluation method is employed to integrate these evaluation criteria and determine the optimal ground motion IMs in different ground conditions. The peak ground acceleration and sustained maximum acceleration are demonstrated to be the optimal ground motion IM candidates for shallowly buried rectangular underground structures in site classes I, II, and III, while the root-mean-square displacement and compound displacement are found to be not suitable for this purpose.

Two new structure-specific scalar intensity measures for plane steel frames under far-field earthquakes are proposed. These intensity measures of the spectral acceleration and spectral displacement type are multi-modal as they take into account the effect of the first four natural periods and multi-level as they are defined for four performance levels and consider inelasticity and period elongation up to the collapse prevention level. This is accomplished with the aid of the equivalent modal damping ratios of a structure previously developed by the authors for performance-based seismic design purposes. These modal damping ratios are period, soil type and deformation dependent and associate the equivalent linear structure to the original nonlinear one. The proposed intensity measures are conceptually simple, elegant and include all the aforementioned features in a rational way without artificially combining terms, defining period ranges and adding coefficients to be determined by optimization procedures as it is the case for all the existing measures, which try to take into account more than one mode and inelasticity. Comparison of the proposed intensity measures against some of the most popular ones existing in the literature, with respect to efficiency (beta), practicality (b), proficiency (zeta), sufficiency in terms of seismic magnitude (M) and source-to-site distance (R), scaling robustness and the range of their values at any damage or performance level demonstrates their very good performance as indicators of the destructive power of an earthquake.

Most natural granular deposits are spatially variable due to heterogeneities in soil hydraulic conductivity, layer thickness, relative density, and continuity. However, existing simplified liquefaction evaluation procedures treat each susceptible layer as homogeneous and in isolation, neglecting water flow patterns and displacement mechanisms that result from interactions among soil layers, the groundwater table, foundation, and structure. In this paper, three-dimensional, fully coupled, nonlinear, dynamic finite-element analyses, validated with centrifuge experimental results, are used to evaluate the influence of stratigraphic layering, depth to the groundwater table, and foundation-structure properties on system performance. The ejecta potential index (EPI) serves as a proxy for surface ejecta severity within each soil profile. The results reveal that among all the engineering demand parameters (EDPs) and geotechnical liquefaction indices considered, only EPI predicted a substantial change in the surface manifestation of liquefaction due to changes in the location of the groundwater table and soil stratigraphy. This trend better follows the patterns from case history observations, indicating the value of EPI. Profiles with multiple critical liquefiable layers at greater depths resulted in base isolation and reduced permanent foundation settlement. Ground motion characteristics have the highest influence on EDPs, among the properties considered. The outcropping rock motion intensity measures with the best combination of efficiency, sufficiency, and predictability were identified as cumulative absolute velocity (for predicting foundation's permanent settlement and free-field EPI) and peak ground velocity (for peak excess porepressure ratio). These results underscore the importance of careful field characterization of stratigraphic layering in relation to the foundation and structural properties to evaluate the potential liquefaction deformation and damage mechanisms. The results also indicate that incorporating EPI alongside traditional EDPs shows promise.

Seismic fragility analysis can quantitatively evaluate the seismic performance of structures from a probabilistic viewpoint and accurately characterize the relationship between the degree of structural damage and ground motion intensity. This study investigates the seismic fragility of shield tunnels in three different liquefiable and non-liquefiable soils. A plane-strain finite element model of the saturated soil and shield tunnel is established via the OpenSees computational platform employing the multi-yield surface elastoplastic PressureDependMultiYield and PressureIndependMultiYield models to simulate the constitutive behaviour of liquefiable and non-liquefiable soils. The developed model is utilized to conduct nonlinear dynamic effective stress time history analyses to generate the seismic fragility curves and surfaces based on the incremental dynamic analysis method. Meanwhile, appropriate scalar- and vector-valued intensity measures are identified based on their correlation, efficiency, practicality and proficiency. Compared with the fragility curves based on scalar-valued intensity measures, the fragility surfaces based on the vector-valued intensity measures can better describe the effect of ground motion characteristics on the structural seismic demand, and thus can more accurately assess the structural seismic performance. The seismic damage probabilities derived from the fragility curves and surfaces reveal that the seismic damage risk of the shield tunnel in sandwiched liquefiable soil deposit is higher than that of the tunnel structure located in entirely liquefiable or non-liquefiable soil profiles. This finding underscores the importance of carefully evaluating the seismic safety of shield tunnels situated in sandwiched liquefiable soil deposits.

Large diameter shield tunnels traversing liquefiable soil-rock strata are highly susceptible to seismic hazards, as earthquake-induced soil liquefaction significantly reduces soil strength and stiffness. Therefore, it is crucial to accurately assess the seismic performance of these tunnels. This study first establishes a numerical model for tunnel seismic response analysis, considering soil liquefaction, segment nonlinearity, and joint deformation. The validity of the model is affirmed through experimental, theoretical, and additional numerical simulations. The probabilistic seismic demand models are established employing the seismic database consisting of 120 ground motion records. Subsequently, a quantitative selection method for the optimal Intensity Measure (IM) based on fuzzy comprehensive evaluation is proposed, identifying Velocity Spectrum Intensity (VSI) as the most suitable among 29 commonly used IMs, and the IMs related to duration exhibit poor performance. The study then categorizes tunnel damage into three states: minor, moderate, and extensive, using joint opening as the damage measure. Finally, seismic fragility analysis is employed to assess seismic performance of tunnel, and fragility curves derived using VSI and Peak Ground Acceleration (PGA) is compared. The results indicate that PGA, a commonly used IM, significantly underestimates the probability of damage to the tunnel, with a maximum underestimation of 22.4%.