Seismic Vulnerability Curves Research Articles

Analysis of the Seismic Vulnerability of a Masonry Pagoda Based on Increasing Dynamic Analysis

ABSTRACTFor the seismic vulnerability analysis method of masonry pagodas, the dynamic characteristic of the Bayun Pagoda in China was conducted by using environmental excitation technology. A numerical model of the masonry pagoda was established with the finite element software Abaqus. Ten seismic waves were selected as excitation signals to conduct incremental dynamic analysis (IDA) on the pagoda. The Sa(T1,5%) served as the seismic intensity indicator, whereas the damage factor (d) and relative stress () were employed as damage indicators for seismic vulnerability analysis of the pagoda. The failure probability of the structure reaching the limit state under different seismic intensities was determined. The results indicate that, comparing the IDA curves and seismic vulnerability curves under two different damage indicators, the Sa(T1,5%) range required for the IDA curves under the damage factor (d) is smaller than the relative stress (), with lower dispersion. Additionally, the failure probability of the pagoda reaching different limit states is higher under the damage factor (d). Considering the existing damage status of the masonry pagoda, the damage factor (d) is more reasonable as the damage indicator.

Vulnerability-based seismic resilience and post-earthquake recovery assessment for substation systems

The function of substation systems is significantly influenced by earthquakes. To assess the seismic resistance of substation systems and improve post-earthquake recovery efficiency, this study constructs a multi-module framework for seismic vulnerability assessment of substations. Based on the equipment functional status analysis module, a functional network model was established considering the structural function and electrical load of substation systems. The system functional state matrix was obtained through Monte Carlo simulation, and the seismic vulnerability was assessed from the aspects of electrical transmission reliability and the importance of power users. Subsequently, a substation functional index was established based on seismic vulnerability parameters. Post-earthquake functional recovery strategy analysis frameworks were constructed to quantitatively evaluate the recovery process. A stepped functional time-varying function was proposed through iterative analysis, thereby converting the probability parameters of functional status into seismic resilience deterministic indices. Through seismic resilience analysis of a typical 220 kV step-down substation, seismic vulnerability curves for both electrical transmission and power users were obtained. Furthermore, the seismic sensitive intervals of the substation and key equipment for post-earthquake recovery were clarified. Notably, the seismic resilience level and optimal recovery strategy of the typical 220 kV step-down substation were determined.

Seismic vulnerability analysis of hospitals and school buildings considering the Gaussian regression algorithm

This study combines the Gaussian regression algorithm to propose a nonlinear regression model that can be used to evaluate the seismic vulnerability of regional hospitals and school buildings. The failure features and disaster mechanisms of hospital and school buildings affected by the Jishishan (JSS) earthquake on December 18, 2023, and the Wenchuan (WC) earthquake on May 12, 2008, were reported. The samples of 252 damaged buildings (37 hospitals and 215 schools) in Dujiangyan city affected by the Wenchuan earthquake for which the author participated in the survey were collected and counted. Hospitals and school buildings were classified according to the types of reinforced concrete (RC) and masonry structures, and earthquake vulnerability probability matrices for hospital and school building clusters were established considering the actual failure probabilities. A total of 2103,213 acceleration records (from the Wenchuan earthquake) monitored by 12 real stations were selected. Using dynamic time history and response spectrum analysis methods, time history and spectrum curves were generated, considering the influence of different seismic directions. Using the developed Gaussian regression model, vulnerability comparison curves and parameter matrices considering multiple regression algorithms were generated. This paper considers the effects of the construction year and number of floors on the seismic vulnerability of hospital and school buildings. Seismic vulnerability curves and failure probability matrices were generated and established on the basis of actual structural failure probabilities. According to regression and vulnerability surface analysis, the evaluation results of the proposed model are highly consistent with actual field observations.

Dynamic response and seismic vulnerability assessment of the near-fault steep slope

Existing field data demonstrates that structures situated near faults, such as slopes, dams, and bridges, are particularly vulnerable to damage. Near-fault ground motions exhibit marked disparities from their far-field counterparts, necessitating thorough investigation. This study conducts a comprehensive analysis of ground motion characteristics utilizing response spectra, Hilbert-Huang Transform (HHT), and marginal spectra to discern near-fault pulse-like ground motions (PLGMs), near-fault non-pulse-like ground motions (NPGMs), and far-fault ground motions (FFGMs). PLGMs distinguished by their heightened energy content, typically induce more pronounced amplification effects compared to NPGMs and FFGMs. Employing an efficacy criterion, optimal intensity measures (IMs) are identified and linked to dynamic response, referred to as engineering demand parameters (EDPs). Velocity-based IMs demonstrate substantial correlations across diverse ground motion types for both plastic volume ratio (PVR) and crest displacement (Dc). Lastly, probabilistic seismic demand models are leveraged to establish seismic vulnerability curves for steep slopes exposed to PLGMs and NPGMs. Notably, with Dc as the EDP, the exceedance probabilities associated with the three IMs under PLGMs generally surpass those under NPGMs. This underscores the propensity of PLGMs to trigger larger displacements in slopes, rendering them more prone to failure.

Comparative Study on the Seismic Vulnerability of Continuous Bridges with Steel–Concrete Composite Girder and Reinforced Concrete Girder

For medium- and small-span bridges, the weight of the superstructure in steel–concrete composite girder bridges is lighter than that of a reinforced concrete girder bridge. However, it is still uncertain whether steel–concrete composite girder bridges exhibit superior seismic performance compared to reinforced concrete girder bridges. This study quantitatively compared the seismic performance of the two types of bridges. Using the theory of probabilistic seismic demand analysis, the seismic vulnerability curves of bridges were derived. To conduct seismic demand analysis for probabilistic analysis on the OpenSEES platform, bridge samples were generated using the Latin hypercube stratified sampling method, which considers the uncertainties associated with the two types of bridges. The vulnerability curves of the piers, bearings, abutments, and the system of the two bridges were established using probabilistic analysis of the time history analyses. The results showed that the seismic vulnerabilities of components and the overall system of the steel–concrete composite girder bridge were both lower than those of the reinforced concrete girder bridge. When the peak ground acceleration (PGA) of the ground motion was 0.3 g, the moderate and serious damage probabilities of the piers in the steel–concrete composite bridge were only 54.61% and 60.89%, respectively, of those of the reinforced concrete bridge. Consequently, replacing the upper reinforced concrete girders with steel–concrete composite girders can significantly improve the seismic performance of a large number of existing bridges.

Seismic Vulnerability Curves for Non-reinforced Asymmetric Masonry Buildings Retrofitted with External Shotcrete: A Case Study on Control and Switchgear Room of Power Substations

Seismic Vulnerability Curves for Non-reinforced Asymmetric Masonry Buildings Retrofitted with External Shotcrete: A Case Study on Control and Switchgear Room of Power Substations

Sensitivity of seismic vulnerability curves of high-speed railway bridges to the quantity of ground motion inputs

Ground motion input uncertainties may significantly affect structural seismic responses, resulting in an overestimation or underestimation of structural vulnerability results. To address this issue, a typical high-speed railway (HSR) bridge is taken as an example in this study, and a minimum quantity of ground motion inputs to balance computational costs and calculation accuracy. Seismic responses and vulnerabilities of multiple bridge components are first obtained using incremental dynamic analysis (IDA) and probabilistic seismic demand model (PSDM). The system vulnerability is then evaluated by using first-order bounds. Finally, the sensitivity of seismic vulnerability to the quantity of ground motion inputs is explained through statistical theory. Analytical results show that increasing the quantity of ground motion inputs from 3 to 7 can effectively reduce the calculation error from ±38% to ±15%. A minimum quantity of 11 ground motion inputs is strongly recommended for seismic vulnerability analysis to ensure acceptable calculation accuracy (≥94%).

Post-earthquake seismic assessment of residential buildings following Sarpol-e Zahab (Iran) earthquake (Mw7.3) – Part 2: Seismic vulnerability curves using quantitative damage index

One of the most crucial steps in disaster management and decision-making is a quick and reliable seismic evaluation of structures following an earthquake. Vulnerability curves, which relate the earthquake intensity measure to damage states, are key terms in performing post-earthquake assessments. In most previous research, empirical vulnerability curves were roughly developed using qualitative criteria. Current research proposes a novel damage index based on the suggested damage states resulting from field investigation of more than 81 damaged steel and RC buildings after the Sarpol-e Zahab (Iran) earthquake. The proposed damage index provides relatively precise information about damaged buildings. Then, using the spectral acceleration derived from the conditional ground motion intensity and the proposed damage index, empirical vulnerability curves are generated for RC and steel buildings and non-structural walls. The developed empirical vulnerability curves are valuable due to the lack of similar field studies on damaged buildings under severe earthquakes and are consistent with common practice of construction in Iran. Past earthquakes' data can be used in seismic risk assessment and planning for mitigation of losses in the future.

Earthquake Economic Loss Assessment of Reinforced Concrete Structures Using Multiple Response Variables

For buildings that meet the requirements of current seismic design codes, damage to nonstructural components and the internal objects of buildings often become the main source of the seismic economic losses of these buildings. However, the current specifications only consider the safety of ‘no collapse under strong earthquake’ and do not consider ‘functional recoverability’. In this paper, a six-story frame building was taken as an example. Four joint performance limit states were proposed, as per FEMA 273, to establish a two-dimensional probabilistic seismic demand model that considers parameter correlations. The limit state function was established, and the two-dimensional seismic vulnerability curve was calculated. The seismic intensity–economic loss curve and the annual average economic loss established by one-dimensional and two-dimensional seismic vulnerability curves were compared. The results showed that the seismic performance of the structure was lower than expected when using only a one-dimensional seismic vulnerability curve. However, the situation was more serious under high-intensity earthquake and high-performance levels.

Seismic Vulnerability Analysis of Long-Span Prestressed Concrete Composite Box Girder Bridge with Corrugated Steel Webs under Construction

In order to address the difficulty in determining the seismic damage probability of continuous girder bridges under construction, the seismic vulnerability analysis method of the construction state is proposed in this study. Firstly, taking a long-span prestressed concrete composite box girder bridge with corrugated steel webs (OSW) as an example, the finite element models (FEMs) of dynamic calculation in different phases of cantilever construction are simulated by OpenSEES. Secondly, by selecting reasonable seismic waves and seismic intensity measures, the non-linear time-history analysis is carried out, followed by the demand parameters and damage indexes suitable for the construction state proposed. Finally, the probabilistic seismic demand model (PSDA) of the continuous box girder bridge during the construction stage is constructed by using the “cloud method”, and the seismic vulnerability curves of the piers and temporary bearings are established to evaluate the seismic performance during the construction stage. The results indicate that the damage probability of piers and temporary bearings increases with the progress of construction. The initial formation of the cantilever structure and the sudden change in the size of the construction segmental girder correspond to a high probability of damage, and seismic protection measures should be strengthened during this construction state. Moreover, significantly higher damage probability of the components under construction compared to the completed bridge after it is built.

Study on seismic vulnerability analysis of the interaction system between saturated soft soil and subway station structures

The seismic vulnerability of interaction system of saturated soft soil and subway station structures was explored in this paper. The coupled nonlinear numerical models of interaction system were established using the u–p formulation of Biot′s theory to describe the saturated two-phase media. A refined finite element model of interaction system was developed to study its nonlinear seismic responses and seismic hazard mechanism. In this study, the multi-yield elastoplastic constitutive model was adopted for the soil, while a fiber section elastoplastic constitutive model was used for the structure. The seismic response of the structure was calculated by inputting the artificial seismic wave obtained from the power spectrum-triangular series method. The maximum inter-story drift angle was taken as a structural performance parameter for the subway station structure. The structural demand cloud was obtained under random ground motion sequences. Based on the probabilistic seismic demand model analysis method, the seismic vulnerability curve of the subway station structure was plotted, and the seismic vulnerability curve was analyzed as per the vulnerability of performance parameters. With the increase of soil strength, the vulnerability index of subway station structure under different peak acceleration ground motion decreased correspondingly. Based on the above vulnerability theory and analysis methods, it can be found from the above vulnerability theory and analysis methods that the subway station structure with established buried depth in saturated soft soil site exhibits a certain degree of safety and reliability, and can meet the seismic fortification goal of "no damage in small earthquakes, repairable in medium earthquakes and no collapse in large earthquakes". The results of vulnerability analysis are in line with the actual seismic survey, and the vulnerability analysis method proposed in this paper can be applied to the vulnerability analysis of underground structures on saturated soft soil foundation.

Seismic Vulnerability Analysis of Multi-main-span High Pier Continuous Rigid-frame Bridge in Terms of Cloud Method

Due to the complex canyon topography in southwestern regions of China, several multi-main-span high pier continuous rigid-frame bridges (MHPCRFBs) are built to meet the special terrain. Owing to the great effect of high-order modes, the seismic responses of MHPCRFBs are more complicated than the conventional signal main span continuous rigid-frame bridges. However, there has been very limited researches focus on the seismic vulnerability of MHPCRFBs. This study selects a practical five-span (three main span) high pier continuous rigid-frame bridge as a study object to investigate the seismic vulnerability of MHPCRFBs under near-field pulse-like seismic wave excitation. And a finite element model of the example bridge is built by OpenSees incorporating the influence of abutment, and simultaneously 100 near-field pulse-like seismic waves are chosen to research their effect on the seismic vulnerability of the MHPCRFB. The dynamic nonlinear time-history analyses are carried out to record the peak demand values of the example bridge under three seismic excitation calculation cases (longitudinal earthquake, biaxial earthquake, and triaxial earthquake). Thirty-three intensity measures are compared with respect to two statistical parameters including correlation efficient and root mean square error, the peak ground velocity (PGV) turns out to be the optimal intensity measure for seismic vulnerability analysis of MHPCRFB. Subsequently, by using the analysis procedures of the cloud method, the seismic vulnerability curves of MHPCRFB are developed and compared. The results of this study show that the bottom and top areas of the high piers are more fragile at the slight and moderate damage stages along longitudinal direction, and only the bottom areas are prone to damage along transverse direction. And the seismic wave excitation directions have an obvious influence on the seismic damage probability of the MHPCRFB. In addition, the zone with larger failure probabilities of the lower pier is significantly longer than the higher pier. The obtained results provide helpful reference for the seismic-resistant design and consolidation of MHPCRFBs, shed light on the lower pier of MHPCRFBs should be paid high concern to the anti-seismic design.

Seismic risk to beam end corner in railway bridges

The beam end of the railway bridge is the crucial part of the whole bridge, and the earthquake will cause damage to the beam end. In order to ensure the safety of the bridge and track system. To investigate the risk of seismic deformations at the beam end in railway bridges, a three-span continuous rigid frame bridge was taken as a case study and a three-dimensional finite element model of the whole bridge was established in ABAQUS. The deformation angle of the beam end was selected as the damage index, and the seismic vulnerability and risk curves of the beam end were calculated by the incremental dynamic analysis (IDA) method using 22 scaled ground motion time histories. The results show that in the same range of peak ground accelerations (PGAs), the influence of cross-bridge ground motion on the corner deformations of the beam end was much greater than that of the along-bridge ground motion. Under the along-bridge seismic excitation, the damage probabilities for the rotation angles in X, Y and Z-directions did not exceed 50 %. In different damage states, increasing in PGA correlated positively with the beam end damage probability. The vulnerability curves for PGA can be used for the seismic risk assessment of the beam end and can also provide decision support for prioritizing the seismic reinforcement of bridges.

Seismic Vulnerability Analysis of Masonry Structures Built with Disassembled Brick Wall Sections

Disassembling brick wall pieces into brick wall sections and constructing masonry buildings with disassembled brick wall sections (DBWSs) can reduce construction waste production at source and help achieve carbon peak and carbon neutrality. A finite element model (FEM) for typical MSBD is established based on the calibrated finite element analysis method to evaluate the seismic performance of masonry structures built with disassembled brick wall sections (MSBD). Subsequently, the peak ground acceleration is selected as the ground motion intensity index, and the maximum inter-story displacement angle is chosen as the structural damage index. The 20 ground motion records are selected and scaled by peak acceleration in 0.2 g steps to form 120 structure-ground vibration samples for incremental dynamic analysis (IDA) and seismic vulnerability analysis. The IDA results indicated that with the gradual increase in peak ground acceleration, the maximum inter-story displacement angle increases and the model transits from the elastic stage to the elastoplastic stage. Because the characteristics of ground motion records are different, the order of structural plasticity development will be different and the number of ground motion records needs to be considered in the seismic performance assessment. The calculation model will not collapse under the 7 and 8 degree design-based earthquake and the probability of moderate and severe damage of the structure under the rare earthquake is minimal, according to the seismic vulnerability curves. The seismic vulnerability analysis results indicate that MSBD has good seismic performance under earthquakes and meets the requirements of “perfect subjected to frequent earthquake, reparable subjected to design based earthquake, no collapse subjected to rare earthquake.” The seismic vulnerability analysis based on probability statistics can provide a reference for seismic design and evaluation of earthquake damage.

SEISMIC VULNERABILITY ANALYSIS OF CABLE-STAYED BRIDGE DURING ROTATION CONSTRUCTION

Due to the swivel construction, the structural redundancy of cable-stayed bridge is reduced, and its seismic vulnerability is significantly higher than that of non-swirling construction structure and its own state of formation. Therefore, it is particularly important to study the damage changes of each component and stage system during the swivel construction of cable-stayed bridge under different horizontal earthquakes. Based on the construction of Rotary Cable-stayed Bridge in Haxi Street, the calculation formula of damage exceeding probability is established based on reliability theory, and the damage calibration of cable-stayed bridge components is carried out, and the finite element model of cable-stayed bridge rotating structure is established. The vulnerable parts of the main tower and the stay cable components of the cable-stayed bridge are identified and the incremental dynamic analysis is carried out. Finally, the seismic vulnerability curves of the main tower section, the stay cable and the rotating system are established. The results of the study show that the vulnerable areas of the H-shaped bridge towers are the abrupt changes in the main tower section near the upper and lower beams, and the vulnerable diagonal cables are the long cables anchored to the beam ends and the short cables near the main tower；At the same seismic level, the damage exceedance probability of main tower vulnerable section of cable-stayed bridge under transverse earthquake is greater than that under longitudinal earthquake, the damage exceedance probability of vulnerable stay cables under transverse seismic action is less than that under longitudinal seismic action；On the premise of the same damage probability, the required ground motion intensity of the system can be reduced by 0.35g at most compared with the component；Under the same seismic intensity, the system damage probability is 6.60 % higher than the component damage probability at most. The research results have reference significance for the construction of rotating cable-stayed bridges in areas lacking seismic records.

Influence of spiral anchor composite foundation on seismic vulnerability of raw soil structure

A typical single-layer raw soil structure in villages and towns in China is taken as the research object. In the probabilistic seismic demand analysis, the seismic demand model is obtained by the incremental dynamic time history analysis method. The seismic vulnerability analysis is carried out for the raw soil structure of non-foundation, strip foundation, and spiral anchor composite foundation, respectively. The spiral anchor composite foundation can reduce the seismic response and failure state of raw soil structure, and the performance level of the structure is significantly improved. Structural requirements sample data with the same ground motion intensity are analyzed by linear regression statistics. Compared with the probabilistic seismic demand model under various working conditions, the seismic demand increases gradually with the increase of intensity. The seismic vulnerability curve is summarized for comparative analysis. With the gradual deepening of the limit state, the reduction effect of spiral anchor composite foundation on the exceedance probability becomes more and more obvious, which can reduce the probability of structural failure to a certain extent.

Seismic vulnerability analysis for shallow-buried underground frame structure considering 18 existing subway stations

The variability of structural engineering parameters is not accounted for in available literature on seismic vulnerability of underground frame structures. This study investigates the seismic vulnerability of 18 existing subway stations with different site condition, structural stiffness, reinforcement ratio and buried depth employing two-dimensional (2D) finite element analysis considering soil-structure interaction. The peaks of structure inter-story drift ratio under different earthquake intensity of different ground motion records are obtained from non-linear dynamic time-history analysis. Taking the inter-story drift ratio as the damage measure (DM) and the peak ground acceleration (PGA) as the ground motion intensity measure (IM), the seismic vulnerability curves of 18 subway stations are constructed. The comparison of seismic fragility curves of different subway stations demonstrates that site conditions are critical to the post-earthquake structure probability of failure. Furthermore, representative seismic fragility curves are established based on the data collected form the computed results of 18 subway stations, which can aid in evaluating the seismic performance of existing urban underground frame structures in China. The results of this study can provide reference for the performance-based seismic design of urban underground frame structures.

System Vulnerability Analysis Simulation Model for Substation Subjected to Earthquakes

To evaluate the earthquake-resistance capability of an entire substation, which is a complex multi-input-multi-output system (MIMOS) composed of many various types of electrical equipment interconnected by conductors, a flow-based analysis model integrating the merit of the flow block diagram and state tree method was introduced. Two performance indicators of a substation were defined from different stakeholders, one is the expected total power transmission capacity and the other is the power accessibility to the targeted users from the substation. And directed graph logic system analysis models were developed on the Simulink platform based on the original internal logic relationship among distributed components and the power delivery path in the substation with different function types. Afterward, the defined reliability indicators associated with the overall system under a certain seismic intensity level can be obtained by combining the seismic vulnerability curve at the equipment level through the Monte Carlo simulation method. The feasibility and accuracy of the proposed system vulnerability analysis model were verified by comparison with the analytical solution through the illustrative simple MIMOS. Then A case study on a practical 220/110 kV substation was conducted, the analysis results can assist decision-makers in seismic optimization of different retrofitting measures and distribution plans for substations.

Seismic vulnerability analysis of vertical pile-supported wharf structure

In order to study the seismic vulnerability of pile-supported wharf structure, taking a vertical pile-supported wharf as the research object and considering the influence of the site, seismic spectrum characteristics and the uncertainty of ground motion intensity, we establish a dynamic nonlinear numerical model of structure-foundation soil coupling of vertical pile-supported wharf by using the geotechnical finite element software of Midas GTS NX. Selecting the maximum strain of pile foundation in soil as the damage index, we obtain the seismic vulnerability curves and the corresponding damage state probability based on the the incremental dynamic analysis method. The analysis results show that when peak ground acceleration is less than 0.80<italic>g</italic>, the wharf structure is mainly in mild damage state or moderate damage state, otherwise the probability of serious damage basically exceeds 50% and the structure will lose operational capacity. Based on the vulnerability analysis of pile foundation damage in foundation soil, the influence of earthquake on the vertical pile-supported wharf is described from macroscopic and quantitative point of view, which can provide reference for seismic design and disaster prevention prediction of vertical pile-supported wharf.

Seismic loss dynamics in three Asian megacities using a macro-level approach based on socioeconomic exposure indicators

Scrutinizing the evolving exposure and possible consequent forthcoming seismic losses in rapidly urbanizing megacities is essential for decision-makers. Here we present a framework for the evaluation of spatio-temporal seismic loss dynamics where we propose a probabilistic macro-level loss estimation approach that is based on socioeconomic exposure indicators. We follow this framework to model the urban growth, disaggregate population to urban cells, and estimate grid-level wealth in three Asian megacities, namely Jakarta, Metro Manila, and Istanbul. Then, we calculate present and future probabilistic risk metrics based on the combination of evolving exposure, probabilistic seismic hazard analysis and vulnerability curves. The results reveal that our approach can produce present loss estimates that are in the same order of magnitude as the conventional approaches. The predictions suggest that present average annual loss could increase almost twofold in Jakarta and in Metro Manila, and by almost 57% in Istanbul by 2030. Our framework can be used to trigger discussions between scientific community and decision-makers for better long-term risk reduction and risk awareness strategies.