Probabilistic Seismic Analysis Research Articles

Probabilistic seismic risk analysis of electrical substations considering equipment-to-equipment seismic failure correlations

When an earthquake occurs, electrical equipment in a substation exhibits a certain level of seismic failure correlation since they suffer similar ground motions and share similar structural characteristics. However, this equipment-to-equipment seismic failure correlation (E2ESFC) was neglected in previous substation-level probabilistic seismic risk analyses due to the lack of awareness and practical approach. To investigate the effect of different degrees of the E2ESFC on the substation seismic risk, an efficient method for considering partially correlated seismic failure was proposed. The concepts of “damage demand probability” and “damage capacity probability” were derived from the equipment's fragility curve. Then the partial correlation of equipment's capacity probabilities can be easily introduced and incorporated into the substation-level risk analysis through the combination of Copula functions and the Monte Carlo simulation. A case study on a real-world 220/110 kV substation using an equi-correlation model demonstrated that ignoring the E2ESFC among the same type of equipment will lead to an underestimate of the probability of seeing high seismic loss. Furthermore, a general method to assess the E2ESFC coefficients between equipment was also proposed, laying the foundation to facilitate applications of the introduced E2ESFC simulation method and to generate a more reliable system risk assessment result.

Probabilistic resilience assessment framework of structures considering the combined functionality-recovery-duration uncertainty

In the current stage, the risk-guided performance-based earthquake engineering (PBEE) has become the main direction in the earthquake community. As an important part of risk, seismic resilience indicators have been increasingly emphasized and elevated to new levels in recent years. Seismic resilience refers to the capacity of social entities to reduce disaster risks and to facilitate recovery efforts with the least social disruption in possible. Currently, the calculations of resilience indicators are commonly based on the deterministic approach. In fact, resilience indicators are also random variables, and the corresponding recovery time, recovery function or residual function in resilience calculation may vary within a range for different intensity levels and limit states. Therefore, characterizing resilience indicators through probabilistic models or confidence intervals can be a more practically valuable and meaningful strategy for future research. In this paper, a probabilistic resilience assessment framework of structures is proposed, and a sinusoidal-based continuous recovery function characterized by different limit states and recovery modes is given. The combined uncertainties of functionality, recovery and duration are incorporated into the framework, and an application example via the reinforced concrete frame is given to implement the framework. Besides, the sensitive analysis of different variables to the resilience assessment result is performed, and the comparison between the deterministic and probabilistic analysis is further discussed. In general, the framework consists of three parts, i.e., (1) Generating samples, fragility and damage states; (2) Calculating total stochastic recovery functions for resilience analyses; and (3) Performing probabilistic seismic resilience analyses. If deterministic analysis is used, the resilience index is only a value, while if probabilistic analysis is used, the resilience index will be a variable with a corresponding probability and distribution range. Compared with other variables, the amplitude and wavelength have a stronger influence in the result of resilience index. This is because these two parameters are function-dependent and will directly affect the envelope curve in the resilience calculation. Although the changes in coefficient of variation (COV) will affect the curve results, the macro characteristics are consistent when comparing different target resilience index. Moreover, as the intensity rises, there is a statistical decrease in both the average residual functionality and resilience indicators, along with a statistical increase in the average recovery durations. The annual exceeding probability decreases as the target resilience level increases, while the life-cycle exceeding probability increases when the target resilience level decreases for the same year. In a sense, the integrated probabilistic resilience framework realizes the decoupling of resilience indicators for different performance groups and limit states, and provides a reference for the further stochastic resilience assessment from a probabilistic perspective.

Impact of local site conditions on seismic performance of free‐spanning submarine pipelines: Underwater shaking table tests and numerical simulations

AbstractLocal site conditions may pose a significant influence on the seismic responses of submarine pipelines by altering both the offshore motion propagation and soil‐structure interaction (SSI). This paper aims to provide an in‐depth understanding of the influence regularity of local site conditions on the seismic performance of free‐spanning submarine pipelines (FSSPs). For this purpose, a suite of underwater shaking table tests were performed to investigate the seismic responses of FSSP subjected to the offshore spatial motions at three site categories. Response comparison factor () is defined to quantify the structural response discrepancies caused by the seismic inputs at different sites. The test results indicate that responses of the studied model FSSP gradually increase as spatial offshore motions at softer soil sites are employed as inputs; and the values of vary with a maximum magnitude of up to 40%–60% for different response indices when the site soil changes from fine sand to clay. Subsequently, the corresponding numerical simulations are carried out to reproduce the seismic responses of the test model. The experimental and numerical results meet a good agreement, indicating that the developed numerical modeling method can accurately predict the seismic responses of FSSPs. Following this verified modeling method and using the p‐y approach to address the SSI effect, fragility surfaces of the studied FSSP are derived in terms of PGA and site parameter (shear‐wave velocity in the top 30 m of the soil profile) via probabilistic seismic demand analyses. The impact of local site conditions on the seismic performance of the FSSP is quantitatively examined by comparing the fragility curves corresponding to various . Furthermore, a fast seismic damage assessment method is proposed for efficiently evaluating the performance of FSSPs buried in various offshore soil conditions. This approach proves beneficial for designers and decision‐makers, enabling accurate estimation of seismic damage and facilitating the implementation of post‐earthquake maintenance measures for FSSPs.

Probabilistic Seismic Stability Analysis of Reinforced Soil Retaining Structures in Partially Saturated Conditions

Probabilistic Seismic Stability Analysis of Reinforced Soil Retaining Structures in Partially Saturated Conditions

Probabilistic seismic hazard model and vulnerability analysis for typical regional structures

Probabilistic seismic hazard model and vulnerability analysis for typical regional structures

Damping‐dependent correlations between horizontal‐horizontal, horizontal‐vertical, and vertical‐vertical pairs of spectral accelerations

AbstractCorrelation coefficients for 5%‐damped spectral accelerations (SAs) of horizontal ground‐motion components have been extensively studied and applied in probabilistic seismic analysis using vector‐valued intensity measures (IMs). Such correlations are, however, not sufficient for structures with different damping ratios under multidirectional earthquake shakings. This paper presents a comprehensive study on the correlations between horizontal‐horizontal (H‐H), horizontal‐vertical (H‐V), and vertical‐vertical (V‐V) pairs of SAs for different damping ratios based on the NGA‐West2 ground motion database. The correlations of SAs with peak ground acceleration (PGA) and peak ground velocity (PGV) are also investigated. The uncertainty in correlations is measured by integrating the bootstrap method into the logic‐tree framework. Comparative results indicate that the correlation coefficients generally increase for IMs of larger damping ratios. The relative difference between the damping‐dependent and conventional 5%‐damped correlation coefficients can be notable, reaching 100% and 35% in the SA‐SA and SA‐PGV (or PGA) pairs, respectively. Based on the empirical correlation results, an artificial neural network is utilized to develop parametric models of the correlations and the executive files for implementing these models are provided. The ANN‐aided damping‐dependent correlation models developed can be considered as a generalization of the conventional 5%‐damped correlation models, and may serve as useful tool in applications such as ground‐motion selection and vector‐valued probabilistic seismic risk assessment for structure systems.

Optimizing net present values of risk avoidance for mountain railway alignments with seismic performance evaluation

AbstractRailway alignment optimization in earthquake‐prone mountainous (EPM) regions should quantify and trade off construction investments and seismic risks. Unfortunately, slight attention has been previously devoted to this trade‐off. To this end, based on the FEMA‐P58 methodology, a net present value (NPV) model of risk avoidance is presented and solved. In the model, alignment alternatives are first segmented into structural groups with different probabilistic seismic fragility curves, which are then used to generate structural repair cost and repair time curves. Afterward, a probabilistic seismic hazard curve is introduced to estimate the expected annual repair cost and time for computing railway direct and indirect seismic losses. Hence, the railway total annual loss caused by seismic activity can be obtained. Next, a benefit–cost analysis is performed to combine construction cost and seismic loss as the risk‐cost NPV. To optimize this objective function, a particle swarm algorithm is used as the basic approach. For implementing the probabilistic seismic performance analysis, a Monte Carlo simulation (MCS) is employed as the risk assessment module. Furthermore, due to the computationally intensive nature of MCS, a CPU‐based parallelization is embedded into the algorithm to expedite the search. Finally, the proposed model and method are applied to a representative real‐world railway case in an EPM region. Their effectiveness is discussed and verified in five experiments, including algorithm convergence analysis, alignment solution comparison, seismic risk interpretation, computational efficiency test, and a specific sensitivity analysis.

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.

Study of seismic vulnerability of steel frame structures on soft ground considering group effect

Earthquakes have caused increasingly severe casualties and economic losses in coastal urban areas where soft soils are widely distributed. To mitigate disaster losses, this paper aims to investigate the mechanism of the group effect, the interaction between a group of buildings (at least three) through the foundation, on seismic vulnerability in coastal urban areas. Firstly, the analysis models are established, and the validity is subsequently verified. Meanwhile, a self-built automatic iterative calculation program for multilayer soils is adopted to consider the nonlinearity of the soft soils. On this basis, probabilistic seismic demand analyses are further performed using ten earthquake ground motions. The seismic vulnerability formulas of the structures are obtained in combination with the probabilistic seismic demand models. Finally, the influence of the group effect on the seismic performance of the structures is evaluated from different perspectives based on the vulnerability formulas. The results indicate that the group effect of the steel frame structures makes the performance margin ratio (PMR) significantly higher and reduces the seismic vulnerability of the structures in coastal urban areas. The mechanism revealed in this paper presents a more accurate way to conduct earthquake-resistant design, provides guidelines for setting the criteria, and is likewise instructive to the seismic design of other structural forms.

Probabilistic Seismic Sensitivity Analyses of High-Speed Railway Extradosed Cable-Stayed Bridges

It is known that the extradosed cable-stayed bridge, a hybrid bridge, possesses the virtues of both classic cable-stayed bridges and girder bridges in mechanical behaviors. In this paper, the sensitivity of seismic fragility demand parameters (SFDP) of a high-speed railway extradosed cable-stayed bridge is studied systematically along with the consideration of structural parameter uncertainty. Based on the probability distribution and correlation of random parameters, the Latin hypercube sampling method is adopted herein. The dynamic 3D finite element model of the employed bridge is established by using powerful and attractive OpenSEES nonlinear software. A nonlinear incremental dynamic analysis is performed to consider the randomness of structural parameters using sampling analysis. Some important conclusions are drawn indicating that the structural design parameter uncertainty predominantly has influence on the SFDP for fragility analysis of bridge structures. The design parameters of extradosed cable-stayed bridges are categorized and identified as primary, secondary and insensitive parameters. The high sensitivity parameters of extradosed cable-stayed bridges for fragility analysis include friction coefficient of bearing, concrete bulk density, damping ratio, peak compressive strength of confined concrete, component size and peak strain of confined concrete. Additionally, the strength and strain of unconfined concrete cannot be ignored. Furthermore, the uncertainty of structural design parameters fails to be responsible for the cable force responses due to larger girder stiffness. The structural design parameter uncertainty has a significant influence on the responses of extradosed cable-stayed bridges for seismic fragility analysis.

Nonparametric probabilistic seismic demand model and fragility analysis of subway stations using deep learning techniques

A novel and computationally efficient method for developing a nonparametric probabilistic seismic demand model (PSDM) is proposed to conduct the fragility analysis of subway stations accurately and efficiently. The probability density evolution method (PDEM) is used to calculate the evolutionary probability density function of demand measure (DM) without resort to any assumptions of the distribution pattern of DM. To reduce the computational cost of a large amount of nonlinear time history analyses (NLTHAs) in the PDEM, the one-dimensional convolutional neural network (1D-CNN) is used as a surrogate model to predict the time history of structural seismic responses in a data-driven fashion. The proposed nonparametric PSDM is adopted to conduct the fragility analysis of a two-story and three-span subway station, and the results are compared with those from two existing parametric PSDMs, i.e., two-parameter lognormal distribution model and probabilistic neural network (PNN)-based PSDM. The results show that the PDEM-based PSDM has the best performance in describing the probability distribution of seismic responses of underground structures. Different from the fragility curves, the time-dependent fragility surface of the subway station shows how the exceedance probability of damage state changes over time. It can be used to estimate the escape time and thus the number of casualties in an earthquake, which are important indexes when conducting the resilience-based seismic evaluation.

Two-Parameter–Based Damage Measure for Probabilistic Seismic Analysis of Concrete Structures

Traditional seismic fragility analysis defines the structural damage measure (DM) as a single parameter based on either strength, displacement, damage, or energy to evaluate the postearthquake performance of the structure, thus it is difficult to fully catch the behavior characteristics of the structures, e.g., both the maximum deformation capacity and the repairability of the structure. In this paper, we developed a multiparameter-based DM (mDM) index (here actually two parameters) for the probabilistic seismic analysis of reinforced concrete (RC) structures to capture a more comprehensive view of structural performance. Two parameters (i.e., the maximum interstory drift ratio θmax and the maximum residual interstory drift ratio θr,max) are combined to represent the overall structural performance, and different combination rules are investigated. To verify the superiority of the proposed mDM, the fragility analysis of three different structures is conducted, i.e., ordinary RC structure, aging RC structure, and new self-centering structure. The fragility curves derived from single DM and mDM are compared, and it is found that fragility curves with mDM can reflect both the maximum displacement and residual displacement features of the structure, thus mDM gives a more comprehensive and synthesis assessment of the postearthquake performance of the structure, which is beneficial for informed decision-making.

Seismic Fragility Assessment of RC Columns Exposed to the Freeze-Thaw Damage

Freeze–thaw damage is one of the primary causes deteriorating the seismic resistance of reinforced concrete (RC) structures. This paper proposed a freeze–thaw damage deterioration model for C30 concrete, and it can be employed to study the time-varying seismic performance of aging RC columns. Next, this study developed a seismic fragility analysis framework for deteriorating RC columns considering the effect of freeze–thaw damage. Considering the geometric parameters of the case-study bridge, the deterioration characteristics of material, and the uncertainties involved in structural modeling and ground motions, a probabilistic seismic fragility analysis on aging RC columns was conducted. The results indicate that the influence of freeze–thaw damage cannot be ignored in studying the seismic performance of aging RC structures. The seismic fragilities of deteriorating RC columns shown a nonlinear increase trend as the increased of freeze–thaw cycles and severity of the damage state. In the early stage of freeze–thaw cycles, the seismic fragilities of RC columns increased slowly. However, the closer to the later stage of freeze–thaw cycles, the more significant of the increase in the seismic fragilities of the columns.

Assessment of various seismic fragility analysis approaches for structures excited by non-stationary stochastic ground motions

A probabilistic assessment is performed using different seismic fragility analysis approaches for structures under non-stationary stochastic ground motions. Four commonly used probabilistic seismic fragility analysis (PSFA) approaches are adopted, which are least squares regression (LSR), maximum likelihood estimation (MLE), kernel density estimation (KDE) and Monte Carlo simulation (MCS). The principles of the four PSFA approaches are first introduced, and the theories of non-stationary stochastic acceleration time series are introduced in light of the spectral representation of random functions. Then an analytical procedure of different PSFA approaches is constructed for structures under non-stationary stochastic motions. After that a case study is carried out to analyze the results of the four PSFA approaches. The demand distributions of univariate random variable under certain intensity measure levels are discussed, and multiple fragility curves under different limit states for all the approaches are compared. In general, the MCS approach is set as the benchmark to verify the effectiveness of other approaches, but it is computationally consuming. The non-parametric KDE approach is recommended to estimate the univariate distribution under specified IM levels, because it can reflect the real distribution characteristics with combined efficiency and accuracy. For the seismic fragility under different limit states, the LSR approach is suitable for efficient data processing and general trend assessment, at the expense of accuracy. The MLE approach indicates a better applicability under a smaller response threshold and slighter damage conditions, while the KDE approach shows a better applicability under a larger response threshold and severer damage conditions. The paper compares the accuracy and applicability of various PSFA approaches under multiple conditions, and provides a basis to link probabilistic hazard and risk analyses for performance assessment in the future research.

Probabilistic assessment of seismic response of toe-excavated hillslopes retained using anchored sheet-pile-wall

This paper reports the probabilistic seismic stability analyses conducted for toe-excavated hillslopes, both for unsupported slopes and that retained by anchored sheet pile wall system. Both pseudo-static and nonlinear dynamic analyses are carried out to decipher the seismic response of toe-excavated hillslope. It is found that due to incorporation of uncertainty in the soil parameters or seismic coefficients, slope sections otherwise rendered safe from deterministic analyses can exhibit significant probability of failure. Further study highlights that pseudo-static analysis overestimates the slope failure probability as compared to the nonlinear dynamic analysis. In this study, the probability of failure of the cut slope obtained from the nonlinear analysis (ranges between 21.4% and 70.1%, with a mean Pf value hovering at approximately 45%) is highly overestimated in a pseudostatic analysis, approximately in the tune of 68%. A significant effect of the correlation length characterizing the spatial variation of soil shear strength parameters on the seismic response of toe-excavated slopes is also manifested and reported. The present study shows that a cut slope retained with SPAR system exhibits a very low probability of failure for dimensionless correlation length value up to 0.1 under the cases of dynamic excitation.

Exploring benefit cost analysis to support earthquake risk mitigation in Central America

We performed benefit-cost analysis to identify optimum retrofitting interventions for the two most vulnerable building typologies in Central America, unreinforced masonry and adobe, considering the direct costs due to building damage and the indirect costs associated with the injured and fatalities. We reviewed worldwide retrofitting techniques, selected those that could be applied in the region for these building types, and derived vulnerability functions considering the impact of each retrofitting intervention in the strength, stiffness, and ductility of the structures. Probabilistic seismic risk analyses were performed considering the original configuration of each building class, as well as the retrofitted version. We calculated average annual losses to estimate the annual savings due to the different structural interventions, and benefit cost ratios were estimated based on the associated cost of each retrofitting technique. Based on the benefit-cost analyses, for a 50-year time horizon and a 4% discount rate, retrofitting these building classes could be economically viable along the western coast of Central America.

Time-Dependent Seismic Fragility of Typical Concrete Girder Bridges under Chloride-Induced Corrosion.

Recent studies highlighted the importance of the combined effects of prestress loss and corrosion deterioration for concrete girder bridge structures when the effect of damage on the performance level is estimated. The multi-deterioration mechanisms connected with chloride erosion include the cross-sectional area loss of longitudinal bars and stirrups, the reduction in the ductility, the decrease in the strength of steels and the strength loss of concrete in RC columns. For the corroded RC columns and corroded elastomeric bridge bearings, analytical models of the material degradation phenomena were employed for performing the probabilistic seismic performance analysis, which could obtain the system seismic fragility of aging bridges by considering the failure functionality of multiple correlated components (e.g., columns, bearings). The combined effects of prestress loss and cracking were also considered when developing time-dependent system seismic fragility functions. Here, a typical multi-span reinforced concrete girder bridge was used as a case study for studying the time-variant seismic performance. The results revealed the importance of the joint effects of the multi-deterioration mechanisms when modeling the time-dependent seismic fragility of aging bridge systems, as well as the significance of considering the combined effects of prestress loss and cracking.

Probability seismic demand and fragility analyses of novel SMA-based self-centring eccentrically braced frames

This paper performs the seismic assessment of novel shape memory alloy (SMA)-based self-centring (SC) eccentrically braced frames (EBFs) by using probabilistic seismic demand analysis (PSDA) and probabilistic seismic fragility analysis (PSFA). The structural finite element models are established based on a previous prototype building and verified through test results. The PSDA is based on a set of 176 seismic records, and Sa avg is chosen as the proper intensity measure for max inter-storey drift ratio (MIDR) and max inter-storey residual drift ratio (MIRR); whereas peak ground acceleration is more suitable for peak floor acceleration (PFA). After the PSDA results are obtained, time-history analyses and PSFA are conducted. Compared with traditional steel EBFs, the SMA-based SC-EBF shows a slight weakness in MIDR due to the comparatively small energy dissipation capacity but has an apparent advantage in controlling MIRR due to a good SC capacity provided by SMA angles. Furthermore, although the steel EBF with fixed column bases has the smallest MIDR, the fixed bases cause extra damage in column bases, which will bring other problems in post-earthquake rebuild and deviate from the design target of concentrating damage in link beams. The variability of the PFA is small, showing that the influence of structural forms on PFA is not apparent. Considering the overall structural seismic performances in terms of MIDR, MIRR and PFA, SMA-based SC-EBF can be a promising alternative in future seismic-resistant designs.

Probabilistic seismic responses and failure analyses of free-spanning subsea pipelines under offshore spatial earthquake motions

A comprehensive literature review in seismic analysis of free-spanning offshore pipelines (FSOPs) reveals that two critical aspects, i.e. the offshore earthquake motions and various uncertainty sources, have been normally ignored in numerous previous studies. Specifically, the offshore pipelines are usually modeled by assuming all the structural parameters to be fixed and are excited using the onshore earthquake motions. Such analytical schemes may result in severe misestimates of seismic response predictions of FSOPs. In this paper, a probabilistic approach is developed for numerically investigating the seismic responses and failure mechanisms of FSOPs subjected to the offshore spatial earthquake motions (Off-SEMs). For this purpose, a buried offshore pipeline of API X65 with a free span of 30 m is selected and the corresponding three-dimensional finite element (3D FE) model is established in the ABAQUS software, where the soil–pipe and water–pipe interactions are modeled using the nonlinear soil springs and added mass and damping methods, respectively. Then, the three-dimensional Off-SEMs are stochastically synthesized by explicitly considering the effects of spatial variability and overlying seawater. Next, the general law of dynamic responses and failure modes of FSOPs subjected to the Off-SEMs is analyzed and summarized by the deterministic dynamic analysis. Defining the earthquake motions, structural modeling and soil properties as uncertain sources, the relative sensitivity of seismic behaviors to uncertain parameters involved in these uncertain sources is identified separately by the sensitivity analysis. Finally, uncertainty analysis is performed to examine and discuss the influence of different types of uncertainty sources on the seismic behaviors of FSOPs. Numerical results indicate that the pipeline diameter has the highest influence on the seismic behaviors of FSOPs, while the Poisson’s ratio of pipeline material has the smallest effect; uncertainties in earthquake motions, structural modeling and soil properties have significant contributions to the dynamic characteristics and seismic behaviors.

Probabilistic seismic analysis of bridges through machine learning approaches

Probabilistic seismic demands of bridge components such as bridge column and deck are conventionally expressed as a power-law function of a single ground motion intensity measure. This unidimensional probabilistic seismic demand model (PSDM) was introduced more than two decades ago, and since then, it was commonly used to estimate seismic demands. Over the recent years, an extensive body of research has been evolved to propose alternative PSDMs, but none has been proved to be dominantly superior over other approaches. There yet remains a milestone to enrich predictions provided by PSDMs and expanding their application beyond certain methodology, particular functional form, and corresponding assumptions on the distribution of the demands. Given the advancements in computational technologies which lead to the growth of diverse analytically-driven data, machine learning (ML) approaches have a tremendous potential to revolutionize predictions of seismic demands. This study presents a comprehensive appraisal of ML-based PSDMs to further expand the research advances in this domain and leverage the efficiency and advantages that ML methods offer compared to the unidimensional model. To this end, the efficiency of a variety of parametric and non-parametric ML algorithms with different degrees of flexibility are explored to estimate the demands associated with the primary bridge components. Moreover, by applying ML-based variable selection techniques, this study assesses the level of influence of the random variables on the generated PSDMs. These variables are used for the treatment of inherent uncertainties in material, geometric, structural, and ground motion parameters. As part of the appraisal, a ranking is provided for the investigated 39 models, such as Generalized Linear Models, Multi-order regressions, Bagging and Boosting, and Kernel-based models, according to their statistical performance in estimating the individual demands.