Probabilistic Seismic Assessment Research Articles

Effects of probability model misspecification on the number of ground motions required for seismic performance assessment

The number of ground motions used in nonlinear response history analysis (NRHA) determines the precision of the parameter estimates obtained in seismic performance assessments. While this issue has been extensively studied in the earthquake engineering literature, the relationship of probability model misspecification to parameter estimation uncertainty, and the implication to the required number of ground motions needed for NRHA, has not been examined. Probability model misspecification has the potential to increase estimation uncertainty and hence requires a greater number of ground motions to achieve the same precision compared to when misspecification is disregarded. This study develops a procedure to determine the required number of ground motions in seismic code-prescriptive and risk-based assessments with possible probability model misspecification. Specifically, we employ the quasi-maximum likelihood estimation (QMLE), which is robust to probability model misspecification, to evaluate estimation uncertainty. The QMLE approach is applied to an archetype California bridge under the two seismic assessment scenarios. In the code-prescriptive assessment, misspecification errors are identified for dispersion estimates of the bridge column ductility demand. In the most extreme case of the risk-based evaluation, misspecification increases the estimation uncertainty of the mean annual frequency of exceeding a limit state by as much as three times, which substantially increases the required number of ground motions. Based on the findings from this study, we advocate for the use of QMLE to detect and rectify the implications of model misspecification to estimation uncertainty and the number of ground motions used in probabilistic seismic performance assessments.

The probabilistic performance-based seismic assessment of concrete bridge piers with SMASC reinforcing bars: Effect of pulse-like ground motion and vertical load-to-capacity ratio

Concrete bridge piers are critical components of bridge structures and their performance under seismic loading is of utmost importance. Traditional reinforced concrete bridge piers have shown limitations in terms of residual deformations and seismic resilience. This has led researchers to explore alternative reinforcement materials, such as Shape Memory Alloy (SMA) coupled with steel reinforcing bars, which have demonstrated promising attributes like energy dissipation as well as self-centering capacity. This study aims to fill this gap by evaluating the performance of concrete bridge piers with SMA-Steel coupled (SMASC) reinforcing bars under various intensities of vertical gravity loads and the action of pulse-like ground motion components, throughout a probabilistic framework. To this end, a group of bridge piers with different reinforcement types, including pure steel and SMASC are considered. These piers are subjected to 55 near-fault (NF) pulse-like records as well as 32 far-fault (FF) ground motions, throughout the Incremental Dynamic Analysis (IDA). The influence of distinct frequency components is analyzed by decomposing NF records into low-frequency pulses and high-frequency residual components. Also, the role of pulse to the 1st modal period of the piers (Tp/T1) is investigated by evaluating the piers’ response under the action of NF records, which were clustered into four groups. Results were assessed by evaluating the intensity measure and capacity of the studied piers at the desired performance objectives according to the FHWA manual. Moreover, the mean annual frequencies of exceeding performance limit states and the confidence levels of meeting performance objectives are studied. The results of the study indicate that the dominance of the component of NF ground motions depends on factors such as the intensity of gravity loads, ground motion characteristics, and the Tp/T1 ratio. The components of NF records within certain clusters of the Tp/T1 ratio are necessary for accurate response assessment, while FF records can be used for conservative design purposes, depending on the level of ground motion intensity and the intensity of applied gravity load. The SMASC-reinforced piers with specific λ factors (i.e. λ = 0.5 or λ = 1.0) and low intensity of gravity loads lead to a higher (1.6 times higher) mean annual frequency of exceeding a limit state, compared to pure steel rebars. Also, the confidence levels for meeting performance objectives vary depending on the ground motions, but, as gravity load intensity increases, confidence levels decrease, particularly for piers with a λ factor of 0.5.

Probabilistic damage evaluation of isolated steel box-girder bridge excited by near-field earthquakes

Modern civilization regards bridges as lifelines, and their failure due to significant earthquakes in the past has raised concerns about their seismic vulnerability. The effect of near-fault earthquakes on the bridge vulnerability is a significant problem that has not been well explored. The present work utilizes fragility analysis to assess the probabilistic seismic risk evaluation of a continuous isolated steel box girder bridge exposed to near-field ground motions (NFGMs). Probabilistic seismic demand models (PSDMs) of the bridge are explored to reliably associate key demand and intensity measures to capture the seismic performance of the system. This study examines a steel box girder bridge in Guwahati, India, isolated with lead rubber (LRB) bearings and a friction pendulum system (FPS). To achieve a comparable seismic response, each bearing system is designed for a similar isolation period. The PGV/PGA ratio is a useful metric for classifying ground motion suites and estimating their frequency content by classifying the input excitations into low- and high-frequency motions. To perform probabilistic seismic risk assessments, two ensembles of forward directivity records with PGV: PGA >160 cm/s/g (high frequency) and PGV: PGA <160 cm/s/g (low frequency) are considered. Moreover, one ensembles of near-field incorporating the fling effect and far-field are also utilized. The failure probability under the seismic hazards for isolated bridges is assessed utilizing different damage measures (DM) such as maximum displacement ductility of pier (DDP), displacement of deck (MDD), drift ratio of pier (PDR), and rotational ductility (RDP). The near-field earthquake damage probability is significantly impacted by the PGV/PGA ratio, as a high PGV/PGA ratio results in a greater probability of damage than a low PGV/PGA ratio. In conclusion, guidelines are provided that will help the design engineers for designing bridges with LRB and FPS isolators for seismic isolation in the event of varying ground motion characteristics.

Utilization of stochastic ground motion simulations for scenario-based performance assessment of geo-structures

Probabilistic seismic performance assessments of engineered structures can be highly sensitive to the seismic input excitation and its variability. In the present study, the scenario-based performance assessment recommended by Federal Emergency Management Agency (FEMA) P-58 guidelines is adopted to estimate seismic fragility of concrete dams for various seismic hazard scenarios. Due to the scarcity of recorded ground motions and thereby their poor representation of uncertainties, stochastic ground motion simulation methods are utilized to obtain the required input excitations. Moreover, to understand the uncertainty in ground motion simulation models, two broadband stochastic simulation models are used to generate input excitations representing six seismic hazard scenarios defined by earthquake magnitude, source-to-site distance, and soil conditions.Optimal intensity measure parameters for each scenario are identified using a systematic procedure that considers criteria such as efficiency, practicality, proficiency, sufficiency, and hazard compatibility. Fragility curves and surfaces are derived using the cloud analysis technique, taking into account various damage measures and limit state functions. The study finds that the derived fragility curves are particularly sensitive to the selection of earthquake scenarios, the choice of records, and the methods used to calculate fragility curves, with less sensitivity observed to different engineering demand parameters. Given this sensitivity, particularly to ground motion selection, the study highlights the necessity of incorporating both model-to-model variability (epistemic uncertainty) and record-to-record variability (aleatory uncertainty), alongside the established material and modeling uncertainties, in the probabilistic seismic assessment.

Influence of Incidence Direction of Seismic Wave on the Probabilistic Seismic Fragility Assessment of Bridges

Influence of Incidence Direction of Seismic Wave on the Probabilistic Seismic Fragility Assessment of Bridges

Two-Scale Probabilistic Seismic Fragility Assessment for a Prestressed Concrete-Steel Hybrid Wind Turbine Tower with Incremental Dynamic and Multiple Stripe Analysis

ABSTRACT To evaluate the seismic performance of a prestressed concrete-steel hybrid (PCSH) wind turbine tower, the seismic fragility curves based on incremental dynamic analysis (IDA) and multiple stripe analysis (MSA) on a two-scale model are presented and compared. The peak ground acceleration (PGA) and peak lateral drift on the top of the tower are adopted as the intensity measure (IM) and engineering demand parameter (EDP) of analysis, respectively. Finally, the seismic performance of the PCSH tower subjected to seismic action at different soil is investigated. The fragility curves obtained by IDA and MSA methods are compared.

Fusing physics-based and machine learning models for rapid ground-motion-adaptative probabilistic seismic fragility assessment

Performance-based earthquake engineering (PBEE) has asserted probabilistic seismic fragility assessment (PSFA) as the main research content in light of its irreplaceable significance for seismic decision-making in recent decades. Among the multiple approaches of PSFA implementation, the classical linear regression method (LRM) dominates over practice regarded as one of the most widely-used. However, the general LRM adopts quantile regression method (QRM) on the group of fragility curves to approximate a deterministic probability density distribution (PSD) of structural fragility against certain intensity measure (IM) of potentially confronting earthquake. Consequently, the QRM-derived fragility representation might not be credible enough while evaluating a newly-occurred seismic event owing to its neglect of specificity of stochastic ground motion. To address this issue, a fusing physics-based and machine learning models towards rapid ground-motion-adaptative probabilistic seismic fragility assessment (GmaPSFA) is proposed in present study. With sophisticated framework design and novel fragility hyperparameters estimation, the involved design philosophy and mechanism translating are both elaborated. To validate the method, both the LRM and GmaPSFA were conducted on a six-story frame structure, where a novel fully-automatic batch processing approach fusing APDL and coding languages was propounded for structural analysis. The comprehensive validating cases confirmed the powerful capability and significant superiority of proposed GmaPSFA in realizing rapid ground-motion-adaptative probabilistic seismic fragility assessment catering for modern PBEE.

Effects of important characteristics of earthquake ground motions on probabilistic seismic demand assessment of long-span cable-stayed bridges

The uncertainties of earthquake ground motions have the most important effects on seismic responses of bridge structures, especially long-span bridges, because of complex and special dynamic properties. The nonlinear dynamic time-history analysis is conducted for a two-pylon long-span cable-stayed highway bridge by using real earthquake ground motions rationally selected. The correlation between the important characteristics of earthquake ground motions and the probabilistic seismic demand assessment of the cable-stayed bridge reveals that the geometric means and dispersions of response spectra from selected ground motions have very significant effects on mean values, dispersions and probabilistic distributions of seismic demands of long-span bridges. The spectral shape of geometric mean spectra in the period ranges with large cumulative modal mass participation factors that should be well matched to the target spectrum to improve the precision and computational efficiency of probabilistic seismic demand assessment. If earthquake ground motions are rationally selected, response spectral values at the periods with comparatively large modal participation mass ratios or PGA can be used as intensity measures and even provide more precise probabilistic seismic demand assessment than response spectral values at the fundamental periods.

Hybrid-self-centring steel frames: Insights and probabilistic seismic assessment

This paper comprehensively discusses the seismic performance of steel moment-resisting frames with hybrid-self-centring connections (SMRF-HSCC) employing energy dissipation sequences by probabilistic seismic assessment. The hysteretic model of the HSCC was first developed based on experimental results, and a simplified nonlinear-spring-based model to simulate the behaviour of the connection was proposed and verified by physical test data. A series of codified prototype structures were developed, considering the fracture behaviour of post-tensioned (PT) steel strands in the connections. The seismic performance of prototype structures was assessed in terms of nonlinear static analyses and nonlinear dynamic analyses. The results indicated that the hysteretic response of SMRF-HSCC exhibited trilinear hysteretic features with the expected energy dissipation sequences. The influence of the high-mode effects on SMRF-HSCC was mitigated with the increase in energy dissipation and post-yield stiffness of the structure. Finally, the fragility analyses of the prototype structures were further performed, and the risk assessment was also made considering a 50-year service period. The collapse probability and the exceedance probability of target residual drift over a 50-year service period of SMRF with conventional self-centring connections showing flag-shaped hysteresis were higher than that of SMRF-HSCCs. The results also confirmed that the collapse probability and exceedance probability of target residual drift over a 50-year service period of SMRF-HSCC can be adjusted by reasonably modulating the arrangement of the HSCCs.

On the use of machine learning for fragility analysis of multi-span girder bridges

Companies and enterprises managing the transportation networks are in charge of performing seismic risk assessments for a sensible number of bridges designed, over the past decades, without fulfilling requirements of anti-seismic codes. Recent research studies have focused on leveraging machine learning strategies to enhance the efficiency of probabilistic seismic assessments. This study tackles the integration of machine learning algorithms in the case of bridge-specific applications to predict probabilistic seismic demand models for substructure components such as piers, accounting for knowledge-based uncertainties.The machine-learning-based methodology employed builds on the results of nonlinear time history analyses and considers features related to seismic excitation and structural parameters. Random Forest algorithm is employed to investigate the methodology for a multi-span simply supported girder bridge, which is a representative example of the most prevalent bridge class in Europe. Aiming to reduce the need for extensive nonlinear time history analyses in the risk assessment of bridges belonging to this specific class, the methodology proposed shows promising potential highlighted in the results.

Probabilistic seismic assessment of multispan RC highway bridges considering soil-structure interaction and chloride-induced corrosion

Deterioration mechanisms, such as chloride-induced corrosion, affect bridges in aggressive environments, making them more vulnerable to extreme events like earthquakes. Although many studies have assessed the impact of chloride-induced corrosion on the seismic vulnerability of reinforced concrete (RC) highway bridges, several gaps still need to be addressed. Accordingly, this research primarily focuses on evaluating the seismic performance of RC highway bridges in aggressive environments susceptible to chloride-induced corrosion and earthquakes. To achieve this, a probabilistic framework is employed, which incorporates uncertainties associated with corrosion progression, seismic events, and the impact of different modeling approaches for boundary condition. The framework considers the time-dependent effects of corrosion on the physical and material properties of steel and concrete in bridge columns. Monte Carlo Simulations (MCS), probabilistic seismic hazard analysis (PSHA), and record selection strategies are utilized to address the uncertainties in corrosion and seismic demand. Nonlinear dynamic models and multiple stripe analysis (MSA) are employed to obtain fragility surfaces and curves for main bridge components and the entire system under different boundary conditions. The study focuses on a five-span highway bridge with simply-supported prestressed concrete I-girder and RC multi-column bents located in Chile. The results reveal that elastomeric bearings are the most vulnerable components, exhibiting varying vulnerability levels under different corrosion exposure and boundary conditions. Abutments, although the second most susceptible, are unaffected by corrosion uncertainty in terms of seismic fragility. Bridge columns are identified as the third most vulnerable components, with the probability of exceeding slight damage state consistently increasing with more prolonged corrosion exposure. It is noted that only flexure failure mode in column is analyzed and possible shifting to shear or flexure-shear modes is not accounted for. The findings of this study underscore the exceptional resilience of Chilean highway bridge columns to seismic demand and corrosion uncertainties, contrasting with the situation in US regions where columns are more vunerable. Additionally, the study indicates that Soil-Structure Interaction (SSI) tends to reduce bridge vulnerability under combined corrosion and earthquake effects. The insights obtained from this study and the proposed framework can inform the development of maintenance programs based on bridge performance expectations and enhance the seismic resilience of bridge systems worldwide.

Simulation of non-stationary ground motions and its applications in high concrete faced rockfill dams via direct probability integral method

Many high concrete face rockfill dams (CFRDs) have been constructed in earthquake-prone areas in recent years, and it is essential to evaluate the seismic safety performance of these dams considering the randomness of seismic excitation. In this paper, the relationship between the stochastic ground motion generation method and the direct probability integral method (DPIM) is established by using the number theory point selection method as the bridge. The DPIM is introduced into the field of stochastic dynamic analysis and multi-index reliability evaluation of high CFRD for the first time. First, a non-stationary stochastic excitation model at five sites is established based on the latest standard for the seismic design of hydraulic structures. Then, taking a practical project as an example, stochastic dynamic response analysis and reliability assessment based on dam crest settlement deformation and dam slope cumulative slippage are conducted by using DIPM. Finally, the influence of these two indexes on reliability is explored by drawing the equal failure probability curve. The results show that the stochastic dynamic analysis and reliability assessment framework established in this paper can provide probabilistic seismic safety assessments for high CFRDs. Sliding damage of the dam slope is more likely than the deformation damage of the rockfill from the perspective of probability.

Uncertainty and bias in generic ground motion sets used for PBEE

Probabilistic assessment of seismic structural reliability relies on the simulation of structural behavior using nonlinear dynamic analysis of numerical models. This typically involves analyzing samples of ground motions that are assumed to represent specific populations of signals recorded at the site of interest. While the literature extensively discusses uncertainties arising from material properties, modeling randomness, and ground motion record-to-record (RTR) variability, there are two factors that are often overlooked: (1) variability in ground motion sets and (2) the interaction between ground motion RTR variability and other sources of uncertainty. Ideally, the ground motion records selected for probabilistic analyses should reflect the seismic hazard characteristics at the site of interest. However, in practice, researchers and practitioners often rely on pre-collected generic ground motion sets (a.k.a. standardized sets of ground motions). This study aims to address this gap by quantifying the variability and bias in dispersion and median values within different generic ground motion sets. To achieve this, the incremental dynamic analysis is performed on a series of nonlinear single-degree-of-freedom systems. The results are summarized in terms of inter- and intra-set variability, and are contrasted with other techniques based on resampling plans belonging to the bootstrap family. The findings will contribute to the development of improved framework for selecting and incorporating ground motion records in probabilistic seismic assessments, enabling more reliable predictions of structural performance.

Probabilistic seismic safety assessment of bridges with random pier scouring

Foundation scour has been a reason for several cases of river-bridge earthquake-induced failure during recent decades. However, practising engineers often do not consider its direct effect on the seismic design procedure of such structures. The cavity around a bridge foundation is a random phenomenon depending on several uncertain parameters. This study provides a probabilistic platform to investigate the effect of random scouring on the seismic performance of a particular bridge. The procedure is implemented on an existing multi-span reinforced concrete bridge. To this end, the Monte Carlo simulation technique is utilised to generate samples of the random variables of the scour model to develop the scour hazard curve. A common type of reinforced concrete multi-span bridge is considered as a model. The Latin hypercube sampling method is employed to generate random scouring scenarios in the finite-element model, including uniform and non-uniform scour. Then, fragility curves are developed utilising cloud dynamic analysis. The results reveal that the scouring pattern is one of the most crucial sources of uncertainty. In most circumstances, uniform scour scenarios are more effective than the average of non-uniform cases. However, in some specific patterns, the effect of non-uniform scouring is dominant.

Influence of uncertainties on the seismic performance assessment of chevron braced frames

In the framework of the probabilistic seismic response assessment of buildings, a key aspect is the evaluation of the influence of uncertainties on the mean annual frequency of exceedance of assigned limit states. In this regard, this study is focused on the seismic performance of concentrically braced frames in the chevron configuration. Out of the possible sources of uncertainties related to the numerical model (e.g. modelling of infills, soil-structure interaction), the effects of modelling of connections at the ends of braces are investigated by considering three different models: a model with pinned braces, a model with braces connected to beams and columns by means of rigid links simulating the gusset plates and a model with braces connected to beams and columns by means of elements with axial and flexural stiffnesses based on the real size of the gusset plates. In the two latter models out of plane buckling of braces is allowed. All the considered models are first validated against an experimental test and then used to estimate the fragility curves and the mean annual frequency of exceedance of Damage Limitation, Significant Damage and Near Collapse limit states of four case-study buildings. In addition to the uncertainty in the main characteristics of the seismic input, the uncertainties in the yield strength of material, equivalent viscous damping ratio, permanent and variable loads are also considered. The effects of these additional sources of uncertainty on the structural response are determined by comparing results provided by numerical models with random values of the uncertain variables with results provided by a single model with median values of the same variables. Finally, a simplified approach is proposed to simulate the effects of the additional uncertain variables in analyses of models with only variability in the seismic input.

Probabilistic seismic performance assessment of low-damage self-recovering prefabricated concrete frame subjected to near-field pulse-like earthquakes

The low-damage self-recovering prefabricated concrete (SRPC) frame using modular mild steel dampers is illustrated. Six low-cyclic repeated loading tests adopted 5 types of modular mild steel dampers were performed on the same fabricate joint specimen in turn. Based on the field test results and the displacement-based seismic design (DBSD) approach, a new SRPC deficient frame with four sizes of mild steel dampers are established, and elastoplastic time history analysis are conducted on four scenarios under near-field earthquakes respectively. To evaluate the collapse resistance of the new structure moduli designed in accordance with current design codes without considering the near-field earthquakes in the earthquake-prone regions, the probabilistic seismic performance assessments (i.e., hazard, fragility, risk) are conducted at the DBE and MCE earthquake levels under near-field ground motions. Annual and 50-year probability of exceedance (POE) results reflect that the new framework relieves the failed progression with a lower POE and meets the performance safety criteria under the near-field earthquakes. Furthermore, setting appropriate dimensions of mild steel dampers at the beam-column joints can effectively enhance the collapse resistance and whole safety of the new SRPC frame. This research will further promote the establishment of a reliable earthquake design method for new low-damage SRPC structures under near-field earthquakes.

Optimal Intensity Measures for Probabilistic Seismic Stability Assessment of Large Open-Pit Mine Slopes under Different Mining Depths

The dynamic stability of slopes is the key to ensure the safety of a large open-pit mine during and after a strong earthquake. This study was mainly focused on the identification of optimal intensity measures (IMs) for the probabilistic seismic stability assessment of large open-pit mine slopes within the framework of performance-based earthquake engineering (PBEE). To this end, four open-pit slopes with different mining depths were constructed as the reference cases for the numerical investigation. The randomness of input ground motions and the uncertainty of material properties of the slopes were also considered. A total of 96 ground-motion records and 29 common IMs were selected for testing. By a series of nonlinear time-history analyses, the probabilistic seismic demand models (PSDMs) between the minimum factor of safety (FOS) of slopes and all considered IMs were developed. The optimal IMs with respect to FOS were identified based on the evaluation of five criteria: correlation, efficiency, practicality, proficiency, and sufficiency. The impacts on seismic fragility and FOS response hazard of the slopes were discussed when using different IMs. The results reveal that sustained maximum velocity (SMV) and velocity spectrum intensity (VSI) are recognized as the optimal IM for a mining depth of 50 m and 100 m, respectively. However, Housner intensity (HI) is observed to have the best predictability for both the mining depths of 200 m and 300 m. Moreover, for the three most commonly used IMs, peak ground velocity (PGV) is superior to peak ground acceleration (PGA) and spectral acceleration at first mode period (Sa (T1)) for different mining depths. Finally, based on the evaluations of seismic fragility and FOS response hazard, the uncertainty of seismic stability prediction of open-pit slopes can be greatly reduced when using a more appropriate or optimal IM.

Probabilistic seismic assessment of innovative concrete bridge piers with Engineered Cementitious Composites (ECC) by different types of shape memory alloys (SMAs) bars

Critical role of bridges in post-earthquake rescue activities has made their seismic safety a major concern of structural engineers. While preventing collapse is one of essential requirements in bridge engineering, recent earthquakes have shown that bridges may also cease functionality due to residual deformations. To address this, shape memory alloys (SMAs) have received wide attentions according to their ability to recover the initial shape even after large plastic deformations. Two types of SMAs (NiTi and Cu–Al–Mn) are used in this paper to reinforce nine different concrete bridge piers in which Engineered Cementitious Composite (ECC) is also used for enhancing ductility in plastic hinge region. Each of the piers is subjected to 56 near field ground motions and collapse capacity of the piers is evaluated probabilistically using incremental dynamic analysis. The comparative results indicate that simultaneous use of steel and NiTi reinforcement in a plastic hinge area filled with ECC concrete can lead to a 30% improvement in median collapse capacity of the studied pier.

Influence of Near Fault Earthquakes with Forward Directivity and Fling Step on Seismic Response of Steel Box-Girder Bridge

The existing bridge seismic design guidelines that rely on the ground acceleration in the far fault zone,ignore the potential impact of near fault forward directivity and fling-step effects on the bridge structures. In the current study probabilistic seismic damage evaluation of a continuous four-span box girder bridge under the impact of near-fault forward directivity and fling step effect is studied employing the fragility analysis. The incremental dynamic analysis is used to construct the fragility curves which shows a range of damage states from minor to collapse for the different damage metrics and for the considered peak ground acceleration varying between 0.1g and 1.2g. Damage metrics such displacement pier ductility, rotational pier ductility and displacement of girder are used to develop the fragility curves and the probabilistic seismic damage model. To evaluate the bridge vulnerability, a probabilistic seismic damage assessment is performed using an ensemble of forward directivity and an ensemble of fling-step comprising permanent ground offset. The suggested probability-based earthquake damage framework is anticipated to be a well-versed model able to estimate the seismic damages to the continuous box girder bridges while taking into account the variation of near fault earthquakes. The findings show that, even at low PGA values the forward directivity and the fling-step ground motions represent a significant risk to the bridge.

Probabilistic seismic vulnerability assessment of RC frames with vertical irregularities using fragility curves

Probabilistic seismic vulnerability assessment of RC frames with vertical irregularities using fragility curves