Probabilistic Seismic Performance Research Articles

Probabilistic Seismic Performance of Pipeline Supporting CBFs According to Seismic Design Parameters and Requirements

Probabilistic Seismic Performance of Pipeline Supporting CBFs According to Seismic Design Parameters and Requirements

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.

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.

Spatial correlation in building seismic performance for regional resilience assessment

Probabilistic seismic performance assessment method for buildings offers a valuable approach to simulate the broader regional impacts: economic losses, downtime, and casualties. A crucial aspect of this process entails accounting for the spatial correlation of building performances, aiming for an accurate estimation of the probability of extreme regional losses, such as the simultaneous collapse of buildings with similar structural characteristics. In this study, a correlation model based on a Gaussian random field is employed, and several key challenges associated with its application are addressed. In addition, efficiency of five different methods of selecting station records from the same earthquake scenario is compared. The minimum number of earthquake records necessary to achieve a stable correlation result is determined. Additionally, spatial correlations derived from different history earthquake events are compared. By addressing these critical issues, this research contributes to refining the reliability of probabilistic methods for regional resilience assessment.

Impact of Component Correlation on Probabilistic Seismic Responses of Steel Frames by Modifying Non-Positive Definite Correlation Matrices

ABSTRACT This paper studies the effects of spatial correlation between the structural components on probabilistic seismic performance of steel moment resisting frames, using extended incremental dynamic analysis (IDA) method to consider the effects of aleatoric uncertainties caused by ground motion records. In this probabilistic assessment, a combination of Latin hypercube sampling (LHS) and Cholesky decomposition (CD) methods are utilized to take the epistemic uncertainties of the numerical model into account. In case the target correlation matrix is not positive definite, two powerful optimization algorithms are employed to find the closest positive definite correlation matrix.

Seismic fragility analysis of slopes based on large-scale shaking table model tests

Seismic fragility analysis is one probabilistic method that represents the conditional probabilities of exceeding different predetermined damage states for various given earthquake hazard levels, which is the essential part of probabilistic seismic risk assessment. It has gained much popularity recently because much more comprehensive and richer results than traditional probabilistic methods can be provided. The classical seismic fragility analysis of slopes is always performed through analytical approaches. In the present study, a novel seismic fragility analysis framework combined with shaking table model test results is proposed for probabilistic seismic performance and risk assessment of slopes. The shaking table model tests of a rock slope reinforced by pile-anchor structures were firstly performed subjected to a suite of real earthquake records with different intensity levels. Subsequently, the seismic responses from shaking table model tests were then gathered for the optimal analysis to determine the optimal engineering demand parameter (EDP) and earthquake intensity measure (IM) for seismic fragility analysis of slopes. At last, the identified most appropriate IM and EDP were selected to construct the scalar-valued fragility curves, vector-valued fragility surfaces and fragility surfaces considering acceleration elevation amplification effect by the proposed framework. The results indicate that using single IM to construct scalar-valued fragility functions may result in different failure probabilities depending on the chosen earthquake IM. The vector-valued fragility surfaces provide more information than ordinary fragility curves, and lead to more proper and realistic evaluations of seismic hazard of slopes. The methods and results presented in this paper also provide the basis for the probabilistic seismic risk and loss assessment of earthquake-induced slope geological disaster.

Probabilistic Seismic Performance Assessment of Tall RC Special Moment-resisting Frame Buildings Equipped with Buckling-restrained Braces under Near-field Excitations

Many tall buildings have already been constructed near faults throughout the world, several of which have sustained casualties and economic losses during strong ground motions. This study investigates the effect of near-fault excitations on the vulnerability of tall, reinforced concrete (RC) special moment-resisting frame (SMRF) buildings equipped with buckling-restrained braces (BRBs) using seismic fragility curves. After attaining the structure’s response modification factor (R), three-dimensional (3D) models of 15-, 25- and 35-story frames were developed by the OpenSees software according to the Iranian code provisions. Thus, the seismic response of the elements was obtained. Subsequently, incremental dynamic analysis (IDA) was conducted by selecting a suitable number of compatible accelerograms in two near-field and far-field groups. Considering the maximum story drift as the demand parameter and selecting the interstory drift ratios (IDR) for the slight, moderate, extensive, and complete collapse seismic performance levels proposed by Hazus, IDA curves were plotted. Then, the seismic fragility curves were produced using the structural reliability relations. The median fragility at complete collapse damage level reduced from 0.73g, 0.62g, and 0.61g to 0.68g, 0.59, and 0.57g for the 15-, 25, and 35-story near-field and far-field earthquake models, respectively. This was attributed to increasing vulnerability and seismic fragility of the structures as a result of both height increase and distance reduction from fault. Based on the results, the most vulnerable structure, i.e., the 35-story near-fault model, experienced a 40, 17, 18, and 6% increase in median fragility at slight, moderate, extensive, and complete collapse damage levels, respectively.

Probabilistic seismic performance estimation through surrogate model and unbiased multi‐fidelity Monte Carlo predictor

AbstractThis study introduces an approach for probabilistic seismic performance estimation, which focuses on the probability of intensity measures exceeding a specified value based on engineering demand parameters. Conventional methods face challenges owing to the increase in computational costs associated with the uncertainties in earthquake scenarios. To address this, we use high‐fidelity (HF) and low‐fidelity (LF) model data to develop a multilevel hierarchy of surrogate models, which improves the simulation‐based probabilistic estimation. However, designing a reliable LF model and ensuring the accuracy of the surrogate model hierarchy remains challenging. Herein, we present a multi‐fidelity Monte Carlo (MFMC) predictor combined with a conventional surrogate model to improve probabilistic seismic performance estimation, thereby leveraging LF model efficiency and HF data accuracy for unbiased results. We addressed the challenge of constructing a suitable LF model by using a surrogate model trained from limited HF data. The MFMC predictor improves the accuracy of probabilistic analysis than the surrogate models trained from limited HF data. Further, the automatic relevance determination method is introduced to select the most appropriate inputs for the surrogate model. A case study featuring a special moment‐resistant frame, subject to uncertainties from both ground motion and structural properties, illustrates the efficiency of the method. A LF model is developed using the Kriging method, followed by the construction of the MFMC predictor for probabilistic analysis, thereby leveraging both limited HF and numerous LF data. Comparing the exceedance probability curves obtained from the MFMC predictor with those from direct Monte Carlo simulations and conventional Kriging showed that our proposed method offers a promising tool for probabilistic seismic performance estimation under uncertainty.

Feature selection of ground motion intensity measures for data‐driven surrogate modeling of structures

AbstractIn the probabilistic seismic performance assessment of structures, intensity measures (IMs) represent seismic characteristics and variations. Traditional fragility analysis method based on the assumption of linear regression requires selecting an optimal IM as input variable. By introducing machine learning (ML) techniques, nonparametric fragility analysis theoretically allows for considering all potential IMs as inputs. Nevertheless, to reduce input dimensionality and improve training efficiency, the feature selection of IMs remains imperative. This paper proposes a method to select optimal ground motion IMs for data‐driven surrogate modeling of structures. Specifically, the elastic net algorithm is employed to select the optimal multiple IMs based on the coefficient of determination and regression coefficient, differing from the efficiency and practicality emphasized in the traditional method. Using the optimal multiple IMs as input variables, several ML techniques are employed to construct surrogate models for seismic damage assessment of structures, thereby developing fragility functions, that is, the conditional probability of exceeding a damaged state given seismic intensity. A 3‐span, 6‐storey, reinforced concrete frame is utilized to illustrate the proposed methodology. The predictive performance of all ML models with the optimal multiple IMs outperforms that of the models with the commonly used IM (e.g., peak ground acceleration, PGA) as sole input and all candidate IMs as inputs. Additionally, the surrogate models with the optimal multiple IMs enable a more comprehensive seismic fragility modeling of structures under two or more IMs simultaneously, such as the fragility surface under spectral acceleration at 1.0s (Sa‐1.0s) and velocity spectrum intensity (VSI).

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.

Case studies on the seismic resilience of reinforced concrete shear wall buildings and steel dual concentrically braced buildings

This paper investigates various performance measures to assess the seismic resilience of low-to-high-rise multistory RC shear wall and steel dual concentrically braced buildings as dual seismic force-resisting systems in California. The performance measures include the risk of structural collapse, earthquake-induced repair costs, life-cycle cost, repair times, and seismic resilience. Six buildings, consisting of five-, 10-, and 15-story configurations, were selected and analyzed using the response spectrum method. The design of these buildings followed the provisions of ASCE/SEI 7-16, ACI 318-14, and AISC 341-16. To accurately simulate the structural behavior, nonlinear numerical models of the buildings were developed in the OpenSees software. Response history analyses were conducted to evaluate the dynamic behavior of each building until structural collapse, considering far-field ground motion records from FEMA P-695. The study also utilized a probabilistic building-specific loss assessment methodology provided in FEMA P-58 guideline, which explicitly accounts for the main sources of variability related to earthquake hazards and structural response. In general, the results of the probabilistic seismic performance assessment demonstrated that the code-compliant steel dual concentrically braced buildings performed poorly compared to the RC shear wall buildings, regardless of the number of stories. Specifically, the steel dual concentrically braced buildings exhibited a lower resilience index, especially in the case of low-rise buildings (i.e., five-story) during strong earthquake events.

Effect of soil spatial variability on characteristics of depth-varying multi-support seismic motions at offshore sites

The purpose of this study is to evaluate the influence of soil spatial variability (SSV) on the simulation of depth-varying multi-support seismic motions (DMSMs) at offshore sites. Firstly, the random field theory is used to quantify the extent of SSV, and a series of random field models with different characteristics are established for an offshore site by changing the coefficient of variation (COV) and correlation distance of soil parameters. Then, the simulation approach for random ground motion transfer functions (GMTFs) and DMSMs at offshore sites are introduced. The sensitivity of each uncertain soil parameter on the offshore seismic motions is explored using the single variable method. Finally, the effects of SSV on the GMTFs and DMSMs are investigated, in which the effects of COV and correlation distance are studied in detail. The results demonstrate that SSV has a remarkable influence on the GMTFs of offshore sites, which results in a large intensity variation of DMSMs. The sensitivity analysis indicates that the soil density and shear modulus are influential factors for the horizontal components of DMSMs; except these two parameters, the Poisson’s ratio also significantly affects the vertical DMSMs. Moreover, both COV and correlation distance can lead to certain variability in the GMTFs and DMSMs, and the effect of COV is more prominent than the correlation distance. This study provides an effective approach for the simulation of DMSMs at random offshore sites, which is valuable for rational probabilistic seismic performance assessment of offshore engineering structures.

Probabilistic seismic performance assessment of steel moment‐resisting frames considering exposed column‐base plate connections with ductile anchor rods

AbstractThis paper presents a numerical study assessing the seismic performance of steel moment‐resisting frames (SMRFs) designed with ductile exposed column‐base plate (ECBP) connections employing yielding anchor rods. For their potential use as weak bases, the proposed ECBP detail is designed to accommodate plastic deformations in the anchors. The seismic performance of 2‐ and 4‐story archetype SMRFs with ECBPs is investigated to examine the effects of various base‐connection strengths on the frame collapse mechanisms and probabilities. To this aim, the ECBP connections of each frame are designed for a set of three strength levels, ranging from reduced seismic loads to capacity‐designed forces of the adjoining columns. These designs enable the base responses to vary from highly inelastic (i.e., weak‐base design) to elastic (i.e., strong‐base design) when subjected to earthquake‐induced ground shaking. Nonlinear time history analysis (NLTHA) is extensively performed, applying a suite of assembled ground‐motion sequences (i.e., two ground motions in series) to assess the ECBP connection response and the corresponding frame behavior. Fragility analyses accounting for only the first ground motions in each considered sequence (to derive fragility curves), and the entire ground‐motion sequences (to derive fragility surfaces) are also performed to evaluate the probabilities of frame collapse and base connection failure. Finally, key findings regarding the seismic performance of ductile ECBP connections and their effects on the frame collapse are discussed. The limitations of the study are also outlined.

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.

Risk-based optimization of seismic mitigation devices constrained by user-defined components importance

The system optimization of complex structures is to achieve the overall best behaviour, however, specifications and engineers often pay more attention to the seismic performance of critical components. To comprehensively consider the requirement from theoretical research and practical engineering, a constrained optimization method of seismic mitigation devices for complex structures is proposed in this study, considering the user-defined importance of critical components. The seismic damage probability of individual components is defined as constrained functions (CFs). The overall probabilistic seismic performance of the bridge system is formulated as the objective function (OF) to carry out optimization analysis within the admissible region obtained by CFs. The surrogate functions between the variables and OF/CFs are formulated by the proposed Hazard-related Response Surface Method (H-RSM). A three-dimensional long cable-stayed bridge with a mitigation device of the fluid viscous damper (FVD) is constructed as the case-study model via FEM. Three constrained conditions are imposed by restricting the CFs less than a user-defined threshold to satisfy different safety requirements of the pylon, bearing and FVD. Different protection levels of the pylon are investigated to compare the constrained and unconstrained optimization methods. The influence of the maximum displacement of FVD on the optimal variables is also investigated.

Probabilistic seismic performance assessment of nuclear containment structure considering statistical uncertainty

Statistical uncertainty is inherently involved in probabilistic seismic performance assessment of containment structure due to heavy computational efforts of nonlinear dynamic analysis. Aiming at the statistical uncertainty involved in seismic fragility and seismic risk evaluation of containment structure, this study proposes a method for quantifying the statistical uncertainty in probabilistic seismic performance assessment of the containment structure. Taking a three story reinforced concrete frame as an example, effectiveness and efficiency of the proposed method for confidence interval estimation of seismic fragility curve is verified. Then, the proposed method is applied to fragility analysis and seismic risk evaluation of the containment structure. Roof drift of the containment structure under different ground motion intensity levels is discussed. Confidence interval for seismic fragility curve and seismic risk of the containment structure considering statistical uncertainty is quantified by the proposed method. The results highlighted the necessity for quantifying the impact of statistical uncertainty involved in probabilistic seismic performance evaluation of the containment structure.

A paradigm for seismic resilience assessment of subway system

Seismic resilience of subway systems is a cornerstone for developing resilient megacities. It depends on infrastructures’ fragility and aftermath recovery features at both local and global scales. Yet it remains obscure how to propagate the probabilistic seismic performance of single structures to the overall probabilistic seismic performance of subway systems at the global scale. Here, a paradigm is established for the seismic resilience of subway systems by integrating the seismic performance of single structures, interrelations among single structures, and post-seismic recovery. The seismic performance of single structures is assessed by nonlinear time-history analysis and quantified in terms of analytical fragility curves. The interrelations among single structures are represented by mapping the subway route map into a directed and weighted topological graph, dictated by the graph theory. Subsequently, the overall seismic performance of subway systems is quantified by network indicators and estimated by a Monte Carlo algorithm. The post-seismic recovery is determined by adopting appropriate simplified recovery functions and recovery strategies. The proposed paradigm is implemented to assess the seismic resilience of a typical subway system. It reveals that the seismic resilience of subway system is extremely sensitive to the repair sequence, e.g., decreased by 63% when switching from the order of damage state to the reverse one. Moreover, it is recognized that reliability and uncertainty are coupled, e.g., an increase in the reliability of single structures may depress the uncertainty of the system’s seismic performance.

Seismic loss and resilience assessment of tall-coupled cross-laminated timber wall building

Balloon-type cross-laminated timber coupled-wall (CLT-CW) structure is an emerging and sustainable option for constructing tall timber buildings. The structure features buckling restrained brace (BRB) hold-downs, balloon-type CLT walls, and coupling beams with replaceable shear links. This study investigates the probabilistic seismic performance (including economic loss, downtime, and resilience index) of a 20-story CLT-CW building. A three-dimensional (3D) structural model is developed to perform incremental dynamic analysis using 30 pairs of ground motion records that represent the seismicity of Vancouver, Canada. Intensity- and time-based loss assessments are conducted to estimate probability distributions of seismic losses according to the FEMA P-58 methodology. Post-earthquake recovery trajectories of the housing function are also presented to calculate the seismic resilience indices under different intensities. The results reveal that the coupling beams contribute the most to repair cost among all structural components. In light of the replaceability and energy dissipating role of coupling beams, the efficiency and resiliency of the CLT-CW building are validated.

Towards probabilistic seismic performance of vehicle‐bridge interaction systems: From stochastic dynamic model to fragility analysis

AbstractThis paper aims to assess the seismic fragility of vehicle‐bridge‐interaction (VBI) systems considering the effects of vehicle types, traffic conditions, and road surface qualities. A stochastic nonlinear mechanical model for the earthquake‐VBI system is developed, and the fragility functions for the proposed VBI model are derived by considering the relevant probabilistic seismic demand parameters. On the basis of a typical four‐span continuous prestressed concrete highway bridge in China, a complete numerical model for the VBI system is built considering multiple uncertainties from bridge and vehicle parameters, as well as the road surface qualities. A total of 120 real ground motion records with different combinations of magnitude‐source‐to‐site distance (M‐R) and earthquake intensity characteristics are selected. Meanwhile, 80 scenarios in terms of different combinations of vehicle types, vehicle speeds, and road surface irregularities are defined. In this context, 96,000 nonlinear time‐history analyses are performed, and the developed fragility models are applied to the VBI system at both component and system levels. Results indicate that the fragilities of pier drift, bearing shear strain, and the overall VBI system increase with the increase of the vehicle weight or the decrease of the vehicle speed, while the vertical deck displacement is dominated by the vehicle weight. It is also found that the road surface quality has a negligible effect on both component and system fragilities.

Probabilistic seismic performance assessment of offshore jacket structures as a basis for engineering decision-making

Jacket structures play an ever-increasing role in meeting the world’s burgeoning energy demand by providing support structure for exploiting offshore wind energy and oil and gas resources. Many of these structures are past their design lifetimes, and thus may have suffered significant degradation, highlighting the importance of investigating their earthquake response in seismically active regions. This study investigates the seismic performance of a typical offshore jacket platform, denoted as baseline structure, as well as four versions with two longer (25% and 50% larger) and two shorter (25% and 50% smaller) natural vibration periods accounting for two levels of degradation and retrofit effects on structural performance. For each case, eleven ensembles of ground motions compatible with the site’s seismic hazard are selected using the generalized conditional intensity measure methodology. The loading uncertainty is incorporated in the performance assessment procedure via probabilistic seismic demand analysis and the demand hazard is quantified. The results provide valuable information regarding reliability of these structures both at design stage and during service life, which can aid decision-making around rehabilitation of older platforms, the suitability of reusing obsolete platforms beyond service lifetime, and risk-based design of new platforms.