Probabilistic Structural Analysis Research Articles

Seismic correlation coefficient evaluation for the application of separation of variables approach in fragility assessment

Seismic correlation can affect seismic probabilistic risk assessment results when components within the system have similar dynamic characteristics. While the fragility assessment methodology is well established, researches to evaluate and apply seismic correlation in fragility are still in progress. In this study, the seismic correlation coefficient (SCC) was quantitatively analyzed based on fragility assessment methods. In order to evaluate the SCC of several random variables associated with structure response in fragility assessment, a numerical analysis model of the structure was constructed and statistical analysis of the numerical results was performed. The SCC of the floor responses of the structural model considering random variables was evaluated from two perspectives. The first perspective involved applying variables individually or simultaneously when performing probabilistic structural analysis. The second perspective aimed to assess whether simplification of the structural analysis model affects the SCC. For this purpose, SCCs were calculated for each method and applied to a simplified failure sequence model to compare the combined fragility curves. The results of this study demonstrate the applicability of separation of variables method to the evaluation and generalization of the SCC for random variables of the fragility curve.

Data-driven reliability framework for qualitative damage states of reinforced concrete beams under blast loading

The incessant demand for protective infrastructure research has been motivated by recent accidental and intentional explosion events. This has led to a significant increase in blast design approaches and modern methods of structural analysis. When considering the analysis and response of blast-loaded members, like the identification of crack patterns and failure modes (CP & FM) of reinforced concrete (RC) beams, the current literature heavily depends on complex numerical modeling. Recently, the adoption of machine learning (ML) modeling to readily predict damage state labels of blast-loaded RC beams has emerged as a competitor to numerical methods. In either modeling method, outputs of damage states are often oversimplified as deterministic labels without elaborating on the possibility of alternative damage state. To extend on the practical usage of deterministic modeling, the present study introduces a probabilistic framework which integrates ML models towards ascertaining the probability of different CP & FM classes via the Monte Carlo simulation. The framework accounts for the uncertainties of different beam and blast parameters and incorporates four damage states of flexural cracking, bending failure, flexural-shear cracking, and crushing failure. The developed framework was evaluated against forty-two blast-loaded RC beams available from several previous experimental studies and exhibited excellent predictive performance while providing significant insight to the occurrence of all four damage states. In addition, extensive Blast Reliability Curves (BRC) were developed for eighteen RC beam cases over a wide range of blast intensities and the effects of beam and blast parameters on qualitative damage states were evaluated. The most notable observation was that the sensitivity of both concrete and steel strengths on damage state probabilities increased with reinforcement ratio. The BRCs depicted an elaborate transition of damage states with varying blast magnitudes. Also, the limitations, sources of error, and further improvements associated with the proposed methodology were clearly defined. Overall, the resulting probabilistic structural blast analysis introduced by the proposed framework serves as an intricate approach to providing greater comprehension to the CP & FM response of RC beams under blast loading which aims to promote confidence in decision making within protective design processes.

Probabilistic structural analysis of a composite beam considering random field of interface

The interlayer component is the weak layer of the composite beam. For the post-strengthened beam, the upper and lower layers are connected by glue bonding. The glue is mainly applied manually, and the craft has great randomness, and the randomness has spatial variability, which affect the normal use and bearing capacity reliability of the composite beams. In order to study the probability response of composite beams considering the spatial random field characteristics of interlayer materials, a finite element model was established. The upper and lower beams were both Euler beam, and the interlayer components were regarded as continuous springs, which were discretized and used as springs to connect the upper and lower beams into system stiffness. The random field characteristics of the continuous spring were expressed by Karhunen-Loéve expansion, and the statistical moments of the response were calculated by the reduced-dimension point estimation method, forming the calculation strategy of KLE-PEM. The comparison with MCS shows that this strategy has high accuracy and efficiency. Probabilistic structural response of composite beams with different correlation length, coefficient of variation of interface stiffness and interface stiffness of were analysis. The results show that the correlation length has little effect on the probability distribution of the response compared with the interlayer stiffness and its coefficient of variation (COV). The COV of interlayer stiffness has little influence on the mean value of the response but has great influence on the dispersion of the result. The greater the COV is, the greater the dispersion of the result is. The interlayer stiffness has a great influence on the statistical characteristics of the response, and within a certain range, the greater the interlayer stiffness, the smaller the deformation of the composite beam and the smaller the probability range.

Seismic Fragility Curves for Reinforced Concrete Dual System Buildings

A seismic fragility curve is a visual representation that illustrates the likelihood of a structure surpassing a particular damage or performance limit state caused by an earthquake with a specific intensity or ground motion level. This curve is typically generated using probabilistic seismic hazard analysis and structural reliability analysis methods. It is based on statistical models that rely on past earthquake data and simulations of future earthquake scenarios to predict the structure or system’s behavior under seismic forces. In this study, the seismic performance of 30 stories of 95 m height dual system reinforced concrete buildings located in Erbil is evaluated by analyzing three distinct ground motions. A non-linear platform is used to simulate and analyze data, followed by the generation of seismic inter-story drift fragility curves using Incremental Dynamic Analysis. The buildings’ seismic structural performance is assessed based on five different performance levels, including operational phase, immediate occupancy, damage control, life safety, and collapse prevention (CP). Each level is associated with different levels of damage and corresponding degrees of functionality and safety. The fragility curves show that the building has a 50% chance of achieving or exceeding the (CP) level with highly intense ground vibrations with peak ground acceleration = 1.6 g. In addition, these curves can be beneficial in creating future local design codes and provide significant support in evaluating the seismic performance of existing buildings.

A multivariate model to estimate environmental load on an offshore structure

Offshore structures such as oil platforms are subjected to significant environmental loads caused by wind, waves, and current. The complexity of offshore environment requires robust and reliable models to capture dependencies among environmental variables. A vine copula is a powerful tool that can be used to construct multivariate models by decomposing the complex structure into a series of simple pair copulas. Previous studies have shown that simple and symmetric copulas can be used as building blocks to construct vine copula models. In this study, symmetric and asymmetric copula functions are considered building blocks to capture all possible dependency structures. The c-vine model is then used to estimate the total environmental load on an offshore structure. Estimated loads are compared with those using the traditional independent variable approach and a multi-Gaussian distribution function-based method. The results reveal that both symmetric and asymmetric copula functions can be fitted to build c-vine copula models for the trivariate case. C-vine copulas, constructed using asymmetric copulas, provide a better estimation of the total environmental load than the independent and multivariate Gaussian methods. The result of this study is useful in probabilistic structural analysis of offshore structures for design and resilience analysis.

Potential bias of conventional structural seismic fragility for bridge structures under pulse-like ground motions: Bias evaluation and strategy improvement

Previous studies have highlighted the serious biases that may happen in probabilistic structural fragility analysis (PSFA) due to the ignorance of the effect of pulse period under pulse-like excitations. However, the distribution characteristics of the bias associated with structure-pulse damage parameters are less quantitatively investigated. This paper, therefore, focuses on the influence mechanism of the structure-pulse coupled period (defined by pulse period normalized by structural fundamental period) in PSFA and quantitatively describes the bias that occurred in different damage states. Meanwhile, the PSFA of ductile columns conditioned on two different groups of intensity measures are systematically presented and compared based on Artificial Neural Network prediction. Results reveal that the bias of PSFA, with the variation of the normalized period, can be divided into three different stages, including two ranges of normalized period overestimating structural damage probability and one interval indicating the underestimated condition. Additionally, significant biases (larger than 50%) have been frequently observed in the PSFA of structures with different fundamental periods under various damage states. Moreover, the formulas for quickly obtaining the interval that dangerously underestimates structural damage probability and bias modification factor are correspondingly proposed, which can provide a quite useful method and tool for fragility, risk, and resilience analysis of bridge structures in near-field regions.

Probabilistic structural analysis of a real-life corroding concrete bridge girder incorporating stochastic material and damage variables in a finite element approach

A combined probabilistic approach based on response surface sampling (RSS) and importance sampling (IS) is developed to efficient assess the structural reliability of corroding concrete structures. In this approach, the failure probability and the corresponding reliability index can be calculated for any stochastic system, independent of the material and model complexity or the limit state function(s). The combined approach is applied to a real-life example where a corroding post-tensioned concrete bridge girder is considered. This bridge girder is modelled in a dedicated finite element analysis to assess the structural reliability under corrosion damage. Serviceability and ultimate limit state requirements are taken into account and the material and damage properties are the stochastic variables. A converged solution is found in 8 and 128 limit state function evaluations for the RSS and IS, respectively. The importance factors for the different variables are calculated. The full analysis highlights non-important parameters (strength of the traditional reinforcement) and indicates that the ultimate limit state of the girder is the limiting factor in all analyses. Further computational optimizations are proposed and implemented, highlighting the capabilities of the reduced model and the robustness of the proposed approach.

A multi-scale framework for probabilistic structural analysis of PSC girders considering pit corrosion of prestressing wires

Many standards and studies have emphasized the importance of considering various uncertainty factors of material properties and corrosion in assessing the structural performance of bridges. In such an analysis, however, high computational cost is a major issue because a probabilistic structural analysis requires multiple structural analyses. In this study, an efficient framework for constructing a probabilistic structural analysis model is proposed. First, a surrogate model is constructed using Gaussian process regression for the given structural analysis model. Next, random samples of model inputs and structural responses, which are assumed to be correlated non-Gaussian random variables, are generated based on the Cholesky decomposition and Morgenstern model. Finally, the statistical properties of structural responses are derived by a goodness-of-fit test; hence, they can be considered as probabilistic inputs for an upper-scale model in the form of random variables. This three-step process can be introduced accumulatively from the lower-scale to upper-scale models about a structure; accordingly, it is termed as a multi-scale framework for probabilistic structural analysis. The proposed framework was applied to construct probabilistic models for prestressed concrete (PSC) girders with corroded prestressing wires, and the probabilistic prediction results for the ultimate load and displacement showed a good agreement with the experimental data.

Copula-based joint probabilistic model of earthquakes and rain for the failure assessment of masonry-adobe structures

Earthquakes are the most harmful natural hazard to engineering structures. During a rain event, the increased moisture content in the adobe walls of masonry-adobe composite structures may lead to short-term degradation in wall capacity. Neglecting this degradation will result in large errors in the risk assessment of structures subjected to an earthquake that occurs after a heavy rain. In this paper, marginal probability distribution models of the earthquake intensity and rain intensity were separately established based on a large amount of measured data for areas with frequent high-intensity rainfall events. A copula-based joint probabilistic model of earthquake intensity and rain intensity was proposed and subjected to a goodness-of-fit test to obtain the multihazard joint return period and annual exceedance probability. Additionally, a failure risk assessment method for masonry-adobe composite structures was proposed based on the multihazard joint probabilistic model and structural vulnerability analysis. The proposed method was used for the risk assessment of a single-story masonry-adobe composite structure. The results showed that the seismic failure probability of the structure was 142% higher when the rain-based degradation of the adobe wall was considered than when this degradation was neglected. Therefore, the accuracy of failure probability calculations for masonry-adobe composite structures can be improved by using the multihazard joint distribution.

Vision for Mechanistic-Empirical Railway Track System and Component Analysis and Design

Many analytical methods and other processes have been developed for the evaluation of railway track and its components, but these have largely been used for analysis. Design is often driven by development projects that do not engage research, resulting in designs that may not be optimized in the context of the broader track structure. This paper proposes a mechanistic-empirical (M-E) analysis and design framework that encourages an understanding of mechanical load-response behavior and comparison of loading demands, and the capacity of the track infrastructure component under study. The approach builds on similar advancements in the field of highway pavement research, including the development and use of the Mechanistic-Empirical Pavement Design Guide (MEPDG). Rail applications present unique economies to a focused M-E design approach, given that loads are concentrated in localized regions and beneath the rails. This paper first reviews prior design and analysis approaches, then presents the essential features of an M-E railway track system and component analysis and design, and, in the end, notes gaps that will require future research before proper implementation of M-E design within rail engineering. The authors also discuss the role of probabilistic design and structural reliability analysis in future design practices. Finally, governing mechanistic failure modes for the track system as well as components and associated life cycle data to achieve full implementation of such an M-E design process are identified and a path forward for implementation is proposed.

A research into the development of models of random variables as part of the structural reliability analysis performed in the absence of some statistical information

Introduction. The scientific review article addresses the approaches to the modeling of random variables performed as part of the structural reliability analysis of elements provided that some statistical information missing (limited). The objectives of the research include the statement of the problem of the probabilistic structural reliability analysis subject to incomplete statistical data, the study of the development of approaches to the generation of models of random variables within the framework of this problem, as well as the assessment of the current state of affairs in this field and some development prospects for the coming years.
 Materials and methods. The principal model of a random variable, considered in the article, represents a p-box (pro­bability box) model. A p-box is an area of possible functions of distributed probabilities of a random variable generated by the two boundary functions of the probability distribution. The article addresses p-boxes generated using the fuzzy set theory, the probability theory, Kolmogorov–Smirnov boundaries, etc.
 Results. The approaches, considered in the article, are illustrated by the numerical examples of p-boxes that use the same statistical data. P-boxes, based on the probability theory, allow to accurately simulate a random variable; however, a priori information about the type of the distribution function is needed. P-boxes, based on the possibility theory, can be used even if an extremely small amount of statistical data is available, and it is also necessary to carefully address the issue of assigning the cutoff (risk) level. P-boxes based on the Chebyshev inequality and the Kolmogorov–Smirnov statistics allow to effectively simulate random variables regardless of the type of the probability distribution. However, these approaches may generate an assessment that is too uninformative for decisions to be made in a number of tasks.
 Conclusions. The choice of a probabilistic model of a random variable for the further reliability analysis of structural elements will depend on the amount and type of statistical data obtained about the random variable. In particular cases, if the statistical information represents a subset of intervals, special approaches based on the Dempster–Shafer theory can be used. A promising and relevant method that underlies both the development of probabilistic models of random variables and the analysis of structural reliability in case of missing statistical information encompasses the employment of numerical modeling methods that employ surrogate models (kriging, Bayesian networks, interval predictors, etc.) and neural network algorithms.

Effect of the Bracing System on the Probability of Collapse of Steel Structures under Maximum Credible Earthquake

Simple bracing frames can be divided into two types in terms of concentric or eccentric. Concentric bracing frames are frames that intersect with other structural members at one point in the structure along the bracing members. Otherwise, the braced frame will be eccentric. It is said empirically that due to this type of shaping, eccentric bracing frames exhibit more ductile behavior and concentric bracing frames exhibit more stiff behavior. This behavioral difference caused this study to be numerically computing for five frames, including unique concentric and eccentric bracing frames of 5 and 10 stories and an ordinary 5‐story concentric bracing frame. Their tensions and drift ratios should be acceptable for the use of residential buildings. Using the primary two steps of the new PEER probabilistic framework, namely, probabilistic seismic hazard analysis and structural analysis, which leads to the drawing of fragility curves, the probability of collapse is obtained to compare the safety capability of these frames according to their different characteristics against earthquakes. The results show that increasing the ductility or increasing the number of floors or the height of these systems can reduce collapse. Also, according to the results of the probability of collapse obtained in frames with 5‐story concentric bracing frames, it can be said that some of the current regulations, which work based on previous approaches of analysis, can lead to unsafe structures with a high probability of collapse.

Intensity Measures for Regional Seismic Risk Assessment of Low-Rise Wood-Frame Residential Construction

AbstractGround motion intensity measures (IMs) provide a link between the probabilistic seismic hazard analysis and probabilistic structural response analysis. IMs that are well correlated with the...

Probabilistic structural reliability analysis of a horizontal axis tidal turbine blade by considering the moisture effects on the blade material

The use of composite materials in marine structures like the horizontal axis tidal turbine blade introduces inherent uncertainties in the material properties of the blade. Further, the blade material ages because of the absorption of seawater into the material. Hence, whilst performing the static structural analysis of the blade, the probabilistic nature of the material properties, as well as its degradation due to ageing, must be considered. In this study, the probabilistic structural response of a 0.5 m blade was estimated by considering the experimentally determined statistical distributions of the dry and aged material properties. The polynomial chaos expansion (PCE) method was used to build a surrogate model to mimic the static analysis of the blade, which was used in conjunction with the Monte Carlo simulation to estimate the distributions of the structural response of the blade and the probability of failure of the dry and aged blade. Stochastic convergence was used to check the accuracy of the surrogate model built via the PCE method. The study revealed a statistically significant increase in the probability of failure of the blade due to the ageing induced degradation of the blade material. Further, the need for a probabilistic structural analysis was also established.

Probabilistic structural analysis of São João Bridge based on the on‐site study of the time‐dependent behavior of concrete

AbstractThis article aims to present a procedure to take into account the variability of the time‐dependent behavior of concrete on its structural effects, evaluated from the study of creep and shrinkage based on experimental data obtained on‐site. For this purpose, the São João Bridge, a railway bridge built in Porto, Portugal in 1991, is presented as a case study. São João Bridge is a railway bridge crossing the river Douro. It is a prestressed concrete structure, with a total length of 1,028 m, including the main span of 250 m, two side spans of 125 m, six approaching spans on the left river bank, and three approaching spans on the right river bank (Porto). During bridge construction, a comprehensive structural health monitoring (SHM) system was set up, as well as an on‐site study of time‐dependent behavior of concrete. This study was based on creep 15 specimens and 15 shrinkage specimens, prepared simultaneously with some segments of the deck, using the same material, and it was kept running during almost 20 years. The results of this study were treated statistically and used as random variables in a probabilistic analysis of the time‐dependent behavior of the bridge. After a brief description of the mentioned on‐site study and the bridge SHM system, the paper presents the procedure followed on the bridge numerical probabilistic analysis. Finally, the values computed by the numerical model are presented and compared with the experimental values provided by the SHM.

A case study of design decision-making for an exemplar steel portal-framed building under fire exposure using a hybrid analysis technique

This paper demonstrates how stakeholder decision-making can be optimised in the design of steel-framed buildings that may be exposed to destructive fires. A novel hybrid technique, proposed in a previous study by the same authors, for combining stakeholder opinions on different fire protection options and probabilistic structural fire analysis outcomes is tested on an exemplar building. The hybrid analysis method is presented, followed by the description of the case study portal-framed building and the stakeholder engagement employed in the process. The remainder of the paper presents the qualitative and quantitative analyses outcomes and their integration to access an optimal design decision based on a decision management framework adapted from the risk management guidelines of AS/NZS ISO 31000:2009. The results show the seamless aggregation, prioritisation and synthesis of conflicting design decision attributes in ranking competing fire protection options to confirm the viability of the technique. The results also show that not protecting the steel members is the optimal/cost-effective option given the influence of participant-stakeholder weights and the building type.

Comparing different contour methods with response-based methods for extreme ship response analysis

Environmental contours are often applied in probabilistic structural reliability analysis to identify extreme environmental conditions that may give rise to extreme loads and responses. They facilitate approximate long term analysis of critical structural responses in situations where computationally heavy and time-consuming response calculations makes full long-term analysis infeasible. The environmental contour method identifies extreme environmental conditions that are expected to give rise to extreme structural response of marine structures. The extreme responses can then be estimated by performing response calculations for environmental conditions along the contours.Response-based analysis is an alternative, where extreme value analysis is performed on the actual response rather than on the environmental conditions. For complex structures, this is often not practical due to computationally heavy response calculations. However, by establishing statistical emulators of the response, using machine learning techniques, one may obtain long time-series of the structural response and use this to estimate extreme responses.In this paper, various contour methods will be compared to response-based estimation of extreme vertical bending moment for a tanker. A response emulator based on Gaussian processes regression with adaptive sampling has been established based on response calculations from a hydrodynamic model. Long time-series of sea-state parameters such as significant wave height and wave period are used to construct N-year environmental contours and the extreme N-year response is estimated from numerical calculations for identified sea states. At the same time, the response emulator is applied on the time series to provide long time-series of structural response, in this case vertical bending moment of a tanker. Extreme value analysis is then performed directly on the responses to estimate the N-year extreme response. The results from either method will then be compared, and it is possible to evaluate the accuracy of the environmental contour method in estimating the response. Moreover, different contour methods will be compared.

A Bayesian model updating framework for robust seismic fragility analysis of non-isolated historic masonry towers.

Seismic assessment of existing masonry structures requires a numerical model able to both reproduce their nonlinear behaviour and account for the different sources of uncertainties; the latter have to be dealt with since the unavoidable lack of knowledge on the input parameters (material properties, geometry, boundary conditions, etc.) has a relevant effect on the reliability of the seismic response provided by the numerical approaches. The steadily increasing necessity of combining different sources of information/knowledge makes the Bayesian approach an appealing technique, not yet fully investigated for historic masonry constructions. In fact, while the Bayesian paradigm is currently employed to solve inverse problems in several sectors of the structural engineering domain, only a few studies pay attention to its effectiveness for parameter identification on historic masonry structures. This study combines a Bayesian framework with probabilistic structural analyses: starting from the Bayesian finite element model updating by using experimental data it provides the definition of robust seismic fragility curves for non-isolated masonry towers. A comparison between this method and the standard deterministic approach illustrates its benefits. This article is part of the theme issue 'Environmental loading of heritage structures'.

3-dimensional environmental contours based on a direct sampling method for structural reliability analysis of ships and offshore structures

ABSTRACTThis paper derives a simple way of calculating 3-dimensional environmental contours for structural reliability assessment and design of ships and offshore structures. The 3-dimensional contours are based on Monte Carlo sampling from the joint distribution of the input parameters for response calculations and are an extension of previously proposed 2-dimensional contours. The 3-dimensional contours offers a practical way of identifying multivariate joint extremes of relevant input variables in order to provide for analyses of extreme structural responses. The contour estimation method is applied to some simple example cases and is demonstrated to work well and give reasonable results. Hence, the 3-dimensional contours represent a practical tool for anyone involved in probabilistic structural reliability analysis and design of ships and offshore structures.

A PROBABILISTIC ANALISYS OF THE FORCES IN THE PILES OF A CONTAINER TERMINAL WHARF UNDER SHIP BERTHING ACTIONS

ABSTRACTIn this work a probabilistic structural analysis of a container terminal wharf is presented. Through the application of the Monte Carlo Simulations in a finite element structural model, the statistics of the axial forces at the pile heads were evaluated. Considering only ship berthing conditions, but varying equipment type, number and positions, ten external load combinations were analyzed and compared. Both finite element model and probabilistic analysis were performed in ANSYS software, v.16, on its APDL Mechanical and Probabilistic Design System packages respectively. The random input parameters considered were the concrete structure, pavement and rear landfill self-weight, live loads and ship sizes, for which statistical parameters were attributed based on bibliography or data collection. PIANC’s berthing energy method for fender systems design was applied for the evaluation of ship berthing forces acting on the structure. Considering the axial forces as the main parameters in the design of partially embedded piles, the random output parameters obtained were the minimum and maximum axial forces on each simulation. That approach, applied due to the possibility of ANSYS to be programmed through its Parametric Design Language (APDL), proved to be a powerful tool for probabilistic analysis of complex structural systems. The results present a comparison between the statistical parameters and probability density curves for the ten cases analyzed, by which the worst combinations from a probabilistic point of view could be defined. Keywords: Container terminal berth; Probabilistic Analisys; Monte Carlo Method; Finite Element Method; ANSYS.