Failure Probability Of Structure Research Articles

Uncertainty quantification in free vibration and aeroelastic response of variable angle tow laminated composite plate

The influence of uncertainty in material properties on free vibration and aeroelastic response of variable angle tow (VAT) laminated plates is presented in this work. Free vibration analysis is conducted by a finite element model based on third-order shear deformation theory. The FE model is further coupled with MSC. Nastran to carry out aeroelastic analysis of VAT laminates in the subsonic regime. MSC. Nastran helps to extract the aerodynamic influence coefficient matrix at discrete values of reduced frequencies using Doublet Lattice Method. The accuracy and adaptability of the highly efficient radial basis neural network (RBFN) based surrogate model developed for uncertainty analysis are checked by comparing the result with that of the Monte Carlo simulation. Stochastic analysis of natural frequencies and flutter characteristics of VAT laminates are conducted through various parametric studies. Variance-based sensitivity analysis is used to calculate the contribution of individual material properties to the free vibration and aeroelastic response of VAT laminates. Further, the influence of the highly sensitive properties on the structural failure probability is estimated. This research can be leveraged to predict the probability of failure of the structure at different levels of material uncertainty present in it.

Seismic resilience of corroded mid-rise reinforced concrete structures under mainshock-aftershock sequences

Numerous existing structures exposed to an aggressive environment would also face to a threat from potential strong earthquakes. The coupling effect of environmental aggression and earthquakes could significantly increase the structural damage and failure probabilities of aging buildings. This paper presents a practical methodology of seismic resilience assessment for the corroded reinforced concrete (RC) buildings under mainshock-aftershocks. In this methodology, a piecewise resilience function is introduced, and the structural resilience will drop to zero when performing replacement. An economic loss ratio is adopted to determine the boundary point in the piecewise resilience function. Moreover, a vector-valued approach is employed to evaluate the structural fragility under mainshock-aftershock sequences. To illustrate the proposed methodology, a RC frame building designed according to Chinese codes is used as an example, and four cases with no, low, moderate, and high degrees of corrosion damage are considered with the corrosion rates (ηs) of 0%, 5%, 10% and 15%, respectively. A set of 662 real mainshock-aftershock sequences are selected as the input ground motions from PEER database. The resilience curves are then developed for the uncorroded and corroded RC frame cases under mainshocks alone and mainshock-aftershock sequences. The results show that the coupling effect due to both corrosion and aftershocks lead to a more significant reduction on the structural resilience (ΔR) than the individual effect due to either corrosion or aftershocks. For the condition of ηs = 15% and the PGV of aftershock equals to 0.1 m/s, it is found that there is a 95% of increase on the ΔR due to the coupling effect which is larger than either aftershock (31.6%) or corrosion alone (70%). Moreover, the reduction scale of the structural resilience due to both factors is even larger than the summation of those due to any individual factor alone. The results of this study highlight the importance to consider the two scenarios of aging and aftershocks simultaneously when evaluating the seismic resilience of structures in the lifespan.

Integrated analysis of soil-structure interaction for statically indeterminate beams on spatially random soils

ABSTRACT This study aimed to develop an integrated approach to analyse the interaction between soils and beams. The research methods involved placing a statically indeterminate beam on spatially random soils, where soil springs acted as supports for the beam. The soil spring stiffness values were simulated using random field theory. This integrated approach was embedded in the Monte Carlo simulation framework to facilitate probabilistic assessment. This study concluded that the force method solution accurately determined the bending moment and shear diagrams for a beam supported by soil springs. Additionally, soil spatial variability had a significant impact on the beam responses, including the variations in footing settlements, support reactions, bending moment, and shear force. This study also identified a critical scale of soil fluctuation that coincides with the beam span, which resulted in the highest probability of structural bending failure. Overall, this study highlights the importance of accounting for soil spatial variability in an integrated geotechnical and structural design approach.

Response Surface Method for Reliability Analysis Based on Iteratively-Reweighted-Least-Square Extreme Learning Machines

A response surface method for reliability analysis based on iteratively-reweighted-least-square extreme learning machines (IRLS-ELM) is explored in this paper, in which, highly nonlinear implicit performance functions of structures are approximated by the IRLS-ELM. Monte Carlo simulation is then carried out on the approximate IRLS-ELM for structural reliability analysis. Some numerical examples are given to illustrate the proposed method. The effects of parameters involved in the IRLS-ELM on accuracy in reliability analysis are respectively discussed. The results exhibit that a proper number of samples and neurons in hidden layer nodes, an appropriate regularization parameter, and the number of iterations for reweighting are of important assurance to obtain reasonable precision in estimating structural failure probability.

Deflection-based failure probability analysis of low shrinkage-creep concrete structures in presence of non-stationary evolution of shrinkage and creep uncertainties

Reasonable assessment of the failure probability caused by long-term deflection is essential to ensure the service performance of low shrinkage-creep concrete (LSCC) structures. In this paper, the shrinkage and creep models applicable to LSCC are proposed and verified by comparing their results with the experimental data. Then, the non-stationary evolution models of uncertainties of concrete creep and shrinkage are developed. Finally, a long-term deflection-based assessment method of failure probability of LSCC structures is also proposed considering the effect of non-stationary evolution of creep and shrinkage uncertainties. The case analysis results show that ignoring the effect of the non-stationary evolution of creep and shrinkage uncertainties overestimates the long-term deflection, and the deviation in this case study is 10.13%. Compared with the uncertainty of creep, the cumulative failure probability of the case structure is more sensitive to the non-stationary evolution of shrinkage uncertainty. The use of LSCC can greatly reduce the cumulative failure probability of concrete structures caused by excessive long-term deflection. Additionally, the cumulative failure probability of concrete structures is greatly underestimated by using the traditional characteristic parameters of uncertainties of concrete creep and shrinkage.

Structural failure assessment system exemplified by dumbbell-shaped CFST arch

The study of structural failure law is the basis of structural safety assessment, but engineering structures present complex nonlinearities and diversity, which make it difficult to analyze the failure laws of structures. However, the failure of ductile structure is a process of quantitative cumulation to qualitative change, and this turning point is the key to structural failure analysis. Based on this view, we propose a new system for structural failure assessment, which includes the identification of mutation locations, strain data visualization, structural internal force estimation, and finite element stochastic simulation, etc. Moreover, every new method is compared and validated. Experimental data of a dumbbell CFST arch model are used throughout the paper for illustration. Finally, the time-varying failure probability of the whole structure is evaluated. In summary, this paper organically combines experiment, simulation and engineering practice to provide a new approach to structural safety analysis, structural health monitoring and structural design.

Calculation of Instantaneous Reliability of Grain Structure Under Small Samples

Under the condition of small sample, the performance parameters’ interval quantization and instantaneous reliability calculation of solid rocket motor grain structure are researched. Two important mechanical properties of material: Relaxation modulus and Poisson’s ratio are obtained by experiments of grain material. Since the data of parameters obtained are a small sample, the method of gray theory is used to mine the experimental data. It realizes the uncertainty quantitative analysis of grain material performance parameters and obtains the quantitative interval of performance parameters. Considering that the evidence theory can directly attribute probabilistic mass to the set or interval, the instantaneous reliability of grain structure is analyzed based on the evidence theory. By establishing the relationship between failure surface and the frame of discernment, and using the belief function and plausibility function to obtain the upper and lower bound probability distribution of structural reliability and failure probability, the instantaneous reliability probability interval of structure is obtained.

Reliability analysis of an inter-story isolated structure under a main-aftershock sequence based on the Laplace asymptotic method

After a strong mainshock, subsequent ground motion is the result of a sequence of multiple aftershocks, and the damage to a structure under these conditions is more severe than from a single earthquake. Most seismic studies are based on a single earthquake event. To explore the influence of a main-aftershock sequence on an isolated inter-story structure, we constructed a three-dimensional finite-element model of such a structure and subjected it to repeated main-aftershock sequences. The Laplace asymptotic method of second-order second-moment was used to calculate the reliability of the structure under the action of a single mainshock and after a main-aftershock sequence at different seismic levels. The effects of the number of aftershocks, the location of the isolation layer, and the stiffness of the isolation bearing in the structure were analyzed. The results showed that aftershocks increased the failure probability of each sub-structural part of the inter-story isolated structure. The failure probability of the lower structure had the greatest influence, which was about 3.89 times that for the mainshock alone. The probability of failure from multiple vs single aftershocks was similar, but the magnitude of the aftershock plays a major role in failure. The number of aftershocks reduced the overall reliability of an inter-story isolation structure. In the case of different isolation layer positions, the placement of the isolation layer at the top of the seventh story under an extremely rare earthquake level resulted in a reduction of 6.01%. With isolation bearings of different stiffness, the largest decrease was 7.88% when the stiffness was 50%.

Post-earthquake reliability assessment of segmental column structures based on nonlinear model updating

In this study, a Bayesian based nonlinear model updating approach is developed to enhance the post-earthquake reliability assessment of posttensioned segmental column structures. According to the proposed procedure, dynamic global sensitivity analysis (DGSA) approach is firstly performed to analyze the sensitivity of the model outputs to the model parameters, which aims to select the appropriate parameters for model updating, and then, the likelihood function of Bayesian estimation is constructed based on the residual errors between the measured and simulated dynamic responses of segmental column structures. Since the decomposed structural dynamic responses are conducted for model updating, the simulated error variance parameters are also considered as unknown. To simultaneously estimate the unknown model parameters and variance parameters, the maximum likelihood estimation approach is employed in this study. Then, the Cram-Rao lower bound (CRLB) analysis method is applied to estimate uncertainty of the identified model parameters that caused by measurement noise. Once nonlinear model updating is completed, the earthquake-induced failure probability of segmental column structure can be evaluated by performing reliability analysis. In numerical simulations, the feasibility of the proposed reliability assessment approach is validated by using a planar posttensioned segmental column model subjected to seismic loads. Furthermore, a scaled posttensioned segmental column structure subjected to bi-directional earthquake exactions is applied to verify the effectiveness of the proposed approach. Both numerical and experimental results have shown that the proposed strategy is accurate and effective for nonlinear model updating of segmental column structures, and the updated results are capable of using to evaluate the failure probability of such type of structures subjected to strong external excitations.

An adaptive Kriging method based on K-means clustering and sampling in n-ball for structural reliability analysis

PurposeAssessing the failure probability of engineering structures is still a challenging task in the presence of various uncertainties due to the involvement of expensive-to-evaluate computational models. The traditional simulation-based approaches require tremendous computational effort, especially when the failure probability is small. Thus, the use of more efficient surrogate modeling techniques to emulate the true performance function has gained increasingly more attention and application in recent years. In this paper, an active learning method based on a Kriging model is proposed to estimate the failure probability with high efficiency and accuracy.Design/methodology/approachTo effectively identify informative samples for the enrichment of the design of experiments, a set of new learning functions is proposed. These learning functions are successfully incorporated into a sampling scheme, where the candidate samples for the enrichment are uniformly distributed in the n-dimensional hypersphere with an iteratively updated radius. To further improve the computational efficiency, a parallelization strategy that enables the proposed algorithm to select multiple sample points in each iteration is presented by introducing the K-means clustering algorithm. Hence, the proposed method is referred to as the adaptive Kriging method based on K-means clustering and sampling in n-Ball (AK-KBn).FindingsThe performance of AK-KBn is evaluated through several numerical examples. According to the generated results, all the proposed learning functions are capable of guiding the search toward sample points close to the LSS in the critical region and result in a converged Kriging model that perfectly matches the true one in the regions of interest. The AK-KBn method is demonstrated to be well suited for structural reliability analysis and a very good performance is observed in the investigated examples.Originality/valueIn this study, the statistical information of Kriging prediction, the relative contribution of the sample points to the failure probability and the distances between the candidate samples and the existing ones are all integrated into the proposed learning functions, which enables effective selection of informative samples for updating the Kriging model. Moreover, the number of required iterations is reduced by introducing the parallel computing strategy, which can dramatically alleviate the computation cost when time demanding numerical models are involved in the analysis.

Effect of parameters associated with soil-to-structure relative stiffness on seismic fragility curves of subway station

Seismic response and vulnerability of subway station underground structures are greatly influenced by kinematic soil-structure interaction, which is a function of soil properties and stiffness. Therefore, this paper investigates the influence of parameters associated with soil-to-structure relative stiffness (F) on the seismic fragility curves of underground structures. Incremental dynamic analysis method is conducted employing finite element analysis to establish the fragility curves of the station structure considering 44 earthquake records. The soil was simulated as a two-dimensional (2D) finite element domain and its nonlinear behavior is described employing the Davidenkov constitutive model. Appropriate plasticity models simulated the nonlinearity of concrete and reinforcing rebars. It was found that the failure probability of the structure decreases significantly as soil shear wave velocity increases, and the change of probability of structural failure was quantified for changes in shear wave velocity within the range 200 m/s to 600 m/s. It was also found that the failure probability of subway station in heterogeneous soil is significantly higher than that of a structure buried in homogeneous soil. On the other hand, the cross-section type of the structure has less influence on its seismic vulnerability. The seismic performance of the structure with higher F is relatively better, while there are special cases where some structures with high F that are more susceptible to failure under earthquake than structures with lower F. The findings can provide helpful guide for the performance-based seismic design of underground structures.

Seismic risk analysis based on imprecise distribution and failure probability function under multidimensional limit state

Traditional probabilistic seismic risk analysis (PSRA) often adopts accurate probabilistic model to measure the uncertainties of structural response and capacity, which cannot evaluate the effect of the number of seismic waves on structural failure probability. A novel PSRA method based on imprecise distribution and failure probability function is proposed to solve the above problems. Multidimensional limit state function is adopted to measure the structural limit state. Based on lognormal distribution assumption, the means and standard deviations of engineering demand parameters (EDPs) and thresholds are all regarded as uncertain parameters, and the traditional PSRA formula is extended to the field of imprecise probability distribution. Interval estimation is used to evaluate the confidence interval and measure the uncertainties of the means and standard deviations at the given confidence level. Bayes formula method is adopted to solve the failure probability function and obtain the upper and lower bounds of vulnerability curve and mean annual failure probability. The results show that: The proposed method can measure the uncertainty of failure probability caused by the number of seismic waves through the width of vulnerability curve, which is very helpful to judge the reliability of estimated parameters. The wider width means the greater discreteness of structure response and the lower reliability of failure probability based on accurate parameters. With the increase of damage degree, the influence of the number of seismic waves on structural failure probability increases gradually.

Risk assessment method of gas explosion based on quantification of margins and uncertainties (QMU):a case study on beam structures in buildings

Combustible gas explosions are common accidents in residential areas. Key building structural components, such as beams, slabs and columns, can be quickly damaged and destroyed by explosive overpressure loads, which may also result in continual collapse. Risk of interior gas explosions in buildings should be assessed to analyze the ability of structures to withstand disasters, which can also offer a theoretical basis for improving the structural design and construction of buildings. In this study, reinforced concrete beams in buildings were selected as the research object, and the risks to beam structures under mixed methane and air explosions were assessed using the quantification of margins and uncertainties (QMU) method. First, the uncertainty of the existing methods to calculate gas explosion and beam bending loads was analyzed. Through an influence regularity analysis, the expansion factor of combustible gas combustion products in enclosed explosion chamber, the initial density of the gas mixture in the explosion chamber before deflagration, the compressive strength of concrete, and the tensile strength of reinforcement were selected as the key uncertainty parameters. Furthermore, the Monte Carlo method was used to create 5000 samples of the selected uncertainty parameters, and statistical analysis was conducted to obtain the probability distribution of the gas explosion overpressure load and reinforced concrete beam bending load. Based on the sampling results, the beam structure’s safety margin and uncertainty analysis were analyzed to determine the probability of structural failure at the 90% confidence level. Finally, this paper provides guidelines for determining structural failure under different boundary value conditions of combustion explosion overpressure loads and reveals the sensitivity of different uncertainty parameters to structural safety margins using stepwise regression analysis. Compared to previous methods, this work includes the uncertainty features of disasters and disaster-bearing items when analyzing combustible gas explosion accidents; we anticipate it offers a fresh perspective on the quantitative assessment of gas explosion risks in buildings.

Structural global failure probability function estimation based on adaptive augmented line sampling method

A global failure probability function estimation method based on the adaptive augmented line sampling method is proposed to solve the parameter failure probability functions in structural reliability analysis and design. The proposed method uses an adaptive strategy to carry out a series of local failure probability function estimations at specific values in the design parameter space by using the augmented line sampling method. Then an optimal combination algorithm based on the minimum variation of coefficient is proposed to integrate all the local failure probability function estimations into a global estimation. Compared with the existing methods, the proposed method further improves the accuracy and efficiency of estimating failure probability functions. Finally, numerical and engineering examples are provided to demonstrate the applicability and superiority of the proposed method in analyzing calculation accuracy and efficiency.

Infrared thermography detection of grouting defects in external post-tensioned tendon ducts under construction hydration heat excitation

Most duct grouting defects are caused during the construction period, and its existence will seriously affect the safety performance of the structure. Timely detection and remediation during the construction period will reduce the high inspection and maintenance costs and the probability of structural failure later. This study proposed an approach for detecting grouting defects in external post-tensioned tendon ducts using infrared thermography (IRT) under the hydration heat of duct grouting material. IRT semi real-time detection of four different grouting defect specimens was performed indoors in the first 48 h after grouting completion to validate the proposed approach. Results showed that grouting defects with 0%, 40%, and 70% grouting compactness in high-density polyethylene ducts could be identified simultaneously from 12 h to 21.5 h after grouting completion, while defects in galvanized steel pipes (GSP) could also be identified after improving the emissivity and reflectivity of the pipe surface. Furthermore, grouting compactness could be quantified by the distance between the half maximum contrast, and PCA-based image preprocessing could reduce the quantitative error of grouting compactness detection. In addition, the detection in high temperature environment should be avoided because the rise in ambient temperature would reduce the identification ability of grouting defects. IRT technique could guide the grouting construction of external tendon ducts in actual engineering because of its ability to efficiently identify grouting defects during the hydration heat release stage of grouting material.

Influence of Rock Properties on Structural Failure Probability—Caprock Shale Examples from the Horda Platform, Offshore Norway

In any geological subsurface fluid injection, a viable top seal is required to contain the vertical movement of the injected fluid plume. However, seal integrity assessment is challenging because of the uncertainties possessed by various parameters. A probabilistic solution might be more appropriate when significant uncertainties are present. In this study, we evaluate Drake shale caprock structural reliability using a stochastic method. Drake shale is the primary top seal in the Aurora CO2 storage site, located in the Horda Platform area in the northern North Sea. Based on the lithological variations, Drake caprock shale is divided into two parts designated by upper and lower units. Six model scenarios from the upper and lower Drake units have been tested. The probabilistic structural failures of varying model scenarios are estimated using the First-Order Reliability Method (FORM). Drake Formation shale shows a considerably low probability of failure (~0) with a high reliability index in the initial stress-state condition and after-injection scenarios. Moreover, the parameter sensitivity study indicates that horizontal stress and cohesion are the most influential input parameters during reliability estimation. Comparative analysis between the caprock properties and failure probability reveals that rock strength properties such as cohesion and friction angle strongly dictate the probability of failure estimation. Moreover, comparing two caprock shale formations indicates that the structural failure values are not correlatable; hence, a formation-specific failure assessment is recommended.

Seismic fragility analysis for subway station considering varying ground motion ensembles

The seismic fragility analysis involves employing an ensemble of ground motion records to establish the seismic performance. This paper investigates the effect of number of ground motion records in the considered ensemble on the calculated post-earthquake failure probability of subway structure. A two-dimensional (2D) finite element model was established considering the soil-subway station underground structure interaction. The cloud and incremental dynamical analysis (IDA) methods are employed to compute the seismic demand of the structure and the seismic fragility curves considering different ensembles of ground motion records. The results revealed that the number of records have a significant influence on the structure seismic fragility analysis in both cloud and IDA methods. It is suggested that the optimal ensemble size should comprise 300 ground motion records in the cloud-based seismic fragility analysis, and 24 ground motion records in the IDA method. The results also showed that the failure probability of structure predicted by the cloud method is greater than that predicted by the IDA method. These findings provide practical guidance for the performance-based seismic design of underground structures.

Enhanced Adaptive Kriging Method for Estimating Fuzzy Failure Probability with Profust Model

Aiming at analyzing the structural fuzzy failure probability with probability inputs and fuzzy-state assumption (profust model), an adaptive kriging model-based sequentially truncated Monte Carlo simulation (MCS) method is investigated, where estimating the fuzzy failure probability can be transformed into identifying the absolute safety domain, the absolute failure domain, and the exact performance function values of the fuzzy safety–failure transition domain. To this end, in this study, three kriging models are sequentially constructed to realize the three aims, respectively. To further improve the efficiency of adaptively updating kriging model, adaptive radial-based importance sampling technique is embedded to divide the whole MCS candidate sampling pool (CSP) into several sub-CSPs. Then, the kriging model is updated sequentially in each sub-CSP instead of the whole CSP, and the samples dropped into the optimal hypersphere of the absolute safety domain can be truncated and do not participate in the CSP of updating the kriging model so that the size of whole MCS CSP and the size of CSP in each learning process of updating kriging are reduced simultaneously. As a result, the efficiency of estimating the fuzzy failure probability is enhanced. The results of two examples verify the effectiveness of the proposed method.

Evaluating structural failure probability during aftershocks based on spatiotemporal simulation of the regional earthquake sequence

Engineering structures damaged in a mainshock become much more vulnerable to the subsequent aftershocks. Estimating the aftershock hazard and the subsequent structural fragility is of significant interest for post-mainshock decision-making. This study introduced the spatiotemporal epidemic-type aftershock sequence (ETAS) model to simulate the regional aftershock sequence and developed a framework for evaluating the aftershock-induced failure probability of structures. The procedure includes: aftershock sequence modeling, aftershock hazard estimation, aftershock ground motion generation, fragility analysis, and structural damage probability estimation. The procedure can quantitatively estimate the failure probability of a mainshock-damaged structure during aftershocks considering the influence of spatial location of aftershock and time interval between the mainshock and aftershock. As an example, the 2021 Yangbi earthquake sequence was fitted by the ETAS model, and the failure probability of a local 5-story concrete frame structure was analyzed. The variation of the failure probability of the structure with the increase of time was investigated.

Empirical resilience and vulnerability model of regional group structure considering optimized macroseismic intensity measure

An optimized macroseismic intensity index, which integrates the traditional macroseismic intensity scale and the instrument intensity evaluation model, is proposed to evaluate regional buildings’ empirical resilience and vulnerability. The traditional failure probability of the group structure is modified and improved. The parameters and probability indexes used to assess the resilience and vulnerability of group structure in urban and rural areas are innovatively proposed. The empirical group structure seismic loss data from the actual field investigation of the Jiuzhaigou earthquake in Sichuan Province, China, on August 8, 2017, were statistically analysed, the vulnerability of the sample data was assessed by using the optimized Chinese seismic intensity scale (OCSIS-20), European Macroseismic Scale (EMS-98) and the Modified Mercalli Intensity (MMI), and the assessment and comparison model of multidimensional modal resilience and probability index was established. To improve the rationality and accuracy of typical building resilience in the macrointensity quantification region, a new quantitative model of resilience and vulnerability based on optimizing the macrointensity index and updating the lognormal distribution is proposed, and the group structure resilience comparison models for typical macrointensity standard evaluation are established. The structural vulnerability database of the Jiuzhaigou earthquake is utilized to verify the rationality of the innovative model. Ultimately, field loss inspection and damage mechanism analysis are conducted based on the characteristics of regional structural seismic resilience and the actual vulnerability of the Jiuzhaigou earthquake.