Target Reliability Levels Research Articles

Target reliabilities for heritage structures derived from cost optimization

AbstractIn the last decade, structural reliability and safety efforts have been oriented toward the assessment of existing structures and the development of related target reliability levels. However, up‐to‐date there is no consensus on the reliability philosophy that should be followed when considering the assessment of heritage structures, and the level of reliability which is appropriate to them. In this study, a framework is proposed which derives new values for the economically optimal target reliability for the upgrade of a structure, , and the reliability threshold for upgrade, , considering the cultural heritage value of the structure. The total expected life cycle cost is minimized, assuming that the structure is given up after collapse, as heritage value is typically lost after failure. The target reliability values are based on three main parameters: the relative annual benefit of using the structure (affected by its heritage value), the relative cost of failure and the relative cost of increasing the reliability. Target reliability values are proposed specifically for heritage structures, considering a range of the main input parameters.

Shallow foundation design: a comparative study of partial safety factors and full probabilistic methods

In the past two decades, Europe has witnessed a significant transition in the design codes used for assessing foundation structures, with the widespread adoption of the Eurocodes (EC). This shift remains a pertinent topic within the engineering community, particularly concerning the transition from traditional design methodologies to those prescribed by the Eurocodes, as well as the potential for fully probabilistic design. While the Eurocodes’ methodology is described as probabilistic, it is crucial to recognize that the achievement of the target reliability level is predominantly facilitated through a system of partial safety factors. These factors are integrated into the calculation algorithm as fixed values, rendering the process essentially deterministic. To refine these calculations for more accurate reliability estimates—expressed in terms of failure probability—a genuinely probabilistic framework is required, termed as fully probabilistic computation. This paper aims to elucidate the fully probabilistic calculation approach for the broader professional community, using the geotechnical application of shallow foundations as an illustrative example. We present a comparative analysis of this advanced approach with the standard foundation design according to EC7 and ČSN 731001, the latter being a precursor in Europe for implementing the partial safety factor method. The discussion extends to a practical demonstration of full probabilistic design juxtaposed against the conventional partial safety factor method, using a shallow foundation case study. Furthermore, the paper delves into the impact of the tail behavior of uncertain or spatially varying soil parameters on the theoretical probability of failure, underscoring its significance in foundation design.

Determining target levels of power distribution system reliability indices using machine learning

Electrical distribution system (EDS) reliability has always been a critical subject due to the considerable share of distribution systems in power interruptions to end-users. Meeting regulatory service quality standards requires distribution companies to achieve defined reliability levels for performance improvement. Conventionally, specialists determine target reliability based on experience, experimental knowledge, and rules of thumb. However, these methods are error-prone and may result in suboptimal investments, economic inefficiency, and inadequate resource allocation in EDS operation and planning. Accordingly, this paper presents a machine learning-based method to determine the target level for EDS's reliability indices based on its historical performance. The approach involves comprehensive analysis of historical EDS reliability data, followed by a data envelopment analysis (DEA) to assess performance across subdivisions like substations or feeders, identifying the most effective units. Subsequently, machine learning models—Random Forest (RF), Support Vector Machine (SVM), and Radial Basis Function (RBF) network—are trained on optimal subdivisions from the DEA stage. These models accurately estimate target reliability for all subdivisions, contributing to the overall determination of the EDS target reliability level. A three-scenario case study validates the proposed method, suggesting its potential applicability as a valuable tool for regulatory agencies in setting EDS reliability targets. While admitting the potential challenges, notably the method's reliance on the quality and completeness of the historical data collected by distribution companies, the paper emphasizes the importance of collaborative efforts to ensure data accuracy and sufficiency. The proposed method leads to a fair mechanism to determine the target level for a real EDS's reliability indices in comparison with a business-as-usual scenario. Moreover, it provides a reliability performance ranking for the EDS's subdivisions.

Partial safety factor calibration using surrogate models: An application for running safety of ballasted high-speed railway bridges

Traditionally, regulations employ semi-probabilistic methods with partial safety factors to control design limits. Calibrating these partial safety factors involves estimating the target reliability level and optimizing the partial safety factor values in order to minimize the deviation of the safety index between the considered design scenarios and the target value. This procedure necessitates performing a demanding amount of reliability analyses and is often carried out for simplified design situations. Therefore, high computational costs must be accepted for design problems formulated with complex computational models. This study implements a meta-modeling approach based on active learning in the partial safety calibration procedure, enabling its application to computationally intensive problems. Subsequently, the approach is applied to the running safety of ballasted high-speed railway bridges. This limit state implicitly accounts for the phenomenon of ballast destabilization, the occurrence of which disturbs the load path from the rail level to the bridge structure. The dramatic increase in train operating speeds in recent decades has increased the possibility of this design limit state being violated due to resonance. Despite the evident safety concerns, the adopted safety factors appear to be solely based on engineering judgments rather than calibration through higher-level reliability analysis. Therefore, the proposed calibration method is employed to determine the corresponding partial safety factors for various maximum allowable operating train speeds. The newly calibrated partial safety factors allow for a permissible maximum vertical acceleration of the bridge deck approximately 25% higher than the conventional design approaches. Therefore, incorporating these factors into the design procedure may lead to the construction of lighter bridges.

A consistent approach to the calibration of partial factors for permanent and variable loads in the 2nd generation of the Eurocodes

In view of the development of the 2nd generation of structural Eurocodes, a discussion about target reliability levels and the calibration of partial factors for actions has started and it is currently ongoing. In the paper, a consistent approach for the calibration of partial factors for permanent and variable loads is presented, duly considering the role of additional safeties which are generally introduced in the design when dealing with climatic actions. The presence of increased (biased) load values in wind and snow hazard maps is detected for several countries in Europe, and its role in the calibration of partial factors and evaluation of reliability levels is investigated and discussed. The results prove the importance of accounting for such safe-sided assumptions in the calibration process in a consistent approach for the definition of climatic hazard maps at the national level. Considering that values of climatic actions provided by the hazard maps are affected by such a bias, the target reliability levels recommended by the Eurocodes are met; on the opposite, disregarding the bias, an unjustified increase of recommended values of partial factors is apparently needed to achieve the target reliability, so inducing higher building material consumptions and, consequently, less sustainable constructions.

DATA‐INFORMED SAFETY ASSESSMENT OF EXISTING TRANSPORT INFRASTRUCTURES

AbstractBridges and tunnels are critical elements of the transport infrastructures network as they have often reached their design service life and are subject to unforeseen effects due to accidental actions, climate change or degradation processes. A thorough assessment process of the existing structures, aimed to support a preventive maintenance approach, is crucial at both European and national level. The assessment of existing concrete structures differs from the design of new assets, as the resisting models given are no longer valid with ongoing deterioration mechanisms. It is recommended to formulate the limit states considering the suspected damage mechanisms, with respect to adjusted target reliability levels in verifications. Existing assets also benefits from the availability of information related to the structural condition and the action effect on structures. As such, the EU Commission opened in 2019 the CSA call “Monitoring and safety of transport infrastructure”, granted to the IM‐SAFE project consortium and addressed in this paper, which specifically focuses on the proposal for further amendments to the existing EU standards on reliability assessment considering inspections, monitoring and testing and a new standard for preventive maintenance of transport infrastructure.

Quality of Security Guarantees for and with Physical Unclonable Functions and Biometric Secrecy Systems.

Unique digital circuit outputs, considered as physical unclonable function (PUF) circuit outputs, can facilitate a secure and reliable secret key agreement. To tackle noise and high correlations between the PUF circuit outputs, transform coding methods combined with scalar quantizers are typically applied to extract the uncorrelated bit sequences reliably. In this paper, we create realistic models for these transformed outputs by fitting truncated distributions to them. We also show that the state-of-the-art models are inadequate to guarantee a target reliability level for all PUF outputs, which also means that secrecy cannot be guaranteed. Therefore, we introduce a quality of security parameter to control the percentage of the PUF circuit outputs for which a target security level can be guaranteed. By applying the finite-length information theory results to a public ring oscillator output dataset, we illustrate that security guarantees can be provided for each bit extracted from any PUF device by eliminating only a small subset of PUF circuit outputs. Furthermore, we conversely show that it is not possible to provide reliability or security guarantees without eliminating any PUF circuit output. Our holistic methods and analyses can be applied to any PUF type, as well as any biometric secrecy system, with continuous-valued outputs to extract secret keys with low hardware complexity.

Probabilistic Assessment of the Equilibrium of a Steel Railway Bridge Based on Wind Tunnel and Traffic Records

The European railway network includes many steel truss girder bridges, often dating back to the end of the nineteenth century. Assessment by the partial factor method according to Eurocodes often reveals insufficient reliability of these bridges. In particular, they fail to satisfy the equilibrium limit state when a strong wind occurs simultaneously with an unloaded train crossing the bridge. To avoid unnecessary structural interventions and expensive traffic restrictions, representative types of these bridges are tested in a wind tunnel to refine the force coefficients of wind pressure for the specific shape of the bridge and selected types of lightweight train. The values of force coefficients based on wind tunnel tests correspond to 70–80% of those provided in EN 1991–1–4. Traffic flow records for the railway line under consideration are then utilised to obtain distributions of weights and heights of lightweight trains. Detailed probabilistic analysis focused on a long-span truss bridge with an intermediate bridge deck demonstrates that the reliability of this bridge is close to the target reliability level when wind tunnel force coefficients are considered along with site-specific free-field wind and railway traffic records.

Evaluating the design value of the bearing capacity of steel elements designed using numerical models

Introduction. Using numerical models to analyze the behavior of complex or new structural solutions becomes increasingly popular. New software can be used by a beginner to easily create numerical models of structures, and this is, on the one hand, an undeniable advantage, which, on the other hand, raises concerns about the accuracy and reliability of the results to be obtained. It is noteworthy that the regulatory engineering framework ignores this area. Moreover, research and design communities lack any uniform approaches to modeling, and, more importantly, to interpreting results and ensuring the structural reliability of solutions.
 
 Materials and methods. The article proposes a method for analyzing design values of the bearing capacity designated for target reliability levels, taking into account the changeability of basic variables and the modeling error. This method was developed using the Bayesian approach to quantile prediction provided that the number of validation results was limited.
 
 Results. The article presents the implementation of the proposed method of analyzing the design value of the bearing capacity using the results of FEM (finite element method) modeling of the bearing capacity of corrugated steel beams. The influence of the assumption about the standard deviation of the modeling error is analyzed.
 
 Conclusions. The work presents a method for determining the design values of the bearing capacity for the target levels of reliability, taking into account the changeability of basic variables and the modeling error. The factors, having a great impact on evaluating the design value of the bearing capacity and deserving further research, are substantiated. First, it is necessary to draw attention to the justification and regulation of target levels of structural reliability in regulations. Second, it is necessary to draw attention to studying statistical parameters of the modeling error and developing recommendations about the designation of apriori statistical data and maximum evaluations in respect of the standard deviation of the modeling error. Thirdly, attention must be drawn to development of criteria and formats for checking limit states in the course of design based on numerical models of the bearing capacity.

Risk-Based Assessment of the Reliability Level for Extreme Limit States in IEC 61400-1

The annual target reliability level for structural components is given as β = 3.3 in the main design standard for wind turbines IEC 61400-1 ed. 4. However, since the same safety factors are used for a range of load cases and limit states, deviations in the obtained reliability level can be expected, and it should be considered how to handle this in relation to the development of the IEC TS 61400-9 on probabilistic design measures. In this paper, structural reliability analyses were performed for components designed using safety factors for a range of extreme load cases, and by using the correlation between limit states for different years, the development of the reliability level over time was calculated. A relative risk-based assessment was applied to assess the optimal target reliability level and safety factors. The risk-based assessment explicitly includes the uncertainties, benefits, and costs and can motivate differentiation of the annual reliability level between load cases. Annual reliability indices were found to be in the range of 2.9–3.4, and although this includes values below the target of 3.3, it was also found that the optimal reliability indices were in the same range. The variation in reliability level can be motivated since the optimal target reliability is found to be lower than the current target for load cases with high correlation, as this causes the lifetime reliability level to be comparable to that of other extreme load cases with less correlation.

Validation of the harmonized partial factor method for design and assessment of concrete structures as proposed for fib model code 2020

AbstractWhen considering the assessment of concrete structures, a consistent approach to assess the safety level of existing structures in an objective and well‐founded way is currently still lacking in practice. As such, fib TG3.1 has developed proposals for the quantification of adjusted partial factors for the assessment of existing structures and has harmonized these proposals with partial factors for design. This resulted in a set of equations and tabulated values for the determination of partial factors for the design of new structures as well as the assessment of existing structures, currently under consideration for the fib Model Code 2020 (MC2020). In this contribution, the equations and tabulated values for partial factors as proposed for MC2020 are briefly summarized and applied in a full‐probabilistic first order reliability method (FORM) analysis in order to assess the accuracy of the proposal with respect to reaching chosen target reliability levels. The proposals appear to lead to a consistent and adequate framework for both design and assessment, that enables targeted safety levels to be achieved.

Reliability‐based partial factors for seismic design and assessment consistent with second‐generation Eurocode 8

AbstractSecond‐generation Eurocode 8 introduces displacement‐based design alongside the traditional force‐based one with reduced equivalent forces; it provides resistance models needed to apply the approach to reinforced concrete, steel and composite frame or wall‐frame structures: chord rotation for members, and shear strength for members and joints; finally, it declares a target reliability level for near collapse. This paper discusses the formulation of partial factors to achieve a target reliability when using the displacement‐based approach. The factors are derived following a traditional, time‐invariant way of performing code‐calibration for other non‐seismic design situations, starting from the probability distributions for the seismic action effect and the resistance. It is shown that the problem can be simplified to one with two Lognormal variables, a uniform reliability can be achieved over the calibration space when both a load‐side and a resistance‐side factor are used, and constant sensitivity coefficients can be used, with values different from the original König and Hosser ones and reflecting the larger weight of the action‐related uncertainty in the seismic case. The problem with this otherwise good result is that a partial factor on the load side must be used and, further, that its value is site dependent. This approach is not in line with current European practice, thus a corrected site‐independent resistance‐side partial factor is proposed, which is compatible with the framework of Eurocode 8. As a further advantage, the proposed format coincides with that proposed in the second‐generation EN1990/EN1992 for the assessment of existing structures under non‐seismic design situations.

Data‐driven reliability and cost‐based design optimization of steel fiber reinforced concrete suspended slabs

AbstractThe governing failure mode for flat slabs is punching shear, which occurs when the punching forces exceed the slab resistances in the critical area around the column surface. Recently, considerable knowledge has been obtained on understanding steel fiber reinforced concrete (SFRC) suspended slabs as a sustainable and reliable technique to enhance post‐cracking behavior and resist loading effects, including punching shear. The properties of the materials, loading, and dimension vary inevitably and may be represented in the form of statistical distributions. In this study, all parameters affecting the punching shear of the SFRC suspended slabs were treated as random variables. Monte Carlo simulations (MCS) and punching shear model developed previously using Artificial Neural Network (ANN) were combined (ANN‐MCS) to conduct a reliability analysis, cost optimization, and model calibration. Reliability results have shown that the inclusion of fibers increased the safety level (20% in terms of the reliability index β) of the slabs against punching shear. Furthermore, a reliability‐based cost optimization was performed on the ANN‐MCS model. The optimization outcomes demonstrated steel ratio has a significant impact on SFRC slab cost, and thus it should be minimized/reduced when the steel fibers are included in the mix. Moreover, the ANN model was calibrated following a code calibration procedure to account for the model, material, and fabrication uncertainties. The calibration results have shown that a reduction factor of 0.6 should be applied to the ANN‐based model to achieve the target reliability level, β ≥ 2.5.

A case study of resistance factors for bearing capacity of shallow foundations using plate load test data in Korea

ABSTRACT Ground conditions comprised of slightly or completely weathered rock are frequently encountered in design of bridge foundations in Korea. It is rather challenging to assess the accuracy of the common design methodologies for shallow foundations in these ground conditions as the foundation bearing capacity depends on the degree of weathering. This paper presents reliability-based derivation of resistance factors for the bearing capacity of shallow foundations on slightly and completely weathered rock using field plate load test data. More than 140 plate load tests were performed at 52 sites, 33 of which were considered to be of high quality and reliable. These high-quality tests were used to evaluate the uncertainties associated with the bearing capacity equations, and the resistance factors corresponding to current prescribed load factors. A reliability-based approach, with target annual failure probabilities of 1.0 × 10−3, 2.0 × 10−4, 1.0 × 10−4, was adopted to estimate the required resistance factors for different design equations. A Bayesian approach was adopted to facilitate quantification and propagation of statistical parameter uncertainty due to limited available data. The best estimates of the calibrated resistance factors range from 0.40 to about 0.47 for the considered target reliability levels, which is in good agreement with currently used values in Korea.

Comparison of approaches to reliability verification of existing steel structures

Many existing steel structures are exposed to degradation due to corrosion or fatigue and to increasing loads. Their reliability assessment is then needed. The key question is whether a particular structure can be preserved ‘as it is’, or needs to be strengthened, or whether it needs to be replaced. Unnecessary replacements of existing structures may be avoided and the remaining service life of existing steel structures may be authorized by: using advanced reliability verification techniques, optimizing target reliability, and obtaining data for a specific site or structure. In this contribution, the application of advanced reliability approaches is illustrated by the assessment of an existing steel structure. The case study demonstrates that such approaches may significantly improve assessment and allow to increase the load-bearing capacity of the structure (in the case under investigation by 10 to 20%). Improvements in reliability assessment are attributed to the use of an optimal target reliability level, case-specific statistical parameters and probabilistic distributions of the basic variables, and adjusted partial factors.

Adaptive sampling strategy for characterizing spatial distribution of soil liquefaction potential using cone penetration test

Characterizing spatial distribution of soil liquefaction potential is critical for assessing liquefaction-related hazards (e.g. building damages caused by liquefaction-induced differential settlement). However, in engineering practice, soil liquefaction potential is usually measured at limited locations in a specific site using in situ tests, e.g. cone penetration tests (CPTs), due to the restrictions of time, cost and access to subsurface space. In these cases, liquefaction potential of soil at untested locations requires to be interpreted from limited measured data points using proper interpolation method, leading to remarkable statistical uncertainty in liquefaction assessment. This underlines an important question of how to optimize the locations of CPT soundings and determine the minimum number of CPTs for achieving a target reliability level of liquefaction assessment. To tackle this issue, this study proposes a smart sampling strategy for determining the minimum number of CPTs and their optimal locations in a self-adaptive and data-driven manner. The proposed sampling strategy leverages on information entropy and Bayesian compressive sampling (BCS). Both simulated and real CPT data are used to demonstrate the proposed method. Illustrative examples indicate that the proposed method can adaptively and sequentially select the required number and optimal locations of CPTs.

Composite overwrap repair of pipelines-reliability based design framework

Considering the ages and need for repairment of the gas and oil transmission pipes in the world, in the past years, lab and field experiments were performed on fiber reinforced polymer (FRP) wrapping to steel pipes. Although this technology has widely been employed for decades, further improvement on the design guidelines is still needed. In this context, this study proposes a reliability structural design framework for the repairment of corroded pipelines using FRP composite wrapping. To be consistent with international structural design standards, reliability-based design framework is to be proposed within a semi-probabilistic approach by calibrating safety factors to account for the associated uncertainties in capacity and load effects to best meet the cost-safety balance in design. Currently, the repair design practice for corroded pipelines is based on a deterministic approach, and it cannot ensure the proper consideration of uncertainties and meeting a consistent level of target reliability in design. This study involves comprehensive experiments of FRP materials under two different environmental conditions for onshore and offshore pipes, which were used to propose the best-fit statistical models to the design parameters to realistically represent the random variables in the proposed safety factor based structural design framework. Through extensive reliability analyses, the values for the safety factors for composite and steel have been proposed according to the target reliability indices and the corrosion rate. The proposed design framework for corroded steel pipes with FRP overwrap repairment is expected to improve the current design practice and optimize the cost and safety by meeting the target reliability level.

Load Resistance Factor for Vertical Caisson Breakwater in Korea

The load resistance factor according to the target reliability level was proposed using 16 vertical breakwaters constructed along the coast of Korea. Limit state functions for sliding and overturning limit states were defined. Reliability analysis was performed to obtain the sensitivity of the limit state function to the design variables. The partial safety factors of the design variable were obtained using the sensitivity, and the load resistance factor was calculated in turn. The representative value of load resistance factors was obtained by optimizing the load resistance factors for 16 vertical breakwaters, and it was verified that the breakwater designed using the representative value had a reliability index greater than the target value.

Probability-Based Crack Width Estimation Model for Flexural Members of Underground RC Box Culverts

Crack control for slabs and beams in current design practices in Korea are based on the Frosch’s model, which is adapted in ACI 318. It is more difficult to have consistent quality control in underground construction sites, such as the RC box culverts used for electric power distribution built below the ground level. There are more discrepancies between the as-built dimensions and the design dimensions provided in drawings in these structures. Due to this variability in construction error, the crack widths measured in such structures have higher potential to have more differences than the calculated values. Although crack control is a serviceability concern, if the owner chooses to have a target crack width that needs better control, crack width estimations can be improved by considering such construction variability. The probability-based crack width model suggested in this study will allow minimizing the discrepancies between the measured and calculated crack widths and provide reliable estimations of crack widths. Typical size of slabs and beams ranging between 300 mm (12 in.) to 500 mm (20 in.) used in underground RC box culverts in Korea were tested under the four-point bending test program. The thicker specimens had smaller bar spacings which created more cracks with smaller crack widths. However, with smaller crack widths generated in these specimens, there were more errors between the measurements and calculated values. From site investigations in Korea, the thickness of slabs in underground box culverts varied the most among all parameters. As a result, the bottom concrete covers had the highest variability. Bottom concrete covers and bar spacings are the two most important parameters in concrete crack control. A probability-based crack width estimation model for flexural members was developed in this study to consider this construction variability. Monte Carlo simulations were performed to evaluate the probabilistic characteristics of the design surface crack widths with a target width of either 0.3 mm (12 mils) or 0.5 mm (20 mils). The probabilistic models of design variables included in the crack width estimation model were generated based on field-collected information from construction sites in Korea. Because the surface crack widths in RC flexural members are sensitive to the construction errors of concrete cover depths, and since there are differences between the assumed and actual stress distribution closer to the reinforcing bars, the probability of having surface cracks of 0.3 mm width (12 mils) is found to be quite high, such as 89% at the positive moment region (mid-span, bottom surface) of the top slab in RC box culverts and 45% for the negative moment region (support area, top surface) of the top slab with current design practice. In order to ensure crack widths to be smaller than the design target width, probability-based crack width factors are recommended in this study to improve estimations depending on the selected target reliability levels.

Stochastic Air Quality Dispersion Model for Defining Queuing Ships Seaport Location

This work develops a stochastic air quality dispersion to predict the pollution concentration originating from ships queuing in a seaport. The Gaussian dispersion model for five ships operating in the Black Sea queuing in the front of the port of Varna as sources of gas emission of NOx, SOx and PM10 is used to define the air pollution concentration at receptors (crowded areas of the port and other reference points) and consequently the distance to the seaport queuing location. Uncertainties, which are inherent in the input data and mathematical model, are accounted for to estimate the propagating uncertainties of the emission concentration at the receptors accounting for the wind speed, horizontal and vertical dispersion parameters as a function of the geographical location of the emission sources (ships), effective emission height and weather conditions. The estimated uncertainties of the air quality prediction are of significant importance for the decision-making on the regulatory purposes, and the probability of exceeding the threshold limits needs to be quantified. The most expected value and the probability of exceeding the acceptable limits of pollution concentration are defined by employing the first-order reliability method. The target reliability level is defined as the failure cause and mode used for identifying the safety calibration factors that may be employed for defining the most suitable location of the ship queuing seaport. Several conclusions about the applicability of the developed stochastic model and its use for regulatory purposes are also provided.