Code Calibration Research Articles

IM-based seismic reliability assessment of the pre-code masonry building stock in metropolitan area of Lisbon

Earthquakes have a long history of causing catastrophic damage to communities, resulting in structural collapses, loss of life, and economic turmoil. To enable informed decision-making and reduce the impact of these events in earthquake-prone regions, seismic risk studies provide relevant information to support stakeholders in the implementation of effective risk-based policies. The present work addresses the seismic reliability of the pre-code masonry building stock in the Metropolitan Area of Lisbon, which is the region of Portugal that faces the highest seismic risk due to the coexistence of moderate to high seismic hazard and highest demographic-economic exposure. The adopted general framework combines several hazard studies developed for the region under investigation and a synthetic database of masonry buildings representative of the pre-code building stock in Lisbon. Through analytical–numerical probabilistic approaches, new second-order hazard solutions with structural dependency are derived for the mean annual frequency of limit-state exceedance, which can be integrated into national application documents for Eurocode 8. In light of these results, the reliability assessment of the building stock is conducted in several Local Administrative Units by means of an improved SAC/FEMA formulation. The study represents the first comprehensive investigation of its kind in this region, providing essential information to define appropriate target safety level for code calibration and support future risk studies.

An international benchmark for wind plant wakes from the American WAKE ExperimeNt (AWAKEN)

This article introduces the first benchmark study within the International Energy Agency Wind Task 57 framework, focusing on wind plant wakes. Leveraging data from the American WAKE ExperimeNt (AWAKEN), the benchmark aims to assess the accuracy of simulation tools in modeling wind plant wakes and their impact on the downstream flow under diverse inflow conditions. The AWAKEN field campaign, conducted in Oklahoma from 2022 to 2024, provides unprecedented observations of wind plant-atmosphere interactions, thus offering a large dataset to validate numerical models of different complexity. The benchmark will include three phases—code calibration, blind comparison, and iteration—allowing participants to refine their numerical models based on the feedback from the benchmark team. This article describes the benchmark case study selected from observations providing details on atmospheric conditions, wake evidence, and wind turbine operation. The benchmark’s structure and timeline, along with the expected publication of results, are discussed as well. This collaborative effort aims to enhance the accuracy of wind plant wake simulations, thus contributing to the improvement of wind energy production estimates.

Comparative study on semi-probabilistic design methods to calibrate load and resistance factors for sliding stability design of caisson breakwaters

The partial safety factor method commonly necessitates a set of multiplying factors (MFs) to modify the basic variables; hence, when multiple variables are included, it is complicated for design practice. Conversely, the load and resistance factor design (LRFD) format is more practical since it utilizes fewer factors to adjust loads and resistance. This study carries out a comparative study of the two semi-probabilistic design formats and four calibration methods to determine the more suitable design approach and establish associated factors for sliding stability designs of caisson breakwaters under wave and seismic conditions. To fulfill the aforementioned purposes, 12 perforated caisson breakwaters are first selected; thereafter, four calibration methods, which include a closed-form solution and three scenarios based on Monte Carlo simulation (MCS), are executed to determine individual MFs for each case. The final single set of MFs for design practice is calibrated via an optimization process. The present study shows that the two design formats can provide similar solutions. Hence, the LRFD-based concept is recommended to be applied owing to its easier implementation in code calibrations and design practices. Moreover, the performance of the shifting-technique-MCS-based calibration (the simplest simulation) is thoroughly investigated, and it is then found that this approach must be used with care if the target safety considerably varies from the initial safety level. In the present work, an efficient and accurate approximation method to specify the final MFs set is proposed because the optimization-based calibrations to determine the final set of MFs are time-consuming and expensive to evaluate.

Probabilistic framework for robust optimal code calibration through minimization of the lifecycle cost and its uncertainty

Probabilistic framework for robust optimal code calibration through minimization of the lifecycle cost and its uncertainty

Determination of load combination factors for code calibration

Semi-probabilistic methods are widely used for structural engineering design and assessment. In such methods, the safety and performance adequacy of structures are typically tied to partial safety factors for load and resistance, and load combination factors. There exist some heuristic strategies for estimating these partial factors, such as the design value method and first order reliability coefficient method. However, when adopted for the estimation of load combination factors, these strategies are either inaccurate or have non-unique estimates. Excessive conservatism in factor estimates is not desirable, particularly for the performance assessment of existing structures. In this study we propose a method for estimating load combination factors using a matrix linear algebra approach. Specifically, we develop a closed-form analytical expression to estimate unique load combination factors for typical code calibration problems. A comparative study of the existing heuristic approaches with the new approach is presented and demonstrated on two case studies. It is shown that the proposed method offers a valuable means of deriving load combination factors: one that avoids hueristics, and conservatism.

Probabilistic demand models and reliability based code calibration for reinforced concrete column and beam subjected to blast loading

Probabilistic demand models and reliability based code calibration for reinforced concrete column and beam subjected to blast loading

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.

Modelos probabilísticos para a ação de utilização em edifícios: análise crítica, comparação com normas brasileiras de projeto, e calibração dos fatores parciais de segurança

abstract: Nowadays, structural “limit state” design is made using characteristic or nominal values of actions, partial safety factors and load combination factors. The actual loading that a structure will be subjected to throughout its life is not known at the design phase. Yet, probabilistic models of such loadings are useful for the rational determination of partial safety factors and load combination factors. The probabilistic model leading to nominal live loads of NBR 6120:2019 (Design Loads for Structures) has never been openly discussed. Herein a simple probabilistic model describing spatial and temporal variabilities of live loads in buildings is presented and discussed. The model is built as a sum of two stochastic processes representing the sustained and intermittent parts of the live load. Model parameters are the ones recommended by the Joint Committee on Structural Safety (JCSS), based on extensive surveys done in several countries. By way of Monte Carlo simulations, sample values of live load actions are obtained for buildings of different occupancy types. These values are compared with those recommended by international standards, and those recommended in NBR 6120:2019 and NBR 8681:2003 (Actions and Safety of Structures). The corresponding statistics for the fifty-year extreme and arbitrary point-in-time distributions of live loads are presented; these statistics are very relevant for reliability analyses and for reliability-based code calibration. The stochastic live load model is also employed in a reliability-based calibration to obtain partial safety factors and load combination factors to be used in Brazilian design codes, for ultimate and serviceability limit state verifications.

Calibration of resistance factors for design of shallow foundations against sliding

The design of shallow foundations typically proceeds by using the load and resistance factor design (LRFD) methodology to avoid various limit states with some probability. This paper looks at the sliding limit state of shallow foundations, and the sliding resistance factors required for the LRFD approach are estimated using reliability analyses of surface strip foundations. Cohesive and frictional soils are separately studied under wind loading conditions. Monte Carlo simulations are used to estimate the sliding failure probability of foundation designs on cohesive soils, and an analytical method is developed for frictional soils. The results indicate the existence of a “worst case” correlation length for cohesive soils, and the sliding resistance factor required to achieve target maximum lifetime failure probabilities is around 0.4–0.65 for moderate soil variability. For frictional soils, the required sliding resistance factor is about 0.5–0.85 for ν ϕ′ = 0.15. Overall, the sliding resistance factors recommended here agree well with the resistance factors of ϕ gu = 0.6 for cohesive soils and ϕ gu = 0.8 for frictional soils stipulated by geotechnical LRFD code provisions in Canada. The analyses can be used to estimate the reliability of current designs and can also aid the calibration of geotechnical design codes.

Reliability-based calibration of site-specific design typhoon wind and wave loads for wind turbine

The wind turbines (WTs) that are designed, constructed, and installed near the coastline of mainland China are faced with geographically varying tropical cyclone hazards; failure of WTs due to the tropical cyclone (TC) hazards has been observed in this considered region. The reliability-based Chinese design code calibration of WTs subjected to TC hazards for the considered region seems missing in the literature. In the present study, we calibrate the site-specific design TC wind and wave loads for designing offshore and onshore WTs located in the considered region for selected target reliability indices. The calibration considers the correlated TC wind speed and significant wave height during the passage of TC events. Also, the companion load factors by considering wind load and inertial wave load effects are calibrated. Moreover, the statistics of the responses of the onshore and offshore versions of the National Renewable Energy Laboratory 5 MW wind turbines are calculated using the software package FAST. The statistics of the responses are used in the reliability-based verification analysis by considering the calibrated design TC wind load and wave load requirements. The results indicated that using the calibrated geographically varying TC wind and wave loads is adequate and can be used to aid structural design code making.

Reliability analysis & performance-based code calibration for slabs/walls of protective structures subject to air blast loading

A multilevel performance-based design (PBD) framework is developed for panels of Protective structures subjected to air blast. These provisions improve the existing design approach of blast resistance structures for ultimate limit state. Present study develops probabilistic deflection-based capacity and demand models for three performance levels associated with four damage states occurring during an air blast. The chosen protective structures for current study are reinforced Normal Strength Concrete (NRC) and reinforced Ultra-High Strength Concrete (UHSC) panels. The probabilistic models are developed using Bayesian inference (Posterior Statistics). The database is generated through numerical experimental design using finite element (FE) based software, LS-DYNA. The influence of air blast on panel is validated on a panel and obtained results shows the trustworthiness of numerical model. Grounded on these models the fragility estimation is carried out and attained plots demonstrates the consistency. Using a reliability based approach, the Load and Resistance Factors for Design (LRFD) are developed associated with the proposed three performance levels. Hazard curves and total probability are estimated using established dataset from literature available. The estimated LRFD factors can be used for the design of NRC & UHSC panel of slab/walls of protective structure subjected to air blast.

First-Principles Study on the Effect of Lithiation in Spinel LixMn2O4 (0 ≤ x ≤ 1) Structure: Calibration of CASTEP and ONETEP Simulation Codes

Lithium–manganese–oxide (Li-Mn-O) spinel is among the promising and economically viable, high-energy density cathode materials for enhancing the performance of lithium-ion batteries. However, its commercialization is hindered by its poor cyclic performance. In computational modelling, pivotal in-depth understanding of material behaviour and properties is sizably propelled by advancements in computational methods. Hence, the current work compares traditional DFT (CASTEP) and linear-scaling DFT (ONETEP) in a LiMn2O4 electronic property study to pave way for large-scale DFT calculations in a quest to improve its electrochemical properties. The metallic behaviour of LixMn2O4 (0.25 ≤ x ≤ 1) and Li2Mn2O4 was correctly determined by both CASTEP and ONETEP code in line with experiments. Furthermore, OCV during the discharge cycle deduced by both codes is in good accordance and is between 5 V and 2.5 V in the composition range of 0 ≤ x ≤ 1. Moreover, the scaling of the ONETEP code was performed at South Africa’s CHPC to provide guidelines on more productive large-scale ONETEP runs. Substantial total computing time can be saved by systematically adding the number of processors with the growing structure size. The study also substantiates that true linear scaling of the ONETEP code is achieved by a systematic truncation of the density kernel.

Asymptotic behavior of seismic hazard curves

Hazard curves from probabilistic seismic hazard analysis (PSHA) are plots of the rate of earthquakes exceeding ground motion intensity values vs such threshold values, for a site of interest. In classical PSHA, these curves can be transformed to provide the probability of exceedance of ground motion intensity values in any time interval, utilizing the properties of the homogeneous Poisson process (HPP). In turn, these probability curves can be seen as the plot of the complementary cumulative distribution function of the maximum intensity observed, at the site, in the time interval of interest. One consequence of the HPP framework, within which PSHA is developed, is that, for large time intervals, it can be argued that these curves could asymptotically lead to a probabilistic model for extreme value (EV) random variables. This is discussed, with a simple engineering approach, in this short note, where it is found – via case studies – that exceedance hazard curves seem to converge towards an EV distribution (i.e., the EV type II or Fréchet), with a pace that is impacted by the discontinuity inherent to the curves. It is also seen that other common models, typically used to provide an analytical format to probabilistic curves, do not show the same level of convergence. Besides providing further insights on the results of PSHA, this study can possibly be useful for those cases where a closed-form equation for the hazard curve could be needed, such as reliability-based calibration of building codes, or seismic risk studies involving seismic hazard approximation/extrapolation.

Performance-Based Code Calibration and Total Probability of Failure of the Nuclear Containment Structure Subjected to Missile Impact

The multifarious calamities upon nuclear containment structures (NCS) and insufficient reliability-based factors inspired the current study for the investigation of hard missile impact. Available codes for design and construction of NCS suggest a load factor of 1.0 and basic information for the missile impact scenarios. However, the current study proposes novel reliability-based load and resistance factors for NCS subjected to a hard missile impact. The performance-based probabilistic energy capacity and demand models have been used for the code calibration process. These models were based on three performance levels associated with four levels of damage. The levels were chosen based on local damage due to its rigidity from insignificant penetration to complete perforation of the missile. This study also developed hazard curves for various distributions of missile mass and velocity. The total probability of failure of NCS was calculated based on a realistic range of material and geometrical variables and globally existing cruise missiles, wind-borne missiles, pressure pipes, iron rods, and others. The current investigation considers all the inherent uncertainties of target and missile. This study circumvents the limitations and develops performance-based load and resistance factors based on probabilistic models. The developed load and resistance factors for codal provisions are tied in turn to the different performance levels of the NCS. These factors can be used for the design of NCS, bunkers, silos, storage tanks, slabs, and others without performing exhaustive analysis and/or experiments.

Simplified expressions for reliability assessments in code calibration

First Order Reliability Methods (FORM) have been used by specification committees in the reliability analyses required for the calibration of resistance and safety factors for the past 40 years. However, these methods are iterative, require input information that may not be readily available, and make comparisons between different approaches or design frameworks difficult. This paper presents a set of simplified equations to estimate reliability indices β, resistance factors ϕ and partial safety factors γM based on simpler First Order Second Moment (FOSM) considerations for the US and Eurocode frameworks, which are particularized for different load cases, and on the semi-probabilistic approach prescribed in the Eurocode 0. The equations provide direct relationships between the reliability calibration results corresponding to different design frameworks, and can be used to estimate resistance factors as simple cross-checks for the US framework based on the partial safety factors derived for the Eurocode (or vice versa) from basic statistical input information and given target reliability, including when the data available in the literature is insufficient to perform FORM analyses. The accuracy of the proposed equations is assessed against reliability results derived using FORM techniques for an extensive database of steel and stainless steel frames subjected to gravity and combined gravity plus wind load cases collected from the literature, and limitations for their applicability are recommended. The results demonstrate that the set of equations proposed in this paper provides accurate estimations of the reliability index β, resistance factors ϕ and partial safety factors γM and can assist specification committees in the process of calibrating suitable ϕ and γM-factors.

Reliability analysis of concrete beams reinforced with FRP bars

The strength reduction factors (ϕ) adopted by ACI-440.1R-15 standard code for the flexure design of Fiber Reinforced Polymers Reinforced Concrete (FRP-RC) beams are calibrated in this study. The code calibration process aims to achieve a particular target reliability index (βT) for the selected FRP-RC rectangular beams. An extensive experimental database is collected and used in the calibration process of the resistance factors. It was found that the calibrated ϕ led to a more economical and less conservative design while satisfying the safety requirements imposed by the design code. To meet the βT, a recommended value of ϕ, is found to be 0.70 for cast-in-situ beams failing in compression and 0.65 for tension-controlled cast-in-situ beams. Thus, the proposed values are slightly greater than comparable factors adopted by the ACI code of 0.65 for compressioncontrolled and 0.55 for tension-controlled cast-in-situ beams.

Reliability updating of partial factors for empirical codes: Application to Super-T PSC girders designs at the ultimate limit state in bending

Reliability design code calibrations typically involve the comparison of calculated levels of safety (β) of designs to a range of prospective partial safety factors with the minimum acceptable level of safety (βT). When updating the calibration and the original βT is unknown or undocumented, design-specific probability models and the code-implied level of safety are necessary. This study presents a methodology for updating capacity reduction factors ϕ for a suite of PSC bridge girder section designs for ultimate strength in bending for a design code for which βT is unknown. In the methodology, the code-implied safety as inferred from the notional traffic design load, and the designed girder safety under actual traffic loading are computed. The method is applied to the suite of prestressed concrete Super-T girders designed to the Australian bridge standards AS5100, in which the implicit βT is not known. The results find both code-implied safety and designed girder safety far surpasses the usual recommendations for βT for all designs and regardless of ϕ. As such, only through the relative comparison of code-implied safety and designed girder safety can recommendations be made on increasing ϕ in AS 5100 for Super-T girder ultimate strength in bending. Moreover, the comparison with code-implied safety is taken to indicate the desired degree of reserve capacity available for future traffic growth. The results inform on possible improvements for the next version of AS5100. More significantly, the work illustrates a way to reliability-update partial factors of design codes when βT is not known, and future-proofing structures is seen as necessary.

A reliability-based approach and code calibration of FRP-Confined rectangular RC columns subjected to concentric loading

This study aims to present an approach to investigate the reliability levels of reinforced concrete (RC) columns confined by Fiber Reinforced Polymers (FRP) subjected to concentric loading. First, the statistical properties of random variables such as model error, FRP strain efficiency factor (FSE factor) and axial resistance of columns are investigated. Then in respect to the existing correlation between variables and extensive collected database, an appropriate probabilistic model for model error, FSE factor and compressive resistance of RC column is proposed. In addition, the effects of live-to-dead load ratio, reinforcement ratio and the confinement levels on the reliability of FRP-confined columns are studied through a reliability analysis. Furthermore, based on existing studies, reliability indices for various levels of confinement are calculated. Finally, a calibration analysis on safety factors of ACI 440.2R-17 guideline and shape factor of rectangular cross-section is presented.

Reliability-based assessment and calibration of standards for the lateral vibration of pedestrian bridges

Ensuring vibrations remain tolerable to occupants is central to the serviceability limit state (SLS) design of lightweight pedestrian bridges. In general, pedestrians tend to be more sensitive to lateral bridge vibrations compared to vertical vibrations, which underscores the importance of serviceability limit state (SLS) design in the lateral direction. Significant uncertainties associated with the pedestrian loading and bridge behaviour motivate the need to treat serviceability design provisions from a reliability standpoint. This paper is a first attempt towards such an assessment and code calibration of SLS provisions applicable to the lateral direction in the existing major pedestrian bridge design guidelines (ISO 10137, Eurocode 5 and SÉTRA). For this purpose, this study adopts a reliability-based framework, which accounts for the uncertainties arising from the pedestrian loading, perceptions of vibration by pedestrians, and structural damping. Furthermore, SLS design generally considers commonly occurring design traffic densities only. However, several historical lateral vibration serviceability failures of pedestrian bridges have occurred under infrequent loading events. Hence, this paper also incorporates infrequent traffic event (load case) in the reliability assessment and calibration of the design guidelines. Results show that metal truss-type pedestrian bridges under design and infrequent traffic events need to be designed to a higher reliability level (through calibration) than currently achieved by these provisions under the design event. Adopting traffic density and frequency-dependent acceleration limits can mitigate overdesigns resulting from the calibration exercise. The desired reliability index required to achieve minimum acceptable performance of the designs under both the design and infrequent events is estimated iteratively in the proposed procedure, followed by the calculation of design calibration factors. This study shows that the calibration of some design provisions (e.g., SÉTRA) depends on amplitude-dependent damping values, while this is not the case with other provisions. This dependency can be attributed to differences in the form of the limit state function. Finally, it is shown that the proposed calibration process achieves sufficient and consistent reliability across all bridge classes under design and infrequent traffic events in the lateral direction, while ensuring economic designs using traffic density and frequency-based comfort limits.

Ramifications of blind adoption of load and resistance factors in building codes: reliability-based assessment

This paper presents a probabilistic approach to reveal the negative consequences of overlooking code calibration when adopting the provisions of nonindigenous building codes in design. A taxonomy of the national building codes of various countries whose provisions are adopted from one or more original standards is first presented. Next, the reliability-based approach to quantify the lack of safety that may arise due to the absence of code calibration is presented. This approach is then applied to the case study of the National Building Code of Iran, whose load and resistance factors are directly adopted from ASCE/SEI 7. To this end, seven steel building archetypes with various structural systems at various regions with different seismicity levels and site classes are designed according to the Iranian loading and steel design codes. Subsequently, 2510 structural elements, including beams, columns, and braces, from these archetypes are subjected to reliability analysis to compute their reliabilities. In this analysis, the uncertainty of material properties are quantified using local laboratory test data and the uncertainties associated with manufacturing tolerances of steel elements are quantified through extensive field surveys. The analysis results in reliability indices that are markedly smaller than the targets set by the original standards the Iranian code has adopted from, which exposes the notable lack of safety in the ensuing designs. Subsequently, the load and resistance factors are calibrated to achieve the target reliabilities. Among other changes, the results indicate the need for a 25% increase in the earthquake load factor, which reveals the lack of safety that is implicit in the current practice. Reliability sensitivity analysis is then employed to determine the sources of uncertainty that are most influential on the resulting reliabilities. The presented approach is immediately applicable to the assessment of the building codes of other countries.