Reliability-based Calibration Research Articles

Probabilistic calibration of fatigue safety factors for offshore wind turbine concrete structures

Current fatigue design rules for offshore concrete structures were adopted from the oil and gas industry. When better models or more information are available, partial safety factors can be re-calibrated according to target reliability levels for offshore wind turbines. This paper describes a framework for reliability-based calibration of fatigue partial safety factors for offshore wind turbine concrete structures. Offshore wind turbine loads accounting for the statistical distribution of turbulence intensity are estimated using a fully-integrated aeroelastic model. Based on available experimental fatigue tests, a fatigue reliability model for concrete is formulated and applied in two numerical examples. Results indicate that the recommended material partial safety factor in the DNV standard for Offshore Concrete Structures can be lowered without compromising structural safety. The proposed modification can potentially contribute to structural design optimization and further cost reduction in offshore wind energy.

Reliability-based calibration of partial factors for the design of membrane structures

Membrane structures are widely used because of their lightweight properties and expressive architectural shapes. However, there does not yet exist a unified design approach for membrane structures as is available for conventional buildings. Because of their flexibility, membrane structures exhibit a different structural behaviour than conventional buildings. Membrane structures are doubly curved, prestressed and the prestress contributes to the stiffness. The structural response of these structures is non-linear, and the hanging and arching directions interact.A probabilistic framework for tensioned membrane structures is developed herein. Using this tool, partial factors are calibrated for a representative tensioned hypar membrane structure made of PVC-coated polyester fabric. Reliability analyses are performed using a First Order Reliability Method in combination with Latin Hypercube Sampling. The approach is illustrated for two load cases, i.e. considering snow load and wind uplift load, respectively. Three hypars are investigated, each with a different rise to span ratio.The partial factors are determined through a minimisation process. As a result of the performed process, the recommended partial factor for prestress is 1.0, for snow load is 2.0 and for wind uplift load is 2.0 for the investigated membrane structure. In this study, the hanging direction under snow load proves to be decisive for the calibration of the partial factors. The obtained partial factors are not in line with the partial factors found in the Eurocode (1.5 for variable loads). Alternatively, when considering a partial factor for snow load and wind uplift load of 1.5, partial factor for prestress should be increased to 1.2 for the structural type which have been investigated.The application of Latin Hypercube Sampling in combination with the structural analysis of membrane structures enables to perform the reliability analysis calculations in a more computationally efficient way. Moreover, the used optimisation procedure for the calibration of the partial factors makes it possible to interpret the obtained results with respect to the complex non-linear behaviour of the investigated tensile membrane structures.

Fatigue reliability of large monopiles for offshore wind turbines

Upscaling of traditional monopiles to support larger offshore wind turbines introduces fatigue-related design challenges. The design becomes mainly driven by wave-induced fatigue loads, and potential resonant responses can have significant contributions to fatigue. It is essential that these changes in load characteristics be reflected in the design codes. In this paper, fatigue reliability analysis of a wave sensitive, large monopile supporting a 10 MW offshore wind turbine is demonstrated. Reliability-based calibration of fatigue design factors is based on an extensive set of numerical simulations, where the statistical distribution of turbulence intensity and preservation of wave-induced resonant responses are considered. Results show that a minimum fatigue design factor, FDF⩾3 is recommended. The results and methodology presented in this study can assist with identifying the technical limitations and economic viability of upscaling monopiles.

Reliability-based calibration of main Brazilian structural design codes

Abstract Structural reliability theory has long been recognized as the proper tool to guide selection of partial safety factors in limit state structural design codes. Brazilian design codes, however, have never been through this calibration process. This paper addresses the reliability-based calibration of partial safety factors of Brazilian design codes for loads (NBR8681:2003), and for steel (NBR8800:2008) and concrete (NBR6118:2014) structures. The study is based on an extensive dataset of load and strength variables, addressing the Brazilian reality, as much as possible. Calibration minimizes the variations of reliability indexes of the most diverse structures designed according to the codes of interest, with regard to a target reliability index chosen by the analyst. The main result of calibration is to make reliability indexes more uniform, for different design configurations. In case of Brazilian codes, this could be achieved by increasing main variable loads, and reducing the combination values of secondary loads. This paper presents results that are not (yet) recommended for adoption in Brazilian codes, but which should be discussed with the community in order to reach minimal consensus.

Reliability-based calibration of Brazilian structural design codes used in the design of concrete structures

Abstract This paper presents a reliability-based calibration of partial safety factors for Brazilian codes used in the design of concrete structures. The work is based on reliability theory, which allows an explicit representation of the uncertainties involved in terms of resistances and loads. Regarding the resistances, this study considers beams with concrete of five classes (C20, C30, C40, C50 and C60), three ratios between base and effective depth (0.25, 0.50 and 0.75), three longitudinal reinforcement ratios (ρmin, 0.5% and ρmax) and three transverse reinforcement ratios ( A s s m i n, 5 . A s s m i n and A s s m a x). In terms of loads, this work considers seven ratios between live loads and permanent loads (qn/gn), and seven ratios between wind loads and permanent loads (wn/gn). The study also adopts a single value for the target reliability index (βtarget = 3.0). Results show that the optimized set of partial safety factors leads to more uniform reliability for different design situations and load combinations.

Reliability-based calibration of partial factors for the design of temporary scaffold structures

In this work, partial factors for the design of temporary scaffold structures are calibrated based on reliability calculations. Scaffolds are commonly designed in accordance with the rules in standards (e.g. EN12811, EN12810) and information found in codes of good practice. However, there is no clear proof that these design procedures result in an appropriate and consistent safety level for scaffold structures. The present study proposes appropriate target reliability levels for façade scaffolds, based on which partial factors are determined. The results are based on simulations of different scaffold design situations, considering samples generated by Latin Hypercube Sampling (LHS). The results of these simulations are processed by applying FORM analyses for buckling and yielding of the scaffold elements. As such, the inherent reliability corresponding to current design practice is determined. Based on the inherent and target reliabilities, partial factors are calibrated using two methods: the Adjusted Partial Factor Method and an optimisation procedure based on least-square averaging. Concluding, annual reliability indexes in the range 2.5–3.5 are found. These lead to partial factors lower than or equal to those used in current design practice. Hence, there is an optimisation possible in the design of temporary structures compared to current practice, leading to more economical scaffold designs.

Fatigue reliability analysis of crêt de l’Anneau viaduct: a case study

Fatigue of reinforced concrete is often not considered for civil engineering structures since the self-weights of reinforced concrete structures are very high (in case of normal strength concrete) while live loads are relatively small, which leads to very small stress variations during service duration of the structure. However, particularly for bridge structures with increased use of high strength concrete and increase in traffic loads, this scenario is reversed and fatigue verification becomes much more important for the safety. This paper presents a probabilistic approach for reliability assessment of existing bridges along with reliability-based calibration of fatigue-design-factors based on the S-N approach, calibration of S-N approach with fracture-mechanics approach and reliability updating using inspections along with a case study for the Crêt de l’Anneau viaduct in Switzerland. It has been observed that, a designer needs to design the structure for fatigue life of 3.5–4.5 times the planned service life, in order to achieve the target annual reliability index of 3.7 at the end of the service life. Further, the presented framework can easily be extended to any other viaducts to estimate the fatigue reliability and maintain the safety level throughout the entire service duration.

Reliability-Based Calibration of Resistance Factors in LRFD Method for Driven Pile Foundations on Inshore Regions of Iran

This paper presents the improvement of load and resistance factor design (LRFD) method for axially loaded driven piles in Iran. The LRFD method has been well developed and successfully implemented in geotechnical engineering, especially in the design of pile foundations in different parts of the world. To extend the use of this method in Iran, it is necessary to use the results of reliable local pile load tests and construction records to calibrate LRFD resistance factors regionally. To this end, we first collected a comprehensive database of static and dynamic load tests which have been performed on driven piles in fine-grained soils across Iran. Based on this database, we calculated the resistance factors for different design methods using three different methods of reliability analysis (FORM, FOSM, and MCS) and for two levels of reliability (βT = 2.33 and 3). Finally, we used these calculations together with experience and engineering judgment to propose resistance factors for the National Building Code of Iran.

Safety factor calibration for a new model of shear strength of reinforced concrete building beams and slabs

When assessing existing structures, the availability of adequate safety factors, calibrated with the most accurate models, and for established target reliability indexes, is of critical importance in order to take the right decision regarding the maintenance/repair/strengthening interventions. In the case of shear resistance in reinforced concrete (RC) structures, when using the current design codes provisions for new constructions in assessment results that, in many cases, existing structures may be considered unsafe, implying large economic costs in strengthening or even dismantling. In this research, a proposal of safety factor relative to a recently developed model for shear strength, for elements with and without transversal reinforcement, based on a reliability-based calibration is presented. A formulation is proposed to determine the adequate strength factor for a selected target reliability index of the existing structure and desired remaining service life by means of a safety factor format, considering the load factors present in the Eurocodes. The calibration is carried out considering typical geometry and load ratios of building floors, as well as normal and high strength concrete. The derived safety factor is almost independent of the chosen remaining service life.

Mathematical models for prediction of safety factors for a simply supported steel beam

The reliability-based calibration of safety factors for the design of a simply supported steel beam, based on BS5950 (2000) is presented in this research work. The calibration was undertaken using a specialized computer program in Microsoft excel environment developed by the Joint Committee for Structural Safety (JCSS) CODE-CAL 2001. The design variables considered were modeled using the software, and the safety factors for the material, dead and live load were calibrated by varying the safety index. From the results obtained, mathematical prediction models were developed using a least square regression analysis for bending, shear and deflection modes of failure considered in the study. The results showed that the safety factors for material, dead and live load are not unique, but they are influenced by safety index and it was also shown that the safety factors for material, dead and live load vary from 0.61 to 1.15, 1.44 to 1.91 and 1.40 to 1.65 respectively for both bending and shear modes of failure. For deflection mode of failure, the results showed that the safety factors for material, dead and live load vary from 1.08 to 1.56, 1.10 to 1.17 and 0.83 to 1.25 respectively for target safety index (βt) of 2.0 to 4.5. The mathematical prediction models developed for both bending and shear modes of failure are the same. Therefore, it is recommended that the mathematical prediction models developed in this study for bending and deflection modes of failure could be used when designing a simply supported steel beam to BS 5950 (2000).Keywords: reliability, code calibration, load factor, safety factor, design, steel beam

Reliability-based code calibration applied to thin elements made of UHPFRC

A semi-probabilistic approach used in current design codes requires calibrated partial factors to secure safety of structures and people. The current code calibration procedure has an inefficient and imprecise iterative loop and it also neglects economical aspects which should be an integral part of any code calibration. This paper suggests a modified approach to the reliability-based code calibration which eliminates disadvantages of the original procedure and it is defined in a way to take advantage of the current computation means such as parallel and cloud computing. The modified approach was used to calibrate the partial factors for the structural verification of UHPFRC thin elements predominantly loaded in bending. The described example proves efficiency of the modified approach and it illustrates the advantages of the reliability-based code calibration. Indeed, the design method of UHPFRC with the calibrated partial factors allows better exploitation of the material without compromising the safety requirements. Because of the straightforward procedure, independent reliability and design computations, and selection of the ideal partial factors at the end of the calibration procedure, the modified approach is an ideal option for various code calibrations. It is worth noting that the modified approach can “grow” with development of material, knowledge, applications, and safety requirements due its simple updating which was not possible before. Moreover, the removal of the iterative loop allows using Monte Carlo methods (among other options) which are normally time-consuming and impractical for code calibration.

Reliability of partially encased steel-concrete composite columns under eccentric loading

Abstract The Brazilian design code for composite buildings (NBR8800) has never been subject to a reliability-based calibration of the partial factors used in design. As a consequence, the level of structural safety achieved by using these factors is, in general, unknown. This paper presents a study of the reliability of partially encased steel-concrete composite columns, subject to compression and bending. Literature statistics are used to quantify uncertainty in strength of structural materials and in loads. Reliability indexes are evaluated, via FORM, for two ratios between dead and live loads, and for some values of load eccentricity. It was found that larger load eccentricity leads to a reduction in reliability indexes. These values are larger than minimum values recommended in international design codes; hence one concludes that design of such columns using NBR8800 leads to acceptable safety levels.

Calibration of Australian Standard AS3600 concrete structures part II: reliability indices and changes to capacity reduction factors

Capacity reduction factors (ϕ) for flexure, shear and axial loadings are derived for reinforced concrete (RC) structures based on a reliability-based calibration of the Australian Concrete Structures Standard AS3600. The structural reliability analysis considers the bias and variability of material properties, dimensions, loads and model error. The target reliabilities (βT) are selected based on consideration of past practice and Australian and international standards. The capacity reduction factors (ϕ) for the new code AS3600-2009 are selected using the most recent statistical parameters for material strengths for 20–100 MPa strength concrete using Class N (ductile) 500N reinforcement. The reliability-based calibration found that the ϕ-factor can be increased from 0.80 to 0.85 for members in bending, and increased from 0.60 to 0.65 for axial loading of short (stocky) columns where the ratio of the live load to the dead load is at least 0.25. No changes are recommended for shear or torsion, at this time, or for slender columns; further research is needed to better refine the design models for these cases and reduce the variation in their model error. The proposed increases in capacity reduction factors will result in up to an 8.3% increase in design strength that, in turn, provides efficiency in the use of materials. The proposed changes provide for modest savings in greenhouse gas emissions.

Characteristic soil strength for axial pile capacity and its estimation with confidence for offshore applications

Many offshore design codes require the characteristic soil strength for axial pile capacity to be estimated with caution or conservatism, i.e. – in statistical terms – it has to be estimated with confidence. This study is concerned with a reliability-based calibration of the necessary minimum confidence for such estimation. The study demonstrates how to estimate characteristic soil strength for axial pile capacity with confidence and provides an approach to such estimation that will render an incentive to obtain more soil strength data and thereby give credit to the geotechnical designer who opts to test more. The study capitalizes on existing load and resistance models for an offshore example pile from the literature and refers to a number of relevant offshore foundation design codes. In order to accomplish the purpose, a number of prerequisites for a successful study are dealt with before the confidence calibration itself is presented.A suitable approach to represent model uncertainty associated with axial pile capacity predictions is presented and implemented in the reliability analyses that are used for the calibrations. The approach implies that the standard deviation of the ratio between true and predicted capacity is represented as a function of the pile length rather than as a constant. This approach is supported both by theory and by data.Based on stochastic models for load and resistance in conjunction with a method for prediction of axial pile capacity, a second-order reliability analysis of the example pile is carried out. With an assumption of perfect knowledge of the soil strength, with characteristic soil strength defined as the mean value and with prescribed load factors for permanent and environmental loads, the necessary requirement for the material factor on the characteristic soil strength is calibrated by tuning the reliability analysis to meet a prescribed target failure probability.With the calibrated material factor kept unchanged, the reliability analysis is repeated, now with the stochastic model for soil strength altered to include statistical uncertainty owing to limited soil data. The value of the characteristic soil strength is adjusted downward until the result of the reliability analysis again meets the prescribed target failure probability. The resulting value of the characteristic soil strength is interpreted as “the conservatively assessed value” to be used in design when soil data are limited and this value is subsequently used to find the corresponding minimum confidence for characteristic value estimation by capitalizing on the properties of the Student’s t distribution. Results are presented for target annual failure probabilities in the range 10−5–10−4.

Identification of the Uncertainties for the Calibration of the Partial Safety Factors for Load in Tidal Turbines

Tidal energy is nowadays one of the fastest growing types of marine renewable energy. In particular, Horizontal Axis Tidal Turbines (HATTs) are the most advanced designs and the most appropriate for standardization. This paper presents a review of actual design criteria focusing on the identification of the uncertainties that technology developers need to address during the design process. Key environmental parameters like turbine inflow conditions or predictions of extreme values are still grey areas due to the lack of site measurements and the uncertainty in metocean model predictions. A comparison of turbulence intensity characterization using different tools and at different points in time shows the uncertainty in the prediction of this parameter. Numerical models of HATTs are still quite uncertain, often dependent on experience of the people running them. In the reliability-based calibration of partial safety factors, the uncertainties need to be reflected on the limit state formulation. This paper analyses the different types of uncertainties present in the limit state equation. These uncertainties are assessed in terms of stochastic variables in the limit state equation. In some cases, advantage can be taken from the experience from offshore wind and oil and gas industries. Tidal turbines have a mixture of the uncertainties present in both industries with regard to partial safety factor calibration.

Estimating fatigue design load for overhead steel sign support structures under truck-induced wind pressure

Experimental results of the truck-induced wind gust pressure were used as the basis to develop the equivalent static truck-induced wind pressure for fatigue design in the American Association of State Highway and Transportation Officials (AASHTO). The development does not explicitly quantify the stress range distribution, nor does the development discuss the implied reliability. No recommendation is given to consider truck-induced pressure for fatigue design in the Canadian Highway Bridge Design Code (CHBDC). This study quantifies the stress range due to truck traffic, and calibrates the equivalent static truck-induced wind pressure for fatigue design of overhead steel sign support structures. The reliability-based calibration is focused on the CHBDC. For the vertical excitations, the calibrated pressure is less than 50% of that suggested in the AASHTO. For the horizontal excitations, the calibrated pressure can be greater or smaller than that for the site-dependent natural wind gusts. Therefore, the truck-induced horizontal wind pressure could govern the fatigue design for some sites.

Design Live-Load Factor Calibration for Michigan Highway Bridges

AbstractIn this study, a reliability-based calibration of live-load factors for bridge design specific to the state of Michigan was conducted. Two years of high-frequency weigh-in-motion (WIM) data from 20 representative statewide sites were analyzed, and load effects were generated for bridge spans from 6 to 122 m (20 to 400 ft), considering simple and continuous moments and shears, and single-lane and two-lane effects. Seventy-five-year statistics for maximum live load were then estimated with probabilistic projection. Bridge girders considered for the calibration included composite steel, prestressed concrete, side-by-side and spread box beams, and special long-span structural members. In some cases, it was found that Michigan load effects were greater than those previously assumed, often requiring higher load factors than those in current use. Moreover, significant variation in the required load factor was found, potentially resulting in significant inconsistencies in reliability if a single load fact...

Reliability-based calibration for a mechanics-based fatigue cracking design procedure

Most pavement design procedures incorporate reliability to account for design inputs-associated uncertainty and variability effect on predicted performance. The load and resistance factor design (LRFD) procedure, which delivers economical section while considering design inputs variability separately, has been recognised as an effective tool to incorporate reliability into design procedures. This paper presents a new reliability-based calibration in LRFD format for a mechanics-based fatigue cracking analysis framework. This paper employs a two-component reliability analysis methodology that utilises a central composite design-based response surface approach and a first-order reliability method. The reliability calibration was achieved based on a number of field pavement sections that have well-documented performance history and high-quality field and laboratory data. The effectiveness of the developed LRFD procedure was evaluated by performing pavement designs of various target reliabilities and design conditions. The result shows an excellent agreement between the target and actual reliabilities. Furthermore, it is clear from the results that more design features need to be included in the reliability calibration to minimise the deviation of the actual reliability from the target reliability.

A database to ensure reliability of bored pile design in Egypt

A new electronic database has been developed to house reliable results for more than 318 load tests of large-diameter bored piles in Egypt, including comprehensive records of soil profile, in situ tests and pile characteristics. Using information from the database, the load and resistance factor design reliability-based calibration approach was applied to established pile design methods and another two local methods. Resistance factors were developed using the Monte Carlo simulation, covering several nominal capacity determination criteria from the pile load–displacement response. The analysis was then extended to assess the reliability of the load test results, which represent the key construction control measure for bored piles. This was achieved by connecting the number of load tests conducted per-site basis with an indicative level of soil variation.

Safety factors for CFRP strengthening in bending of reinforced concrete bridges

Concerning the strengthening in bending of reinforced concrete bridge decks, the use of fiber reinforced polymers (FRP) has increased due to its easy application and excellent mechanical and chemical properties. However, due to the lack of codes and standards and the lack of experience in the long term behavior, uncertainties exist in the calculation bases along the dimensioning of this reinforcement and more precisely in the partial coefficients of safety to be adopted for the material properties. As a consequence, bridge engineers are reluctant to use composite materials in the strengthening of damaged reinforced concrete bridge decks. To try to overcome this problem, this paper describes the methodology for a reliability-based calibration of the partial safety factors to be used for the CFRP material in the design of strengthening to bending. The method requires the definition of a response model jointly with the statistical definition of the model error. This is discussed in the first part of the paper. The reliability-based procedure is developed based on the design equation and the corresponding model. A simple set of partial safety factors is finally proposed for a representative population of RC bridges. The conclusions highlight the importance of incorporating the model error in the calibration. In addition, the paper shows how in some cases it is not feasible to design a flexural strengthening by using CFRP.