Calibration Of Partial Factors Research Articles

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.

Context-Dependent Parameter Sensitivities in Rock Slope Stability

Context-dependent sensitivities of parameters and reliability-based design (RBD) of rock slopes are the subjects of this paper. The similarities and differences between the design points in RBD and those of partial factor design methods are discussed. It is demonstrated that partial factors provided by the design point of the first-order reliability method (FORM) can provide case-specific insights and guidance to partial factor design methods like Eurocode 7 (EC7) and the load and resistance factor design (LRFD). It is suggested that conducting RBD-via-FORM in tandem with partial factor designs is more illuminating and meaningful than calibration of partial factors of parameters which can be sensitive in one case but insensitive in another case. Three cases are analysed probabilistically with respect to plane sliding in rock slopes with one or more discontinuities. In the first two cases, different deterministic solution procedures are used for the single block and two-block mechanisms, for comparison with stereographic projection method and closed form equation, respectively, prior to extending the cases into RBD. The third case involves a failed slope in a limestone quarry, analysed using FORM in this paper, for comparison with Monte Carlo simulation.

Eurocode Shear Design of Coarse Recycled Aggregate Concrete: Reliability Analysis and Partial Factor Calibration.

This paper contributes to the definition of design clauses for coarse recycled aggregate concrete. One of the main reasons for scepticism towards recycled aggregate concrete is the perceived notion that the heterogeneity of recycled aggregates may increase the uncertainty of the behaviour of concrete. Therefore, the paper uses structural reliability concepts to propose partial factors for recycled aggregate concrete’s design for shear failure. The paper builds upon a previous publication by the authors, in which the model uncertainty of recycled aggregate concrete elements designed for shear, with and without shear reinforcement, was compared with that of natural aggregate concrete elements. In that paper, the statistics of the model uncertainty for recycled aggregate concrete shear design were indeed found to be less favourable than those of natural aggregate concrete. Therefore, a partial factor for recycled aggregate concrete design is needed to ensure safety. This paper presents partial factors calibrated with explicit reliability analyses for different cases of design concerning beams (in the case of shear design of elements with shear reinforcement) and slabs (for the design of elements without shear reinforcement). For full incorporation of coarse recycled concrete aggregates and the design of elements without shear reinforcement, the calibrated partial factor reduces the design value of shear resistance by 10% (design with EN1992) or 15% (design with prEN1992) in comparison to natural aggregate concrete’s design. For the shear design of elements with shear reinforcement, the partial factor decreases resistance by 5% but a sensitivity analysis showed that the reduction might be, under pessimistic expectations, of up to 20%.

Structural safety of pultruded FRP profiles for global buckling. Part 1: Approach to material uncertainty, resistance models, and model uncertainties.

This two-part paper proposes a resistance format and partial factors for the global buckling of FRP profiles based on reliability analysis and partial factor calibration. Most current recommendations for the design of structural members made with FRP materials are not grounded on reliability concepts and this poses questions concerning safety and economy. Part 1 of this paper presents the resistance format proposed, the approach to the variability of material properties, the resistance models, and the design equations for the following global buckling modes: (i) flexural, (ii) flexural-torsional, and (iii) lateral-torsional; all of them refer to well-known formulations available in the literature. Probability distributions for the model uncertainties of the resistance models are defined based on all trustworthy experiments collected by the authors from the literature. In general, the three resistance models proposed provide estimates of the critical buckling stress with good accuracy when compared to the observed (tested) buckling resistance, resulting in an average bias close to one. The coefficient of variation of the model uncertainties varies between 11% (flexural buckling) and 19% (flexural-torsional buckling). Preliminary partial factors are proposed in this part and their reliability-based calibration is presented in Part 2.

Structural safety of pultruded FRP profiles for global buckling. Part 2: Reliability-based evaluation of safety formats and partial factor calibration

This two-part paper presents a study about the structural safety of pultruded fibre-reinforced polymer (FRP) profiles with respect to global buckling phenomena, which often govern their ultimate limit states design: flexural buckling, flexural-torsional buckling and lateral-torsional buckling. The first part [1] presented the resistance models for those buckling mechanisms, the probability models for model uncertainties of resistance, and a preliminary set of partial factors related to the model uncertainty, all consistent with the Eurocodes. Aiming at validating the resistance format proposed and that set of partial factors, this second part presents explicit reliability analyses of pultruded FRP profiles designed for the different global buckling failure mechanisms, so that the design equations proposed comply with the target reliability index recommended in EN 1990 for common structural elements. The reliability-based calibration followed similar methodology of documents that assessed the reliability of design with the Eurocodes, including the stochastic modelling of loads and geometry. Partial factor calibration was made through iterative reliability analyses on representative structural elements defined from the proposed design equations. This calibration process allowed defining (i) recommendations for partial factor γRd and (ii) the representative material property used to define γm for each buckling mechanism. The final part of the paper includes recommendations for future research, towards the validation of assumptions made in this study and the standardization of FRP materials.

Structural member stability verification in the new Part 1‐1 of the second generation of Eurocode 3

AbstractThis two‐part article gives an overview of the developments of the structural member verification in prEN 1993‐1‐1:2020 ”Eurocode 3: Design of steel structures – part 1‐1: General rules and rules for buildings“, one of the second generation of Eurocodes. These developments were undertaken by Working Group 1 (WG1) of Subcommittee CEN/TC250/SC3 and by Project Team 1 (SC3.PT1) responsible for drafting the new version of EN 1993‐1‐1. In the past, WG1 collected many topics needing improvement, and the systematic review conducted every five years also yielded topics needing further development. Based on this, the current version of EN 1993‐1‐1 has been developed into a new draft version prEN 1993‐1‐1:2020 enhancing ”ease of use“. The technical content of this new draft was laid down at the end of 2019. Many improvements to design rules have been established with respect to structural analysis, resistance of cross‐sections and stability of members. This two‐part article focuses on member stability design rules and deals with the basis for the calibration of partial factors, the introduction of more economic design rules for semi‐compact sections, methods for structural analysis in relation to the appropriate member stability design rules, new design rules for lateral torsional buckling plus other developments and innovations. This second part of the article is dedicated to illustrating the most relevant changes to member buckling design rules.

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.

Structural member stability verification in the new Part 1‐1 of the second generation of Eurocode 3

AbstractThis two‐part article gives an overview of the developments of the structural member verification in prEN 1993‐1‐1:2020 “Eurocode 3: Design of steel structures – part 1‐1: General rules and rules for buildings”, one of the second generation of Eurocodes. These developments were undertaken by Working Group 1 (WG1) of Subcommittee CEN/TC250/SC3 and by Project Team 1 (SC3.PT1) responsible for drafting the new version of EN 1993‐1‐1. In the past, WG1 collected many topics needing improvement, and the systematic review conducted every five years also yielded topics needing further development. Based on this, the current version of EN 1993‐1‐1 has been developed into a new draft version prEN 1993‐1‐1:2020 enhancing “ease of use”. The technical content of this new draft was laid down at the end of 2019. Many improvements to design rules have been established with respect to structural analysis, resistance of cross‐sections and stability of members. This two‐part article focuses on member stability design rules and deals with the basis for the calibration of partial factors, the introduction of more economic design rules for semi‐compact sections, methods for structural analysis in relation to the appropriate member stability design rules, new design rules for lateral torsional buckling plus other developments and innovations. This first part of the article primarily serves to explain the general background to the European Commission Mandate M/515 that led to the further evolution of the Eurocodes and to illustrate the developments in prEN1993‐1‐1:2020 that pertain to new material grades, partial factors, cross‐sectional classification and structural analysis. These form the necessary background to the changes to member buckling design rules, which are treated more specifically in the second part.

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.

Probabilistic assessments of flood defence performance subject to induced seismicity

Gas extraction in the Groningen Province in the Netherlands has caused seismicity. A method was needed for probabilistic assessments of the seismic performance of the levees that protect low-lying polders against flooding. By combining the First Order Reliability Method with response surfaces it proved possible to strongly reduce the required number of simulations with advanced numerical models to obtain reliable failure probability estimates. To illustrate the workings of the method, an application to a levee cross-section along the Eemscanal with a sheet pile wall is presented. The probabilistic method can be used for probabilistic assessments and the probability-based calibration of partial factors, and it could serve as a starting point for quantitative risk analyses for levee systems in earthquake prone regions.

Analysis of Partial Factors for New EN 1990 Basis of Design

Abstract Presently the new generation of Eurocodes is under development. It is expected that the basis of structural design given in current EN 1990 will be considerably revised including the format for load combinations in the Ultimate Limit States and new categorisation of consequence classes for construction works. It is expected that the partial factors for self-weight of structural members could be reduced and factors for variable loads more differentiated. Calibration of partial factors should be performed for actions and materials including also structural glass and FRP polymers.

Material properties and partial factors for resistance of high-strength steels in China

High strength structural steels (HSS) with a nominal yield strength fy≥460MPa have begun to be applied in many steel structures. This paper focuses on material properties of the HSS fabricated in China and calibration of partial factors for resistance based on the theory of structural reliability. An extensive range of material property data of 500MPa, 550MPa and 690MPa steels produced by major steel manufacturers in China (over 10,000 samples) was collected. Besides, independent material tests were carried out. The statistical parameters of the material properties were then obtained with the influence of test machine types and strain rates being incorporated. Uncertainties of the resistance model of HSS were subsequently investigated through finite element (FE) analyses, including members under axial compression, flexural members and members under combined axial compression and bending. By combining the statistical parameters of both the material properties and the resistance model uncertainties as well as that of geometric properties investigated in the previous research, the statistical parameters of resistance uncertainties of HSS were gained. It may provide a significant statistical evidence for the following reliability analyses. Based on structural reliability theories, partial factors for resistance of HSS were eventually calibrated. As an important part of the Design Specification of High Strength Steel Structures in China, these partial factors for resistance developed herein are helpful for promoting the application of HSS in China. In addition, based on the massive material properties data, a constitutive model of HSS under monotonic loading was suggested.

Assessment of model uncertainties for structural resistance

Uncertainties in resistance models play a significant role in the reliability analysis of structures and code calibration of partial factors for semi-probabilistic design. In spite of this importance, existing knowledge concerning model uncertainties and their characteristics seems to suffer from imprecise definitions and lack of available experimental data. Currently used probabilistic models and derived factors for model uncertainties are mostly based on intuitive judgements and limited data. This often leads to an unrealistic description of model uncertainties. The present study attempts to improve definitions of model uncertainties and proposes a general methodology for their quantification by comparing experimental and model results. It appears that model uncertainty should be always related to a specific model and scope of its application. The proposed approach seems to offer better understanding of model uncertainties and enables the specification of their real characteristics.

Partial Factors in Modelling of Steel Structures Reliability According to Eurocodes / Współczynniki Częściowe W Eurokodowym Modelu Niezawodności Konstrukcji Stalowych

Abstract Problems associated with the estimation of partial factors for structural systems, subsystems and buckling of individual elements are dealt with in this paper. Aspects related to resistance factors for the section resistance and member resistance are in particular referred to. The Eurocode’s approach of resistance partial factor calibration assisted by experimental data for subframe systems is also summarized.

Reliability assessment of structures subjected to fatigue failure

Structural calculation, and more especially design, is widely based on mechanical computations from characteristic values of design variables and from the so-called partial (safety) factors listed in the design rules. These design rules are the results of both designer know-how and epistemic knowledge. Their deterministic use hides the existence of the structural probability of failure due to several structural imperfections and uncertainties. Lots of structural failures are due to fatigue problems. This work aims at describing a probabilistic methodology for the calibration of partial factors for the design of structures subjected to potential fatigue failure. The general calibration procedure is based on the resolution of an optimisation problem. This solution can easily be found using optimisation algorithms when the mechanical model is explicit but it is very computer time expensive when the mechanical model is based on finite elements. This paper presents an original economical method to solve this optimisation problem. The application to fatigue problems needs the essential computation of an equivalent load factor (Thomas JJ. 2002. Fatigue modeling for automotive applications. SAE paper 2002-01-065.) briefly covered in this paper.

Time-variant reliability of retaining walls and calibration of partial factors

A methodology for the time-variant reliability analysis of geotechnical structures, particularly retaining walls, is presented. Calculation of the reliability of a wall, at any time during its lifetime, is enabled through the consideration of the degradation of soil shear strength parameters with time. In addition, the effects of spatial variability and model uncertainty are accounted for. Following an initial application with regard to British and European design standards, the methodology is extended in order to enable the calibration of partial factors for design to Eurocode 7. It is concluded that the values recommended for these factors are excessively high, at least for temporary structures that should be designed to withstand loads for just a few years. Therefore, a procedure for calculating reduced values of the partial factors that correspond to an appropriate safety level is further proposed.