Milan Holicky

Target reliability for existing structures considering economic and societal aspects

Abstract Specification of target reliability levels is one of the key issues of the assessment of existing structures. ISO 13822:2010 and ISO 2394:2015 indicate procedures for specification of target reliability levels by optimisation of the total cost related to an assumed remaining working life of a structure. These approaches are critically compared with human safety criteria, with target levels based on a marginal life-saving costs principle, and with recommendations of present standards. Optimal target reliability levels are then derived in the representative case study for an existing structural member. It appears that the requirement to reach the same target reliability levels for existing and new structures is uneconomical. Decisions made in the assessment can result in the acceptance of the actual state or in the upgrade of an existing structure. Two reliability levels are thus needed – the minimum level below which the structure is unreliable and should be upgraded, and the target level indicating an optimum upgrade strategy. It is recommended that these levels be established using economic optimisation and the marginal life-saving costs principle, as both the approaches take into account the costs of safety measures and the failure consequences.

Failures of Roofs under Snow Load: Causes and Reliability Analysis

Collapses of a number of roofs in Europe during the winter 2005/2006 initiated discussions concerning reliability of the roofs exposed to snow loads. Presented overview of extensive investigations of structural failures is focused on causes and consequences of failures. Main observed causes may be subdivided into human errors and insufficient code provisions. Collapses developed from local failures particularly in cases of insufficiently robust structures. Probabilistic reliability analysis reveals that the model for snow loads in the Eurocodes should be modified. Obtained experiences provide valuable background information for future revision of current standards and for forensic assessments of failures of structures exposed to snow loads.

Assessment of Uncertainties in Mechanical Models

Resistances of mechanical systems are primarily dependent on material properties, geometry and uncertainties associated to an applied resistance model. While materials and geometry can be relatively well described, the resistance model uncertainty is not yet well understood. The present contribution proposes a general concept of the model uncertainty. Factors affecting results obtained by tests and models and influences of actual structural conditions are overviewed. Application of theoretical principles is illustrated by an example of historic iron columns considering a simple mechanical model. Proposed probabilistic description of the model uncertainty consists of the lognormal distribution having the mean 1.35 and coefficient of variation of 0.12.

Robustness of Structures: Lessons from failures

Abstract Robustness is considered as an attribute of a structural system that relates to its ability to fulfil its function in the face of adverse events. It is difficult to quantify robustness. The focus of COST action TU0601 has been on developing a framework to quantify robustness and on identifying methods and strategies to improve the robustness of structures. The objectives of this paper are to present an analysis of different failures from the point of view of robustness and to identify measures that directly or indirectly contribute to robustness. It is concluded that structural form plays a major role but it is essential to ensure good management processes for design and construction.

Evaluation of Compressive Strength of Historic Masonry Using Measurements

Historic structures are made of different types of masonry with significantly different properties. As a rule the information on mechanical properties of masonry components has to be obtained by testing. Estimation of masonry strength from measurements with due regard to relevant uncertainties may be a key issue of the reliability assessment. The probabilistic model of masonry strength is developed considering uncertainties in basic variables and testing procedures. It appears that the characteristics of masonry strength can be well estimated using fundamental statistical methods.

Determination of target safety for structures

Codes of practice aim at guaranteeing structures having the risks acceptable to the public and the minimum total costs over a design working life. However, current criteria for structural design provide a broad range of target reliability indices, specified often for different reference periods even though their recalculation for different reference periods is indeterminate due to mutual dependence of failure events. General approaches for selecting target reliability levels are discussed in view of costbenefit optimisation and human safety aspects. Design strategies seem to be driven by economic arguments rather than by human safety criteria.

Specification of the Target Reliability Level

The target reliability levels recommended in national and international documents vary within a broad range, while the reference to relevant costs and failure consequences is mentioned only very vaguely. In some documents the target reliability index β is indicated for one or two reference periods (1 year and 50 years) without providing any link to the design working life. This contribution attempts to clarify the relationship between the target reliability levels, construction costs, failure consequences, reference period, the design working life and the discount rate. The theoretical study based on probabilistic optimization is supplemented by recommendations useful for code developers and practicing engineers. It appears that the optimal reliability level depends primarily on the construction costs, failure costs, and relative cost for improving structural safety, and less significantly on the discount rate and the time to failure.

Target Reliability for Existing Civil Engineering Systems

Specification of the target reliability levels is one of the key issues of the assessment of existing systems. ISO 2394:2015 indicate procedures for specification of the target reliability levels by optimisation of the total cost related to an assumed remaining working life of a structural system. These approaches are critically compared with human safety criteria and with recommendations of present standards. It appears that the requirement on the same target reliability levels for existing civil engineering systems as for newly designed is uneconomical. Decisions in the assessment can result in the acceptance of the actual state or in upgrade of the existing structure, two reliability levels are thus needed - the minimum level below which the structure is unreliable and should be upgraded, and the target level indicating an optimum upgrade strategy. When reliability of a system or its key component is verified (as compared to design of a common component), the target reliability index should be increased by about 0.5.

Probabilistic Models for Wind Actions

In common cases the wind actions may be expressed as a product of time invariant and time variant components. The time invariant components, originated primarily from the pressure factor, gust factor and roughness, are represented by the product a single factor. The time variant component is caused by the basic wind pressure dependent on square of wind speed. Four types of distributions are considered here to describe involved random variables: three parameter Weibull distribution WB3, general extreme value distribution GEV, three parameter lognormal distribution LN3 and the Gumbel distribution GU, which is a special case of GEV. Available data indicate that the statistical parameters of annual wind speed depend significantly on local conditions. The average coefficient of variation is about 0.12, the skewness around 0.3. The time invariant component C has the coefficient of variation about 0.2 and skewness around 0.35. The annual wind pressure w, has the coefficient of variation about 0.3 and skewness 0.8. Then the 50 years extreme wind pressure w has the coefficient of variation 0.23 and skewness 0.56. Considering the above mentioned data it is shown that both the annual wind speed and wind pressure can be best described by LN3 that provide similar predictions as lower bounded WB3 distribution. Further research should be primarily focused on probabilistic models for the annual wind speed and the time invariant components.

Compressive strength of deteriorated historic masonry based on measurements

Historic structures are made of various types of masonry with significantly different material properties and different degrees of degradation. As a rule the information on mechanical properties of masonry components has to be obtained by testing. Estimation of masonry strength from measurements with respect to relevant uncertainties may be a key issue of the reliability assessment. The probabilistic model of masonry strength is developed considering uncertainties in basic variables and testing procedures. It appears that the characteristics of masonry strength can be well estimated using fundamental statistical methods. The attached case study indicates that the design value of masonry strength obtained by the probabilistic approach may be about double of the value obtained deterministically.