Semi-probabilistic Design Research Articles

Assessment of the Safety Level of Concrete Slabs during Fire

During the last decades research has provided many new insights in the structural behavior of concrete structures subjected to fire. However, most studies and also the semi-probabilistic design methods in the Eurocode EN 1992-1-2 focus on the maximum time of fire resistance, without mentioning the impact of fire on the safety level of the structure. In order to assess the effect of fire on the safety level of concrete slabs, a full-probabilistic model is developed, using Monte Carlo simulations for modeling the uncertainty regarding the bending moment capacity. Results indicate that the calculated safety level is highly sensitive to the uncertainty of temperature effects on material properties. Furthermore, it is shown that the safety level at the fire resistance time is not the same for all the design approaches mentioned in EN 1992-1-2. Also, a generalized target value for the safety index ? during fire is proposed, which allows for an objective comparison of the fire resistance time for different design alternatives.

Toward a probabilistic design of reinforced concrete durability: application to a marine environment

This work aims to propose a complete design methodology for concrete durability problems based on a probabilistic method including an original chloride diffusion modelling compatible with the new performance-based approaches. This is illustrated by the study of a concrete immersed in sea water. The physical and chemical processes that lead to the corrosion of the concrete reinforcement bars are presented first. A chloride penetration model based on Fick’s second law is proposed. Next, the durability modelling parameters chosen among the durability indicators (Baroghel-Bouny, Concrete design for structures with predefined service life—durability control with respect to reinforcement corrosion and alkali–silica reaction, 2004; Alexander et al., Mater Struct 41:921–936, 2008) are assessed. They depend on the concrete formulation and the chemical composition of the cement. These indicators are characterized by their statistical distributions, which are realistically specified from a wide literature review. The whole probabilistic modelling is included in a Bayesian network so that it can be easily updated to include new experimental data. The evaluation of the time dependant corrosion risk is estimated for two types of cement: CEM I and CEM I with silica fume. The result shows the effect on the Lind–Hasofer reliability index of the type of cement, the concrete quality and the design options. The quality is integrated through the mean value and the standard deviation of the modelling parameters. The method could be used either directly for cover design or for semi-probabilistic design code calibration.

Semi-probabilistic design of rockfall protection layers

Increasing rockfall activity in the European Alps raises the need for designing systems protecting Alpine infrastructure. So far, layout of rockfall protection layers was carried out in a quasi-deterministic manner. This paper is concerned with the extension towards a semi-probabilistic design of the thickness of gravel layers covering steel pipelines. Quantities with little scatter such as geometric dimensions and elasto-plastic material constants of steel and gravel are treated as deterministic. By contrast, strongly scattering quantities such as the indentation resistance of gravel, R, and rockfall characteristics including boulder mass m and height of fall h f are considered as probabilistic variables. While 5 and 95% quantiles of R (obtained from statistical evaluation of a series of real-scale impact tests onto gravel) represent probability-based interval bounds for designing the gravel layer thickness, the lack of statistical data from rare rockfall events motivates to follow the philosophy of EUROCODE 1, i.e., to define a design rockfall: m = 10,500 kg and h f = 80 m. Based on this input, a standard burying depth of steel pipelines (H = 1 m) is assessed, by comparing estimates of (i) boulder penetration depth into gravel and of (ii) the maximum impact force, respectively, with corresponding quantities related to a suitable real-scale impact test. This comparison shows the need to increase the height of the gravel overburden. In order to prove that a gravel layer thickness H = 2.7 m is sufficient to prevent the pipeline from inelastic deformations when the structure is hit by the design rockfall, several structural analyses with different values for R are carried out. This is done by means of a validated Finite Element model. As a by-product of the proposed semi-probabilistic design procedure, three different deformation modes of the hit pipeline are identified.

Numerical prediction of wave-induced long-term extreme load effects in a flexible high-speed pentamaran

The theory and procedure established by Wu and Moan in 1996 and 2005 and Wu and Hermundstad in 2002 were applied to a high-speed transatlantic pentamaran containership. Nonlinear time-domain simulations of ship motions and load effects were carried out in different sea states. The simulated responses were validated against model tests with satisfactory results. The short-term probabilities of exceedance were estimated by using different stochastic analysis procedures. The long-term probabilities of exceedance were obtained based on the short-term results. These served as information about loading in a reliability-based design approach. The load effects in a semiprobabilistic design were also calculated at an appropriate probability of exceedance level.

Structural Design Using Simulation Based Reliability Assessment

The concept of Simulation Based Reliability Assessment (SBRA) for Civil Engineering structures is presented. SBRA uses bounded histograms to represent variable material and geometric properties as well as variable load effects, and makes use of the Monte Carlo technique to perform a probability-based reliability assessment. SBRA represents a departure from the traditional deterministic and semi-probabilistic design procedures applied in codes and as such requires a "re-engineering" of current assessment procedures in accordance with the growing potential of computer and information technology. Three simple examples of how SBRA can be used in Structural Engineering design are presented: 1) the reliability assessment of a steel beam, 2) a truss bar subjected to variable tension and compression, and 3) the pressure on the wall of an elevated water tank due to earthquake load.

Models of reinforced concrete structures for reliability analysis

The semi-probabilistic design approach to reinforced concrete structures may be substantially improved through probabilistic analysis of the systems or their members. Models are proposed for this purpose, covering all possible failures, the deformability characteristics of the failure zones, and the variability of the general factors. Members in compression (columns and walls) and the cracking resistance of beams are considered. It is shown that, in important specific cases, the analysis may be reduced in practice to use of constants.