PSI - Issue 22

2

H. Daou, W. Raphael, A. Chateauneuf, F. Geara/ Structural Integrity Procedia 00 (2019) 000 – 000

18 Peer-review under responsibility of the First International Symposium on Risk and Safety of Complex Structures and Components organizers H. Daou et al. / Procedia Structural Integrity 22 (2019) 17–24

Keywords: Probabilistic analysis; Structural safety; Complex structure; Roissy.

Introduction During the past four decades, the importance of reliability theory for addressing safety issues of civil structures has increased significantly; motivated by the fundamental nature of uncertainties arising from both structural performance and external loads (Wang et al. (2019)).The parameters which define the geometrical and mechanical properties cannot be considered as deterministic quantities as they are affected by several sources of uncertainties (Biondini et al. (2004)). These uncertainties are termed as stochastic parameters but they could be also epistemic such as those due to a lack of knowledge regarding the real values of some parameters in existing buildings (Abdelouafi et al. (2015)). Reliability analysis provides a measure of a structure ’s ability of fulfilling the design purpose for some specified design lifetime. Therefore, it focuses on the ability to meet specific design requirements during the planned period of use where the structure or a part of the structure is to be used for its intended purpose without the need for general repairs. The standard ISO 2394, the probabilistic model code developed by the Joint Committee on Structural Safety (JCSS) and the structural Eurocode are the three main documents that have been drawn on reliability based design. Deterministic, semi-deterministic and probabilistic approaches are used for reliability verification. Deterministic verification methods, which are based on a single global safety factor, do not properly account for the uncertainties associated with strength and load evaluation; noting that the global safety factor is defined as the ratio of the resistance over the load effect. Semi-probabilistic verification methods are based on the limit state principle and make use of partial safety factors for checking the structural safety and are considered as simplified methods but they can account for uncertainties of some design parameters. Probabilistic verification procedures, which are also based on the principle of limit states and take into account explicitly the uncertainties, check that predefined target structural reliability levels are not exceeded (Skrzypczak et al. (2017)). Regardless of the uncertainties in different parameters accounting for the analysis and design of a structure, it is very difficult to measure its absolute safety using deterministic analysis. Therefore, the structural reliability index (or the probability of failure) is considered as the fundamental performance indicator for structural safety and performance assessment of structures (Tu et al. (2017)). Reliability of building structures depends on a number of correlated factors: the quality of materials, protection against environmental influences and maintenance level during exploitation, building precision and level of control, design details and technologies, specific period of use, adopted solutions for the construction materials, standard requirements regarding capacity, exploitation and durability, adopted loads (both their values and combinations), standard requirements regarding capacity, exploitation and durability, quality of computational models used in the design process and methods for assessing reliability of the structure In the reliability analysis, the failure probability is calculated as shown in Equation 1. where x is a random vector that represents the design variables, G(X) is the performance function or the limit state function defined in X-space and f X (x) is the joint probability density function (PDF) of random vector x. Simulation is one of the most applicable techniques used in case where is difficult to solve analytically an equation. The basic Monte Carlo Simulation (MCS) is one of the well-known and common procedures in solving complex engineering problems (Gordini et al. (2018)). It is therefore adopted in reliability problems to calculate Eq. 1 for estimating the failure probability. But MCS is time consuming and expensive for problems with implicit performance functions or low failure probability. This problem can be solved with Response Surface Method (RSM) which contributes to the acquisition of a polynomial function of the performance function G(x). The approximate performance function was widely used in the literature in the quadratic polynomial form (Hamrouni et al. (2017)). (x)dx G(x) f X )   0 P(G(X) P f    0 (1)