PSI - Issue 64

Cedric Eisermann et al. / Procedia Structural Integrity 64 (2024) 1224–1231 Eisermann et al./ Structural Integrity Procedia 00 (2019) 000–000

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2.2. Introduction to Bulletin 80 The fib Bulletin 80 (Caspeele et al. 2016) provides two reliability-based partial factor formats for the assessment of existing concrete structures: DVM and APFM. Both methods are consistent with EN 1990:2002 and are applicable to common assessment situations. The Bulletin allows the inclusion of additional information about the basic variables of existing structures in the adjustment process of the partial factors. The new state of information about a variable X is represented by the updated coefficient of variation V x . Furthermore, the fib Bulletin 80 differentiates the target reliability level β for existing structures with respect to those intended for new structures by considering economic and human safety criteria, as well as the remaining service life. This paper focuses on the integration of additional information in the adjustment process of the self-weight related partial factor rather than modifying the reliability index. With this objective, the DVM and AFPM are applied and explained below. 2.3. Design value method The design value method (DVM) allows to derive partial factors γ x from the actual probabilistic distributions of the variable X taking into account prior information (e.g., inspection results), or results of tests and measurements. In addition, modified target reliability levels can be included in the adjustment process. Assuming a normal distribution of permanent actions, the partial factor for the dead load γ G is calculated as the product of γ Ed,G accounting for model uncertainty in estimation of the load effect using the load model and γ g considering the variability of permanent loads: = , (1) The fib Bulletin 80 assumes that model uncertainties are the same for both new and existing structures, and recommends using a model uncertainty factor of 1.07 for unfavorable actions. The partial factor for the permanent load γ g is a function of the desired reliability index β , the coefficient of variation V G as a measure for the variability of the basic variable, and the sensitivity factor α E , see equation 2. The sensitivity α E factor depends on both the standard deviations of actions and resistances, and is different for each combination. For practical application, a decoupling of the actions and resistances has been established and the sensitivity factor for actions has been set to -0.7 (König and Hosser 1982). =1 − (2) The self-weight of a structure depends on the uncertainties in its geometry and concrete density as well as the reinforcement content. According to the law of variation propagation, the coefficient of variation for the dead load V G can be calculated as follows (Löschmann et al. 2017): V G = � V g 2 eo + V d 2 en (3) Herein V geo represents the coefficient of variation for the geometry, and V den the coefficient of variation for the density of the composite material. The values can either be determined precisely through in-situ measurements or conservatively estimated using empirical data from literature. In this paper, a combination of both is used. The variation of geometry is calculated by comparing the as-design model and as-is model of the bridge, and the variation of density is determined based on literature. 2.4. Adjusted partial factor method (APFM) APFM allows the adjustment of partial factors γ x by multiplying the partial factors γ x,new provided by Eurocodes for new structures by an adjustment factor ω γ . For the dead load the corresponding partial factor is given by: = , (4)