PSI - Issue 44

Gianfranco De Matteis et al. / Procedia Structural Integrity 44 (2023) 681–688 Gianfranco De Matteis et al. / Structural Integrity Procedia 00 (2022) 000–000

684

4

2.2. Reliability of the numerical model EC2 does not provide specific suggestions on many of the aspects which define the modelling strategy. These include geometrical modelling (kinematic compatibility), triaxial constitutive relationships, solution methods for the nonlinear problem (analysis method, time and space discretisation, convergence criteria, etc.). While some indications may be found in (fib, 2012) or more specific documents (fib, 2008; Hendriks, et al., 2017), it should be clear that any solution strategy, defined as the ensemble of all the choices the analyst makes in the process of building the numerical model, represents a source of uncertainty which needs to be properly quantified. Following (JCSS, 2001), model uncertainty is defined as: θ = (2) where R exp and R NLA are the capacities experimentally observed and predicted by NLA, respectively. θ is a random variabl that is characterized by its probability distribution. By assuming a log-normal distribution, the latter is completely identified by the mean μ θ and variance σ θ 2 , or, equivalently, the coefficient of variation V θ . The actions needed to estimate parameters μ θ and V θ represent the validation stage of NLA. In (Engen, et al., 2017) and (Engen, et al., 2021), a methodology to characterise the log-normal distribution of θ is developed, which is based on Bayesian updating of prior parameters with the sample mean and variance from a series of benchmark analyses. Such analyses should be chosen in order to cover all failure modes expected for the structure under examination, according to clause (105) of EC2-2 (EN 1992-2, 2006). Once the uncertainty has been characterised, it is possible to calculate the modelling uncertainty factor ~ γ Rd , which is specific of the solution strategy. This reads: � = 1 (3) where α R is the sensitivity factor for the resistance modelling uncertainty, and β is the target reliability factor. It is herein suggested that a solution strategy should be accepted and used for NLA if ~ γ Rd ≤ γ Rd , or, alternatively, if the true value of ~ γ Rd is used in Eqs. (1a-c). 2.3. Opportunity of nonlinear analysis The use of nonlinear analyses is usually triggered by the need of achieving a good understanding of the ultimate behaviour of structures. Nonlinear refined numerical models may reveal unexpected resisting mechanisms, not identified by conventional linear analyses, and additional strength resources, particularly for statically indeterminate structures developing ductile mechanisms (e.g., inners slabs of bridge decks, grid reinforced concrete bridge decks), for which nonlinear analysis may give evidence of increased structural performances. However, the goal of achieving a better understanding of the structural behaviour should be pursued through a process that also includes the use of linear analyses, passing from simplified models (e.g. implementing one-dimensional elements) to refined 3D models (e.g. with shell or solid elements), able to capture phenomena as load distribution (e.g. in case of girder bridges), and warping and distortion of cross-sections (e.g. for box-girder bridges). According to previous observations, preliminarily linear analyses performed on refined numerical models of bridge decks prepared for nonlinear applications may provide useful information to select load combinations for maximising bending or shear stresses in specific structural elements, to control validity of nonlinear applications outcomes, and to preliminary predict effects on the safety assessment due to load redistribution and cross-sections distortion. Subsequent nonlinear applications may reveal additional strength resources and provide advantages in terms of safety verification, especially in the case of statically indeterminate reinforced concrete bridges with few critical elements characterised by ductile behaviours. Unfortunately, nonlinear analyses are overall computational demanding due to need of achieving an in-depth knowledge of materials, of validating the computational models, and of solving inherent computational difficulties in terms of computation time and non-convergence of results. In addition, the use of nonlinear local models (e.g. local models for bridge subcomponents) is often problematic and sometimes theoretically wrong because interactions with non-modelled members may strongly affect the overall behaviour; consequently, comprehensive structural models should be considered, with the drawback of increasing the model dimension (e.g. the number of the dof ), but with the advantage of capturing the evolution and sequence of collapse mechanisms, thus