PSI - Issue 64

Fadi Oudah et al. / Procedia Structural Integrity 64 (2024) 1983–1989 Fadi Oudah/ Structural Integrity Procedia 00 (2019) 000 – 000 points ( ) and ( ) , and is a conversion factor converting the lognormal field. The terms ⁡ and are the coefficient of variation of the mesh points ( ) and ( ) , respectively. ′ = = ln⁡(1+⁡ ) √ln(1+ 2 ) ln(1+ 2 ) (7) The number of standard normal variables r is determined such that the ratio of the eigenvalues divided by the trace of the covariance matrix, , does not exceed a threshold value determined based on the desired accuracy, as shown in Eq. (8). = ∑ ⁡ , = 1 ( ) (8) 4. Spatial Variability in RC Structures The spatial variability in reinforced concrete can be categorized into the following: A. Geometric variability . It includes changes in dimensions of constitutive materials: reduction in the cross sectional area of the reinforcing steel due to corrosion, change in concrete volume due to cracking (due to mechanical load or deterioration effects) B. Mechanical properties variability . It includes two types of variabilities: 1) intrinsic variability in concrete properties due to the heterogeneous nature of concrete and quality control of concrete during pouring in formwork, and 2) deterioration-based variability due to deterioration effects including corrosion-induced cracking, freeze-thaw damage, and alkali aggregate reactivity. C. Residual stress variability . It includes changes in the residual stress in restrained concrete elements experiencing deterioration-based cracking such as stresses induced in restrained concrete structures experiencing AAR. 5. RFE in Structural Engineering Consultancy The applications of RFE in structural engineering include 1) capacity assessment of structures (new or in-service) experiencing considerable spatial variability; 2) system-based evaluation of structures as opposed to component-based evaluation; and 3) reliability-based evaluation where the probability of exceedance is assessed for a predefined performance objective. For reliability analysis, RFE can be used to build the capacity histogram of the assessed limit state by running a representative number of RFE models with possible patterns of spatial variations (see Fig. 1) or by utilizing surrogate-based reliability methods such as active learning Kriging (Khorramian et al., 2023b; Petrie and Oudah, 2024). Despite the significant potential of RFE in advancing the methods of evaluation of structures, its use in real-life consultancy is limited. In a fast-paced consulting environment, the choice of the analysis tool is driven by the project constraints to balance accuracy and efficiency. One of the major challenges for utilizing RFE in consulting relates to the fact that most of the existing literature utilizes non-generic computer coding to model the spatial variation and assign it to FE models developed using commercial FE packages. This requires establishing interfaces between the algorithms used to generate random fields and the commercial FE package to generate RFE. Developing such interfaces is not efficient if not automated. For RFE analysis to be utilized in practice, the RFE models need to be developed in a user-friendly manner that can be handled by structural consulting engineers that do not necessarily have a technical background in computer coding, like the case for RF-DYNA. Although RF-DYNA represents a major advancement in improving the efficiency of generating random fields and automatically assigning them to FE models, its application is limited to FE models developed using LS-DYNA – user must have technical experience with generating FE models using LS-DYNA software. 4

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