PSI - Issue 64

Abdalla Elhadi Alhashmi et al. / Procedia Structural Integrity 64 (2024) 1990–1996 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

1991

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1. Introduction Existing reinforced concrete (RC) structures are assessed for code compliance, the need for an upgrade, or the presence of structural deficiencies. Reliability methods are implemented to quantify the structural safety of existing RC structures by considering the uncertainties involved in the applied loads and structural resistance. Uncertainties in structural evaluation can be categorized into two types: aleatoric and epistemic (Díaz-Curbelo et al., 2020). Aleatoric uncertainty is an inherent controlled uncertainty resulting from randomness in a process, and it can be accounted for in the structural design process. An example of aleatoric uncertainty is the variation of concrete material properties (e.g., strength, stiffness) within a beam member. Epistemic uncertainty is related to the uncertainties that cannot be considered in the structural design process due to a lack of knowledge, subjectivity, or inaccurate data. A relevant example of epistemic uncertainty is the inconsistency in visually examining severely cracked concrete structures, which can vary significantly depending on an inspector's judgment and expertise; potentially leading to various opinions about the structure's state and, consequently, incorrect retrofitting decisions. Although the random finite element approach (RFE) has been proven to be an effective tool in addressing aleatoric uncertainties (Botte et al., 2023; Ibrahim and Makhloof, 2024; Liang et al., 2022; Petrie and Oudah, 2023; Srivaranun et al., 2022), literature on reducing epistemic uncertainties remains sparse (Abdelmaksoud et al., 2024; Zhang and Lin, 2022). Epistemic uncertainties can be effectively minimized by utilizing computer vision techniques such as digital image processing (DIP). DIP is employed for analyzing, enhancing, and manipulating digital images, providing a clearer understanding of the structural condition. By accurately mapping the degradation process (i.e., crack patterns) into finite element (FE) simulation, referred to as DIP-FE, practitioners are aided in making informed and reliable decisions about the safety assessment of degraded concrete members (i.e., cracked concrete). Researchers have integrated FE methods with DIP techniques for various applications (Ghahremani et al., 2018; Huang et al., 2016; Yue et al., 2003; Zhang et al., 2023; Zhang and Lin, 2022). A literature review indicates the following gaps in research related to DIP-FE: a) Most DIP-FE studies are focused on the micro-scale analysis of materials rather than the macro scale; b) lack of studies that incorporated both aleatoric and epistemic uncertainties within a DIP-FE reliability framework of analysis; and c) lack of practical implementation of DIP-FE for analyzing and assessing existing concrete structures in three-dimensional (3D). The objective of this paper is to demonstrate the utility of a newly developed framework of analysis that considers both aleatoric and epistemic uncertainties for the reliability assessment of existing concrete structures in 3D. The framework, developed by Alhashmi and Oudah (2024), employs a random field approach to account for material fluctuations (aleatoric uncertainty), while DIP is used to map crack patterns to nonlinear FE (epistemic uncertainty). The functionality of the proposed methodology will be validated through a case study of a corroded cracked concrete column from existing literature. 2. Description of the methodology developed by Alhashmi and Oudah (2024) The proposed methodology is composed of three main parts: RFE, DIP, and reliability analysis. Figure 1 illustrates a schematic outlining the sequential steps of the proposed framework of analysis. The RFE model is initially developed by defining the geometry, loading, and boundary conditions of the structure of interest. The general-purpose FE program ABAQUS (ABAQUS CAE, 2021) is used for this study. Random fields are then generated using the expansion optimal linear estimation (EOLE) method commonly used for engineering applications ( Li and Der Kiureghian, 1993 ; Sudret and Der Kiureghian, 2000). The mathematical formulation of a random field generated using the EOLE method is expressed in Equation 1, while the Nataf transformation is utilized to convert the lognormal random field to a normal distributed random field (Nataf, 1962) = + ∑ √ = 1 (1) where, is the mean of , is the standard deviation of , is the considered number of eigenvalues of the covariance matrix, is the ℎ standard normal random variable, is the ℎ eigenvalue, is the ℎ vector of the eigenvector matrix, and is the ℎ vector of the correlation matrix.