PSI - Issue 64

Fadi Oudah et al. / Procedia Structural Integrity 64 (2024) 1983–1989 Fadi Oudah/ Structural Integrity Procedia 00 (2019) 000 – 000

1984

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1. Introduction Reliability analysis is used to quantify the likelihood of exceedance (often referred to as the probability of failure) of structural systems by establishing load and resistance models. Developing a load model requires knowledge of the load type, frequency, and statistics which are typically obtained by field measurements, while developing the resistance model involves predicting the resistance for the assessed limit state (e.g. ultimate limit state (ULS), fatigue limit state (FLS), etc.). The reliability analysis forms the basis for calibrating the partial safety factors in modern load and resistance factor design codes (LRFD) (Bartlett et al., 2003; Nowak and Szerszen, 2003). Aside from code calibration, reliability analysis can be utilized to assess the safety of existing (or in-service) structures when information about the load history and structural condition can be obtained (Petrie and Oudah, 2021). Establishing an accurate resistance model for the reliability analysis of existing structures is challenging due to the considerable spatial variability in the mechanical properties (i.e., properties vary across the length, width, and depth of structural members), especially if the structure is subjected to active deterioration mechanisms such as corrosion induced cracking, freeze-thaw damage, and alkali aggregate reactivity (AAR). Establishing resistance models that consider the spatial variability in existing reinforced concrete (RC) structures can be achieved by utilizing the random finite element method (RFE), where patterns of continuous mathematical fields representing the variability in the material properties can be calibrated based on limited field data and used in FE environment. Although research related to RFE in concrete design is emerging (e.g. Petrie and Oudah, 2023; Hunter et al., 2021), real-life applications of RFE are limited in practice. The objectives of this paper are to 1) document the application of RFE in real-life case studies of structural reliability assessment projects conducted by the authors, and 2) provide recommendations for future research to improve the practicality of analysis for consulting jobs. The paper does not aim to serve as a literature review of the application of random fields in structural concrete analysis (refer to other papers in literature such as Botte et al. (2023) and Sudret and Der-Kiureghian (2000) for detailed review of historical development and method implementation). Instead, it aims to share insights from practical applications of RFE with the structural engineering community, stimulating research needs and offering practical perspectives. The paper is structured as follows. First, the concept of random field is introduced, followed by its applications in RFE. Then, the spatial variability in concrete is briefly reviewed and relevant case studies are presented. Lastly, recommended future research for practical application of RFE is outlined. 2. Random Field Concept Random fields are mathematical expressions developed to describe the spatial variation or the spatial-time variation (i.e., spatial-temporal) of properties within a continuum. The early formulation and application of random fields are rooted in spatial statistics and probability theory (Sudret and Der-Kiureghian, 2000). In Civil Engineering, some of the earliest applications of random fields are found in geotechnical engineering and earth sciences where the spatial variability of soil properties such as shear modulus, cohesion, and dilation are modeled using continuous random fields within the soil domain (e.g. Beacher and Ingra, 1981). The intuitive application of random fields in geotechnical engineering stems from the significant variability observed in soil properties, which impacts the stability of supported structures. The utility of random fields in modeling the spatial variability of mechanical properties has also been recognized in structural engineering applications. Random fields have been applied to model the spatial variability of mechanical properties such as strength and stiffness properties (e.g. Vanmarcke and Grigoriu, 1983). Random fields have also been used to model deterioration effects including the reduction in concrete strength properties (compressive and tensile) due to cracking caused by environmental effects such as freeze-thaw damage and AAR, and the reduction in member thickness due to pitting corrosion in steel structures (e.g. Hassan and Oudah, 2024). Research related to applying random fields for modeling the deterioration effect in structural elements is generally limited as compared with applications of random fields in modeling the intrinsic variation of material properties due to inherent material randomness or variability in construction. Various techniques for discretizing random fields have been developed. Some rely on point discretization methods like the midpoint (MP), shape function (SF), and optimal linear estimator (OLE) methods. Others utilize average discretization techniques such as spatial averaging (SA) and weighted integral methods. Additionally, series expansion techniques like the Karhunen-Louvé (KL) expansion and the expanded optimal linear expansion (EOLE) method are